Robotics for sustainable future : CLAWAR 2021 9783030862947, 3030862941

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Lecture Notes in Networks and Systems 324

Daisuke Chugo · Mohammad Osman Tokhi · Manuel F. Silva · Taro Nakamura · Khaled Goher   Editors

Robotics for Sustainable Future CLAWAR 2021

Lecture Notes in Networks and Systems Volume 324

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Advisory Editors Fernando Gomide, Department of Computer Engineering and Automation—DCA, School of Electrical and Computer Engineering—FEEC, University of Campinas— UNICAMP, São Paulo, Brazil Okyay Kaynak, Department of Electrical and Electronic Engineering, Bogazici University, Istanbul, Turkey Derong Liu, Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA; Institute of Automation, Chinese Academy of Sciences, Beijing, China Witold Pedrycz, Department of Electrical and Computer Engineering, University of Alberta, Alberta, Canada; Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Marios M. Polycarpou, Department of Electrical and Computer Engineering, KIOS Research Center for Intelligent Systems and Networks, University of Cyprus, Nicosia, Cyprus Imre J. Rudas, Óbuda University, Budapest, Hungary Jun Wang, Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

The series “Lecture Notes in Networks and Systems” publishes the latest developments in Networks and Systems—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNNS. Volumes published in LNNS embrace all aspects and subfields of, as well as new challenges in, Networks and Systems. The series contains proceedings and edited volumes in systems and networks, spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. The series covers the theory, applications, and perspectives on the state of the art and future developments relevant to systems and networks, decision making, control, complex processes and related areas, as embedded in the fields of interdisciplinary and applied sciences, engineering, computer science, physics, economics, social, and life sciences, as well as the paradigms and methodologies behind them. Indexed by SCOPUS, INSPEC, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.

More information about this series at http://www.springer.com/series/15179

Daisuke Chugo Mohammad Osman Tokhi Manuel F. Silva Taro Nakamura Khaled Goher •

•

•

Editors

Robotics for Sustainable Future CLAWAR 2021

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Editors Daisuke Chugo Department of Engineering Kwansei Gakuin University Hyogo, Japan Manuel F. Silva School of Engineering Polytechnic Institute of Porto Porto, Portugal

Mohammad Osman Tokhi School of Engineering London South Bank University London, UK Taro Nakamura Chuo University Bunkyo-ku, Tokyo, Japan

Khaled Goher School of Engineering University of Lincoln Lincolnshire, UK

ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-030-86293-0 ISBN 978-3-030-86294-7 (eBook) https://doi.org/10.1007/978-3-030-86294-7 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Forward

Climbing and Walking Robots (CLAWAR) started with a six-month exploratory phase in 1996 by four European organizations, namely University of Portsmouth, Royal Military Academy, FZI and RISO with the view to identify robotic stakeholders across Europe. The outcome was initiation of the CLAWAR thematic network of excellence supported by the European Commission over two phases, namely CLAWAR1 under the EC Brite Euram programme during 1998–2002 and CLAWAR2 under the EC GROWTH programme during 2002–2005. CLAWAR Association was established by end of 2005 to continue the activities of the CLAWAR Network globally, with the mission to advance robotics for the public benefit. The association was registered in March 2006 with the Companies House in the UK as a non-profit-making limited company by guarantee and in 2012 with the Charities Commission in the UK as a charitable organization. The CLAWAR annual conference series is one of the main activities of CLAWAR Association. The first nine issues of the conference starting from 1998 were held in locations across Europe and further issues in various countries worldwide. The COVID-19 pandemic has had an impact on mode of participation in the conference, and while issues to 22 (2019) were held in physical participation mode, virtual participation mode has been exercised for issues 23 (2020, Russian Federation) and issue 24 (2021, Japan). The CLAWAR conference series has established itself as a popular and high-profile platform for networking and dissemination of research and development findings in the area of mobile robotics and associated technologies.

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Preface

CLAWAR 2021 is the twenty-fourth edition of International Conference Series on Climbing and Walking Robots and the Support Technologies for Mobile Machines. The conference is organized by CLAWAR Association in collaboration with Kwansei Gakuin University on a virtual platform in Takarazuka, Japan, during 30 August – 01 September 2021. CLAWAR 2021 brings new developments and new research findings in robotics technologies within the framework of “robotics for sustainable future”. The topics covered include wearable devices assistive robotics from augmentation to full support for those with mobility disorders, innovative designs of components and full systems and application-specific robotic solutions. The CLAWAR 2021 conference includes a total of 42 regular submission articles from research institutions worldwide. This number has been arrived at through rigorous review of initial submissions, where each paper initially submitted has received at least three reviews. The conference further features three plenary presentations; Categorizing extreme environments and predicting success Robin R. Murphy, Texas A&M University, USA Quadruped robots for challenging tasks on unstructured terrains Claudio Semini, Istituto Italiano di Tecnologia, Italy Service robotics for system integration Hajime Asama, University of Tokyo, Japan It is believed that this book will serve as a source of inspiration and further innovation in research and development in the rapidly growing area of mobile service robotics. August 2021

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Acknowledgements

The editors would like to thank members of the International Scientific Committee and National Organising Committee of CLAWAR 2021 for their efforts in reviewing the submitted articles; Ahmad, S., Malaysia Almeshal, A., Kuwait Armada, M., Spain Banfield, I., Panama Belter, D., Poland Berns, K., Germany Bidaud, Ph., France Bonsignorio, F., Italy Bridge, B., UK Briskin, E., Russia Burlacu, A., Romania Chevallereau, C., France Chrysostomou, D., Denmark Costa, M. T., Portugal Dehghani-Sanij, A., UK Dias, A., Portugal Dillmann, R., Germany El Youssef E. S., Brazil Ermolov I, Russia Faina, A., Denmark Farias, P., Brazil Fernandez, R., Spain Ferreira, P., Portugal Friebe, A., Sweden Gallegos Garrido, G., UK Garcia, D., Panama Grand, C., France

Guedes, P., Portugal Hassan, M. K., Malaysia Hwang, K.-S., Taiwan Ion, I., Romania Kaur, A. P., UK Kiriazov, P., Bulgaria Kobayashi, H., Japan Kozłowski, K., Poland Leon-Rodriguez, H., Colombia Marques, L., Portugal Martins, D., Brazil Meija Rincon, L., Brazil Mohamed, Z., Malaysia Molfino, R., Italy Monje, C. A., Spain Montes, H., Panama Moon, S., Korea Muramatsu, S., Japan Muscato, G., Italy Nunuparov, A., Russia Okui, M., Japan Paraforos, D., Germany Park, H. S., Korea Penders, J., UK Petry, M., Portugal Plentz, P. D. M., Brazil Rachkov, M., Russia ix

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Reina, G., Italy Ribeiro, M., Portugal Rocha, R. P., Portugal Rodríguez Lera, F. J., France Semini, C., Italy Sequeira, J., Portugal Skrzypczynski, P., Poland Su, H., China Tenreiro Machado, J., Portugal Visser, A., The Netherlands

Acknowledgements

Wada, M., Japan Wu, J., China Xie, M., Singapore Yatsun, S., Russia Yigit, A., Kuwait Yokota, S., Japan Zhong, Z. W., Singapore Zhukov, A., Russia Zielinska, T., Poland

CLAWAR’2021 Conference Organization

General Co-chairs Daisuke Chugo M. Osman Tokhi Sho Yokota

Kwansei Gakuin University, Japan London South Bank University, UK Toyo University, Japan

International Scientific Committee Co-chairs Taro Nakamura Manuel F. Silva Manabu Okui

Chuo University, Japan ISEP & INESC TEC, Portugal Chuo University, Japan

International Advisory Committee Chair Gurvinder S. Virk

CLAWAR Association, UK

National Organizing Committee Chair Hiroyuki Kobayashi

Osaka Institute of Technology, Japan

National Organizing Committee Satoshi Muramatsu Keizo Miyahara Takayuki Ishii

Tokai University, Japan Kwansei Gakuin University, Japan Office Ishii Co., Ltd., Japan

Publications Co-chairs Daisuke Chugo M. Osman Tokhi

Kwansei Gakuin University, Japan London South Bank University, UK

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CLAWAR’2021 Conference Organization

Special/Workshop Sessions Chair Khaled M. Goher

University of Lincoln, UK

Local Arrangements Chair Hiroyuki Kobayashi

Osaka Institute of Technology, Japan

Publicity Co-chairs Abdullah Almeshal Masayoshi Wada

College of Technological Studies, Kuwait Tokyo University of Science, Japan

Website Chair Abdullah Almeshal

College of Technological Studies, Kuwait

International Scientific Committee Abbas Dehghani-Sanij Abdullah Almeshal Adrian Burlacu Ahmet Yigit Aman Kaur André Dias Andres Faina Andrey Zhukov Anna Friebe Armen Nunuparov Arnoud Visser Bryan Bridge Christine Chevallereau Christophe Grand Claudio Semini Concepción A. Monje Daniel Martins Deyka Garcia Dimitrios Paraforos Dimitrios Chrysostomou Dominik Belter Ebrahim Samer El Youssef

University of Leeds, UK Public Authority for Applied Education and Training, Kuwait The Gheorghe Asachi Technical University of Iasi, Romania Kuwait University, Kuwait London South Bank University, UK ISEP & INESC TEC, Portugal IT University of Copenhagen, Denmark MAI, Russia Mälardalen University, Sweden Moscow Institute of Physics and Technology, Russia University of Amsterdam, Netherlands TWI, UK Centre National de la Recherche Scientifique, France ONERA, France Istituto Italiano di Tecnologia, Italy University Carlos III of Madrid, Spain Federal University of Santa Catarina, Brazil Universidad Tecnologica de Panama, Panama University of Hohenheim, Germany Aalborg University, Denmark Poznan University of Technology, Poland Universidade Federal de Santa Catarina, Brazil

CLAWAR’2021 Conference Organization

Eugene Briskin Fabio Bonsignorio Francisco Rodríguez Lera Gabriela Gallegos Garrido Giovanni Muscato Giulio Reina Hector Montes Franceschi Hernando Leon-Rodriguez Hong Seong Park Hongye Su Humberto Rodríguez Ilka Banfield Ion Ion Ivan Ermolov Jacques Penders João Sequeira José Tenreiro Machado Jun Wu Kao-Shing Hwang Karsten Berns Krzysztof Kozłowski Leonardo Meija Rincon Lino Marques Manuel Armada Marcelo Petry Maria Teresa Costa Mário Ribeiro Masayoshi Wada Michael Rachkov Ming Xie Mohd Khair Hassan Okui Manabu Patricia Della Méa Plentz Paulo Farias Paulo Ferreira Pedro Guedes Petko Kiriazov Philippe Bidaud Piotr Skrzypczynski Rezia Molfino

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Volgograd State Technical University, Russia Heron Robots, Italy University of Luxembourg, Luxembourg London South Bank University, UK University of Catania, Italy Politecnico di Bari, Italy Universidad Tecnologica de Panama, Panama Nueva Granada Military University, Colombia Kangwon National University, South Korea Zhejiang University, Peoples Republic of China Universidad Tecnológica de Panamá, Panama Universidad Tecnológica de Panamá, Panama Politehnica University of Bucharest, Romania Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia Sheffield Hallam University, UK University of Lisbon, Portugal School of Engineering of the Polytechnic of Porto, Portugal Zhejiang University, Peoples Republic of China National Sun Yat-sen University, Taiwan TU Kaiserslautern, Germany Poznan University of Technology, Poland Federal University of Santa Catarina, Brazil University of Coimbra, Portugal Spanish National Research Council, Spain INESC TEC, Portugal School of Engineering of the Polytechnic of Porto, Portugal ISQ, Portugal Tokyo University of Science, Japan Moscow Polytechnic University, Russia Nanyang Technological University, Singapore Universiti Putra Malaysia, Malaysia Chuo University, Japan Federal University of Santa Catarina, Brazil Universidade Federal da Bahia, Brazil School of Engineering of the Polytechnic of Porto, Portugal School of Engineering of the Polytechnic of Porto, Portugal Bulgarian Academy of Sciences, Bulgaria Sorbonne Université, France Poznan University of Technology, Poland University of Genova, Italy

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Roemi Fernandez Rüdiger Dillmann Rui P. Rocha Salmiah Ahmad Sergey Yatsun Seungbin Moon Teresa Zielinska Z. W. Zhong Zaharuddin Mohamed

CLAWAR’2021 Conference Organization

Spanish National Research Council, Spain University of Karlsruhe, Germany University of Coimbra, Portugal International Islamic University Malaysia, Malaysia Southwest State University, Russia Sejong University, South Korea Warsaw University of Technology, Poland Nanyang Technological University, Singapore Universiti Teknologi Malaysia, Malaysia

Contents

Section–1: Biped Locomotion Studying the Two-Legged Walking System with Video Capture Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexander S. Pechurin, Sergey F. Jatsun, Andrey V. Fedorov, and A. S. Jatsun Stacked Modulation Architecture for Simultaneous Exploration and Navigation of a Biped Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomomichi Sugihara and Takanobu Yamamoto Continuous Inverse Kinematics in Singular Position . . . . . . . . . . . . . . . Patrick Vonwirth and Karsten Berns Analysis of Biped Robot on Uneven Terrain Based on Feed-Forward Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cong Yan, Fumihiko Asano, Yanqiu Zheng, and Longchuan Li

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Section–2: Human-Machine/Human-Robot Interaction The Spherical Pedal Control Device for Omni-Directional Mobile Robot Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thawanrat Siriwattanalerd, Ryosuke Sugimoto, Satoshi Muramatsu, and Katsuhiko Inagaki Modelling of Pedestrians Crossing a Crosswalk and Robot Navigation Based on Its Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shunsuke Yamada, Daisuke Chugo, Satoshi Muramatsu, Sho Yokota, Jin-Hua She, and Hiroshi Hashimoto

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Contents

Section–3: Innovative Actuators and Power Supplies A Compliant Leg Structure for Terrestrial and Aquatic Walking Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter Billeschou, Cao D. Do, Jørgen C. Larsen, and Poramate Manoonpong Design and Modelling of a Modular Robotic Joint . . . . . . . . . . . . . . . . . Marco Rocha, Vitor H. Pinto, José Lima, and Paulo Costa

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Section–4: Innovative Design of CLAWAR The Flatworm-Like Pedal Locomotory Robot WORMESH-II: Fundamental Properties of Pedal Wave Locomotion . . . . . . . . . . . . . . . G. V. C. Rasanga, R. Hodoshima, and S. Kotosaka

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Experimental Investigation of Locomotive Efficiency of a Soft Robotic Eel with a Largely Passive Body . . . . . . . . . . . . . . . . . . . . . . . . 108 Dinh Quang Nguyen and Van Anh Ho Non-assembly Walking Mechanism for Robotic In-Pipe Inspection . . . . 117 George H. Jackson-Mills, Basil A. Shead, James R. Collett, Masego Mphake, Nicholas Fry, Andrew R. Barber, Jordan H. Boyle, Robert C. Richardson, Andrew E. Jackson, and Shaun Whitehead Improved Energy Efficiency via Parallel Elastic Elements for the Straight-Legged Vertically-Compliant Robot SLIDER . . . . . . . . 129 Ke Wang, Roni Permana Saputra, James Paul Foster, and Petar Kormushev Section–5: Inspection Residual Water Removal Mechanism for Obtaining Clear Images with Sewer Pipe Inspection Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Kosuke Uchiyama, Hiroto Sato, Fumio Ito, Shunichi Kurumaya, and Taro Nakamura Wireless Communication with Mobile Inspection Robots Operating While Submerged Inside Oil Storage Tanks . . . . . . . . . . . . . . . . . . . . . . 154 Richard Anvo, Aman Kaur, and Tariq P. Sattar Climbing Robot to Perform Radiography of Wind Blades . . . . . . . . . . . 165 Tariq P. Sattar, Vitor Marques, Richard N’zebo Anvo, Gabriela Gallegos Garrido, Aman Preet Kaur, Peter Routledge, and Karen Markham

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Section–6: Legged Locomotion Simulation-Based Climbing Capability Analysis for Quadrupedal Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Kentaro Uno, Giorgio Valsecchi, Marco Hutter, and Kazuya Yoshida Six-Legged Robot Overturn from an Emergency Position on the Back Under the Influence of Hindrance . . . . . . . . . . . . . . . . . . . 192 Yury F. Golubev, Victor V. Koryanov, and Elena V. Melkumova Passive Gripping Foot for a Legged Robot to Move Over Rough Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Sho Hakamada and Sadayoshi Mikami Enhancing Legged Robot Navigation of Rough Terrain via Tail Tapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Daniel Soto, Kelimar Diaz, and Daniel I. Goldman Section–7: Modelling and Simulation of CLAWAR ClimbLab: MATLAB Simulation Platform for Legged Climbing Robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Kentaro Uno, Warley F. R. Ribeiro, Yusuke Koizumi, Keigo Haji, Koki Kurihara, William Jones, and Kazuya Yoshida Modeling and Motion Analysis of Planar Passive-Dynamic Walker With Tensegrity Structure Formed by Four Limbs and Eight Viscoelastic Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Fumihiko Asano, Yanqiu Zheng, and Longchuan Li Trajectory Planning Strategy for the Links of a Walking Human-Machine System Using a Neural Network . . . . . . . . . . . . . . . . . 255 Sergey F. Jatsun, Andrei V. Malchikov, Alexey A. Postolniy, and Andrey S. Yatsun Passive Motion Analysis of Two Identical Regular Octagonal Objects That Move on Passively Vibrating Tilted Stage . . . . . . . . . . . . . 262 Fumihiko Asano, Longchuan Li, and Isao Tokuda Analysis of Passive Dynamic Gait of Tensegrity Robot . . . . . . . . . . . . . 274 Yanqiu Zheng, Fumihiko Asano, Longchuan Li, and Cong Yan About the Distribution of Traction Efforts Between the Propulsion Devices of Walking Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Eugene S. Briskin, Vitalу N. Platonov, and Liliya D. Smirnaya

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Regularities of Contact Behavior of Small Supporting Elements (Feet) of Walking Machines and Robots with Weakly Bearing and Water-Saturated Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Vladimir V. Arykantsev, Vadim V. Chernyshev, Yaroslav V. Kalinin, and Nikolay G. Sharonov Realistic 3D Simulation of a Hybrid Legged-Wheeled Robot . . . . . . . . . 303 Inês N. Soares, Vítor H. Pinto, José Lima, and Paulo Costa Section–8: Outdoor and Field Robotics Semi-autonomous Mobile Robot for Environmental Surfaces Disinfections Against SARS-CoV-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Héctor Montes, Humberto Rodríguez, Octavio Echeverría, and Víctor Perez Horizontal Drilling with Seabed Robotic Explorer . . . . . . . . . . . . . . . . . 329 Ryosuke Tokoi, Wataru Toyama, Kazuki Tsumura, Tomoki Watanabe, Manabu Okui, Taro Nakamura, and Hiroshi Yoshida Excavation Experiment of Earth Worm Type Seabed Exploration Robot in Actual Sea Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Manabu Okui, Ryosuke Tokoi, Wataru Toyama, Kazuki Tsumura, Keita Isaka, Tomoki Watanabe, Taro Nakamura, and Hiroshi Yoshida Evaluation of Optimal Cleaning Tools for the Development of a Cleaning Robot for Grease from Ventilation Ducts . . . . . . . . . . . . . 348 Yuta Yamanaka, Takehiro Hitomi, Fumio Ito, and Taro Nakamura Development of Automatic Operation System Considering Steering Performance for a Paddy Field Weeding Robot . . . . . . . . . . . . . . . . . . . 357 Hiroaki Uchida, Seiya Moro, Kenzi Nomura, and Satoharu Sekine Development of the Object Transfer Robot with Variable Height Using a Pantograph-Type Jack System . . . . . . . . . . . . . . . . . . . . . . . . . 369 Kazushi Kurasawa, Hyouga Sugiyama, Satoshi Muramatsu, Katsuhiko Inagaki, Daisuke Chugo, and Hiroshi Hashimoto Section–9: Planning and Control Learning and Transfer of Movement Gaits Using Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 David Waidner and Marcus Strand Rolling Resistance Model and Control of Spherical Robot . . . . . . . . . . . 396 Alexander A. Kilin, Yury L. Karavaev, and Tatiana B. Ivanova

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Automatic Generation of Random Step Environment Models for Gazebo Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 Ruslan Gabdrahmanov, Tatyana Tsoy, Yang Bai, Mikhail Svinin, and Evgeni Magid The Motion Control Research of the Mobile Robot with Vibrating Propulsion Device Which Discretely Interacting with the Supporting Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Denis V. Bordyugov, Eugene S. Briskin, and Nikolay G. Sharonov Experimental Investigations of the Controlled Motion of the Roller Racer Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 Alexander Kilin, Yuriy Karavaev, and Kirill Yefremov Generation of the Self-motion Manifolds of a Functionally Redundant Robot Using Multi-objective Optimization . . . . . . . . . . . . . . 438 Ilka Banfield and Humberto Rodríguez Section–10: Wearable Devices and Assistive Robotics Evaluation Method of Gait Motion of a Patient Received Total Knee Arthroplasty Using Correlation Between Measurement Data and Evaluation Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Koji Makino, Masahiro Nakamura, Ryo Hagihara, Hidenori Omori, Yoshinobu Hanagata, Kohei Shirataki, Shohei Ueda, and Hidetsugu Terada Lightweight Locomotion Assistant for People with Mild Disabilities . . . 465 Gonçalo Neves, João S. Sequeira, and Cristina Santos Possibility of Getting On/Off Public Vehicle by Manual Wheelchair with 4 Degrees of Freedom Contact Arm Mechanism . . . . . . . . . . . . . . 477 Fumiaki Takemori and Ryoga Hayashi Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

List of Contributors

Richard N’zebo Anvo School of Engineering, London South Bank University, London, UK Vladimir V. Arykantsev Volgograd State Technical University, Volgograd, Russia Fumihiko Asano School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan Yang Bai Information Science and Engineering Department, College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan Ilka Banfield Mechanical Engineering Faculty, Universidad Tecnológica de Panamá, Panama City, Panama; LEADS-UTP, Universidad Tecnológica de Panamá, Panama City, Panama Andrew R. Barber Department of Mechanical Engineering, University of Leeds, Leeds, UK Karsten Berns Department of Computer Science, Technische Universität Kaiserslautern, Kaiserslautern, Germany Peter Billeschou University of Southern Denmark, SDU Biorobotics, Odense, Denmark Denis V. Bordyugov Department of Theoretical Mechanics, Volgograd State Technical University, Volgograd, Russia Jordan H. Boyle Department of Mechanical Engineering, University of Leeds, Leeds, UK

