Controller design for industrial robots and machine tools: Applications to manufacturing processes [1 ed.] 0857094629, 9780857094629

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Controller design for industrial robots and machine tools

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Controller design for industrial robots and machine tools Applications to manufacturing processes

Fusaomi Nagata aNd Keigo WataNabe

Oxford

Cambridge

Philadelphia

New Delhi

Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge, CB22 3HJ, UK www.woodheadpublishing.com www.woodheadpublishingonline.com Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia, PA 19102-3406, USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com First published in 2013 by Woodhead Publishing Limited © F. Nagata and K. Watanabe, 2013 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors not the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Library of Congress Control Number: 2013951356 Woodhead Publishing ISBN:978-0-85709-462-9 (print); ISBN 978-0-85709-463-6 (online) The Woodhead/Chandos team responsible for publishing this book: Publisher: Dr Glyn Jones Production Editor: Ed Gibbons Cover Designer: Terry Callanan Produced from camera-ready copy supplied by the authors. Printed in the UK and USA

Contents

Preface

xxi

About the authors

xxiii

Introduction

xxv

1 Velocity-based discrete-time control system with intelligent control concepts for openarchitecture industrial robots 1.1 Background . . . . . . . . . . . . . . . . . . . 1.2 Basic Servo System . . . . . . . . . . . . . . . 1.3 Dynamic simulation . . . . . . . . . . . . . . 1.4 In case of fuzzy control . . . . . . . . . . . . . 1.5 In case of neural network . . . . . . . . . . . 1.6 Conclusion . . . . . . . . . . . . . . . . . . .

1 2 3 13 19 27 32

2 Preliminary simulation of intelligent control 2.1 Introduction . . . . . . . . . . . . . . . . 2.2 Impedance model following force control 2.3 Influence of environmental viscosity . . . 2.4 Fuzzy environment model . . . . . . . . 2.5 Conclusion . . . . . . . . . . . . . . . .

35 36 37 42 46 63

v

force . . . . .

. . . . .

. . . . .

Controller design for industrial robots and machine tools

3 CAM system for articulated-type industrial robot 3.1 Background . . . . . . . . . . . . . . . . . . . 3.2 Desired trajectory . . . . . . . . . . . . . . . 3.3 Implementation to industrial robot RV1A . . 3.4 Experiment . . . . . . . . . . . . . . . . . . . 3.5 Passive force control of industrial robot RV1A 3.6 Conclusion . . . . . . . . . . . . . . . . . . .

65 66 68 73 78 80 84

4 3D robot sander for artistically designed furniture 91 4.1 Background . . . . . . . . . . . . . . . . . . . 92 4.2 Feedfoward position/orientation control based on post-process of CAM . . . . . . . . 94 4.3 Hybrid position/force control with weak coupling . . . . . . . . . . . . . . . . . . . . . . . 96 4.4 Robotic sanding system for wooden parts with curved surfaces . . . . . . . . . . . . . . 98 4.5 Surface-following control for robotic sanding system . . . . . . . . . . . . . . . . . . . . . . 100 4.6 Feedback control of polishing force . . . . . . 101 4.7 Feedforward and feedback control of position 103 4.8 Hyper CL data . . . . . . . . . . . . . . . . . 105 4.9 Experimental result . . . . . . . . . . . . . . 106 4.10 Conclusion . . . . . . . . . . . . . . . . . . . 110 5 3D machining system for artistic wooden paint rollers 113 5.1 Background . . . . . . . . . . . . . . . . . . . 113 5.2 Conventional five-axis nc machine tool with a tilting head . . . . . . . . . . . . . . . . . . . 118 5.3 Intelligent machining system for artistic design of wooden paint rollers . . . . . . . . . . 120 5.4 Experiments . . . . . . . . . . . . . . . . . . . 135 5.5 Conclusion . . . . . . . . . . . . . . . . . . . 140 vi

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6 Polishing robot for pet bottle blow molds 6.1 Background . . . . . . . . . . . . . . . . . . . 6.2 Generation of multi-axis cutter location data 6.3 Basic Polishing Scheme for a Ball-End Abrasive Tool . . . . . . . . . . . . . . . . . . . . . 6.4 Feedback Control of Polishing Force . . . . . 6.5 Feedforward and Feedback Control of Tool Position . . . . . . . . . . . . . . . . . . . . . 6.6 Update timing of CL data . . . . . . . . . . . 6.7 Experiment . . . . . . . . . . . . . . . . . . . 6.8 Conclusion . . . . . . . . . . . . . . . . . . .

141 142 146 147 149 150 152 154 161

7 Desktop orthogonal-type robot for LED lens cavities 163 7.1 Background . . . . . . . . . . . . . . . . . . . 164 7.2 Limitation of a polishing system based on an articulated-type industrial robot . . . . . . . 165 7.3 Desktop orthogonal-type robot with compliance controllability . . . . . . . . . . . . . . . 167 7.4 Transformation technique of manipulated values from velocity to pulse . . . . . . . . . . 168 7.5 Desired damping considering the critically damped condition . . . . . . . . . . . . . . . . 170 7.6 Design of weak coupling control between force feedback loop and position feedback loop . . . 172 7.7 Basic experiment . . . . . . . . . . . . . . . . 174 7.8 Frequency characteristics . . . . . . . . . . . 184 7.9 Application to finishing an LED lens mold . . 186 7.10 Stick-slip motion of tool . . . . . . . . . . . . 186 7.11 Neural Network-Based Stiffness Estimator . 191 7.12 Automatic Tool Truing for Long-Time Lapping Process . . . . . . . . . . . . . . . . . . . 199 7.13 Force Input Device . . . . . . . . . . . . . . . 208 7.14 Conclusion . . . . . . . . . . . . . . . . . . . 210 8 Conclusion

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Controller design for industrial robots and machine tools

References

215

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List of figures 1

Industrial robots with an open-architecture controller. . . . . . . . . . . . . . . . . . . . . xxvii

1.1 1.2

PUMA560 manipulator. . . . . . . . . . . . . Block diagram of the resolved acceleration ¨ r are the control method, where xr , x˙ r and x desired position/orientation, velocity and acceleration vectors in Cartesian coordinate system. . . . . . . . . . . . . . . . . . . . . . . . 1.3 Trajectory following control problem. . . . . . 1.4 Desired joint angle θ r , velocity θ˙ r and accel¨ r in joint space. . . . . . . . . . . . . eration θ 1.5 Genotype of K v and K p which means an individual. . . . . . . . . . . . . . . . . . . . . . 1.6 Evolutionary history in case that the resolved acceleration control law was employed. . . . . 1.7 Simulation result in case of using the gains with minimum fitness. . . . . . . . . . . . . . 1.8 Block diagram of impedance model following force control with I-action. . . . . . . . . . . . 1.9 Block diagram of impedance model following force controller, in which xr (k), x˙ r (k) and ¨ r (k) are transformed into the joint driving x torque τ . . . . . . . . . . . . . . . . . . . . . 1.10 Antecedent membership functions for ex (k). . 1.11 Antecedent membership functions for ∆ex (k). 1.12 Profiling control situation. . . . . . . . . . . . ix

5

6 7 8 9 12 14 17

19 21 21 23

Controller design for industrial robots and machine tools

1.13 Time histories of environmental stiffness in xand z-directions. . . . . . . . . . . . . . . . . 1.14 Block diagram of the force control system using a fuzzy reasoning. . . . . . . . . . . . . . 1.15 Force control result using only IMFFC. . . . . 1.16 Force control result using IMFFC with fuzzy force controller. . . . . . . . . . . . . . . . . . 1.17 Position compensations ∆x(k) and ∆z(k) generated from the fuzzy force controller. . . 1.18 A desirable force response sEf z (k) for a teaching signal obtained through simulation. . . . 1.19 Velocity of arm tip sz(k), ˙ which is the teaching signal of output of neural network. . . . . 1.20 Neural network for dynamics learning of contact motion. . . . . . . . . . . . . . . . . . . . 1.21 Learning history of error function E. . . . . . 1.22 Output sz˙nn (k) generated from the learned neural network. . . . . . . . . . . . . . . . . . 1.23 An example of force control result by feedforwardly using the learned NN. . . . . . . . . . 1.24 Block diagram of the force control system using a neural network. . . . . . . . . . . . . . . 1.25 The upper, middle and lower figures show the outputs from IMFFC+NN, NN only and IMFFC only, respectively. . . . . . . . . . . . 2.1 2.2 2.3 2.4

Transformation from position command to joint driving torque . . . . . . . . . . . . . . . Example of force control under known environments . . . . . . . . . . . . . . . . . . . . Stiff end-effector fixed to the tip of the robot arm . . . . . . . . . . . . . . . . . . . . . . . Force control results: (a)Km1 = Km3 = 5000 N/m, (b)Km1 = Km3 = 10000 N/m, (c)Km1 = Km3 = 15000 N/m, (d)Km1 = Km3 = 20000 N/m . . . . . . . . . . . . . . . x

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23 24 25 25 26 28 29 30 31 31 32 33 34 37 42 43

44

List of figures

2.5 2.6 2.7 2.8 2.9 2.10 2.11

2.12 2.13 2.14 2.15 2.16 2.17 2.18 3.1 3.2 3.3

Block diagram of the impedance model following force controller with the FEM . . . . . Fuzzy rules encoded into a chromosome . . . Estimated stiffness for each environment . . . Relationship between true stiffness of environment and desired damping coefficients . . An example of evolutionary history in case of Km1 = Km3 = 17500 N/m . . . . . . . . . . . Learned antecedent membership functions (best individual) in the case of Km1 = Km3 = 17500 N/m . . . . . . . . . . . . . . . . . . . Simulation results using the best individual in the case of Km1 = Km3 = 17500 N/m: (a) force control result, (b), (c) time history ˆ m1 , K ˆ m3 and desired of estimated stiffness K ˜d1 , B ˜d3 . . . . . . . . . . . . . . . . damping B Generalized antecedent membership functions for GFEM . . . . . . . . . . . . . . . . . Hybrid position/force control problem under unlearned environments . . . . . . . . . . . . Force control results in x- and z-directions under an unlearned environment . . . . . . . Position control result in y-direction . . . . . Desired damping coefficients in the x-direction. Desired damping coefficients in the z-direction. Force control results in case that a larger magnitude is given to the desired contact force Desktop-size industrial robot RV1A. . . . . . Relation between CL data cl(i) and desired trajectory wr(k), in which wO is the origin of work coordinate system. . . . . . . . . . . . . Relation between position component p(i) in CL data and desired position wxd (k), in which p(i) − wxd (k) and p(i + 1) − wxd (k + 3) are called the fraction vectors. . . . . . . . . . . . xi

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49 50 52 53 54 55

56 59 60 60 61 61 63 64 68 69

70

Controller design for industrial robots and machine tools

3.4 3.5 3.6

3.7

3.8 3.9 3.10 3.11 3.12 3.13

3.14 3.15 3.16 3.17 3.18 3.19

Block diagram of communication system by using UDP packet. . . . . . . . . . . . . . . . Communication scheme by using UDP packet between PC and Industrial robot RV1A, in which the sampling period ∆t is set to 10 ms. Orientation control of arm tip based on CL data shown in Fig. 3.2, in which the initial orientation is given with [ϕ(k) θ(k) ψ(k)]T = [0 0 0]T . . . . . . . . . . . . . . . . . . . . . . CL data cl(i) = [pT (i) nT (i)]T consisting of position and orientation components, which is used for desired trajectory of the tip of robot arm. . . . . . . . . . . . . . . . . . . . . Initial part of x-component Xd (k) of desired trajectory in robot absolute coordinate system. Initial part of y-component Yd (k) of desired trajectory in robot absolute coordinate system. Initial part of z-component Zd (k) of desired trajectory in robot absolute coordinate system. Initial part of desired roll angle ϕd (k) calculated from the desired trajectory shown in Fig. 3.7. . . . . . . . . . . . . . . . . . . . . Initial part of desired pitch angle θd (k) calculated from the desired trajectory shown in Fig. 3.7. . . . . . . . . . . . . . . . . . . . . Roll angles around x-axis, in which (a) is the initial angle represented by ϕ(k) = 0, (b) is the case of −π ≤ ϕ(k) < 0, (c) is the case of ϕ(k) = ± π, and (d) is the case of 0 < ϕ(k) ≤ π. Control result of x-directional position X(k). Control result of y-directional position Y (k). Control result of z-directional position Z(k). . Control result of roll angle ϕ(k). . . . . . . . Control result of pitch angle θ(k). . . . . . . . Timing chart between a robot controller and a PC through Ethernet, in which UDP packet with 196 bytes is used. . . . . . . . . . . . . . xii

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70 71

74

75 76 77 77 78 78

85 86 86 86 87 87 88

List of figures

3.20 Experimental scene, in which a student is pulling the arm tip with 10 N in x-direction. 3.21 Experimental results when Eq. (3.27) is used in x-direction with several desired stiffness Kdx N/mm. The relations between the time and position are plotted. . . . . . . . . . . . . 3.22 Experimental results when Eq. (3.30) is used in x-direction with several desired dampings Bdx Ns/mm. The relations between the time and position are plotted. . . . . . . . . . . . . 3.23 Experimental results when Eq. (3.32) is used in x-direction with several damping cofficients ζ. The relations between the time and position are plotted. . . . . . . . . . . . . . . 4.1

Handy air-driven sanding tools usually used by skilled workers. . . . . . . . . . . . . . . . 4.2 Example of a whirl path generated based on contour lines. . . . . . . . . . . . . . . . . . . 4.3 Normalized tool vector n(i) represented by θ1 (i) and θ2 (i) in work coordinate system. . . 4.4 Block diagram of the proposed hybrid position/force controller with weak coupling. . . . 4.5 Robotic sanding system developed based on an open-architecture industrial robot KAWASAKI FS30L. . . . . . . . . . . . . . . 4.6 Hardware block diagram between a Windows PC and a PC-based controller. . . . . . . . . 4.7 Polishing force F (k) composed of contact force f (k) and kinetic friction force F r (k). . . 4.8 Zigzag path generated from the mainprocessor of a CAM system. Each through point has a position and an orientation components . . . . . . . . . . . . . . . . . . . . . 4.9 Example of proposed hyper CL data. . . . . . 4.10 Overview of the robot sander developed based on KAWASAKI FS20. . . . . . . . . . . . . . xiii

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89

89

90 92 94 95 96 99 99 102

103 105 107

Controller design for industrial robots and machine tools

4.11 Sanding scenes using the proposed 3D robot sander developed based on a KAWASAKI FS30L. . . . . . . . . . . . . . . . . . . . . . . 109 4.12 Curved surfaces before and after polishing process. . . . . . . . . . . . . . . . . . . . . . 109 4.13 Wooden chair with an artistic curved surface (Courtesy of Furniture Workshop Nishida). . 109 5.1

Conventional five-axis NC machine tool with a tilting head. . . . . . . . . . . . . . . . . . . 120

5.2

Main- and post-processes to compute corrected NC data for five-axis NC machine tool. 121

5.3

Artistic paint roller models designed by 3D CAD. . . . . . . . . . . . . . . . . . . . . . . 121

5.4

Definition of the tool length of a tilting head. 122

5.5

Inclination and rotation of main head. . . . . 122

5.6

Motion of tip of ball-end mill generated from main-processor. . . . . . . . . . . . . . . . . . 123

5.7

Sample model with curved surface and the five-axis machining scene. . . . . . . . . . . . 123

5.8

Overview of the proposed machining scheme for cylindrical wooden workpieces. . . . . . . 127

5.9

Three-axis NC machine tool MDX-650A with a rotary unit. . . . . . . . . . . . . . . . . . . 127

5.10 Relief design illustrated by a 3D CAD. . . . . 128 5.11 An example of zigzag path on a flat model (y_length = y_max − y_min ). . . . . . . . . . . 130 5.12 Typical edge chipping . . . . . . . . . . . . . 130 5.13 An example of relation between the distance and the point density with respect to CL data. 133 5.14 Antecedent membership functions for d(i) and ∆d(i). . . . . . . . . . . . . . . . . . . . . 134 5.15 Carving scene of a wooden paint roller with an artistic design. . . . . . . . . . . . . . . . . 135 xiv

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List of figures

5.16 An example of the feed rate values given to NC machine tool, in which the total number of steps is 400, Fmax and Fmin are set to 2000 mm/min. and 600 mm/min., respectively. . . 137 5.17 Artistic design wooden paint rollers carved by the proposed system. . . . . . . . . . . . . . . 138 6.1

Mold polishing robot developed based on YASKAWA MOTOMAN UP6. . . . . . . . . 145 6.2 Generation of normalized tool vector n(i) at p(i) on a free-formed surface. . . . . . . . . . 147 6.3 Polishing strategy by efficiently using the contour of a ball-end abrasive tool. . . . . . . . . 149 6.4 Force sensor to measure the polishing force ∥F ∥. . . . . . . . . . . . . . . . . . . . . . . . 150 6.5 Relation between the tool’s center and CL data.153 6.6 PET bottle blow mold before polishing process.155 6.7 Experimental setup. . . . . . . . . . . . . . . 156 6.8 Desired trajectories composed of zigzag paths. 157 6.9 Experimental scene using the proposed mold polishing robot. . . . . . . . . . . . . . . . . . 158 6.10 Comparison of CL data and actual trajectory. 160 6.11 X-directional actual trajectory obtained through an experiment. . . . . . . . . . . . . 160 6.12 Constriction part of mold surface after wiped with a cloth containing the polishing compound Cr2 O3 . . . . . . . . . . . . . . . . . . . 161 7.1 7.2 7.3

LED lens mold with several concave areas precisely machined within a tolerance, which is a typical axis-asymmetric workpiece. . . . . 177 Polishing scene of a PET bottle blow mold using a conventional articulated-type industrial robot with a servo spindle. . . . . . . . . . . . 177 Static relation between position and contact force in case of a conventional articulatedtype industrial robot. . . . . . . . . . . . . . . 178 xv

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7.4 7.5

7.6 7.7

7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19

Proposed desktop orthogonal-type robot with compliance controllability. . . . . . . . . . . . Hardware block diagram of the desktop orthogonal-type robot composed of three single-axis devices with a position resolution of 1µm. . . . . . . . . . . . . . . . . . . . . . Static relation between position and contact force in the case of the desktop orthogonaltype robot with a stiff ball-end abrasive tool. Static relation between position and contact force in the case of the desktop orthogonaltype robot with a rubber ball-end abrasive tool. . . . . . . . . . . . . . . . . . . . . . . . Block diagram of the CAD/CAM-based hybrid position/force controller with a velocitypulse converter. . . . . . . . . . . . . . . . . . Relation between the polishing force error Ef (k) and manipulated variable vnormal (k) calculated from Eq. (4.13). . . . . . . . . . . Example of spiral path used for desired trajectory of abrasive tool. . . . . . . . . . . . . 3D model designed for a profiling control experiment. . . . . . . . . . . . . . . . . . . . . Profiling control scene along a spiral path. . . Position control result along the spiral path. . Control result of the polishing force ∥SF (k)∥. Desired contact force in case of 1 Hz. . . . . . Frequency characteristics of the force control system in case of using the elastic ball-end abrasive tool. . . . . . . . . . . . . . . . . . . Frequency characteristics of the force control system in case of using the small wood-stick tool. . . . . . . . . . . . . . . . . . . . . . . . Finishing scene by using a wood-stick tool and diamond lapping paste. . . . . . . . . . . Surface of the LED lens mold before and after the finishing process. The diameter is 4 mm. xvi

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179 179

179 180 180 181 181 182 182 183 184 185 185 187 188

List of figures

7.20 Large-scale photo of the LED lens mold before finishing process. . . . . . . . . . . . . . . 7.21 Image of the small stick-slip motion for an abrasive tool. . . . . . . . . . . . . . . . . . . 7.22 Surface of the LED lens mold before and after the finishing process. The diameter is 4 mm. 7.23 LED lens mold after the conventional finishing process. . . . . . . . . . . . . . . . . . . . 7.24 Undesirable small cusp marks still remain on the surface. . . . . . . . . . . . . . . . . . . . 7.25 Large scale photo of an LED lens mold after finishing process by using the proposed stickslip motion control. . . . . . . . . . . . . . . . 7.26 An example of the static relation between position and contact force in the case of a thin wood-stick tool. The tip diameter is 1 mm. . 7.27 Effective stiffness of the orthogonal-tpe robot with the thin wood-stick tool. . . . . . . . . . 7.28 Neural network for acquiring the nonlinearity of effective stiffness. . . . . . . . . . . . . . . 7.29 Learning result of effective stiffness with nonlinearity in press motion. . . . . . . . . . . . . 7.30 Learning result of effective stiffness with nonlinearity in unpress motion. . . . . . . . . . . 7.31 Block diagram of the force feedback control law shown in Fig. 3.4. . . . . . . . . . . . . . 7.32 Detailed block diagram of the NN-based effective stiffness estimator shown in Fig. 7.31. 7.33 Control result of polishing force ∥SF (k)∥. . . ˆ e estimated by the neural 7.34 Effective stiffness K networks illustrated in Fig. 7.32 . . . . . . . . 7.35 Skilled worker’s hand lapping of an LED lens cavity with multiple concave areas to be finished. . . . . . . . . . . . . . . . . . . . . . . 7.36 Automated lapping of a concave area on LED lens cavity. . . . . . . . . . . . . . . . . . . . 7.37 LED lens cavity after the lapping process. . . xvii

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Controller design for industrial robots and machine tools

7.38 Finished surface of a concave area on an LED lens cavity, in which the controller shown in Fig. 7.32 is used. . . . . . . . . . . . . . . . . 7.39 Simple idea for realizing an automatic tool truing. . . . . . . . . . . . . . . . . . . . . . . 7.40 Truing of a wood-stick tool and its desired shape of contour. . . . . . . . . . . . . . . . . 7.41 Software flowchart of the orthogonal-type robot for realizing a long-time automatic lapping process, in which on-line tool truing function is incorporated. . . . . . . . . . . . . 7.42 Force input device with three-DOFs. . . . . . 7.43 CAD/CAM-based position/force controller with the force input device to manually regulate the desired polishing force Fd (k). . . . . 7.44 Control result of polishing force ∥F (k)∥, in which the desired polishing force Fd (k) is regulated by an operator with the force input device. . . . . . . . . . . . . . . . . . . . . . . 7.45 Dialog window for viewing the variation of each component of force vector f (k) = [fx (k) fy (k) fz (k)]T . . . . . . . . . . . . . . .

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204 205 206

207 208 210

211 212

List of tables 1.1 1.2 1.3

Parameters of GA operation in case of resolved acceleration control law. . . . . . . . . Constant values in consequent part [×10−4 mm]. . . . . . . . . . . . . . . . . . . . . . . . Simulation condition for acquiring teaching signals. . . . . . . . . . . . . . . . . . . . . . .

11 22 28

2.1 2.2 2.3 2.4 2.5 2.6 2.7

Stiffness of environment [N/m] . . . . . . . . Viscosity of environment [Ns/m] . . . . . . . Parameters for GA operation . . . . . . . . . Stiffness of learned environments [N/m] . . . Learned consequent constants (best individual) Learned consequent constants for GFEM . . . Stiffness of unlearned environments [N/m] . .

4.1

Sanding conditions and control parameters

5.1

Consequent constants of fuzzy reasoning part for d(i) and ∆d(i). . . . . . . . . . . . . . . . 136

6.1

Polishing conditions in the case of using the path shown in Fig. 6.8(a) . . . . . . . . . . . 159

7.1

Parameters tuned for profiling iment. . . . . . . . . . . . . . Parameters further tuned for finishing. . . . . . . . . . . . .

7.2

xix

45 45 50 51 57 58 62

. 107

control exper. . . . . . . . . 175 the LED lens . . . . . . . . . 186

Controller design for industrial robots and machine tools

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Preface Although a great deal of research and development has been conducted using industrial robots, it seems that the successful applications are limited to types such as welding, painting, handling, etc. In order to increase the applicability to other complicated manufacturing processes, it is very important for robots to establish a straightforward interface with CAD/CAM and to skillfully deal with the force acting between an end-effector and a workpiece. In this book, position and force control systems are designed for articulated-type industrial robots with an openarchitecture controller and a desktop-size orthogonal-type robot. Position and orientation of the tool attached to the tip of a robot are controlled based on a model designed by a CAD/CAM. Also, force including kinetic friction is delicately controlled through a desired impedance model. The both manipulated values generated from a position control system and a force control system are velocity quantity in Cartesian-coordinate system, so that a hybrid position/force control system can be easily applied to industrial robots with an open-architecture controller. After introducing simulation techniques for a robotic controller with an intelligent control concept, we show four examples of applications being utilized in actual manufacturing process. The first system is the 3D robot sander which sands free-formed surfaces of wooden materials. The finished wooden workpiece with a curved surface is used as a main part in constructing a piece of artistic furniture. The xxi

Controller design for industrial robots and machine tools

second system is 3D machining system for artistic wooden paint rollers. The proposed post-processor not only generates NC codes for a three-axis NC machine tool with a rotary unit but also appends suitable feed rate values by using a fuzzy reasoning approach. The third system is the mold polishing robot that can finish an aluminum PET bottle blow mold with curved surface. The application limit of an articulated-type industrial robot is quantitatively evaluated through a simple static measurement of position and force. The fourth system is a novel desktop-size orthogonal-type robot with higher position and force resolutions to finish an LED lens cavity with a lot of small concave areas. Conventional articulated-type industrial robots and NC machine tools have not been able to deal with the finishing of the LED lens cavity. After basic position and force control performances are shown through simulations, promising applications and present research progress are introduced.

Acknowledgments The authors would like to express gratitude to Prof. J. Paulo Davim, Series Editor of Woodhead Publishing Reviews: Mechanical Engineering, for this opportunity and for his professional support. Fusaomi Nagata Tokyo University of Science, Yamaguchi, Keigo Watanabe, Okayama University

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About the authors Fusaomi Nagata is currently a full professor at the Department of Mechanical Engineering, Faculty of Engineering, Tokyo University of Science, Yamaguchi, Japan. He received the B. Eng. degree from the Department of Electronic Engineering at Kyushu Institute of Technology, Japan in 1985, and the D. Eng. degree from the Faculty of Engineering Systems and Technology at Saga University, Japan in 1999. He was a research engineer with Kyushu Matsushita Electric Co., Japan from April 1985 to December 1988, and a special researcher with Fukuoka Industrial Technology Center, Japan from January 1989 to March 2006. After that, he was an associate professor at the Department of Mechanical Engineering, Faculty of Engineering, Tokyo University of Science, Yamaguchi, Japan from April 2006 to March 2012. His research interests include the intelligent control of industrial robots and its applications, and the development and intelligent control of network-based multiple mobile robot systems. Keigo Watanabe is currently a professor at the Department of Intelligent Mechanical Systems, Graduate School of Natural Science and Technology, Okayama University, Japan. He received the B. Eng. and M. Eng. degrees in mechanical engineering from the University of Tokushima, Japan in 1976 and 1978, respectively, and the D. Eng. degree in aeronautical engineering from Kyushu University, Japan in 1984. From 1980 to 1985, he was a research associate xxiii

Controller design for industrial robots and machine tools

at Kyushu University. From 1985 to 1990, he was an associate professor at the College of Engineering, Shizuoka University, Japan. From April 1990 to March 1993, he was an associate professor, and from April 1993 to March 1998, he was a full professor in the Department of Mechanical Engineering at Saga University, Japan. From April 1998 to March 2009, he was with the Department of Advanced Systems Control Engineering, Graduate School of Science and Engineering, Saga University. His research interests include intelligent signal processing and control using softcomputing, bio-inspired robotics, and nonholonomic systems.

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Introduction Up to now, industrial robots have drastically rationalized many kinds of manufacturing processes in industrial fields. The user interface provided by the robot maker has been almost limited to so-called teaching pendant. The teaching pendant is a useful and safe tool to obtain the position and orientation at the tip of a robot along a desired trajectory, but the teaching is very complicated and time-consuming task. In particular, when the target trajectory is a free curved line, many through points must be given to acquire a smooth trajectory; the task is therefore not an easy one. This decade, open-architecture industrial robots as shown in Fig. 1 have been produced by several industrial robot makers in Japan such as KAWASAKI Heavy Industries, Ltd., MITSUBISHI Heavy Industries, Ltd., YASKAWA Electric Corp., and so on. Open architecture, as described in this book, means that the servo system and kinematics of the robot are technically opened, so that various applications required in industrial fields are allowed to be planned and developed at the user side. For example, non-taught operation using a CAD/CAM system can be considered due to the opened accurate kinematics. Also, force control strategy using a force sensor can be implemented due to the technically-opened servo system. In this book, a position/force control system is first designed for articulated-type industrial robots with an openarchitecture controller and desktop-size NC machine tools. The position and orientation of the tool attached to the xxv

Controller design for industrial robots and machine tools

tip of an industrial robot are controlled based on a model designed by a CAD/CAM. Cutter location data generated from the main-processor of CAM are used to achieve the desired position and orientation. In addition, the force quantity (including kinetic friction) is controlled through a desired impedance model. Both manipulated values generated from the position control system and the force control system are velocity quantity in a Cartesian-coordinate system, so that the hybrid position/force control system can be easily applied to industrial robots with an open-architecture controller. In the second chapter, a velocity-based discrete-time control system with intelligent control concepts is proposed for open-architecture industrial robots. In the third chapter, a preliminary simulation of intelligent force control is conducted and the effectiveness is theoretically evaluated. Then, in the fourth chapter, a CAM system for articulatedtype industrial robots is proposed from the viewpoint of a robotic servo controller. Passive force control methods are designed using the inner servo system. At the beginning of the fifth chapter, the hybrid position/force control scheme is explained in detail. The proposed controller can be applied to industrial machineries with an open-architecture controller such as an articulated-type industrial robot and an orthogonal-type robot. The orthogonal-type robot is also called a Cartesian-type robot or desktop-size NC machine tool. From Chapter 5, we introduce four examples of applications being utilized in actual manufacturing process. The first one is the 3D robot sander which sands the free-formed surface of wooden materials. The finished wooden workpiece with a curved surface is used for a part in constructing a piece of artistic furniture. The second one is a 3D machining system for artistic wooden paint rollers. The carved paint roller can produce an artistic relief wall. The third one is the mold polishing robot which finishes aluminum PET bottle blow molds with curved surfaces. The application xxvi

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List of of tables tables List

KAWASAKI JS10

YASKAWA UP6

MITSUBISHI PA10

Figure1:1: Industrial Industrial robots robots with with an open-architecture open-architecture conFigure controller. troller.

limitofofarticulated-type articulated-type industrial industrial robots robots is limit is quantitatively quantitatively evaluated through a simple static position/force evaluated through a simple static position/force measuremeasurement. The fourth example is a novel desktop orthogonalment. The fourth example is a novel desktop orthogonaltyperobot robot with with higher higher resolutions resolutions of of position type position and and force force to finish a smaller workpiece such as an LED lens cavity to finish a smaller workpiece such as an LED lens cavity which conventional articulated-type industrial robots have which conventional articulated-type industrial robots have not been able to deal with. After the basic position/force not been able to deal with. After the basic position/force control performance is shown, present research progress and control performance is shown, present research progress and promising applications are introduced. promising applications are introduced.

xxvii Published by Woodhead xxviiPublishing Ltd., 2013 Published by Woodhead Publishing Ltd., 2013

Controller design for industrial robots and machine tools

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1 Velocity-based discrete-time control system with intelligent control concepts for open-architecture industrial robots DOI: 10.1533/9780857094636.1 Abstract: A simulation technique of velocity-based discrete-time control system for open-architecture industrial robots is presented by giving and combining examples of intelligent controls such as genetic algorithms, fuzzy control and neural networks. In order to develop a novel control system for an open-architecture industrial robot, it is required with regard to safety, cost and simplicity to preliminarily examine and evaluate the characteristics and the performance. The proposed simulation technique has a high applicability. Key words: servo system, dynamic simulation, PUMA560, gain tuning, genetic algorithms, force control, fuzzy control, neural network 1

Controller design for industrial robots and machine tools

1.1 Background Industrial robots have drastically rationalized many kinds of manufacturing processes in industrial fields. The user interface provided by the robot manufacturer has been almost entirely limited to the so-called teaching pendant. The teaching pendant is a useful and safe tool to obtain positions and orientations at the tip of a robot along a desired trajectory, but the teaching task is very complicated and time-consuming. In particular, when the target trajectory is a free curved line, many through points must be given to acquire a smooth trajectory; the task is therefore not an easy one. In the past decade, open-architecture industrial robots as shown in Fig. 1 have been produced from several industrial robot makers such as KAWASAKI Heavy Industries, Ltd., MITSUBISHI Heavy Industries, Ltd., YASKAWA Electric Corp., and so on. Open architecture, as described in this book, means that the servo system and kinematics of the robot are technically opened, so that various applications required in industrial fields can be planned and developed at the user side. For example, non-taught operation using a CAD/CAM system can be considered due to the opened accurate kinematics. Also, a force control strategy using a force sensor can easily be implemented due to the technically opened discrete-time servo system. It is now possible to model and simulate many types of robots. For example, Chen et al. presented a new design of an environment for the simulation, animation, and visualization of sensor-driven robots. Conventional computergraphics-based robot simulation and animation software packages lacked of capabilities for robot sensing simulation, so the system was designed to overcome the deficiency [1]. Benimeli et al. also addressed the implementation and comparison of indirect and direct identification procedures on an industrial robot provided with an open control architecture. The estimation of dynamic parameters in mechanical sys2

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Velocity-based discrete-time control system

tems constituted an issue of crucial importance for dynamic simulation applications where high levels of accuracy were required [2]. In this chapter, we present a simulation technique of a velocity-based discrete-time control system for openarchitecture industrial robots by giving and combining examples of intelligent control concepts such as genetic algorithms, fuzzy control and neural networks. In order to develop a novel velocity-based control system represented in discrete-time domain for an open-architecture industrial robot, it is required from the points of view of safety, cost and ease to preliminarily examine and evaluate the characteristics and performance. In such a case, the proposed simulation techniques will be useful. The validation and promise are evaluated through simulations, using a dynamic model of a PUMA560 manipulator as shown in Fig. 1.1 [3,4].

1.2 Basic Servo System In order to simulate an industrial robot, first of all, a servo system is considered and designed. Here, the resolved acceleration controller [5] is picked up in a servo system. The resolved acceleration control method or computed torque control method is used for the nonlinear control of industrial manipulators, which are composed of a model base portion and a servo portion. The servo portion is a closed loop with respect to position and velocity. On the other hand, the model base portion has the inertia term, gravity term and centrifugal/Coriolis term, which serve to cancel the nonlinearity of the manipulator. In order to realize high control stability, suitable position and velocity feedback gains used in the servo portion should be selected. In this section, a simple but effective fine tuning method, following the manual tuning process, is introduced for position and velocity feedback gains in the servo portion. At the first step, search space for the gains is roughly narrowed down by a controller designer, e.g. considering the criti3

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Controller design for industrial robots and machine tools

cally damped condition. At the second step, the gains are finely tuned by using genetic algorithms. Genetic algorithms search for a better combination of position and velocity feedback gains.

1.2.1 Resolved acceleration control The dynamic model of a manipulator without friction term is generally given by ¨ + H(θ, θ) ˙ + G(θ) = τ M (θ)θ

(1.1)

where, M (θ) ∈ ℜ6×6 is the inertia term in joint space. ˙ H(θ, θ) ∈ ℜ6×1 and G(θ) ∈ ℜ6×1 are the Coriolis/centrifugal term and gravity term in joint space, respec¨ ∈ ℜ6×1 are the position, tively. θ ∈ ℜ6×1 , θ˙ ∈ ℜ6×1 and θ velocity and acceleration vectors in joint coordinate system, respectively. τ ∈ ℜ6×1 is the joint driving torque vector. In the case that the resolved acceleration control law is employed in the servo system of a manipulator, desired position, velocity and acceleration vectors in Cartesian coordinate system are respectively given to the references of the servo system, so that the joint driving torque is calculated from [

ˆ (θ)J −1 (θ) x ¨ r + K v {x˙ r − x} ˙ + K p {xr − x} τ =M ]

˙ + G(θ) ˆ ˆ − J˙ (θ)θ˙ + H(θ, θ)

(1.2)

where, ˆ denotes the modeled term. x ∈ ℜ6×1 , x˙ ∈ ℜ6×1 ¨ ∈ ℜ6×1 are the position/orientation, velocity and acand x celeration vectors in Cartesian coordinate system, respec¨ r are the desired position/orientation, tively. xr , x˙ r and x velocity and acceleration vectors, respectively. K v = diag(Kv1 , . . . , Kv6 ) and K p = diag(Kp1 , . . . , Kp6 ) are the feedback gains of velocity and position, respectively. J (θ) ˙ is the Jacobian matrix which gives the relation x˙ = J (θ)θ. ˙ Note that θ, θ, x and x˙ in Eq. (1.2) are actual values, 4

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Velocity-based discrete-time control system

Figure 1.1: PUMA560 manipulator.

i.e., controlled variables. The nonlinear compensation terms ˙ and G(θ) ˆ ˆ H(θ, θ) are calculated to cancel the nonlinearity and are effective to achieve a stable trajectory control. Fig. 1.2 shows the block diagram of the resolved acceleration control method, in which F kine(θ) is the function to obtain the forward kinematics.

1.2.2 Fine gain tuning considering the critically damped condition A basic gain tuning method considering the critically damped condition is explained giving an example. If it is assumed that the modeled termsˆare exact, then the nonlinearity of the robot dynamics can be canceled. Substituting Eq. (1.2) into Eq. (1.1) gives the following second order error system. ¨ + K v e˙ + K p e = 0 e

(1.3)

where, e = xr − x. Accordingly, K v and K p are selected suitably, e.g., considering the critically damped condition 5

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Controller design for industrial robots and machine tools

&x&r

+

+ +

Kp

Kv +

x& r

xr

+

− x

Mˆ (θ )J −1 (θ )

−

+

PUMA560

θ θ&

+

Hˆ (θ , θ& ) + Gˆ (θ )

J& (θ )

− x&

τ

J (θ )

Fkine (θ )

Figure 1.2: Block diagram of the resolved acceleration ¨ r are the desired posicontrol method, where xr , x˙ r and x tion/orientation, velocity and acceleration vectors in Cartesian coordinate system.

given by Kvi = 2

√

Kpi (i = 1, . . . , 6)

(1.4)

so that desirable responses can be obtained if under the ideal condition as given by Eq. (1.3). It should be noted, however, that there exists nonlinearity such as Coulomb friction and viscous friction. The robotic dynamic model with the friction term is written by ¨ + H(θ, θ) ˙ + G(θ) + F r (θ, θ) ˙ =τ M (θ)θ

(1.5)

˙ ∈ ℜ6×1 is the friction term composed of where, F r (θ, θ) ˆ (θ), viscous friction and Coulomb friction. Also, because M ˙ and G(θ) ˆ ˆ H(θ, θ) in Eq. (1.2) implicitly include undesirable modeled treatment error, the velocity and position gains in the servo portion should be more finely tuned after basic gain tuning. In the reminder of this section, genetic algorithms are applied to search for more suitable gains.

1.2.3 Desired trajectory For instance, in order to apply the resolved acceleration control method to the manipulator, the desired trajectory 6

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Velocity-based discrete-time control system

Final pose

Initial pose

Figure 1.3: Trajectory following control problem.

¨ r in Cartesian coordinate system composed of xr , x˙ r and x must be prepared. First of all, the desired trajectory in Cartesian coordinate system is designed as shown in Fig. 1.3, in which the manipulator moves from the initial pose to the final pose. In this case, the robot stretches the arm tip 500 mm to the x-direction. The manipulator is still in the initial and final poses. The desired trajectories xr , x˙ r and ¨ r are calculated through a 4-1-4 order polynomial equax tion. We can design trajectories with various combinations of acceleration time, constant velocity time and deceleration time. The desired angle θ r , angle velocity θ˙ r and acceler¨ r in joint space are transformed from xr , x˙ r and x ¨r ation θ by respectively using the inverse kinematics, Jacobian J (θ) and sampling width ∆t. An example that consists of a desired joint angle, angle velocity and acceleration is shown in Fig. 1.4, which ¨ r in Fig. 1.3. The are transformed from the xr , x˙ r and x trajectory in joint space makes the robot follow the motion as shown in Fig. 1.3. To obtain satisfactory and safe control performance without falling a singularity, K v and K p are roughly tuned in advance by trial and error, considering the combination around the critically damped condition. We call this the initial manual tuning process. Two search spaces for K v and K p are obtained after the manual tuning process, so that K v and K p must be further fine7

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Controller design for industrial robots and machine tools

Desired angle rad

1 0.5

J3

0

J1, J4, J6

-0.5 -1

J5 J2

Joint acceleration rad/s2

Joint velocity rad/s

-1.5 0.5 J2

J5

0

J1, J4, J6 -0.5

J3

-1 2 1.5 1 J2

0.5

J5

0

J1, J4, J6 J3

-0.5 -1

0

1

2

3

Time s

Figure 1.4: Desired joint angle θ r , velocity θ˙ r and accel¨ r in joint space. eration θ

8

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Velocity-based discrete-time control system

K v 1 K v 2 K v 3 K v 4 K v 5 K v 6 K p1 K p 2 K p 3 K p 4 K p 5 K p 6 Figure 1.5: Genotype of K v and K p which means an individual.

tuned within the searched spaces to achieve a desirable motion without large overshoots and oscillations. In the next subsection, we propose a systematic tuning method using genetic algorithms which can be applied after the manual tuning process.