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List of Contributors

Eugene S. Briskin Department of Theoretical Mechanics, Volgograd State Technical University, Volgograd, Russia; Center for Technology Components of Robotics and Mechatronics, Innopolis University, Innopolis, Russia Vadim V. Chernyshev Volgograd State Technical University, Volgograd, Russia Daisuke Chugo Kwansei Gakuin University, Sanda, Hyougo, Japan James R. Collett Department of Mechanical Engineering, University of Leeds, Leeds, UK Paulo Costa FEUP—Faculty of Engineering, University of Porto, Porto, Portugal; CRIIS—Centre for Robotics in Industry and Intelligent Systems, INESC TEC— Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal Kelimar Diaz School of Physics, Georgia Tech, Atlanta, GA, USA Cao D. Do University of Southern Denmark, SDU Biorobotics, Odense, Denmark Octavio Echeverría LEADS Research Group, Universidad Tecnológica de Panamá, Panama City, Panama; Fab Lab-UTP, Universidad Tecnológica de Panamá, Panama City, Panama Andrey V. Fedorov South-West State University, Kursk, Russia James Paul Foster Department of Electrical and Electronic Engineering, Imperial College London, London, UK Nicholas Fry Department of Mechanical Engineering, University of Leeds, Leeds, UK Ruslan Gabdrahmanov Laboratory of Intelligent Robotic Systems, Intelligent Robotics Department, Kazan Federal University, Kazan, Tatarstan Republic, Russian Federation Gabriela Gallegos Garrido School of Engineering, London South Bank University, London, UK Daniel I. Goldman School of Physics, Georgia Tech, Atlanta, GA, USA Yury F. Golubev Keldysh Institute of Applied Mathematics, RAS, Moscow, Russia; M.V. Lomonosov Moscow State University, Moscow, Russia Ryo Hagihara University of Yanamashi, Kofu, Japan Keigo Haji Space Robotics Lab (SRL), Department of Aerospace Engineering, Tohoku University, Sendai, Miyagi, Japan Sho Hakamada Graduate School of Systems Information Science, Future University Hakodate, Hokkaido, Hakodate, Japan

List of Contributors

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Yoshinobu Hanagata Kofu Municipal Hospital, Kofu, Japan Hiroshi Hashimoto Advanced Institute of Industrial Technology, Shinagawa, Japan Ryoga Hayashi Department of Engineering, Graduate School of Sustainability Science, Tottori University, Tottori, Japan Takehiro Hitomi Faculty of Science and Technology, Chuo University, Tokyo, Japan Van Anh Ho School of Materials Science, Japan Advanced Institute of Science and Technology (JAIST), Nomi, Ishikawa, Japan R. Hodoshima Department of Mechanical Engineering, Saitama University, Saitama-shi, Saitama, Japan Marco Hutter Robotic Systems Lab (RSL), ETH Zurich, Zürich, Switzerland Katsuhiko Inagaki Tokai University, Hiratsuka, Kanagawa, Japan Keita Isaka Chuo University, Tokyo, Japan Fumio Ito Faculty of Science and Technology, Chuo University, Tokyo, Japan; Precision Mechanics, Chuo University, Tokyo, Japan Tatiana B. Ivanova Udmurt State University, Izhevsk, Russia George H. Jackson-Mills Department of Mechanical Engineering, University of Leeds, Leeds, UK Andrew E. Jackson Department of Mechanical Engineering, University of Leeds, Leeds, UK A. S. Jatsun South-West State University, Kursk, Russia Sergey F. Jatsun South-West State University, Kursk, Russia William Jones VisionSpace Technologies GmbH, Darmstadt, Germany Yaroslav V. Kalinin Volgograd State Technical University, Volgograd, Russia Yury L. Karavaev Kalashnikov Izhevsk State Technical University, Izhevsk, Russia Aman Preet Kaur School of Engineering, London South Bank University, London, UK Alexander A. Kilin Ural Mathematical Center, Udmurt State University, Izhevsk, Russia Yusuke Koizumi Space Robotics Lab (SRL), Department of Aerospace Engineering, Tohoku University, Sendai, Miyagi, Japan

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List of Contributors

Victor V. Koryanov Keldysh Institute of Applied Mathematics, RAS, Moscow, Russia Petar Kormushev Robot Intelligence Lab, Dyson School of Design Engineering, Imperial College London, London, UK S. Kotosaka Department of Mechanical Engineering, Saitama University, Saitama-shi, Saitama, Japan Kazushi Kurasawa Tokai University, Hiratsuka, Kanagawa, Japan Koki Kurihara Space Robotics Lab (SRL), Department of Aerospace Engineering, Tohoku University, Sendai, Miyagi, Japan Shunichi Kurumaya Precision Mechanics, Chuo University, Tokyo, Japan Jørgen C. Larsen University of Southern Denmark, SDU Biorobotics, Odense, Denmark Longchuan Li Graduate School of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan José Lima CRIIS—Centre for Robotics in Industry and Intelligent Systems, INESC TEC—Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal; Research Centre in Digitalization and Intelligent Robotics, CeDRI, Polytechnic Institute of Bragança, Bragança, Portugal Poramate Manoonpong University of Southern Denmark, SDU Biorobotics, Odense, Denmark; Vidyasirimedhi Institute of Science and Technology, School of Information Science and Technology, Rayong, Thailand Evgeni Magid Laboratory of Intelligent Robotic Systems, Intelligent Robotics Department, Kazan Federal University, Kazan, Tatarstan Republic, Russian Federation Koji Makino University of Yanamashi, Kofu, Japan Andrei V. Malchikov South-West State University, Kursk, Russia Karen Markham Risehow Hydraulic Center, FORTH Engineering Ltd., Maryport, UK Vitor Marques School of Engineering, London South Bank University, London, UK Elena V. Melkumova M.V. Lomonosov Moscow State University, Moscow, Russia Sadayoshi Mikami Future University Hakodate, Hokkaido, Hakodate, Japan

List of Contributors

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Héctor Montes LEADS Research Group, Universidad Tecnológica de Panamá, Panama City, Panama; CINEMI Research Group, Universidad Tecnológica de Panamá, Panama City, Panama; ARIeS Research Group, Universidad Tecnológica de Panamá, Panama City, Panama Seiya Moro Department of Mechanical Engineering, National Institute of Technology, Kisarazu College, Kisarazu, Chiba, Japan Masego Mphake Department of Mechanical Engineering, University of Leeds, Leeds, UK Satoshi Muramatsu Tokai University, Hiratsuka, Kanagawa, Japan Masahiro Nakamura Kofu Municipal Hospital, Kofu, Japan Taro Nakamura Faculty of Science and Technology, Chuo University, Tokyo, Japan; Precision Mechanics, Chuo University, Tokyo, Japan Gonçalo Neves Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal Dinh Quang Nguyen School of Materials Science, Japan Advanced Institute of Science and Technology (JAIST), Nomi, Ishikawa, Japan Kenzi Nomura Alnetz Corporation, Yokohama, Japan Manabu Okui Chuo University, Tokyo, Japan Hidenori Omori Kofu Municipal Hospital, Kofu, Japan Alexander S. Pechurin South-West State University, Kursk, Russia Víctor Perez LEADS Research Group, Universidad Tecnológica de Panamá, Panama City, Panama; Fab Lab-UTP, Universidad Tecnológica de Panamá, Panama City, Panama Vítor H. Pinto FEUP—Faculty of Engineering, University of Porto, Porto, Portugal; CRIIS—Centre for Robotics in Industry and Intelligent Systems, INESC TEC— Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal Vitalу N. Platonov Department of Theoretical Mechanics, Volgograd State Technical University, Volgograd, Russia Alexey A. Postolniy South-West State University, Kursk, Russia G. V. C. Rasanga Graduate School of Science and Engineering, Saitama University, Department of Mechanical Engineering, Saitama-shi, Saitama, Japan Warley F. R. Ribeiro Space Robotics Lab (SRL), Department of Aerospace Engineering, Tohoku University, Sendai, Miyagi, Japan

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List of Contributors

Robert C. Richardson Department of Mechanical Engineering, University of Leeds, Leeds, UK Humberto Rodríguez LEADS Research Group, Universidad Tecnológica de Panamá, Panama City, Panama; Fab Lab-UTP, Universidad Tecnológica de Panamá, Panama City, Panama; Mechanical Engineering Faculty, Universidad Tecnológica de Panamá, Panama City, Panama; LEADS-UTP, Universidad Tecnológica de Panamá, Panama City, Panama Marco Rocha Faculty of Engineering, University of Porto, Porto, Portugal Peter Routledge Risehow Hydraulic Center, FORTH Engineering Ltd., Maryport, UK Cristina Santos Universidade do Minho, Braga, Portugal Roni Permana Saputra Robot Intelligence Lab, Dyson School of Design Engineering, Imperial College London, London, UK; Research Center for Electrical Power and Mechatronics, Indonesian Institute of Sciences–LIPI, Bandung, Indonesia Hiroto Sato Precision Mechanics, Chuo University, Tokyo, Japan Tariq P. Sattar London South Bank University Innovation Centre, London, UK; School of Engineering, London South Bank University, London, UK Satoharu Sekine Alnetz Corporation, Yokohama, Japan João S. Sequeira Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal Nikolay G. Sharonov Department of Theoretical Mechanics, Volgograd State Technical University, Volgograd, Russia; Center for Technology Components of Robotics and Mechatronics, Innopolis University, Innopolis, Russia Jin-Hua She Tokyo University of Technology, Tokyo, Japan Basil A. Shead Department of Mechanical Engineering, University of Leeds, Leeds, UK Kohei Shirataki Kofu Municipal Hospital, Kofu, Japan Thawanrat Siriwattanalerd Tokai University, Kanagawa, Japan Liliya D. Smirnaya Department of Theoretical Mechanics, Volgograd State Technical University, Volgograd, Russia; Center for Technology Components of Robotics and Mechatronics, Innopolis University, Innopolis, Russia

List of Contributors

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Inês N. Soares FEUP—Faculty of Engineering, University of Porto, Porto, Portugal Daniel Soto School of Mechanical Engineering, Georgia Tech, Atlanta, GA, USA Marcus Strand Cooperative State University Baden-Württemberg, Karlsruhe, Germany Tomomichi Sugihara Preferred Networks, Inc., Tokyo, Japan Ryosuke Sugimoto Tokai University, Kanagawa, Japan Hyouga Sugiyama Tokai University, Hiratsuka, Kanagawa, Japan Mikhail Svinin Information Science and Engineering Department, College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan Fumiaki Takemori Department of Engineering, Graduate School of Sustainability Science, Tottori University, Tottori, Japan Hidetsugu Terada University of Yanamashi, Kofu, Japan Ryosuke Tokoi Chuo University, Tokyo, Japan Isao Tokuda Graduate School of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan Wataru Toyama Chuo University, Tokyo, Japan Tatyana Tsoy Laboratory of Intelligent Robotic Systems, Intelligent Robotics Department, Kazan Federal University, Kazan, Tatarstan Republic, Russian Federation Kazuki Tsumura Chuo University, Tokyo, Japan Hiroaki Uchida Department of Mechanical Engineering, National Institute of Technology, Kisarazu College, Kisarazu, Chiba, Japan Kosuke Uchiyama Precision Mechanics, Chuo University, Tokyo, Japan Shohei Ueda Kofu Municipal Hospital, Kofu, Japan Kentaro Uno Space Robotics Lab (SRL), Department of Aerospace Engineering, Tohoku University, Sendai, Miyagi, Japan Giorgio Valsecchi Robotic Systems Lab (RSL), ETH Zurich, Zürich, Switzerland Patrick Vonwirth Department of Computer Science, Technische Universität Kaiserslautern, Kaiserslautern, Germany David Waidner Cooperative State University Baden-Württemberg, Karlsruhe, Germany

xxviii

List of Contributors

Ke Wang Robot Intelligence Lab, Dyson School of Design Engineering, Imperial College London, London, UK Tomoki Watanabe Chuo University, Tokyo, Japan Shaun Whitehead Department of Mechanical Engineering, University of Leeds, Leeds, UK Shunsuke Yamada Kwansei Gakuin University, Hyogo, Japan Takanobu Yamamoto Osaka University, Suita, Osaka, Japan Yuta Yamanaka Faculty of Science and Technology, Chuo University, Tokyo, Japan Cong Yan School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan Andrey S. Yatsun South-West State University, Kursk, Russia Kirill Yefremov Kalashnikov Izhevsk State Technical University, Izhevsk, Russia Sho Yokota Toyo University, Saitama, Japan Hiroshi Yoshida Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Kanagawa, Japan Kazuya Yoshida Space Robotics Lab (SRL), Department of Aerospace Engineering, Tohoku University, Sendai, Miyagi, Japan Yanqiu Zheng School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

List of Abbreviations

Abd ABS AC ADC Add AI API ATEX BL BLDC CAD CAN CANOpen CBT CCDF CCW CNC COM COT CPU CW DC DLS DoF DZC ECHA EMW ENG EoM EPA

Abduction Acrylonitrile butadiene styrene Alternating current Analog-to-digital converter Adduction Artificial intelligence American Petroleum Institute Atmospheres explosives Body length Brushless direct current Computer aided design Controlled area network Controlled area network open protocol Canonical biped track Complementary cumulative distribution function Counter clock-wise Computer numerical control Centre of mass Cost of transport Central processing unit Clock-wise Direct current Damped least square Degrees of freedom Dead zone compensation European Chemical Agency Electro-magnetic wave Elevation-and-normal grid Equation of motion Environmental Protection Agency

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EVA EWEA FABRIK FF FK FPS GIA GNSS GP GPS GPU GUI HMS I IBR ID IEC IK IMC IMU IP I2C LED LIDAR LiPo LIRS MCU MDBF MDP ML MOEA MOGA MSS NDT NMT NSGA ODE OpenGL PC PCB PD PI PID PIG PLA

List of Abbreviations

Ethylene-vinyl acetate European Wind Energy Association Forward and backward reaching inverse kinematics Feed forward Forward kinematics Floating processing unit Gravito-inertial acceleration Global navigation satellite system Gaussian process Global positioning system Graphical processing unit Graphical user interface Human machine system Integral Inchworm boring robot Identifier International Electro-technical Commission Inverse kinematics Internal model control Inertial measurement unit Ingress protection Inter integrated circuit Light emitting diode Light detection and ranging Lithium polymer Laboratory of Intelligent Robotic Systems Microprocessor control unit Mean displacement before failure Markov decision process Machine learning Multi objective evolutionary algorithm Multi-objective genetic algorithms Musculoskeletal system Non-destructive testing Network management Non-sorting genetic algorithm Open dynamics engine Open graphics library Personal computer Printed circuit board Proportional derivative Proportional integral Proportional-integral-derivative Pipeline inspection gauge Poly-lactic acid

List of Abbreviations

PPM PPO PVA PVC PWM RC RF RHex RMS ROS RS RSE RTF RTK RW SAC SARS-CoV-2 SC SDLS SE SEAN SLS SSE SSH STL SURF SW SLAM THA TSM UART UCB UGV ULV USAR USB UT UTP UVC WHO WT WTB WTT ZMP

Profile position mode Proximal policy optimization Poly vinyl alcohol Poly-vinyl chloride Pulse width modulation Radio controlled Radio frequency Robotic hexapod Root mean square Robot operating system Recommended standard Random step environment Real time factor Real time kinematic Rimless wheel Soft-actor critic Severe acute respiratory syndrome coronavirus 2 Smart cane Selectively damped least square Squared exponential Simultaneous exploration and navigation Selective laser sintering Screw subsurface explorer Secure shell Stereolithography Speeded up robust features Smart walkers Simultaneous localisation and mapping Total hip arthroplasty Tumble stability margin Universal asynchronous receiver transmitter Upper confidence bound Unmanned ground vehicle Ultra low volume Urban search and rescue Universal serial bus Underwater technology Technological University of Panama Ultra violet C World Health Organization Wind turbine Wind turbine blade Wind turbine tower Zero-moment point

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Section–1: Biped Locomotion

Studying the Two-Legged Walking System with Video Capture Methods Alexander S. Pechurin, Sergey F. Jatsun(B)

, Andrey V. Fedorov, and A. S. Jatsun

South-West State University, Kursk 305040, Russia [email protected]

Abstract. Creation of rehabilitation systems for patients with musculoskeletal system disorders, will reduce the number of such patients. One of the main stages in the development of such devices is the construction of movement patterns depending on the patient anthropometric parameters. The use of simplified feet and the center of mass motion laws can lead to the formation of the humanmachine system (HMS) irrational gait. The solution of the problem is possible due to the accurate construction of the foot movement trajectory, based on gait motion capture or video analysis. The aim of the work is in constructing and processing the human foot movement trajectory on the base of experiment video fragment and creating a rehabilitation exoskeleton gait mathematical model. For this purpose, the tasks of constructing a foot motion trajectory on the base of the experiment video clip, smoothing and approximating this trajectory, and the inverse kinematics problem have been solved. A method of constructing and processing the foot movement trajectory and finding the links rotational movement kinematic characteristics for creating HMS movement patterns is proposed. The simulation results showed that the proposed methods of movement trajectory constructing and exoskeleton gait modeling allow repeat the person gait with satisfactory accuracy with taking into account the anthropometric parameters of the foot. Keywords: Human gait · Mathematical modeling of human gait · Solution of the inverse problem of kinematics of velocity · Exoskeleton · Video analysis of the trajectory

1 Introduction Today, diseases of the musculoskeletal system (MSS) are a widespread problem throughout the world. WHO statistics show that 80% of the population suffers from various diseases of MSS. Moreover, most of them are people of working age: from 30 to 50 years [1]. The consequence of this is an increase in the number of people with injuries of the lower extremities, whose independent movement is difficult or impossible. In recent years [2], exoskeletons have been used for the rehabilitation of patients with injuries of the musculoskeletal system. The use of such modern means can significantly reduce the patient’s recovery time after injuries, increasing the efficiency of the rehabilitation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 3–12, 2022. https://doi.org/10.1007/978-3-030-86294-7_1

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process. For the exoskeletons development and creation, computer modeling methods are used, which make it possible to study in a virtual space the patient’s lower extremities movement nature and exoskeleton for various movement patterns, which allows optimizing the parameters of the HMS control system and designing personalized rehabilitation systems for patient recovery. The most suitable for the restoration of MSS is the lower extremities active exoskeleton - a bipedal robot that allows carrying out various rehabilitation exercises, providing the process of extremities individual elements’ movement or completely imitating a person’s gait [3]. In order to ensure the operation of the exoskeleton in the mode set by the physician-rehabilitation therapist, it is necessary to precisely set the trajectories of movement of the exoskeleton links. When walking, it is necessary to know the trajectory of person feet and center of mass movement. These data make it possible to calculate the optimal control actions and patterns of exoskeleton movement for people with different MSS damage degrees.

2 Trajectory Construction To build the person’s movement trajectory, the “tracker” - a video analysis and simulation program designed for use in physical data education can be used [2] (Fig. 1).

Fig. 1. Building the human foot movement trajectory using a video analysis program

The trajectory of motion of the foot and its derivatives obtained in the course of measurements (Fig. 2) must be processed, since the derivatives have a “sawtooth” shape and are not suitable for further kinematic analysis.

Studying the Two-Legged Walking System with Video Capture Methods

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Fig. 2. Graphs of changes in the experimentally obtained trajectory of foot movement: 1 − XA6 , 2 − X˙ A6 , 3 − X¨ A6 , 4 − ZA6 , 5 − Z˙ A6 , 6 − Z¨ A6

3 Trajectory Smoothing To smooth the resulting values, the “smooth” function of the MATLAB software package is used. The function returns the vector elements sliding value using a fixed window length, which is determined heuristically. The window slides along the length of the vector, calculating the average value over the elements in each window [3]. The result of data smoothing is the trajectory is shown in Fig. 3.

Fig. 3. Graphs of the foot movement smoothed trajectory changes: 1 − sXA6 , 2 − sX˙ A6 , 3 − sX¨ A6 , 4 − sZA6 , 5 − sZ˙ A6 , 6 − sZ¨ A6

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4 Trajectory Polynomization To find the motion law from the numerical data obtained during the motion analysis, it is necessary to apply an approximation by the MATLAB software package “polyfit” function, returning the coefficients of the n-th degree, which are best suited for describing the approximated data [4], polynomial. The resulting laws of the foot coordinates’ changes will be as follows: ⎧ nx  ⎪ ⎪ ai · t i ⎨ XA6 = i=0 , (1) nz  ⎪ ⎪ Z = bj · t j ⎩ A6 j=0

where: nx and nz are the order of the polynomial, t- is the step time, the coefficients ai and bj are found using the “polyfit” function described above (Fig. 4). Coefficients, found with the “polyfit” function: a0 = 0.0063, a1 = 0.0260, a2 = 0.3072, a3 = −0.5846, a4 = 1.1506, a5 = −1.0785, a6 = 0.5224, a7 = −0.1219, a8 = 0.0044, a9 = 0.0034, a10 = 0.0005; b0 = −0.0017, b1 = 0.1832, b2 = −0.2173, b3 = 0.1270, b4 = 2.0544, b5 = −5.0640, b6 = 5.0061, b7 = −2.5956, b8 = 0.7478, b9 = −0.1138, b10 = 0.0071.

Fig. 4. Graphs of the experimentally obtained polynomized foot movement trajectory changes: 1 − pXA6 , 2 − pX˙ A6 , 3 − pX¨ A6 , 4 − pZA6 , 5 − pZ˙ A6 , 6 − pZ¨ A6 .

Studying the Two-Legged Walking System with Video Capture Methods

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5 Solution of the Inverse Problem of Apparatus Kinematics The apparatus for the rehabilitation [5–11] of people with impaired ODA is a controlled exoskeleton of the lower extremities, capable of repeating a given law of motion with an operator without loss of stability (Fig. 5).

Fig. 5. The lower limbs exoskeleton scheme: A0…i – places of actuators installation, C 0…j – elements’ centers of mass, angles q00 -q120 – generalized coordinates describing the relative position of the exoskeleton links, which depends on the foot trajectory

It should be noted that in this work the foot is represented by one link, therefore the angles q80 , q10 , and q00 are not taken into account. Finding the vector of generalized coordinates q(t), having the form: T  q = q70 q67 q56 q45 q34 q23 q12 q6x

(2)

For a given trajectory of movement of the foot, is carried out by solving the inverse problem of the kinematics of speed. Since the number of links in this mechanism exceeds six, it is necessary to use a pseudo inverse Jacobian matrix [5]: q˙ (t) = J + (q) · χ (t)

(3)

In order to correctly set the pattern of movement, the mechanism must also know the law of motion of the center of mass of the exoskeleton - patient system. Since it is very difficult to apply a marker for the center of mass as for a foot, in this work the center of mass will be found theoretically, and instead of the law of motion, the extreme points of stability of the center of mass will be used (Fig. 6).

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Fig. 6. Scheme of a two-support movement phase, with the system stability zone: C – the system center of mass, K 6 , D6 , K 2 , D2 –the stability zone extreme points, L - foot length, W - foot width

However, without a horizontal displacement of the center of mass, the system cannot move, therefore, as an assumption, let us set the law of X C change. Thus, the law of changing the coordinates of point C will have the form: ⎧ 5  ⎪ ⎪ ck · t k , D6 ∧ D2 ≥ XC ≥ K6 ∧ K2 ⎨ XC = ⎪ ⎪ ⎩

i=0

K6 ∧ D6 ≥ YC ≥ K2 ∧ D2 ZCmax ≥ ZC ≥ ZCmin

(4)

Let us define a vector function F(q) that determines the values corresponding to the projections of the center of mass, foot and back position, depending on the generalized coordinates q. F(q) = [r C (q), r A6 (q), q40 (q)]T

(5)

Let’s introduce a vector function: F (t) = [XC (t), YC (t), ZC (t), XA6 (t), YA6 (t), ZA6 (t), q40 (t)]T

(6)

We denote the pseudoinverse Jacobi matrix J+ = (

∂F + ) ∂q

(7)

Then, in discrete form, the expression will be rewritten as: qk+1 = qk + JF+ F (t) where F (t)- is the increment of the function F (t) at the time step t.

(8)

Studying the Two-Legged Walking System with Video Capture Methods

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The resulting relation allows you to find the vector of generalized coordinates q at the k + 1-th time step by the known value at the k-th step.

6 Results and Their Discussion Further, the results of mathematical modeling of an exoskeleton [12–18] with a given trajectory of movement of the foot and center of mass are considered. Figure 7 shows a frame from the motion animation, from which it can be seen that the apparatus is able to move along a given trajectory without losing stability. The result of solving the inverse problem of the velocity kinematics in the course of mathematical modeling are the values of the kinematic characteristics of the rotary motion of the links. As can be seen from the graphs presented in Fig. 8, the angles and their derivatives are mostly smooth in nature, but there are also serious “jumps” due to inaccuracies in the visual marking of the points of the foot trajectory.

Fig. 7. A frame of animation of the movement of the mathematical model of the exoskeleton: 1 geometric model of exoskeleton, 2 - the calculated trajectory of the center of mass, 3 - polynomized experimental trajectory

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Fig. 8. Graphs of changes in the angles and angular velocities of the links of the mechanism: dashed line - angle, dash-dotted - angular velocity, solid line - angular acceleration

Studying the Two-Legged Walking System with Video Capture Methods

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7 Conclusions 1. A mathematical model has been developed for the movement of a two-legged rehabilitation apparatus for people with ODA disorders along a given trajectory obtained during the experiment. 2. A method for planning the trajectory of foot movement, based on video analysis of a person’s gait, as well as further processing and approximation of the resulting trajectory, has been proposed. 3. The simulation results demonstrate that the proposed methods for constructing the trajectory of movement and modeling the gait of the exoskeleton allow with satisfactory accuracy to repeat the gait of a person, taking into account the anthropometric parameters of the foot. The reported study was funded by the Russian Federation President Grant for young candidates of sciences MK-901.2020.8

References 1. Khusainov, R., et al.: Toward a human-like locomotion: modelling dynamically stable locomotion of an anthropomorphic robot in simulink environment. In: 2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO), vol. 2, pp. 141–148. IEEE (2015) 2. Lohmeier, S., Buschmann, T., Ulbrich, H.: System design and control of anthropomorphic walking robot LOLA. IEEE/ASME Trans. Mech. 14(6), 658–666 (2009) 3. Jatsun, S.F., Yatsun, A., Savin, S.: Investigation of Human Locomotion with a Powered Lower Limb Exoskeleton. Handbook of Research on Biomimetics and Biomedical Robotics, p. 26 (2017) 4. Devaev, V.M., Nikitina, D.V., Fadeev, A.Y.: Balancing of the anthropomorphous robot walking. In: IOP Conference Series: Materials Science and Engineering, vol. 134, no. 1, pp. 012004. IOP Publishing (2016) 5. Zhang, C., et al.: Human–machine force interaction design and control for the HIT loadcarrying exoskeleton. Adv. Mech. Eng. 8(4), 1687814016645068 (2016) 6. Huang, Z., et al.: Loss calculation and thermal analysis of rotors supported by active magnetic bearings for high-speed permanent-magnet electrical machines. IEEE Trans. Ind. Electron. 63(4), 2027–2035 (2016) 7. J. Koenemann, A., et al.: Whole-body model-predictive control applied to the hrp-2 humanoid robot. In: IEEE-RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3346–3351 (2015) 8. Skvorchevskiy, A.K., Vorob’yev, Ye.I.: Razrabotkaantropomorfnykhrobotov i protezovdlyareabilitatsiichastichnoobezdvizhennykh i sidyachikhbol’nykh [Development of anthropomorphic robots and prostheses for the rehabilitation of partially immobilized and sedentary patients]. Informatizatsiya i svyaz’ [Informatization and communication] 3, 48–51 (2010) 9. Pobegaylov, O.A., Kravchenko, I.V., Kozhukhovskiy, S.O.: Mobil’nyyerobotyver tikal’nogoperemeshcheniya [Mobile robots of vertical movement]. Inzhenernyyvestnik Dona [Engineering Herald of the Don] 14(4) (2010)

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10. Kulakov, D.B.: Razrabotka i issledovaniyeispolnitel’nogomekhanizma s elektrogidravlicheskimiprivodamidlyasistemyupravleniyadvizheniyemdvunogogoshagayushchegorobota [Development and research of an actuator with electro-hydraulic drives for a bipedal walking robot motion control system]. dis. – M. :avtoref. dis.… kand. tekhn. Nauk [dis ... cand. tech. Sciences] (2009) 11. Shevyrev, A.V., Nevzorov, YU.V., Pimenov, P.N., Fomina, I.A., Pronin, S.A.: Analizustoychivogofunktsionirovaniyarobototekhnicheskikhkompleksovnovogopokoleniya v usloviyakhprednamerennogovozdeystviyasverkhkorotkikhelektromagnitnykhimpul’sov [Analysis of the stable functioning of new generation robotic systems under the conditions of deliberate exposure to ultrashort electromagnetic pulses]. Izvestiya YUFU. Tekhnicheskiyenauki [ews of SFU. Technical sciences ], p. 12 (2014) 12. Davis, S., Caldwell, D.G.: The design of an anthropomorphic dexterous humanoid foot. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2200–2205. IEEE (2010) 13. Pavlyuk, N.A.: i dr. Razrabotkakonstruktsiiuzlanogiantropomorfnogorobota ANTARES naosnovedvukhmotornogokolena [Development of the construction of the foot assembly of the anthropomorphic ANTARES robot based on a twin-engine knee]. IzvestiyaYuzhnogofederal’nogouniversiteta. Tekhnicheskiyenauki [News of the Southern Federal University. Technical science] 174(1) (2016) 14. Lavrenov, R.O., MagidYe, A., Matsuno, F., Svinin, M.M., Sutakorn, D.: Razrabotka i implementantsiyasplayn-algoritmaplanirovaniyaputi v srede ROS/GAZEBO [Development and implementation of the spline-path planning algorithm in the ROS / GAZEBO environment]. Trudy SPIIRAN 18(1), 57–84 (2019) 15. Borisov, A.V.: Upravleniyedvizheniyemodinnadtsatizvennogoantropomorfnogorobotanao snoveinformatsiieksperimental’nopoluchennoynabiologicheskikhob"yektakh [Motion control of an eleven-link anthropomorphic robot based on information experimentally obtained at biological objects]. VestnikVoronezhskogogosudarstvennogouniversitetainzhenernykhtekhnologiy [Bulletin of the Voronezh State University of Engineering Technologies.], pp. 68–71 (2011) 16. Aleksander, R.: Biomekhanika [Biomechanics] - M.: Mir, pp. 340 (1970) 17. Bogdanov, A.A.: i dr. Razrabotka antropomorfnogo robota s interaktivnym upravleniyem [Development of an anthropomorphic robot with interactive control]. Neobratimyyeprotsessy v prirode i tekhnike [rreversible processes in nature and technology] 228–229 (2015) 18. Jatsun, S.F., et al.: Analysis of the effect of the exoskeleton geometrical dimensions on the nature of a linear compensator operation. In: 2019 12th International Conference on Developments in eSystems Engineering (DeSE), pp. 466–471. IEEE (2019)

Stacked Modulation Architecture for Simultaneous Exploration and Navigation of a Biped Robot Tomomichi Sugihara1(B) and Takanobu Yamamoto2 1

Preferred Networks, Inc., 1–6–1 Otemachi, Chiyoda-ku, Tokyo 100-0004, Japan 2 Osaka University, 2–1 Yamada-oka, Suita 565-0871, Osaka, Japan

Abstract. A new control architecture for real-world-oriented robots is presented. Awareness of the issue lies in the conventional subsumption architecture, in which outputs from multiple layers often conflict with each other and a na¨ıve prioritization of the upper layer by an override of the lower layer reduces the system responsivity against accidental events. The proposed architecture fundamentally avoids such a conflict in a way that the upper-layers modify functions of the lower layers through modulations of internal parameters in them and make the sole output from the bottom layer adapt to situations. This architecture provides a design criterion of each unit function module such that it accepts incomplete and noisy information from the upper-layer modules asynchronously. Simultaneous exploration and navigation (SEAN) system for a biped robot was implemented based on the architecture and evaluated on a computer simulation.

Keywords: Stacked modulation architecture exploration and navigation · Biped robots

1

· Simultaneous

Introduction

Robots that can locomote and work robustly in the real world has been strongly demanded for various applications. Such robots have to cope with uncertain conditions in environments and unpredictable events including dynamic changes of surroundings and the destination. It requires a high-level operation supported by a consecutive cycle of observation of the circumstance, perception (mapping) of the terrain profile and obstacles, self-navigation based on the map, and actuation of the body to follow the command through the cooperation of motors. A straightforward idea to design the whole system is to run the above components in sequence based on the logic that the mapping needs an observation, the navigation needs a map, and the actuation needs a navigation command. Actually, several existing systems for autonomous or semi-autonomous locomotion of humanoid robots [1–4] have been implemented in the above serial form. A problem underlying this system is that the sequential relay of information c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 13–23, 2022. https://doi.org/10.1007/978-3-030-86294-7_2

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necessarily reduces the responsivity. This is serious particularly in the case of biped robots, which are always exposed to the risk of falling and collisions with obstacles around footholds. The subsumption architecture proposed by Brooks [5] provided a path to the solution. The idea is to stack up control layers, each of which synthesizes a behavior with a different level of competence, in such a way that an upper layer for a high-level, i.e., more complex behavior that exploits information about a wider range of areas subsumes the lower layers that produce low-level, i.e., simpler but responsive behaviors such as collision-avoidance. The high-level behavior appears on the robot when the upper layer overrides the outputs from the lower layers. However, this architecture has some problems. The most seriously, the upper layer may diminish fundamental functions that should be provided by the lower layers in order to sustain the robot operation. Hence, this is not an appropriate solution to the original question how the system should be designed to achieve a high-level operation without sacrificing responsivity. This paper proposes another type of a stacked architecture to answer the same question, in which the upper layers do not override the outputs but modify the functions of the lower layers by modulating internal parameters in them. Each layer is affected by the upper layers but never loses its function. In this way, the high-level information processing through this stacked modulation consistently results in the robot behavior, where the highly-prioritized low-level reflex remains. An autonomous simultaneous exploration and navigation (SEAN) system for a biped robot in a computer simulation is presented as an example of the proposed architecture.

2 2.1

From Subsumption to Stacked Modulation Architecture Review of Subsumption Architecture

Figure 1 shows the conventional “sequential” architecture. Each block in the figure represents a unit function such as ‘mapping’ and ‘path-planning’. The prior functions usually consume longer time than the subsequent ones since the former have to deal with a large amount of geometric information about a wider range of areas. The latter functions require results from the former ones, and hence, have to pause until the previous function completes, which reduces the system’s responsivity. The subsumption architecture was proposed by Brooks [5] for an alternative. It is a multi-layered system as illustrated in Fig. 2. Each layer accepts sensor information and outputs motor commands, and defines a behavior. The lower layers comprise fewer function modules than the upper layers, and describe reflexive behaviors only based on local information, while the upper layers subsume the low-level behaviors by copying the same modules with the lower layers and embody high-level behaviors by combining them with functions that use more organized information. Example behaviors shown in the original paper are collision-avoidance (level 0), aimless wandering (level 1), exploration (level 2), goal-oriented locomotion including mapping and path-planning (level 3), etc.

Stacked Modulation Architecture

15

Fig. 1. Conventional (sequential) architecture

Fig. 2. Subsumption architecture

The figure has an odd part where the output arrows from the upper layer stick in another arrow from the lower layer. This does not conform to a rule in drawing of the block diagram, but represents the override by the signal from the upper layer. Namely, all the layers output motor commands independently in parallel, while the upper layers inhibit the lower ones as long as they run; output from the lower layer is transmitted to the motors only when the upper layer accidentally fails to output appropriate commands. The efficacy of this architecture was demonstrated on wheeled and hexapod mobile robots. The subsumption architecture has some problems. Let us see the block diagram of the example system introduced in the original paper [5] in Fig. 3. As mentioned above, each layer comprises several unit function modules that are mutually interconnected. Refer the original paper for the meanings of each function module. The pairs of vertically facing triangles mean that the connected lines inhibit the original signals for a predefined duration. The first concern that naturally arises by seeing the figure is that the system is designed in a heuristic way and is so complicated that it is hard to imagine how it works particularly due to many inhibitions, which leads to another question whether the low-level behaviors are really subsumed by the upper layers. Although the modules in level 0 are replicated in level 1 with some additional modules as well as those in level1 copied in level 2, they do not work after all as long as they are inhibited. The outputs from every layers often conflict with each other in dynamic situations; the system lacks responsivity during time when the output from the upper layer is activated, while it may lose chances to regain the high-level behavior once falling

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Fig. 3. An example system introduced in [5] based on the subsumption architecture (reorganized by the authors)

into an emergency in which the low-level reflex is prioritized. Consequently, the system does not run as expected in whichever cases. This is critical in particular for biped robots. 2.2

Stacked Modulation Architecture

The authors propose a novel architecture illustrated in Fig. 4. Each layer has a sole or only a few unit functions, so that it does not define any behavior by itself. The upper layer does not override the output of the lower layer but modifies it through a modulation of internal parameters in it. The lower layer is not explicitly concerned with it and repeats the defined process in order to achieve a function. As the modulations are propagated to the output motor commands, the high-level behavior appears on the robot body without losing the low-level responsive functions; conflicts between different levels of competence never happens in principle. This is named the stacked modulation architecture in this paper. Notice that this scheme does not purpose facilitation of system implementations. The unit functions of the proposed architecture have to accept incomplete

Stacked Modulation Architecture

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Fig. 4. Stacked modulation architecture

Fig. 5. A modified system of Fig. 3 based on the stacked modulation architecture

and noisy information issued from the upper layers asynchronously, i.e., at any timing, so that the modules have to be carefully designed; na¨ıve connection of existing methods fails. Figure 5 shows an alternative of the system depicted in Fig. 3 based on the proposed architecture. The authors tried to use the same names of modules as much as possible. Obviously, it has a slimmed-down structure with less number of modules. Any module does not inhibit other modules, and the system outputs motor commands from a unique module. Some specific points are as follows. – “grabber” module does no longer exist since there is no need to grab the desired destination and inhibit modules that may conflict. – “monitor” and “integrate” modules are merged since they should provide the robot state as one. – “wander” is omitted since “pathplan” should have that function for cases where the map is not fully provided by “sonar.”

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Fig. 6. An example SEAN system for a biped robot based on the Proposed architecture

– “orient” is newly defined in the figure. It converts the artificial force produced by “feelforce” to a coordinated movements of motors. – The functions of “collision,” “runaway,” “avoid,” and “straighten” are distributed into “pathplan” and “feelforce.” As the last item implies, the combination part of “pathplan” and “feelforce” plays a key role for balancing the high-level and low-level behaviors in this system. There does not seem to be any generalized methods to design such a key module, but case-dependent implementations based on the understanding of the system dynamics are required. Also note that such a conversion of a system from the subsumption architecture to the stacked modulation architecture is neither trivial nor always possible since modules of a system built upon the former are not necessarily compatible with that upon the latter as mentioned above. Instead of the above system, a more challenging simultaneous exploration and navigation (SEAN) [6] system for a biped robot developed in the authors’ previous work is presented in the following section as an example.

3

Example: SEAN System for a Biped Robot

The authors have developed a whole-body control method for a biped robot to cope with large perturbations and abrupt changes of the desired landing position of the foot [7], and a navigation method of a biped robot including terrain mapping to respond to dynamic changes of ground profile and the destination [8]. They do neither need planning of a time-dependent motion trajectory nor of the optimal series of foot-placements to the destination. While they omit strict constraints on the motion by intention, a quick on-line motion synthesis flexibly absorbs short-term violation of the constraints. Hence, those methods can provide unit functions of the proposed stacked modulation architecture. Figure 6 depicts a block diagram of the actual SEAN system for a biped robot. It consists of the following four layers in addition to the robot body and the state estimator: Terrain mapping accepts progressive data of the surroundings acquired with a LIDAR or an RGB-D camera, for example, and successively updates the

Stacked Modulation Architecture

Fig. 7. (A) Information of a measured point on the ground is shared by three grids. (B) Each grid contains information of points in six triangular cells.

19

Fig. 8. Nominal path is planned on a thinned-out triangular grid map with a cylindrical body approximation for collision detection.

Fig. 9. Process to determine the next foot placement

stochastic Elevation-and-Normal Grid (ENG) map, which is the internal parameter to be modulated by this module. The map can be updated at the sampling cycle via the recursive least square error method [8] without a heavy computation for segmentation and reasoning. The ambiguity of the map due to the lack of data is represented by covariance matrices at each grid. In the authors’ implementation, the map is spanned by triangular grids for its nearly-isotropic nature with an equidistant property of all adjacent grids as depicted in Fig. 7, where (A) information of a measured point on the ground is shared by three grids, and accordingly, (B) each grid contains information of points in six surrounding triangular cells. Determination of foot-placement finds a preferable landing point of the stepping foot, which is the internal parameter to be modulated by this module, based on the traversability of the terrain, the reachability of the foot, and the capture region [8]. It initially draws a nominal path of the trunk by applying the A* algorithm to a thinned-out triangular grid map, where collision-check was conducted with a cylindrical bounding volume approximation of the robot

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Fig. 10. A model of the test environment in the simulated scenario

body as illustrated in Fig. 8. The ambiguity of the map is taken into account by simply assuming that there is no obstacles in the unobserved area, which is gradually corrected as the exploration proceeds. The nominal path is found in some miliseconds in the authors’ implementation. Then, it provides the Canonical Biped Track (CBT) [8], which is exploited for an efficient initial guess for the foot-placement search. Figure 9 shows the process to find the feasible footplacement within the intersection of the traversable region on the terrain, the foot-reachable region, and the capture region. It typically completes in some hundreds of microseconds. Hence, it can respond to dynamic changes of the destination and the map and also contributes to a reflexive fall-prevention and collision-avoidance. Foot-guided control of COM-ZMP model determines the desired position of the zero-moment point (ZMP) [9], i.e., the desired kicking point on the ground, and the desired movement of the stepping foot as the internal parameters to be modulated from the current state of the center of mass (COM) and the nominal time-to-land [7]. The computation is based on the COM-ZMP model [10] to represent the core reduced-order dynamics of a biped mechanism, and is formulated as an optimization problem to be analytically solved. The time-to-land is automatically adjusted in order to avoid falling based on the capturability condition [11]. Whole-body coordination converts the desired position of the ZMP to that of the COM [12] and resolves it together with the desired movement of the stepping foot into the referential joint displacements via the fast and robust inverse kinematics [13]. The references are given to motor servo controllers. An example simulation was already conducted in the previous paper [8], although the system architecture was not focused on in it. The simulations ran

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Fig. 11. Snapshots of the simulation result

Fig. 12. Time consumed by proposed method in the second scenario

on a PC with Intel Core i7-4700MQ CPU at 2.40 GHz. A miniature humanoid robot mighty [14] was supposed, where the robot dynamics was approximately computed based on the COM-ZMP model. A depth sensor to acquire point cloud of the environment was emulated by utilizing the depth buffer of OpenGL, where the resolution of the sensor was assumed to be 300 × 300. The localization process was omitted. A supposed environment in which the robot explored is shown in Fig. 10. The start and goal points were given as drawn in the figure. Figure 11 shows snapshots of the simulation. It is confirmed that the robot started from a situation where the information about surroundings was not provided, gradually constructed a map through observations, and finally reached the goal by adaptively navigating itself. The time profile of the function modules in this scenario is shown in Fig. 12. It takes about 30 ms for the update of the map, 1∼10

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ms for the nominal path planning, and 0.1 ms for the foot-placement planning, respectively. The time for the foot-guided control and the whole-body coordination control are negligible comparing with the above. Since the fluctuation of time is not large, those functions can be implemented on a realtime multithread program.

4

Conclusion

This paper addresses a problem how to design a system to achieve a high-level operation without losing the low-level responsive functions. Then, the stacked modulation architecture, which was devised through a revisit of the subsumption architecture, was newly proposed as an answer. The points of it are summarized as follows. 1. The upper-layer functions in it do not override the lower-layers’ outputs but modify them through modulations of internal parameters in the low-level function modules. This strategy avoids the modules from conflicts of functions in principle. 2. It provides criteria for designing each unit function module such that it accepts incomplete and noisy information from the upper-layer modules asynchronously. An example system to realize a simultaneous exploration and navigation by a biped robot, which was developed in the authors’ previous work, was introduced. It enabled the robot to efficiently reach the designated destination in a complex environment without stopping during the operation not alike the conventional sequential architecture. A short-term future works is to implement the localization in the system. The authors believe that the proposed architecture is applicable not only to the locomotion tasks but also to various tasks including manipulation. On the other hand, as pointed out in the above, novel implementations of functions that are available in this architecture will be demanded for such applications. Acknowledgment. This work was supported by Grant-in-Aid for Scientific Research (B) #18H03310, Ministry of Education, Culture, Sports, Science and TechnologyJapan.