1.2.4 Fine gain tuning by using genetic algorithms The gain tuning after designing a robotic servo controller is an important and indispensable task if a smooth motion control system is to be realized. The proposed gain tuning process consists of two steps. The first step is conducted in order to narrow down the search space of gains through the operator’s manual gain tuning, while considering the circumference of the critically damped conditions given by Eq. (1.4). The ranges for the gain search are narrowed down between the minimum Kvi , Kpi and maximum Kvi , Kpi . The objective of the second step is to finely search for a superior combination of Kvi and Kpi within the search space by using genetic algorithms [6, 7]. The genetic algorithm is used to optimize Kvi and Kpi (i = 1, . . . , 6) which are the diagonal elements of K v and K p . In order to apply genetic algorithms, Kvi and Kpi are transformed into a genotype. Diagonal elements Kvi and Kpi are encoded into 8-bit binary code; an individual is composed of 96(= 8 × 12) bits. A population has 60 individuals. Each individual in an initial population is generated within expectable range considered in the initial manual tuning process. For example, we have preliminarily confirmed 9

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Controller design for industrial robots and machine tools

by randomly conducted manual tuning that if each element of K v and K p in Eq. (1.2) is set to 50 ≤ Kvi ≤ 200 and 10 ≤ Kpi ≤ 50000 (i = 1, . . . , 6) then an undesirable singularity does not tend to occur. The singularity is a typical result after the system becomes unstable. The elite survivable strategy is adopted in the selection process, where the superior six individuals can survive to next generation as elites. Crossover and mutation, which are the representative GA operations, are not applied to the genotypes of the elites. The remaining 54 individuals are yielded by tournament selection. The genotype including the K v and K p is shown in Fig. 1.5. Each individual is evaluated by applying Eq. (1.2) to the trajectory following the control problem shown in Fig. 1.3. The evaluation value Ev is calculated based on the square root of the sum of each directional error squared every sampling period, which is obtained by v T u 3 ∆t u∑ ∑ t {e (k)}2 Ev = i k=1

(1.6)

i=1

where the error ei (k) (i = 1, 2, 3) is the x-, y- and zdirectional position errors in Cartesian space. T and ∆t are the simulation time needed for a trajectory following control and sampling period, respectively. This is a minimization problem, where individuals with smaller fitness Ev can survive as elites to the next generation.

1.2.5 Tuning result Simulations were carried out using the dynamic model of a PUMA560 manipulator on MATLAB system. Robotic dynamics with the friction torque term given by Eq. (1.5) are applied. The friction torque term F r consists of the viscous friction torque and Coulomb friction torque, which is represented by ˙ ˙ = BG2 θ˙ + Gr τ c {sign(θ)} F r (θ, θ) r 10

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(1.7)

Velocity-based discrete-time control system

Table 1.1: Parameters of GA operation in case of resolved acceleration control law. Population size Number of elites Selection Crossover Mutation Search space of Kvi Search space of Kpi Maximum generation

60 6 Tournament selection Uniform crossover (rate=87.5%) Random mutation (rate=4.17%) 0.001 ≤ Kvi ≤ 220 0.001 ≤ Kpi ≤ 40000 100

where B is the coefficient matrix of viscous friction at each motor, Gr is the reduction gear ratio matrix which repre˙ sents the motor speed to joint speed, and τ c {sign(θ)} is ˙ the Coulomb friction torque at each motor. If sign(θi ) > 0, then τci = τci+ ; if sign(θ˙i ) < 0, then τci = τci− . In simulations, B and Gr are set to diag(0.0015, 0.0008, 0.0014, 0.0001, 0.0001, 0.0000) and diag(-62.6, 107.8, -53.7, 76.0, − 71.9, 76.7), respectively; τ + c and τ c are set to [0.395 0.126 T 0.132 0.011 0.009 0.004] and [-0.435 -0.071 -0.105 -0.017 -0.015 -0.011]T , respectively [3]. Before applying the GA operation, we broadly investigated the characteristics of the trajectory following control, while changing the combination of K v and K p . The results showed that the ranges in which the robot could move without falling a singularity were respectively 0.001 ≤ Kvi ≤ 220 and 0.001 ≤ Kpi ≤ 40000 (i = 1, . . . , 6), so that the search space for GA was limited within these ranges. The uniform crossover was employed to the individuals with a high probability rate 87.5% (7/8) and the reverse action with mutation rate 4.17% (1/24) is given to all bits forming 54 individuals. Other parameters for GA operations are tabulated in Table 1.1. As an example of tuning effectiveness, the variation of minimum fitness is shown in Fig. 1.6. It 11

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Controller design for industrial robots and machine tools

0.59 With considering friction torques

Best fitness Ev

0.58 0.57 0.56 0.55 0.54 0.53 0.52

0

20

60 40 Generation No.

80

100

Figure 1.6: Evolutionary history in case that the resolved acceleration control law was employed.

can be observed that better individuals have been selected through the alternation of generations with GA operations. After 100 generations, the phenotype of the best individual is represented by K v = diag(157, 204, 171, 181, 192, 76)

(1.8)

K p = diag(23137, 7412, 24471, 7922, 13725, 5882)(1.9) When above gains were given, the minimum fitness Ev became 0.5241 by Eq. (1.6). Fig. 1.7 shows the simulation results which are performed by the gains with the minimum fitness. The upper figure in Fig. 1.7 shows the controlled angle trajectories of joints 2 and 3. The second figure similarly shows the angle velocities. The third and lower figures respectively illustrate the friction torques acting at joints 2 and 3, which are given by Eq. (1.7). For example, it can be observed from the second figure in Fig. 1.7 that sign(`˙ 2 ) and sign(`˙ 3 ) are frequently changed around the start time and end time. According to the changes of sign(`˙ 2 ) and sign(`˙ 3 ), the large 12

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Velocity-based discrete-time control system

influence of Coulomb friction can be also observed around the corresponding time area in the third and lower figures. It is also observed that the best combination of Kvi and Kpi among obtained through the GA operation almost has the under-damped condition given by Kvi < 2

√

Kpi (i = 1, . . . , 6)

(1.10)

This suggests that an under-damped situation is suitable for such a robotic trajectory following control with time-varying references as shown in Fig. 1.4. In this subsection, we have preliminarily described the resolved acceleration controller as an example of a robotic servo system which is surely incorporated in openarchitecture industrial robots. A simple but effective finetuning method using genetic algorithms has been also introduced as one of intelligent control methodologies. When an open-architecture industrial robot is provided, the robotic servo system is technically opened. Therefore, we have only to make the desired trajectory composed of position xr , ve¨ r according to each task. Morelocity x˙ r and acceleration x over, when a force control function is needed, we have only to design the force controller so that the manipulated variables are represented by position xr , velocity x˙ r and acceleration ¨ r in discrete-time domain. x

1.3 Dynamic simulation When a computer is used to control an industrial robot, the control law is generally represented by a discrete-time control system. In this section, we describe how to simulate and evaluate the velocity-based discrete-time control system which is implemented into an open-architecture industrial robot. Let us consider the impedance model following force control (IMFFC) as an example of velocity-based discretetime control systems. In order to conduct a simulation with a robotic dynamic model, manipulated variables written by 13

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Controller design for industrial robots and machine tools

Controlled angle rad

1 0.5

J3

J3

0 -0.5 J2

-1

J2

Joint velocity rad/s

-1.5 0.8 J2

0

J3

Friction torque at J3 Nm

Friction torque at J2 Nm

-1 20 J2 10

0 -10 6 4 J3

2 0 -2 -4 -6 -8 0

1

2

3

Time s

Figure 1.7: Simulation result in case of using the gains with minimum fitness.

14

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Velocity-based discrete-time control system

velocity commands in discrete-time domains must be transformed into joint driving torques.

1.3.1 Impedance model following force control Impedance control is one of the effective control strategies for a manipulator to reduce or absorb the external force from an environment [8]. It is characterized by an ability to control mechanical impedances such as mass, damping and stiffness acting at joints. Impedance control does not have a force control mode or a position control mode, but is a combination of force and velocity. In order to control the contact force acting between an arm tip and an environment, we have proposed the impedance model following force control method; this can be easily implemented in industrial robots with an open-architecture controller [9]. The desired impedance equation in Cartesian space for a robot manipulator is designed by ¨ d ) + B d (x˙ − x˙ d ) + SK d (x − xd ) (1.11) M d (¨ x−x = SF + (I − S)K f (F − F d ) ¨ ∈ ℜ3 are the position, vewhere x ∈ ℜ3 , x˙ ∈ ℜ3 and x locity and acceleration vectors, respectively. M d ∈ ℜ3×3 , B d ∈ ℜ3×3 and K d ∈ ℜ3×3 are the coefficient matrices of desired mass, damping and stiffness, respectively. F ∈ ℜ3 is the force vector. K f ∈ ℜ3×3 if the force feedback gain ma¨ d and F d are the desired position, velocity, trix. xd , x˙ d , x acceleration and force vectors, respectively. S is the switch matrix to select force control mode or compliance control mode. If S = 0, Eq. (1.11) becomes force control mode in all directions; whereas if S = I it becomes compliance control mode in all directions. Here, I is the identity matrix. M d , B d , K d and K f are set to positive-definite diagonal matrices. When force control mode is selected in all directions, i.e., S = 0, defining X = x˙ − x˙ d gives ˙ = −M −1 B d X + M −1 K f (F − F d ) X d d 15

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(1.12)

Controller design for industrial robots and machine tools

Here, the stability of Eq. (1.12) is briefly considered at the equilibrium by using Lyapunov stability analysis. The candidate of Lyapunov function [10] is proposed by 1 V (X) = X T X 2

(1.13)

which is continuous and everywhere nonnegative. Differentiating Eq. (1.13) gives ˙ V˙ (X) = X T X = X T (−M −1 d B d X)

(1.14)

= −X T M −1 d BdX which is everywhere non-positive since M −1 d B d is a positive definite diagonal matrix. Therefore, Eq. (1.13) is indeed a Lyapunov function for the system given by Eq. (1.12). V˙ (X) can be zero only at X = 0, everywhere else V (X) decreases, so that Eq. (1.12) is asymptotically stable. In general, Eq. (1.12) can be resolved as −1 X = e−M d B d t X(0)

+

∫

t 0

−1 e−M d B d (t−τ ) M −1 d K f (F − F d )dτ

(1.15)

In the following, we consider the form in the discrete time k using a sampling time ∆t. If it is assumed that M d , B d , K f , F and F d are constant at ∆t(k − 1) ≤ t < ∆tk, then defining X(k) = X(t)|t=∆tk leads to the recursive equation given by −1 X(k) = e−M d B d ∆t X(k − 1)

(

−M d

− e

−1

B d ∆t − I

)

(1.16) B −1 d K f {F (k) − F d }

Remembering X = x˙ − x˙ d , giving x˙ d = 0 in the direction of force control, and adding an integral action, the equation 16

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Velocity-based discrete-time control system

+

+

_

+

_

x&

Inverse Inverse Jacobian Jacobian

+

θ& Servo Servo System System

Ki

Figure 1.8: Block diagram of impedance model following force control with I-action.

of velocity command in terms of Cartesian space is derived by −1 ˙ ˙ − 1) x(k) = e−M d B d ∆t x(k

(

−M d

− e

+ Ki

−1

k ∑

B d ∆t − I

)

B −1 d K f {F (k) − F d } (1.17)

{F (n) − F d }

n=1

where K i ∈ ℜ3×3 is the integral gain matrix and is also set to a positive-definite diagonal matrix. The impedance model following force control method written by Eq. (1.17) is used to control the force which an industrial robot gives an environment. The block diagram of Eq. (1.17) is shown in Fig. 1.8. As can be seen, the force is regulated by a feedback control loop.

1.3.2 How to generate the references for a servo system To simulate the IMFFC given in discrete-time domain, ˙ the velocity x(k) calculated from Eq. (1.17) must be transformed into joint driving torques. Accordingly, we propose ˙ a transformation technique where x(k) is given to the reference value of the Cartesian-based servo controller. The 17

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Controller design for industrial robots and machine tools

˙ joint driving torques transformed from x(k) control each joint independently. Fig. 1.9 shows the block diagram of the transformation technique. First of all, the reference position xr (k) is obtained from ˙ xr (k) = x(k) + x(k)

(1.18)

where x(k) is the current position of the arm tip. Then, the ¨ r (k) are obtained using a velocity x˙ r (k) and acceleration x discrete time k and sampling width ∆t. x˙ r (k) = {xr (k) − xr (k − 1)}/∆t

(1.19)

¨ r (k) = {x˙ r (k) − x˙ r (k − 1)}/∆t x

(1.20)

For example, it is assumed that the resolved acceleration control law is used in the servo system of an industrial robot. ¨ r (k) generated from Eqs. In this case, xr (k), x˙ r (k) and x (1.18)∼(1.20) are respectively given to the references of the servo system as shown in Fig. 1.9, so that the joint torque τ is generated from the resolved acceleration control law given by Eq. (1.2). Thus, the proposed technique allows us to implement the IMFFC in the computer simulations. The interpretation of Fig. 1.9 is as follows: The IMFFC makes ˙ a velocity x(k) using the force error F (k) − F d . Moreover, the current position x(k) is obtained from the forward kine˙ matics of the PUMA560 manipulator. x(k) and x(k) are added together, and the result is given to the desired position xr (k) of the resolved acceleration controller used as a servo system. As mentioned above, the desired velocity ¨ r (k) are and acceleration respectively given to x˙ r (k) and x calculated using xr (k) and ∆t. Manipulated variables written by velocity commands in a discrete-time domain can be transformed to joint driving torques due to the proposed scheme, as shown in Fig. 1.9, so that various velocity-based control methodologies written in discrete-time domain developed for open-architecture industrial robots have been able to be easily simulated. 18

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Velocity-based discrete-time control system F (k ) : Force sensor measurement x (k ) : Current position _

Fd

x& (k )

x r (k )

+

IMFFC +

+ + _

1 z

x& r (k )

1 ∆t

+ _

1 z

IMFFC : Impedance Model Following Force Controller

1 ∆t

&x&r (k )

Resolved τ Acceleration PUMA560 Controller

Figure 1.9: Block diagram of impedance model following ¨ r (k) are transforce controller, in which xr (k), x˙ r (k) and x formed into the joint driving torque τ .

1.4 In case of fuzzy control 1.4.1 Fuzzy force control To improve the force control performance in the environment with unknown dynamics or curved surfaces, we first describe how to construct the fuzzy controller, using the servo system introduced in the previous section. The main feature of the fuzzy force controller is that it generates proper position compensations as feedforward commands, so that overshoots and oscillations in the direction of force control can be suppressed satisfactorily. A profiling control simulation using the dynamics of the PUMA560 manipulator is shown to demonstrate the effectiveness under an environment with time-varying stiffness. If a force controlled manipulator is applied to a profiling task, the change of environmental stiffness or shape causes undesirable force error. The fuzzy force controller works to reduce the force error. The fuzzy controller generates a velocity vector, i.e. a position compensation vector ∆x(k) = [∆x(k) ∆y(k) ∆z(k)]T as a feedforward control according to the force error and its rate every sampling time. For example, let us consider the x-directional compensation. 19

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Controller design for industrial robots and machine tools

Fuzzy inputs are the force error and its rate defined as ex (k) = Fdx − Fx (k) ∆ex (k) =

{ex (k) − ex (k − 1)} ∆t

(1.21) (1.22)

where Fdx and Fx (k) are the desired force and sensed force, respectively. Following the fuzzy approach, if the information on only x-direction is used, the fuzzy rules are described by ˜1 , THEN ∆x(k) = c1 Rule 1 IF ex (k) is A˜1 and ∆ex (k) is B ˜2 , THEN ∆x(k) = c2 Rule 2 IF ex (k) is A˜2 and ∆ex (k) is B ˜ ˜3 , THEN ∆x(k) = c3 Rule 3 IF ex (k) is A3 and ∆ex (k) is B .. . ˜L , THEN ∆x(k) = cL Rule L IF ex (k) is A˜L and ∆ex (k) is B ˜i are the i-th antecedent where A˜i (i = 1, . . . , L) and B fuzzy sets for two fuzzy inputs ex (k) and ∆ex (k); ci is the consequent constant value at the i-th rule; L is the fuzzy rule number. The confidence of the antecedent part at the i-th rule is obtained by ωi = µAi ˜ {ex (k)} ∧ µBi ˜ {∆ex (k)}

(1.23)

where µX (•) denotes the confidence of a fuzzy set labeled by X. Therefore, the fuzzy position compensation is calculated by ∑L

ωi ci j=1 ωj

∆x(k) = ∑i=1 L

(1.24)

The position compensation of other directions, ∆y(k) or ∆z(k) is similarly calculated by the same procedure. Note that, the fuzzy set used is the following Gaussian type membership function µX (x) = exp{log(0.5)(x − ff )2 fi 2 } 20

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(1.25)

Velocity-based discrete-time control system NB

NM

NS

-9

-6

-3

PS

PM

PB

3

6

9

1

0.5

0 0

x 10 - 2

Figure 1.10: Antecedent membership functions for ex (k).

NB

NM

NS

-6

-4

-2

PS

PM

PB

2

4

6

1

0.5

0

Figure 1.11: ∆ex (k).

0

x 10 - 2

Antecedent membership functions for

where α is the center of membership function and β is the reciprocal value of standard deviation. Figures 1.10 and 1.11 show the designed antecedent membership functions for ex (k) and ∆ex (k), respectively. Each reciprocal value of the standard deviation are 66.7 and 100, respectively. The corresponding constant values in consequent part are tabulated in Table 1.2. It is expected that the proposed fuzzy force controller will improve the force control performance. 21

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Controller design for industrial robots and machine tools

Table 1.2: Constant values in consequent part [×10−4 mm]. PP PP ∆ex (k) NB PP ex (k) PP P NB -16.0

NM

NS

PS

PM

PB

-14.0

-12.0

-8.0

-6.0

-4.0

NM

-9.6

-8.4

-7.2

-4.8

-3.6

-2.4

NS

-3.2

-2.8

-2.4

-1.6

-1.2

-0.8

PS

0.8

1.2

1.6

2.4

2.8

3.2

PM

2.4

3.6

4.8

7.2

8.4

9.6

PB

4.0

6.0

8.0

12.0

4.0

16.0

1.4.2 Simulation of fuzzy force control In this subsection, a profiling control as shown in Fig. 1.12 is conducted and analyzed in detail. And the promise of the proposed method shown in Fig. 1.14 is evaluated through the profiling control simulation. There are two important factors that prevent the stable profiling control. One is that the dynamics of the object are almost unknown, and perhaps change frequently. The other is the extent to which the object’s surface is curved. In practice, robots for polishing and sanding must deal with such objects. It is assumed that the object with an inclined and flat plane is fixed in the robot workspace as shown in Fig. 1.12. The end-effector makes contact with the object; an attempt is made to control the contact force from the normal direction of the slope to converge to a reference of 1 N. It is also assumed that the contact force F (k) is generated by ˙ F (k) = −B m x(k) − K m {x(k) − xm }

(1.26)

where B m Ns/m and K m N/m are the viscosity and stiffness coefficients of the object to be positive definite diagonal matrices, and xm is the initial contact position. In the following simulation, the stiffness of the object 22

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Velocity-based discrete-time control system

s

z s

y Top of a robot arm Q so

s

x

P

Bm : Viscosity Km : Siffness

π 6

so - sx sy sz

: Sensor coordinate system

Figure 1.12: Profiling control situation.

X-direction

Z-direction

Stiffness of workpiece

x 10 4 N/m

13 12 11 10 9 8 7

0

1

2 Time s

3

4

Figure 1.13: Time histories of environmental stiffness in x- and z-directions.

23

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Controller design for industrial robots and machine tools F (k ) : Force sensor measurement e (k ) + _

1 z

∆e (k )

1 ∆t

Fuzzy Force Controller

x (k ) : Current position

∆x (k ) _

Fd +

IMFFC

x& (k )

+

x r (k )

+

+ + _

1 z

x& r (k )

1 ∆t

+ _

1 z

IMFFC : Impedance Model Following Force Controller

1 ∆t

&x&r (k )

Resolved τ Acceleration PUMA560 Controller

Figure 1.14: Block diagram of the force control system using a fuzzy reasoning.

K m = diag(Kmx , Kmy , Kmz ) varies as follows: Kmx = 100000 + 30000 × sin(3kπ)

(1.27)

Kmz = 100000 + 30000 × sin(4kπ + π/2) (1.28) which is illustrated as shown in Fig. 1.13. The viscosity is fixed to B m = diag(15, 15, 15) Ns/m. Here, we control the z-directional contact force and y-directional trajectory (i.e., from point P to Q shown in Fig. 1.12) in sensor coordinate system. Also, we set up the manipulator as PUMA560 [3]; its dynamics are given by ˙ + Gx (θ) = J −T (θ)τ + F M x (θ)¨ x + H x (θ, θ)

(1.29)

where H x (θ) is the Coriolis and centrifugal forces, Gx (θ) is the gravity term, J (θ) is the Jacobian matrix, and τ is the joint driving torque. Note that the subscript x means the value in Cartesian space. The dynamics are solved by the Runge-Kutta method on a MATLAB system. In this case, the resolved acceleration controller is used in the servo system shown in Fig. 1.14, and the xr (k) is generated by ˙ xr (k) = x(k) + ∆x(k) + x(k) 24

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(1.30)

Force control result in base coordinate system N

Velocity-based discrete-time control system

1.0

Z-direction

0.5 X-direction

Reference Response

0 0

1

2 Time s

3

4

Force control result in base coordinate system N

Figure 1.15: Force control result using only IMFFC.

1.0

Z-direction Fuzzy force controller is active

0.5 X-direction

Reference Response

0 0

1

2 Time s

3

4

Figure 1.16: Force control result using IMFFC with fuzzy force controller.

25

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Controller design for industrial robots and machine tools 2

Output of fuzzy force controller

x 10 - 4 mm

Fuzzy force controller is active

1

X-direction

Z-direction

0

-1

0

1

2 Time s

3

4

Figure 1.17: Position compensations ∆x(k) and ∆z(k) generated from the fuzzy force controller.

As a first case study, the fuzzy force controller was not used. In this case, it was difficult to suppress the oscillations caused by the change of the object stiffness. Fig. 1.15 shows the force control result. It should be noted that the z-directional contact force in the sensor coordinate system is represented by x- and z-directional forces in robot base coordinate system. Another case study was carried out to evaluate the ability of the fuzzy force controller. The fuzzy force controller was set to active after the passage of one second. The force control result is shown in Fig. 1.16. In this case, x- and z-directional position compensations ∆x(k) and ∆z(k) generated from the fuzzy force controller are shown in Fig. 1.17. It is observed that each directional force acting on the end-effector is improved in spite of the variation of the object stiffness. 26

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Velocity-based discrete-time control system

1.5 In case of neural network 1.5.1 Force control with neural network Next, a force control system using a neural network (NN) is presented to realize a desirable contact motion with high speed response characteristics between a manipulator and an environment. For example, the PC-based controller used in the robot sander provides API (Application Programming Interface) functions to control the position and orientation of the arm tip with velocity commands [11]. Making good use of the API functions, it is expected that if the control method is described by a velocity-based command, then the method can be easily applied to actual open-architecture industrial robots. Thus, if the neural network considered in this section is made up of a model whose output is the quantity of velocity, it will be used for the actual robot with the open-architecture controller without difficulty. First of all, in order to acquire teaching signals, we consider a contact control problem as shown in Fig. 1.12, in which the tip of the PUMA560 comes into contact with the environment from a normal direction with a low speed, and then is stabilized with a suitable contact force using the IMFFC. The required teaching signals are ideal responses without overshoots and oscillations, which are suitable for training patterns of the neural network. Simulations on contact motion were repeatedly conducted with trial and error under the condition tabulated in Table 1.3. Through the simulation with an environmental stiffness Km =1000 N/m, a desirable response of force error sef z (k) = Fdz − Fz (k) as shown in Fig. 1.18 was obtained along normal direction. Note that s denotes the sensor coordinate system and sef (k) is composed of [sef x (k) sef y (k) sef z (k)]T . In this case, the zdirectional velocity sz(k) ˙ yielding at the arm tip was shown in Fig. 1.19. The results given by Figs. 1.18 and 1.19 are one pattern of teaching signals for input and output, respectively. The other two teaching signals for inputs are 27

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Controller design for industrial robots and machine tools

Table 1.3: Simulation condition for acquiring teaching signals. Approaching velocity Desired contact force Fd Stiffness of object Desired damping of IMFFC Bd

18.4 mm/s 20 N 100, 500, 1000 N/m Trial and error

10

Force error N

Km = 1000 N/m

5

0 0

0.2

0.4

0.6

0.8

1.0

1.2

Time s

Figure 1.18: A desirable force response sEf z (k) for a teaching signal obtained through simulation.

∆sef z = sef z (k)− sef z (k−1) and sz(k−1), ˙ respectively. Similarly, other teaching signals with the condition of Km =500 and 100 N/m respectively were obtained through simulations. As an example, we designed a neural network model with three inputs and one output in z-direction of sensor coordinate system. The three inputs are the force error sef z (k), its ˙ − 1) increment ∆sef z (k) and the velocity of the arm tip sz(k in z-direction of sensor coordinate system as illustrated in Fig. 1.12. Moreover, the output of the NN is the velocity sz˙ (k). In order to learn the ideal contact motion, a fournn layered recurrent neural network composed of an input layer, 28

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Velocity-based discrete-time control system 5 Km = 1000 N/m

Velocity cm/s

4

3

2

1

0 0

0.2

0.4

0.6

0.8

1.0

1.2

Time s

Figure 1.19: Velocity of arm tip sz(k), ˙ which is the teaching signal of output of neural network.

two hidden layers and an output layer is used as shown in Fig. 1.20. The two hidden layers have twenty units respectively. The input to the hidden layers or the output layer is a weighted sum of the previous layer. The sum is squashed into ±0.5 by the following nonlinear activation function: f (X) =

1 − 0.5 1 + exp(−X)

(1.31)

The input/output relation of each unit is given by Xi,l =

n ∑

i,l wj,l−1 oj,l−1

(1.32)

j=1 i,l where Xi,l is the state of ith unit in lth layer. wj,l−1 is the interconnection weight between the ith unit in lth layer and the jth unit in (l − 1)th layer. oj,l−1 is the output of the jth unit in (l−1)th layer. n is the number of units in (l−1)th layer. The neural network was trained by the back propagation algorithm to learn the mapping between force and velocity responses without overshoot and oscillation. The

29

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Controller design for industrial robots and machine tools 3rd layer

2nd layer Input s

Input layer

e fz (k ) Output layer

∆ s e fz (k ) s

Output s

z&nn (k )

z& nn (k − 1)

Figure 1.20: Neural network for dynamics learning of contact motion.

learning was iterated until error function E became small sufficiently. Fig. 1.21 shows the learning history, in which the error function E is calculated by E=

N s ∑ | z(k) ˙ − sz˙nn (k)|

k=1

N

(1.33)

where N is the number of the training patter, i.e., total discrete time in the simulation. After the learning process, the NN could give an output as shown in Fig. 1.22, similar to the teaching signal.

1.5.2 Simulation of neural network force controller Fig. 1.24 shows the block diagram of the force control system using the learned neural network, in which the output from the neural network is feedforwardly added to the output of the IMFFC. A force control result in case of Km =1000 N/m is shown in Fig. 1.23. It is observed that the 30

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Velocity-based discrete-time control system

Error function E

0.04 0.03

0.02

0.01

0 0

100 Trial number

200

Figure 1.21: Learning history of error function E.

5 Km = 1000 N/m

Velocity cm/s

4

3

2

1

0 0

0.2

0.4

0.6

0.8

1.0

1.2

Time s

Figure 1.22: Output sz˙nn (k) generated from the learned neural network.

31

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Controller design for industrial robots and machine tools

Force error N

10

5

0 0

0.5

1.0

1.5

Time s

Figure 1.23: An example of force control result by feedforwardly using the learned NN.

response is improved and the raising time is shortened by using the learned neural network. In this case, IMFFC+NN, NN only and IMFFC only generate manipulated variables as shown in Fig. 1.25, respectively. The neural network feedforwardly generates desired manipulated values. However, if the environment had stiffer dynamics than the learned environment, then the contact characteristics tended to become worse. In such a case, an adaptability to unlearned environments should be considered. As an example, the feedback error learning of the neural network will be effective to carry out an on-line learning [12, 13].

1.6 Conclusion In this chapter, a simulation technique of velocity-based discrete-time control system for open-architecture industrial robots has been presented by giving and combining examples of intelligent controls such as genetic algorithms, fuzzy control and neural network. In order to develop a novel control system for an open-architecture industrial robot, it 32

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Velocity-based discrete-time control system F (k ) : Force sensor measurement e (k ) + _

1 z

∆e (k )

1 ∆t

Fd +

IMFFC

x& f (k )

+

+ _

1 z

x (k ) : Current position

x& nn (k )

_

x& (k ) 1 ∆t

Neural Network Force Controller

x r (k )

+

+ + _

1 z

x& r (k )

1 ∆t

+ _

1 z

IMFFC : Impedance Model Following Force Controller

1 ∆t

&x&r (k )

Resolved τ Acceleration PUMA560 Controller

Figure 1.24: Block diagram of the force control system using a neural network.

is required from the points of view of safety, cost and ease of use to preliminarily examine and evaluate the characteristics and performance. In such a case, the proposed simulation technique will be useful. It is important and necessary to realize a simple and accurate simulation environment for industrial robots with an open-architecture controller. When a computer is used to control an industrial robot, the control law is generally represented by a discrete-time control system. For this reason, we have considered how to simulate and evaluate the discrete-time control system which will be implemented into an open-architecture industrial robot. In order to carry out a simulation with a robotic dynamic model, we have shown the scheme in detail which transforms the velocity-based manipulated values into joint driving torques. The effectiveness and promise have been also demonstrated by simulations using a dynamic model of the PUMA560 manipulator. Preliminary evaluation of various new control approaches will be realized easily and safely for industrial robots with an open-architecture controller due to the proposed simulation technique.

33

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Controller design for industrial robots and machine tools

Velocity cm/s

4.5 Output of IMFCC+NN 3.0

1.5

Velocity cm/s

0 Output of NN

3.0 2.0 1.0 0

Velocity cm/s

0.6 0.4

Output of IMFCC

0.2 0 0

0.5

1.0

1.5

Time s

Figure 1.25: The upper, middle and lower figures show the outputs from IMFFC+NN, NN only and IMFFC only, respectively.

34

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and application. IEE Proceedings Control Theory and Applications , 142(3): 161–176, 1995. [16] D.A. Linkens and H.O. Nyongesa, Genetic algorithms for fuzzy control part 2: Online System Development and Application. IEE Proceedings Control Theory and Applications, 142(3): 177–185, 1995. [17] G. Ferretti, G. Magnani, and A. Zavala Rio, Impact modeling and control for industrial manipulators. IEEE Control Systems Magazine, 18(4): 65–71, 1998. [18] T. Sasaki and S. Tachi, Contact stability analysis on some impedance control methods. Journal of the Robotics Society of Japan , 12(3): 489–496, 1994 (in Japanese). [19] H.C. An and J.M. Hollerbach, Dynamic stability issues in force control of manipulators. In IEEE International Conference on Robotics and Automation, pages 890–896, 1987. [20] H.C. An, C.G. Atkeson, and J.M. Hollerbach, Modelbased control of a robot manipulator. The MIT Press classics series, The MIT Press, Massachusetts,1988. [21] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions Systems, Man & Cybernetics, 15(1): 116–132, 1985. [22] F. Nagata, K. Watanabe, K. Sato, and K. Izumi, An experiment on profiling task with impedance controlled manipulator using cutter location data. In IEEE International Conference on Systems, Man, and Cybernetics, pages 848–853, 1999. [23] F. Nagata, K. Watanabe, and K. Izumi, Furniture polishing robot using a trajectory generator based on cutter location data. In IEEE International Conference on Robotics and Automation, pages 319–324, 2001. 217

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Controller design for industrial robots and machine tools

[24] M.H. Raibert and J.J. Craig, Hybrid position/force control of manipulators. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 102: 126–133, 1981. [25] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, CAD/CAM-based position/force controller for a mold polishing robot. Mechatronics, 17(4/5): 207-216, 2007. [26] F. Nagata, K. Watanabe, S. Hashino, H. Tanaka, T. Matsuyama, and K. Hara, Polishing robot using joystick controlled teaching. Journal of Robotics and Mechatronics, 13(5): 517–525, 2001. [27] F. Nagata, K. Watanabe, and K. Kiguchi, Joystick teaching system for industrial robots using fuzzy compliance control. Industrial Robotics: Theory, Modelling and Control, INTECH, pages 799–812, 2006. [28] Y. Maeda, N. Ishido, H. Kikuchi, and T. Arai, Teaching of grasp/graspless manipulation for industrial robots by human demonstration. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1523–1528, 2002. [29] D. Kushida, M. Nakamura, S. Goto, and N. Kyura, Human direct teaching of industrial articulated robot arms based on force-free control. Artificial Life and Robotics, 5(1): 26–32, 2001. [30] S. Sugita, T. Itaya, and Y. Takeuchi, Development of robot teaching support devices to automate deburring and finishing works in casting. The International Journal of Advanced Manufacturing Technology, 23(3/4): 183–189, 2003. [31] C. K. Ahn and M. C. Lee, An off-line automatic teaching by vision information for robotic assembly task. 218

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[39] T.M. Stephien, L.M. Sweet, M.C. Good, and M. Tomizuka, Control of tool/workpiece contact force with application to robotic deburring. IEEE Journal of Robotics and Automation, 3(1): 7–18, 1987. [40] H. Kazerooni, Robotic deburring of two-dimensional parts with unknown geometry. Journal of Manufacturing Systems, 7(4): 329–338, 1988. [41] M.G. Her and H. Kazerooni, Automated robotic deburring of parts using compliance control. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 60–66, 1991. [42] G.M. Bone, M.A. Elbestawi, R. Lingarkar, and L. Liu, Force control of robotic deburring. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 395–400, 1991. [43] D.M. Gorinevsky, A.M. Formalsky, and A.Y. Schneider, Force Control of Robotics Systems, CRC Press, New York, 1997. [44] K. Takahashi, S. Aoyagi, and M. Takano, Study on a fast profiling task of a robot with force control using feedforward of predicted contact position data. In 4th Japan-France Congress & 2nd Asia-Europe Congress on Mechatronics, pages 398–401, 1998. [45] Y. Takeuchi and T. Watanabe, Study on post-processor for 5-axis control machining. Journal of the Japan Society for Precision Engineering , 58(9): 1586–92, 1992 (in Japanese). [46] Y. Takeuchi K. Wada, T. Hisaki, and M. Yokoyama, Study on post-processor for 5-axis control machining centers —In case of spindle-tilting type and table/spindle-tilting type. Journal of the Japan Society for Precision Engineering, 60(1): 75–79, 1994 (in Japanese). 220

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[47] X.J. Xu, C. Bradley, Y.F. Zhang, H.T. Loh, and Y.S. Wong, Tool-path generation for five-axis machining of free-form surfaces based on accessibility analysis. International Journal of Production Research, 40(14): 3253–3274, 2002. [48] S.L. Chen, T.H. Chang, I. Inasaki, and Y.C. Liu, Postprocessor development of a hybrid TRR-XY parallel kinematic machine tool. The International Journal of Advanced Manufacturing Technology, 20(4): 259–69, 2002. [49] W.T. Lei and Y.Y. Hsu, Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part I: design and modeling. Machine Tool & Manufacture, 42(10): 1153–1162, 2002. [50] W.T. Lei, M.P. Sung, W.L. Liu, and Y.C. Chuang, Double ballbar test for the rotary axes of five-axis CNC machine tools. Machine Tool & Manufacture, 47(2): 273–285, 2006. [51] L.X. Cao, H. Gong, and J. Liu, The offset approach of machining free form surface. Part 1: Cylindrical cutter in five-axis NC machine tools. Journal of Materials Processing Technology, 174(1/3): 298–304, 2006. [52] L.X. Cao , H. Gong, and J. Liu, The offset approach of machining free form surface. Part 2: Toroidal cutter in 5-axis NC machine tools. Journal of Materials Processing Technology, 184(1/3): 6–11, 2007. [53] S.D.Timar, R.T. Farouki, T.S. Smith, and C.L. Boyadjieff. Algorithms for time optimal control of CNC machines along curved tool paths. Robotics and ComputerIntegrated Manufacturing, 21(1): 37–53, 2005. [54] E.Y. Heo, D.W. Kim, B.H. Kim, and F.F. Chen, Estimation of NC machining time using NC block distribution for sculptured surface machining. Robotics and 221

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Computer-Integrated Manufacturing, 22(5-6): 437–46, 2006. [55] Y.S. Tarng, H.Y. Chuang, and W.T. Hsu, Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture, 39(10): 1673–1692, 1999. [56] U. Zuperl, F. Cus, and M. Milfelner, Fuzzy control strategy for an adaptive force control in end-milling. Journal of Materials Processing Technology, 164/165: 1472–1478, 2005. [57] R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.F. Yuan, and S. Jee, Variable-feedrate CNC interpolators for constant material removal rates along Pythagoreanhodograph curves. Computer-Aided Design, 30(8): 631–640, 1998. [58] R.T. Farouki, J. Manjunathaiah, and G.F. Yuan. G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on openarchitecture CNC machines. Machine Tools & Manufacture, 39(1): 123–142, 1999. [59] A. Frank and A. Schmid, Grinding of non-circular contours on CNC cylindrical grinding machines. Robotics and Computer-Integrated Manufacturing, 4(1/2): 211–218, 1988. [60] J.A. Couey, E.R. Marsh, B.R. Knapp, and R.R. Vallance, Monitoring force in precision cylindrical grinding. Precision Engineering, 29(3): 307–314, 2005. [61] T. Tawakoli, A. Rasifard, and M. Rabiey, Highefficiency internal cylindrical grinding with a new kinematic. Machine Tools & Manufacture, 47(5): 729–733, 2007. 222

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[62] F. Nagata, Y. Kusumoto, K. Hasebe, K. Saito, M. Fukumoto, and K. Watanabe, Post-processor using a fuzzy feed rate generator for multi-axis NC machine tools with a rotary unit. In International Conference on Control, Automation and Systems, pages 438–443, 2005. [63] F. Nagata and K. Watanabe, Development of a postprocessor module of 5-axis control NC machine tool with tilting-head for woody furniture. Journal of the Japan Society for Precision Engineering, 62(8): 1203–1207, 1996 (in Japanese). [64] K. Fujino, Y. Sawada, Y. Fujii, and S. Okumura, Machining of curved surface of wood by ball end mill – Effect of rake angle and feed speed on machined surface. In 16th International Wood Machining Seminar, Part 2, pages 532–538, 2003. [65] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliance control capability. In 13th International Symposium on Artificial Life and Robotics, pages 779–782, 2008, [66] J. Duffy, The Fallacy of modern hybrid control theory that is based on orthogonal complements of twist and wrench spaces. Journal of Robotic Systems, 7(2): 139–144, 1990. [67] M.C. Lee, S.J. Go, M.H. Lee, C.S. Jun, D.S. Kim, K.D. Cha, and J.H. Ahn, A robust trajectory tracking control of a polishing robot system based on CAM data. Robotics and Computer-Integrated Manufacturing, 17(1/2): 177–183, 2001, [68] F. Nagata, T. Mizobuchi, S. Tani, T. Hase, Z. Haga, K. Watanabe, M.K. Habib, and K. Kiguchi, Desktop orthogonal-type robot with abilities of compliant 223

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motion and stick-slip motion for lapping of LED lens molds. In IEEE International Conference on Robotics & Automation , pages 2095–2100, 2010, [69] O. Bilkay and O. Anlagan, Computer simulation of stick-slip motion in machine tool slideways. Tribology International, 37(4): 347–351, 2004. [70] X. Mei, M. Tsutsumi, T. Tao, and N. Sun, Study on the compensation of error by stick-slip for high-precision table. International Journal of Machine tools & Manufacture, 44(5): 503–510, 2004. [71] M.J. Tsai, J.L. Chang, and J.F. Haung, Development of an automatic mold polishing system. In IEEE International Conference on Robotics & Automation, pages 3517–3522, 2003. [72] M.J. Tsai, J.J. Fang, and J.L. Chang, Robotic path planning for an automatic mold polishing system. International Journal of Robotics & Automation, 19(2): 81–89, 2004, [73] H. Hocheng, Y.H. Sun, S.C. Lin, and P.S. Kao, A material removal analysis of electrochemical machining using flat-end cathode. Journal of Materials Processing Technology, 140(1/3): 264–268, 2003. [74] Y. Uehara, H. Ohmori, W. Lin, Y. Ueno, T. Naruse, N. Mitsuishi, S. Ishikawa, and T. Miura, Development of spherical lens ELID grinding system by desk-top 4-axes Machine Tool. In International Conference on Leading Edge Manufacturing in 21st Century, pages 247–252, 2005, [75] H. Ohmori and Y. Uehara, Development of a desktop machine tool for mirror surface grinding. International Journal of Automation Technology, 4(2): 88–96, 2010, 224

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2 Preliminary simulation of intelligent force control DOI: 10.1533/9780857094636.35 Abstract: In this chapter, simulations of an impedance model following force control using generalized learningbased fuzzy environment model (GFEM) are presented for articulated industrial robots with an open-architecture controller. The desired damping, which is one of the impedance parameters, has a substantial effect on force control performance, so that an important point for successfully using the force controller is how to suitably tune the desired damping according to each environment and task. We introduce an approach that produces the desired time-varying damping, giving the critical damping condition in contact with an object. However, the approach requires that the physical parameters of the object, such as viscosity and stiffness, are known beforehand. In order to deal with unknown environments, the proposed GFEM not only estimates the stiffness of unknown environments but also systematically yields the desired time-varying damping for stable force control. The effectiveness and promise of the proposed method are demonstrated through hybrid position/force control simulations using the dynamic model of a PUMA560 manipulator. Key words: impedance model following force control, resolved acceleration control, critical damping condition, fuzzy environment model, genetic algorithms 35

Controller design for industrial robots and machine tools

2.1 Introduction Simulations of impedance models following force control using generalized learning-based fuzzy environment model are presented for articulated-type industrial robots with an open-architecture controller [81]. The desired damping, which is one of the impedance parameters, mainly has an effect on force control performance. An important question for successfully using conventional impedance control methodologies is: how to suitably tune the desired damping according to each environment and task? However, there are no systematic tuning methods, so that the desired damping is generally tuned by trial and error. To overcome this problem we have already introduced an approach that produces the desired time-varying damping, giving the critically damped condition in contact with an object. However, considering the critically damped condition requires that the physical parameters of the object, such as viscosity and stiffness, are known beforehand. In this chapter, a generalized fuzzy environment model (GFEM) is introduced to deal with unknown environments. The GFEM is designed by integrating several FEMs. Each FEM is respectively optimized by using genetic algorithms under several fixed environments. The GFEM not only estimates the stiffness of unknown environment but also systematically yields the desired time-varying damping for stable force control. The time-varying desired damping allows the impedance model following force controller to have an ability to suppress overshoots and oscillations in force control. The effectiveness and promise are demonstrated through hybrid position/force control simulations using a dynamic model of the PUMA560 manipulator. In order to perform the generalization under unlearned environments, the GFEM is next proposed for the impedance model following force control. The GFEM is designed by integrating several FEMs which are optimized under fixed environments in advance. Since fuzzy rules con36

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Simulation of intelligent force control

Impedance model following force

+

Resolved

controller in the

acceleration

Cartesian space

-

Robot

controller

+ -

Figure 2.1: Transformation from position command to joint driving torque structing each FEM must be suitably designed according to each environment and task, a systematic tuning method of the FEM is further presented using genetic algorithms (GA) [14–16]. The GFEM estimates only the stiffness of the object by using a simple fuzzy reasoning method and generates the desired time-varying damping to keep a stable response. Using the desired damping generated by the GFEM, the impedance model following force controller can improve the contact force stability, suppressing overshoots and oscillations. Finally, we apply the control strategy to a task in which an industrial robot profiles the surface of an isotropic material. The promising results are demonstrated through simple hybrid position/force control simulations under several unknown and unlearned environments.