References 1. Gutmann, J.S., Fukuchi, M., Fujita, M.: 3D perception and environment map generation for humanoid robot navigation. Int. J. Robot. Res. 27(10), 1117–1134 (2008) 2. Nishiwaki, K., Chestnutt, J., Kagami, S.: Autonomous navigation of a humanoid robot over unknown rough terrain using a laser range sensor. Int. J. Robot. Res. 31(11), 1251–1262 (2012)

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3. Morisawa, M., Kita, N. Nakaoka, S., Kaneko, K., Kajita, S., Kanehiro, F.: Biped locomotion control for uneven terrain with narrow support region. In: Proceedings of of the 2014 IEEE/SICE International Symposium on System Integration, pp. 34–39 (2014) 4. Fallon, M.F., et al.: Continuous humanoid locomotion over uneven terrain using stereo fusion. In Proceedings of the 2015 IEEE-RAS International Conference on Humanoid Robots, pp. 881–888 (2015) 5. Brooks, R.: A robust layered control system for a mobile robot. IEEE J. Robot. Autom. 2(1), 14–23 (1986) 6. Zuo, J., Yamamoto, T., Sugihara, T.: SLAM-SEAN for higher autonomy of mobile robots in unknown environment. In: Proceedings of the 2020 JSME Conference on Robotics and Mechatronics, 2P1-K15 (2020) 7. Yamamoto, T., Sugihara, T.: Foot-guided control of a biped robot through ZMP manipulation. Adv. Robot. 34(21–22), 1472–1489 (2020). https://doi.org/10.1080/ 01691864.2016.1150201 8. Yamamoto, T., Sugihara, T.: Responsive navigation of a biped robot that takes into account terrain. Foot reachability and capturability. Adv. Robot. (2021). https:// doi.org/10.1080/01691864.2021.1896382 9. Vukobratovi´c, M., Stepanenko, J.: On the stability of anthropomorphic systems. Math. Biosci. 15(1), 1–37 (1972) 10. Mitobe, K., Capi, G., Nasu, Y.: Control of walking robots based on manipulation of the zero moment point. Robotica 18(6), 651–657 (2000) 11. Koolen, T., de Boer, T., Rebula, J., Goswami, A., Pratt, J.: Capturability-based analysis and control of legged locomotion, Part 1: theory and application to three simple gait models. Int. J. Robot. Res. 31(9), 1094–1113 (2012) 12. Sugihara, T., Nakamura, Y., Inoue, H.: Realtime humanoid motion generation through zmp manipulation based on inverted pendulum control. In Proceedings of the 2002 IEEE International Conference on Robotics and Automation, pp. 1404– 1409 (2002) 13. Sugihara, T.: Solvability-unconcerned inverse kinematics by the LevenbergMarquardt method. IEEE Trans. Robot. 27(5), 984–991 (2011) 14. Sugihara, T., Yamamoto, K., Nakamura, Y.: Hardware design of high performance miniature anthropomorphic robots. Robot. Auton. Syst. 56(1), 82–94 (2007)

Continuous Inverse Kinematics in Singular Position Patrick Vonwirth(B) and Karsten Berns Department of Computer Science, Technische Universit¨ at Kaiserslautern, 67663 Kaiserslautern, Germany {vonwirth,berns}@cs.uni-kl.de https://agrosy.informatik.uni-kl.de

Abstract. The problem of calculating inverse kinematics of a robotic manipulator is known to be non-trivial and not straightforward to solve for centuries. Hence, multiple different approaches have been developed, extended, and further developed that iteratively approximate toward a suitable solution. Unfortunately, all these existing solutions share the problem to get unreliable in singular positions – a standard configuration of human legs, e.g. when standing. Within this work, a simple extension to the iterative Damped Least Square algorithm is presented that covers the problematic, singular configuration case. The proposed algorithm is thereby focusing on continuous solving of small, iterative pose changes. Keywords: Inverse Kinematics position · Humanoid robots

1

· Jacobian · Least square · Singular

Introduction

Inverse Kinematics is one of the basic problems in classical robotics. Every robotic arm that e.g. is performing pick and pace operations, or performs a trajectory following task, requires to solve the inverse kinematic problem. Many different approaches have been developed to solve this problem over the past years, but none of them is universally valid and suitable for all purposes and requirements. The difficulty of the inverse kinematics problem arises from a couple of circumstances that usually makes a solution mathematically hard to calculate, non-unique or not existing. However, the main problems arise from the mechanical construction. Currently, the majority of the existing robot manipulators are built with rotational joints. In Cartesian workspace coordinates, these circular motions require a quadratic representation that completely excludes the usage of linear algebra to calculate closed-form solutions. Furthermore, the kinematic function K(·) is neither injective nor surjective with leads to the result that the inverse kinematic function K−1 (·) mathematically does not exist. Solving the inverse kinematics results in an arbitrary number of possible results, including zero and infinity. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 24–36, 2022. https://doi.org/10.1007/978-3-030-86294-7_3

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Since linear joints are much simpler to handle than rotational ones, the strategy described in the paper at hand is restricted to rotation-only kinematics. Throughout the paper at hand, the angular configuration of all joints is therefore represented by a vector of angles Θ. The inverse kinematic problem is hence defined by finding an angular configuration ΘG that satisfies K(ΘG ) = G for an arbitrary desired pose G, given in the Cartesian workspace. Nevertheless, linear joints can easily be integrated into the proposed methodology. Due to the basic nature of the inverse kinematics, several different strategies have been developed to solve this problem. Popular in the field of robotics, there are iterative gradient descent algorithms, all implementing a Newton-Raphson Approximation variation, of the following general form, iterating over i: ei = G − K(Θi ) −1

δi = ∇

(Θi ) · ei

Θi+1 = Θi + γδ i

Pose Error against Goal Linearized Adaptation

(1)

Damped Joint Update

with ∇(Θi ) being an arbitrary gradient function at the operating point Θi . The parameter γ ∈ (0, 1] specifies the approximation rate of every individual iteration step. Hence, the more inaccurate ∇(·) represents the reality, the smaller γ has to be chosen in order to keep the iteration process stable at the cost of an increasing number of required iteration steps. An initial guess Θ0 is required to start the iteration sequence. Usually, Θ0 is simply set to the actual joint configuration. The iteration process is stopped whenever the workspace squared error drops below a predefined accuracy threshold  ei 2 ≤ e , or no more approximation progress can be observed 0 ≤ ei−1 2 −  ei 2 ≤ p . Furthermore, the iteration process can be limited by a maximum number of iteration steps or computation time. Simple implementations of the inverse gradient function ∇−1 (·) are the Jacobian Inverse, the Jacobian Transpose, the Jacobian Pseudoinverse, or the socalled Damped Least Square (DLS) approach. All of them have been used successfully in early robot control systems, e.g. [2,11,14,16]. While the DLS method especially addresses the problem of K(·) not being bijective, a variety of extensions and adaptations, e.g. Selectively DLS [4] or User-Defined Weighted DLS [5], have been developed to further improve the accuracy, stability around singular positions and approximation speed of the basic DLS algorithm [6,8]. Other, Jacobian-free inverse kinematic strategies also have been developed outside the field of robot control. In CGI applications, for example, inverse kinematics are required to map captured (human) motions onto complex, virtual, animated character models. A representative, but not complete, set of these approaches should be mentioned in the following: Cyclic Coordinate Descent, a heuristic approach, introduced by Wang et al. [15] is especially declared to be suitable for large-distance problems which, unfortunately, contradicts with the motivation of this work. An other heuristic approach, proposed by Courty et al. [7], is based on Sequential Monte Carlo Simulations using particle filtering techniques. The authors Grochow et al. propose an AI-based approach that learns suitable inverse kinematic solutions from

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previously observed and trained poses [10]. As a natural property of all AIapplications, this method strongly depends on the quality, space coverage, and smoothness of the training data set. With respect to continuous control of a robot manipulator, however, such heuristic methodologies always include some rest risk of unpredictable and undesired behavior. Hence, more deterministic approaches should be preferred over heuristic ones in the concrete application of arbitrary, continuous robot control. A geometrically inspired approach for the purpose of virtual rope simulation has been presented by Brown et al. [3] and extended to the so-called FABRIK algorithm (Forward And Backward Reaching Inverse Kinematics) by Aristidou et al. [1]. The FABRIK algorithm shares the exact same singularity problem as the classical Newton-Raphson approximation strategies. However, it comes with the massive drawback that the requirements of rope simulation and robot control are mostly distinct from each other. E.g. introducing joint limits strongly attacks the algorithm’s convergence while blowing up its complexity at the same time. Hence, extending a classical, Jacobian-based approximation strategy best meets the requirements of continuous robot control. Within the work at hand, an extension of the well-known DLS method is presented. The newly introduced extension especially treats the problem of getting stuck in singular positions, i.e. when all gradient vectors are orthogonal to the direction of the desired displacement. In Sect. 2, the basic structure and reasoning of a DLS approximation is introduced. The problem of the DLS iteration getting stuck in singular position is covered in Sect. 3. Section 4 describes the adaptation of the former presented approach for weighted, continuous execution. An experimental validation of the presented methodology is given within Sect. 5 at the example of continuous inverse kinematics calculations of the planar, humanshaped robotic leg Carl. Finally, Sect. 6 concludes the overall results and gives an outlook on the planned operational scenario.

2

Iterative Damped Least Square Approximation

When inverting the kinematics function K(Θ) of an arbitrary, robotic manipulator with only rotational joints, there are three main mathematical problems: 1. K is not linear 2. K is not surjective 3. K is not injective From the non-linearity of K, it can directly be derived that there is no closedform solution existing within linear algebra. Although it is possible to manually calculate closed-form solutions for such non-linear problems, such solutions are specialized to one particular kinematic structure. Hence, they lack both, generality and adaptability to special purposes. Iterative, general-purpose approaches that step-wise approximate the result, as introduced in Eq. (1), are therefore to be preferred over robot-specific solutions. Within every iteration step, these types of algorithms normally linearize K at one particular operating point, the

Continuous Inverse Kinematics in Singular Position

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so-called Gradient Field. Now, simple methods from linear algebra can be used to invert and solve the linearized kinematics. Finally, the operating point is slowly shifted towards the linearized solution. Unfortunately, the usage of an iterative algorithm comes at some additional cost: 4. The number of required iteration steps varies depending on the input 5. The iterative approximation process can get stuck in singular positions Using an upper limit of iteration steps, the input dependency can be handled. Although, aborting the approximation process leads to a loss of accuracy, in the context of this work, i.e. continuous inverse kinematics calculation, the lost accuracy will be caught up by the execution of the follow-up approximation. An extension to the DLS algorithm that offers the ability to break out of singular positions during the iterative approximation process is presented in Sect. 3 With the introduction of using the pseudoinverse, that is doing nothing else than minimizing the least square error, the problem of K not being surjective is solved. Whenever a desired goal pose is outside of the robot’s reachable workspace, the closest possible solution is returned. The problem of K not being injective has been treated by adding an additional damping term. The general DLS method extends the calculation formula of the intermediate approximation step δ i within Eq. (1) to δ i = min  ∇(Θi )δ − ei 2 +λD  δ 2 δ

(2)

with λD > 0 being an arbitrarily chosen parameter that weights the additional damping term against the error minimization. Analyzing the effect of λD , it can be seen that the added damping term is pulling the step-wise change δ i towards zero. Especially, it is slowing down the approximation rate of the overall algorithm which is the identical functionality of the parameter γ. Hence, the approximation rate parameter γ can be removed from the Eqs. (1) in case λD is present. λD has to be chosen large enough in order to keep the approximation process stable, but can automatically be reduced in value while the algorithm is step-wise approaching the desired pose. For some suitable initialization value λ0 > 0, a very simple adaptation rule is to exponentially decrease λD in every iteration step. (3) λD =  + λi > 0 where λi = αλi−1 with 0 < α < 1 being the exponential decrease rate of λi and e >  > 0 being an arbitrary, small constant that assures a minimum amount of positive definiteness of the underlying quadratic minimization problem.

3

Using the Gradient Derivative to Break Out of Singular Positions

The problem of singular positions during the iterative approximation of K−1 is visualized in Fig. 1 at the example of a simple, planar, two-segmented robot

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Fig. 1. The problem of getting stuck in singular position: The two vectors ∇S and ∇E represent the linearized gradients of the two joints S and E respectively. Normal to these, er and its negative eu represent desired directions of motion. While a motion in the direction of er is possible, its negative is not. Due to the motions orthogonality, however, any standard DLS algorithm will stick to the singular position in both cases.

arm. It can be seen that both gradient vectors ∇S/E areparallelto each other. Hence, the combined 2 × 2 gradient matrix ∇(S, E) = ∇S ∇E is not of full rank anymore. As a direct consequence, it can be followed that there is one direction vector u = 0 existing that always becomes zero when being projected into the image of ∇(S, E). I.e. the best possible approximation of u using ∇(S, E) is the null vector u ≈ ∇(S, E)0 which encodes the statement of no further approximation being possible. However, the example shown in Fig. 1 proofs the existence of possible motions in such a singular situation. Corollary: Any iterative approximation algorithm in the general form of Eq. (1) can get stuck, if and only if the rank of the linear gradient field function ∇(·) is able to become less than its number of rows (after removing gradients of joints already being in their limit position in the direction of interest). Obviously, the only solution is to assure that the gradient function ∇(·) always keeps full rank. One solution is to guarantee linear independence of the individual (relevant) gradient vectors, i.e. applying small changes in direction. Unfortunately, the circular nature of the reachable workspace (due to the rotational joints) prohibits any change in orientation to the gradient vectors. If a gradient vector in singular position would differ from the tangential plant at the border of the reachable workspace, either a positive or a negative motion into that gradient’s direction would virtually allow the system to move into the unreachable space. Furthermore, restricting the motion of such an altered gradient to either positive or negative direction cannot be handled in a simple manner, since both directions are geometrically identical and the right choice depends on the context. Since the content of ∇(·) cannot be altered to assure full rank, the gradient matrix has to be extended with additional, orthogonal column vectors. The gradient itself, however, is nothing else than a very rough Taylor approximation of the real motion function. Hence, one further addend of the Taylor series, i.e.

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29

˙ the gradient derivative ∇(·), is a natural extension of ∇(·). Since the second derivative in the Taylor series is multiplied with a square, it is limited to nonnegative multiplication factors. Transferred into the approximation iteration, ˙ this means that it is necessary to limit ∇(·) to non-negative multiples. With respect to the example, shown in Fig. 1, this property is exactly what is required to allow motion in direction of er , but not in its negative direction eu . The  ˙ ˙ . orthogonality of ∇(·) to ∇(·) assures full rank of the combined matrix ∇ ∇ With the extension of the gradient function, also the minimization variables of ˙ T . It is easy to see Eq. (2) have to be extended respectively, i.e. δ → (δ, δ) ˙ that ∇(·) can be reduced to only relevant, non-zero columns. This way, also the number of additional minimization variables δ˙ and hence the computational effort can be reduced. When using the standard Jacobian as gradient function, its derivative represents the curvature of the circular motion of a joint. This curvature is geometrically represented by a normal vector of the circular trajectory, pointing towards the joint axis. Figure 2 sketches these vectors at the example of the already introduced planar, two-link robot arm.

Fig. 2. Extended gradient vectors, visualized at the example of a planar, two-link manipulator in scalar position. Visualized are the gradient vectors ∇S/E , the gradi˙ ± ∇)S/E ˙ S/E as well as two possible gradient-extension-vectors (∇ ent derivatives ∇ respectively to both joints S and E.

The quadratic coupling of the first and second derivative terms in the Taylor series cannot be represented with linear equations. It is therefore not possible to ˙ couple the minimization variables of both, ∇(·) and ∇(·) adequately. However, the second-order terms are only required in singular positions. A linear coupling via the gradient function itself is therefore a suitable solution as long as δ˙ is strongly kept close to zero in non-singular positions. Furthermore, the complete approximation solution of K−1 is kept within the non-extended vector δ. The DLS Eq. (2) hence extends to   δi ˙ ± ∇)(Θi )δ˙ − ei 2 = min  ∇(Θi )δ + (∇ · δ , δ˙ ≥0   +λD  δ 2 +λS  diag ∇T (Θ)ei δ˙ 2 +  δ˙ 2 (4)

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with λS 0 being an arbitrary positive parameter much bigger than zero. Equal to Eq. (3),  is an arbitrary, small constant to assure positive definiteness. diag(·) is a function returning a diagonal matrix with the argument vector as diagonal elements. Its argument ∇T e encodes the scalar product of each gradient vector with the desired motion. Hence, its entries become zero in their singular positions. Since e is continuously decreasing throughout the approximation process, it is necessary to choose λS large enough to compensate for the decreasing length of e. One suitable definition of λS is hence λS =

λinf

0  ei 2

(5)

˙ ± ∇) encodes columnwith λinf being some arbitrary, big constant. The term (∇ wise addition or subtraction. Which columns to add and which to subtract can be chosen arbitrarily or even differently in every iteration step. The chosen operations only should encode a zigzag-like motion of the manipulator. In most robotic applications, it will be sufficient to fix that to a single, constant configuration. Note, that the addition or subtraction has to be chosen complementary to the desired zigzag motion. E.g.: A gradient subtraction from the derivation extension will be compensated by an addition of the original gradient.

4

Continuous, Weighted Inverse Kinematics

As introduced in Eqs. (1) and (4), every iteration step of the overall approximation consists of two internal steps. At first, the linearized approximation δ i is calculated. Second, the operating point, i.e. the approximation result is updated with the former calculated linear approximation. These two sequential steps can be combined into a single equation that directly optimizes the linearized result vector. From Eq. (1), it can be derived that Θi+1 = Θi + γδ i → δ i = Θi+1 − Θi

(6)

with γ = 1 being removed as described in Sect. 2. Inserting that into the extended DLS equation (4) leads to   Θi+1 ˙ ± ∇)(Θi )δ˙ − ei 2 (7) = min  ∇(Θi ) (Θ − Θi ) + (∇ · Θ, δ˙ ≥0   +λD  (Θ − Θi ) 2 +λS  diag ∇T (Θi )ei δ˙ 2 +  δ˙ 2 Physical joint limits can now be introduced by simply adding component-wise lower and upper bounds to the minimization variables Θ since they now encode the physical result joint configuration: Θmin ≤ Θ ≤ Θmax . Since λD and λS are positive, user-defined constants, they both can be moved inside the three appropriate squared length expressions. Let W be a symmetric, positive semidefinite matrix in the same dimension of the desired goal pose G. With that matrix, the n-dimensional relevance of the desired goal pose can be

Continuous Inverse Kinematics in Singular Position

31

encoded in the space of the desired pose G. By a simple left-multiplication of the first minimization term, the goal accuracy gets weighted with respect to W. Equivalently, the two error-based abortion criteria become weighted:  Wei 2 ≤ e and  Wei−1 2 −  Wei 2 ≤ p . More precise, the quadratic error towards the desired pose gets weighted by W2 .   ˙ T and ∇+ := ∇i (∇ ˙ i ± ∇i ) , Defining ∇i := ∇(Θi ) and Θ+ := (Θ, δ) i Eq. (7) can now be rewritten to   2  Θi+1 Θ+ − W (ei + ∇i Θi ) (8) = min W∇+ i · Θ+ 2  √ √ 2 



  0  λD I 0 0 λ D Θi  + +    √ + Θ −  +  0 I + λS diag(∇T ei ) Θ  0 0 0 i In order to apply general-purpose solver (e.g. qpOASES [9]) on the presented minimization problem, it has to be brought into a quadratic normal form:   1 +T Θi+1 Θ HΘ+ + Θ+T g = min (9) · Θ+ 2     Θmax Θmin ≤ Θ+ ≤ (10) s.t. π/2 0 with:



λi I 0 + I + H 0 λS diag(∇Ti ei )2   λ i Θi 2 W (e + ∇ Θ ) − g := − ∇+T i i i i 0 2 + :=∇+T i W ∇i

(11) (12)

Note, that λD has been replaced by  + λi as introduced in Eq. (3).

5

Continuous Inverse Kinematics on the Planar Robotic Leg C ARL

The introduced inverse kinematics approach is especially designed to be executed in singular positions. In classical robotics, especially industry robots, this system state usually is mechanically avoided in order to overcome the associated mathematical problems. On the other hand, in nature, singular leg configurations are one of the key features to lower power demands on muscles. In singular position, the main load is shifted away from the muscles and onto the skeletal structure, hence supporting endurance and energy efficiency. The human-shaped robotic leg Carl, first introduced by Sch¨ utz et al. in [12], therefore offers perfect kinematics to evaluate the proposed inverse kinematics approach. Carl is a compliant, planar robotic leg with three degrees of freedom in hip, knee and ankle joint. A two-legged, bipedal version of Carl is shown in Fig. 3a. The kinematic structure of Carl, as well as its actuation concept, is strongly related to human nature. Thigh and shank are constructed with an equal length

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Fig. 3. Inverse Kinematics applied to the planar robotic leg Carl [12]. On the left side, figure (a) pictures the bipedal version of Carl. The kinematic definitions of one leg are described in figure (b). To the right, figure (c) sketches the desired circular trajectory that has been used to validate the presented inverse kinematics approach. The dashed part indicates an impossible desired trajectory outside the reachable workspace.

of 0.42 m, the foot is a standard medical prosthesis [12]. Figure 3b sketches the angle definitions of the kinematic structure of Carl. Further details on the concrete kinematic equations can be found in [13]. Equivalent to nature, the knee is restricted to backward flexion only. Hence, the zigzag-motion to leave singu˙ ± ∇), as introduced in Eq. (4), can be fixed to a knee flexion combined larity (∇ with hip and ankle rotations in opposite directions. As gradient function ∇(·) the Jacobian matrix J(Θ) is used. In order to evaluate the validity and performance of the proposed inverse kinematics approach, the algorithm is executed on two different continuous trajectories and in both times in comparison to a standard DLS approach. Both algorithms are implemented identically and executed under equal conditions. Standard DLS execution is simply achieved by switching off the newly proposed extension while keeping all other parameters identical. The first desired trajectory is a continuous, circular motion as sketched in Fig. 3c, starting in the lowest point outside the reachable workspace. Second, the projection of that circular motion onto the vertical Y-axis is used as linear trajectory. Both trajectories are especially chosen to be partially outside the reachable workspace of Carl and to pass singular positions with mathemati-

Continuous Inverse Kinematics in Singular Position

Tracking Error SDLS

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Fig. 4. Performance evaluation of the newly introduced inverse kinematics approach (SDLS) on the left side against the pure DLS methodology on the right side at the example of a continuous, circular trajectory as sketched in Fig. 3c.

cally problematic directions of motion. The reachable part of both trajectories approximately correlate with a positive YInput . All four algorithm executions are configured identically with a desired approximation accuracy of 1 μm, i.e. e = 1 × 10−12 , λ0 = 1.5, α = 0.3,  = p = 0.1 · e and λinf = 1 × 109 . The results of the circular and linear experiments are plotted in the Figs. 4 and 5 respectively. It can be seen that the approach, introduced within the work at hand, is capable of tracking both trajectories within the physical limits of the robot. The standard DLS approach, however, produces a sudden motion peak when leaving the singular position at 25% on the circular trajectory. On tracking the linear motion, the pure DLS approach fails in total. This exactly represents the singularity problem of standard gradient-descent methodologies as explained in

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Tracking Error SDLS

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Fig. 5. Performance evaluation of the newly introduced inverse kinematics approach (SDLS) on the left side against the pure DLS methodology on the right side at the example of a continuous, linear trajectory. The linear trajectory is generated as a projection of the circular one as sketched in Fig. 3c onto the pure vertical Y-axis.

Fig. 1 within Sect. 3. The standard DLS approximation is not able to leave the singular position, orthogonal to the direction of all gradients. In both trajectories, the robot passes between reachable and unreachable workspace in singular position. These edge cases are clearly visible at around 25% and 75% by two peaks of the required iterations. The first peak represents the transition into the reachable workspace area and the ability to leave the singular position. The second peak indicates the opposite motion. From the executions of the circular trajectory, it can be seen that the proposed DLS extension produces a much smoother transition than the pure DLS approach when it comes to leave the singular position. Within the rest of the trajectory, no relevant effect can be observed. Hence, it can be summarized that the proposed singularity extension

Continuous Inverse Kinematics in Singular Position

35

to the classical DLS approximation strategy is a valid solution to overcome the problematic edge case of leaving singular position at no relevant additional computational cost. Furthermore, the introduced DLS extension reduces the algorithm’s overall sensitivity to its parametrization.

6

Conclusion and Outlook

The problem of inverse kinematics is a well-known, but still non-trivial problem. One main solution strategy in robotics is to iteratively approximate toward a valid solution. Although able to solve the inverse kinematics problem in general, such a strategy becomes unreliable in and close to singular positions. Unfortunately, being in singular position is a standard configuration of human legs. For human-shaped robots like Carl [12] that are especially designed to offer research on natural, human-like locomotion this single edge case of being in singular position becomes the default and hence a major problem. Within the work at hand, a new extension to the iterative Damped Least Square (DLS) approximation [5] is introduced. The described extension especially treats the mathematically difficult edge case of leaving a singular position while it does not affect the overall rest functionality. Furthermore, a mathematical formulation is derived that specializes the individual iteration steps towards continuous calculations. This way, the proposed algorithm especially supports fast solutions to continuous motions. The functionality of the newly introduced concept is validated at the example of two different, continuous trajectories. Its performance is estimated in comparison to the equivalent algorithm without the newly developed extension. The results show that within the problematic singular position, the reliability and performance of the classical DLS algorithm is clearly increased by the work at hand. However, detailed and in-depth performance optimization is not covered within the scope of this work. Improvements in convergence and calculation performance are hence expected to be possible by combining the work at hand with other DLS variations that e.g. focus on parameter optimization like the so-called Selectively DLS by Buss et al. in [4].

References 1. Aristidou, A., Lasenby, J.: FABRIK: a fast, iterative solver for the Inverse Kinematics problem. Graph. Models 73(5), 243–260 (2011) 2. Balestrino, A., De Maria, G., Sciavicco, L.: Robust control of robotic manipulators. IFAC Proc. Vol. 17(2), 2435–2440 (1984) 3. Brown, J., Latombe, J.C., Montgomery, K.: Real-time knot-tying simulation. Vis. Comput. 20(2), 165–179 (2004) 4. Buss, S.R., Kim, J.S.: Selectively damped least squares for inverse kinematics. J. Graph. Tools 10(3), 37–49 (2005) 5. Chiaverini, S., Egeland, O., Kanestrom, R.: Achieving user-defined accuracy with damped least-squares inverse kinematics. In: Fifth International Conference on Advanced Robotics ’Robots in Unstructured Environments, Pisa, Italy, vol. 1, pp. 672–677. IEEE (1991)

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6. Chiaverini, S., Siciliano, B., Egeland, O.: Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator. IEEE Trans. Control Syst. Technol. 2(2), 123–134 (1994) 7. Courty, N., Arnaud, E.: Inverse kinematics using sequential Monte Carlo methods. In: Perales, F.J., Fisher, R.B. (eds.) AMDO 2008. LNCS, vol. 5098, pp. 1–10. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70517-8 1 8. Duleba, I., Opalka, M.: A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators. Int. J. Appl. Math. Comput. Sci. 23(2), 373– 382 (2013) 9. Ferreau, H.J., Kirches, C., Potschka, A., Bock, H.G., Diehl, M.: qpOASES: a parametric active-set algorithm for quadratic programming. Math. Program. Comput. 6(4), 327–363 (2014) 10. Grochow, K., Martin, S.L., Hertzmann, A., Popovic, Z.: Style-Based Inverse Kinematics. In: ACM SIGGRAPH 2004 Papers, SIGGRAPH 2004, New York, NY, USA, vol. 10, pp. 522–531. Association for Computing Machinery (2004) 11. Nakamura, Y., Hanafusa, H.: Inverse kinematic solutions with singularity robustness for robot manipulator control. J. Dyn. Syst. Meas. Contr. 108(3), 163–171 (1986) 12. Sch¨ utz, S., Nejadfard, A., Mianowski, K., Vonwirth, P., Berns, K.: CARL – a compliant robotic leg featuring mono- and biarticular actuation. In: IEEE-RAS International Conference on Humanoid Robots (2017) 13. Vonwirth, P., Nejadfard, A., Mianowski, K., Berns, K.: SLIP-based concept of combined limb and body control of force-driven robots. In: Zeghloul, S., Laribi, M.A., Sandoval Arevalo, J.S. (eds.) RAAD 2020. MMS, vol. 84, pp. 547–556. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48989-2 58 14. Wampler, C.: manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods. IEEE Trans. Syst. Man Cybern. 16(1), 93–101 (1986) 15. Wang, L.C., Chen, C.: A combined optimization method for solving the inverse kinematics problems of mechanical manipulators. IEEE Trans. Robot. Autom. 7(4), 489–499 (1991) 16. Wolovich, W., Elliott, H.: A computational technique for inverse kinematics. In: The 23rd IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, pp. 1359–1363. IEEE, December 1984

Analysis of Biped Robot on Uneven Terrain Based on Feed-Forward Control Cong Yan1(B) , Fumihiko Asano1 , Yanqiu Zheng1 , and Longchuan Li2 1

School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan {gansou315,fasano,s2020415}@jaist.ac.jp 2 Graduate School of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan [email protected]

Abstract. This paper discusses a concept of using a bipedal robot based on entrainment control to achieve walking on uneven terrain. Keywords: Biped robot

· Uneven terrain · Entrainment

Extended Abstract Limit-cycle dynamic walking such as passive walking [1] has been widely studied as an effective approach to realize efficient walking motion of biped robots. Although it has already been confirmed both theoretically and by experiments on actual machines that highly efficient dynamic walking on level ground is possible by appropriately applying the passive walking principle. From the viewpoint of practicality, it is an indispensable ability for a robot to have the locomotion skills to adapt to uneven terrain and other adverse conditions (mainly surfaces with changing inclination angles). We hope to use an entrained control method [2] to take full advantage of the intrinsic dynamics of the bipedal robot, and it can generate a relatively stable gait on uneven terrain.

Fig. 1. Model of semicircular-footed compass-like biped robot with feed-forward control c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 37–39, 2022. https://doi.org/10.1007/978-3-030-86294-7_4

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Fig. 2. Simulation results of motion generation with feed-forward control

Figure 1 (a) illustrates the model of semicircular-footed compass-like bipedal walker on uneven terrain. It has a waist with mass of mH [kg]. Two identical rigid leg frame with mass of m1 = m2 [kg]. Two legs have semicircular feet, whose radius is R [m]. Here, let (xc , zc ) be the ground contact point, and (x, z) is the center point of the semicircular feet. θ1 [rad] and θ2 [rad] are the angular position of the stance leg and swing leg regard to vertical. The u is the only control input is acted on the hip joint. We set the slope angle to change randomly every 5 steps, and the maximum and minimum angles to be 0.1 [rad] and −0.1 [rad] respectively. Figure 2 are the results of the simulation in which the input torque is set to a general sinusoidal wave, which realizes the control of the robot’s own walking cycle by controlling the change of the input cycle of the given track. Here, the input period is 1.3 [Hz], and the simulation results show that the robot takes 65 steps in 50 s. (a) is the position of the semicircular-foot of the stance leg. The time variation of the positions of the biped angles is shown in (b). (c) shows the time variation of the vertical ground reaction force, which varies violently for the first few steps. We also can see the consumption of kinetic energy as shown in (d). The randomly generated slope angle are shown in (e). In order to verify the stability of the robot’s motion, we show the phase-plan plot of the gait has elapsed in (f). Through numerical simulations, we show the feasibility of the gait on uneven terrain. We will report more detailed analysis results and basic experimental results by using the experimental machine in the Fig. 1 (b) in the presentation.

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References 1. McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990) 2. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: a universal concept in nonlinear science. Am. Assoc. Phys. Teach. 70(6), 655–655 (2002)

Section–2: Human-Machine/Human-Robot Interaction

The Spherical Pedal Control Device for Omni-Directional Mobile Robot Manipulation Thawanrat Siriwattanalerd(B) , Ryosuke Sugimoto, Satoshi Muramatsu, and Katsuhiko Inagaki(B) Tokai University, Kanagawa, Japan [email protected], [email protected]

Abstract. Manipulation of the omni-directional mobile robot is more complicated when compared with the manipulation of a general mobile robot which is controlled by two degrees of freedom. By the reason that the manipulation of the omni-directional mobile robot is required three degrees of freedom controlling, we have developed a new control device for this mobile robot which can be operated by a human’s foot via the spherical pedal control device, not by hands. Through operating the spherical pedal or a new control device, operators can use their hands for another task. At this point, by rotating the spherical pedal control device in each axis direction is possible to control the robot’s three degrees of freedom motion, the velocity vector, and the angular velocity around its body. Keywords: Omni-directional mobile robot · Control device · Spherical pedal

1 Introduction The Omni-directional mobile robot is a mobile robot that can independently control three degrees of freedom of velocity vector and angular velocity around its body on a plane. Due to this characteristic, it can easily realize various movements, such as spot turning and diagonal moving, which is impossible to do with the general mobile robots [1–5]. A typical practical example of an omni-directional mobile robot is a transport robot for an automated warehouse. As the above-mention, many omni-directional mobile robots are controlled autonomously. There is a lot of research on this type of mobile robot, we could see that it is very popular challenging today’s mobile robot trending. On the other hand, this human-controlled type of omni-directional mobile robot is not that popular. Since omni-directional mobile robots have more degrees of freedom than general mobile robots, their operation is clearly more difficult. For the omni-directional mobile robots operating, a control device for general mobile robots is not sufficient; a dedicated control device needs to be developed. Moreover, by considering the practical example of a human-controlled omnidirectional mobile robot, we can assume that it can be used as a boarding-type mobile robot in the cell production system or the line production system of manufacturing industries. In such an environment, workers are often forced to work in a standing position © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 43–53, 2022. https://doi.org/10.1007/978-3-030-86294-7_5

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because they need to move and change direction frequently in a tight space. If an omnidirectional mobile robot can be used in this environment, it will be possible to work in a sitting position. By using the omni-directional mobile robot as the way we mentioned before, both hands of the worker will be free, and they will be able to use other parts of their body to control the robot. In view of the above, this research aims to develop a foot-controlled device or a controlled pedal for an omni-directional mobile robot. For the communication interface, we created a controlled device named a spherical pedal control device, which enables the robot to operate three degrees of freedom: velocity vector and body angular velocity. Afterward, we will descript more details of the spherical pedal control device and the results of experiments to verify its operability.

2 Mechanical Design Our proposal is to utilize a small sports ball (135 mm in diameter) as the spherical pedal control device. The initial position of the ball is set, and the angle of rotation relates to the initial position which indicates the velocity and angular velocity for the three degrees of freedom direction. Specifically, the amount of the ball rotating proportionally around the y-axis is used for indicating the x-component of the robot’s velocity. Similarly, the proportional rotation of the ball around the x-axis is the y-component of the velocity indicator. Consequently, the amount of the ball rotating proportionally around the z-axis is used as the angular velocity around its body (see Fig. 1).

Fig. 1. Rotation of spherical pedal

To achieve this, the mechanism allows freely rotating around each axis while holding the position of the spherical pedal is necessary. Therefore, three omni-wheels were installed under the ball to hold it (see Fig. 2). However, the omni-wheels have another role which is attaching an angle sensor to each omni-wheel and measuring the rotation angle of the ball around three orthogonal axes. For this function, installing the omni-wheel parallel to each of the three axes of the Cartesian coordinate system is desired. If this condition is satisfied, it becomes easily done to find the rotation angle of the ball for each axis. Regrettably, this condition is not suitable for holding the ball which is one of our important purposes. Then we decided to install omni-wheels at equal intervals of the ball with a solid angle of π/2 [sr] from the center and we hold the omni-wheel and motor by the metal-based was to avoid the

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occurrence of distortions. In this case, the conversion is required to get the position of the ball for each axis from rotation angles which is detected from each omni-wheel.

Fig. 2. Prototype

By this mechanism design, we can assume whether the solid angle is too large, the omni-wheel will not be able to support the ball and it will fall between the omni-wheels. On the other hand, if the solid angle is too small, the ball will go over the omni-wheels when the ball is rotated by the foot. As a result of trial and error, we found that there was no solid angle that satisfied both conditions, then we decided to make the solid angle slightly smaller and attach a cover to prevent the ball from falling off (see Fig. 3). This cover has a cross-section hole which is inserted amount of iron balls inside. These iron balls are partially exposed through the hole to support the sports ball for friction reduction. We can say that this idea came from the rolling bearing. Even this cover structure is not a perfect ball bearing, but it is functional enough. For the omni-wheel, we applied a special structure as shown in Fig. 4. For barrel-shaped wheels in this omni-wheel, two different shapes are applied. As a result, this omni-wheel can seamlessly support the sports ball and rotate smoothly while the barrel-shaped wheel’s surface remains in contact with the sports ball.

Fig. 3. Appearance of the cover

Fig. 4. Appearance of omni-wheel

Additionally, the encoders of the angle-measuring motors and the direct current motors (DC motors) are connected to each of the omni-wheels to generate a restoring force for returning the spherical pedals to their initial orientation, thereby improving operability. This restoring force and the force of an automobile’s pedal, which has accelerator and brake function, are similar. If we put our foot on the spherical pedal control

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device or the sports ball, the restoring force will occur. After finishing the work or take the foot out of the spherical pedal, the sports ball will turn back to the start position by this restoring force as the automobile’s pedal which can go back to the start position after pushing it down for accelerator or break. In this design, none of the reduction gears is inserted between the omni-wheel and the DC motors because generating a large frictional force may cause operability problems. Moreover, the rotary encoder is used as a component of the feedback control system to achieve the restoring force.

3 System Configuration

Fig. 5. System configuration

This section describes the spherical pedal type control system. Its system configuration is shown in Fig. 5. In the first place, DC motors connected to each omni-wheel are individually controlled by a “servo module for DC motors” which is developed in our laboratory formerly [6]. This servo module has the Microcontroller Unit (MCU) for controlling and another MCU for encoder counting, separately. By this servo module, we can realize position control of the DC motors easily by external position command signals. In other words, this module has the accessibility of the Radio Control servo (RC servo) which is often used for small robots. Conversely, this module can solve or reduce the problems of RC servos such as poor accuracy and small output. The servo module is connected to another host MCU via the Inter-Integrated Circuit communication (I2 C communication). Furthermore, this MCU is used for transmitting the amount of operating command to the robot. The original servo module is designed to receive position command signals from the outside via I2 C communication. Nevertheless, in this system, the position command signals are sent from inside of the servo module and the firmware of MCU on this servo module has been modified to use the position command value for fixing the initial angle of each omni-wheel, i.e., the initial orientation of the sports ball. While rotating the sports ball by an external force of the operator, this servo motor will be lightly locked, and the restoring force will be generated to return the sports ball to its initial orientation. Through this robot, three servo modules

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measure the angle of the omni-wheel and transmit to the upper MCU via I2 C communication then the orientation of the sports ball is calculated by using this information. Hence, the velocity vector and angular velocity of the robot are obtained and sent to the omni-directional mobile robot via some type of communication such as Universal Serial Bus (USB), Bluetooth, and so on. Furthermore, in the part of the original servo module firmware, the ProportionalIntegral-Derivative control (PID control) is used as the control law for the feedback control to relocate the object. Meanwhile, the Integral control (I term) of the control law on this control system is removed and the Proportional and Derivative control (PD terms) are applied. If the integral term remains, the restoring force will increase over time as the operator continues to maintain the speed of the robot.

4 Derivation of Operating Volume As mentioned above, the angle around the orthogonal axes of the ball is calculated on the MCU by using the angles of the omni-wheels from servo modules. Figure 6 shows a view of the ball from above and its coordinate system. This omni-wheel is defined as n = 0, 1, and 2 in counterclockwise order from the one located on the y-axis (Table 1).

Fig. 6. Coordinate system

Table 1. Definition of each parameter. Symbol

Meaning

Actual size

Rw

Omni-wheel radius

30.0 mm

Rt

Radius of sphere support circle

48.0 mm

Rb

Radius of sphere

67.5 mm

θn(i)

Omni-wheel at n angle for n = 0, 1, 2

ωn

Angular velocity of omni-wheel number n for n = 0, 1, 2

vn

Driving speed of omni-wheel number n for n = 0, 1, 2 (continued)

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T. Siriwattanalerd et al. Table 1. (continued)

Symbol

Meaning

Actual size

t

Sampling time

vx , vy

Relative velocity of omni-wheel robot

ωb

Relative angular velocity of omni-wheel robot

ωx , ωy , ωz

Angular velocity around each axis of the sphere

θx(i) , θx(i) , θx(i)

Angle around each axis of the sphere

Calculation of the orientation of the sports ball can be performed as the following equation. First, the angular velocity ωn of each omni-wheel is calculated by Eq. 1. ωn =

θn(i) − θn(i−1) t

(1)

Then, the driving speed of each omni-wheel can be expressed by Eq. 2. vn = ωn Rn

(2)

Next, Eq. 3 expresses the relationship between relative speed and relative angular velocity of the omni-directional mobile robot and the driving speed of wheels. ⎞⎛ ⎞ ⎛ ⎞ ⎛ 1 √0 −R v0 vx ⎟ ⎝ v1 ⎠ = ⎜ (3) ⎝ − 21 2√3 −R ⎠⎝ vy ⎠ 3 1 v2 ω b − − −R 2

2

Thus, Eq. 4 shows the relationship between relative speed and relative angular velocity of omni-directional moving robot from the driving speed of wheels. ⎞−1 ⎛ ⎞ ⎞ ⎛ 1 √0 −R vx v0 ⎟ ⎝ ⎠ 3 1 ⎝ vy ⎠ = ⎜ v1 ⎝ − 2 2√ −R ⎠ ωb v2 − 21 − 23 −R ⎛

(4)

From Eq. 4, we could find the angular velocity around each axis of the ball as Eq. 5. ωx =

vy vx , ωy = , ωz = ωb Rb Rb

(5)

After that, Eq. 6 can be calculated the angle around each axis of the ball as follows. θx(i) = θx(i−1) + ωx t θy(i) = θy(i−1) + ωy t θz(i) = θz(i−1) + ωz t

(6)

Thus, the rotation angle of the ball is obtained by the integrating components and proportional values used as the command of velocity vector and body angular velocity.

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5 Experiment 5.1 Basic Experiment for Restoring Force First, we conducted a basic experiment to confirm the measurement accuracy of the spherical pedal controller. The ball on the control device was rotated around the x, y, and z axes at an angle of approximately π/2 [rad] for 2 s. After the foot was removed from the sports ball, the ball will be returned to the origin by restoring force as the automobile’s accelerator or brake pedal which relocates automatically. 5.2 Evaluation of the Operability Next, we experimented to evaluate the operability of the spherical pedal. As mentioned above, this control system was developed to use with the boarding-type omni-directional mobile robot. Therefore, if we conducted experiments by using an actual robot, it would be a passenger-type robot which is exactly required the development of a large and expensive robot. Commonly, developing a robot to evaluate only this robot’s control system is not a good idea. Hence, we decided to develop a simulator of a boarding-type omni-directional mobile robot that runs on the personal computer (PC) then connect it to the actual spherical pedals model and build a system to control it. For the simulation software, we used the Open Dynamics Engine (ODE) which is a popular physics engine. After that, the simulation was written in C programming language.

Fig. 7. Construction of omni-directional mobile robot

Fig. 8. Simulation from the operator’s point of view

In the simulation (see Figs. 7 and 8), the operator’s viewpoint (the camera’s view on the simulation) was fixed at the top of the robot in order to reproduce a boarding-type robot. By doing that, we need to fix the position and orientation of the camera to the robot. Nevertheless, on ODE, the operator’s position and orientation are defined absolutely relate to the coordinate system. Accordingly, we solved this problem by obtaining the position and orientation of the robot during the simulation. For the orientation, the angle around the z-axis of the robot’s body coordinate system or the yaw angle is particularly important. If the camera direction is not adjusted to this angle, the direction of the pilot and the robot will be inconsistent. Equation 7 below is the rotation matrix of the robot

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around the z-axis which obtain from the simulation software. By using this result, the yaw angle can be calculated through Eq. 8. ⎛ ⎞ α −β 0 Rz = ⎝ β α 0 ⎠ (7) 0 0 1 θz = Atan2(β,α)

(8)

In order to evaluate the operability of the spherical pedals, we prepared the simulation environment by constructing the complex shape white line route on the plane as shown in Fig. 9. Afterwards the omni-directional mobile robot will be able to show its full capabilities in the experiment. The first experiment was conducted as a time trial around this route. In the second experiment, as Fig. 9, we set up many objects in four different colors around the route. The test subjects are ordered to count the number of objects of four specified colors while moving freely regardless of the route. After that, the time measuring until the test is done will be obtained. The test subjects were six students in their twenties aged. As a comparison of the operability evaluation, we also conducted two experiments. One is by using a generalpurpose controller with a pair of joysticks as shown in Fig. 10 and the other one is by using the spherical pedal. The time test was measured by using both types of controllers. First-round experiment, time was measured without training. After that, trainees took a few minutes of practicing, and then the second round of tests will be measured.