2.2 Impedance model following force control 2.2.1 Impedance model in Cartesian space A desired impedance equation for a robot manipulator in Cartesian space is designed by M x (θ)¨ x + B d (x˙ − x˙ d ) + K d (x − xd ) = SF + (I − S)K f (F − F d ) 37

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(2.1)

Controller design for industrial robots and machine tools

¨ ∈ ℜ6 are the position, velocwhere x ∈ ℜ6 , x˙ ∈ ℜ6 and x ity and acceleration vectors, respectively. M x (θ) ∈ ℜ6×6 is the inertia matrix, θ ∈ ℜ6 is the vector of generalized joint coordinates describing the pose of the manipulator. F ∈ ℜ6 is the force-moment vector acting on the endeffector defined by F T = [f T nT ], where f ∈ ℜ3 and n ∈ ℜ3 are the force and moment vectors, respectively. K f = diag(Kf 1 , . . . , Kf 6 ) is the force feedback gain matrix. xd , x˙ d and F Td = [f Td nTd ] are the desired position, velocity, force and moment vectors; B d = diag(Bd1 , . . . , Bd6 ) and K d = diag(Kd1 , . . . , Kd6 ) are the coefficient matrices of desired damping and desired stiffness, respectively. S = diag(S1 , . . . , S6 ) and I are the switch matrix and identity matrix. It is assumed that K f , B d , and K d are all positive-definite diagonal matrices. Note that if S = I, then Eq. (2.1) becomes a compliance control system in all directions; on the other hand if S is the zero matrix, it becomes a force control system in all directions. It is assumed that the acceleration of Eq. (2.1) is very small, so the inertia term can be ignored. Defining X := x − xd , then Eq. (2.1) can be rewritten as ˙ = AX + Bu X where

A: = −B −1 d K d, B : = B −1 u d , : = SF + (I − S)K f (F − F d )

(2.2)

(2.3)

In general, Eq. (2.2) is solved as X = eAt X(0) +

∫

t

eA(t−τ ) Bu(τ )dτ

0

(2.4)

In the following, we consider the form in discrete-time system using a sampling width ∆t. It is assumed that u 38

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Simulation of intelligent force control

and A are constant at ∆t(k − 1) ≤ t < ∆tk. Defining X(k) = X(t)|t=∆tk (k = 0, 1, . . . ), Eq. (2.4) is transformed into the discrete-time domain description: (

X(k) = eA∆tk X(0) +

∫

∆tk

e−Aτ Bu(τ )dτ

0

= eA∆t X(k − 1) + eA∆tk

∫

∆tk

)

e−Aτ dτ Bu(k)

∆t(k−1)

= eA∆t X(k − 1) + eA∆t − I A−1 Bu(k) (2.5) (

)

Remembering X(k) = x(k) − xd (k) leads to −1 x(k) = xd (k) + e−B d K d ∆t {x(k − 1) − xd (k − 1)}

(

)

−1 − e−B d K d ∆t − I K −1 d {SF

(2.6)

+ (I − S)K f (F − F d )}

where x(k) consists of position vector [x(k) y(k) z(k)]T and orientation vector [ϕ(k) ξ(k) ψ(k)]T expressed by Z-Y-Z Euler angles. In order to realize the impedance given by Eq. (2.1), x(k) is given to the reference of robotic servo system every sampling period.

2.2.2 How to generate the reference for servo controller To simulate the impedance model following force control method using an industrial robot model, the manipulated variable x(k) calculated from Eq. (2.6) has to be transformed into joint driving torques. Accordingly, we propose a transformation technique where x(k) is given to the reference value of the Cartesian-based servo controller. The block diagram of this transformation is illustrated in Fig. 2.1. The joint driving torques transformed from x(k) control each joint independently. 39

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Controller design for industrial robots and machine tools

First of all, a velocity and acceleration are generated by using a discrete time k and sampling width ∆t. ˙ x(k) = {x(k) − x(k − 1)}/∆t

(2.7)

¨ (k) = {x(k) ˙ ˙ − 1)}/∆t x − x(k

(2.8)

For example, in the case that the resolved acceleration control law is used in the servo system of an industrial robot, ˙ ¨ (k) generated from Eqs. (2.6), (2.7) and x(k), x(k) and x ¨r (2.8) are respectively given to the references xr , x˙ r and x of the servo system, so that the joint torques are generated from [ ¨ r + K v (x˙ r − x) ˙ τ = M (θ)J −1 (θ) x (2.9) ] ˙ + G(θ) + K p (xr − x) + H(θ, θ)

where, M (θ) ∈ ℜ6×6 is the inertia term in joint space; J −1 (θ) is the inverse matrix of Jacobian with the rela˙ K v = diag(Kv1 , . . . , Kv6 ) and K p = tion x˙ = J (θ)θ. diag(Kp1 , . . . , Kp6 ) are the gains of velocity and position, ˙ and G(θ) are the Coriolis and cenrespectively. H(θ, θ) trifugal forces term and gravity term in joint space, respec˙ x and x˙ in Eq. (2.9) are actual tively. Note that θ, θ, values, i.e., controlled variables. The non-linear compensa˙ and G(θ) are effective to achieve a stable tion terms H(θ, θ) control system. Thus, the proposed method allows us not only to implement the impedance model following force controller in the computer simulations, but also to easily apply it to industrial robots with an open-architecture control system.

2.2.3 Design of desired damping considering the dynamics of environment In the previous section, we have introduced the impedance model following force control for articulated industrial robots with an open-architecture controller. The problem now is how to tune the desired damping that mainly affects 40

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Simulation of intelligent force control

the force control performance. In this section we propose a tuning method of desired damping using known physical parameters. Fig. 2.2 shows an example where an industrial robot is making contact with an object inclined at q degrees from the floor. It is assumed that a stiff end-effector is fixed to the tip of the robot arm as shown in Fig. 2.3. The contact force from the normal direction of the slope is controlled to converge to a reference value Sf d . Here, the left superscript S means the value in sensor coordinate system. The end-effector is controlled to exert a small force on the object along the normal direction. The rotation matrix in the sensor coordinate system based on the base coordinate system is described as 



cos(q) 0 − sin(q)   B 0 1 0 RS =   sin(q) 0 cos(q)

(2.10)

Therefore, the desired force vector in the base coordinate system is obtained by f d = BRS Sf d

(2.11)

For example, Sf Td = [0 0 Sfdz ] is transformed into f Td = [−Sfdz sin(q) 0 Sfdz cos(q)]. Here, it is assumed that the contact force f = [fx fy fz ]T acting on the end-effector is represented by f = −B m x˙ − K m (x − xm )

(2.12)

where B m = diag(Bm1 , Bm2 , Bm3 ) and K m = diag(Km1 , Km2 , Km3 ) are the object’s viscosity and stiffness coefficients to be positive-definite diagonal matrices. It is also assumed that the tip of the robot arm contacts the object at the position xTm = [xm ym zm ]. The transition from unconstrained motion to constrained motion is simply considered by Eq. (2.12), since it has been reported that analyzing the contact force at impact with proper models is difficult and complex [17]. 41

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Controller design for industrial robots and machine tools

Figure 2.2: Example of force control under known environments ˜ d considIn force control mode, the desired damping B ering the critical damping condition of Eq. (2.1) is given by ˜di = 2 B

√{

J −T (θ)M (θ)J −1 (θ)

− Kf i Bmi

}

i

{Kdi + Kf i Kmi } (2.13)

Here, i(i = 1, 2, 3) denotes the i-th diagonal element of each matrix. When the impedance model following force con˜di is given as a reference of desired damptroller is applied, B ing so that promising force control suppressing overshoots and oscillations can be realized. It should be noted that when this tuning method is used, physical parameters of environments, i.e. Bmi and Kmi , are indispensable to calculate ˜di . B

2.3 Influence of environmental viscosity In this section, it is evaluated that how much influence the environmental viscosity gives to force control performance 42

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Simulation of intelligent force control

End-effector

Object

q

Figure 2.3: Stiff end-effector fixed to the tip of the robot arm

when the impedance model following force control is applied. The contact force given by Eq. (2.12) is considered under sixteen kinds of different environments where the combination of the stiffness and viscosity are shown in Tables 2.1 and 2.2, respectively. As can be seen from these tables, it is assumed that the physical characteristics in x- and z-directions are equivalent, i.e., Km1 = Km3 and Bm1 = Bm3 . Force control simulations illustrated in Fig. 2.4 are conducted under above sixteen conditions. The slope angle q is set to 30◦ . The orientation of the end-effector is controlled to be fixed with [0 150◦ 0] so that the robot arm can exert the force on the surface of the slope along the normal direction. When f is obtained by Eq. (2.12), the four kinds of environmental viscosity shown in Table 2 are used. On the other hand, when the desired damping given by Eq. (2.13) is calculated, B m is fixed to diag(15, 0, 15). By means of these conditions, force control schemes given by Eq. (2.6) with and without the information of environmental viscosity are compared. Simulations are carried out using the kinetic and dynamic parameters of the PUMA560 manipulator [3]. The dynamic 43

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Controller design for industrial robots and machine tools

1.0

1.0 z-direction

Reference Response [ Response [ Response [ Response [

0.4 0.2 0

] ] ] ]

-0.2 -0.4 -0.6

1 Time [ s ] (a)

0.2 0

] ] ] ]

-0.2 x-direction 0

1 Time [ s ] (c)

2

1.0 z-direction

0.8

0.8

0.6 0.4

Reference Response [ Response [ Response [ Response [

0.2 0

Contact force [N]

Contact force [N]

Reference Response [ Response [ Response [ Response [

0.4

-0.6

2

1.0

] ] ] ]

-0.2 -0.4 -0.6

0.6

-0.4

x-direction 0

z-direction

0.8

0.6

Contact force [N]

Contact force [N]

0.8

1 Time [ s ] (b)

Reference Response [ Response [ Response [ Response [

0.4 0.2 0

-0.6

2

] ] ] ]

-0.2 x-direction

-0.4

x-direction 0

z-direction

0.6

0

1 Time [ s ] (d)

2

Figure 2.4: Force control results: (a)Km1 = Km3 = 5000 N/m, (b)Km1 = Km3 = 10000 N/m, (c)Km1 = Km3 = 15000 N/m, (d)Km1 = Km3 = 20000 N/m

44

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Simulation of intelligent force control

Table 2.1: Stiffness of environment [N/m]

Table 2.2: Viscosity of environment [Ns/m]

(1)

Km1 = Km3 = 5000

(a)

Bm1 = Bm3 = 0

(2)

Km1 = Km3 = 10000

(b)

Bm1 = Bm3 = 1

(3)

Km1 = Km3 = 15000

(c)

Bm1 = Bm3 = 15

(4)

Km1 = Km3 = 20000

(d)

Bm1 = Bm3 = 20

equation is written by ¨ + H(θ, θ) ˙ + G(θ) = τ + J T (θ)F M (θ)θ

(2.14)

The simulation time and sampling width are set to 2 sec. and 0.01 sec., respectively. In this case, the initial contact position xm was given to the desired position xd in Eq. (2.6). The desired stiffness and force feedback gain are set to Kd1 = Kd3 = 400 N/m and Kf 1 = Kf 3 = 10, respectively. Fig. 2.4 show the sixteen kinds of results. For example, Fig. 2.4(a) shows the compared results of force control responses when the combination of Bm1 , Bm3 to Km1 , Km3 = 5000 N/m are changed with values shown in Table 2.1. It is observed from the result that the environmental viscosity does not affect the force control performance because there is little superiority or inferiority of each response shown in Fig. 2.4(a). The similar tendency are observed also from Figs. 2.4(b)-(d). In other words, it is confirmed from these simulations that the instability of the manipulator’s force control mainly depends on the stiffness of the environment. Furthermore, it is also shown that the response becomes more unstable when the end-effector comes in contact with stiffer environments. An et al. [19] and Sasaki et al. [18] have already reported two kinds of detailed stability analysis of this behavior using a conventional force control and impedance control, respectively: the stability problem in contact with an environment is general and 45

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not limited to force control methodologies used, because the manipulated variables in most force control methods have a term consisting of the product of the environmental stiffness and force feedback gain. Therefore, the force feedback system is forced to have a high gain feedback loop, if the robot deals with a stiff environment. When a robot comes in contact with its environment in actual tasks, there are several factors that decrease the total stiffness of the system. They are called clearance, strain and deflection, all of which exist not only in the robot itself but also in the end-effector, force sensor and so on. That is the reason why such a total stiffness should be carefully addressed in designing a robotic force control system. Hereafter, it is assumed that the environmental stiffness includes that of the robot itself. By considering these preliminary simulation results, estimating the stiffness of environment is expected to be sufficient to realize a stable force control system suppressing overshoots and oscillations. In the next section, the fuzzy environment model (FEM) that estimates the stiffness of unknown environment is proposed for the impedance model following force controller.

2.4 Fuzzy environment model 2.4.1 Design of fuzzy environment model The fuzzy environment model (FEM), based on fuzzy reasoning theory, estimates the stiffness of environment. We design the FEM by using the simple fuzzy reasoning theory, which is regarded as a kind of model, developed by Takagi et al. [21]. In this section, we describe how to construct the FEM giving an example of force control shown in Fig. 2.2. According to the former definition, the position vector and the force vector at the tip of the robot arm are given with xT = [x(t) y(t) z(t)] and f T = [fx (t) 0 fz (t)], respectively. The motivation behind the proposed concept is to simplify the construction of the FEM, so each reasoning in the x46

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Simulation of intelligent force control

or z-direction is conducted independently. Fuzzy inputs for reasoning are defined by (2.15)

x∗ (t) = fx (t)/{xm − x(t)}

(2.16)

∗

z (t) = fz (t)/{zm − z(t)}

If the information on only x-direction is used, the FEMs are described by Rule 1: IF x∗ (t) is A˜1 , THEN B 1m x˙ + K 1m (x − xm ) = −f Rule 2: IF x∗ (t) is A˜2 , THEN B 2m x˙ + K 2m (x − xm ) = −f .. . Rule L:

˙ + KL IF x∗ (t) is A˜L , THEN B L m (x − mx

xm ) = −f where A˜i (i = 1, . . . , L) is the antecedent fuzzy set and L is the number of labels. If the x-directional element Km1 of stiffness coefficient matrix K m is estimated in parallel with above fuzzy environment models, the reasoning rules are represented by Rule 1: Km1 = Km11

Rule 2:

IF

x∗ (t)

is

A˜1 ,

THEN

IF

x∗ (t)

is

A˜2 ,

THEN

A˜L ,

THEN

Km1 = Km12 Rule L:

.. . IF

x∗ (t)

is

Km1 = Km1L where Km1i (i = 1, . . . , L) denotes the consequent con47

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ˆ m1 in stant. Using these rules, the estimated stiffness K the x-direction is computed by the weighted mean method expressed as ˆ m1 = K

L ∑

(2.17)

pi {x∗ (t)}Km1i

i=1

where pi {x∗ (t)} denotes the normalized confidence given by µ ˜ {x∗ (t)} pi {x∗ (t)} = ∑L Ai ∗ ˜ {x (t)} j=1 µAj

(2.18)

∗ with the antecedent confidence µAj ˜ {x (t)} described by the following Gaussian membership function

[

∗ ∗ 2 2 µAj ˜ {x (t)} = exp log(0.5){x (t) − αj } βj

]

(2.19)

where, αj is the center of membership function and βj is the reciprocal value of standard deviation, and j(j = 1, . . . , L) denotes the number of fuzzy rules. The Gaussian type membership function is shaped by only the center of membership function and the reciprocal value of standard deviation. In optimizing the FEM using genetic algorithms (GA), the confidence is calculated after the genotype of each FEM is decoded to the phenotype. In this case, the Gaussian type membership function allows the system to easily calculate the confidence, compared with triangular type membership functions. Because of this advantage, we use the Gaussian type membership function. The weighted mean method is generally used in the simple fuzzy reasoning method. This method requires no centroidal calculations, so that high speed operation and analysis can be realized, compared to the min-max centroidal method or the product-sum centroidal method. In the same manner, the estimated stiffness ˆ m3 in the z-direction is computed by giving Eq. (2.16) to K the input of fuzzy reasoning. Fig. 2.5 shows the block diagram of the impedance model following force controller with the FEM. The FEM estimates the environmental stiffness 48

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Figure 2.5: Block diagram of the impedance model following force controller with the FEM sensing the force measurements and provides the desired ˜ d based on Eq. (2.13) to maintain the system damping B in critically damped condition. The impedance model following force controller generates the manipulated variable ˜ d. x(k) for the servo system with B As can be seen from the above arguments, the key point for the design of the FEM is to appropriately adjust α, β in the antecedent part and consequent constant given by γ. However, the effective design method for such parameters has not been developed. This means that if we want to use the FEM then the complicated parameter tuning through many simulations or experiments by trial and error is unavoidable. In the remainder of this paper, we propose a systematic tuning method for the FEM using a GA approach.

2.4.2 Offline learning of FEMs using genetic algorithms Fortunately, if the model of a manipulator used is known, then the robust FEM can be derived in advance using the GA. Before optimizing the FEM by using GA, we design the base of a FEM as follows: the type of membership functions is Gaussian; the fuzzy rule number is five; consequent parts have constant values; and so on. The GA is used to auto49

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Controller design for industrial robots and machine tools Rule 1

Rule 2

Rule 5

β1 α1 γ1 β2 α2 γ2

β5 α5 γ5

Figure 2.6: Fuzzy rules encoded into a chromosome Table 2.3: Parameters for GA operation Population size

60

Number of elites

6

Selection

Tounament selection

Crossover

Uniform crossover

Mutation

Random mutation(rate=1/240)

Maximum generation

100

matically adjust the parameters associated with the fuzzy rules. In other words, the GA optimizes the parameters of fuzzy rules such as the center of membership function αj , reciprocal value of standard deviation βj and constant value of consequent part γj . αj , βj and γj are the phenotypes of FEM, and each phenotype is encoded into the genotype of 16 bits binary code. An individual, i.e. a FEM, is composed of 5 fuzzy rules (L = 5) as shown in Fig. 2.6. In our proposed FEM, a parameter space model deals with the viscosity and the stiffness independently. It is also assumed that the parameter space can be partitioned abstractly and formally, in which the combinations of the viscosity and the stiffness are not considered. In this case, the partition number of the parameter space is equal to the number of fuzzy rules. We empirically designed the FEM (i.e., an individual) with five fuzzy rules. For example, we can design the fuzzy labels as Further Soft, Rather Soft, 50

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Table 2.4: Stiffness of learned environments [N/m] (1)

Km1 = Km3 = 350

(2)

Km1 = Km3 = 3500

(3)

Km1 = Km3 = 7000

(4)

Km1 = Km3 = 10500

(5)

Km1 = Km3 = 14000

(6)

Km1 = Km3 = 17500

(7)

Km1 = Km3 = 21000

Approximately Same, Rather Stiff, and Further Stiff. Of course, it is possible to use more fuzzy rules, e.g. 7 fuzzy rules for finer reasoning. Each individual is evaluated by applying the proposed method shown in Fig. 2.5 to the force control problem given in Fig. 2.2. The evaluation function Ev of each individual is the sum of squared error between the force f acting on the tip of the robot arm and the reference value f d at every sampling time ∆tk, which is calculated by Ev =

T /∆t [

∑

{fx (∆tk) − fdx }2 + {fz (∆tk) − fdz }2

k=1

]

(2.20)

where T is the total simulation time. This is a minimization problem and therefore if the individual has the minimum Ev then it can survive as an elite. When an overshoot, oscillation or a non-contact state appears, a large dummy fitness (penalty) is given to the individual to be excluded, because such an individual is undesirable in a stable force control system. The parameters used in the GA operation are tabulated in Table 2.3. To learn the FEM, the seven kinds of environments shown in Table 2.4 are selected. Because of the aforementioned reason, the viscosity of the environments was fixed to 15 Ns/m. In addition, it was assumed that the 51

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Controller design for industrial robots and machine tools 10 5

8

[N/m]

7 6

Estimated stiffness

5 4 3 2 1 0 0

5000 10000 15000 Stiffness of environment

20000 25000 [N/m]

Figure 2.7: Estimated stiffness for each environment stiffness and the viscosity of the environments have the same characteristics in x- and z-directions, respectively. Here, we examine the computational cost for learning. When a PC (CPU: Intel Celeron 1.73 GHz) is used on Windows XP Professional, it takes about 15 seconds to evaluate one individual, i.e., to integrate the dynamic model given by Eq. (2.14) for the simulation time of 2 seconds by using a Runge-Kutta algorithm. Hence, at least 15 seconds × 60 individuals × 100 generations × 7 environments = 175 hours are required to finish the whole learning.

2.4.3 Learning results Figure 2.7 shows the relationship between the true stiffness Km1 (or Km3 ) of an environment and the estimated ˆ m1 (or K ˆ m3 ) in a steady state which has been stiffness K obtained with best individuals. Figure 2.8 shows the relationship between the Km1 (or Km3 ) and the desired damping 52

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Simulation of intelligent force control 10 4

[Ns/ m]

2.5

2.0

Desired damping coefficient

z-direction 1.5 x-direction Intersection point 1.0

0.5

z-direction x-direction

0 0

5000 10000 15000 Stiffness of environment

20000 25000 [N/m]

Figure 2.8: Relationship between true stiffness of environment and desired damping coefficients

˜d1 (or B ˜d3 ) in the x- or z-direction given from Eq. (2.13). B ˜d1 , In Fig. 2.8, the solid lines show the desired damping (N:B ˜ ˆ ˆ •:Bd3 ) in using Km1 and Km3 . On the other hand, the dot˜d1 , ◦:B ˜d3 ) in using Km1 and ted lines represent the one (△:B Km3 in which it is assumed that Km1 and Km3 are known. It can be observed from the result that they intersect at near the stiffness 1000 N/m. These learned results suggest that the desired damping, considering the critical damping condition with Km1 (or Km3 ), could achieve stable force control without overshoots and oscillations if the Km1 (or Km3 ) is under 1000 N/m and its neighborhood. However, if the Km1 (or Km3 ) is larger than the range, then a larger desired damping is needed to suppress the overshoots and oscillations. This means that if the Km1 (or Km3 ) becomes larger than 1000 N/m and its neighborhood, then the environmental stiffness in Eq. (2.13) must be estimated to be 53

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Controller design for industrial robots and machine tools

18 16

Fitness

14 12 10

Average

8 6

Best

4 0

20

40 60 Generation

80

100

Figure 2.9: An example of evolutionary history in case of Km1 = Km3 = 17500 N/m much larger than the true one in order to realize a desirable response. Furthermore, it can also be observed that there is a proportional relation between the real stiffness and the desired damping coefficient. It is supposed that the slope would change depending on how to evaluate and select the individuals. As an example of the learning effectiveness on seven kinds of environments, the average and minimum values of fitness are shown in Fig. 2.9, which is the evolutionary history in the case of Km1 = Km3 = 17500 N/m. It is recognized that more excellent individuals have been selected through the alternation of generations with GA operations. Figure 2.10 and Table 2.5 respectively show the antecedent membership functions and consequent constants which mean the best elite individual (a best FEM) after 100 generations. Figure 2.11 shows the simulation results using the best individual in the case of Km1 = Km3 = 17500 N/m. Figure 2.11(a) shows the force control result using the desired damping which is calculated by substituting the estimated stiffness into Eq. (2.13). Certainly, the desirable 54

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Simulation of intelligent force control 1.0 Model 1 Model 2

Model 3,4 Model 5

Confidence

0.8 0.6 0.4 0.2 0

10000

14000 18000 Fuzzy inputs

22000

Figure 2.10: Learned antecedent membership functions (best individual) in the case of Km1 = Km3 = 17500 N/m

performance without overshoots and oscillations is observed. ˆ m1 , K ˆ m3 and B ˜d1 , B ˜d3 are varied as shown At this time, K in Figs. 2.11(b), (c), respectively. It should be noted, however, that there are nonoverlapping membership functions in Fig. 2.10. In this environment, since fuzzy inputs are generated around 17500 N/m, the non-overlapping part has no impact on the response. However, the robot must deal with all supposed cases (i.e., range) in real applications, so that some flexibility (referred to as generalization) is required. At this stage, seven FEMs exist as many as the learned environments. Of course, it is not guaranteed that the desired performance can be achieved except for the learned environments. The most important function required for the FEMs is that the desired damping can be generated for all environments with any stiffness within an assumed range. In order to address this function, we consider on how to construct the learned FEMs for the generalization, where the antecedent part has no non-overlapping membership function. 55

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1.0 Contact force [N]

z-direction 0.5

Reference Response

0

x-direction

-0.5 0

[N/ m] Estimated stiffness

1 Time [ s ] (b)

2

4 3 2 1 0

[Ns/m]

2

105

5

Desired damping coefficient

1 Time [ s ] (a)

0

104

2.0

z-direction x-direction

1.5

1.0

0.5

0

0

1 Time [ s ] (c)

2

Figure 2.11: Simulation results using the best individual in the case of Km1 = Km3 = 17500 N/m: (a) force control ˆ m1 , K ˆ m3 result, (b), (c) time history of estimated stiffness K ˜ ˜ and desired damping Bd1 , Bd3

56

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Table 2.5: Learned consequent constants (best individual) Model 1

Model 2

Model 3

Model 4

Model 5

225180

588010

247500

102110

383570

2.4.4 Generalization of FEMs Each FEM discussed in the previous section has five fuzzy rules. If those are simply combined, then the number of fuzzy rules becomes 35 and the antecedent membership functions overlaps each other on the support set. When the combined FEMs are used, it might be that a suitable force control cannot be achieved even under a learned environment. The reason is that the fuzzy rules undesirably influence each other. Therefore, we propose a design method for the generalization which can make the FEMs work well for any environment only if the stiffness is within the range (e.g., from 3500 N/m to 21000 N/m) shown in Fig. 2.7. In order to generalize the FEMs learned under seven fixed environments, it should be considered how to interpolate the antecedent parts between two adjacent FEMs. The approach for the generalization is as follows: Although the number of learned environments is seven as shown in Table 2.4, the generalized fuzzy environment model (GFEM) is composed of six results except for Table 2.4(1) (i.e., Km1 = Km3 = 350). It is assumed that Table 2.4(1) is included in Table 2.4(2). The stiffness values of Table 2.4(2)-(7) are used for the centers of antecedent membership functions in the GFEM, and also a suitable value is given to the standard deviation of Gaussian membership functions so that there is no nonoverlapping area. On the other hand, in the design of the consequent part, the estimated stiffness coefficients shown in Fig. 2.7 are directly used for the consequent constant values. The concrete design method is that the antecedent membership functions are placed within the range (e.g., from 57

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Table 2.6: Learned consequent constants for GFEM Model1

Model2

Model3

Model4

Model5

Model6

11752

69647

175078

353109

480732

765972

3500 N/m to 21000 N/m) with the same interval as shown in Fig. 2.12, and the estimated values of environmental stiffness shown in Fig. 2.7 are set to the corresponding consequent constants. Taking account of the fact that the number of FEMs (from 3500 N/m to 21000 N/m) integrated for the generalization is six, we design the GFEM with six fuzzy rules. Km1 (or Km3 ) shown in Table 2.4(2)-(7) are used as the center of each membership function so that they are allocated on the support set [3500, 21000] with an equal interval. Furthermore, we give 1750 to the standard deviation in order that the membership functions disposed side by side can intersect at the fitness 0.5 each other. In the design of the consequent part, the consequent models as many as the antecedent labels are prepared. The estimated stiffness coefficients, which are obtained by giving the center values of the antecedent membership functions to the horizontal values shown in Fig. 2.7, are used for the consequent constants as tabulated in Table 2.6. Fig. 2.12 and Table 2.6 show the designed antecedent membership functions and consequent constant values, respectively. The designed GFEM requires no additional acquirements and modifications of fuzzy rules during the execution of force control.

2.4.5 Results of hybrid position/force control In this section, the property of robustness is proved using the impedance model following force controller with the GFEM. Here, a simple hybrid position/force control problem shown in Fig. 2.13 is conducted under the four kinds of unlearned environments shown in Table 2.7. The de58

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Simulation of intelligent force control Model 4 Model 2 Model 6 Model 1 Model 3 Model 5

1.0

Confidence

0.8

0.6

0.4

0.2

0

0

5000

10000 15000 20000 Fuzzy inputs x*, z*

25000

Figure 2.12: Generalized antecedent membership functions for GFEM

gree of slope is set to 30◦ . The contact force in the zdirection and the trajectory from point P to point Q in the y-direction in the sensor coordinate system are simultaneously controlled. To perform this task, the switch matrix S is set to diag(0, 1, 0) . The desired contact force is given as

S T f d (t)

=

  (0 0 2.0) (0 ≤ t < 1)     (0 0 1.5) (1 ≤ t < 2)       (0 0 1.0) (2 ≤ t < 3)

(0 0 0.5) (3 ≤ t < 4)

(2.21)

   (0 0 1.0) (4 ≤ t < 5)     (0 0 1.5) (5 ≤ t < 6)    

(0 0 2.0) (6 ≤ t < 7)

Using Eq. (2.11), Sf Td (t) is transformed to f Td (t) in the 59

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Controller design for industrial robots and machine tools

Figure 2.13: Hybrid position/force control problem under unlearned environments

2.0

Reference Response (a), (b), (c), (d)

Contact force [N]

1.5 1.0 0.5

z-direction 0 -0.5

x-direction

-1.0 0

1

2

3 4 Time [ s ]

5

6

7

Figure 2.14: Force control results in x- and z-directions under an unlearned environment

60

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0.4

Position [m]

0.3 0.2

y-direction

0.1 0 Reference Response(a)-(d)

-0.1 -0.2

0

1

2

3 4 Time [ s ]

5

6

7

[Ns/m]

Figure 2.15: Position control result in y-direction

104

2.5

Desired damping coefficient

2.0 (d) 1.5

(c) (b)

1.0 0.5 0

(a)

0

1

2

3

4

5

6

7

Time [ s ]

Figure 2.16: direction.

Desired damping coefficients in the x-

61

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Table 2.7: Stiffness of unlearned environments [N/m] (a)

Km1 = Km3 = 4000

(b)

Km1 = Km3 = 9000

(c)

Km1 = Km3 = 14000

(d)

Km1 = Km3 = 19000

base coordinate system such as

f Td (t) =

  (−1.00 0 1.732) (0 ≤ t < 1)     (−0.75 0 1.299) (1 ≤ t < 2)       (−0.50 0 0.866) (2 ≤ t < 3)

(−0.25 0 0.433) (3 ≤ t < 4)

(2.22)

   (−0.50 0 0.866) (4 ≤ t < 5)     (−0.75 0 1.299) (5 ≤ t < 6)    

(−1.00 0 1.732) (6 ≤ t < 7)

Where Z-Y-Z Euler angles, which represent the orientation of the tip of the robot arm, are fixed to [0 150◦ 0]. The experimental results of hybrid position/force control are shown in Figs. 2.14 and 2.15. It was confirmed that the contact forces could follow the changes of the reference without overshoots and oscillations under four environments. In this case, the desired damping coefficients in the x- and z-directions are generated from the GFEM as shown in Figs. 2.16 and 2.17, respectively. Figure 2.18 demonstrates another result, in which the desired contact force was set to larger magnitudes. From these simulation results, it was proved that the proposed GFEM could systematically generate the desired damping for stable force control even under unlearned environments. 62

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Desired damping coefficient

[Ns/m]

Simulation of intelligent force control 104

3.0 2.5

(d)

2.0

(c)

1.5 (b) 1.0 (a)

0.5 0

0

Figure 2.17: direction.

1

2

3 4 Time [ s ]

5

6

7

Desired damping coefficients in the z-

2.5 Conclusion In this chapter, simulations of impedance model following force control using generalized learning-based fuzzy environment model (GFEM) have been presented for articulated industrial robots with an open-architecture controller. The desired damping, which is one of the impedance parameters, has a substantial effect on force control performance, so that an important goal for successfully using the force controller is working out how to suitably tune the desired damping according to each environment and task. However, the desired damping is generally tuned by trial and error since there are no systematic tuning methods. To overcome this problem we have introduced an approach that produces the desired time-varying damping, giving the critical damping condition in contact with an object. This approach requires that the physical parameters of the object, such as viscosity and stiffness, are known beforehand. In order to deal with unknown environments, the GFEM 63

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Controller design for industrial robots and machine tools

25 20 Contact force [N]

15 10 Reference Response (a), (b), (c), (d)

5 0 -5 -10 -15

0

1

2

3

4 5 6 Time [ s ]

7

8

9

Figure 2.18: Force control results in case that a larger magnitude is given to the desired contact force has been also proposed. The GFEM is designed by integrating several FEMs. Each FEM is optimized under several fixed environments in advance, using genetic algorithms. The GFEM not only estimates the stiffness of unknown environments but also systematically yields the desired timevarying damping for stable force control. The desired timevarying damping allows the impedance model following force controller to have an ability to suppress overshoots and oscillations in force control. The effectiveness and promise of the proposed method are demonstrated through hybrid position/force control simulations by using the dynamic model of a PUMA560 manipulator.

64

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[24] M.H. Raibert and J.J. Craig, Hybrid position/force control of manipulators. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 102: 126–133, 1981. [25] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, CAD/CAM-based position/force controller for a mold polishing robot. Mechatronics, 17(4/5): 207-216, 2007. [26] F. Nagata, K. Watanabe, S. Hashino, H. Tanaka, T. Matsuyama, and K. Hara, Polishing robot using joystick controlled teaching. Journal of Robotics and Mechatronics, 13(5): 517–525, 2001. [27] F. Nagata, K. Watanabe, and K. Kiguchi, Joystick teaching system for industrial robots using fuzzy compliance control. Industrial Robotics: Theory, Modelling and Control, INTECH, pages 799–812, 2006. [28] Y. Maeda, N. Ishido, H. Kikuchi, and T. Arai, Teaching of grasp/graspless manipulation for industrial robots by human demonstration. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1523–1528, 2002. [29] D. Kushida, M. Nakamura, S. Goto, and N. Kyura, Human direct teaching of industrial articulated robot arms based on force-free control. Artificial Life and Robotics, 5(1): 26–32, 2001. [30] S. Sugita, T. Itaya, and Y. Takeuchi, Development of robot teaching support devices to automate deburring and finishing works in casting. The International Journal of Advanced Manufacturing Technology, 23(3/4): 183–189, 2003. [31] C. K. Ahn and M. C. Lee, An off-line automatic teaching by vision information for robotic assembly task. 218

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motion and stick-slip motion for lapping of LED lens molds. In IEEE International Conference on Robotics & Automation , pages 2095–2100, 2010, [69] O. Bilkay and O. Anlagan, Computer simulation of stick-slip motion in machine tool slideways. Tribology International, 37(4): 347–351, 2004. [70] X. Mei, M. Tsutsumi, T. Tao, and N. Sun, Study on the compensation of error by stick-slip for high-precision table. International Journal of Machine tools & Manufacture, 44(5): 503–510, 2004. [71] M.J. Tsai, J.L. Chang, and J.F. Haung, Development of an automatic mold polishing system. In IEEE International Conference on Robotics & Automation, pages 3517–3522, 2003. [72] M.J. Tsai, J.J. Fang, and J.L. Chang, Robotic path planning for an automatic mold polishing system. International Journal of Robotics & Automation, 19(2): 81–89, 2004, [73] H. Hocheng, Y.H. Sun, S.C. Lin, and P.S. Kao, A material removal analysis of electrochemical machining using flat-end cathode. Journal of Materials Processing Technology, 140(1/3): 264–268, 2003. [74] Y. Uehara, H. Ohmori, W. Lin, Y. Ueno, T. Naruse, N. Mitsuishi, S. Ishikawa, and T. Miura, Development of spherical lens ELID grinding system by desk-top 4-axes Machine Tool. In International Conference on Leading Edge Manufacturing in 21st Century, pages 247–252, 2005, [75] H. Ohmori and Y. Uehara, Development of a desktop machine tool for mirror surface grinding. International Journal of Automation Technology, 4(2): 88–96, 2010, 224

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3 CAM system for articulated-type industrial robot DOI: 10.1533/9780857094636.65 Abstract: In this chapter, a CAM system for an articulated-type industrial robot RV1A is proposed in order to raise the relationship between a CAD/CAM and industrial robots spread to industrial manufacturing fields. A simple and flexible CAM system is designed from the viewpoint of the cooperation between CL data and robotic servo system. The CAM system required for an industrial robot is realized as an integrated system including not only a conventional main-processor of CAM but also a robotic servo system and kinematics, so that the RV1A can be directly controlled without any conventional teaching process. The basic design of the CAM system and experimental results are shown using the industrial robot RV1A. The effectiveness is demonstrated through a trajectory following a control experiment along multi-axis CL data consisting of position and orientation components and passive force control experiments. Key words: CAD/CAM, cutter location (CL) data, industrial robot RV1A, Ethernet, roll-pitch-yaw angles, passive force control 65

Controller design for industrial robots and machine tools

3.1 Background Many studies focusing on teaching of industrial robots have already been conducted. The authors developed a joystick teaching system for a polishing robot to safely obtain suitable orientation data of a sanding tool attached to the tip of robot arm [26,27,82]. Maeda et al. proposed a simple teaching method for industrial robots by human demonstration. The proposed automated camera calibration enabled labor-saving teaching and compensated the absolute positional error of industrial robots [28]. Also, Kushida et al. proposed a method of force-free control for industrial articulated robot arms. The control method was applied to the direct teaching of industrial articulated robot arms, in which the robot arm was directly moved by human force [29]. Furthermore, Sugita et al. developed two kinds of teaching support devices, i.e., a three-wire type and an arm-type, for a deburring and finishing robot. The validity of the proposed devices was verified through experiments using an industrial robot [30]. As for off-line teaching, Ahn and Lee proposed an off-line automatic teaching method using vision information for robotic assembly task [31]. Moreover, a CAD-based off-line teaching system was proposed by Neto et al., which allows users with basic CAD skills to generate robot programs off-line, without stopping the production by using a robot [32]. Besides, Ge et al. showed a basic transformation from CAD data to position and orientation vectors for a polishing robot [33]. As surveyed above, several promising teaching systems for industrial robots have been already developed for each task. However, it seems that a CAM system from the viewpoint of a robotic servo system has not been sufficiently discussed yet. In this book, it is assumed that a CAM system includes an important function which allows an industrial robot to be accurately controlled along cutter location data (CL data) consisting of position and orientation components. Another important point is that the pro66

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CAM system for articulated-type robot

posed CAM system has a high applicability to other industrial robots whose servo systems are technically opened to engineering users. At the present stage, the relationship between CAD/CAM and industrial robots is not well established compared to NC machine tools widely used in manufacturing industries. In general, the main-processor of CAD/CAM calculates CL data according to each model’s shape and cutting strategy, then the post-processor produces suitable numerical control data (NC data) for an NC machine tool which is actually used. The controller of an NC machine tool sequentially deals with NC data and accurately controls the position and the orientation of the main head as an example. Thus, it seems that CAM system for NC machine tools is a mature one. On the other hand, a CAM system for industrial robots has not yet been sufficiently considered and standardized. That is the reason why, when an industrial robot is applied to a task, the required position and orientation data are acquired by on-line and/or off-line teaching systems instead of CAM systems in almost all cases. In this book, a CAM system for an articulated-type industrial robot RV1A shown in Fig. 3.1 is described from the viewpoint of a robotic servo controller. It is defined here that a CAM system includes an important function which allows an industrial robot to move along CL data consisting of position and orientation components. Another important point is that the proposed CAM system has a high applicability to other industrial robots whose servo systems are technically opened to end-user engineers. The CAM system works as a flexible interface between CAD/CAM and industrial robots. At the present stage, the relationship between CAD/CAM and industrial robots is not well established compared to NC machine tools widely used in manufacturing industries. Generally, the main-processor of CAD/CAM generates CL data according to each model shape and cutting conditions, then the post-processor produces suitable NC data for an NC machine tool which is actually used. The controller of 67

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Controller design for industrial robots and machine tools

Robot controller

RV1A Teach pendant

Figure 3.1: Desktop-size industrial robot RV1A.

NC machine tool sequentially deals with NC data and accurately controls the positions of main head and the angles of other axes. Thus, CAM systems for NC machine tools are already established. On the other hand, CAM systems for industrial robots have not been sufficiently considered and standardized yet. A teaching pendant is used in almost all cases to obtain position and orientation data from the arm tip before an industrial robot can work well. Here, in order to improve the relationship between conventional CAD/CAM and an industrial robot, a simple and flexible CAM system is proposed. The basic design of the CAM system and an experimental result are shown.

3.2 Desired trajectory 3.2.1 Main-processor of CAM Various kinds of 3D CAD/CAM such as Catia, Unigraphics, Pro/Engineer, etc. are widely used in manufac68

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CAM system for articulated-type robot

wO

cl (i−1)

cl (i) cl (i+1)

wr(k−1)

wr(k) w r(k+1)

Figure 3.2: Relation between CL data cl(i) and desired trajectory wr(k), in which wO is the origin of work coordinate system.

turing industries. The main-processor of each CAD/CAM can generate CL data consisting of position and orientation components along a 3D model. In this section, a method for calculating the desired position and orientation for a robotic servo system is described in detail. For example, a robotic sanding task needs a desired trajectory so that the sanding tool attached to the tip of the robot arm can follow the object’s surface, keeping contact with the surface from the normal direction. In executing a motion using an industrial robot, the trajectory is generally obtained in advance, e.g., through conventional robotic teaching process. When the conventional teaching for an object with complex curved surface is conducted, the operator has to input a large number of teaching points along the surface. Such a teaching task is complicated and timeconsuming. However, if the object is fortunately designed by a CAD/CAM and manufactured by an NC machine tool, then CL data can be referred to as the desired trajectory consisting of position and orientation elements. It is important to show the guideline on how to improve the relationship between the main-processor of CAD/CAM and an industrial robot, which is the role of the CAM system proposed after this section. 69

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p (i) w

w

w

xd (k+1)

xd (k)

w

xd (k−1)

w w

w

xd (k+2)

xd (k−2)

xd (k+4)

xd (k+3)

p (i+1)

p (i−1)

Figure 3.3: Relation between position component p(i) in CL data and desired position wxd (k), in which p(i) − wxd (k) and p(i + 1) − wxd (k + 3) are called the fraction vectors. 192.168.0.2

Real-time PC controller based on CL data

UDP packet

192.168.0.1

Servo system

Industrial robot RV1A

HUB

Figure 3.4: Block diagram of communication system by using UDP packet.

3.2.2 Position and orientation In order to realize non-taught operation, we have already proposed a generalized trajectory generator [80] using CL data, which yields desired trajectory wr(k) at the discrete time k given by w

r(k) =

]T

[

w T xd (k) woTd (k)

(3.1)

where the superscript w denotes the work coordinate system. wxd (k) = [wxd (k) wyd (k) wzd (k)]T and wod (k) = [wodx (k) wody (k) wodz (k)]T are the position and orientation components, respectively. wod (k) is the normal vector at the position wxd (k). In the following, we explain in detail how to make wr(k) using the CL data. A target workpiece with curved surface is generally designed by a 3D CAD/CAM, so that CL data can be calcu70

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CAM system for articulated-type robot

Dialogue application Timer interrupt WSAStartup( ) sendto( ) socket( ) select( )

Idling loop

End request

Yes

error ? No

closesocket( )

recvfrom( )

WSACleanup( )

Figure 3.5: Communication scheme by using UDP packet between PC and Industrial robot RV1A, in which the sampling period ∆t is set to 10 ms.

lated by the main-processor. The CL data consist of sequential points along the model surface given by a zigzag path or a whirl path. In this approach, the desired trajectory wr(k) is generated along the CL data. The CL data are usually calculated with a linear approximation along the model surface. The i-th step is written by cl(i) = [px (i) py (i) pz (i) nx (i) ny (i) nz (i)]T {nx

(i)}2

+ {ny

(i)}2

+ {nz

(i)}2

=1

(3.2) (3.3)

where p(i) = [px (i) py (i) pz (i)]T and n(i) = [nx (i) ny (i) nz (i)]T are position and orientation vectors based on the origin wO, respectively. wr(k) is obtained by using both linear equations and a tangential velocity scalar vt called feed rate. A relation between cl(i) and wr(k) is shown in Fig. 3.2. In this case, assuming wr(k) ∈ [cl(i − 1), cl(i)] we obtain wr(k) through the following procedure. First, a direction vector t(i) = [tx (i) ty (i) tz (i)]T is given by t(i) = p(i) − p(i − 1) 71

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(3.4)

Controller design for industrial robots and machine tools

so that each component of vt in work coordinate system is obtained by vtj = vt

tj (i) (j = x, y, z) ∥t(i)∥

(3.5)

Using a sampling width ∆t, each component of the desired position wxd (k) is represented by (3.6)

w

xd (k) = wxd (k − 1) + vtx ∆t

w

w

(3.7)

w

w

(3.8)

yd (k) = yd (k − 1) + vty ∆t zd (k) = zd (k − 1) + vtz ∆t

Next, how to calculate the desired orientation od (k) is considered. By using the orientation components of two adjacent steps in CL data, a rotational direction vector tr (i) = [trx (i) try (i) trz (i)]T is defined as (3.9)

tr (i) = n(i) − n(i − 1)

Each component of desired orientation can be linearly calculated with tr (i) as w

odj (k) = nj (i − 1) + trj (i)

∥xd (k) − p(i − 1)∥ ∥t(i)∥

(j = x, y, z) (3.10)

and wod (k) shown above are directly obtained from the CL data without either any conventional complicated teaching process or recently proposed off-line teaching methods. The desired position and orientation in the discrete-time domain are very important to control the tip of an industrial robot in real time, i.e., to design a feedback control system. If the linear approximation is applied when CL data are generated by the main-processor of CAD/CAM, CL data forming a curved line are composed of continuous minute lines such as ∥p(i) − p(i − 1)∥ and ∥p(i + 1) − p(i)∥ shown in Fig. 3.3. In this case, it should be noted that each position vector in CL data such as p(i) and p(i + 1) shown wx

d (k)

72

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in Fig. 3.3 have to be carefully dealt with in order to be accurately followed along the CL data. For example, wxd (k+ 1) and wxd (k + 4) are not calculated by using Eqs. (3.6), (3.7) and (3.8) but have to be directly set with p(i) and p(i + 1), respectively, just before the feed direction changes. ∥p(i) − wxd (k)∥ and ∥p(i + 1) − wxd (k + 3)∥ are called the fraction.

3.3 Implementation to industrial robot RV1A 3.3.1 Communication between PC and robot controller A Windows PC as a controller and the RV1A are connected via Ethernet as shown in Fig. 3.4. The servo system in the Cartesian coordinate system of the RV1A is technically opened to users, so that absolute coordinate vectors of position and orientation can be given to the reference of the servo system. The servo rate of the robot is fixed to 7.1 ms. Fig. 3.5 illustrates the communication scheme by using UDP packet, in which sampling period is set to 10 ms. The data size in a UDP pachet is 196 bytes. The packet transmitted by ‘sendto( )’ includes values of desired position [Xd (k) Yd (k) Zd (k)]T [mm] and desired orientation [ϕd (k) θd (k) ψd (k)]T [rad] in robot absolute coordinate system. ϕd (k), θd (k), ψd (k) are the rotational angles about x-, y- and z-axes, respectively, which are called X-Y-Z fixed angles or roll, pitch and yaw angles. The desired position and the desired orientation are set in a UDP packet as the reference of the arm tip in the Cartesian servo system. Moreover, the packet received by ‘recvfrom( )’ includes values of current position [X(k) Y (k) Z(k)]T [mm] and current orientation [ϕ(k) θ(k) ψ(k)]T [rad] in robot absolute coordinate system, which can be used for feedback quantity. 73

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Controller design for industrial robots and machine tools Initial orientation

Figure 3.6: Orientation control of arm tip based on CL data shown in Fig. 3.2, in which the initial orientation is given with [ϕ(k) θ(k) ψ(k)]T = [0 0 0]T .

3.3.2 Desired position and orientation for arm tip In this subsection, the making of [Xd (k) Yd (k) Zd (k)]T and [ϕd (k) θd (k) ψd (k)]T based on the position and the orientation given by Eq. (3.1) is discussed in detail by using an example shown in Fig. 3.2, in which the tip of robot arm follows the trajectory, keeping the orientation along the normal direction to the surface. Each component of [Xd (k) Yd (k) Zd (k)]T is represented with the initial position [Xd (0) Yd (0) Zd (0)]T as Xd (k) = Xd (0) + wxd (k)

(3.11)

w

(3.12)

w

(3.13)

Yd (k) = Yd (0) + yd (k) Zd (k) = Zd (0) + zd (k)

where [Xd (0) Yd (0) Zd (0)]T means the values of wO in robot absolute coordinate system. Next, we consider the rotational components. Generally, rotational matrices RX , RY and RZ around x-, y- and z-axes 74

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CAM system for articulated-type robot

Figure 3.7: CL data cl(i) = [pT (i) nT (i)]T consisting of position and orientation components, which is used for desired trajectory of the tip of robot arm.

are given by RX





(3.14)





(3.15)





(3.16)

1 0 0   =  0 cos ϕ(k) − sin ϕ(k)  0 sin ϕ(k) cos ϕ(k)

cos θ(k) 0 sin θ(k)   0 1 0 RY =   − sin θ(k) 0 cos θ(k)

cos ψ(k) − sin ψ(k) 0   RZ =  sin ψ(k) cos ψ(k) 0  0 0 1

Accordingly, the rotational matrix RZ RY RX with a roll angle ϕ(k), a pitch angle θ(k), and a yaw angle ψ(k) is given by 



Cθ Cψ Sϕ Sθ Cψ − Cϕ Sψ Cϕ Sθ Cψ + Sϕ Sψ    Cθ Sψ Sϕ Sθ Sψ + Cϕ Cψ Cϕ Sθ Sψ − Sϕ Cψ  (3.17) −Sθ Sϕ Cθ Cϕ Cθ 75

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Desired position in x-direction mm

Controller design for industrial robots and machine tools 324 322 320 318 316 314 312 310 308 0

50

100 Time s

150

200

Figure 3.8: Initial part of x-component Xd (k) of desired trajectory in robot absolute coordinate system.

where, for example, Sθ and Cθ means sin θ(k) and cos θ(k), respectively. Fig. 3.6 illustrates the trajectory following control along CL data shown in Fig. 3.2. As can be seen, the direction of wod (k) is just inverse to the one of the arm tip. When referring the orientation components in CL data, the arm tip can be determined only with the roll angle and the pitch angle except for the yaw angle. That means ψ(k) can be always fixed to 0 [rad]. Thus, Eq. (3.17) is simplified by giving 0 to ψ(k) as

RZ RY RX





Cθ S ϕ S θ Cϕ S θ   Cϕ −Sϕ  = 0 −Sθ Sϕ Cθ Cϕ Cθ

(3.18)

The roll angle ϕ(k) and the pitch angle θ(k) at the discrete time k are obtained by solving 









0 −wodx (k) Cθ S ϕ S θ Cϕ S θ      w Cϕ −Sϕ   0  (3.19)  − ody (k)  =  0 w 1 −Sθ Sϕ Cθ Cϕ Cθ − odz (k)

where [0 0 1]T is the initial orientation vector in robot absolute coordinate system as shown in Fig. 3.6. Finally, ϕ(k) 76

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Desired position in y-direction mm

CAM system for articulated-type robot 16 14 12 10 8 6 4 2 0 0

50

100 Time s

150

200

Desired position in z-direction mm

Figure 3.9: Initial part of y-component Yd (k) of desired trajectory in robot absolute coordinate system.

339.4 339.3 339.2 339.1 339.0 338.9 338.8 338.7 0

50

100 Time s

150

200

Figure 3.10: Initial part of z-component Zd (k) of desired trajectory in robot absolute coordinate system.

and θ(k) are calculated by using inverse trigonometric functions as ϕ(k) = atan2 {−wodx (k), −wodz (k)}

(3.20)

θ(k) = asin { ody (k)}

(3.21)

w

If the yaw angle is always fixed to 0, then the desired roll angle ϕd (k) and pitch angle θd (k) at the discrete time k can be calculated with Eqs. (3.20) and (3.21), respectively. 77

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Desired roll angle φd (k) rad

4 3 2 1 0 -1 -2 -3 -4 0

50

100 Time s

150

200

Figure 3.11: Initial part of desired roll angle ϕd (k) calculated from the desired trajectory shown in Fig. 3.7.

Desired pitch angle θd (k) rad

0.2

0.1

0

-0.1

-0.2 0

50

100 Time s

150

200

Figure 3.12: Initial part of desired pitch angle θd (k) calculated from the desired trajectory shown in Fig. 3.7.

3.4 Experiment In this section, an experiment of trajectory following control is conducted to evaluate the effectiveness of the proposed CAM system. Fig. 3.7 shows the desired trajectory generated by using the main-processor of 3D CAD/CAM Pro/Engineer, which consists of position and orientation components written by multi-lined ”GOTO/” statements. In this experiment, it is tried that the arm tip is controlled so as to follow the position and orientation. Figs. 3.8, 3.9 78

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CAM system for articulated-type robot

and 3.10 show the initial parts of x-component Xd (k), ycomponent Yd (k) and z-component Zd (k)of the desired trajectory in robot absolute coordinate system, respectively. Moreover, Figs. 3.11 and 3.12 show the initial parts of the roll angle ϕd (k) and the pitch angle θd (k), respectively, of the desired trajectory in the robot absolute coordinate system. In the trajectory following control experiments, the value of feed rate, i.e., tangential velocity, is set to 1 mm/s; the desired values composed of Xd (k), Yd (k), Zd (k), ϕd (k), θd (k) and ψd (k) are given to the references of the servo controller of RV1A every sampling period with UDP packets. When the desired position [Xd (k) Yd (k) Zd (k)]T and orientation [ϕd (k) θd (k) ψd (k)]T is transmitted to the robotic servo system, the roll angle ϕd (k) has to be given within the range from −π to π. Fig. 3.13 shows four examples of roll angle around x-axis, in which (a) is the initial angle represented by ϕ(k) = 0, (b) is the case of −π ≤ ϕ(k) < 0, (c) is the case of ϕ(k) = ± π, and (d) is the case of 0 < ϕ(k) ≤ π. It should be noted how to calculate the desired roll angle ϕd (k) as an manipulated value if the orientation changes as (b)→(c)→(d) or (d)→(c)→(b), i.e., in passing through the situation (c). In such cases, the sign of ϕd (k) has to be suddenly changed as shown in Fig. 3.11. In order to smoothly control the orientation of the arm tip , the following control rules were applied for the correction of roll angle.

if ϕd (k) > 0 and ϕ(k) < 0, then ∆ϕ(k) = Kp {ϕd (k) − ϕ(k) − 2π} else if ϕd (k) < 0 and ϕ(k) > 0, then ∆ϕ(k) = Kp {ϕd (k) − ϕ(k) + 2π} else if sgn{ϕd (k)} = sgn{ϕ(k)}, then ∆ϕ(k) = Kp {ϕd (k) − ϕ(k)} (3.22) where ϕd (k) and ϕ(k) are the desired roll angle transmitted 79

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Controller design for industrial robots and machine tools

to the robotic servo controller and actual roll angle transmitted from the robotic servo controller, respectively. ∆ϕ(k) is the output of proportional control action with a gain Kp . In fact, the desired roll angle ϕd (k + 1) is generated as ϕd (k + 1) = ϕ(k) + ∆ϕ(k)

(3.23)

Figs. 3.14, 3.15, 3.16, 3.17 and 3.18 show the actual results controlled based on the references shown in Figs. 3.8, 3.9, 3.10, 3.11 and 3.12, respectively. It was confirmed from the experiment that the desired control results of position and orientation could be obtained. The arm tip could gradually move up from the bottom center along the spiral path shown in Fig. 3.7. In this case, the orientation of the arm tip was simultaneously controlled so as to be in a normal direction to the surface. It was successfully demonstrated that the proposed CAM system allows the tip of the robot arm to desirably follow the desired trajectory given by multi-axis CL data without any complicated teaching tasks.

3.5 Passive force control of industrial robot RV1A 3.5.1 Derivation of passive force control laws by using a inner servo system In this subsection, passive force control methods of the industrial robot are introduced. They are called stiffness control, compliance control and impedance control. The relative position vector ∆x is written by ∆x = K p (xd − x)

(3.24)

where xd and x are the desired position and current position vectors, respectively. K p = diag(Kpx , Kpy , Kpz ) is the position feedback gain. ∆x is the manipulated variable from 80

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CAM system for articulated-type robot

the outer position control system to the technically-opened high-rate servo system in the robot controller. First of all, a stiffness control is simply considered. The desired stiffness model is designed by (3.25)

K d (x − x0 ) = F

where K d = diag(Kdx , Kdy , Kdz ) is the desired stiffness, F is the external force given to the arm tip. x0 is the initial position in the case of F = 0. Eq. (3.25) is represented with x as (3.26)

x = x0 + K −1 d F

Eq. (3.26) is substituted into xd in Eq. (3.24) to realize a stiffness control by using the servo system, so that the following equation is obtained. (3.27)

∆x = K p (x0 + K −1 d F − x)

Next, a compliance control is also considered, in which the velocity is further controlled according to the external force. The desired compliance model is designed by (3.28)

B d (x˙ − x˙ 0 ) + K d (x − x0 ) = F

where B d = diag(Bdx , Bdy , Bdz ) is the desired damping, x˙ 0 and x˙ are the initial velocity and current velocity, respectively. As can be seen, Eq. (3.28) is regarded as a first-order lag system. When F is constantly given, the following step response in time domain is obtained by solving Eq. (3.28) under the condition of x˙ 0 = 0. x = x0 + K −1 I − exp −B −1 d K dt d {

(

)}

F

(3.29)

where I is the identity matrix. The external force F is absorbed by Eq. (3.29). Eq. (3.29) is substituted into xd in Eq. (3.24) to realize a compliance control by using the inner 81

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servo system. The relative position command to perform the compliance control is given by ∆x = K p x0 + K −1 I − exp −B −1 d d K dt [

{

(

)}

F − x (3.30) ]

When an impedance control is applied, the acceleration is further controlled. The desired impedance model is designed by (3.31)

¨ 0 ) + B d (x˙ − x˙ 0 ) + K d (x − x0 ) = F M d (¨ x−x

¨0 where M d = diag(Mdx , Mdy , Mdz ) is the desired mass, x ¨ are the initial acceleration and current acceleration, and x respectively. Solving Eq. (3.31) under the condition of ¨ 0 = 0 and x˙ 0 = 0, damping coefficients ζi < 1 (i = x, y, z), x the following response in time domain is obtained. x = x0 + K −1 d

[

I−

(√

× exp(−ζω n t) sin

I −ζ

2

)−1

{√

I − ζ 2ωnt + tan

−1

(

−1

ζ

√

I −ζ

2

)}]

F

(3.32)

where the damping coefficient matrix ζ = diag(ζx , ζy , ζz ) and natural frequency matrix ω n = diag(ωnx , ωny , ωnz ) are given by ( √

ζ = Bd 2

M dK d

)−1

,

ωn =

√

M −1 d Kd

(3.33)

By substituting Eq. (3.32) into xd in Eq. (3.24), an impedance control can be easily realized by using the servo 82

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CAM system for articulated-type robot

system as (3.34)

∆x [

{

I− = K p x0 + K −1 d × exp(−ζω n t) sin

(√

(√

I − ζ2

)−1

(

I − ζ 2 ω n t+tan−1 ζ −1

√

I − ζ2

−x

]

))}

3.5.2 Experiments of passive force controllers As the first case study, the stiffness control law given by Eq. (3.27) is applied. In the experiment on stiffness control, a student is pulling the force sensor attached to the arm tip with 10 N as shown in Fig. 3.20. Fig. 3.21 shows the experimental results when Eq. (3.27) is used in x-direction with several desired stiffnesses Kdx N/mm, where the relations between the time and the position are plotted. As can be seen, the mechanical stiffness is controlled according to the desired stiffness. As the second case study, the compliance control law given by Eq. (3.30) is applied. In this case, the mechanical damping and stiffness in x-direction can be regulated by changing Bdx and Kdx , respectively. Fig. 3.22 shows experimental results when Eq. (3.30) is used in x-direction with several desired damping Bdx Ns/mm, in which the relations between the time and position are plotted. It is observed that the mechanical damping is successfully varied according to the desired damping. Note that the Kdx is set to a constant value of 0.4 N/mm. As the third case study, the impedance control law given by Eq. (3.32) is used. In this case, the mechanical impedance in x-direction can be regulated by changing the damping coefficient ζ. Fig. 3.23 shows experimental results when Eq. (3.32) is used in x-direction with several damping coefficients ζ, in which the relations between the time and the position are plotted. It is observed that the mechanical 83

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F

Controller design for industrial robots and machine tools

impedance is also successfully varied according to the damping coefficient. Note that the Kdx is also set to a constant value of 0.4 N/mm.

3.6 Conclusion In this chapter, a CAM system for an articulated-type industrial robot RV1A has been proposed in order to improve the relationship between a design tool such as CAD/CAM and industrial robots spread across industrial manufacturing fields. A simple and flexible CAM system has been proposed from the viewpoint of cooperation between CL data and robotic servo system. The CAM system required for an industrial robot is realized as an integrated system including not only a conventional main-processor of CAM but also a robotic servo system and kinematics. Basic design of the CAM system and experimental results have been shown using the desktop-size industrial robot RV1A. The effectiveness has been demonstrated through a trajectory following control along multi-axis CL data consisting position and orientation components. In future work, we plan to develop a 3D carving machine for wooden materials based on an industrial robot, in which the concept of the proposed CAM system will be incorporated as an important interface between CAD/CAM and the industrial robot. Then, passive force control methods called stiffness control, compliance control and impedance control were proposed and also the controllers were designed using the robotic inner servo system of the RV1A. It was successfully demonstrated that the industrial robot RV1A could perform desired compliance against an external force.

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(a)

+

−

(d)

(b) (c)

Figure 3.13: Roll angles around x-axis, in which (a) is the initial angle represented by ϕ(k) = 0, (b) is the case of −π ≤ ϕ(k) < 0, (c) is the case of ϕ(k) = ± π, and (d) is the case of 0 < ϕ(k) ≤ π.

85

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Position in x-direction mm

324 322 320 318 316 314 312 310 308 0

50

100 Time s

150

200

Figure 3.14: Control result of x-directional position X(k).

Position in y-direction mm

16 14 12 10 8 6 4 2 0 0

50

100 Time s

150

200

Figure 3.15: Control result of y-directional position Y (k).

Position in z-direction mm

339.4 339.3 339.2 339.1 339.0 338.9 338.8 338.7 0

50

100 Time s

150

200

Figure 3.16: Control result of z-directional position Z(k).

86

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4

Roll angle φ (k) rad

3 2 1 0 -1 -2 -3 -4 0

50

100 Time s

150

200

Figure 3.17: Control result of roll angle ϕ(k).

Pitch angle θ (k) rad

0.2

0.1

0

-0.1

-0.2 0

50

100 Time s

150

200

Figure 3.18: Control result of pitch angle θ(k).

87

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UDP packets

Robot controller

Windows PC Ethernet

Cycle of motion control : 7 msec

Robot controller

PC (10 msec) Sending of position command

Receiving of current position

Figure 3.19: Timing chart between a robot controller and a PC through Ethernet, in which UDP packet with 196 bytes is used.

Pulling in x-direction

Figure 3.20: Experimental scene, in which a student is pulling the arm tip with 10 N in x-direction.

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30 0.4 N/mm

Position [mm]

25

20

15 0.8 N/mm 10

1.2 N/mm 1.6 N/mm

5

0

2 N/mm

0

1

2

3

4 5 Time [s]

6

7

8

9

Figure 3.21: Experimental results when Eq. (3.27) is used in x-direction with several desired stiffness Kdx N/mm. The relations between the time and position are plotted.

30

0.01 Ns/mm 0.04 Ns/mm

Position [mm]

25

20

15

0.07 Ns/mm 0.10 Ns/mm

10 0.15 Ns/mm 5

0

0

3

6

9

12

15

Time [s]

Figure 3.22: Experimental results when Eq. (3.30) is used in x-direction with several desired dampings Bdx Ns/mm. The relations between the time and position are plotted.

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40

ζ = 0.2

35

ζ = 0.4 ζ = 0.6

Position [mm]

30 25 20

ζ = 0.8 15 10 5 0 0

5

10

15

20

25

Time [s]

Figure 3.23: Experimental results when Eq. (3.32) is used in x-direction with several damping cofficients ζ. The relations between the time and position are plotted.

90

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[47] X.J. Xu, C. Bradley, Y.F. Zhang, H.T. Loh, and Y.S. Wong, Tool-path generation for five-axis machining of free-form surfaces based on accessibility analysis. International Journal of Production Research, 40(14): 3253–3274, 2002. [48] S.L. Chen, T.H. Chang, I. Inasaki, and Y.C. Liu, Postprocessor development of a hybrid TRR-XY parallel kinematic machine tool. The International Journal of Advanced Manufacturing Technology, 20(4): 259–69, 2002. [49] W.T. Lei and Y.Y. Hsu, Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part I: design and modeling. Machine Tool & Manufacture, 42(10): 1153–1162, 2002. [50] W.T. Lei, M.P. Sung, W.L. Liu, and Y.C. Chuang, Double ballbar test for the rotary axes of five-axis CNC machine tools. Machine Tool & Manufacture, 47(2): 273–285, 2006. [51] L.X. Cao, H. Gong, and J. Liu, The offset approach of machining free form surface. Part 1: Cylindrical cutter in five-axis NC machine tools. Journal of Materials Processing Technology, 174(1/3): 298–304, 2006. [52] L.X. Cao , H. Gong, and J. Liu, The offset approach of machining free form surface. Part 2: Toroidal cutter in 5-axis NC machine tools. Journal of Materials Processing Technology, 184(1/3): 6–11, 2007. [53] S.D.Timar, R.T. Farouki, T.S. Smith, and C.L. Boyadjieff. Algorithms for time optimal control of CNC machines along curved tool paths. Robotics and ComputerIntegrated Manufacturing, 21(1): 37–53, 2005. [54] E.Y. Heo, D.W. Kim, B.H. Kim, and F.F. Chen, Estimation of NC machining time using NC block distribution for sculptured surface machining. Robotics and 221

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Computer-Integrated Manufacturing, 22(5-6): 437–46, 2006. [55] Y.S. Tarng, H.Y. Chuang, and W.T. Hsu, Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture, 39(10): 1673–1692, 1999. [56] U. Zuperl, F. Cus, and M. Milfelner, Fuzzy control strategy for an adaptive force control in end-milling. Journal of Materials Processing Technology, 164/165: 1472–1478, 2005. [57] R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.F. Yuan, and S. Jee, Variable-feedrate CNC interpolators for constant material removal rates along Pythagoreanhodograph curves. Computer-Aided Design, 30(8): 631–640, 1998. [58] R.T. Farouki, J. Manjunathaiah, and G.F. Yuan. G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on openarchitecture CNC machines. Machine Tools & Manufacture, 39(1): 123–142, 1999. [59] A. Frank and A. Schmid, Grinding of non-circular contours on CNC cylindrical grinding machines. Robotics and Computer-Integrated Manufacturing, 4(1/2): 211–218, 1988. [60] J.A. Couey, E.R. Marsh, B.R. Knapp, and R.R. Vallance, Monitoring force in precision cylindrical grinding. Precision Engineering, 29(3): 307–314, 2005. [61] T. Tawakoli, A. Rasifard, and M. Rabiey, Highefficiency internal cylindrical grinding with a new kinematic. Machine Tools & Manufacture, 47(5): 729–733, 2007. 222

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motion and stick-slip motion for lapping of LED lens molds. In IEEE International Conference on Robotics & Automation , pages 2095–2100, 2010, [69] O. Bilkay and O. Anlagan, Computer simulation of stick-slip motion in machine tool slideways. Tribology International, 37(4): 347–351, 2004. [70] X. Mei, M. Tsutsumi, T. Tao, and N. Sun, Study on the compensation of error by stick-slip for high-precision table. International Journal of Machine tools & Manufacture, 44(5): 503–510, 2004. [71] M.J. Tsai, J.L. Chang, and J.F. Haung, Development of an automatic mold polishing system. In IEEE International Conference on Robotics & Automation, pages 3517–3522, 2003. [72] M.J. Tsai, J.J. Fang, and J.L. Chang, Robotic path planning for an automatic mold polishing system. International Journal of Robotics & Automation, 19(2): 81–89, 2004, [73] H. Hocheng, Y.H. Sun, S.C. Lin, and P.S. Kao, A material removal analysis of electrochemical machining using flat-end cathode. Journal of Materials Processing Technology, 140(1/3): 264–268, 2003. [74] Y. Uehara, H. Ohmori, W. Lin, Y. Ueno, T. Naruse, N. Mitsuishi, S. Ishikawa, and T. Miura, Development of spherical lens ELID grinding system by desk-top 4-axes Machine Tool. In International Conference on Leading Edge Manufacturing in 21st Century, pages 247–252, 2005, [75] H. Ohmori and Y. Uehara, Development of a desktop machine tool for mirror surface grinding. International Journal of Automation Technology, 4(2): 88–96, 2010, 224

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4 3D robot sander for artistically designed furniture DOI: 10.1533/9780857094636.91 Abstract: This chapter introduces a robotic sanding system for attractively designed furniture with free-formed surfaces. The system is developed using an industrial robot with an open-architecture controller. The system has two novel features. One is that the surface-following controller developed for robotic sanding allows the robot to simultaneously realize a delicate polishing force control and smooth position/orientation control. The other is that a conventional and complicated teaching task is not required at all. The proposed robot sander directly handles CL data generated from 3D CAD/CAM, so that such a teaching process can be omitted. It is demonstrated that the proposed system can successfully sand the curved surface of attractive furniture with an extremely good quality. Key words: wood, furniture, curved surface, sanding, hybrid position/force control, CL data, KAWASAKI FS30 91

Controller design for industrial robots and machine tools

Figure 4.1: Handy air-driven sanding tools usually used by skilled workers.

4.1 Background In the wooden furniture manufacturing industry, CAD/CAM systems and NC machine tools have been introduced widely and generally, so that the design and machining processes are rationalized. However, the sanding process after machining process is hardly automated yet, because it requires delicate and dexterous skills so as not to spoil the beauty and quality of the wooden surface. Up to now, several sanding machines have been developed for wooden materials. For example, the wide belt sander is used for flat workpieces constructing furniture. Also, the profile sander is suitable for sanding around edges. However, these conventional machines can not be applied to the sanding task of the workpiece with a free-formed surface. Accordingly, we must depend on skilled workers who can not only perform appropriate force control of sanding tools but also deal with complex curved surface. Skilled workers usually use smaller, air-driven tools such as a double-action sanding tool and an orbital sanding tool as shown in Fig. 4.1. Industrial robots have progressed remarkably and been applied to several tasks such as painting, welding, handling 92

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and so on. In these cases, it is important to precisely control the position of the end-effector attached to the tip of the robot arm. When robots are applied to polishing, deburring or grinding tasks, it is important to use some force control strategy so as not to damage the object. For example, polishing robots and finishing robots were presented in [34–38]. Automated robotic deburring systems and grinding systems were also introduced in [39–43]. Surface-following control is a basic sanding strategy for industrial robots. It is known that two control schemes are needed to realize the surface-following control system. One is the position/orientation control of the sanding tool attached to the tip of the robot arm. The other is the force control to stably keep in contact along the curved surface of the workpiece. It should be noted that if the geometric information on the workpiece is unknown, then it is so difficult to satisfactorily control the contact force moving with a high speed [44]. To suppress overshoots and oscillations, for example, the feed rate must be given a small value. Furthermore, it is also difficult to control the orientation of the sanding tool, keeping in contact with the workpiece from normal direction. In this chapter, a robotic sanding system is integrated for new designed furniture with free-formed curved surface. The robotic sanding system provides a practical surface-following control that allows industrial robots not only to adjust the polishing force through a desired impedance model in Cartesian space but also to follow a curved surface keeping contact with from normal direction. The polishing force is assumed to be the resultant force of contact force and kinetic friction force. We also describe how to apply the robotic sanding system to the task of sanding a wooden workpiece without complicated teaching process. A few experiments involving the sanding of wooden parts are shown to demonstrate the effectiveness and promise of the proposed robotic sanding system. 93

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Figure 4.2: Example of a whirl path generated based on contour lines.

4.2 Feedfoward position/orientation control based on post-process of CAM First of all, we discuss position/orientation control of an end-effector attached to the tip of a robot arm. A key point is that the position/orientation control system is designed feedforwardly so as not to disturb the force feedback control loop. In almost all cases, target workpieces are designed and machined by CAD/CAM systems and NC machine tools. Therefore, cutter location data can be referred to as the desired trajectory of position and orientation. The cutter location data are called CL data, and are generated from the main-processor of the CAM. The CL data have sequential points along the model surface given by a zigzag path, whirl path or spiral path. Fig. 4.2 shows an example of a whirl path based on contour lines, which are outputted by the main-processor of 3D CAD/CAM Unigraphics. In order to realize non-taught operation, we have already proposed a feedforward trajectory generator [22, 23] using the CL data, which yields the desired trajectory r(k) at the discrete time k given by Eq. (3.1). Here, the desired orientation vector od (k) is considered from the viewpoint of the post-processor of CAM . We define two angles θ1 (i), θ2 (i) as 94

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nz (i ) n(i )

θ1 (i ) p(i )

n y (i )

nx (i ) θ 2 (i )

X

Y

Figure 4.3: Normalized tool vector n(i) represented by θ1 (i) and θ2 (i) in work coordinate system.

shown in Fig. 4.3. θ1 (i) and θ2 (i) are the tool angles of inclination and rotation, respectively. Using θ1 (i) and θ2 (i), each component of n(i) is represented by nx (i) = sinθ1 (i)cosθ2 (i)

(4.1)

ny (i) = sinθ1 (i)sinθ2 (i)

(4.2)

nz (i) = cosθ1 (i)

(4.3)

The desired tool angles θr1 (k), θr2 (k) of inclination and rotation at the discrete time k can be calculated as θrj (k) = θj (i) + {θj (i + 1) − θj (i)}

∥xd (k) − p(i)∥ ∥t(i)∥

(4.4)

where j = 1, 2. If Eq. (4.4) is substituted into Eqs. (4.1), (4.2), (4.3), we finally obtain odx (k) = sinθr1 (k)cosθr2 (k)

(4.5)

ody (k) = sinθr1 (k)sinθr2 (k)

(4.6)

odz (k) = cosθr1 (k)

(4.7)

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DesiredPosition Position and and Direction Direction Desired GeneratorBased Basedon on CL CL Data Data Generator

Controller design for industrial robots and machine tools

Fd od (k)

xd (k)

Force ForceFeedback Feedback Control ControlLaw Law

F(k) : force measurement x (k) : current position

vn (k)

F (k)

Position/Orientation Position/Orientation Feedforward Feedforward Control ControlLaw Law

vt (k)

Position PositionFeedback Feedback Control ControlLaw Law

vp (k)

+

F/T F/TSensor Sensor

+ Cartesian-Based Cartesian-Based Servo Servo Controller Controller

Σ +

Weak coupling with Sp

Industrial Industrial Robot Robot

xd (k) : desired position od (k) : desired direction

x (k)

Fd : desired polishing force norm

Figure 4.4: Block diagram of the proposed hybrid position/force controller with weak coupling.

xd (k) and od (k) mentioned above are directly obtained from the CL data without any conventional complicated teaching, and used for the desired position and orientation of a sanding tool attached to a robot arm. Orientation velocity vector [vrx vry vrz ]T according to the translational velocity vector given by Eqs. (3.6), (3.7) and (3.8) is obtained by odj (k) = odj (k − 1) + vrj (k)∆t (j = x, y, z)

(4.8)

4.3 Hybrid position/force control with weak coupling When an industrial robot conducts a task involving the maintaining of contact with a workpiece, the position and force must be controlled simultaneously and dexterously. The hybrid position/force control method was proposed to control compliant motions of a robot manipulator, by combining force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system [24]. Here we consider a practical and applicable hybrid position/force control method which can easily be applied to 96

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open-architecture industrial robots. Basically, the proposed hybrid controller consists of force feedback loops and position feedforward loops in a Cartesian coordinate system. Hence, the position control system and force control system do not interfere with each other, so that the position will gradually deviate from the desired trajectory due to the manipulated variable of the force feedback loop. This phenomenon is a serious problem, for example, when developing an accurate mold polishing robot. The mold polishing robot is required to be able to exert stable force control and regular pick feed control. That means the compatibility between position control and force control should be realized. In order to cope with this problem, we have proposed a novel hybrid position/force control method with weak coupling between the position feedback loop and the force feedback loop. Fig. 4.4 shows the block diagram of the proposed controller, in which position feedback loops become active only in selected directions by using a switch matrix S p = [Spx Spy Spz 0 0 0]T . Note that the force feedback control law generates the normal velocity v n = [vnx vny vnz 0 0 0]T given by Eq. (1.17), the position feedback law outputs the velocity v p = [vpx vpy vpz 0 0 0]T given by Eq. (4.15), and the position/orientation feedforward control law produces the velocity vector v t = [vtx vty vtz vrx vry vrz ]T given by Eqs. (3.6), (3.7), (3.8) and (4.8). The summation of the vectors v n , v p and v t is output to the reference of the servo controller of the robot.

After this section, three applied examples of the proposed hybrid position/force control method are introduced. They are the 3D robot sander [11], the mold polishing robot [25] and the desktop-size orthogonal-type robot [76]. 97

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4.4 Robotic sanding system for wooden parts with curved surfaces

Recently, open-architecture industrial robots have been proposed to comply with various users’ requests with regard to application developments. The industrial robot has an open programming interface for Windows or Linux, so that we can try to program new functions such as force control, compliance control and so on. The six-DOFs (Degree of Freedoms) industrial robot shown in Fig. 4.5 is a model called FS30L with a PC-based controller provided by Kawasaki Heavy Industries. The proposed robotic sanding system is developed based on the industrial robot whose tip has a compact force sensor. A small sanding tool as shown in Fig. 4.1 can be easily attached to the tip of the robot arm via the force sensor. A PC is connected to the PC-based controller via an optical fiber cable. The PC-based controller provides several Windows Application Programming Interface (API) functions, such as servo control with joint angles, forward/inverse kinematics, coordinate transformation and so on. By using such API functions and a Windows timer, for instance, the position/orientation control at the tip of the robot arm can be realized easily and safely. In the following subsection, the surface-following controller is implemented for robotic sanding using the Windows API functions. Fig. 4.6 shows the hardware block diagram between the controller and Windows PC. Although the standard Windows timer was set to 10 msec, the actual rate measured by an oscilloscope was sometimes about 15 msec. To solve the problem, a stable and high sampling rate of 1 msec could be easily realized using the Windows multimedia timer. We confirmed the sampling rate of 1 msec by using a digital data logger. 98

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KAWASAKI FS30L

Figure 4.5: Robotic sanding system developed based on an open-architecture industrial robot KAWASAKI FS30L.

Windows PC( Multimedia Timer : 1 msec. )

Impedance Model Following x& (k ) Force Controller

API

Device Driver

F (k )

Receiver Board

DSP

DPRAM

Receiver Board

AS Program

DPRAM

3D Robot Sander

Servo Controller Industrial Robot FS30L

Force Sensor

Robot

Figure 4.6: Hardware block diagram between a Windows PC and a PC-based controller.

99

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4.5 Surface-following control robotic sanding system

for

The robotic sanding system has two main features: one is that neither conventional complicated teaching tasks nor post-processor (CL data → NC data) is required; the other is that the polishing force acting on the sanding tool and the tool’s position/orientation are simultaneously controlled along free-formed curved surface. In this section, a surface-following control method, indispensable for realizing the features, is described in detail. A robotic sanding task needs a desired trajectory so that the sanding tool attached to the tip of the robot arm can follow the object’s surface, keeping contact with the surface from the normal direction. In executing a motion using an industrial robot, the trajectory is generally obtained in advance, e.g., through conventional robotic teaching process. When the conventional teaching for an object with a complex curved surface is conducted, the operator has to input a large number of teaching points along the surface. Such a teaching task is complicated and time-consuming. Next, a sanding strategy for dealing with the polishing force is described in detail [11, 83]. The polishing force vector F (k) = [Fx (k) Fy (k) Fz (k)]T is assumed to be the resultant force of contact force vector f (k) = [fx (k) fy (k) fz (k)]T and kinetic friction force vector −F r (k) = −[Frx (k) Fry (k) Frz (k)]T that are given to the workpiece as shown in Fig 4.7, where the sanding tool is moving along on the surface from (A) to (B). F r (k) is written by F r (k) = −diag(µx , µy , µz )∥f (k)∥

v t (k) − diag(ηx , ηy , ηz )v t (k) ∥v t (k)∥ (4.9)

where diag(µx , µy , µz )∥f (k)∥(v t (k)/∥v t (k)∥) is the Coulomb friction, and 100

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diag(ηx , ηy , ηz )v t (k) is the viscous friction. µi and ηi (i = x, y, z) are the i-directional coefficients of Coulomb friction per unit contact force and of viscous friction, respectively. Each friction force is generated by f (k) and v t (k), respectively. F (k) is represented by (4.10)

F (k) = f (k) − F r (k)

The polishing force magnitude can be easily measured using a three-DOFs force sensor attached between the tip of the arm and the sanding tool, which is given by ∥F (k)∥=

√{

SF

}2

x (k)

+

{

SF

y (k)

}2

+

{

SF

}2

z (k)

(4.11)

where SFx (k), SFy (k) and SFz (k) are the each directional component of force sensor measurements in sensor coordinate system. The force sensor used is the NITTA IFS67M25A with a sampling rate of 8 kHz. Although the IFS67M25A is a six-DOFs force/moment sensor, the moment components were ignored because the moment data were not needed in force control system. In the following subsection, the error Ef (k) of polishing force magnitude is calculated by Ef (k) = ∥F (k)∥−Fd

(4.12)

where Fd is a desired polishing force.

4.6 Feedback control of polishing force In the wooden furniture manufacturing industry, skilled workers usually use small, air-driven tools to finish the surface after machining or painting. These types of tools cause high frequency and large magnitude vibrations, so that it is difficult for the skilled workers to sand the workpiece keeping the polishing force a desired value. Consequently, undesirable unevenness tends to appear on the sanded surface. 101

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Tip of robot arm

Force sensor NITTA: IFS-67M25A Sampling rate: 8 kHz

(A)

Sanding tool

Fr

vt (B)

f Workpiece

F

Figure 4.7: Polishing force F (k) composed of contact force f (k) and kinetic friction force F r (k).