Fig. 9. Simulated course of experiment

Fig. 10. Appearance of joystick type controller

6 Results and Discussion 6.1 Results for Basic Experiment for Restoring Force The results of the basic experiment for restoring force are shown in Fig. 11. In each graph, the horizontal axis shows time, and the vertical axis shows the calculated rotational angles around each axis. The sampling time for the servo module control is performed in 1 [ms]. The sampling time to transmit and receive data by I2 C communication is 10 [ms]. As the results, the angle rapidly approached 0 after 2 s is the time to remove the foot from the pedal. By the restoring force, the ball will return to the origin after the operation

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is realized. The angles are also temporarily displaced for the other axes. In part of the maximum angle, a rotation of π/2 [rad] is added in each experiment but at this time the results vary from 0.8 to 2.5 [rad].

Fig. 11. Rotate 90° for forward, left and twist

6.2 Results for Evaluation of the Operability The results of the operability evaluation are shown in Figs. 12, 13, 14 and 15. Figures 12 and 14 show the individual results respectively of test subjects named from A to F and their variability for the time of experimental results, respectively. Furthermore, Figs. 13 and 15 show the results of the objects counting experiment, respectively. The experimental results of the time trial show that the spherical pedals are generally better than the general-purpose controller, this might indicate the effectiveness of the spherical pedal. From this experiment, we consider that the spherical pedal requires only one foot operation, while the general-purpose controller requires two joysticks to operate simultaneously. In addition, comparing the results of each controller from the first round and the second round after practicing. From 5 out of 6 test subjects or students, they can control the spherical pedal faster and after practicing with the spherical pedal they can do better results. Accordingly, the effectiveness of the spherical pedal controller can be considered to show in terms of habituation.

Fig. 12. Result of lap time trial

Fig. 13. Time to complete the counting task

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Fig. 14. Variation of lap time trial

Fig. 15. Variation of the counting task

On the point of the object counting experiment, it was found that the general-purpose controller was generally able to finish the task faster. In this experiment, the objects can be counted by observing the situation in all directions without moving. According to the specifications of the general-purpose controller use in this research, the movement of one joystick such as forward/backward and left/right indicates the velocity vector of the robot, and the left/right movement of the other joystick indicates the angular velocity around the robot’s body. For this reason, to realize the turning on spot capability of the spherical pedal with a simple movement of one joystick is possible and the experimental task can accomplish easily. Conversely, in the case of the spherical pedal, to perform turning on the spot is to rotate the ball around the z-axis, which is the only one operation and simply. However, the rotation around the x and y axes is done by moving the foot forward/backward or left/right, while the rotation around the z-axis requires the foot twisting. Mostly, this motion has a limitation for humans, and individual differences exist. As show on the spherical pedal’s first result in Fig. 15, there are apparently individual differences. In such a way, the terms of habituation after practice, the variation of the spherical pedals converged sufficiently, while the variation of the general-purpose controller became the same or larger. For the problem of the foot twisting, a larger gain is necessary to the body’s angular velocity which is related to the angle of rotation of the ball around the z-axis then turning the spherical pedal by the foot twisting is not much need.

7 Conclusion In this research, the boarding-type omni-directional mobile robot’s typical example of practical application can propose that a spherical pedal controller can control the robot by free hand. The spherical pedal operation’s ability was evaluated in experiments by using a simulation environment connected to the actual spherical pedal. The results showed that the spherical pedals performed as well as or might be better than the generalpurpose controller. Hence, we can show the utility of the spherical pedals by the freehand controlled ability compared to the general-purpose controller, which requires both hands to control the robot. In the future, we will need to devise a better way to deal with the problem of the twist of the foot that is necessary to give the amount of direction around the z-axis. From this point forward, we would like to develop an actual boarding type

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omni-directional mobile robot, apply the control system of the spherical pedal, and evaluate its operability.

References 1. Li, X., Zell, A.: Motion Control of an Omnidirectional Mobile Robot. In: Filipe, J., Cetto, J.A., Ferrier, J.L. (eds.) Informatics in Control, Automation and Robotics, Lecture Notes in Electrical Engineering Book Series, vol. 24. Springer, Heidelberg (2009). https://doi.org/10. 1007/978-3-540-85640-5_14 2. Qian, J., Zi, B., Wang, D., Ma, Y., Zhang, D.: The design and development of an omnidirectional mobile robot oriented to an intelligent manufacturing system. Sensors 17(9), 2073 (2017) 3. Ma, S., Ren, C., Ye, C.: An omnidirectional mobile robot: concept and analysis. In: 2012 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 920–925. IEEE, Guangzhou (2012) 4. Al Mamun, M.A., Nasir, M.T., Khayyat, A.: Embedded system for motion control of an omnidirectional mobile robot. IEEE Access 6, 6722–6739 (2018). https://doi.org/10.1109/ACCESS. 2018.2794441 5. Song, J.-B., Byun, K.-S.: Design and control of a four-wheeled omnidirectional mobile robot with steerable omnidirectional wheels. J. Robot. Syst. 21, 193–208 (2004). https://doi.org/10. 1002/rob.v21:4 6. Kumai, Y., Sugimoto, R., Muramatsu, S., Inagaki, K.: A servo module with DC motor for education and R&D in robotics. In: 2020 13th International Conference on Human System Interaction (HSI), pp.257–280 (2020). https://doi.org/10.1109/HSI49210.2020.9142683

Modelling of Pedestrians Crossing a Crosswalk and Robot Navigation Based on Its Characteristics Shunsuke Yamada1 , Daisuke Chugo1(B) , Satoshi Muramatsu2 , Sho Yokota3 , Jin-Hua She4 , and Hiroshi Hashimoto5 1 Kwansei Gakuin University, Hyogo, Japan

{s.yamada,chugo}@chugolab.com 2 Tokai University, Kanagawa, Japan 3 Toyo University, Saitama, Japan 4 Tokyo University of Technology, Tokyo, Japan 5 Advance Institute of Industrial Technology, Tokyo, Japan

Abstract. In this paper, we propose an autonomous mobile robot navigation system that considers pedestrian flow in a crosswalk. Recently, autonomous mobile robots have been introduced into the real world. Such a robot is required to move efficiently; however, it should avoid pedestrians and obstacles safely. On a normal sidewalk, if there is a risk of a collision with a pedestrian, the mobile robot can wait until this danger is gone. However, at crosswalks, there is a high risk of collision with pedestrians due to multiple pedestrians coming and going. There is a time constraint of having to cross while the signal is green. The conventional mobile robot navigation methods cannot be used in this situation. The pedestrians move in the direction of each other in response to their movements. This walking way enables a large number of people to pass through the crosswalk in a short period when the signal is green. Therefore, this study analyses the movement of pedestrians passing through the crosswalk in a group. We investigate a mechanism of generating pedestrian flow on a crosswalk. Furthermore, we propose a mobile robot navigation method that can avoid the risk of collisions with pedestrians and pass through crosswalks while the signal is green, using an algorithm to guide a mobile robot along the pedestrian flow that we investigated. Keywords: Pedestrian flow · Crosswalk · Robot navigation on crosswalk

1 Introduction Recently, there has been an increasing demand for robots worldwide [1]. In particular, the service robot market is projected to expand from 154 to 704.2 billion yen in 2015 and 2020, respectively [2]. Service robots support our daily lives with several tasks, such as mobility and security. A characteristic of service robots is that they automatically move in an environment where they can coexist with humans. Moving between pedestrians requires the ability to avoid obstacles and arrive at a destination. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 54–66, 2022. https://doi.org/10.1007/978-3-030-86294-7_6

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There are several studies aimed at the real-world application of autonomous mobile robots. The robotic navigation algorithms developed in these studies emphasise the task of avoiding obstacles, including pedestrians, and guide the robot to its destination only when safe pedestrian avoidance is possible. Therefore, when obstacles, including pedestrians, approach the robot vicinity, the robot often stops for safety [3–5]. While such robotic navigation algorithms perform effectively on sidewalks, navigation through crosswalks becomes a challenging task. This is because, on the cross-walk, the robot has to pass through the crosswalk in a short time while the signal is green, avoiding many pedestrians. The conventional robotic navigation algorithms may safely avoid collisions with pedestrians because the robot stops until pedestrians are gone, but the robot will not complete crosswalk passage while the signal is green. To solve these problems, several studies tried to guide the robot using pedestrian flow [6–9]. By using the pedestrian flow, the robot can move efficiently since it does not interfere with the movement of pedestrians and moves along the movement direction of a group of pedestrians. However, these studies require the robot to detect the pedestrian flow currently present, so the robot cannot travel with no pedestrian flow. Generally, many pedestrians wait for a signal at a pedestrian crossing (there is no pedestrian flow). When the signal turns green, pedestrians start moving simultaneously, and pedestrians whose paths intersect with each other naturally avoid each other; thereby, generating pedestrian flow. Therefore, the robot travelling in the crosswalk must predict the process of generating pedestrian flow in a crosswalk and anticipate pedestrian flow. Several attempts have been made to clarify the mechanism of generating pedestrian flow in crosswalks [10, 11]. In these studies, it is assumed that the gait flow can be observed from above, and the entire pedestrian flow is analysed and understood. However, the robot is unable to observe the walking current from above in real environment. Therefore, it is necessary to develop a technology for estimating the pedestrian flow on a crosswalk only with equipped sensors on the robot. This study proposes a robot navigation method that can estimate the walking flow on a pedestrian crossing using sensor information mounted on the robot, avoid collision with pedestrians and pass through the pedestrian crossing in time.

2 Pedestrian Model on a Crosswalk 2.1 Investigation of Walking Rules on Crosswalks To achieve robotic navigation on a pedestrian crossing, we analyse a pedestrian walking through a crosswalk (Fig. 1). When passing a crosswalk, the pedestrian maintains the direction of travel where he or she was initially walking, and then gently adjusts to the other pedestrians around him or her. Walking flow is generated by changing the path and avoiding collisions with other pedestrians. According to previous studies [10, 11], the process of generating pedestrian flow in crosswalks is explained as follows: (1) the generation of pedestrian groups (Figs. 1(b) and (c)), (2) the intersection of multiple pedestrian groups (at which point the pedestrian group forms a wedge shape, Fig. 1(d)) and (3) growth into a pedestrian flow (Fig. 1(e)). Based on the process of generating pedestrian flow, we observed the way pedestrians walk across a crosswalk. In the process of generating pedestrian flow in a crosswalk,

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pedestrians can be classified into two categories. The first category is a pedestrian who is at the head of pedestrian flow and is the leading edge of the wedge-shaped pedestrian group. The second is the neighbouring pedestrian that joins and moves with the pedestrian group (Fig. 2). These roles can be determined from the standby position at the start of the crossing (Fig. 1(a)). The leader pedestrian essentially takes on this role when there are no other pedestrians in front of him or her when waiting. The leader pedestrian recoganises the leader pedestrian on the opposite side of the crosswalk and avoids the leader pedestrian on the opposite side who is in the direction of his or her path. The follower pedestrian follows a neighbouring pedestrian in the forward direction. By merging with pedestrians in the same walking direction as themselves, they form a pedestrian group to avoid collision with oncoming pedestrians. The pedestrian flow occurs along the path of the leader pedestrian. From the above, the implicit movement rules for pedestrians crossing the crosswalk can be summarised as follows: • At the start of the crossing, if there is no other pedestrian in the same direction in front of you, you will be the leader pedestrian. However, if other pedestrians are crossing in the same direction, you will be the follower pedestrians. • The leader pedestrian finds the leader pedestrian in the group of pedestrians approaching from the opposite side and walks to the target direction, which avoids the leader pedestrians approaching. • The follower pedestrians avoid conflicting with oncoming pedestrians from the opposite side by approaching neighbouring pedestrians to generate pedestrian flow.

(a) People waiting for the signal. The person (b) Just before the light turned green, people (c) The leader pedestrian passed an oncoming pedestrian. The leader pedestrian surrounded by a coloured circle is the started to cross the street. has taken a path into space with fewer pedestrian who is the first in the pedestrian oncoming pedestrians. group when crossing.

(d) A pedestrian flow began to form. The pedestrian group was advancing in a wedge shape into space where there were few oncoming pedestrians.

(e) Pedestrian flow was complete. The pedestrians crossed the crosswalk without colliding with each other.

Fig. 1. Pedestrian flow generation process at crosswalks in front of Osaka Terminal, Japan. The signal is green for 45 s, while pedestrians must pass a crosswalk.

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2.2 Implementation of the Pedestrian Model Based on the pedestrian flow generation process found in the previous section, we propose an agent-based pedestrian flow simulation. Each agent, which shows each. pedestrian is assumed to be aware of its own surroundings. Considering the range of the pedestrian’s field of view, each agent determines the direction of travel based on its position with other agents within 180° in front of the agent.

(a) Leader pedestrian

(b) Follower pedestrian

Fig. 2. How to avoid oncoming pedestrians at the crosswalk.

Pedestrians who are crossing make a gradual change in the walking path according to the pedestrians around them. So, the agent’s moving velocity vector is expressed as (1) and Fig. 3. When there are no other agents within 3 m of its walking direction, the agent proceeds at its walking velocity. However, when there are other agents within 3 m in its walking direction, it adjusts its walking velocity according to the distance l close to another agent as in (2). ˙ − 1) + F P(t ˙ P(t) =  ·w P(t ˙ − 1) + F2  1.2ki m/sec (if l ≥ 3 m) w= 0.4ki l m/sec (if l ≺ 3 m)

(1)

(2)

where P˙ is the velocity vector of agents which shows a pedestrian moving. F is the path change vector, which varies with the position of the surrounding agents. w is the walking velocity of the agent. ki is a parameter describing the difference in walking velocity between people, and is given randomly to each agent with values of 0.8, 1.0, and 1.2. From investigated knowledge in the previous section, three rules are defined as the factors considered between agents: separation, alignment and merging. The path change vector F is determined by adding up the vectors calculated for each rule as (3). F = ks Fs + ka Fa + km Fm

(3)

where ks , ka , km are constants. Fs , Fa , Fm are defined as follows. • Separation vector Fs (Figs. 4(a) and (b)): The separation vector is a vector for avoiding collisions with nearby agents. The positional relationship with nearby agents is represented as a vector to prevent agents from colliding as (4). i the identification number

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of agents the identification number of agents (i = 1, · · · , n). Only agents within a radius of rso (for agents from the opposite direction) or rss (for agents with the same direction) in front of the agent are considered. Usually, rso is set to a larger value than rss . This is because people generally avoid a larger distance from pedestrians coming from the opposite direction than pedestrians walking in the same direction. Based on the observations of pedestrians walking in the crosswalk (Fig. 2), in this paper, we set rso = 7 m and rss = 3 m. Since the separation vector is only for avoiding collision with other agents in the left-right direction, the y-direction value of the separation vector is zero.  n T  xp − xpi ,0 (4) Fs = − li i=1

  • Alignment vector Fa (Fig. 4(c)): The alignment vector is set as in (5) to fit average P˙ i (the walking velocity and direction of the nearby agents) to move at a velocity that matches the pedestrian flow. Only other agents within a radius of ra (we set ra = 3 m) in front of the agent are considered. Furthermore, to coordinate a pedestrian flow with agents moving in the same direction, the alignment vector is obtained by using only other agents that travel within ±60° of the agent’s travel direction according to (6). n

Fa =

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(5)

n P·Pi ≥ if |P|·|P i| else

1 2

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• Merging vector Fm (Fig. 4(d)): To generate a pedestrian flow, the merging vector is set as in (7) to merge into nearby agents. The merging vector is defined as a vector from its position to the centre of gravity of the nearby agents’ positions. Only other agents within a radius of rm (we set rm = 3 m) in front of the agent are considered. To avoid merging into pedestrian flow of agents moving from the opposite direction, only agents that move in the same direction are considered by (8). n T     x   n kd xpi kd ypi  , i=1 (7) Fm =  ave  =  i=1  yave n n

P·Pi ≥0 1 if |P|·|P i| kd = (8) 0 else Since the way a pedestrian walks in a crosswalk differs according to the roles of the leader and follower pedestrians, a path change vector F is defined for each case. • A leader pedestrian: If there is no pedestrian in the same direction in his or her front, he or she will be the leader pedestrian. Therefore, if no other agent is moving in

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the same direction ahead of the agent within rl (we set rl = 3 m), (9) and (10) is satisfied. This agent is a leader pedestrian. Here, the merge into pedestrian flow is not necessary since no pedestrian is walking in the same direction in his or her front. Only the passing of the leader pedestrian on the other side of the crosswalk needs to be considered when deciding walking direction. There is enough time to pass an oncoming pedestrian because no pedestrian is walking in the same direction in his or her front. Thus, the leader agent only needs to avoid other oncoming agents, and the path change vector F is applied only to the separation vector Fs as (11).  yp = max kl yp1 , kl yp2 , · · · , kl ypn (9)



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• A follower pedestrian: If there are other agents ahead of the agent moving in the same direction within rl , (9) is not satisfied, and this agent is a follower pedestrian. Here, the agent must avoid oncoming agents and determine its position in relation to other agents in the same travel direction. It is necessary to measure its and nearby other agent’s position and merge into pedestrian flow. Therefore, the path change vector applies all separation, alignment and merging vectors as (12). ks = 1.2, ka = 0.6, km = 1.2

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Fig. 3. Relationship Fig. 4. Three path change vectors that determine the agent’s between velocity vector and moving rules. the path change vector.

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2.3 Computer Simulation The above methods were implemented in a computer simulation to confirm the occurrence of pedestrian flow. In this simulation, the size of the agent was set as a circle with a diameter of 0.46 m, referring to the shoulder width of an average Japanese adult male (JIS E 7104). The length and width of the crosswalk were 21 and 10 m, respectively. We set up 30 agents to start crossing immediately, with 13 agents on one side and 17 on the other. The initial positions of the agents were arranged in such a way as to create places with many agents and places with few agents, referring to the waiting positions of pedestrians (Fig. 2(a)). This is because pedestrians do not necessarily cross the sidewalk in the shortest path but tend to approach in the desired direction [11]. Figure 5 shows the simulation results. First, agents started moving to the opposite side (Fig. 5(a)). Second, agent groups arose (Fig. 5(b)) and changed their walking direction to an area with fewer agents on the other side (Fig. 5(c)). The agent groups then passed each other (Fig. 5(d)) and pedestrian flow occurred (Fig. 5(e)). The agent movement in the simulation has the same characteristics as the movement of a pedestrian in a real crosswalk (Fig. 2). Thus, we can confirm that the proposed pedestrian model on crosswalks is reasonable. 10[m]

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Fig. 5. Simulation results. Agents whose destinations are above are red, and agents whose destinations are below are blue.

3 Robotic Navigation Based on a Pedestrian Model 3.1 Overview of Our Proposed Navigation Scheme In this section, we incorporate the pedestrian model on crosswalks found in the previous section into robot’s navigation algorithm. Since robots cannot recognise and move in the same way as pedestrians, we develop a path determination algorithm suitable for specifying robots, such as the robot’s movement function and sensors. Here, the robot at the crosswalk should not block the passage of the pedestrians around it. Therefore, the following two points should be reflected in the robot navigation algorithm:

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1 The robot should not stop when crossing. Stopping while crossing the road leads to disruption in the walking flow. The robot should continue to move forward unless there is a risk of collision due to other pedestrian’s sudden jumping out in front of the robot or otherwise. For safety reasons, if the distance between the robot and an oncoming pedestrian present in the walking direction is less than 1 m, the robot will decelerate and stop. 2 The robot should avoid sudden path changes. A sudden path change while crossing the crosswalk will lead to a disturbance of the walking flow and cause a collision with pedestrians around the robot. In conventional path planning, the robot may move backwards. However, this must also be avoided since the robot must complete the crossing while the light is green. The robot, like the pedestrians, goes straight ahead and changes its course slowly according to the surrounding pedestrians. 3.2 Potential Based Robot Navigation Scheme The robot’s movement is based on the artificial potential method [12–14]. In the potential method, a potential function is defined based on destination and obstacle points. The motion direction of the robot is calculated using the gradient of the potential function. As a result, the robot can choose the appropriate travel direction that allows it to reach the destination without colliding with any obstacle (Fig. 6(a)) [15]. This method is a local search method and does not require complex environmental calculations. This is because the robot can change the planned path in response to the information received in real-time. The destination of a robot crossing a crosswalk is not a specific point, but a range (Fig. 6(b)). Since the purpose of a robot passing through a crosswalk is to finish crossing it, any place where the robot finishes crossing the crosswalk can be its destination. Therefore, this paper proposes the following destination-setting method for robot travelling in a crosswalk. A leader pedestrian: If there are no other pedestrians in the identification range, the robot becomes a leader pedestrian. Here, since there is enough distance between the robot and oncoming pedestrians before they pass each other, the robot avoids them to the position where they do not make contact with each other, just like real pedestrians. When there are no oncoming pedestrians, the robot aims to complete the crossing task in the shortest path.

Goal Area

Start Position

(a) Trajectory of the robot on potential method (b) Crosswalk Goal Fig. 6. Potential based Robot Navigation.

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At the start of the crosswalk, a tentative goal point is set on the opposite bank on the extension of the robot’s direction (Fig. 7(a)). Then, after the start of crossing, the robot avoids the oncoming pedestrians via the path change vector F (Fig. 7(b)). Fg is the attraction to the goal point due to the artificial potential field. F and Fg leads the robot to P˙ direction. After the robot moves, it is expected that there will be oncoming pedestrians between it and the original goal point. Since the robot needs to complete the crossing in time, the robot sets a new goal point on the opposite side of the crosswalk, which is the shortest path of the crossing (Fig. 7(c)). Pedestrians also avoid the robot, it is expected that sufficient avoidance has been completed by the time the robot passes all oncoming pedestrians, and the update of the target point converges. This procedure is repeated until the robot crosses completely. A follower pedestrian: If there are other pedestrians in the identification range rl , the robot becomes a follower pedestrian. Here, the robot follows a pedestrian moving in the same direction at the closest distance ahead. At the start of the crosswalk, a tentative goal point is set on the opposite bank on the extension of the robot’s direction (Fig. 8(a)). Then, after the start of crossing, the robot merges into a nearby pedestrian flow by the path change vector F (Fig. 8(b)). Fg is the attraction to the goal point due to the artificial potential field. The combination of F and Fg causes the robot to move in the P˙ direction. To complete the crossing task as quickly as possible, the robot follows the pedestrian at a walking velocity close to the max . First, the robot selects a pedestrian who is walking in robot’s maximum speed p˙ robot the same direction among the pedestrians in the identification range rl , i.e., a pedestrian who satisfies kl = 1 in (10), as a candidate for tracking. Next, the walking velocity of the candidate pedestrian is compared with the robot’s maximum speed. The pedestrian walking at the speed closest to the robot’s maximum speed is selected for tracking. This procedure is repeated until the robot finishes the crossing.