In order to achieve a good surface finish, it is fundamental to stably control the polishing force. When the robotic sanding system runs, the polishing force is controlled by the impedance model following force control with integral action given by B

− Md ∆t

vnormal (k) = vnormal (k − 1) e )K

−1

f

Bd

d

(

Ef (k) + Kf i

k ∑

B

− Md ∆t

− e

d

(4.13) Ef (n)

n=1

where vnormal (k) is the velocity scalar; Kf is the force feedback gain; Kf i is the integral control gain; Md and Bd are the desired mass and desired damping coefficients, respectively. ∆t is the sampling width. Using vnormal (k), the normal velocity vector v n (k) = [vnx (k) vny (k) vnz (k)] at the center of the contact point is represented by v n (k) = vnormal (k)

od (k) ∥od (k)∥

(4.14)

where od (k) is the normal vector at the contact point, which are obtained from Eqs. (4.5), (4.6) and (4.7). 102

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Figure 4.8: Zigzag path generated from the main-processor of a CAM system. Each through point has a position and an orientation components

4.7 Feedforward and feedback control of position Currently, wooden furniture is designed and machined with 3D CAD/CAM systems and NC machine tools, respectively. Accordingly, the CL data generated from the mainprocessor of the CAM (as shown in Fig. 4.8) can be used to obtain the desired trajectory of the sanding tool. The tool path (CL data) as shown in Fig 4.8, which is calculated in advance based on a zigzag path, is considered to be a desired trajectory of the sanding tool. The block diagram of the surface-following controller implemented in the robot sander is shown in Fig. 4.4. The position and orientation of the tool attached to the tip of the robot arm are feedforwardly controlled by the tangential velocity v t (k) and rotational velocity v r (k), respectively referring xd (k) and od (k). v t (k) is given through an open-loop action so as not to interfere with the force feedback loop. The polishing force is regulated by v n (k) which is perpendicular to v t (k). v n (k) is given to the normal direction referring the 103

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orientation vector od (k). It should be noted, however, that using only v t (k) is not enough to precisely carry out the desired trajectory control along the CL data: Actual trajectory tends to deviate from the desired one, so that the constant pick feed (e.g., 20 mm) cannot be performed. This undesirable phenomenon leads to a lack of uniformity on the surface. To overcome this problem, a simple position feedback loop with small gains is added as shown in Fig. 4.4, so that the tool does not seriously deviate from the desired pick feed. The position feedback control law generates another velocity v p (k) given by {

v p (k) = S p K p E p (k) + K i

k ∑

n=1

}

E p (n)

(4.15)

where S p = diag(Spx , Spy , Spz ) is a switch matrix to realize a weak coupling control in each direction. If S p = diag(1, 1, 1), then the coupling control is active in all directions; whereas if S p = diag(0, 0, 0), then the position feedback loop does not contribute to the force feedback loop in all directions. E p (k) = xd (k) − x(k) is the position error vector. x(k) is the current position of the sanding tool attached to the tip of the arm and is obtained from the forward kinematics of the robot. K p = diag(Kpx , Kpy , Kpz ) and K i = diag(Kix , Kiy , Kiz ) are the position feedback gain and its integral gain matrices, respectively. Each component of K p and K i must be set to small values so as not to obviously disturb the force control loop. Finally, recomposed velocities v ˜n (k) = [v Tn (k) 0 0 0]T , v ˜t (k) = [v Tt (k) v Tr (k)]T T T and v ˜p (k) = [v p (k) 0 0 0] are summed up to a velocity command v(k), and the v(k) is given to the reference of the Cartesian-based servo controller of the industrial robot. It can be guessed that the complete six constraints, which consist of three-DOFs positions and three-DOFs forces in a constraint frame, cannot be simultaneously satisfied [10]. However, the delicate cooperation between the position feedback loop and force feedback loop is an important 104

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FORCE/1.0 POWER/4.0 CONTACT/2.0 VELOCITY/50.0 GOTO/20.0008,300.0000,-6.8004,0.0096482,0.0893400,0.9959545 GOTO/32.1883,300.0000,-6.9395,0.0130900,0.0850632,0.9962896 GOTO/44.3758,300.0000,-7.1206,0.0165358,0.0769387,0.9968987 GOTO/56.5633,300.0000,-7.3438,0.0199903,0.0649396,0.9976890 GOTO/68.7508,300.0000,-7.6090,0.0234558,0.0490319,0.9985218 FORCE/0.000,0.000,2.000,0.000,0.000,0.000 POWER/6.0 VELOCITY/30.0

Figure 4.9: Example of proposed hyper CL data.

key point to achieve successful robotic sanding with a curved surface.

4.8 Hyper CL data One of the features of the robot sander is that the CL data are referred to as the desired trajectory of the sanding tool attached to the tip of the arm. Therefore, the complicated teaching process can be completely omitted. It is also useful that no post-processor optionally included in CAM is required to transform the CL data into the NC data, i.e., the robot sander does not run based on the NC data but the CL data. The conventional CL data mainly deal with static positions and orientations along the curved surface of a model. In order to realize such a skillful sanding as skilled workers perform, we propose hyper CL data that can describe serviceable items as shown in Fig. 4.9. For example, the following conditions can be specified: 1. Desired polishing force acting between a sanding tool and a workpiece. 2. Sanding power such as motor torque or air pressure. 105

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3. Feed rate (tangential velocity along a curved surface) 4. Task mode change (contact mode ↔ noncontact mode), etc. The desired polishing force Fd N is recognized by FORCE/Fd

(4.16)

The air pressure P Pa of an air-driven sanding tool is regulated by POWER/P

(4.17)

The feed rate norm ∥v t ∥ mm/s in contact state is set by VELOCITY/∥v t ∥

(4.18)

The task mode change from contact mode to noncontact mode is switched by NONCONTACT/vm , d

(4.19)

where the sanding tool takes off from the workpiece with vm mm/s to the normal direction; d mm is the distance to be moved. On the other hand, the task mode change from noncontact mode to contact mode is switched by CONTACT/v

(4.20)

where v mm/s is the approaching velocity from the normal direction. Due to the hyper CL data, it has become possible to record sanding ability in detail.

4.9 Experimental result In this subsection, the result of an experiment involving surface sanding experiment using the proposed robot sander is given. The overview of the robot sander developed, based on the KAWASAKI FS20, is shown in Fig. 4.10. The orbital 106

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Electro pneumatic regulator

Robot sander

Regulated compressed air

Compressed air

D/A Force sensor measurement

Air compressor

D/A

Sanding parameters 3D data Hyper CL data

Robot control application

Servo controller

Figure 4.10: Overview of the robot sander developed based on KAWASAKI FS20.

Table 4.1: Sanding conditions and control parameters Conditions or parameters Robot Force sensor Workpiece Size (mm) Diameter of sandpaper (mm) Grain size of sandpaper (#) Desired polishing force Fd (kgf) Feed rate ∥v t ∥ (mm/s) Pick feed of CL data (mm) Air pressure of orbital sanding tool (kgf/cm2 ) Desired mass coefficient Md (kgf·s2 /mm) Desired damping coefficient Bd (kgf·s/mm) Force feedback gain Kf Integral control gain for polishing force Kf i Switch matrix for weak coupling control S p Position feedback gain matrix K p Integral control gain matrix K i for position Sampling width ∆t (ms)

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Values KAWASAKI FS30L NITTA IFS-100M40A Japanese oak 1200 × 425 × 85 65 80→220→400 1.0 30 15 4.0 0.01 20 1 0.001 diag(0, 1, 0) diag(0, 0.01, 0) diag(0, 0.0001, 0) 0.01

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sanding tool is widely used by skilled workers to sand or finish a workpiece with curved surfaces. The base of the orbital sanding tool can perform eccentric motions. That is why the orbital sander is not only a powerful sanding tool but also gives good surface finishing with fewer scratches. In this experiment, an orbital sanding tool is selected and attached to the tip of the robot arm via a force sensor. The diameter of the circular base and the eccentricity are 90 mm and 4 mm, respectively. The weight of the sanding tool is about 1.5 kg. When a sanding task is conducted, a circular pad with sanding paper is attached to the base. Fig. 4.11 shows the sanding scene using the robot sander based on a KAWASAKI FS30L. In this case, the polishing force was satisfactorily controlled to a suitable value. Smaller, air-driven tools are usually used by skilled workers to sand wooden material used in furniture. These types of tools cause large amounts of noise and vibration. Furthermore, the system of force control consists of an industrial robot, force sensor, attachment, small air-driven tool, jig and wooden material. Because each is quite stiff, it is not easy to keep the polishing force a constant value without overshoot and oscillation. That is why the measured value of the polishing force tends to have spikes and noise. However, the result would be much better than the one given by skilled workers. Although it is difficult for skilled workers to simultaneously keep the polishing force, tool position and orientation correct even for a few minutes, the robot sander can perform the task more uniformly for greater amounts of time. The photograph on the left of Fig. 4.12 shows an example of the target workpieces after NC machining, i.e., before sanding, which is a typical shape that the conventional sanding machines cannot sand sufficiently. The pick feed in the NC machining is set to 3 mm. The surface before sanding shown has undesirable cusp marks higher than 3 mm every pick feed. The robot sander first removed the cusp marks using a rough sanding paper ♯80, then sanded the surface us108

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Figure 4.11: Sanding scenes using the proposed 3D robot sander developed based on a KAWASAKI FS30L.

Large cusp marks

Smooth surface

Before sanding

After sanding

Figure 4.12: Curved surfaces before and after polishing process.

Figure 4.13: Wooden chair with an artistic curved surface (Courtesy of Furniture Workshop Nishida).

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ing a sanding paper with a middle roughness ♯220 and finally a smooth paper ♯400. The diameters of the pad and paper were cut to 65 mm, which were so larger than that of the ball-end mill (17 mm) used in the NC machining process. The pad is put between the base and the sanding paper. Therefore, we regenerated the CL data with a pick feed 15 mm for the robotic sanding and substituted the CL data for the controller shown in Fig. 4.10. The contour was made so as to be a small size with an offset of 15 mm to prevent the edge of the workpiece from over-sanding. Table 4.1 shows the other sanding conditions and parameters of the surfacefollowing controller. These semi-optimum values were found through trial and error. The photograph on the right of Fig. 4.12 shows the surface after the sanding process. The surface felt very satisfactory when touched with both the fingers and the palm. Undesirable cusp marks were not observed at all. Moreover, there was no over-sanding around the edge of the workpiece and no swell on the surface. Furthermore, we conducted a quantitative evaluation using a stylus instrument, so that the measurements obtained by the arithmetical mean roughness (Ra) and max height (Ry) were around 1 µm and 3 µm, respectively. Figure 4.13 shows a piece of new artistic furniture using the workpiece sanded by the robot sander. It was confirmed from the experimental result that the proposed robotic sanding system could successfully sand wooden workpieces with curved surfaces.

4.10 Conclusion This chapter has dealt with a robotic sanding system for attractively designed furniture with free-formed surfaces. The system has been developed using an industrial robot with an open-architecture controller. The system has two novel features. One is that the surface-following controller developed for robotic sanding allows the robot to simultaneously realize a delicate polishing force control and 110

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smooth position/orientation control. The other is that conventional and complicated teaching task is not required at all. When conventional sanding systems based on an industrial robot are used, the desired trajectory for a tool’s position/orientation control is obtained through a complicated teaching process. In this case, the operator has to input a large number of teaching points along the object’s surface. However, the proposed robot sander directly handles CL data generated from the 3D CAD/CAM, so that this teaching process can be omitted. Experimentally, the sanding tool attached to the tip of the robot arm could smoothly follow the curved surface, keeping a contact from the normal direction with a desired polishing force. It was also demonstrated that the proposed system could successfully sand the curved surface of attractive furniture, resulting in very high-quality products. The process parameters such as sanding conditions and control gains given in the experiments were tuned with trial and error in consideration of efficiency and sanded surface quality, and worked well for the examples shown in this paper. However, if the robot sander is applied to different materials, desirable parameters (i.e., semi-optimized parameters) should be found again, because the desirable parameters tend largely to depend on the type of wood. In the future, we plan to accumulate a database that has promising relations between the type of wooden material and desirable parameters. Although the parameters should be further tuned time-varyingly and delicately in compliance with intra-species variations as well as directionality and changes in a single workpiece, no practical on-line assessment techniques for wooden materials seem to be being proposed at this stage.

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5 3D machining system for artistic wooden paint rollers DOI: 10.1533/9780857094636.113 Abstract: In this chapter, an intelligent machining system based on an NC machine tool with a rotary unit is introduced to efficiently and easily produce many kinds of artistically designed wooden paint rollers. A post-processor with the fuzzy feed rate generator is also presented to effectively make the machining system run. The post-processor allows the NC machine tool to easily transcribe a relief design from the surface on a flat model to the one on a cylindrical workpiece. The fuzzy feed rate generator generates suitable feed rate values according to the curvature of each relief design. Experimental results show that artistically designed wooden paint rollers can be successfully carved using the proposed machining system. Key words: wooden paint roller, five-axis NC machine tool with a tilting head, post processor, NC machine tool with a rotary unit, fuzzy feed rate generator

5.1 Background Fukuoka prefecture is one of the largest furniture manufacturers in Japan. The interior city Ohkawa is located at 113

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the south part of Fukuoka. Although furniture is mainly made from various wooden materials, the production of furniture has been gradually decreased in two decades because of changes in consumer preference and industrial structure. As a result, other promising wooden products are currently being considered in order to efficiently use wood resources in Fukuoka. As one example, wooden paint rollers attract our attention. In the home-decorating industry, handheld paint rollers with a simple pattern are generally used to transcribe a design to a wall just after painting. Interior planners and decorators want to use more artistically designed paint rollers to cope with various user needs, but the pattern designs are limited to several common ones. In order to efficiently provide user-oriented roller designs, a new 3D design and machining system should be considered for limited production with a wide variety of wooden paint rollers. However, it is not easy to perform its elaborate carving even when the latest woodworking machinery is used, because wooden paint rollers have a cylindrical shape. In the furniture manufacturing industry, since three-axis NC machine tools and five-axis NC machine tools with a tilting head are generally used, a new machining system for wooden paint rollers should be designed, keeping the use of such conventional machine tools in order to save investment in equipment. Five-axis NC machine tools have a major advantage over three-axis ones when machining a free-form surface efficiently. Up to now, 3D machining systems based on a five-axis NC machine tool have been actively developed and studied in various manufacturing industries. Takeuchi et al. [45,46] proposed a general method for generating NC data from the collision-free tool path of five-axis control machining centers. The post-processor they developed can convert CL data to actual NC data, taking account of the structure of machining centers, linearization, feed rate control and spindle rotation control. Xu et al. [47] presented a technique to avoid inefficient five-axis machining practices by automat114

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ically creating and verifying a feasible tool-path prior to the actual metal cutting. Chen et al. [48] developed a hybrid five-DOFs parallel kinematic machine tool constructed using the TRR-XY mechanism and its post-processing system. The effects of the cutter shapes and the machine construction on the post-processing were investigated. Lei et al. [49] developed a novel probe-ball measurement device which was designed to measure the overall position errors of a five-axis machine tool, and a method using double ballbar [50] was proposed to inspect the motion errors of the rotary axes out of five-axes. Furthermore, Cao et al. [51,52] proposed an offset approach of machining freeform surfaces using a five-axis NC machine tool with a cylindrical cutter or toroidal cutter, in which Archimedes’ helicoidal surface, pseudo-sphere and hyperbolic paraboloid surfaces were successfully machined. When a five-axis NC machine tool with a tilting head, generally used in the furniture manufacturing industry, is applied to cylindrical machining or carving, a workpiece can not be made in a single pass, i.e. it needs to perform complicated repositionings several times as well as achieving a special jig. Such a five-axis NC machine tool does not seem to be successfully used for the manufacturing of wooden paint rollers with a relief design at present, due to the complexity of the process and the resulting workpiece setup time. There are several research projects which tackle feed rate problems. For example, Timar et al. [53] developed an algorithm which computes the time-optimal feed rate variation along a curved path. Heo et al. [54] proposed a machining time estimation model using NC block distributions. An intelligent contour control strategy was investigated to improve the contour error of CNC machine tools by Tarng et al. [55], in which a cross-coupled fuzzy feed rate control scheme was presented to reduce the contour error. Zuperl et al. [56] discussed the application of a fuzzy adaptive control strategy to the problem of cutting force control in high-speed end-milling operations, in which it is designed to adaptively maximize the feed-rate subject to an allowable 115

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cutting force on the tool. Farouki et al. [57] reported variable feed rate CNC interpolators for constant material removal rates along Pythagorean hodograph (PH) curves. The proposed curvature-compensated feed rate scheme has important potential applications in ensuring part accuracy and in optimizing part programs consistent with a prescribed accuracy. Furthermore, a new class of machine codes for the specification of PH curve tool paths and associated feed rate functions was proposed in [58]. In that study, experimental results from an implementation of real-time PH curve interpolators on an open-architecture CNC milling machine are described. However, it is not easy for engineering users to apply such methods to conventional NC machine tools without using an open-architecture controller. In addition to the above research, there are already in commercial use machines that incorporate nonlinear interpolation (e.g. the non-uniform rational B-spline curve interpolation known as the NURBS interpolation) into NC programs to improve overall machining. Optimization programs are available to automatically adjust the feed rate based on NURBS curves. However, it requires not only a special controller which can deal with NC program interpolated by an NURBS curve, but also a corresponding CAM system which can generate an NURBS code such as G06. From the viewpoint of equipment cost, it is also important to consider how to effectively utilize conventional machine tools in the manufacturing of wooden products. Improvements to advanced cylindrical grinding machines have been also proposed. For example, Frank et al. [59] developed a CNC cylindrical grinding machine for non-circular workpieces. Although parts with circular and non-circular cross-sections could be completely machined in one operation, the performance on circular cross-sections with small edges was not mentioned. Therefore, the grinding machine would not be able to carve a wooden paint roller, the cylindrical surface of which has many small edges. Couey et al. [60] showed that force measurements were capable of 116

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providing useful feedback in precision grinding with excellent contact sensitivity, resolution, and detection of events occurring within a single revolution of the grinding wheel. Tawakoli et al. [61] developed a prototype internal grinding machine based on new kinematics. The target was to defeat some problems of internal grinding such as poor enrichment of coolant lubricant, deflection of grinding tool, and so on. Summarizing the above, it can be seen that the easy suppression of undesirable edge chippings in machining cylindrical wooden workpieces with a relief design has not been discussed yet. In this chapter, a 3D design and machining system based on a three-axis NC machine tool with a rotary unit is introduced efficiently and at a low price to produce wooden paint rollers with an artistic design. A key point is to use common, conventional three-axis NC machine tools. In order to realize the machining system effectively, the following two points are considered in designing a corresponding post-processor. One is a basic function which efficiently generates suitable NC data to carve a relief design on a cylindrical wooden workpiece. The proposed postprocessor transforms a base tool path called cutter location data to NC data, mapping the y-directional pick feed to the rotational angle of the rotary unit [62]. The other is a systematic generation of feed rate values to suppress edge chippings on a relief design and to shorten the cycle time required for machining. Edge chipping is a particular problem when a wooden workpiece is machined by a router bit, because wooden workpieces are considerably more brittle than metallic materials. Edge chipping tends to appear with the increment of feed rate. Our proposed post-processor generates suitable feed rate values using a simple fuzzy reasoning method based on an operator’s experience and skill, while checking edges and curvatures calculated based on positions in CL data. The variation of curvature can be estimated by calculating the variation of the distance between two adjacent positions in CL data. The results of the experiment show that wooden paint rollers with an artistic relief design 117

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can be successfully carved without any chipping.

5.2 Conventional five-axis nc machine tool with a tilting head In this section, a 3D machining system based on a fiveaxis NC machine tool with a tilting head is evaluated as a conventional system [63]. The five-axis NC machine tool is one of the most representative and popular machine tools in wood product manufacturing. The machining system consists of a 3D CAD/CAM with variable axis function and a post-processor. Fig. 5.1 shows the five-axis NC machine tool (HEIAN FF-151MC). The NC machine tool has a tilting head that can be simultaneously inclined and rotated. It should be noted however that corrected NC data are required to run the NC machine tool as a computer simulation. The post process generally means to compute corrected NC data from CL data. Fig. 5.2 shows the general process to calculate the corrected NC data for the five-axis NC machine tool. Examples of paint rollers with a relief design are shown in Fig. 5.3. We first draw the model of the relief design using a 3D CAD. Secondly, the CAM parameters such as pick feed, path pattern (e.g., zigzag path), in/out tolerances and so on are set according to the requirement of actual machining. The main-processor of the CAM calculates cutter paths using the parameters. The cutter paths are called CL data. The i-th step CL(i) in CL data is composed of position vector p(i) = [x(i) y(i) z(i)]T and normal direction vector n(i) = [vx (i) xy (i) vz (i)]T as written by CL(i) = [x(i) y(i) z(i) vx (i) vy (i) vz (i)]T 2

2

2

{vx (i)} + {vy (i)} + {vz (i)} = 1

(5.1) (5.2)

Finally, the post-processor generates the corrected NC data for the five-axis NC machine tool with a tilting head, by only considering a tool length [63]. Fig. 5.4 shows the tiltable 118

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main head which has a ball-end mill at the tip. The tool length L1 + L2 is defined as the distance from the center of swing to the tip of the end mill, which should be measured in advance. The post-processor transforms the CL data into NC data for five-axis NC machine tools as shown in Fig. 5.1. The main head can be inclined around y-axis and rotated around z-axis within the range ± 90 and ± 180 degrees, respectively. The inclined and rotated axes are called the fourth axis (B-axis) and fifth axis (C-axis), respectively. The i-th step in the corrected NC data is written by N C(i) = [˜ x(i) y˜(i) z˜(i) b(i) c(i)]T ˜j(i) = j(i) + vj (i)(L1 + L2 ), j = x, y, z

(5.3) (5.4)

where b(i) and c(i) are the head angles of the inclination and rotation as shown in Fig. 5.5, respectively. The CL data generated from the main-processor of the CAM are composed of sequential points on the model surface as shown in Fig. 5.6. If the NC data are transformed from the CL data without considering the tool length and are given to the NC machine tool, then the center of swing is obliged to directly follow the NC data. As can be guessed, this would result in a serious and dangerous interference between the main head and the workpiece. However, if the center of swing follows the corrected NC data given by Eq. (5.3) and Eq. (5.4), the tip of the ball-end mill can desirably move along the model surface as shown in Fig. 5.6. Fig. 5.7 shows a designed model with a curved surface and the machining scene. It has been proved from the machining experiment that the proposed post-processor can generate suitable NC codes for the five-axis NC machine tool with a tilting head. Recently, such a five-axis NC machine tool with a tilting head has become the subject of attention in wooden product manufacturing. However, it has been recognized from a machining experiment that the five-axis NC machine tool is not good at carving roller models, as shown in Fig. 5.3. Although its high machining performance is expected to exceed the capability of standard NC machine tools, it has 119

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Figure 5.1: Conventional five-axis NC machine tool with a tilting head.

hardly been used for carving roller models yet. The main reason is that the roller models as shown in Fig. 5.3 cannot be machined in a single path of the cutter, i.e. models must be machined using several paths of the cutter, requiring extensive cutter repositioning; thus the 3D machining of artistically designed paint rollers is complicated and time consuming. Furthermore, it is not easy to model a relief design on a cylindrical shape. To overcome these problems, a 3D machining system based on a three-axis NC machine tool with a rotary unit is introduced in the next section.

5.3 Intelligent machining system for artistic design of wooden paint rollers As described in the previous section, wooden paint rollers have a cylindrical shape with an artistic design, so that it is not easy to achieve elaborate carving even when the latest woodworking machinery such as a five-axis NC machine tool with a tilting head is used. Generally, metallic cylin120

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Creating Creating aa 3D 3D model model Considering Considering machining machining parameters parameters Generating Generating CL CL data data by by main-processor main-processor Generating Generating NC NC data data by by post-processor post-processor Figure 5.2: Main- and post-processes to compute corrected NC data for five-axis NC machine tool.

Figure 5.3: Artistic paint roller models designed by 3D CAD.

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Tool length

Controller design for industrial robots and machine tools

L1

L2

Figure 5.4: Definition of the tool length of a tilting head.

Side view

Front view

Z

Z

Y

X

+B

-C

-B

+C

Figure 5.5: Inclination and rotation of main head.

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Center of swing

Tip of ball-end mill

Figure 5.6: Motion of tip of ball-end mill generated from main-processor.

(a) Model with curved surface

(b) Five-axis machining

Figure 5.7: Sample model with curved surface and the five-axis machining scene.

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drical parts are precisely processed by an expensive CNC turning centre with milling capability. However, three-axis NC machine tools and five-axis NC machine tools with a tilting head have been widely used in the furniture manufacturing industry, and therefore it is necessary (when considering equipment cost) that new woodworking machinery for wooden paint rollers should be designed to utilize existing NC machine tools. In this section, a three-axis NC machine tool with a rotary unit and its post-processor are proposed to efficiently produce artistic wooden paint rollers of many kinds of designs. The proposed machining system is realized easily and at a low price only by adding a simple rotary unit to a conventional three-axis NC machine tool. The post-processor provides two effective functions. One is technique to transform CL data without feed rate values to NC data, mapping the y-directional pick feeds to rotational angles of the rotary unit. The post-processor allows a well-known three-axis NC machine tool to easily transcribe a relief design from the surface of a flat model to that of a cylindrical model. The other is an elaborate addition of feed rate values according to the curvature of each design to protect the cylindrical surface from undesirable edge chippings. The post-processor generates safe feed rate values by using a simple fuzzy reasoning method while checking edges and curvatures in a relief design, and appends them into NC data. The post-processed NC data act gently on the fragile edges of wooden paint rollers.

5.3.1 Post-processor for a three-axis NC machine tool with a rotary unit Conventional paint rollers generally have no artistic designs at all, and the designs are limited to flat or simple patterns even if they have. As mentioned in the previous section, unfortunately, it is not easy to carve a relief design on a cylindrical model even if the five-axis NC machine tool with a tilting head is used. First of all, we discuss a 124

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problem concerning the 3D machining of wooden cylindrical shapes with a relief design. When the modeling of a roller is conducted using a 3D CAD, a base cylindrical shape is modeled in advance. Then a relief design is drawn on the cylindrical model. However, the modeling of the relief design on the cylindrical shape, as shown in Fig. 5.3, is a complicated task, even when 3D CAD software is used. Next, it is also not easy to realize 3D machining using the five-axis NC machine tool with a tilting head, in which the NC data generated from the CAM are composed of x-, y-, z-, b- and c- directional components. Thus, to easily provide many kinds of paint rollers with a wide variety and low volume to the home decorating industries, a machining system that can directly carve an artistic relief design on a cylindrical workpiece must be developed. In this subsection, to solve these problems, a new 3D machining system is considered based on a three-axis NC machine tool with a rotary unit, and a post-processor is proposed for the rotary unit. The overview of the proposed machining scheme is illustrated in Fig. 5.8. The post-processor allows such conventional woodworking machinery as the three-axis NC machine tool to elaborately produce wooden paint rollers. An artistic design drawn on a flat model surface can be easily transcribed to a cylindrical model surface. In the remainder of this section, the system is described in detail. A three-axis NC machine tool with x-, y- and z-axes must be first prepared to realize the proposed concept. As an example, an NC machine tool MDX-650A provided by Roland D.G. as shown in Fig. 5.9 is used for experiments. The NC machine tool is equipped with an auto tool changer ZAT-650 and a rotary unit ZCL-650A. The mechanical resolution of the rotary unit is about 0.0027 degrees. The NC machine tool has four DOFs, i.e., three translations and one rotation. This subsection addresses how to easily make a wooden paint roller with an artistic relief design. The most important point is that proper NC data for the NC machine tool with a rotary unit can be generated in 125

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one step. To meet this aim, the post-processor generates the NC data which transcribe the design on a flat model to that on a cylindrical model. By applying the post-processed NC data, the NC machine tool can directly carve an artistic relief design on a cylindrical workpiece. Next, we describe on the feature of the post-processor. A desired relief design is first modeled on a flat base model as shown in Fig. 5.10. CL data are secondly generated with a zigzag path as shown in Fig. 5.11. In this case, the coordinate system should be set so that the pick feed direction is parallel to the table slide direction of the NC machine tool, i.e., y-direction. The proposed post-processor transforms the CL data without ฀gFEDRAT/฀h statements into the corresponding NC data, mapping the y-directional position to the rotational angle of the rotary unit. As can be seen from the components of the NC data, when the rotary unit is active, the table slide motion in y-direction is inactive. The post-processor first checks all steps in the CL data, and extracts the minimum value y_min and the maximum value y_max in y-direction. The angle a(i) for the rotary unit at the i-th step is calculated from

a(i) =

360 × {y(i) − y_min } y_length

(5.5)

where y_length is the length in y-direction, which is easily obtained by y_max − y_min . The CL data p(i) = [x(i) y(i) z(i)]T at the i-th step is transformed into the NC data composed of [x(i) a(i) z(i)]T by using Eq. (5.5). The length in y-direction is transformed into the circumference of the roller model. It is expected that the relief design shown in Fig. 5.10 is desirably carved on the surface of a cylindrical workpiece. Thus, the proposed system provides a function that easily transcribes an artistic design from the surface on a flat model to that on a cylindrical wooden workpiece fixed to the rotary unit. 126

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Post Post processor processor ロータリー加工用ポストプロセッサ with with aa fuzzy fuzzy feed feed による加工データの変換 rate generator

rate generator Artistic design on a flat model・通常の加工データを生成

Wooden paint roller

Post process for a rotary unit and wood material

Generating a zigzag path without feed rates

Efficient machining suppressing edge chippings

Figure 5.8: Overview of the proposed machining scheme for cylindrical wooden workpieces.

Figure 5.9: Three-axis NC machine tool MDX-650A with a rotary unit.

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Figure 5.10: Relief design illustrated by a 3D CAD.

5.3.2 Feed rate generation using fuzzy reasoning It is generally known that feed rate is one of the most important parameters to smoothly control NC machine tools and to reduce the total machining time. Wooden materials are essentially brittle in machining, so the regulation of feed rate is especially significant to protect the surface from an edge chipping as shown in Fig. 5.12. The key factors that affect the feed rate to be set are mainly the complexity of the relief design and the kind of wooden material. The feed rate must be adjusted not only to avoid the edge chipping on the cylindrical wooden workpiece, but also to shorten the machining time. When a common 3D CAD/CAM is used, the feed rate values are given with a ฀gFEDRAT/฀h statement in the CL data through the main process of CAM, and Fcodes such as F3000.0 (i.e., 3000 mm/min.) corresponding to the feed rate values are written in NC data through post process. Thus, the feed rate value cannot be considered and generated in the post process, which is very inconvenient and a drawback for the case of using a common 3D CAD/CAM. Feed rates should be recalculated rapidly according to an 128

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actual machining situation. Also, if the cutter path has a large curvature or small edge then undesirable material chipping becomes easy to occur. This means that the machining accuracy tends to decrease, and therefore we cannot obtain a shape faithful to the model designed by 3D CAD. In particular, when a wooden paint roller with a relief design is machined, the problem of edge chipping cannot be avoided. Therefore, the feed rate should be slowed down suitably so that a small artistic design is not damaged by the edge chipping. Note, however, that conventional post-processors do not possess the function to systematically and elaborately decrease feed rate values according to linear interpolated positions given by ฀gGOTO/฀h statements in CL data. In other words, the operator must return to the main-process of CAM to correct the feed rate values.

The proposed post-processor has a function that can automatically generate feed rate values, e.g. F1000.0, from CL data without using feed rate statements according to the curvature of each model, not only to stop edge chipping but also to shorten the machining time. When the postprocessor is used, the operator sets only two parameters, which are the minimum and maximum values of the feed rate. Of course, the post-processor is easily applied to NC machine tools that do not have an open-architecture controller. Generally, the main-processor of CAM calculates the CL data p(i) = [x(i) y(i) z(i)]T with a linear approximation so that a workpiece can be machined within the tolerance of a designed model. Therefore, the larger the curvature, the higher its point density. Accordingly, considering the curvature results in acquiring the distance d(i) = ∥p(i + 1) − p(i)∥ between two adjacent steps in CL data and its increment ∆d(i) = d(i + 1) − d(i). Fig. 5.13 shows an example for the relation between the distance and the point density with respect to CL data. 129

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y_max

y_pick k fe P ic ed n ctio d i re (y)

y_min

on ( x recti i d d Fee

)

Figure 5.11: An example of zigzag path on a flat model (y_length = y_max − y_min ).

Router bit

Chipping

Figure 5.12: Typical edge chipping

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5.3.3 Fuzzy feed rate generator

In this section, we propose a fuzzy feed rate generator that generates suitable feed rate values according to d(i) and ∆d(i). The fuzzy feed rate generator consists of two simple fuzzy reasoning parts whose consequent parts have constant values. When the current position X(k) = [X(k) Y (k) Z(k)]T of the end mill at the discrete time k is X(k) ∈ [p(i), p(i + 1)], the fuzzy rules are described by Rule 1: IF d(i) is Rule 2: IF d(i) is .. .

A˜1 THEN FA˜ (i) = cA 1 A˜2 THEN FA˜ (i) = cA 2

Rule L: IF d(i) is A˜L THEN FA˜ (i) = cA L and Rule 1: ˜1 THEN F ˜ (i) = cB IF ∆d(i) is B 1 B Rule 2: ˜2 THEN F ˜ (i) = cB IF ∆d(i) is B 2 B .. . Rule L: ˜L THEN F ˜ (i) = cB IF ∆d(i) is B L B ˜j are the j-th antecedent fuzzy where A˜j (j = 1, . . . , L) and B B sets for two fuzzy inputs d(i) and ∆d(i); cA j and cj are the consequent constants at the j-th rule for the feed rate FA˜ (i) and its compensation FB˜ (i); L is the total number of fuzzy rules. The confidence of each antecedent part at the j-th 131

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rule is obtained by ωjA = µAj ˜ {d(i)}

(5.6)

ωjB = µBj ˜ {∆d(i)}

(5.7)

where µX (•) denotes the confidence of a fuzzy set labeled by X. Therefore, the fuzzy reasoning results for the feed rate F (i) and its compensation ∆F (i) are respectively calculated by ∑L

A A j=1 ωj cj A k=1 ωk

F (i) = ∑L ∑L

B B j=1 ωj cj B k=1 ωk

∆F (i) = ∑L

(5.8)

(5.9)

The resultant fuzzy feed rate F˜ (i) is realized in the form F˜ (i) = F (i) + ∆F (i)

(5.10)

Note that the fuzzy set used is the following Gaussian membership function µX (x) = exp{log(0.5)(x − p)2 q 2 }

(5.11)

where p is the center of membership function and q is the reciprocal value of standard deviation. Figures 5.14 (a) and (b) show the antecedent membership functions designed for d(i) and ∆d(i), respectively. The reciprocal values of the standard deviations are 0.2 and 0.1, respectively. These antecedent membership functions are designed by analyzing d(i) and ∆d(i) included in several CL data files for machining paint rollers. An example of corresponding constant values in consequent parts is tabulated in Table 5.1, in which Fmax and Fmin are the maximum and minimum values (mm/min.) of feed rate; Fbase denotes Fmax − Fmin . Consequent constant values determined with Fmax and Fmin must be suitably tuned according to each wooden material, e.g., 132

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Pick feed

Pick fee d directio

n

Figure 5.13: An example of relation between the distance and the point density with respect to CL data.

based on the experience of a skilled NC operator. It is better that the parameters Fmax and Fmin are given according to the kind of wooden material through a preliminary experiment, while checking the occurrence of an edge chipping and considering the efficiency. It should be noted also that the allowable values of the parameters tend to depend on the complexity of relief design, the depth of material removal, the kind of wooden materials and the direction of the woodgrain. As can be seen from the table, the key parameters that affect the feed rate are only Fmax and Fmin . The operator sets the two parameters according to the relief design and the target wood material. Furthermore, note that the fuzzy reasoning part yields not only larger values than Fmax but also smaller values than Fmin by using the combination of d(i) and ∆d(i). Our proposed post-processor performs the post process for the linear approximated CL data without ฀gFEDRAT/฀h statements and generates suitable feed rate values, so that conventional NC machine tools can be effectively utilized. Also, it need not go back to the main process to recalculate feed rate values. It is expected that the post-processor allows a three-axis NC machine tool with a rotary unit to easily carve an artistic relief design on a cylindrical wooden workpiece, without causing any undesirable edge chipping. 133

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~ A1

1

~ A2

~ A3

10

20

~ B2

~ B3

-30

-10

~ A4

~ A5

30

40

~ B4

~ B5

10

30

~ A6

µ A~ j 0.5

0

0

~ B1

1

(a)

50

d (i) [mm] ~ B6

µ B~ j 0.5

0 -50

(b)

50

∆d (i) [mm]

Figure 5.14: Antecedent membership functions for d(i) and ∆d(i).

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Figure 5.15: Carving scene of a wooden paint roller with an artistic design.

5.4 Experiments In the previous section, a three-axis NC machine tool with a rotary unit and its post-processor have been introduced to efficiently machine cylindrical wooden workpieces. The machined workpiece can be used as a paint roller with an artistic design, which is very useful and convenient to directly transcribe a relief design to a wall just after painting. In this section, an actual machining experiment using a cylindrical wooden workpiece is conducted using the proposed system. Although up to now there have been few studies to investigate the optimal machining conditions with respect to the machined curved surface of wood, Fujino et al. [64] examined the influences of machining conditions such as feed rate and feed direction to the grain by using two wood species, in which constant feed rate values under 2000 mm/min. were evaluated. The roughness of machined surfaces was measured on 3D profiles obtained by laser scan135

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Fmin + 0.2Fbase

cB 2

−0.2Fmin

cB 1

−0.5Fmin

cA 2

Fmin + 0.1Fbase

cA 1

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136 −0.1Fmin

cB 3

Fmin + 0.4Fbase

cA 3

0.1Fmin

cB 4

Fmin + 0.6Fbase

cA 4

0.2Fmin

cB 5

Fmin + 0.8Fbase

cA 5

cA 6

0.5Fmin

cB 6

Fmin + Fbase

Table 5.1: Consequent constants of fuzzy reasoning part for d(i) and ∆d(i).

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[mm]

100

50

0

(a)Distance

between two adjacent steps in CL data

[mm]

100

0

-100

[mm/min]

(b)The increment 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400

0

100

of the distance

200 step i

300

400

(c) Variable feed rate

Figure 5.16: An example of the feed rate values given to NC machine tool, in which the total number of steps is 400, Fmax and Fmin are set to 2000 mm/min. and 600 mm/min., respectively.

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Figure 5.17: Artistic design wooden paint rollers carved by the proposed system.

ning, where the surface roughness was shown to be improved as the feed rate was decreased. It is expected from the above result that the decrease of feed rate must be certainly effective also to suppress an edge chipping. Wood materials are essentially brittle compared to metallic materials, so that the increase of feed rate results in some undesirable edge chipping. Such a tendency was confirmed in preliminary machining tests, in which a feed rate override, i.e., a variable control function that allows the NC operator to manually increase or decrease programmed feed rates, was used. Fig. 5.15 shows an example of a paint roller being machined without any undesirable edge chipping. In this case, the feed rate values generated from the fuzzy feed rate generator described in the previous section are shown in Fig. 5.16. The maximum and minimum values Fmax and Fmin of feed rates were determined to be 2000 mm/min. and 600 mm/min. respectively through a preliminary machining test. The type of wooden material used is glued laminated wood. The maximum cutting depth of material removal is 3 mm. In the case that this wooden material was machined 138

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with the design shown in Fig. 5.10 giving the maximum cutting depth of 3 mm, an undesirable edge chipping occurred when feed rate values higher than about 800 mm/min. were given. From this fact, 600 mm/min. was set to Fmin as a safe value. Also, although a higher value than 2000 mm/min., e.g. 3000 mm/min. was able to be given to Fmax within a long straight path, a safety margin of 1000 mm/min. was considered to avoid an edge chipping. By using these parameters, a sufficient reduction in machining time was also achieved. It is observed, from the results shown in Fig. 5.16, that the feed rate F˜ (i) is varied according to the curvature of the model surface. Note that the feed rate of 600 mm/min. appearing periodically is forcibly given every pick feed motion, when the rotary unit is rotated with a small angle (e.g., 0.56 degrees). The amount of the small angle depends on the ratio of y_length to y_pick as shown in Fig. 5.11. NC data were given to the NC machine tool MDX-650A through a standard RS232C interface using DNC (Direct Numerical Control) software. Generally DNC systems with a RS232C interface do not provide real-time communication but an asynchronous serial communication using XON/XOFF flow control, so that the variation of actual feed rate for time can not be obtained from the NC machine tool. Instead, the relation among the feed rate value F˜ (i) given to the NC machine tool, the distance d(i) and its increment ∆d(i) is plotted using the step number as the abscissa, as shown in Fig. 5.16. The relation between F˜ (i) and the point density in CL data can be observed from the result. The curvature can be estimated from the point density because the main-processor generates points written with ฀gGOTO/฀h statement in CL data according to the curvature and the tolerance. In the case of Fig. 5.16, the total machining time was reduced about 20% compared with the case of using a constant feed rate value of 600 mm/min. As can be seen, the proposed fuzzy feed rate generator provides a more intuitive and finely tunable feed rate function for the post 139

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process; however, the quantitative performance evaluation would depend on the combinatorial condition between the complexity of the relief design and the kind of the wooden material. Fig. 5.17 shows the paint rollers with an artistic design carved by the proposed system.

5.5 Conclusion In this chapter, an intelligent machining system based on a three-axis NC machine tool with a rotary unit has been introduced to efficiently and easily produce many kinds of artistic designed wooden paint rollers. A post-processor with the fuzzy feed rate generator has been also presented to effectively run the machining system. The post-processor allows the NC machine tool to easily transcribe a relief design from the surface on a flat model to it on a cylindrical workpiece. The fuzzy feed rate generator generates suitable feed rate values from CL data without using a feed rate statement according to the curvature of each relief design. By the fuzzy feed rate generator, it has been confirmed that not only the edge chippings on the cylindrical surface can be excluded but also the total machining time can be reduced about 20%. Experimental results, thus, have shown that artistically designed wooden paint rollers can be successfully carved using the proposed machining system. In future works, we may plan to conduct similar machining experiments using other kinds of wooden materials than the glued laminated wood, and different relief designs. By evaluating the performances and taking the results in fuzzy rules, the fuzzy feed rate generator would be more flexible to the kinds of both wooden materials and relief designs for artistic paint rollers.

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6 Polishing robot for pet bottle blow molds DOI: 10.1533/9780857094636.141 Abstract: In this chapter, a CAD/CAM-based position/force controller in Cartesian space is presented for a mold polishing robot. CL data with normal vectors are referred to as not only the desired trajectory of tool translational motion but also the desired contact direction given to a mold surface, so that a complete non-taught operation of both position and contact direction can be realized. The controller also regulates the polishing force consisting of the contact force and kinetic friction forces. When the robot carries out polishing tasks, the position control loop delicately contributes to the force control loop to achieve both a regular pick feed control along CL data and a stable polishing force control on curved surface. The effectiveness and promise of the polishing robot is proved by actual polishing experiments using an industrial robot YASKAWA MOTOMAN UP6. Key words: mold polishing robot, PET bottle blow mold, industrial robot, MOTOMAN UP6, ball-end abrasive tool, hybrid position/force control with weak coupling, CL data, non-taught operation 141

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6.1 Background Recently, open-architecture industrial robots, whose kinematics and servo system are technically opened, have been developed. Using such a robot we can explore new skillful applications without conventional complicated teaching. In the previous section, a 3D robot sander was introduced for the furniture manufacturing industry. The robot sander realized a non-taught operation regarding the position and orientation of the sanding tool attached to the robot arm. As the next stage, we attempt to apply an industrial robot to the polishing process of PET(Poly Ethylene Terephthalate) bottle blow molds. As can be guessed, the size of the target workpieces are smaller than parts used in constructing furniture. That means the radius of curvature is also smaller. In the PET bottle molds manufacturing industry, 3D CAD/CAM systems and machining centers are being used widely, and these advanced systems have drastically rationalized the design and manufacturing process of metallic molds. On the contrary, the almost polishing process after machining process has been supported by skilled workers who have capabilities concerning both dexterous force control and skillful trajectory control for an abrasive tool. The skilled workers usually use mounted abrasive tools with several sizes and shapes. In using these types of tools, keeping contact with the metallic workpiece with a desired contact force and a tangential velocity is the most important factor to obtain a high-quality surface. When performing a polishing task, it is also a key point that skilled workers reciprocatingly move the abrasive tool back and forth along the object surface. Generally, since the repetitive position accuracy at the tip of articulated-type industrial robots is 0.1 mm or within its neighborhood [65], it is very difficult to polish the surface of the metallic mold using only a position control strategy. In the polishing process of PET bottle molds, a surface accuracy Ra (arithmetical mean roughness) of 0.1 µm or less 142

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is finally required for mirror-like finishing. Especially, when an industrial robot makes contact with a metallic workpiece, several factors that decrease the total stiffness of the system are involved. They are called clearance, strain and deflection, all of which exist in not only the robot itself but also in the force sensor, abrasive tool, jig, base frame and so on. Therefore, it is meaningless to discuss the position accuracy at the tip of the abrasive tool attached to the robot arm. If a position control only is used for a polishing task where an abrasive tool and metallic workpiece contact to each other, then both the stiffness of the robot itself and the total stiffness including the abrasive tool must be extremely high. However, it would be really beyond our power and also the uncertainty of workpiece positioning would not be covered. Up to now, several robots in which force control methods are implemented have been developed; they have allowed us to achieve successful automations required in each manufacturing process. For example, polishing robots and finishing robots were presented in [37, 38]. In [37], a dynamic model that describes the dynamic behavior of the robot for surface finishing tasks is developed. Also, a robotic surface finishing system based on a planar robot with a force sensor and a deburring tool is proposed. In [38], the process development of a robotic system for automatically grinding and polishing vane airfoils is reported. However, each paper suggests that it is not easy to flexibly achieve the target tasks by using only the force control method. The difficulty is clear from the results that special hardware mechanisms such as manipulators, tools, sensors and measuring systems have been considered according to each manufacturing process. There also exists a serious problem that should be overcome at the present stage. When a polishing robot is designed, an end-effector with a force sensor is proposed for polishing; however, friction force acting between the end-effector and workpiece has not been successfully handled. The friction force in mold polishing has large effect on the quality and efficiency. Unfortunately, curved surfaces with large curva143

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tures must be addressed in the case of polishing PET bottle molds, so that the required goal is considerably higher than the already introduced furniture sanding robot. Additionally, when a force-controlled robot contacts with a stiff environment such as a metallic mold, dynamic stability issues should be dealt with [19]. The force control system becomes unstable with the increase in stiffness. It is known that no advanced polishing robots have been successfully developed yet on a commercial basis for such metallic molds with curved surfaces as PET bottle blow molds, due to the poor polishing quality and the complicated operation. The reasons why conventional polishing robots based on an industrial robot could not satisfactorily finish the curved surface of molds are as follows: 1. Conventional industrial robots provide only a teaching pendant as a user-interface device. Precise teaching along a curved surface is extremely difficult and complicated. 2. Kinematics and servo control, which are indispensable to develop a real-time application for mold polishing, have not been technically opened to engineers and researchers. 3. No successful control strategy has been proposed yet for mold polishing with curved surface. Compatibility between force control and position control is need for higher surface quality. In this subsection, dexterous techniques are presented for realizing a skillful mold polishing robot as shown in Fig. 6.1. Normalized tool vectors are first generated from three-axis CL data. The CL data with normal vectors called multi-axis CL data can be used for not only a desired trajectory of tool translational motion but also contact directions given to a mold. The impedance model following force control method adjusts the polishing force composed of a contact force and 144

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Polishing robot based on YASKAWA MOTOMAN UPUP-6

Abrasive tools

Force sensor

Figure 6.1: Mold polishing robot developed based on YASKAWA MOTOMAN UP6.

kinetic friction force. A CAD/CAM-based position/force controller in Cartesian space by referring such multi-axis CL data is proposed for the polishing robot with a ball-end abrasive tool. The surface polishing is achieved by controlling both the tool position along the CL data and the polishing force. The differences with the block diagram shown in Fig. 4.4 are that the orientation of the tool is always fixed to z-axis in work coordinate system; the orientation component in CL data is used for the force direction to be given to a mold. The CAD/CAM-based position/force controller is applied to an industrial robot with an open-architecture controller. The effectiveness and validity of a mold polishing robot with the CAD/CAM-based position/force controller are demonstrated through actual polishing experiments. 145

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6.2 Generation of multi-axis cutter location data Although high-end 3D CAD/CAM systems generally have the multi-axis function, ordinary CAD/CAM systems do not support the function. When the 3D CAD/CAM used has no multi-axis functions, multi-axis CL data can not be generated. In this subsection, we describe how to construct multi-axis CL data from three-axis ones. The multi-axis CL data are composed of position and normalized tool vectors. The three-axis CL data have position vectors p(i) = [px (i) py (i) pz (i)]T along the tool motion in work coordinate system, where i denotes the i-th step in CL data. Fig. 6.2 shows the generation image of normal vector n(i) at p(i). First of all, a direction vector t(i) = [tx (i) ty (i) tz (i)]T which represents the tool moving direction is given by (6.1)

t(i) = p(i + 1) − p(i)

Next, p(i + j)(1 ≤ j ≤ 100), which is the nearest point to p(i), is searched. Another vector s(i) = [sx (i) sy (i) sz (i)]T is obtained by (6.2)

s(i) = p(i + j) − p(i)

Note here that j is selected so that t(i) and s(i) are not parallel to each other. The normalized tool vector n(i) = [nx (i) ny (i) nz (i)]T at p(i) on the free-formed surface is perpendicular to both t(i) and s(i), so that it yields the following relations: nx (i)tx (i) + ny ty (i) + nz (i)tz (i) = 0

(6.3)

nx (i)sx (i) + ny (i)sy (i) + nz (i)sz (i) = 0

(6.4)

{

}2

=1

(6.5)

nz (i) ≥ 0

(6.6)

nx (i)}2 + {ny (i)}2 + {nz (i)

n(i) is calculated from Eqs. (6.3), (6.4), (6.5) and (6.6). The multi-axis CL data CL(i) = [pT (i) nT (i)]T (i = 146

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n(i) p(i-1) p(i) p(i+1)

t(i)

s(i) P(i+j)

Figure 6.2: Generation of normalized tool vector n(i) at p(i) on a free-formed surface.

1, 2, 3, · · · , l) which have information of normal direction can be composed by applying the above operations to all steps in three-axis CL data. l is the total number of steps in CL data. When the polishing robot runs, p(i) and n(i) are used to calculate the references of position and contact direction given to curved surface, respectively. The multi-axis CL data allow the polishing robot to simply realize a nontaught operation of position and contact direction. Desired position xd (k) and desired contact direction od (k) at the discrete time k are similarly obtained as explained in the sections 4 and 5. The position/force controller described in next section refers xd (k) and od (k) as desired values given to a ball-end abrasive tool, respectively.

6.3 Basic Polishing Scheme for a BallEnd Abrasive Tool In this section, a control strategy efficiently using the contour of a ball-end abrasive tool is introduced for the mold 147

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polishing with curved surface. In polishing, the polishing force acting between the abrasive tool and target mold is controlled. The polishing force is the most important physical factor that largely affects the quality of polishing, and assumed to be the resultant force of contact and kinetic friction forces. The image of the proposed mold polishing robot is shown in Fig. 6.1, in which a ball-end abrasive tool with a radius of 5 mm is attached to the tip of a six-DOFs articulated industrial robot through a force sensor. The abrasive tool is generally attached to a portable electric sander, so that the power of polishing is obtained by its high rotational motion, e.g., 10,000 rpm. In this case, however, it is so difficult for skilled workers to suitably keep regulating the power, contact force and tangential velocity for many minutes according to object’s shapes, i.e., undesirable over-polishing tends to occur frequently. Thus, to protect the mold surface against over-polishing, the proposed polishing robot keeps the rotation of the tool fixed, and polishes the workpiece using the resultant force F r of the Coulomb friction and the viscous friction. Each friction force is generated by the contact force f = [fx fy fz ]T in normal direction and the tangential velocity v t = [vtx vty vtz ]T , respectively. Fig. 6.3 shows the control strategy taking account of the kinetic friction forces. In this figure, f is given by the normal velocity v n = [vnx vny vnz ]T at the contact point between the abrasive tool and mold. v n is yielded by the IMFFC given by Eq. (1.17). In this chapter, the polishing force is defined as the resultant force of F r and f , which can be measured by a force sensor. Fig. 6.4 shows an example of force sensor, ATI Mini40 six-DOFs force/torque sensor. It is assumed that the polishing is performed by a hybrid control of the tool position and polishing force. In order to avoid the interference between the abrasive tool and mold, the orientation of the tool is not changed and always fixed to z-axis in work coordinate system. Fortunately, since PET bottle blow molds 148

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Cross section

Figure 6.3: Polishing strategy by efficiently using the contour of a ball-end abrasive tool.

have no over hang, a suitable contact point between the ballend abrasive tool and the mold can be always obtained. The proposed polishing robot does not need to use any complex tools, vision sensors and jigs, so that it can be realized in a simple manner.

6.4 Feedback Control of Polishing Force As mentioned above, if it is assumed in polishing that the friction force F r acting on the abrasive tool is mainly composed of Coulomb and viscous frictions, then F r is represented by Eq. (4.9). The polishing force assumed in the previous section is obtained by the resultant force of the contact force f (k) in normal direction and the friction force F r (k) in tangential direction. The force vector F (k) = [Fx (k) Fy (k) Fz (k)]T measured by the force sensor as shown in Fig. 6.4 is regarded as the polishing force, so that it can be also written by Eq. (4.10). The polishing force given by Eq. (4.10) is controlled by the IMMFC given 149

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Controller design for industrial robots and machine tools S

Fz Polishing force

F =

S

Fx

( S Fx )2 + (S Fy )2 + (S Fz )2

S

Force sensor

Fy

Tool axis Force sensor: ATI Mini40 Polishing force yields at the contact point.

Figure 6.4: Force sensor to measure the polishing force ∥F ∥.

by Eq. (1.17). In the proposed mold polishing robot, the IMFFC is applied only in normal direction at the contact point, and the control law yields a velocity vnormal (k) given by Eq. (4.13). Using the vnormal (k) and normal direction vector od (k) included in Eq. (3.1), the normal velocity vector v n (k) to control the polishing force is obtained from Eq. (4.14).

6.5 Feedforward and Feedback Control of Tool Position Currently, the molds for PET bottle manufacturing are designed and machined with 3D CAD/CAM systems and machining centers, respectively. Accordingly, multi-axis CL data or three-axis CL data generated from the main processor of the CAM can be used for the desired trajectory of an abrasive tool. If only three-axis CL data can be generated, normal direction vectors needed are obtained by a simple calculation described in section 7.2. The block diagram of the CAD/CAM-based position/force controller implemented in the mold polishing robot is almost same as Fig. 4.4, except 150

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the tool axis is always fixed to z-axis in work coordinate system. In other words, the tool orientation is not made to change in order to keep the force control stability and to uniformly abrade the contour of the ball-end abrasive tool. The position of the abrasive tool is feedforwardly controlled by the tangential velocity v t (k) given by

v t (k) = vtangent

xd (k) − xd (k − 1) ∥xd (k) − xd (k − 1)∥

(6.7)

where vtangent is a velocity norm which means the feed rate. v t (k) is given through an open-loop action so as not to interfere with the normal velocity v n (k). On the other hand, the polishing force is regulated by v n (k) which is perpendicular to v t (k). v n (k) is given to the normal direction referring od (k). It should be noted, however, that using only v t (k) is not enough to execute desired trajectory control along the CL data, i.e., the tool would not be able to conduct regular pick feed motion, e.g., with a given pick feed of 0.1 mm. To avoid this undesirable phenomenon, a simple position feedback loop with a small gain is added as shown in Fig. 4.4 so that the abrasive tool does not deviate from the desired pick feed motion. The position feedback control law generates another velocity v p (k) given by Eq. (4.15). Finally, the velocities v n (k), v t (k) and v p (k) are summed up, which is given to the reference of the Cartesian-based servo controller of the industrial robot. The CAD/CAM-based position/force controller deals with neither the moment nor rotation, and also the origin of the constraint space (force space) is always chosen at the contact point. Accordingly, although a paper by Duffy [66] states the fallacy of modern hybrid control theory such as dimensional inconsistency, dependence on the choice of origin of the coordinates, our proposed system is not affected at all. 151

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6.6 Update timing of CL data Here, we describe how to update the current step i of the CL data, i.e., defining the next step as i+1, to realize a smooth feed motion. The main-processor of the CAM generally produces the CL data CL(i) = [pT (i) nT (i)]T so as to machine a workpiece within a given tolerance to a designed model. p(i) = [px (i) py (i) pz (i)]T and n(i) = [nx (i) ny (i) nz (i)]T (i = 1, 2, 3, . . . , l : l is the number of steps) are the position and normal direction components, respectively. Figure 6.5 shows an image of the proposed polishing strategy where the tool contour is efficiently utilized. One of the key points is that the tool does not go up over the situation (1) or (5) shown in Fig. 6.5 in order to avoid an undesirable over-polishing around the edges of the workpiece. The positions of the situation (1) and (5) are called the max-height. Another key point is that the tool axis is always fixed to z-axis in the work coordinate system to efficiently abrade the contour of the ball-end abrasive tool. Actually, the tangential velocity of the ball-end abrasive tool is linearly calculated based on the following direction vector. t(i) = p(i + 1) − p(i)

(6.8)

If the CL data are used in the robotic controller, it is very important to realize a smooth feed motion that how to determine the timing of reading the next step i+1, i.e., when the step number i should be updated. From now on, the following three conditions are evaluated. a) Detection of the current position x(k) of tool tip b) Consideration of the force measurement in normal direction besides the condition a). c) Detection of the sum of the manipulated variable v t (k) given to the servo controller Concerning the condition a), when the tool tip x(k) becomes out of [p(i), p(i + 1)], i.e., x(k) reaches to p(i + 1), i is updated. However, it does not work well around the situations 152

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Polishing robot for pet bottle blow molds

Z-axis

(５)

(1) CL data p(i -1)

(２)

(４) (３)

p(i)

p(i+1)

Workpiece

X-axis

B A

Figure 6.5: Relation between the tool’s center and CL data.

(1) and (5) in Fig. 6.5. The reason is that the constraint caused by a contact between the tool contour and the workpiece prevents the tool tip from reaching to the next step p(i + 1). For example, even if the tool tip approaches to the point A in situation (5) through (4), it can not arrive at the point B. Consequently, the next step is not read out. In the condition b), to solve the problem, the force measurement is further considered in addition to the condition a). In other words, when a large x-directional force such as |Fx |> Fd is detected, then the next step is immediately read in. In this case also, however, incorrect detections tend to occur. This is because the force control system in the finishing robot is a so-called high gain system,:its stiffness in the tool contact direction is about 120 N/mm, so that an undesirable spike over Fd sometimes breaks out. Through the trial and error mentioned above, the condi153

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tion c) is now introduced. In the condition c), if the following equation is satisfied, then i is updated to i + 1. k ∑

∥v t (n)∥≥ ∥t(i)∥

(6.9)

n=ki

where ki is the discrete time when the last updating is conducted. In Eq. (6.9), when the sum of the value of manipulated variable in the tangential direction, which has been given to the servo system after the last updating, goes beyond the current distance ∥t(i)∥ between two adjacent steps, i is updated to i + 1. Calculating the update timing by using Eq. (6.9), the feed motion can be smoothly carried out even under the constrained situations (1) and (5) shown in Fig. 6.5.

6.7 Experiment 6.7.1 Experimental setup To evaluate the validity and effectiveness of the mold polishing robot using the CAD/CAM-based position/force controller, a fundamental polishing experiment is conducted using an aluminum mold machined by a machining center as shown in Fig. 6.6. The main objective of the fundamental polishing is to remove all cusp marks on the curved surface whose heights are roughly 0.3 mm. The fundamental polishing before the finishing process is one of the most important processes to make the best-quality, mirror-like surface finishing. If the undesirable cusp marks are not uniformly removed in advance, then it is very difficult to finish the mold with a mirror-like surface without scratches, swells and overpolishing however much time would be spent for the finishing process. Fig. 6.7 shows the mold polishing robot developed based on an industrial robot YASKAWA MOTOMAN UP6 with open control architecture used in the polishing experiment. 154

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Figure 6.6: PET bottle blow mold before polishing process.

The industrial robot provides several useful Windows API functions such as a Cartesian-based servo control and kinematics. A ball-end abrasive tool is attached to the tip of the robot arm via a force sensor. The robot also has a tiltable jig to incline the workpiece flexibly, and an oil mist to clean the surface of the mold and abrasive tool.

6.7.2 Polishing condition and experiment An aluminum mold is fixed along the y-axis in robot work coordinate system with a tiltable jig. The mold is inclined by 45 degrees about the x-axis. One of the CL data used was generated with a zigzag path along the cross section as shown in Fig. 6.8(a). Mounted abrasive tools are usually attached to a portable electric sander, whose torque makes the abrasive tools rotate. When skilled workers manually use an electrically-driven tool swuch as this, the contact force is given under about 10 N. On the other hand, when a skilled worker polishes a mold by friction forces using a simple bamboo stick covered with a sand paper, the 155

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Controller design for industrial robots and machine tools

Figure 6.7: Experimental setup.

156

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Pick feed Pick feed (a) Cross sectional path

(b) Longitudinal path

Figure 6.8: Desired trajectories composed of zigzag paths.

contact force is given as from about 10 to 40 N. In this experiment, since the rotation of the mounted abrasive tool is locked and the polishing task is conducted using the contact and kinetic friction forces, the desired polishing force is set to 20 N. Locking the rotation of the tool reduces undesirable high-frequency vibrational noises which are one of the serious problems in the case of locating the force sensor between the tip of the robot arm and the abrasive tool. The force values sensed every 125 µsec were filtered with a cutoff frequency of 500 Hz. The surface was polished through three steps, making the grain size of the abrasive tool smaller gradually, i.e., from ♯220, ♯320 to ♯400. To obtain a higher quality surface, another zigzag path as shown in Fig. 6.8(b) was also used for the basic trajectory of the abrasive tool. These two paths shown in 6.8 were used alternately. Fig. 6.9 shows the polishing scene using the proposed robot. When the polishing robot runs, the abrasive tool is made to reciprocatingly rotate with ±40 deg/sec using the sixth axis of the robot so that the contour can be abraded uniformly. If the abrasive tool is uniformly abraded keeping the ball-end shape, the 157

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Controller design for industrial robots and machine tools

Figure 6.9: Experimental scene using the proposed mold polishing robot.

robot can keep up the initial performance of polishing. Although the tool length gradually becomes shorter due to the tool abrasion, the force controller absorbs the uncertainty of tool length. Other polishing conditions in the case of using the path shown in Fig. 6.8(a) are tabulated in Table 6.1. As can be seen from the values of the force and position feedback gains, the y-directional position feedback loop delicately contributes to the force feedback loop in order to keep the constant pick feed even around the inclination part shown in Fig. 6.9.

6.7.3 Compliant motion of a ball-end abrasive tool The CAD/CAM-based position/force controller allows the polishing robot to perform a compliant motion so as not to damage the mold surface as illustrated in Fig. 6.10. The CL data shown in Fig. 6.10 are extracted from Fig. 6.8(a). First of all, the abrasive tool approaches to the initial contact point (3) with a low speed of 1 mm/s from a just above 158

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Polishing robot for pet bottle blow molds

Table 6.1: Polishing conditions in the case of using the path shown in Fig. 6.8(a) Conditions Robot Force sensor Zigzag path along curved surface Pick feed in longitudinal direction Radius of abrasive tool R Grit size of abrasive tool Rotational velocity of 6-th axis Rotational limits of 6-th axis Desired polishing force Fd Tangent directional velocity ∥v t ∥ Desired mass coefficient Md Desired damping coefficient Bd Force feedback gain Kf Force integral control gain Ki Position feedback gain Kvx , Kvy , Kvz Sampling time ∆t

Values YASKAWA MOTOMAN UP6 NITTA IFS-67M25A Cross section 0.2 mm 5 mm ♯220, ♯320, ♯400 40 or −40 deg/s −90 < θ6 < 90 deg 20 N 8 mm/s 0.01 N·s2 /mm 30 N·s/mm 1 0.0001 0, 0.02, 0 10 ms

point. The position/force controller immediately becomes active when a contact occurs, i.e., the force sensor detects a small value more than 2 N in z-direction. Then, the abrasive tool starts a trajectory-tracking motion along the CL data. As can be seen from Fig. 6.10, the force controller absorbs position errors in x-direction caused by the radius of the abrasive tool; the higher the tool position, the larger the position error between the CL data and actual trajectory. If the tip of the abrasive tool moves stiffly along the CL data, then the mold or tool would be fractured. Fig. 6.11 shows an x-directional actual trajectory acquired from an experiment in which the CL data as shown in Fig. 6.10 were used in the cross section and ∥v t ∥ was set to 6 mm/s. It is observed from this result that the abrasive tool attached to the tip of the robot arm was controlled with a desirable compliance in x-direction. Of course, such compliant motion also works well in the other two directions according to the shape of mold. 159

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Controller design for industrial robots and machine tools 40

70 mm

Abrasive tool

(1)

(5)

(4) CL data

(5) (4)

20 10 0

(3)

(3) X-directional actual trajectory

-10 -20

(2)

(2)

(1)

-30

(2) (3)

X-directional position (mm)

30

-40 Actual trajectory 0

Desired trajectory based on CL data

5

10

15

20

Time (sec)

Metallic mold (x-directional cross section)

Figure 6.11: Xdirectional actual trajectory obtained through an experiment.

Figure 6.10: Comparison of CL data and actual trajectory.

6.7.4 Experimental result It was confirmed that the significant resolution in the force domain was almost about 1.2 N with a position resolution of 0.01 mm in the case that the repetitive position accuracy at the tip of the abrasive tool shown in Fig. 6.1 was about 0.1 mm [65]. Although the force resolution is not so fine compared with skilled workers taking charge of the mold polishing process, the polishing robot can perform each task more uniformly and stably for many hours. The surface state after polishing was evaluated by both eye checking and touch feeling with fingers, and consequently a successful surface without over-polishing around the edges was observed. Furthermore, we conducted a quantitative evaluation using a stylus instrument, so that the measurements obtained by the arithmetical mean roughness (Ra) and maximum depth (Ry) were around 0.1 µm and 1.6 µm, respectively. It can be seen from the result that the polishing force could be more uniformly given to the surface on the average com160

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25

30

Polishing robot for pet bottle blow molds

Figure 6.12: Constriction part of mold surface after wiped with a cloth containing the polishing compound Cr2 O3 .

pared to skilled workers due to the proposed position/force controller. This is a main reason why such an effective polishing quality was obtained drastically. Fig. 6.12 shows the curved surface after being wiped with a cloth containing a polishing compound Cr2 O3 .

6.8 Conclusion Up to now, it has been widely discussed and believed in manufacturing industries of metallic molds that it would be impossible for articulated-type industrial robots, whose position accuracy is 0.1 mm at most, to polish and finish metallic molds with curved surfaces. However, our proposed polishing robot could satisfactorily overcome this problem due to the CAD/CAM-based position/force controller. In this chapter, we have proposed a CAD/CAM-based position/force controller in Cartesian space for a mold polishing robot. The CL data with normal vectors are referred to as not only the desired trajectory of tool translational motion but also the desired contact direction given to molds, 161

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so that a complete non-taught operation of both position and contact direction can be realized. The controller also regulates the polishing force consisting of the contact force and kinetic friction forces. When the robot carries out polishing tasks, the position control loop delicately contributes to the force control loop to achieve both a regular pick feed control along the CL data and a stable polishing force control on curved surface. The effectiveness and promise of the polishing robot using the CAD/CAM-based position/force controller have been proved by actual polishing experiments using an industrial robot YASKAWA MOTOMAN UP6.

162

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[62] F. Nagata, Y. Kusumoto, K. Hasebe, K. Saito, M. Fukumoto, and K. Watanabe, Post-processor using a fuzzy feed rate generator for multi-axis NC machine tools with a rotary unit. In International Conference on Control, Automation and Systems, pages 438–443, 2005. [63] F. Nagata and K. Watanabe, Development of a postprocessor module of 5-axis control NC machine tool with tilting-head for woody furniture. Journal of the Japan Society for Precision Engineering, 62(8): 1203–1207, 1996 (in Japanese). [64] K. Fujino, Y. Sawada, Y. Fujii, and S. Okumura, Machining of curved surface of wood by ball end mill – Effect of rake angle and feed speed on machined surface. In 16th International Wood Machining Seminar, Part 2, pages 532–538, 2003. [65] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliance control capability. In 13th International Symposium on Artificial Life and Robotics, pages 779–782, 2008, [66] J. Duffy, The Fallacy of modern hybrid control theory that is based on orthogonal complements of twist and wrench spaces. Journal of Robotic Systems, 7(2): 139–144, 1990. [67] M.C. Lee, S.J. Go, M.H. Lee, C.S. Jun, D.S. Kim, K.D. Cha, and J.H. Ahn, A robust trajectory tracking control of a polishing robot system based on CAM data. Robotics and Computer-Integrated Manufacturing, 17(1/2): 177–183, 2001, [68] F. Nagata, T. Mizobuchi, S. Tani, T. Hase, Z. Haga, K. Watanabe, M.K. Habib, and K. Kiguchi, Desktop orthogonal-type robot with abilities of compliant 223

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motion and stick-slip motion for lapping of LED lens molds. In IEEE International Conference on Robotics & Automation , pages 2095–2100, 2010, [69] O. Bilkay and O. Anlagan, Computer simulation of stick-slip motion in machine tool slideways. Tribology International, 37(4): 347–351, 2004. [70] X. Mei, M. Tsutsumi, T. Tao, and N. Sun, Study on the compensation of error by stick-slip for high-precision table. International Journal of Machine tools & Manufacture, 44(5): 503–510, 2004. [71] M.J. Tsai, J.L. Chang, and J.F. Haung, Development of an automatic mold polishing system. In IEEE International Conference on Robotics & Automation, pages 3517–3522, 2003. [72] M.J. Tsai, J.J. Fang, and J.L. Chang, Robotic path planning for an automatic mold polishing system. International Journal of Robotics & Automation, 19(2): 81–89, 2004, [73] H. Hocheng, Y.H. Sun, S.C. Lin, and P.S. Kao, A material removal analysis of electrochemical machining using flat-end cathode. Journal of Materials Processing Technology, 140(1/3): 264–268, 2003. [74] Y. Uehara, H. Ohmori, W. Lin, Y. Ueno, T. Naruse, N. Mitsuishi, S. Ishikawa, and T. Miura, Development of spherical lens ELID grinding system by desk-top 4-axes Machine Tool. In International Conference on Leading Edge Manufacturing in 21st Century, pages 247–252, 2005, [75] H. Ohmori and Y. Uehara, Development of a desktop machine tool for mirror surface grinding. International Journal of Automation Technology, 4(2): 88–96, 2010, 224

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[76] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliant motion capability. Artificial Life and Robotics, 13(2): 423–427, 2009. [77] F. Nagata, S. Tani, T. Mizobuchi, T. Hase, Z. Haga, M. Omoto, K. Watanabe, and M.K. Habib. Basic performance of a desktop NC machine tool with compliant motion capability. In IEEE International Conference on Mechatronics and Automation, WC1–5, pages 1–6, 2008. [78] F. Nagata, K. Watanabe, K. Sato, and K. Izumi, Impedance control using anisotropic fuzzy environment models. Journal of Robotics and Mechatronics, 11(1): 60-66, 1999. [79] F. Nagata, A. Otsuka, S. Yoshitake and K. Watanabe, Automatic control of an orthogonal-type robot with a force sensor and a small force input device, In The 37th Annual Conference of the IEEE Industrial Electronics Society, pages 3151–3156, 2011. [80] F. Nagata and K. Watanabe, Feed rate control using a fuzzy reasoning for a mold polishing robot. Journal of Robotics and Mechatronics, 18(1): 76–82, 2006. [81] Japanese Patent 4094781, Robotic force control method, F. Nagata, and K. Watanabe, 2008. [82] Japanese Patent 4447746, Robotic trajectory teaching method, F. Nagata, K. Tsuda, and K. Watanabe, 2010. [83] Japanese Patent 4216557, Polishing apparatus and polishing method, K. Tsuda, K. Yasuda, F. Nagata, Y. Kusumoto, and K. Watanabe, 2008.

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7 Desktop orthogonal-type robot for LED lens cavities DOI: 10.1533/9780857094636.163 Abstract: In this chapter, a desktop-size orthogonal-type robot with compliance controllability is developed to finish an axis-asymmetric workpiece with multiple small concave areas. Elemental technologies such as the transformation of manipulated values from velocity to pulse, desired damping considering the critically damped condition, weak coupling control method between force and position feedback loops, stick-slip motion control method, neural network-based stiffness estimator, automatic truing of a thin wood-stick tool for long-time lapping process, and force input device for manual operation are explained in detail. The finishing performance of the proposed orthogonal-type robot is evaluated through finishing experiments of an LED lens cavity with multiple small concave areas of 4.0 mm. Key words: LED lens cavity, desktop-size orthogonal-type robot, effective stiffness, weak coupling control, polishing force control, stick-slip motion control, neural network, wood-stick tool, automatic tool truing, force input device 163

Controller design for industrial robots and machine tools

7.1 Background The polishing of LED lens mold after the machining process requires high accuracy, delicateness and skill, so that the process has not also been automated yet. Generally, a target mold has several concave areas precisely machined with a tolerance of ±0.01 mm as shown in Fig. 7.1. In this case, each diameter is 4 mm. That means the target mold is not axis-symmetric, so that conventional effective polishing systems, which can deal with only axis-symmetric workpiece, cannot be applied. Accordingly, such an axis-asymmetric lens mold as shown in Fig. 7.1 is polished by skilled workers in almost all cases. Skilled workers generally polish a small lens mold using a wood-stick tool with diamond paste while checking the polished area through a microscope. However, the smaller the workpiece is, the more difficult the task. In particular, it is necessary for a pickup lens mold to handle the surface uniformly and softly, so high resolutions of position and force are indispensable. As an example of using an NC machine tool with high position resolution, Lee et al. proposed a polishing system composed of two subsystems: a three-axis machining center and a two-axis polishing robot. Although a sliding mode control algorithm with velocity compensation was implemented to reduce tracking errors, a method which could absorb undesirable positioning errors in each workpiece was not considered [67]. In this chapter, a new desktop orthogonal-type robot with compliance controllability is presented for finishing metallic molds with small curved surfaces [65]. The orthogonal-type robot consists of three single-axis devices. A tool attached to the tip of the z-axis has a ball-end shape. Also, the control system of the orthogonal-type robot is composed of a force feedback loop, position feedback loop and position feedforward loop. The force feedback loop controls the polishing force consisting of tool contact force and kinetic friction force; the position feedback loop controls the position in the direction of spiral motion; and the position 164

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feedforward loop leads the tool tip along a spiral path. It is expected that the orthogonal-type robot delicately smooths the surface roughness with about 50 µm height on each concave area, and produces a high-quality finish for the surface. In order to first confirm the application limit of a conventional articulated-type industrial robot to a finishing task, we evaluate the backlash that causes the position inaccuracy at the tip of the abrasive tool, through a simple position/force measurement. Through a similar position/force measurement and a surface-following control experiment along a lens mold, the basic position/force controllability of the proposed orthogonal-type robot is demonstrated.

7.2 Limitation of a polishing system based on an articulated-type industrial robot Effective stiffness is one of the important factors to objectively evaluate the property of industrial machineries. It has already been reported that effective stiffness has a large influence on force control stability [19, 20]. Therefore, gains written in force control laws have to be tuned according to the effective stiffness so as to maintain the force control stability. Here, as a preliminary experiment, the effective stiffness in an articulated-type industrial robot YASKAWA MOTOMAN UP6, as shown in Fig. 7.2, is examined. The arm tip has a force sensor with a stiff ball-end tool. The effective stiffness means the total stiffness including the characteristics composed of an industrial robot itself, force sensor, attachment, abrasive tool, workpiece, jig and floor. The effective stiffness, valid position resolution of Cartesian-based servo systems and resultant force resolution are evaluated simply by measuring the static position and contact force. Fig. 7.3 shows the relation between the position and contact force obtained by a simple contact experiment. The po165

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sition written in the horizontal axis is the z-directional component at the tip of an abrasive tool, which is calculated by the forward kinematics using the joint angles obtained from the inner sensors. The force written in the vertical axis is yielded by contacting the tool tip with an aluminum workpiece and measured by a force sensor. When the tool tip contacts to the workpiece, small manipulated variables under 10 µm could not cause any effective force measurements, so we conducted the experiment while giving the minimum resolution −10 µm in press motion and 10 µm in unpress motion. In the experiment, the tool tip approaches an aluminum workpiece at a low speed, and after touching the workpiece, i.e., after detecting a contact force, the tool tip was pressed against the workpiece with every 0.01 mm. The graph written with  in Fig. 7.3 shows the relation of the position and contact force. The force is about 36 N when the position of the tool tip is −0.3 mm, so the effective stiffness within the range can be estimated at 120 N/mm. After the contact motion, the tool tip was away from the workpiece once, and returned to the position again where 36 N had been obtained. After that, the tool tip was unpressed every 10 µm. The graph written with • in Fig. 7.3 shows the relation of the position and contact force of this case. It is observed from the result that there exists a large backlash around 0.1 mm. This value is almost the same as the general one that is guaranteed as a repetitive position accuracy of articulatedtype industrial robots. That is the reason why in order to design a polishing system using an articulated-type industrial robot we must consider a force control system with the force resolution of 1.2 N under a position uncertainty of 0.1 mm. A little nonlinearity in unpress motion is also observed from the graph. The undesirable backlash and nonlinearity should be suitably eliminated or dealt with when a force control system is employed in the robot as shown in Fig. 7.2. Unfortunately, the backlash of about 0.1 mm in Carte166

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sian space is a unpreferable property for the articulated-type industrial robot, however, it is too difficult to decrease the value. Accordingly, for example, it is almost impossible for the industrial robot to finish an LED lens mold which has the several small machined areas precisely arranged within the tolerance of 0.01 mm as shown in Fig. 7.1. The diameter of one concave area is 4.0 mm.

7.3 Desktop orthogonal-type robot with compliance controllability In order to polish a small concave area as shown in Fig. 7.1, a novel polishing system is proposed in this section. Fig. 7.4 shows the proposed desktop orthogonal-type robot consisting of three single-axis devices with a position resolution of 1 µm. The three single-axis devices are used for x-, y- and z-directional motions. A servo spindle motor is also used for the rotational motion of the tool axis. A compact three-DOFs force sensor is fixed between the z-axis and the attachment of the tool. The servo spindle motor with a reduction gear and the tool axis work together with a belt. The size of the robot is 850 × 645 × 700 mm. The single-axis device is a position control robot ISPA with high-precision resolution provided by IAI Corp., which is composed of a base, linear guide, ball-screw, AC servo motor and so on. The effective strokes in x-, y- and z-directions are 400, 300 and 100 mm, respectively. The hardware block diagram is shown in Fig. 7.5. Fig. 7.6 shows the static relation between position and contact force in the case of the proposed orthogonal-type robot with a stiff ball-end abrasive tool. The experiment was conducted in the same condition as shown in Fig. 7.3. It is observed that the undesirable backlash is largely decreased and the effective stiffness is about 30/0.2=150 N/mm. On the other hand, Fig. 7.7 shows the relation in the case that an elastic ball-end abrasive tool is used. It is observed that 167

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the effective stiffness changes down to about 30/0.36≈83.3 N/mm according to the property of the elastic abrasive tool. As can be seen, the effective stiffness of the force control system is largely affected by the kinds of the abrasive tool used. In the case of the elastic abrasive tool called a rubber abrasive tool, it is expected that the force resolution about 0.083 N can be performed due to the position resolution of 1 µm.

7.4 Transformation technique of manipulated values from velocity to pulse From the viewpoints of programming interface, torque command, position command and pulse command are available for the control of servo motors. Recently, a positionbased servo controller in Cartesian coordinate system is provided for articulated-type industrial robots with an open-architecture, such as KAWASAKI FS20, MITSUBISHI PA10 and YASKAWA MOTOMAN UP6. The position manipulated values less than the repetitive position resolution guaranteed, e.g. 0.1 mm, are valid and can be given to the servo controller with “float” type or “double” type data in the C programming language. On the other hand, the pulsebased servo controller is widely spread to the mechatronics field because of its performance and easiness of the treatment, and is also employed in the servo motor to control each axis in the proposed NC machine tool. The pulsebased servo controller transforms the pulse command into the motor driving torque. However, when realizing a precise position control system by using the pulse-based servo controller, a relationship between one pulse and the corresponding minimum resolution should be noted. The position control of a single axis of the robot is performed by the number of pulses, and the relative position per one sampling time can be regarded as 168

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the velocity. For example, assume that the minimum resolution in position is 1 µm for a single axis of the robot, i.e., the robot can move 1 µm by one pulse. In this case, the single-axis of the robot does not move, even if the manipulated value of 0.1 µm is continuously given to the pulse-based servo controller every sampling time period with 1 msec in order to achieve the velocity control of 100 µm/s. This is attributed to the fact that the pulse-servo controller generally ignores a fraction (i.e., values below one decimal point) less than one pulse. Fig. 7.9 shows an example of the normal velocity vnormal (k) that was generated by the impedance model following force controller, according to the force error Ef (k) in the profiling control experiment. The values in Fig. 7.9 mean relative position commands (µm) per one sampling time with 1 msec. Observe that almost all values are plotted within the range of ± 1 µm. It should be noted, however, that the values less than 1 µm can not be treated with the pulse-based servo controller. To overcome this problem, a transformation technique called the velocity-pulse conversion is proposed here. The velocity-pulse converter transforms the fine manipulated value in velocity into the pulse command given by an integer, which can be outputted to the pulse-based servo controller. The velocity-pulse converter for the pulse-based servo controller is located after the CAD/CAM-based position/force controller as shown in Fig. 7.8. Every sampling time period, to obtain the output of the velocity-pulse converter in x-direction, Wv˜x (k), calculate the summation of fractions, S(k), such as

S(k) =

k ∑

W

vx (n)

(7.1)

n=ki

where Wvx (n) denotes the fraction value at time n and ki is the latest discrete time when the velocity-pulse converter generated non-zero value. If the absolute value of S(k) is 169

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greater than one, then the velocity-pulse converter generates the following pulse: W

v˜x (k) =

{

Int(S(k)) if |S(k)|≥ 1 µm 0 otherwise

(7.2)

where Int(·) is the function that extracts only the part of an integer with sign from the value of (·). Furthermore, the fraction value should be calculated, for the next step, as W

vx (k + 1) =

{

S(k) − Wv˜x (k) if |S(k)|≥ 1 µm S(k) otherwise

(7.3)

where update ki_new = k as a new nonzero output time when satisfying |S(k)|≥ 1 µm. Similarly, Wv˜y (k) and Wv˜z (k) in y- and z-directions are obtained. Thus, applying the proposed velocity-pulse converter, the velocity vector Wv(k) for Cartesian-based servo controller can be transformed into the ˜ (k) = [Wv˜x (k) Wv˜y (k) Wv˜z (k)]T pulse command vector Wv which can be given to the pulse-based servo controller.

7.5 Desired damping considering the critically damped condition The tool tip is basically controlled similar to the mold polishing robot in the previous chapter. Next, a tuning method of desired damping is proposed by using the effective stiffness of the robot. When the polishing force is controlled, the characteristics of force control system can be varied according to the combination of impedance parameters such as desired mass and desired damping. In order to increase the force control stability the desired damping, which has much influence on force control stability, should be tuned suitably. In this section, a desired damping tuning method using the effective stiffness of the robot is proposed based on the critically damped condition. When the force control mode is selected in a direction, the desired impedance model 170

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is simply written by (7.4)

Md (¨ x−x ¨d ) + Bd (x˙ − x˙ d ) = Kf (F − Fd )

where x ¨, x˙ and F are the acceleration, velocity and force scalars in the direction of force control, respectively. x ¨d , x˙ d and Fd are the desired acceleration, velocity and force, respectively. When the force control is active, x ¨d and x˙ d are set to zero. It is assumed that F is the external force given by the environment and is model as (7.5)

F = −Bm x˙ − Km x

where Bm and Km are the viscosity and stiffness coefficients of the environment, respectively. Eqs. (7.4) and (7.5) lead to the following second order lag system. x ¨+

Kf Km Bd + Kf Bm x˙ + x=0 Md Md

(7.6)

The characteristics equation of Eq. (7.6) is written by s2 +

Kf Km Bd + Kf Bm s+ =0 Md Md

(7.7)

In this case, the damping coefficient ζ and natural frequency ωn are given by Bd + Kf Bm ζ= √ , 2 Md Kf Km

ωn =

√

Kf Km Md

(7.8)

Further, solving Eq. (7.7) for Bd using the critical damping condition, the following condition is obtained. Bd = 2

(7.9)

√

Md Kf Km − Kf Bm

Thus Hurwitz stability criterion leads to the following two relations. Bd + Kf Bm >0 (7.10) ∆1 = Md ∆2 =

Bd +Kf Bm Md

1 171

0 Kf Km Md

>0

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(7.11)

Controller design for industrial robots and machine tools

Because Md , Bd and Kf are all set to positive values in advance, and Km and Bm generally have positive values. Accordingly, it is confirmed that the force control system is asymptotically stable. In the profiling control experiment, the base value for the desired damping is calculated with Eq. (7.9). If possible, the desired damping should be fine-tuned and varied around the base value because Km has nonlinear characteristics as shown in Fig. 7.6 or 7.7.