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Goal Point ( xrobot ( 0 ) , ygoal )

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4 Experiment 4.1 Computer Simulation To confirm the effectiveness of the proposed method, we conducted an experiment using a prototype robot. The prototype is a wheeled mobile robot with a length, width and height of 4.6, 0.6 and 0.82 m, respectively. It is equipped with a three-dimensional laser range sensor for pedestrian detection. In this experiment, the maximum speed of the prototype was set to 1.0 m/s. The length and width of the crosswalk were set to 7 and 10 m, respectively. The number of pedestrians was set to 12, 24 and 36, with half the pedestrians on each side of the crosswalk, and 10 trials were performed for each condition. Figure 9 shows the results when the robot is in the leader pedestrian mode. As shown in Fig. 9, the robot travels ahead of the pedestrian flow as a leader pedestrian, avoiding the oncoming other pedestrians. Figure 10 shows the result when the robot is in the follower pedestrian mode. As shown in Fig. 10, the robot sets a goal point for pedestrian to be tracked and travels to join the pedestrian flow. Figure 11(a) shows that the time required for crossing is shorter using the proposed method than the previous method. Figure 11(b) shows that the number of times that the robot abnormally approached within 0.5 m of other pedestrians is lower using the proposed method than the previous method. Additionally, Fig. 11 shows that the proposed method is effective, particularly when there are more people in the crosswalk. From these results, we can confirm the effectiveness of the proposed method. 10[m] Goal Point

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Fig. 9. Simulation results in the case of the leader mode. The robot is yellow. Pedestrians whose destinations are above are red, and pedestrians whose destinations are below are blue.

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The robot set Goal Point on this pedestrian.

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4.2 Experiment with Our Prototype To confirm the effectiveness of the proposed method, we conducted an experiment using a prototype robot. The prototype is a wheeled mobile robot with a length, width and height of 4.6, 0.6 and 0.82 m, respectively. It is equipped with a three-dimensional laser range sensor for pedestrian detection. In this experiment, the maximum speed of the prototype was set to 1.0 m/s. In this experiment, an area of 5 m width and 7 m length is assumed to be a cross-walk, and five subjects from each side cross the crosswalk. To verify the robot’s behaviour in different roles, two modes were conducted: the leader pedestrian and follower pedestrian modes. Figure 12 shows the experimental results. In the leader pedestrian mode (Fig. 12(a)), the robot travelled on a trajectory to avoid the oncoming pedestrian as the leading pedestrian for 4 s after the start. After that, other pedestrians moving in the same direction preceded the robot. Thus, the robot switched to the follower pedestrian mode and completed the passage through the crosswalk by following the two pedestrians while switching between them. In the follower pedestrian mode (Fig. 12(b)), a pedestrian in front of the robot was targeted for following immediately after the start of the walk, and the robot passed through the crosswalk without any change. In both cases, the robot did not interfere with the path of other pedestrians. These results confirmed the effectiveness of the proposed method.

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5 Conclusion This study analyses the pedestrian movement on the crosswalk in a group and investigates a mechanism for generating pedestrian flow on the crosswalk. We propose a robot navigation method that can avoid the risk of colliding with pedestrians and pass through crosswalks while the signal is green, using an algorithm to guide a robot along the pedestrian flow that we investigated. In simulation and experiments with our robot implementing the proposed method, the robot completed the crossing in a shorter time, even at busy pedestrian crossings. Our prototype robot was able to move with the pedestrian flow on a crosswalk appropriately using only the sensor information equipped on it.

References 1. 2. 3. 4. 5. 6. 7. 8.

9.

NEDO. http://www.meti.go.jp/english/press/data/20100423_01.html Robot Business. http://www.projectdesign.jp/201501/robotbiz/001839.php Xiang, J., Tazaki, Y., Suzuki, T.: IEEJ Trans. Electron. Inf. Syst. 132, 1 (2012) Iwata, K., et al.: Real time mobile robot control with a multiresolution map representation. In: Inst. of Elec. Engineers Ind. Measurement and Control Workshop, IIC-06–21(2006) Van den Berg, J., Overmars, M.: Int. J. Robot. Res. 24 (2005) Kumahara, W., et al.: J. Soc. Instrum. Control Eng. 50, 1 (2014) Takayanagi H., et al.: J. Archit. Plan. 66, 185 (2001) Yuqing, D., et al.: Group surfing: a pedestrian-based approach to sidewalk robot navigation. In: Proceedings of the of 2019 International Conference on Robotics and Automation, vol. 6518 (2019) Tamura, Y., et al.: Smooth collision avoidance in human-robot coexisting environment. In: Proceedings of the of 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3887(2010)

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10. Zhang, X., et al.: J. Jpn. Soc. Civil Eng. (D3) 70, 1031 (2014) 11. Asano, I., et al.: Analysis of pedestrian speed change behavior at signalized crosswalks. In: Proceedings of 2015 Road Safety and Simulation International Conference, Orlando, USA (2015) 12. Balch, T., Hybinette, M.: Social potentials for scalable multi-robot formations. In: Proceedings of 2000 IEEE International Conference on Robotics and Automation, vol. 73 (2000) 13. Satou, K.: J. Robot. Soc. Jpn. 11, 702 (1993) 14. Suzuki, T., et al.: Autonomy control based on potential method for two-wheel mobile robot. In: Proceedings of the 224th SICE Workshop, No. 224–6 (2005) 15. Akiyoshi, K., et al.: Autonomous mobile robot navigation considering the pedestrian flow intersections. In: Proceedings of the 2020 IEEE/SICE International Symposium on System Integration, vol. 428 (2020) 16. Nishino, N., et al.: Robot navigation according to the characteristics of pedestrian flow. In: Proceedings of the 42nd Annual Conference of the IEEE Industrial Electronics Society, vol. 5947 (2016)

Section–3: Innovative Actuators and Power Supplies

A Compliant Leg Structure for Terrestrial and Aquatic Walking Robots Peter Billeschou1(B) , Cao D. Do1 , Jørgen C. Larsen1 , and Poramate Manoonpong1,2(B) 1

2

University of Southern Denmark, SDU Biorobotics, Odense 5230, Denmark {pebil,cdd,jcla,poma}@mmmi.sdu.dk Vidyasirimedhi Institute of Science and Technology, School of Information Science and Technology, Rayong 21210, Thailand https://www.sdu.dk/en/forskning/sdu biorobotics

Abstract. The legs and transmissions of walking robots need to fulfill dynamic and load-bearing movements while also enabling more applications by being resistant to challenging outdoor- and aquatic environments. Furthermore, the physical behaviour of the robot legs needs to be predictable throughout their service life to enable torque-dependent control. Therefore, weathering and wear of leg components must not alter the movement resistance in order to avoid frequent maintenance. Hence, we present a new leg design that obtains low inertia and fluid resistance by using four-bar linkages with compliant mechanisms of either stainless spring steel or super-elastic nickel-titanium. The leg mechanisms were tested to formulise their torque behaviour, axial deflections, and fatigue life in saltwater (≈12% salinity). Conventional sealed stainless steel ball bearings were also tested to provide data references. Our experiments show that nickel-titanium outperform stainless spring steel with more predictable behaviour, less resistance, and longer fatigue life. Keywords: Legged robots · Durability · Bio-inspired · Compliant mechanism · Cross-axial flexural pivot · Underwater robotics

1

Introduction

Legged robots are prospected to fulfill applications where wheeled- and flying robots are unsuitable. Legged robots enable greater payload with a lower costof-transport than flying robots while potentially surpassing wheeled robots with the ability to traverse challenging outdoor terrains and tight multi-planar indoor corridors in limited time without significant trade-offs [1]. Current applications particular suited for legged robots include: 1) Rescue and emergency management - Locating people and scouting dangerous areas inside buildings in the aftermath of disasters such as fires, earthquakes, or floods. 2) Delivery - Assisting personnel by carrying tools, first aid equipment, or materials to sites which are difficult to reach. 3) Industrial site inspections - Continuously assessing safety by c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 69–80, 2022. https://doi.org/10.1007/978-3-030-86294-7_7

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measuring parameters such as temperature, gas, and radioactivity in industrial facilities such as refineries and power plants. 4) Exploration - Scouting difficult to reach areas on the Earth such as seafloors, or celestial objects and bodies like Mars and the Moon. 5) Security - Surveying areas and properties. However, legged robots are often hindered from fulfilling such applications due to the functional limitations of hardware and control [2,3]. The mechanical structure and transmission of legged robots risk being affected or even damaged by the high levels of particulates and fluids present in the application environments. Particulates can minimise the field vision of sensors, blind encoders, short-circuit electronics, increase the frictional resistance of bearings, obstruct gear transmission, and compromise protective surfaces. Fluids are even more ingressive, especially with high underwater pressure, and may carry particulates into the robot. This can result in the previously mentioned effects as well as corrosive damage. Hence, legged robots without sufficient protection are limited from operating in terrestrial, aquatic, and manmade environments with open fields, deserts, rivers, rain, humidity, and oceans [3]. ANYmal is one of very few legged robots that has sufficient protection (IP67 and ATEX certified) to operate in such environments [3]. Consequently, other legged robots are limited to dry indoor areas, thereby losing their advantage over other mobile robots. Therefore, while improvements in durability and stability have been made through advances in robot morphologies [4,5], robot controllers [6,7], and actuator impedance controllers [8,9], this paper then focuses on increasing robotic durability and resistance to challenging environments by improving the leg structure, transmission and joint mechanisms. A great variety of transmissions are used in legged robots, such as timing belts [10], and four-bar parallelogram mechanisms [11], since they have certain advantages such as low backlash, linear behaviour, and low mass. However, such transmissions have been found to limit the robot’s dynamics and task completion in difficult environments. Hence, we present a robot leg design that obtains high environmental resistance and durability by, similar to other durable legged robots [3,11], sealing the electromechanical parts and using corrosive resistant materials, but in addition also replacing sealed and sensitive components from the exposed extremities, such as bearings, with frictionless compliant mechanisms made from corrosive resistant and super-elastic materials (Fig. 1-b). Furthermore, we show that the leg design has linear, predictable behaviour and slight off-axis deflection, enabling it to be implemented in robot models and impedance controllers. The following section presents the entire leg design. Meanwhile, the analysis only investigates the mechanical leg (Fig. 1-b red area), since the remaining components, such as the controllers 04 [9] and foot sensors 10 [12], have already been evaluated in other studies, or are standard industrial components like the lip seals 05 .

2

A Low-Cost, Lightweight, and Compliant Leg Structure for Terrestrial and Aquatic Walking Robots

The leg structure has three degrees-of-freedom (DOF), actuated by brushless DC (BLDC) motors with integrated speed reducers (Fig. 1-b). The leg mass is

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accumulated proximally to lower its movement inertia, which is reduced further by balancing the rotating mass around the joint axes and the absence of bearings in knee transmission. Furthermore, aluminium 6061-T6 (2.72 g/cm3 ) is used to lower the mass and provide corrosive resistance to structures such as the motor housings 01 02 03 , gaskets 05 , flanges 06 , and distal leg components like the femur 07 , tibia 08 and foot 11 (Fig. 1-b). The leg is fully submersible in fluids, since lip seals protect the motor electronics while compliant mechanisms replace sensitive joint components such as bearings. This makes the leg structure suitable for terrestrial and aquatic four- and six-legged robots. 2.1

Improving Dynamics and Impact Mitigation Capability

Walking robots experience ground reaction forces for every step, jump, or fall, which accumulate to a high number of impacts and fatigue throughout their service life. This makes it necessary to implement impact mitigation strategies to protect vulnerable components, such as gears and electronics. Compliant rubber dampeners on the feet 11 can help absorb small impacts while also improving traction. Implementing virtual compliance through impedance controlled motors [9] can

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mitigate larger impacts and oscillations. Large gap radius BLDC motors [8] are a suitable match for impedance controllers with high bandwidth [9]. Impedance controlled BLDC motors with 9:1 speed reducers, called quasidirect drives [10], are used in multiple-legged robots like the Mini Cheetah [10] and Aliengo by Unitree. Their speed and torque enable virtual compliance for impact mitigation and dynamic leg movements such as jumping and running. Ready-available quasi-direct drives (9:1), like the AK80-9 from T-Motor 01 02 03 (Fig. 1-b), were chosen as actuation for the leg. These were combined with an in-house developed third-generation motor controller 04 [9]. The drive for DOF1 01 was positioned as the base of the leg with its mass attached to the robot, thereby lowering inertia by avoiding adding its own mass to leg movements. Meanwhile, the drives for the DOF2 and DOF3 were mounted onto the moving leg structure, thereby actuating movement inertia. However, the actuation inertia of the DOF1 drives was minimised by 1) positioning the DOF2 and DOF3 drives as proximal as possible, and 2) developing the robot leg so that its centre of mass is directly on the rotary axis of the DOF1 drive. The actuation inertia of DOF2 drive was lowered by aligning the DOF3 drive’s centre of mass with the rotary axis of DOF2. The DOF2 and DOF3 drives are positioned back-to-back to link their controllers, but the DOF2 drive can also be placed front-to-back, so it does not need to rotate in its own mass. Moving the DOF3 drive from the knee to the hip significantly lowered the actuation inertia of the DOF1 and DOF2 drives, enabling faster leg movement. Subsequently, this made it necessary to implement a transmission mechanism to transfer the rotation from the DOF3 drive to the distal knee joint. 2.2

Environmental Resistant Joint Mechanisms

We have implemented a parallelogram mechanism in the leg for transmission (Fig. 1-b) to increase the feasibility and structural strength. However, while bearings or bushings are often used as joints in parallelogram mechanisms to lower friction and increase rigidity, they then also require additional protection and maintenance. Bearings constructed of stainless steel or ceramics with an integrated seal can limit corrosion. However, it is common to apply additional lip seals to further minimise the entry of contaminants. Therefore, we propose combining the parallelogram mechanism with compliant joint mechanisms made from corrosion-resistant alloys, which are frictionless and require no lubrication [13]. A large variety of designs for compliant mechanisms can be implemented into the parallelogram, such as a circular flexure hinge, cross-axial flexural pivot, butterfly pivot, or a split-tube [14]. Each compliant mechanism provides a different range of motion and deflection, resistance, volume, and methods of manufacture. For example, a circular flexure hinge has great off-axis stiffness that limits rotation in undesired directions, however it also has very limited motion range and high angular resistance [14]. The cross-axial flexural pivot (flexures) was found to be the most suitable compliant mechanism due to its large angular range (Fig. 2-a) and off-axis stiffness that prevents undesired deflections in other directions than its rotational axis. Furthermore, flexures are compatible with multiple manufacturing techniques such as

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Fig. 2. Movement range of the joints utilizing (a) cross-axial flexures and (b) bearings. A motor rotates one of two parallel femur segments, which are jointed with the tibia segment. The second femur segment is also jointed to the static base frame to enable a parallelogram movement of ±60o .

CNC milling and laser cutting, which lowers production cost and makes it possible to use materials like carbon fibre, stainless steel, and nickel-titanium alloys. Compliant mechanisms typically function as springs, where the exerted torque can be calculated with Hooke’s law for torsion springs: τ = −κ · θ

(1)

where τ is the torque generated by the compliant mechanisms in newton-meters, θ is the angle of rotation from the equilibrium position in radians and κ is the torsion coefficient in newton-meters per radian. Since the parallelogram structure has three flexures, κ can be defined as the sum of these springs. A modular parallelogram type leg structure was developed to analyse the joints using either flexures or bearings. The femur and tibia were dimensioned according to the bioinspired dung beetle morphology, like the robot ALPHA [5], with 180 mm between the hip and knee joints and 180 mm between the knee and end-effector (Fig. 2). The parallelogram enabled an angular range of ±60o before the femur segments collided with the joint structures. The threaded joint flanges (Fig. 1-b) of the leg segments facilitated attachment of either the flexures (Fig. 2-a), or a housing and shaft to hold the bearings (Fig. 2-b). 2.3

Analysing Leg Behaviour and Operational Life

The leg design was analysed to define its mechanical behaviour and compliant mechanism compatibility with the robot features, such as proprioceptive control, and the ability to function in challenging terrain. A bench test (Fig. 3) was constructed to test and determine the joints: 1) angular torque resistance, 2) torque linearity, 3) resistance to wet environments, and 4) operational life. The bench test uses a Dynamixel XM540-W270-T motor A (Fig. 3) to actuate and control the tested robot leg E . The motor utilises absolute position sensors for accurate position control and provides other sensor outputs, such as current sensing (Fig. 4-b). An HBM T22 torque sensor B links the motor output shaft with the robot leg and measures the torque resistance of the robot leg during the motor rotations. A housing with two bearings and a lip seal C aligns the output axis and seals the electronics from fluids in the saltwater

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A B C E E D Fig. 3. The accelerated ageing test chamber and components: A geared Dynamixel XM540-W270-T motor with internal current sensor, B HBM T22 torque sensor, C housing for shaft bearings and lip seals, D saltwater (≈12%), and E a interchangeable leg structure. The chamber enables saltwater submersion.

chamber D . The rotary shaft is angled vertically to avoid gravitational influence on the measurements, particularly the outer angles of the leg. For example, trials with horizontal actuation experienced additional torque caused by an moment increase, as the leg’s mass was rotated outwards (Fig. 2 and 4). An experiment was conducted to measure the linearity, hysteresis, and torque behaviour of cross-axis flexures of stainless spring steel and nickel-titanium alloy (Fig. 4). The torque resistance of stainless steel bearings was also measured as reference. The experiment investigated the initial behaviour (Fig. 4) prior to any mechanical work (Fig. 6) and the water chamber was therefore kept empty during the experiment. The leg performed 15 cycles of ±60o oscillating motion. The movement speed was lowered to 6.67o /seconds to increase the measuring resolution and counter inertia. Subsequently, a set of fatigue tests was performed to investigate the reaction of the mechanisms to repetitive work and fatigue-induced fractures. Furthermore, the water chamber was filled with a ≈12% saltwater solution during the test to observe the reaction of the mechanisms to challenging and aquatic environments. The saline level of the water was 3.5 times higher than ocean water to accelerate any potential oxidising and corrosive reactions. In addition, the chamber contained 0.3% detergent to accelerate the deterioration of mechanical lubrication, which may further accelerate wear. Finally, an experiment was performed to investigate the deflection of flexures along the X, Y, and Z axes (Fig. 5), since the compliance of the flexures will result in deflection besides its rotational axis. For example, forces in the X, Y, and Z direction to the end-effectors during gait will induce elastic deflection (Fig. 5). Therefore, a set of nickel-titanium flexures were mounted onto the leg, which were then loaded in the X, Y, and Z direction. The test proceeded by 1) locking the motor axis in the equilibrium position, 2) aligning either the X, Y, or Z-axis of the end-effector with the gravity vector, 3) applying payload to the end-effector, and 4) measuring the deflection. The end-effector were loaded up to 6.5 kg in increments of 0.5 kg.

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3 3.1

Results Angular Joint Torque and Resistance

The experiments involving the joint components showed large differences in torque behaviour, where the bearings had low constant resistance, while the flexures of nickel-titanium exhibited linear behaviour according to the angle (Fig. 4-a). The ability of the flexures to store energy was also proven (Fig. 4-b), with a higher motor current being exerted when rotating outwards and loading the springs, while the motor exerted 50% less current when returning to the zero position as the springs released the stored energy. The linearity of the torque exerted by the nickel-titanium during rotation makes it possible to calculate the joint torque during leg movements. This means it is a suitable joint mechanism for torque-controlled actuators, since the torque can be 1) calculated and 2) subtracted for any position, making it possible to calculate the ground reaction force. The torsion coefficient (κ) for the nickeltitanium flexures is derived from Fig. 4-a, with different coefficients for flexion and extension (Table 1). Table 1. κ ranges for flexing or extending the leg with cross-axis flexures of either nickel-titanium or stainless steel. κf lex Nickel-titanium flexure [4.18; 4.58] Stainless steel flexure [5.65; 8.94]

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Meanwhile, the stainless steel flexures showed non-linear behaviour in the angular range (±60o ), since the equilibrium position is changed with every rotation due to permanent plastic deformation (Fig. 4), resulting in a hysteresis with larger κ ranges and torque values. Furthermore, the torque output of the stainless steel flexures becomes challenging to estimate since the equilibrium position changes continuously. This makes the stainless steel flexures unsuitable for use in walking robots utilising torque control.