7.6 Design of weak coupling control between force feedback loop and position feedback loop A skillful control strategy is proposed as a control strategy for LED lens molds with aspherical surfaces. An abrasive tool moves along a spiral path as shown in Fig. 7.10 while keeping the polishing force stable. The weak coupling controller has been already proposed for the PET bottle polishing robot, in which the force feedback loop and position feedback loop are coupled in a selected direction such as pick feed direction. In this case, a zigzag path is generally used for the desired trajectory, so that a position feedback control is active only in the pick feed direction, e.g., y-direction. On the contrary, in the case of the spiral path for an LED lend mold as shown in Fig. 7.10, the directions of the position feedback loops must be changed gradually all the time when the abrasive tool contacts the center of the workpiece and rises along the spiral path. Since the contact force is given to the normal direction at the contact point, the following three conditions are considered. 1. Around the bottom area in Fig. 7.10, the x- and ydirectional components of the normal vector are almost 0. Therefore the force feedback control system should be constructed in z-direction, and the position 172

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feedback control system also should be given to the xand y-directions. 2. Around the upper area in which the z-directional component of the normal vector is almost 0, so that the direction of the force control system should be changed x- and y-directions according to the spiral path. The position feedback control system is assigned only in the z-direction. 3. Around the middle area, the x-, y- and z-directional components of the normal vector changes every moment along the spiral path, so that the force feedback control system should be designed in x-, y- and zdirections. The coupling control is not needed in cases 1 and 2. In case 3, however, the weak coupling control is indispensable if the the regular pick feed motion in z-direction is to be realized while performing the stable polishing force. Furthermore, it is important to independently regulate the weight of the coupling control coping with the shape of the workpiece. To deal with the problem, each component of the position feedback gain K p = diag(Kpx , Kpy , Kpz ) is varied by Kpx = Kp nz

(7.12)

Kpy = Kp nz

(7.13)

Kpz = Kp (1 − nz )

(7.14)

where Kp is the basic gain for the weak coupling control. nz (0 ≤ nz ≤ 1) is the z-directional component of the normal direction vector calculated by using CL data. When the abrasive tool rises along the spiral path, nz varies from 1 to 0. For example, if Kp is given the value 0.001, Kpx and Kpy varies from 0.001 to 0, and Kpz varies from 0 to 0.001. 173

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7.7 Basic experiment In this section, the fundamental performance of the proposed desktop orthogonal-type robot is evaluated with respect to force control and position control. A profiling control experiment is conducted by using a plastic lens mold as shown in Fig. 7.11. The target mold is precisely machined based on the forms as shown in Fig. 7.11, where the diameter and depth under the partition line are 30 mm and 5 mm, respectively. At the start of the experiment, an elastic small ball-end abrasive tool approaches to the center of machined part with 2 mm/s. After detecting 5 N, which is 1/2 of the desired polishing force 10 N, the tool tip starts to follow a spiral path. Control parameters in the profiling control are tabulated in Table 7.1. The effective stiffness Km is estimated 30/0.36≈83.3 N/mm from Fig. 7.7 in case of the elastic ball-end abrasive tool. The desired mass Md and force feedback gain Kf are set to 0.01, respectively. Also, it is assumed that Kf Bm ≈0 since the viscosity of the force control system is considerably small. Accordingly, Eq. (7.8) leads to Bd =0.183 N·s/mm. Next, control systems in x-,y- and z-directions are explained. The polishing force and z-directional position are regulated by feedback control laws, and also x- and ydirectional positions are feedforwardly controlled based on CL data. The CL data (which are the desired trajectory) form a spiral path with a 0.8 mm pitch viewed in x-y plane. Fig. 7.12 shows the profiling control. Also, Fig. 7.13 shows the position control result, in which the pitch in x-y plane at the height 4 mm becomes about 0.7 mm. This is caused because the manipulated variable from the force feedback control law gradually yields in x- and y- directions when the tool goes up along the spiral path. In other words, the reason is that only the z-direction is designed with a position closed loop, so that the positions in x- and y-directions are corrected by the manipulated variable of the force control system, i.e., by the constraint of the force control system. 174

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Table 7.1: Parameters tuned for profiling control experiment. Conditions Robot Force sensor Desired trajectory along curved surface Pitch in X−Y plane Radius of ball-end abrasive tool R Grain size of abrasive tool Desired polishing force Fd Tangent directional velocity ∥v t ∥ Desired mass coefficient Md Desired damping coefficient Bd Force feedback gain Kf Diagonal elements of switch matrix S p Position feedback gain Kpx , Kpy , Kpz Integral control gain Kix , Kiy , Kiz Sampling time ∆t

Values Orthogonal-type robot NITTA IFS-67M25A Spiral path 0.8 mm 5 mm ♯220 10 N 5 mm/s 0.01 N·s2 /mm 0.183 N·s/mm 0.01 0, 0, 1 0, 0, 0.001 0, 0, 0.00001 1 ms

Also, the z-directional position was designed with a weak closed loop using small PI gains, so that a weak coupling was conducted against to the force feedback loop. In spite of such a situation, the mean error of z-directional position in the profiling motion was about 2.7 µm. The mean error of z-directional position was evaluated by EP z =

∑N

n=1

√

[xdz (n) − xz (k)]2 N

(7.15)

where N is the total step number in CL data, i.e., the number of ’GOTO’ statement. xdz (n) is the z-directional component at the n step in CL data, xz (k) is the z-directional position at the tool tip obtained from an encoder. k is the discrete time when the xdz (n) is set. Fig. 7.14 illustrates the control result of the polishing force. The upper, second and third figures show x, y- and z-directional forces in sensor coordinate system, respectively. The lower figure shows the norm ∥SF ∥= 175

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Controller design for industrial robots and machine tools

(SFx )2 + (SFy )2 + (SFz )2 . It is observed from the SFx and SF in Fig. 7.14 that the direction of force control periodiy cally varies due to the position control along the spiral path. Also, although the force measurements in x- and y-directions increase with the rise of the tool and the z-directional force one decreased gradually, it can be confirmed that the polishing force ∥SF ∥ could satisfactorily follow the reference value 10 N. The cutoff frequency of the force sensor was set to 500 Hz. Fig. 7.9 shows the normal velocity vnormal (k) which the impedance model following force controller generated according to the force error Ef (k) in the profiling control experiment. The values in Fig. 7.9 mean relative position commands µm per sampling time of 1 ms. √

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4 mm

Figure 7.1: LED lens mold with several concave areas precisely machined within a tolerance, which is a typical axisasymmetric workpiece.

(a) Rear view

(b) Side view

Figure 7.2: Polishing scene of a PET bottle blow mold using a conventional articulated-type industrial robot with a servo spindle.

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40 Stiff type

Contact force N

30

20

e Pr

s

ot sm

ion

s es pr n U

10

0

n io ot

-0.2

-0.1

0

m

-0.3

Z-directional position mm

Figure 7.3: Static relation between position and contact force in case of a conventional articulated-type industrial robot.

Z-axis Force sensor

Y-axis X-axis

(a) Overview

(b) Tool axis fixed under a force sensor

Figure 7.4: Proposed desktop orthogonal-type robot with compliance controllability.

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Encoder signal

Motor controller Pulse signal (C-V870)

Driver

AC servo motor + Single-axis device (x-axis)

PC

Driver

AC servo motor + Single-axis device (y-axis)

OS: Windows XP Sampling rate: 1 msec (Multimedia timer)

Driver

AC servo motor + Single-axis device (z-axis)

Driver

AC servo spindle motor (rotation of tool axis)

Receiver board (PCI-2184Q)

Force sensor

Force signal

Figure 7.5: Hardware block diagram of the desktop orthogonal-type robot composed of three single-axis devices with a position resolution of 1µm.

40 Stiff type

Elastic type

30

20

sm Pres

10

otion

s es pr Un

m

Contact force N

Contact force N

30

n io ot

20

10

e Pr

tio mo ss

n

s es pr Un

m

n io ot

0

0 0

-0.05

-0.1

-0.15

0

-0.20

-0.1

-0.2

-0.3

Z-directional position mm

Z-directional position mm

Figure 7.7: Static relation between position and contact force in the case of the desktop orthogonaltype robot with a rubber ball-end abrasive tool.

Figure 7.6: Static relation between position and contact force in the case of the desktop orthogonaltype robot with a stiff ballend abrasive tool.

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CAD/CAM-based position/force controller

Fd Wo

d (k)

Force Force Feedback Feedback Control Control Law Law

Wv

Wv

Position Position Feedback Feedback Control Control Law Law

Wv (k)

t (k)

Σ + Wv

d (k)

SF (k)

+

Position PositionFeedforward Feedforward Control ControlLaw Law Using CL Using CLData Dataand and Fuzzy FuzzyReasoning Reasoning

Wx

Fd : desired polishing force Wx (k) : desired position d Wo (k) : desired direction d

n (k)

p (k)

VelocityVelocityPulse Pulse Converter Converter

W ~ (k)

v

Pulse-Based Pulse-Based τ Servo Servo Controller Controller

NC NC Machine Machine Tool Tool

+ W ~ (k)

Sp

v

: pulse command

Wx (k)

τ : driving torque

Manipulated variable in normal direction μm/ms

Figure 7.8: Block diagram of the CAD/CAM-based hybrid position/force controller with a velocity-pulse converter.

1.5

1.0 0.5

0

-0.5

-1.0

-1.5 -2.0

0

-1.0

1.0

2.0

Polishing force error N

Figure 7.9: Relation between the polishing force error Ef (k) and manipulated variable vnormal (k) calculated from Eq. (4.13).

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z

o x y Figure 7.10: Example of spiral path used for desired trajectory of abrasive tool.

30 mm

Figure 7.11: 3D model designed for a profiling control experiment.

181

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Force sensor

Spindle

Ball end abrasive tool Lens mold

Figure 7.12: Profiling control scene along a spiral path.

wZ

mm

5 wY

wX

0 wO

10 5 0 mm

5 -5

-5 -10

-10

10

0 mm

Figure 7.13: Position control result along the spiral path.

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sFx

N

8

0

sFy

N

-8 8

0

-8

sFz

N

10

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||sF || N

10 Reference

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Figure 7.14: Control result of the polishing force ∥SF (k)∥.

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Desired force N

7 6 5 4 3 2 0

0.5

1 Time s

1.5

2

Figure 7.15: Desired contact force in case of 1 Hz.

7.8 Frequency characteristics Next, the frequency characteristics of the force control system are evaluated through a simple force control experiment. Two types of tools attached to the tip of the spindle are the elastic ball-end tool (ϕ=10 mm) and wood-stick tool (ϕ=1 mm). Fig. 7.15 shows an example of the desired force, the frequency of which is set to 1 Hz. The peak-to-peak value of desired force is 4 N. The frequency characteristics are measured within the range from 0 Hz to 15 Hz in this order. The frequency of 0 Hz means that the desired force is set to the constant value 5 N. Figures 7.16 and 7.17 show the frequency characteristics of magnitude in the cases of the elastic ball-end abrasive tool and wood-stick tool, respectively. Although 0 dB is the ideal result in the force control system, results of more than 0 dB tend to occur with the increase of frequency. This phenomena is caused by undesirable overshots and oscillations in the stiff force control system. However, the desired polishing force in actual finishing tasks is generally set to a constant value, so that the frequency characteristics are almost no problem. 184

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4 2

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0 -2 -4 -6 -8 Elastic ball-end tool -10 0

5

10

15

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Figure 7.16: Frequency characteristics of the force control system in case of using the elastic ball-end abrasive tool.

8 Wood stick tool

Gain dB

6

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-2 0

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10

15

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Figure 7.17: Frequency characteristics of the force control system in case of using the small wood-stick tool.

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Table 7.2: Parameters further tuned for the LED lens finishing. Conditions Desired trajectory along curved surface Pitch of CL data viewed in X−Y plane Radius of ball-end abrasive tool R Grain size of diamond lapping paste Desired polishing force Fd Tangent directional velocity ∥v t ∥ Tool revolution per minute

Values Spiral path 0.01 mm 1 mm 4 µm 5N 0.1 mm/s 400 rpm

7.9 Application to finishing an LED lens mold In this section, the proposed system is applied to the finishing of the LED lens mold as shown in Fig. 7.1. A small ball-end tool lathed from a wood stick is used, the tip diameter of which is 1 mm. Other parameters further tuned for the LED lens mold finishing are tabulated in Table 7.2. Fig. 7.18 shows the finishing scene of the LED lens mold, into which a special oil including the diamond lapping paste is poured. Fig. 7.19 shows the surfaces before and after the finishing process. A large-scale photo before finishing process is also shown in Fig. 7.20. It is observed that the concave surface area is of an extremely good quality like a mirror surface reflecting the room lights. Although oily spots are also observed, they can be cleaned easily.

7.10 Stick-slip motion of tool In this section, the effectiveness of the tool’s stick-slip motion is evaluated to improve the surface quality [68]. Fig. 7.21 shows the image of the stick-slip motion. Generally, the stick-slip motion is an undesirable phenomenon and should be eliminated [69, 70]. However, the proposed orthogonal186

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Figure 7.18: Finishing scene by using a wood-stick tool and diamond lapping paste.

type robot employs a small stick-slip motion to improve the finishing quality. The stick-slip motion is given along curved surface and also to orthogonal directions of tool profiling velocity Wv t (k), i.e., tangential velocity. Here, how to generate small stick-slip motion vectors is explained in detail by using Fig. 7.22. In Fig. 7.22, point O is the origin in work coordinate system, where the tool tip initially contacts the workpiece. Point P is the current contact point. p = [px py pz ]T is the position vector viewed from O; n = [nx ny nz ]T is the normalized normal vector at the point P; t = [tx ty tz ]T is the tangential vector at the point P; vv = [vvx vvy vvz ]T is the small stick-slip motion vector. In this example, the tool approaches to the workpiece with a low speed and follow the spiral path after contacting the point O. Because vv is perpendicular to n, the following relation is obtained. nx vvx + ny vvy + nz vvz = 0

(7.16)

Also, vv and t are orthogonal each other, so that tx vvx + ty vvy + tz vvz = 0 187

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Before finishing

After finishing

Figure 7.19: Surface of the LED lens mold before and after the finishing process. The diameter is 4 mm.

Figure 7.20: Large-scale photo of the LED lens mold before finishing process.

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Normal motion

Curved path

Straight path

Figure 7.21: Image of the small stick-slip motion for an abrasive tool.

Further, vv is located in a plane which includes both n and p, so that the components of vv are represented by vvx = inx + jpx

(7.18)

vvy = iny + jpy

(7.19)

vvz = inz + jpz

(7.20)

where i and j are the real numbers. Substituting Eqs. (7.19), (7.20) and (7.20) into Eq. (7.16) leads to i(nx nx + ny ny + nz nz ) + j(nx px + ny py + nz pz ) = 0(7.21) ∥n∥=1 further leads to i = −j(nx px + ny py + nz pz )

(7.22)

Accordingly, by giving Eq. (7.21) to Eqs. (7.17), (7.19) and (7.20), the following equations are obtained. vvx = j{px − (nx px + ny py + nz pz )nx }

(7.23)

vvy = j{py − (nx px + ny py + nz pz )ny }

(7.24)

vvz = j{pz − (nx px + ny py + nz pz )nz }

(7.25)

Because both n and p are known, v v is normalized as v v /∥v v ∥. By using a gain kv , the stick-slip motion vector 189

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t

v Pv

n

O

Top view

n

v P

v

p

O

Front view

Figure 7.22: Surface of the LED lens mold before and after the finishing process. The diameter is 4 mm.

is finally obtained as kv v v /∥v v ∥. kv v v /∥v v ∥ is a velocity vector to yield a novel polishing energy, and which is given to the tool alternatively changing the sign every sampling period. Next, the effectiveness of the stick-slip motion control is examined through an actual finishing test. Fig. 7.23 shows a workpiece of an LED lens mold after the conventional finishing process. Although the workpiece may seem to be a high-quality surface, spotted areas are observed as shown in Fig. 7.24 in which cusps still remain. Fig. 7.25 shows a 190

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Figure 7.23: LED lens mold after the conventional finishing process.

large-scale photo of the LED lens mold after the finishing process using the proposed stick-slip motion control. It is observed that the undesirable cusp marks can be removed uniformly. It has been confirmed from the results that the proposed finishing strategy using the stick-slip motion control has significant effectiveness to achieve a higher-quality surface.

7.11 7.11.1

Neural Network-Based Stiffness Estimator Nonlinear effective stiffness

In this section, an impedance model following force control (IMFFC) using neural networks is proposed to deal with the nonlinear effective stiffness. In advance, the nonlinearity is examined by a simple static position and force measurement. The effectiveness stiffness is easily obtained by the measurement. The desired damping in IMFFC is statically calculated from the critically damped condition of the force control system. The neural networks learn the relation be191

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Figure 7.24: Undesirable small cusp marks still remain on the surface.

Figure 7.25: Large scale photo of an LED lens mold after finishing process by using the proposed stick-slip motion control.

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Contact force N

30 25 20 15 10 5 0 0

-0.05

-0.1 -0.15 Z-directional position mm

-0.2

Figure 7.26: An example of the static relation between position and contact force in the case of a thin wood-stick tool. The tip diameter is 1 mm.

tween the contact force and effective stiffness, so that the desired damping can be dynamically generated according to the contact force. The effectiveness is demonstrated by experiments using the orthogonal-type robot. Fig. 7.26 shows the static relation between the position and contact force obtained by a simple contact experiment. The quantity of the position is the z-directional component at the tip of a wood-stick tool. The quantity of force is yielded by contacting the tool tip with a workpiece and measured by the force sensor. The experiment was conducted while giving the relative position −0.01 mm in press motion and 0.01 mm in unpress motion. In the experiment, the tool tip approaches an aluminum workpiece with a low speed, and after touching the workpiece, i.e., after detecting a small contact force, the tool tip was pressed to the workpiece with every 0.01 mm. The graph drawn as  in Fig. 7.26 shows the relation the position and contact force. After the press motion, the tool tip was away from the workpiece once, and returned to the position again where 32 N had been obtained. After that, the 193

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tool tip was unpressed every 0.01 mm. The graph drawn as • in Fig. 7.26 shows the relation of the position and contact force of this case. It is observed that a small backlash exists. Also, the force is about 32 N when the position of the tool tip is −0.18 mm, so that the effective stiffness within the range can be estimated as 177.7 N/mm. It is expected that a force resolution of about 0.178 N can be performed due to a position resolution of 1 µm. It has been confirmed from the experimental results that orthogonal-type robot has unpreferable nonlinearity and hysteresis. The effective stiffness is largely affected by the kinds of abrasive tools used.

7.11.2 Learning of nonlinearity of effective stiffness The orthogonal-type robot has a CAD/CAM-based position/force controller. The force control method used is called the impedance model following force control (IMFFC). When the force controller is applied, the desired damping should be suitably tuned according to the effective stiffness. Since unstable phenomena such as overshoot and oscillation tend to appear in the force control system with the increase of the effective stiffness, the desired damping has to use larger values. A systematic tuning method for the desired damping was already proposed in consideration of the critically damped condition in the force control system [77]. The calculation of the critically damped condition requires the effective stiffness of the force control system with nonlinearity [78]. Fig. 7.27 shows the nonlinear variation of effective stiffness in press and unpress motions obtained from Fig. 7.26. The number of measured points is 19, respectively. In this subsection, three examples of nonlinearity have been introduced, in which a stiff abrasive tool, an elastic abrasive tool and a thin wood-stick tool are used. As can be seen, the orthogonal-type robot has to deal with many kinds of abrasive tools with both different nonlinearity and 194

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hysteresis. In order to deal with the nonlinearity as shown in Fig. 7.27, a recurrent neural network (RNN) is employed as shown in Fig. 7.28. The RNN is chosen for the proposed robot in consideration of the following generally-known four reasons. 1. A multi-layered neural network works as an effective nonlinear regression model. 2. The learning method known as the back propagation algorithm is simple to implement in software. The learning result obtained as an input/output model can also easily be applied to the control system. 3. The learned RNN has a promising generalization ability for unlearned input data. 4. It has a superior extensibility to a multi-input and multi-output system. In order to make a map of a single-input and singleoutput system, a straightforward method based on the sampling points shown in Fig. 7.27 is to use linear functions to interpolate them. However, when the system is extended to a multi-input and single-output system, the NN-based design will perform more suitable role. In the first subsection, in order to compare with the property of a conventional industrial robot that had already been tested in section 8.2, a simple static effective stiffness of the orthogonal-type robot was similarly measured. As a next step, it is planned to measure a dynamic effective stiffness and to utilize the model in the controller. When the dynamic effective stiffness is modeled, the corresponding NN is designed as a three-input and single-output system. The inputs are contact force, its rate and velocity in force control, and the output is the dynamic effective stiffness. That is the reason why the NN-based design has been selected from the initial stage of the development. In the proposed orthogonal-type robot, two RNNs are used for press motion and unpress motion. Each RNN 195

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Effective stiffness N/mm

200

150

100 Press motion Unpress motion 50

0 0

5

10

15

20

25

30

35

Contact force N

Figure 7.27: Effective stiffness of the orthogonal-tpe robot with the thin wood-stick tool.

consists of an input layer, two hidden layers and an output layer. Each layer has 2, 30 and 1 unit(s), respectively. Each unit is activated by a sigmoid function. Note that the output layer does not have an activate function, i.e., sigmoid function. Therefore, the RNN yields an estimated effective stiffness from the calculation of weighted sum. The RNN acquires the relation between the contact force and the effective stiffness shown in Fig. 7.27 by back propagation algorithm. Teaching patterns are given in the order left to right on the horizontal axis in Fig. 7.27.

7.11.3 NN-based effective stiffness estimator Fig. 7.31 shows a detailed block diagram of the force feedback control law illustrated in Fig. 7.8. Fig. 7.32 also shows the detailed block diagram of the NN-based effective stiffness estimator illustrated in Fig. 7.31. The two NNs in Fig. 7.32 are switched by the sign of ∆∥SF (k)∥= ∥SF (k)∥−∥SF (k − 1)∥ 196

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(7.26)

Desktop orthogonal-type robot

Input layer

1st hidden layer

2nd hidden layer

. . .

. . .

output layer

Contact force Effective stiffness

Figure 7.28: Neural network for acquiring the nonlinearity of effective stiffness.

Effective stiffness N/mm

200

150

100 Teaching signal 1000 times learning 10000 times learning 100000 times learning 1000000 times learning

50

0 0

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10

15

20

25

30

Contact force N

Figure 7.29: Learning result of effective stiffness with nonlinearity in press motion.

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Effective stiffness N/mm

200

150

100

Teaching signal 1000 times learning 10000 times learning 100000 times learning 1000000 times learning

50

0 0

5

10

15

20

25

30

Contact force N

Figure 7.30: Learning result of effective stiffness with nonlinearity in unpress motion.

If ∆∥SF (k)∥> 0, then a NN learned with the teaching patterns in press motion is selected, whereas, if ∆∥SF (k)∥< 0, then NN learned with the teaching patterns in unpress motion is used. For example, when the desired polishing force Fd is set to 10 N, the points of 10 N in Figs. 7.29 and 7.30 become the operating points. The NN-based effective stiffˆe ness estimator generates time-varying effective stiffness K around the operating points. In the next example, a critically damped condition in the force control system generates the desired damping for stable force control. Fig. 7.33 shows the example, in which the polishing force is successfully controlled around 20 N in spite of oscillations caused by a tool rotation of 400 rpm. In this case, it is observed that the NN-based effective stiffness estimator ˆ e as shown in Fig. 7.34. Since yielded the effective stiffness K the viscosity Bm in Eq. (7.9) could be regarded as zero, the ˆ e as given by desired damping was calculated with K Bd = 2

√

ˆe Md Kf K 198

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(7.27)

Desktop orthogonal-type robot Kˆ e : estimated effective stiffness Bd : desired damping

NN-Based NN-BasedEffective Effective Stiffness StiffnessEstimator Estimator

Kˆ e

Critical Critical Damping Damping Condition Condition

Bd SF (k)

Fd Wo (k) d

Wv (k) n

Force ForceController Controller Based Basedon on an an Impedance ImpedanceModel Modelto toFollow Follow

Figure 7.31: Block diagram of the force feedback control law shown in Fig. 3.4.

S

F (k )

. . .

. . . If ∆ S F (k ) > 0

Kˆ e

NN learned with the teaching patterns in press motion

If ∆ S F (k ) < 0

. . .

. . .

NN learned with the teaching patterns in unpress motion

Figure 7.32: Detailed block diagram of the NN-based effective stiffness estimator shown in Fig. 7.31.

7.12 Automatic Tool Truing for LongTime Lapping Process When a polishing compound such as a diamond paste is used, the finishing or polishing process is called the lapping 199 Published by Woodhead Publishing Ltd., 2013

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Polishing force N

30

20

10

Reference Response

0 0

40

80

120

160

200

240

280

320

360

400

Time s

Figure 7.33: Control result of polishing force ∥SF (k)∥. 200

Estimated effective stiffness N/mm

180 160 140 120 100 80 60 40 20 0 0

40

80

120

160

200

240

280

320

360

400

Time s

ˆ e estimated by the neural Figure 7.34: Effective stiffness K networks illustrated in Fig. 7.32

process. It is not easy to automate the lapping process of a metallic LED lens cavity because the cavity itself is not axis-symmetric and a lot of concave areas on the cavity to be finished are very small, e.g., each diameter is 4 mm. Tsai 200

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et al. developed a novel mold-polishing robot [71] and its path-planning technique [72], however, the applicability to the lapping process of an axis-asymmetric LED lens cavity was not described. We could not find previous literature concerning the finishing of an axis-asymmetric LED lens cavity. That is the reason why such an LED cavity is being dexterously finished by the hand lapping of a skilled worker in the related industrial field. However, hand lapping over a long period of time cannot be successfully carried out even by a skilled worker, consequently, defective products caused by the dispersion of quality tend to occur. Recently, desktop-type machine tools have been developed for various industrial machining fields [73–75]. In the previous section, a computer-controlled orthogonal-type robot has been proposed to finish a concave area on an LED cavity [76]. The orthogonal-type robot is comprised of three single-axis devices with a high position resolution of 1 µm. A thin wood-stick tool is attached to the tip of the z-axis. A compact force sensor with three-DOFs is built in the zaxis. The robot has two functional applications. One is the 3D machining function, which is easily realized by using the position control mode. It is expected that the 3D machining function can be applied to the truing of a wood-stick tool. The other is the profiling function, which is performed using the hybrid position/force control mode along a spiral path. It is also expected that the profiling function can be applied to the lapping of concave areas on a metallic LED lens cavity. We have experimentally found that a thin wood stick with a ball-end tip is very suitable for the lapping tool of an LED lens cavity. When the lapping is conducted, a special oil including diamond lapping paste, the grain size of which is about 3 µm, is poured into each concave area on the cavity. The wooden material tends to fit both the metallic material of the LED lens cavity and the diamond lapping paste due to the soft characteristics of wood compared with other conventional metallic abrasive tools. The serious problem in 201

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using a wood-stick tool is the abrasion of the tool tip. For example, an actual LED lens cavity has 180 concave areas so that the cavity can form small plastic LED lenses using mass production. However, after about five concave areas are finished, the tool tip of the wood stick is deformed from the initial ball shape as a result of the abrasion. Therefore, in order to realize a complete automatic finishing system, some truing function must be developed to systematically cope with the undesirable tool abrasion. The truing of a wood-stick tool means the reshaping to the original shape, i.e., ball-end tip. In this section, a novel and simple automatic truing method using CL data is proposed for the long-time lapping process of an LED lens cavity and its effectiveness and validity are evaluated through an experiment. The CL data can be produced from the main-processor of 3D CAD/CAM widely used in industrial fields. The proposed orthogonaltype robot can easily carry out the truing of a wood-stick tool based on the generally-known CL data, which is another important feature of our proposed robot. The structure is very simple for the provided functions. For example, the 3D machining function is easily realized using the position control mode. Also, compliant motion to a workpiece is performed due to the profiling control mode along a desired trajectory, which will be able to be applied to the lapping process of a metallic LED lens cavity. Here, a lapping experiment is conducted to show the effectiveness of the orthogonal-type robot. And, an automatic truing function for a thin wood-stick tool is further proposed to achieve the long-time finishing process. The idea and the detailed software flowchart are described in detail.

7.12.1 Lapping experiment The effectiveness of the orthogonal-type robot is examined through an actual lapping test of an LED lens cavity. Fig. 7.35 shows an example of a skilled worker’s hand lap202

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Figure 7.35: Skilled worker’s hand lapping of an LED lens cavity with multiple concave areas to be finished.

ping, where an LED lens cavity with multiple concave areas is being finished. The lapping process has been being required to be automated; however, its complete achievement is not easy even at the present stage. Fig. 7.36 shows the lapping scene by using the orthogonal-type robot. In this case, the polishing force acting between the tool and the LED lens cavity was successfully controlled, in which the desired value was set to 20 N. The high frequency vibrations are caused by the tool rotation of 400 rpm. Fig. 7.38 shows the surfaces before and after the lapping process. It can be observed that the undesirable cusp marks can be almost removed uniformly. It has been confirmed from the result that the proposed orthogonal-type robot has the ability to achieve a higherquality surface.

7.12.2 Automatic on-line truing function for a thin wood-stick tool In the previous subsection, a lapping process of an LED lens cavity is introduced as one of the applications of the 203

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LED lens mold after finishing

Figure 7.37: LED lens cavity after the lapping process.

4 mm

Figure 7.36: Automated lapping of a concave area on LED lens cavity.

Before finishing

After finishing

Figure 7.38: Finished surface of a concave area on an LED lens cavity, in which the controller shown in Fig. 7.32 is used.

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(A) (B) Wood-stick tool

Radius R

Fixed tool bit Radius R

Figure 7.39: Simple idea for realizing an automatic tool truing.

proposed robot. In order to apply the robot to an actual industrial manufacturing line, the problem of the abrasion of a wood-stick tool should be overcome. Finally, an interesting and important peripheral technique is described briefly. Here, an automatic on-line truing function is proposed for the orthogonal-type robot to be able to continuously finish multiple concave areas machined on an LED lens cavity. Although the tool tip has a ball-end shape with a radius of R [mm] at the start time of the finishing, its ball shape is gradually deformed by the contour abrasion with the passage of the finishing time. Therefore, to maintain the initial performance of the tool, the truing of the tool tip plays a vital role. Fig. 7.39 shows the proposed simple scheme for an automatic wood-stick tool truing. A tool bit for automatic truing is fixed precisely on the table of the robot, so that the contour of the wood-stick tool can be easily reformed to the initial shape, i.e., the radius of R, by moving the rotating abraded tool along the trajectory from point (A) to point (B). Note that the desired trajectory written with a dotted 205

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CAD model

P

Fixed tool bit

O

Figure 7.40: Truing of a wood-stick tool and its desired shape of contour.

line, where the tool with a radius of R is reversed in top and bottom, can be easily drawn by using 3D CAD, and the CL data are generated using the main-processor of the CAM. Fig. 7.40 shows the truing of a wood-stick tool, in which its desired contour shape is illustrated. The CL data used is generated within the area from point O to point P. As can be seen, the tool is being reshaped like the CAD model. The diameter of the wood-stick tool is 3 mm, so that the stiffness in the side directions is lower than the one in the vertical direction. Hence, if the truing is not conducted with a small machining force, then undesirable tool flexure will appear. The machining method used is the position feedforward control law given by Wv t (k) in the block diagram shown Fig. 7.8. It has been confirmed from the experiment that the automatic on-line truing function is successfully realized by using the proposed method. Fig. 7.41 shows the software flowchart of the orthogonaltype robot in running. First of all, if all concave areas, e.g. 206

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Start

Completed?

yes

no

Putting diamond paste on Positioning to next concave area Lapping concave area Truing wood-stick tool

End Figure 7.41: Software flowchart of the orthogonal-type robot for realizing a long-time automatic lapping process, in which on-line tool truing function is incorporated.

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180, are all finished, then the task is completed. Otherwise, the ball-end tip of the wood-stick tool puts the diamond paste on, and goes to the slightly above position of the next concave area. Then, the tool tip approaches to the concave area with a low speed of 1 mm/s. After detecting a contact with the center of the concave area, a lapping action based on the proposed control scheme starts immediately. Next, the truing of the wood-stick tool is conducted by using the method as introduced in this section, and the completion of the task is checked at the top of the flowchart. Due to the automatic truing method, the orthogonal-type robot will be able to be applied to the long-time lapping process.

7.13 Force Input Device fz

fx

fy 18 mm

Figure 7.42: Force input device with three-DOFs. Generally, when an industrial robot is used for machining, operators cannot intervene in the motion, because the motion is programmed in advance with a teaching pendant. Finally, a promising force input device is introduced for an operator to manually regulate the desired feed rate vtangent (k) as written in Eq. (6.7) or the desired polish208

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ing force Fd (k) as written in Eq. (1.17) [79]. The device is designed based on a small capacitive force sensor with three-DOFs. The force sensor is the model PD3-32-05-080 provided by Nitta Corporation. The operator’s skill can be reflected in the robotic behavior using the force input device. The desired polishing force is varied by Fd (k) = α∥f (k)∥+Fd_base

(7.28)

where f (k) = [fx (k) fy (k) fz (k)]T is the force vector given by an operator’s finger. α is the gain for decay or amplification, and Fd_base is the base value of the desired polishing force. Also, the desired feed rate, i.e, tangent velocity, is regulated by vtangemt (k) = β∥f (k)∥+vtangent_base (k)

(7.29)

where β is the gain for decay or amplification, and Vtangent_base (k) is the output of the fuzzy feed rate generator [80]. The force sensor has three-DOFs, so that it is effective to deal with the resultant force in order to give suitable force easily and steadily by operator’s finger. Fig. 7.43 shows the CAD/CAM-based position/force controller with the force input device to manually regulate the desired polishing force Fd (k). As an example, Fig. 7.44 shows the control result of the polishing force, in which Fd_base is set to 5 N and the desired polishing force is regulated with the force input device by an operator. As can be seen, the polishing force ∥F (k)∥ can follow the desired one F d (k). Although the force input device is not equipped with any feedback factors, it is suitable for a finger tip to give small manipulated values. The operator can use the force input device while viewing the variation of the response F (k) or the force input f (k) through the dialog window as shown in Fig. 7.45. 209

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Force ForceInput Input Fd (k) Device Device Wod (k)

Wxd (k)

Fd (k) : Desired polishing Wxd (k) : Desired position

Force Force Feedback Feedback Control Control Law Law

Position Position Feedforward Feedforward Control ControlLaw Law Using UsingCL CLData Dataand and Fuzzy FuzzyReasoning Reasoning Position Position Feedback Feedback Control Control Law Law

Wod (k)

Wvn (k)

force

: Desired direction SF (k)

+

Wvt (k)

+

Wv (k)

Σ +

+

Cartesian-Based Cartesian-Based Servo ServoController Controller

Desktop Desktop Orthogonal Orthogonal Type TypeRobot Robot Wx (k)

Wvp (k)

W~ vv (k )

Sp

Stick-Slip Stick-SlipMotion Motion Control ControlLaw Law

Figure 7.43: CAD/CAM-based position/force controller with the force input device to manually regulate the desired polishing force Fd (k).

7.14 Conclusion In this chapter, we have first examined the resolution of position and force, and effective stiffness through an experiment using an automatic polishing system based on an articulated-type industrial robot with six-DOFs. Also, technical points to be improved have been considered to develop a new finishing system which can be applied to small workpieces such as an LED lens mold. Next, an orthogonal-type robot with a static position resolution of 1 µm and force resolution of 0.083 N has been designed by combining single-axis robots. A CAD/CAM-based position/force controller with a velocity-pulse converter has been also proposed for a desktop-size orthogonal-type robot with a pulse-based servo controller, in which position control, force control or their weak coupling control can coexist together according to each finishing strategy. The velocity-pulse converter can transform minute manipulated values of velocity into a pulse com210

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Reference Response

Polis shing force N

12 11 10 9 8 7 6 5 4 0

1

2

3

4

5

Time s

Figure 7.44: Control result of polishing force ∥F (k)∥, in which the desired polishing force Fd (k) is regulated by an operator with the force input device.

mand which is directly given to the pulse-based servo controller employed in various mechatronics systems. Further, we have introduced a systematic tuning method of the desired damping. The desired damping is calculated from the critically damped condition using the static relation between the position and force. Then, a profiling control experiment using a plastic lens mold with axis symmetric surface has been conducted along a spiral path to evaluate the characteristics of position and force control. Consequently, it has been confirmed that the proposed orthogonal-type robot has a desirable control performance of position and force which would be applied to the finishing task of plastic lens molds. Furthermore, a force input device has been introduced for an operator to manually regulate the desired feed rate or the desired polishing force. It is expected that the force input device will allow industrial machineries to realize cooperative motion between an automatic control and a manual control based on the operator’s skill, which is another im211

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Controller design for industrial robots and machine tools

fz fx

fy

Figure 7.45: Dialog window for viewing the variation of each component of force vector f (k) = [fx (k) fy (k) fz (k)]T .

portant advantage of the proposed orthogonal-type robot. In future work, we plan to develop a much smaller ballend abrasive tool for finishing a workpiece with smaller concave areas of 3.6 mm and to conduct a finishing experiment by using the proposed orthogonal-type robot with compliance controllability.

212

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References [1] C. Chen, M.M. Trivedi, and C.R. Bidlack, Simulation and animation of sensor-driven robots. IEEE Trans. on Robotics and Automation, 10(5): 684–704, 1994. [2] F. Benimeli, V. Mata, and F. Valero, A comparison between direct and indirect dynamic parameter identification methods in industrial robots. Robotica, 24(5): 579–590, 2006. [3] P. Corke, A Robotics Toolbox for MATLAB. IEEE Robotics & Automation Magazine, 3(1): 24–32, 1996. [4] P. Corke, MATLAB Toolboxes: robotics and vision for students and teachers. IEEE Robotics & Automation Magazine, 14(4): 16–17, 2007. [5] J.Y.S. Luh, M.H. Walker, and R.P.C. Paul, Resolved acceleration control of mechanical manipulator. IEEE Trans. on Automatic Control, 25(3): 468–474, 1980. [6] F. Nagata, K. Kuribayashi, K. Kiguchi, and K. Watanabe, Simulation of fine gain tuning using genetic algorithms for model-based robotic servo controllers. In IEEE International Symposium on Computational Intelligence in Robotics and Automation, pages 196–201, 2007. [7] F. Nagata, I. Okabayashi, M. Matsuno, T. Utsumi, K. Kuribayashi, and K. Watanabe, Fine gain tuning 215

Controller design for industrial robots and machine tools

for model-based robotic servo controllers using genetic algorithms. In 13th International Conference on Advanced Robotics, pages 987–992, 2007. [8] N. Hogan, Impedance control: An approach to manipulation: Part I - Part III. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 107: 1–24, 1985. [9] F. Nagata, K. Watanabe, S. Hashino, H. Tanaka, T. Matsuyama, and K. Hara, Polishing robot using a joystick controlled teaching system. In IEEE International Conference on Industrial Electronics, Control and Instrumentation, pages 632–637, 2000. [10] J.J. Craig, Introduction to ROBOTICS —Mechanics and Control Second Edition—. Addison Wesley Publishing Co., Reading, Mass., 1989. [11] F. Nagata, Y. Kusumoto, Y. Fujimoto, and K. Watanabe, Robotic sanding system for new designed furniture with free-formed surface. Robotics and ComputerIntegrated Manufacturing, 23(4): 371–379, 2007. [12] M. Kawato, The feedback-error-learning neural network for supervised motor learning. Advanced Neural Computers, Elsevier Amsterdam, pages 365–373, 1990. [13] J. Nakanishi and S. Schaal, Feedback error learning and nonlinear adaptive control. Neural Networks, 17(10): 1453–1465, 2004. [14] T. Furuhashi, K. Nakaoka, H. Maeda, and Y. Uchikawa, A proposal of genetic algorithm with a local improvement mechanism and finding of fuzzy rules. Journal of Japan Society for Fuzzy Theory and Systems, 7(5): 978–987, 1995 (in Japanese). [15] D.A. Linkens and H.O. Nyongesa, Genetic algorithms for fuzzy control part 1: Offline system development 216

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References

and application. IEE Proceedings Control Theory and Applications , 142(3): 161–176, 1995. [16] D.A. Linkens and H.O. Nyongesa, Genetic algorithms for fuzzy control part 2: Online System Development and Application. IEE Proceedings Control Theory and Applications, 142(3): 177–185, 1995. [17] G. Ferretti, G. Magnani, and A. Zavala Rio, Impact modeling and control for industrial manipulators. IEEE Control Systems Magazine, 18(4): 65–71, 1998. [18] T. Sasaki and S. Tachi, Contact stability analysis on some impedance control methods. Journal of the Robotics Society of Japan , 12(3): 489–496, 1994 (in Japanese). [19] H.C. An and J.M. Hollerbach, Dynamic stability issues in force control of manipulators. In IEEE International Conference on Robotics and Automation, pages 890–896, 1987. [20] H.C. An, C.G. Atkeson, and J.M. Hollerbach, Modelbased control of a robot manipulator. The MIT Press classics series, The MIT Press, Massachusetts,1988. [21] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions Systems, Man & Cybernetics, 15(1): 116–132, 1985. [22] F. Nagata, K. Watanabe, K. Sato, and K. Izumi, An experiment on profiling task with impedance controlled manipulator using cutter location data. In IEEE International Conference on Systems, Man, and Cybernetics, pages 848–853, 1999. [23] F. Nagata, K. Watanabe, and K. Izumi, Furniture polishing robot using a trajectory generator based on cutter location data. In IEEE International Conference on Robotics and Automation, pages 319–324, 2001. 217

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Controller design for industrial robots and machine tools

[24] M.H. Raibert and J.J. Craig, Hybrid position/force control of manipulators. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 102: 126–133, 1981. [25] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, CAD/CAM-based position/force controller for a mold polishing robot. Mechatronics, 17(4/5): 207-216, 2007. [26] F. Nagata, K. Watanabe, S. Hashino, H. Tanaka, T. Matsuyama, and K. Hara, Polishing robot using joystick controlled teaching. Journal of Robotics and Mechatronics, 13(5): 517–525, 2001. [27] F. Nagata, K. Watanabe, and K. Kiguchi, Joystick teaching system for industrial robots using fuzzy compliance control. Industrial Robotics: Theory, Modelling and Control, INTECH, pages 799–812, 2006. [28] Y. Maeda, N. Ishido, H. Kikuchi, and T. Arai, Teaching of grasp/graspless manipulation for industrial robots by human demonstration. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1523–1528, 2002. [29] D. Kushida, M. Nakamura, S. Goto, and N. Kyura, Human direct teaching of industrial articulated robot arms based on force-free control. Artificial Life and Robotics, 5(1): 26–32, 2001. [30] S. Sugita, T. Itaya, and Y. Takeuchi, Development of robot teaching support devices to automate deburring and finishing works in casting. The International Journal of Advanced Manufacturing Technology, 23(3/4): 183–189, 2003. [31] C. K. Ahn and M. C. Lee, An off-line automatic teaching by vision information for robotic assembly task. 218

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References

In IEEE International Conference on Industrial Electronics, Control and Instrumentation, pages 2171–2176, 2000. [32] P. Neto, J. N. Pires, and A. P. Moreira, CAD-based offline robot programming. In IEEE International Conference on Robotics Automation and Mechatronics, pages 516–521, 2010. [33] D. F. Ge, Y. Takeuchi, and N. Asakawa, Automation of polishing work by an industrial robot, – 2nd report, automatic generation of collision-free polishing path –. Transaction of the Japan Society of Mechanical Engineers, 59(561): 1574–1580, 1993 (in Japanese). [34] F. Ozaki, M. Jinno, T. Yoshimi, K. Tatsuno, M. Takahashi, M. Kanda, Y. Tamada, and S. Nagataki, A force controlled finishing robot system with a task-directed robot language. Journal of Robotics and Mechatronics, 7(5): 383–388, 1995. [35] F. Pfeiffer, H. Bremer, and J. Figueiredo, Surface polishing with flexible link manipulators. European Journal of Mechanics, A/Solids, 15(1): 137–153, 1996. [36] Y. Takeuchi, D. Ge, and N. Asakawa, Automated polishing process with a human-like dexterous robot. In IEEE International Conference on Robotics and Automation, pages 950–956, 1993. [37] P.R. Pagilla and B. Yu, Robotic surface finishing processes: modeling, control, and experiments. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 123: 93–102, 2001. [38] H. Huang, L. Zhou, X.Q. Chen, and Z.M. Gong, SMART robotic system for 3D profile turbine vane airfoil repair. International Journal of Advanced Manufacturing Technology, 21(4): 275–283, 2003. 219

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Controller design for industrial robots and machine tools

[39] T.M. Stephien, L.M. Sweet, M.C. Good, and M. Tomizuka, Control of tool/workpiece contact force with application to robotic deburring. IEEE Journal of Robotics and Automation, 3(1): 7–18, 1987. [40] H. Kazerooni, Robotic deburring of two-dimensional parts with unknown geometry. Journal of Manufacturing Systems, 7(4): 329–338, 1988. [41] M.G. Her and H. Kazerooni, Automated robotic deburring of parts using compliance control. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 60–66, 1991. [42] G.M. Bone, M.A. Elbestawi, R. Lingarkar, and L. Liu, Force control of robotic deburring. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 395–400, 1991. [43] D.M. Gorinevsky, A.M. Formalsky, and A.Y. Schneider, Force Control of Robotics Systems, CRC Press, New York, 1997. [44] K. Takahashi, S. Aoyagi, and M. Takano, Study on a fast profiling task of a robot with force control using feedforward of predicted contact position data. In 4th Japan-France Congress & 2nd Asia-Europe Congress on Mechatronics, pages 398–401, 1998. [45] Y. Takeuchi and T. Watanabe, Study on post-processor for 5-axis control machining. Journal of the Japan Society for Precision Engineering , 58(9): 1586–92, 1992 (in Japanese). [46] Y. Takeuchi K. Wada, T. Hisaki, and M. Yokoyama, Study on post-processor for 5-axis control machining centers —In case of spindle-tilting type and table/spindle-tilting type. Journal of the Japan Society for Precision Engineering, 60(1): 75–79, 1994 (in Japanese). 220

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Computer-Integrated Manufacturing, 22(5-6): 437–46, 2006. [55] Y.S. Tarng, H.Y. Chuang, and W.T. Hsu, Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture, 39(10): 1673–1692, 1999. [56] U. Zuperl, F. Cus, and M. Milfelner, Fuzzy control strategy for an adaptive force control in end-milling. Journal of Materials Processing Technology, 164/165: 1472–1478, 2005. [57] R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.F. Yuan, and S. Jee, Variable-feedrate CNC interpolators for constant material removal rates along Pythagoreanhodograph curves. Computer-Aided Design, 30(8): 631–640, 1998. [58] R.T. Farouki, J. Manjunathaiah, and G.F. Yuan. G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on openarchitecture CNC machines. Machine Tools & Manufacture, 39(1): 123–142, 1999. [59] A. Frank and A. Schmid, Grinding of non-circular contours on CNC cylindrical grinding machines. Robotics and Computer-Integrated Manufacturing, 4(1/2): 211–218, 1988. [60] J.A. Couey, E.R. Marsh, B.R. Knapp, and R.R. Vallance, Monitoring force in precision cylindrical grinding. Precision Engineering, 29(3): 307–314, 2005. [61] T. Tawakoli, A. Rasifard, and M. Rabiey, Highefficiency internal cylindrical grinding with a new kinematic. Machine Tools & Manufacture, 47(5): 729–733, 2007. 222

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[62] F. Nagata, Y. Kusumoto, K. Hasebe, K. Saito, M. Fukumoto, and K. Watanabe, Post-processor using a fuzzy feed rate generator for multi-axis NC machine tools with a rotary unit. In International Conference on Control, Automation and Systems, pages 438–443, 2005. [63] F. Nagata and K. Watanabe, Development of a postprocessor module of 5-axis control NC machine tool with tilting-head for woody furniture. Journal of the Japan Society for Precision Engineering, 62(8): 1203–1207, 1996 (in Japanese). [64] K. Fujino, Y. Sawada, Y. Fujii, and S. Okumura, Machining of curved surface of wood by ball end mill – Effect of rake angle and feed speed on machined surface. In 16th International Wood Machining Seminar, Part 2, pages 532–538, 2003. [65] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliance control capability. In 13th International Symposium on Artificial Life and Robotics, pages 779–782, 2008, [66] J. Duffy, The Fallacy of modern hybrid control theory that is based on orthogonal complements of twist and wrench spaces. Journal of Robotic Systems, 7(2): 139–144, 1990. [67] M.C. Lee, S.J. Go, M.H. Lee, C.S. Jun, D.S. Kim, K.D. Cha, and J.H. Ahn, A robust trajectory tracking control of a polishing robot system based on CAM data. Robotics and Computer-Integrated Manufacturing, 17(1/2): 177–183, 2001, [68] F. Nagata, T. Mizobuchi, S. Tani, T. Hase, Z. Haga, K. Watanabe, M.K. Habib, and K. Kiguchi, Desktop orthogonal-type robot with abilities of compliant 223

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motion and stick-slip motion for lapping of LED lens molds. In IEEE International Conference on Robotics & Automation , pages 2095–2100, 2010, [69] O. Bilkay and O. Anlagan, Computer simulation of stick-slip motion in machine tool slideways. Tribology International, 37(4): 347–351, 2004. [70] X. Mei, M. Tsutsumi, T. Tao, and N. Sun, Study on the compensation of error by stick-slip for high-precision table. International Journal of Machine tools & Manufacture, 44(5): 503–510, 2004. [71] M.J. Tsai, J.L. Chang, and J.F. Haung, Development of an automatic mold polishing system. In IEEE International Conference on Robotics & Automation, pages 3517–3522, 2003. [72] M.J. Tsai, J.J. Fang, and J.L. Chang, Robotic path planning for an automatic mold polishing system. International Journal of Robotics & Automation, 19(2): 81–89, 2004, [73] H. Hocheng, Y.H. Sun, S.C. Lin, and P.S. Kao, A material removal analysis of electrochemical machining using flat-end cathode. Journal of Materials Processing Technology, 140(1/3): 264–268, 2003. [74] Y. Uehara, H. Ohmori, W. Lin, Y. Ueno, T. Naruse, N. Mitsuishi, S. Ishikawa, and T. Miura, Development of spherical lens ELID grinding system by desk-top 4-axes Machine Tool. In International Conference on Leading Edge Manufacturing in 21st Century, pages 247–252, 2005, [75] H. Ohmori and Y. Uehara, Development of a desktop machine tool for mirror surface grinding. International Journal of Automation Technology, 4(2): 88–96, 2010, 224

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[76] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliant motion capability. Artificial Life and Robotics, 13(2): 423–427, 2009. [77] F. Nagata, S. Tani, T. Mizobuchi, T. Hase, Z. Haga, M. Omoto, K. Watanabe, and M.K. Habib. Basic performance of a desktop NC machine tool with compliant motion capability. In IEEE International Conference on Mechatronics and Automation, WC1–5, pages 1–6, 2008. [78] F. Nagata, K. Watanabe, K. Sato, and K. Izumi, Impedance control using anisotropic fuzzy environment models. Journal of Robotics and Mechatronics, 11(1): 60-66, 1999. [79] F. Nagata, A. Otsuka, S. Yoshitake and K. Watanabe, Automatic control of an orthogonal-type robot with a force sensor and a small force input device, In The 37th Annual Conference of the IEEE Industrial Electronics Society, pages 3151–3156, 2011. [80] F. Nagata and K. Watanabe, Feed rate control using a fuzzy reasoning for a mold polishing robot. Journal of Robotics and Mechatronics, 18(1): 76–82, 2006. [81] Japanese Patent 4094781, Robotic force control method, F. Nagata, and K. Watanabe, 2008. [82] Japanese Patent 4447746, Robotic trajectory teaching method, F. Nagata, K. Tsuda, and K. Watanabe, 2010. [83] Japanese Patent 4216557, Polishing apparatus and polishing method, K. Tsuda, K. Yasuda, F. Nagata, Y. Kusumoto, and K. Watanabe, 2008.

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8 Conclusion DOI: 10.1533/9780857094636.213 Abstract: This chapter briefly sums up the book. Key words: summary In this book, discrete-time control systems with intelligent control approaches have been proposed for openarchitecture industrial machineries. Then, a novel and practical position/force control strategy has been designed for industrial machineries, such as an articulated-type industrial robot or an orthogonal-type robot, with an open-architecture controller. Three types of polishing robots and a machining system, listed below, have been introduced to show the effectiveness and promise of the proposed controllers. • 3D robot sander developed based on KAWASAKI FS30L or FS20, which sands wooden parts used to construct furniture with artistic free-formed surfaces. • Mold polishing robot developed based on YASKAWA MOTOMAN UP6, which polishes aluminum PET bottle blow molds with curved surfaces. • Orthogonal-type industrial robot developed based on three single-axis devices ISPA provided by IAI Corp., which can be applied to the finishing process of an LED lens mold with about 180 small concave areas, e.g. each diameter is 4 mm. 213

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• 3D machining system developed based on Roland MDX-650A with a rotary unit, which can carve an artistic wooden paint roller to produce a relief wall. The goal of our study was the development of an orthogonal-type industrial robot with compliance controllability which can be flexibly applied to from the cusp mark removing process to the final finishing process for an LED lens mold with a lot of concave areas of about 4 mm. In such a case, there existed two key points to be overcome. One is a CAM system for industrial robots with an openarchitecture controller, which can automatically generate a desired trajectory with orientation components. The other is a delicate, skillful and balanced control method of position and force which is ordinarily performed by skilled workers. The proposed methods described from the second chapter to the eighth chapter could achieve the above objectives. We hope that the readers of this book will know the related technologies theoretically and experimentally and will try to develop a novel manufacturing system required from other industrial fields. In such cases, intelligent control approaches such as fuzzy control, genetic algorithms and neural network will enable the industrial machineries not only to further improve the conventional performance but also to produce an advanced function and a novel technology.

214

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References [1] C. Chen, M.M. Trivedi, and C.R. Bidlack, Simulation and animation of sensor-driven robots. IEEE Trans. on Robotics and Automation, 10(5): 684–704, 1994. [2] F. Benimeli, V. Mata, and F. Valero, A comparison between direct and indirect dynamic parameter identification methods in industrial robots. Robotica, 24(5): 579–590, 2006. [3] P. Corke, A Robotics Toolbox for MATLAB. IEEE Robotics & Automation Magazine, 3(1): 24–32, 1996. [4] P. Corke, MATLAB Toolboxes: robotics and vision for students and teachers. IEEE Robotics & Automation Magazine, 14(4): 16–17, 2007. [5] J.Y.S. Luh, M.H. Walker, and R.P.C. Paul, Resolved acceleration control of mechanical manipulator. IEEE Trans. on Automatic Control, 25(3): 468–474, 1980. [6] F. Nagata, K. Kuribayashi, K. Kiguchi, and K. Watanabe, Simulation of fine gain tuning using genetic algorithms for model-based robotic servo controllers. In IEEE International Symposium on Computational Intelligence in Robotics and Automation, pages 196–201, 2007. [7] F. Nagata, I. Okabayashi, M. Matsuno, T. Utsumi, K. Kuribayashi, and K. Watanabe, Fine gain tuning 215

Controller design for industrial robots and machine tools

for model-based robotic servo controllers using genetic algorithms. In 13th International Conference on Advanced Robotics, pages 987–992, 2007. [8] N. Hogan, Impedance control: An approach to manipulation: Part I - Part III. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 107: 1–24, 1985. [9] F. Nagata, K. Watanabe, S. Hashino, H. Tanaka, T. Matsuyama, and K. Hara, Polishing robot using a joystick controlled teaching system. In IEEE International Conference on Industrial Electronics, Control and Instrumentation, pages 632–637, 2000. [10] J.J. Craig, Introduction to ROBOTICS —Mechanics and Control Second Edition—. Addison Wesley Publishing Co., Reading, Mass., 1989. [11] F. Nagata, Y. Kusumoto, Y. Fujimoto, and K. Watanabe, Robotic sanding system for new designed furniture with free-formed surface. Robotics and ComputerIntegrated Manufacturing, 23(4): 371–379, 2007. [12] M. Kawato, The feedback-error-learning neural network for supervised motor learning. Advanced Neural Computers, Elsevier Amsterdam, pages 365–373, 1990. [13] J. Nakanishi and S. Schaal, Feedback error learning and nonlinear adaptive control. Neural Networks, 17(10): 1453–1465, 2004. [14] T. Furuhashi, K. Nakaoka, H. Maeda, and Y. Uchikawa, A proposal of genetic algorithm with a local improvement mechanism and finding of fuzzy rules. Journal of Japan Society for Fuzzy Theory and Systems, 7(5): 978–987, 1995 (in Japanese). [15] D.A. Linkens and H.O. Nyongesa, Genetic algorithms for fuzzy control part 1: Offline system development 216

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References

and application. IEE Proceedings Control Theory and Applications , 142(3): 161–176, 1995. [16] D.A. Linkens and H.O. Nyongesa, Genetic algorithms for fuzzy control part 2: Online System Development and Application. IEE Proceedings Control Theory and Applications, 142(3): 177–185, 1995. [17] G. Ferretti, G. Magnani, and A. Zavala Rio, Impact modeling and control for industrial manipulators. IEEE Control Systems Magazine, 18(4): 65–71, 1998. [18] T. Sasaki and S. Tachi, Contact stability analysis on some impedance control methods. Journal of the Robotics Society of Japan , 12(3): 489–496, 1994 (in Japanese). [19] H.C. An and J.M. Hollerbach, Dynamic stability issues in force control of manipulators. In IEEE International Conference on Robotics and Automation, pages 890–896, 1987. [20] H.C. An, C.G. Atkeson, and J.M. Hollerbach, Modelbased control of a robot manipulator. The MIT Press classics series, The MIT Press, Massachusetts,1988. [21] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions Systems, Man & Cybernetics, 15(1): 116–132, 1985. [22] F. Nagata, K. Watanabe, K. Sato, and K. Izumi, An experiment on profiling task with impedance controlled manipulator using cutter location data. In IEEE International Conference on Systems, Man, and Cybernetics, pages 848–853, 1999. [23] F. Nagata, K. Watanabe, and K. Izumi, Furniture polishing robot using a trajectory generator based on cutter location data. In IEEE International Conference on Robotics and Automation, pages 319–324, 2001. 217

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Controller design for industrial robots and machine tools

[24] M.H. Raibert and J.J. Craig, Hybrid position/force control of manipulators. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 102: 126–133, 1981. [25] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, CAD/CAM-based position/force controller for a mold polishing robot. Mechatronics, 17(4/5): 207-216, 2007. [26] F. Nagata, K. Watanabe, S. Hashino, H. Tanaka, T. Matsuyama, and K. Hara, Polishing robot using joystick controlled teaching. Journal of Robotics and Mechatronics, 13(5): 517–525, 2001. [27] F. Nagata, K. Watanabe, and K. Kiguchi, Joystick teaching system for industrial robots using fuzzy compliance control. Industrial Robotics: Theory, Modelling and Control, INTECH, pages 799–812, 2006. [28] Y. Maeda, N. Ishido, H. Kikuchi, and T. Arai, Teaching of grasp/graspless manipulation for industrial robots by human demonstration. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1523–1528, 2002. [29] D. Kushida, M. Nakamura, S. Goto, and N. Kyura, Human direct teaching of industrial articulated robot arms based on force-free control. Artificial Life and Robotics, 5(1): 26–32, 2001. [30] S. Sugita, T. Itaya, and Y. Takeuchi, Development of robot teaching support devices to automate deburring and finishing works in casting. The International Journal of Advanced Manufacturing Technology, 23(3/4): 183–189, 2003. [31] C. K. Ahn and M. C. Lee, An off-line automatic teaching by vision information for robotic assembly task. 218

Published by Woodhead Publishing Ltd., 2013

References

In IEEE International Conference on Industrial Electronics, Control and Instrumentation, pages 2171–2176, 2000. [32] P. Neto, J. N. Pires, and A. P. Moreira, CAD-based offline robot programming. In IEEE International Conference on Robotics Automation and Mechatronics, pages 516–521, 2010. [33] D. F. Ge, Y. Takeuchi, and N. Asakawa, Automation of polishing work by an industrial robot, – 2nd report, automatic generation of collision-free polishing path –. Transaction of the Japan Society of Mechanical Engineers, 59(561): 1574–1580, 1993 (in Japanese). [34] F. Ozaki, M. Jinno, T. Yoshimi, K. Tatsuno, M. Takahashi, M. Kanda, Y. Tamada, and S. Nagataki, A force controlled finishing robot system with a task-directed robot language. Journal of Robotics and Mechatronics, 7(5): 383–388, 1995. [35] F. Pfeiffer, H. Bremer, and J. Figueiredo, Surface polishing with flexible link manipulators. European Journal of Mechanics, A/Solids, 15(1): 137–153, 1996. [36] Y. Takeuchi, D. Ge, and N. Asakawa, Automated polishing process with a human-like dexterous robot. In IEEE International Conference on Robotics and Automation, pages 950–956, 1993. [37] P.R. Pagilla and B. Yu, Robotic surface finishing processes: modeling, control, and experiments. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 123: 93–102, 2001. [38] H. Huang, L. Zhou, X.Q. Chen, and Z.M. Gong, SMART robotic system for 3D profile turbine vane airfoil repair. International Journal of Advanced Manufacturing Technology, 21(4): 275–283, 2003. 219

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Controller design for industrial robots and machine tools

[39] T.M. Stephien, L.M. Sweet, M.C. Good, and M. Tomizuka, Control of tool/workpiece contact force with application to robotic deburring. IEEE Journal of Robotics and Automation, 3(1): 7–18, 1987. [40] H. Kazerooni, Robotic deburring of two-dimensional parts with unknown geometry. Journal of Manufacturing Systems, 7(4): 329–338, 1988. [41] M.G. Her and H. Kazerooni, Automated robotic deburring of parts using compliance control. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 60–66, 1991. [42] G.M. Bone, M.A. Elbestawi, R. Lingarkar, and L. Liu, Force control of robotic deburring. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 395–400, 1991. [43] D.M. Gorinevsky, A.M. Formalsky, and A.Y. Schneider, Force Control of Robotics Systems, CRC Press, New York, 1997. [44] K. Takahashi, S. Aoyagi, and M. Takano, Study on a fast profiling task of a robot with force control using feedforward of predicted contact position data. In 4th Japan-France Congress & 2nd Asia-Europe Congress on Mechatronics, pages 398–401, 1998. [45] Y. Takeuchi and T. Watanabe, Study on post-processor for 5-axis control machining. Journal of the Japan Society for Precision Engineering , 58(9): 1586–92, 1992 (in Japanese). [46] Y. Takeuchi K. Wada, T. Hisaki, and M. Yokoyama, Study on post-processor for 5-axis control machining centers —In case of spindle-tilting type and table/spindle-tilting type. Journal of the Japan Society for Precision Engineering, 60(1): 75–79, 1994 (in Japanese). 220

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[47] X.J. Xu, C. Bradley, Y.F. Zhang, H.T. Loh, and Y.S. Wong, Tool-path generation for five-axis machining of free-form surfaces based on accessibility analysis. International Journal of Production Research, 40(14): 3253–3274, 2002. [48] S.L. Chen, T.H. Chang, I. Inasaki, and Y.C. Liu, Postprocessor development of a hybrid TRR-XY parallel kinematic machine tool. The International Journal of Advanced Manufacturing Technology, 20(4): 259–69, 2002. [49] W.T. Lei and Y.Y. Hsu, Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part I: design and modeling. Machine Tool & Manufacture, 42(10): 1153–1162, 2002. [50] W.T. Lei, M.P. Sung, W.L. Liu, and Y.C. Chuang, Double ballbar test for the rotary axes of five-axis CNC machine tools. Machine Tool & Manufacture, 47(2): 273–285, 2006. [51] L.X. Cao, H. Gong, and J. Liu, The offset approach of machining free form surface. Part 1: Cylindrical cutter in five-axis NC machine tools. Journal of Materials Processing Technology, 174(1/3): 298–304, 2006. [52] L.X. Cao , H. Gong, and J. Liu, The offset approach of machining free form surface. Part 2: Toroidal cutter in 5-axis NC machine tools. Journal of Materials Processing Technology, 184(1/3): 6–11, 2007. [53] S.D.Timar, R.T. Farouki, T.S. Smith, and C.L. Boyadjieff. Algorithms for time optimal control of CNC machines along curved tool paths. Robotics and ComputerIntegrated Manufacturing, 21(1): 37–53, 2005. [54] E.Y. Heo, D.W. Kim, B.H. Kim, and F.F. Chen, Estimation of NC machining time using NC block distribution for sculptured surface machining. Robotics and 221

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Controller design for industrial robots and machine tools

Computer-Integrated Manufacturing, 22(5-6): 437–46, 2006. [55] Y.S. Tarng, H.Y. Chuang, and W.T. Hsu, Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture, 39(10): 1673–1692, 1999. [56] U. Zuperl, F. Cus, and M. Milfelner, Fuzzy control strategy for an adaptive force control in end-milling. Journal of Materials Processing Technology, 164/165: 1472–1478, 2005. [57] R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.F. Yuan, and S. Jee, Variable-feedrate CNC interpolators for constant material removal rates along Pythagoreanhodograph curves. Computer-Aided Design, 30(8): 631–640, 1998. [58] R.T. Farouki, J. Manjunathaiah, and G.F. Yuan. G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on openarchitecture CNC machines. Machine Tools & Manufacture, 39(1): 123–142, 1999. [59] A. Frank and A. Schmid, Grinding of non-circular contours on CNC cylindrical grinding machines. Robotics and Computer-Integrated Manufacturing, 4(1/2): 211–218, 1988. [60] J.A. Couey, E.R. Marsh, B.R. Knapp, and R.R. Vallance, Monitoring force in precision cylindrical grinding. Precision Engineering, 29(3): 307–314, 2005. [61] T. Tawakoli, A. Rasifard, and M. Rabiey, Highefficiency internal cylindrical grinding with a new kinematic. Machine Tools & Manufacture, 47(5): 729–733, 2007. 222

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Controller design for industrial robots and machine tools

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[39] T.M. Stephien, L.M. Sweet, M.C. Good, and M. Tomizuka, Control of tool/workpiece contact force with application to robotic deburring. IEEE Journal of Robotics and Automation, 3(1): 7–18, 1987. [40] H. Kazerooni, Robotic deburring of two-dimensional parts with unknown geometry. Journal of Manufacturing Systems, 7(4): 329–338, 1988. [41] M.G. Her and H. Kazerooni, Automated robotic deburring of parts using compliance control. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 60–66, 1991. [42] G.M. Bone, M.A. Elbestawi, R. Lingarkar, and L. Liu, Force control of robotic deburring. Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, 113: 395–400, 1991. [43] D.M. Gorinevsky, A.M. Formalsky, and A.Y. Schneider, Force Control of Robotics Systems, CRC Press, New York, 1997. [44] K. Takahashi, S. Aoyagi, and M. Takano, Study on a fast profiling task of a robot with force control using feedforward of predicted contact position data. In 4th Japan-France Congress & 2nd Asia-Europe Congress on Mechatronics, pages 398–401, 1998. [45] Y. Takeuchi and T. Watanabe, Study on post-processor for 5-axis control machining. Journal of the Japan Society for Precision Engineering , 58(9): 1586–92, 1992 (in Japanese). [46] Y. Takeuchi K. Wada, T. Hisaki, and M. Yokoyama, Study on post-processor for 5-axis control machining centers —In case of spindle-tilting type and table/spindle-tilting type. Journal of the Japan Society for Precision Engineering, 60(1): 75–79, 1994 (in Japanese). 220

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[47] X.J. Xu, C. Bradley, Y.F. Zhang, H.T. Loh, and Y.S. Wong, Tool-path generation for five-axis machining of free-form surfaces based on accessibility analysis. International Journal of Production Research, 40(14): 3253–3274, 2002. [48] S.L. Chen, T.H. Chang, I. Inasaki, and Y.C. Liu, Postprocessor development of a hybrid TRR-XY parallel kinematic machine tool. The International Journal of Advanced Manufacturing Technology, 20(4): 259–69, 2002. [49] W.T. Lei and Y.Y. Hsu, Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part I: design and modeling. Machine Tool & Manufacture, 42(10): 1153–1162, 2002. [50] W.T. Lei, M.P. Sung, W.L. Liu, and Y.C. Chuang, Double ballbar test for the rotary axes of five-axis CNC machine tools. Machine Tool & Manufacture, 47(2): 273–285, 2006. [51] L.X. Cao, H. Gong, and J. Liu, The offset approach of machining free form surface. Part 1: Cylindrical cutter in five-axis NC machine tools. Journal of Materials Processing Technology, 174(1/3): 298–304, 2006. [52] L.X. Cao , H. Gong, and J. Liu, The offset approach of machining free form surface. Part 2: Toroidal cutter in 5-axis NC machine tools. Journal of Materials Processing Technology, 184(1/3): 6–11, 2007. [53] S.D.Timar, R.T. Farouki, T.S. Smith, and C.L. Boyadjieff. Algorithms for time optimal control of CNC machines along curved tool paths. Robotics and ComputerIntegrated Manufacturing, 21(1): 37–53, 2005. [54] E.Y. Heo, D.W. Kim, B.H. Kim, and F.F. Chen, Estimation of NC machining time using NC block distribution for sculptured surface machining. Robotics and 221

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Computer-Integrated Manufacturing, 22(5-6): 437–46, 2006. [55] Y.S. Tarng, H.Y. Chuang, and W.T. Hsu, Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture, 39(10): 1673–1692, 1999. [56] U. Zuperl, F. Cus, and M. Milfelner, Fuzzy control strategy for an adaptive force control in end-milling. Journal of Materials Processing Technology, 164/165: 1472–1478, 2005. [57] R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.F. Yuan, and S. Jee, Variable-feedrate CNC interpolators for constant material removal rates along Pythagoreanhodograph curves. Computer-Aided Design, 30(8): 631–640, 1998. [58] R.T. Farouki, J. Manjunathaiah, and G.F. Yuan. G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on openarchitecture CNC machines. Machine Tools & Manufacture, 39(1): 123–142, 1999. [59] A. Frank and A. Schmid, Grinding of non-circular contours on CNC cylindrical grinding machines. Robotics and Computer-Integrated Manufacturing, 4(1/2): 211–218, 1988. [60] J.A. Couey, E.R. Marsh, B.R. Knapp, and R.R. Vallance, Monitoring force in precision cylindrical grinding. Precision Engineering, 29(3): 307–314, 2005. [61] T. Tawakoli, A. Rasifard, and M. Rabiey, Highefficiency internal cylindrical grinding with a new kinematic. Machine Tools & Manufacture, 47(5): 729–733, 2007. 222

Published by Woodhead Publishing Ltd., 2013

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[62] F. Nagata, Y. Kusumoto, K. Hasebe, K. Saito, M. Fukumoto, and K. Watanabe, Post-processor using a fuzzy feed rate generator for multi-axis NC machine tools with a rotary unit. In International Conference on Control, Automation and Systems, pages 438–443, 2005. [63] F. Nagata and K. Watanabe, Development of a postprocessor module of 5-axis control NC machine tool with tilting-head for woody furniture. Journal of the Japan Society for Precision Engineering, 62(8): 1203–1207, 1996 (in Japanese). [64] K. Fujino, Y. Sawada, Y. Fujii, and S. Okumura, Machining of curved surface of wood by ball end mill – Effect of rake angle and feed speed on machined surface. In 16th International Wood Machining Seminar, Part 2, pages 532–538, 2003. [65] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliance control capability. In 13th International Symposium on Artificial Life and Robotics, pages 779–782, 2008, [66] J. Duffy, The Fallacy of modern hybrid control theory that is based on orthogonal complements of twist and wrench spaces. Journal of Robotic Systems, 7(2): 139–144, 1990. [67] M.C. Lee, S.J. Go, M.H. Lee, C.S. Jun, D.S. Kim, K.D. Cha, and J.H. Ahn, A robust trajectory tracking control of a polishing robot system based on CAM data. Robotics and Computer-Integrated Manufacturing, 17(1/2): 177–183, 2001, [68] F. Nagata, T. Mizobuchi, S. Tani, T. Hase, Z. Haga, K. Watanabe, M.K. Habib, and K. Kiguchi, Desktop orthogonal-type robot with abilities of compliant 223

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Controller design for industrial robots and machine tools

motion and stick-slip motion for lapping of LED lens molds. In IEEE International Conference on Robotics & Automation , pages 2095–2100, 2010, [69] O. Bilkay and O. Anlagan, Computer simulation of stick-slip motion in machine tool slideways. Tribology International, 37(4): 347–351, 2004. [70] X. Mei, M. Tsutsumi, T. Tao, and N. Sun, Study on the compensation of error by stick-slip for high-precision table. International Journal of Machine tools & Manufacture, 44(5): 503–510, 2004. [71] M.J. Tsai, J.L. Chang, and J.F. Haung, Development of an automatic mold polishing system. In IEEE International Conference on Robotics & Automation, pages 3517–3522, 2003. [72] M.J. Tsai, J.J. Fang, and J.L. Chang, Robotic path planning for an automatic mold polishing system. International Journal of Robotics & Automation, 19(2): 81–89, 2004, [73] H. Hocheng, Y.H. Sun, S.C. Lin, and P.S. Kao, A material removal analysis of electrochemical machining using flat-end cathode. Journal of Materials Processing Technology, 140(1/3): 264–268, 2003. [74] Y. Uehara, H. Ohmori, W. Lin, Y. Ueno, T. Naruse, N. Mitsuishi, S. Ishikawa, and T. Miura, Development of spherical lens ELID grinding system by desk-top 4-axes Machine Tool. In International Conference on Leading Edge Manufacturing in 21st Century, pages 247–252, 2005, [75] H. Ohmori and Y. Uehara, Development of a desktop machine tool for mirror surface grinding. International Journal of Automation Technology, 4(2): 88–96, 2010, 224

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[76] F. Nagata, T. Hase, Z. Haga, M. Omoto, and K. Watanabe, Intelligent desktop NC machine tool with compliant motion capability. Artificial Life and Robotics, 13(2): 423–427, 2009. [77] F. Nagata, S. Tani, T. Mizobuchi, T. Hase, Z. Haga, M. Omoto, K. Watanabe, and M.K. Habib. Basic performance of a desktop NC machine tool with compliant motion capability. In IEEE International Conference on Mechatronics and Automation, WC1–5, pages 1–6, 2008. [78] F. Nagata, K. Watanabe, K. Sato, and K. Izumi, Impedance control using anisotropic fuzzy environment models. Journal of Robotics and Mechatronics, 11(1): 60-66, 1999. [79] F. Nagata, A. Otsuka, S. Yoshitake and K. Watanabe, Automatic control of an orthogonal-type robot with a force sensor and a small force input device, In The 37th Annual Conference of the IEEE Industrial Electronics Society, pages 3151–3156, 2011. [80] F. Nagata and K. Watanabe, Feed rate control using a fuzzy reasoning for a mold polishing robot. Journal of Robotics and Mechatronics, 18(1): 76–82, 2006. [81] Japanese Patent 4094781, Robotic force control method, F. Nagata, and K. Watanabe, 2008. [82] Japanese Patent 4447746, Robotic trajectory teaching method, F. Nagata, K. Tsuda, and K. Watanabe, 2010. [83] Japanese Patent 4216557, Polishing apparatus and polishing method, K. Tsuda, K. Yasuda, F. Nagata, Y. Kusumoto, and K. Watanabe, 2008.

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Index back propagation algorithm, 3D robot sander, xxvi 29, 195 4-1-4 order polynomial equabacklash, 165 tion, 7 ball-end abrasive tool, 145 bamboo stick, 155 acceleration vector, 4 activation function, 29 aluminum mold, 154 antecedent part, 131 API, 98 application programming interface, 27 arithmetical mean roughness, 160 arithmetical mean roughness (Ra), 110 articulated-type industrial robot, xxvi, 165 artistic furniture, xxvi, 110 artistic relief wall, xxvi asymptotically stable, 172 auto tool changer ZAT-650, 125 automatic on-line truing function, 205 axis-asymmetric LED lens cavity, 201 axis-asymmetric workpiece, 177

CAD, 66 CAD/CAM, xxv, 67, 103, 142 CAD/CAM-based position/force control, 145, 158, 209 CAM, 66 capacitive force sensor, 209 Cartesian coordinate system, 4 Cartesian-based servo control, 155 Cartesian-based servo controller, 151, 170 Cartesian-type robot, xxvi centrifugal/Coriolis term, 3 CL data, 103, 124, 141, 173, 174 compliance control, 15, 83 compliance controllability, 164 compliant motion, 158 computed torque control, 3

226

Index

consequent part, 131 contact force, 144, 155 corrected NC data, 118 Coulomb friction, 6, 13, 100, 148 coupling control, 173 critically damped condition, 4, 5, 7, 36, 170 cross section, 155 crossover, 10 curved surface, 148 cusp mark, 110, 154, 191 cutoff frequency, 157, 176 cutter location data (CL data), xxvi, 66, 94, 117 defective product, 201 desired contact direction, 161 desired damping, 36, 38, 170, 198 desired feed rate, 208 desired mass, 174 desired orientation, 72 desired polishing force, 101, 174, 209 desired stiffness, 38, 45, 81 desired trajectory, 2, 6, 68, 161 desktop-size NC machine tool, xxvi diamond lapping paste, 186 diamond paste, 208 direction of force control, 176 direction vector, 71 discrete-time control system,

3 dispersion of quality, 201 DNC, 139 double-action sanding tool, 92 dynamic effective stiffness, 195 dynamic model, 4 dynamic stability, 144 edge chipping, 117, 128 effective stiffness, 165, 170 elastic ball-end abrasive tool, 167 elite survivable strategy, 10 estimated stiffness, 48 Ethernet, 73 Euler angle, 39 evolutionary history, 54 feed rate, 71, 106, 128 feedback gain, 3 finishing quality, 187 finishing robot, 143 first-order lag system, 81 five-axis NC machine tool, 114 force control, 2, 143 force control stability, 151, 165 force feedback gain, 45, 174 force feedback loop, 103, 164 force input device, 208 force resolution, 165 force sensor, 2, 101, 143, 166 force vector, 15, 149 forward kinematics, 5 free curved line, 2

227

Published by Woodhead Publishing Ltd., 2013

Controller design for industrial robots and machine tools

frequency characteristics, 184 friction force, 143 fuzzy control, 3 fuzzy environment model, 36, 46 fuzzy feed rate generator, 131, 209 fuzzy force control, 19 fuzzy reasoning, 37 fuzzy rule, 20, 131 fuzzy set, 20, 132

impedance model following force control (IMFFC), 191 impedance model following force controller, 176 industrial robot, xxv inertia term, 3 input layer, 196 integral action, 102 intelligent control, xxvi inverse kinematics, 7

Jacobian, 4 Gaussian membership func- joint coordinate system, 4 joint driving torque, 4, 15 tion, 132 Gaussian type membership joystick teaching system, 66 function, 48 KAWASAKI FS20, 106 genetic algorithms, 3, 4, 9, 37 KAWASAKI FS30L, 108 genotype, 9 kinematics, 142 glued laminated wood, 138 kinetic friction force, 100, grain size, 157 145 gravity term, 3 hand lapping, 201 hidden layer, 196 high frequency vibration, 203 Hurwitz stability criterion, 171 hybrid position/force control, xxvi, 36, 58, 96 hyper CL data, 105

lapping experiment, 202 large curvature, 144 LED lens cavity, xxvii LED lens mold, 164, 186 linear approximation, 71 Lyapunov function, 16

machining time, 128 main processor, 152 MATLAB, 10 max height (Ry), 110 impedance control, 15, 82 maximum depth, 160 impedance model following mean error, 175 force control, 13, 37, mechanical resolution, 125 membership function, 20 102, 144 228

Published by Woodhead Publishing Ltd., 2013

Index

minimization problem, 10 mirror-like surface, 154 modeled treatment error, 6 mold polishing robot, xxvi mounted abrasive tool, 142 multi-layered neural network, 195 mutation, 10 NC machine tool, xxv, 67 NC machine tool MDX650A, 125 NC machine tool with a rotary unit, 120 neural network, 3, 27, 191 NN-based effective stiffness estimator, 196 non-taught operation, 2, 147, 162 nonlinear control, 3 nonlinear effective stiffness, 191 nonlinearity, 166 normal direction vector, 118 normal vector, 146 normal velocity vector, 102 numerical control data (NC data), 67 NURBS, 116 oil mist, 155 open control architecture, 154 open-architecture industrial robot, xxv, 2, 142 open-loop action, 151 operating point, 198 orbital sanding tool, 92, 108

orthogonal-type robot, xxvi, 164, 167 output layer, 196 over-polishing, 148 override, 138 partition line, 174 passive force control, 80 PET bottle blow mold, 142 phenotype, 12 pick feed, 108, 151 pick feed direction, 126 planar robot, 143 polishing compound, 161 polishing force, 100, 108, 144, 148, 160, 198 polishing robot, 66, 143 position and orientation, 4 position command, 168 position control, 142 position feedback loop, 104, 151, 164 position feedforward loop, 164 position resolution, 165 position uncertainty, 166 position vector, 4, 118 post-processor, 119 profiling control, 22 profiling control experiment, 174 pulse command, 168 pulse-based servo control, 168 pulse-based servo controller, 170 PUMA560, 3, 10, 43

229

Published by Woodhead Publishing Ltd., 2013

Controller design for industrial robots and machine tools

recurrent neural network, 28, 195 reduction gear ratio, 11 relative position command, 176 relief design, 115, 135 repetitive position accuracy, 142, 166 resolved acceleration control, 3, 40 roll, pitch and yaw angles, 73 rotary unit, 124 rotary unit ZCL-650A, 125 rotational direction vector, 72 Runge-Kutta method, 24 RV1A, 67 sandpaper, 107 second order error system, 5 second order lag system, 171 servo system, 2, 3, 142 sigmoid function, 196 simple fuzzy reasoning method, 48, 117, 124 singularity, 10 skilled worker, 164, 201 spiral path, 172 stick-slip motion, 186 stick-slip motion control, 190 stick-slip motion vector, 187 stiff ball-end abrasive tool, 167 stiffness control, 81, 83 stylus instrument, 110, 160 surface accuracy, 142

surface-following control, 93 tangential velocity, 71, 148 teaching patterns, 196 teaching pendant, xxv, 2, 68, 144 teaching signal, 27 tiltable jig, 155 tilting head, 118 time-varying effective stiffness, 198 tool abrasion, 158 tool length, 118 torque command, 168 tournament selection, 10 trajectory following control, 10, 76 UDP pachet, 73 uncertainty of tool length, 158 under-damped condition, 13 uniform crossover, 11 unknown environment, 36 velocity vector, 4 velocity-pulse converter, 169 viscous friction, 6, 101, 148 weak coupling, 97 weak coupling control, 104 weighted mean method, 48 Windows multimedia timer, 98 wood-stick tool, 164, 184, 208 wooden furniture, 103 wooden material, xxvi

230

Published by Woodhead Publishing Ltd., 2013

Index

wooden paint roller, xxvi, 114 work coordinate system, 145, 187 XON/XOFF flow control, 139 YASKAWA MOTOMAN UP6, 154, 165 zigzag path, 155, 172

231

Published by Woodhead Publishing Ltd., 2013