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Axial Deflections

One set of super-elastic nickel-titanium flexures was tested by loading the endeffector with 6.5 kg in increments of 0.5 kg. The deflection tests showed minimal deflection at the maximum payload for the Y (3.5 mm) and Z-axis (2 mm) (Fig. 5). As such, the Y-axis deflects with 0.05 mm/N, and the Zaxis deflects with 0.03 mm/N. Meanwhile, larger deflections were observed for the X-axis. The deflections increase 0.78 mm/N until a payload of 45 N, at which point the deflections rate started to increase at a faster rate of 1.22 mm/N. Accelerated Ageing

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Discussion

The parallelogram was proven to be advantageous due to its smooth operation, zero backlash, and small deflections. Far larger deflections were observed in other prototype legs that only had one femur segment, since the second segment no longer stiffened the structure. This subsequently excluded cable and belt transmissions. The remaining level of deflection along the X-axis (Fig. 5) can provide compliance and mitigate lateral impacts from hitting undetected obstacles or steps during gait. In addition, the flexures provided resistances opposite to torques generated by ground reaction force (Fig. 4-a), and can be used to lower the energy consumption of a robot while standing upright (Fig. 4-b). Hence, robots utilising bearings need to constantly use motor power to remain in a standing position, while the flexures’ equilibrium can be angled to provide a standing resting position. Furthermore, the energy stored from rotating the flexures during stance phases can be released as the robot leg pushes off the ground. Accordingly, the flexures can provide energy saving during the robot stance phase and additional torque during leg push-off. Though, further investigation is required to quantify its effects on the robot’s cost of transport. The linear and elastic torque behavior of the nickel-titanium flexures resulted in lower κ values and ranges of ±0.11 Nm/rad (Table 1). Meanwhile, the stainless steel flexures experienced higher κ values and plastic deformation that altered the equilibrium for every movement, resulting in a dramatically increased κ ranges of ±1.65 Nm/rad. Accordingly, stainless steel flexures’ non-linear torque behaviour and large hysteresis make them unpredictable in dynamic applications, and thereby unsuitable for legged robots utilising torque control [9]. For example, at a 12o extension the stainless steel flexures can generate a torque resistance between 0.0 and 2.0 Nm, which makes it problematic for proprioceptive actuators to estimate the actual ground reaction force and perform the adaptations required to maintain a desired motion. The torque values of the accelerated ageing experiments (Sect. 3.3) differs from the initial investigation (Sect. 3.1), due to factors such as angular speed and fluid resistance. Table 2. Specifications of joint mechanism (a) sealed ball bearings, (b) stainless steel spring, and (c) super-elastic Ti-Ni cross-axial flexures. *Estimated (a) Bearing (b) Steel Flexion torque Extension torque Footprint Mass exc. housing Mass inc. housing Additional % mass to robot leg Additional % mass to drone arm X deflection Y deflection Z deflection Operational life (cycles) Production cost IP classification

0.13 Nm 0.13 Nm 31.5 cm2 31 g 115 g 15.3% 110.6% N/A N/A N/A >30,000 e 46.00 IP68*

m [5.65; 8.94] N rad m [3.28; 5.04] N rad 27.9 cm2 7 g (22.6%) 27 g (23.5%) 3.6% 26.0% N/A N/A N/A 1,000 e 192.60 IP68*

(c) Ni-ti m [4.18; 4.58] N rad m [2.24; 2.46] N rad 27.9 cm2 6 g (19.4%) 26 g (22.6%) 3.4% 25.0% 0.78 mm N * 0.05 mm N 0.03 mm N 1,200 e 40.40 IP68*

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The stainless steel flexures seemingly have a lower service life of 1,000 cycles instead of the 1,200 cycles provided by nickel-titanium (Fig. 6). A larger sample size is needed to confirm the average service life of the materials. However, the service life of nickel-titanium is lower than anticipated. Furthermore, more significant wear induced resistance in the bearings was initially anticipated (Fig. 6). As such, the flexures could prove advantageous with a greater service life in wet and corrosive environments due to their corrosion resistance, lack of friction, with no need for lubrication. However, the sealed stainless steel bearings were proven to have great environmental resistance, thereby ensuring low movement resistance with minimal change after 30,000 cycles. Indefinite service life can only be obtained when limiting the rotation range of the flexures to lower angles [15], such as ±5o . Although limiting the angular movement range can increase service life, as a consequence, it also lowers the movement range of the leg. Meanwhile, increasing the rotary range while maintaining an indefinite service life is possible with a compound compliant mechanism, which arranges multiple cross-axial flexures in series to increase the overall range while limiting deformation of the metal sheets [15,16]. A series of flexures further risks increasing deflection along the X-axis, but this can be countered by utilising compound joints with a parallel series of flexures [16]. Also, different flexure materials may also provide additional services life, such as carbon fiber composites. Moreover, guards around the compliant joints can be implemented to prevent the insertion of large objects and limit deflections from being too large along the X-axis. Hence, further investigation of compliant joint designs are materials are needed to extend the service life. The lower service life of the current single flexures at the maximum angular range (±60o ) makes them unsuitable for walking robot applications requiring low maintenance. Single flexures should be considered in applications where: 1) low-cost, a lightweight structure, and compliance are K crucial, and 2) the frequency of large range rotations is low, or maintenance is frequent. This includes walking robots that need a higher payload, M and environmental resistance N in disaster relief and emerL gency management, or suffiO ciently lightweight for climbP ing and inspecting industrial Q structures. Furthermore, the compliant structure can be applied Fig. 7. K Drone with L manipulator arm made of as an arm L to flying drones carbon fiber and plastic, and M a drive unit with K (Fig. 7) for object grasping N two geared motors, O worm drives and P a conQ , docking onto structures, troller PCB that is used to position the Q endeffector.

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drilling, and similar. The weight of the arm, excluding the joint components of the parallelogram is 208 g, increasing to 260 g (additional 25.0%) when using flexures or 438 g (additional 110.6%) when using bearings (Table 2). Hence, the joint components take up a large portion of the arm mass when the remaining components are made of lightweight materials such as carbon fiber and plastic. Geared motors O actuate the arm, while the worm drives P change the axis of rotation with ninety degrees and has self-locking properties that can prevent the flexures from back driving the arm position. Accordingly, the worm drives can lower power consumption, since it is not necessary for the motors to be active to work against the flexure torque to keep the arm in position. However, this will limit the usage of proprioceptive motor torque feedback.

5

Conclusion

The compliant leg structure, utilising cross-axial flexural pivots, has been proven to have great stiffness and compliance, as well as mechanical advantages in volume and mass. Furthermore, constructing the compliant joint mechanism in nickel-titanium instead of stainless steel provided lower torque resistance, greater elasticity, and more linear mechanical behaviour. This makes the compliant leg structure suitable for legged robots, since its mechanical behaviour can be implemented into torque controllers. However, according to the fatigue test, the compliant joint structure had a relatively low service life of 1,200 work cycles when the mechanisms were overexerted to their full angular range (±60o ). Future studies will further investigate designs and materials that can improve the service life of the compliant mechanisms, such as compound compliant mechanisms and carbon reinforced plastics. Furthermore, future studies will also investigate drone applications that can utilise the proposed compliant structure as lightweight and controllable robot arms for flying drones. Acknowledgement. The authors would like to thank Mathias Neerup for his support in developing the software to control the bench test and experiments. This work is supported by the Human Frontier Science Program under grant agreement no. RGP0002/2017.

References 1. Rubio, F., Valero, F., Llopis-Albert, C.: A review of mobile robots: concepts, methods, theoretical framework, and applications. Int. J. Adv. Robot. Syst. 16(2) (2019) 2. Kenneally, G., De, A., Koditschek, D.E.: Design principles for a family of directdrive legged robots. IEEE Robot. Autom. Lett. 1(2), 900–907 (2016) 3. Hutter, M., et al.: ANYmal-toward legged robots for harsh environments. Adv. Robot. 31(17), 918–931 (2017) 4. Roennau, A., Heppner, G., Pfotzer, L., Dillmann, R.: Lauron V: Optimized leg configuration for the design of a bio-inspired walking robot. In: Nature-Inspired Mobile Robotics, pp. 563–570 (2013). https://www.worldscientific.com/doi/abs/ 10.1142/9789814525534 0071

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5. Billeschou, P., Bijma, N.N., Larsen, L.B., Gorb, S.N., Larsen, J.C., Manoonpong, P.: Framework for developing bio-inspired morphologies for walking robots. Appl. Sci. (Switzerland), 10(19), 1–20 (2020). https://www.mdpi.com/2076-3417/10/ 19/6986 6. Leung, B., Thor, M., Manoonpong, P.: Modular neural control for bio-inspired walking and ball rolling of a dung beetle-like robot. In: Artificial Life Conference Proceedings, vol. 30, pp. 335–342, July 2018. https://www.mitpressjournals.org/ doi/abs/10.1162/isal a 00064 7. Pitchai, M., et al.: CPG driven RBF network control with reinforcement learning for gait optimization of a dung beetle-like robot. In: Artificial Neural Networks and Machine Learning - ICANN 2019, pp. 698–710. Springer, Cham (2019). http://link. springer.com/10.1007/978-3-030-30487-4 53 8. Wensing, P.M., Wang, A., Seok, S., Otten, D., Lang, J., Kim, S.: Proprioceptive actuator design in the MIT cheetah: Impact mitigation and high-bandwidth physical interaction for dynamic legged robots. IEEE Trans. Robot. 33(3), 509–522 (2017) 9. Lund, S.H.J., Billeschou, P., Larsen, L.B.: High-bandwidth active impedance control of the proprioceptive actuator design in dynamic compliant robotics. Actuators 8(4) (2019). https://www.mdpi.com/2076-0825/8/4/71 10. Katz, B., Carlo, J.D., Kim, S.: Mini Cheetah: A platform for pushing the limits of dynamic quadruped control. In: 2019 International Conference on Robotics and Automation (ICRA), pp. 6295–6301. IEEE (2019) 11. Hubicki, C.: ATRIAS: design and validation of a tether-free 3D-capable springmass bipedal robot. Int. J. Robot. Res. 35(12), 1497–1521 (2016). https://doi. org/10.1177/0278364916648388 12. Billeschou, P., Albertsen, C., Larsen, J.C., Manoonpong, P.: A low-cost, compact, sealed, three-axis force/torque sensor for walking robots. IEEE Sens. J. (2021) 13. Howell, L.L.: Compliant mechanisms. In: McCarthy, J. (eds.) 21st Century kinematics, pp. 189–216. Springer, London (2013). https://doi.org/10.1007/978-14471-4510-3 7 14. Farhadi, D.M., Tolou, N., Herder, J.L.: A review on compliant joints and rigidbody constant velocity universal joints toward the design of compliant homokinetic couplings. J. Mech. Des. 137(3), 032301 (2015) 15. Liu, L., Bi, S., Yang, Q., Wang, Y.: Design and experiment of generalized triplecross-spring flexure pivots applied to the ultra-precision instruments. Rev. Sci. Instr. 85(10), 105102 (2014) 16. Merriam, E.G., Lund, J.M., Howell, L.L.: Compound joints: Behavior and benefits of flexure arrays. Precis. Eng. 45, 79–89 (2016)

Design and Modelling of a Modular Robotic Joint Marco Rocha1(B) , Vitor H. Pinto1,2 , Jos´e Lima2,3 , and Paulo Costa1,2 1

Faculty of Engineering, University of Porto, Porto, Portugal [email protected], {vitorpinto,paco}@fe.up.pt 2 INESC TEC–Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal 3 Research Centre in Digitalization and Intelligent Robotics, CeDRI, Polytechnic Institute of Bragan¸ca, Bragan¸ca, Portugal [email protected]

Abstract. The industry tends to increasingly automate as many processes as possible, and to make this possible, they often resort to the use of robotic arms. This paper presents the development of a proposal for a modular joint for robotic arms that allows: to obtain the best possible torque/weight ratio; to be controlled in speed and/or position; to communicate with other joints and external microcontrollers; to keep the cost as low as possible; and to be easily reconfigurable. The proposed prototype was validated with real results.

Keywords: Manipulator

1

· Modular joint · Gearbox · Error control

Introduction

As the variety of processes to be automated in the industry represents a wide range of options, robotic arms must be as flexible as possible in terms of their configuration. Consequently, the modular joints allow to easily configure a robotic arm with the desired characteristics for a given process. In other words, as many joints as the number of degrees of freedom desired can be used, and links between the joints can be placed in order to constitute the manipulator. Modular joints, as they are intended to have the most flexibility performing tasks, they have to bring together a set of characteristics that allow them to perform at the level of traditional robotic manipulators. However, these joints usually have associated characteristics such as low torque/weight ratio, high backlash and cost, which represent the opposite characteristics to the intended ones. That is, if the joint has to produce more torque, the motor can be replaced by one with more power, or the gearbox can be modified for a higher speed reduction. However, a more powerful motor implies an increase in cost and weight, and a gearbox with a bigger reduction implies an increase in backlash. If backlash reduction is desired, one of two approaches is usually chosen: design and production of gears according to more precise techniques; or it is c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 81–92, 2022. https://doi.org/10.1007/978-3-030-86294-7_8

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opted for an architecture for the gearbox that implies a lower backlash. However, both options usually involve higher production and projection costs. As such, the projection of a modular joint consists of a trade-off between the torque/weight ratio, backlash and cost. Consequently, for the modular joint proposed, that can be seen in Fig. 1, it was opted to use a compound planetary gearbox, since it allows to obtain a high reduction ratio without dramatically increasing backlash.

Fig. 1. The developed modular robotic joint.

Regarding the motor, a brushed DC one was used, which contributes to the low final cost. An 8-bit microcontroller was also incorporated, where the joint control algorithms are executed. In order to make possible to carry out the control safely, the joint has the following sensors: voltage, current, temperature, absolute magnetic encoder, and an Hall sensor to detect the Home Position. The rest of the paper is organized as follows. After the introduction, Sect. 2 presents the related work and Sect. 3 addresses the system architecture. Then, in Sect. 4 the modular joint design is presented while in Sect. 5 different control methods are addressed. Section 6 presents the results and its discussion whereas last section concludes the paper and points out the future work.

2

Related Work

The study of modular joints is a subject of interest that has been extensively explored both at the academic and industrial levels. In this way, there are already other proposals developed, some of which are simply the result of a study and others that are already commercially available. Regarding the solutions developed academically, [1] presents an approach composed by: gearbox, motor, encoder, limit switch and accessory components. In this case, a gearbox of the harmonic type, to which a brushless DC motor and

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an incremental optical encoder are connected, was used. The controller used is a DSP that receives commands via the CAN protocol. The biggest disadvantage of this joint is its high weight of 7.2 kg and its large footprint. As mentioned earlier, there are models already commercially available such as [2]. This version has two absolute magnetic encoders, a brushless AC motor and an harmonic gearbox. There are 5 options within this model, the most powerful option, which is also the heaviest, produces 333 Nm of peak torque and weighs 3.9 kg. However, the big disadvantage of this option is the high cost: 3370.60 e. Consequently, the proposal made in this article intends to stand out from those mentioned in the following aspects: low cost, low weight, more compact, and easily reconfigurable.

3

System Architecture

The joint’s development started from an initial concept for its operation, according to which the entire system architecture was developed. So, the general architecture can be seen explicitly in Fig. 2.

Fig. 2. Developed system architecture.

This system has an 8-bit microcontroller as its operating brain. It receives through Serial Communication, using RS-485 as a physical layer, commands that represent the control (speed and/or position) that must be carried out. When these commands are received, they have information about the references used for control. Consequently, since the microcontroller carries out all the processing, it receives the data from the absolute magnetic encoder via I2C, which allows it to be aware of the joint’s speed and position. With that, it communicates with the motor driver through PWM inducing the proper motor movement.

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In addition, to guarantee the motor’s safe operation, a temperature sensor was added, which communicates the motor’s temperature to the microcontroller through the 1-Wire protocol. The supply voltage is monitored using a resistive divider and the microcontroller’s analog-to-digital converter (ADC). In order to monitor current, a current sensor was also added. A 12V DC Power Supply is used to supply the system. This way, only four wires are needed to make the joint work: two for communication and two for power supply. During the development of this joint, the desired specifications were: to have a build cost of less than 150e; to weigh less than 1 kg; to have a backlash less than 0.5◦ ; and to be able to lift 0.5 kg with a 0.5 m extension, which is equivalent to produce 2.45 Nm of torque.

4

Modular Joint Design

The modular joint projection is based on the following principles: low cost, high physical connectivity, easily reconfigurable, low backlash and built-in control. In addition, it had to be able to house all the sensors already mentioned. Thus, in the following subsections the different parts of the joint construction process and the reasoning that underlies on each one will be explained. 4.1

Modular Joint Mechanical Design

As it is intended to produce as much torque as possible while maintaining the joint compact, it was decided to select a reduction ratio that allowed to maximize the torque production while using a low-cost and low power DC motor. Thus, after investigating the different types of gearboxes, a compound planetary type was developed. This type of gearbox allows to achieve high reduction ratios without significantly hindering its compactness [3]. A compound planetary gearbox basically consists of two different planetary gearbox sets with their planets physically connected. This way, the sun of the first gearbox acts as the input and the ring of the second gearbox as the output. Each set is composed by one ring, one sun and four planets. In Fig. 3 it is possible to see the composition of the developed gearbox. As it can be seen, Ring 1, Planet 1 and Sun 1 are the components related to the first planetary gearbox. Doing the same reasoning, Ring 2, Planet 2 and Sun 2 are the components related to the second one. Additionally, it is possible to check the Home Position sensor and Magnetic Encoder location. The encoder has an offset relative to the output axis, however it rotates synchronously through a 1:1 ratio. The reduction ratio Ng of the compound planetary gearbox is calculated as: Ng =

P1 R1 P1 S1

− +

P2 R2 P1 R2

(1)

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Fig. 3. Compound planetary gearbox sectional view.

In Eq. 1, R1 refers to the number of teeth in Ring 1, P2 refers to the number of teeth in Planet 2, and so on. In this case, the different components of the gearbox have as many teeth as those in Table 1. Taking into account these parameters and the Eq. 1, the gearbox’s reduction ratio is about 75.8:1. Table 1. Number of teeth per gearbox component. Component Number of Teeth

4.2

R1

49

P1

15

S1

19

R2

48

P2

14

S2

20

Modular Joint Production

One of the main goals for this joint was a low final cost. As the production process can bring high added costs, this factor has become relevant to the development process. Consequently, the method chosen to produce this joint, and similar ones, was the additive manufacturing (3D Printing). This method, in addition to being extremely low cost when compared to others, such as metal machining, also allows it to be easily accessible. Additionally, as the prototyping process is fast and affordable using 3D Printing, it also contributes for the joint to be extremely reconfigurable. That is, if

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it is necessary to adapt it to a new application, the necessary modifications are quickly made and the new components are printed without adding high costs. However, during the development process, the selection of this manufacturing method implied that the CAD design was modified in order to account for the lack of tolerances coming from 3D Printing. These could not be too tight because after printing the components do not fit properly, and they could not be too loose because they meant a significant increase in backlash. After 3D printing the complete joint and attaching the motor and the electronics, the final result from this process can be seen in Fig. 4.

Fig. 4. Complete 3D printed robotic joint.

4.3

Modular Joint Connection

In order to maximize the joint’s modularity, the fixation fittings have been developed so that it does not restrict any type of positioning. As can be seen in Fig. 5, the fixation consists of a rectangular pattern (40 × 43 mm) to which any type of adapter with the same pattern can be built and connected using standard M3 bolts. Consequently, this joint can be placed either vertically, horizontally, or even in any other way that meets the requirements of a specific application. The output shaft has a square bolt pattern (18 × 18 mm), as can be seen in Figs. 1 and 4, to which any type of physical connection, or even another modular joint, can be connected directly. The output shaft also uses standard M3 bolts that allows an adapter to be connected to it according to a given application.

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Fig. 5. Modular joint fixation points (bottom view).

4.4

Modular Joint Electronics

The electronic part of the robotic joint is divided into four different groups: controller, sensorization, communication and motor. The controller is an 8-bit microcontroller, more specifically an ATmega328P. The choice of this controller made it possible to satisfy the control requirements while maintaining the final cost low. It is responsible for carrying out the speed and/or position control of the joint and for monitoring the system variables. That is, it captures the motor’s temperature with a frequency 1 Hz, and updates the voltage, current, position and speed with 40 Hz frequency. Since the encoder communicates via I2C, and this is not a very fast protocol, it has been determined through tests 40 Hz is the fastest possible control frequency that allows to maintain the control period constant. Regarding sensorization, it has a Maxim Integrated DS18B20 temperature sensor that communicates through the 1-Wire protocol. This sensor has a variable resolution between 9 and 12 bits, and in this case it is programmed to work at 9 bits, which allows to have a resolution of 0.5 ◦ C and a fast conversion and reading time. To monitor the supply voltage, a resistive divider converts this voltage into a value within the safe parameters of the microcontroller’s ADC. In order to obtain the current consumed by the motor, an ACS712-30A current sensor is used. It generates a voltage proportional to the consumed current that is read by the microcontroller’s ADC. Finally, the joint’s position reading, which also allows to calculate speed, is made using a AS5600 absolute magnetic encoder with 12-bit resolution. For the joint to receive commands, the communication was established using RS-485 as a physical layer, due to allowing the use of several joints simultaneously on the same line of communication. The RS-485 transceiver used is a Maxim Integrated MAX485CSA. Using this method, a serial communication is established between the Master, which is a main computer/controller, and the Slaves, which are the joints. The transmitted packet has the Slave address on the first byte, the type of command ordered on the second byte, and the next 4 bytes identify the float-type variable that serves as a reference for joint control. The commands can specify control in speed, position, or both. The DC motor

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used is a Surpass Hobby 550-35T, which consists of a brushed motor that holds up to a maximum current of 20 A and supports up to 7.2 V.

5

Joint Control

In addition to having the main goal of building a modular robotic joint, it also intends that this joint has built-in functional controllers. Thus, the implemented controllers are: PD Position Controller, PI Speed Controller with Inverse Dynamic Feedforward, and a Cascade PID Controller with Dead Zone Compensation (DZC). The following subsections will detail each one of the controllers. The PI Speed Controller was tuned using the Internal Model Control (IMC) method [4] whereas the PD Position Controller was tuned using the second order Bessel propotype. 5.1

PD Position Controller

The PD Position Controller consists, as the name implies, of a controller with a proportional and a derivative component. With that, the notation used to represent the controller is as follows: e(t) is the position error, Kc the proportional gain, Td the derivation time and as a controller’s result is u(t). With this, the controller can mathematically be represented as:  u(t) = Kc

e(t) + T d

 d e(t) dt

(2)

Since it is intended to control position, it must be considered that it is a result of the speed’s integration. Consequently, the controller can be represented in a block diagram as in Fig. 6.

Fig. 6. PD Position Controller represented in a Block Diagram.

5.2

PI Speed Controller with Inverse Dynamic Feedforward

The PI Speed Controller differs from the PD by replacing the derivative component with an integrative one. This way, its mathematical representation uses Ti to represent the integration time, as:  u(t) = Kc

1 e(t) + Ti



 e(t)dt

(3)

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An Inverse Dynamic Feedforward (FF) block was added to the PI Speed Controller. This component is the joint’s inverse transfer function and acts directly on the controller output. The FF’s main goal is to improve the system’s response without affecting its stability, by reducing the response time and overshoot [5]. It’s interaction with the PI Controller can be represented as in Fig. 7.

Fig. 7. PI Speed Controller with feedforward block represented in a block diagram.

5.3

Cascade PID Controller with Dead Zone Compensation

The Cascade Controller differs from the previous ones mainly in the fact that it consists of two controllers connected. More specifically, the first controller, which in this case is a PD, acts directly on the external reference and generates a new reference signal for the next controller, which in this case is a PI. The Cascade Controller has the main advantage of being able to guarantee stable control when load variations occur [6]. A motor’s Dead Zone Compensation (DZC) component has been added to the Cascade Controller as can be seen in Fig. 8. This component intends to compensate the motor’s dead zone as it represents a non-linearity. The DZC component consists on the motor’s inverse model. More specifically, knowing the voltage from which the motor leaves the dead zone, it is possible to compensate the output of the controller so that it operates in the linear zone while it has not reached the reference. Therefore, its implementation is encoded below, where output is the real output value of the Cascade Controller, posError is the current position error, minP osError is the threshold value for the minimum position error and of f set is the minimum voltage that puts the motor outside the dead zone. if ((abs(posError) > minPosError) and (abs(output) < offset)) output = (output / abs(output)) * offset; The value of output is divided by its absolute value in order to preserve the motor’s direction of rotation.

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Fig. 8. Cascade controller with dead zone compensation block represented in a block diagram.

6

Results

As it was initially intended to develop a modular, low-cost joint, with easy reconfiguration and built-in control, the following subsections will present the results about these aspects. 6.1

Architectural Results

After the joint was built and all the components were added to it, the characteristics represented in Table 2 were obtained. Additionally, the joint has a backlash of 0.00453 radians, which is equivalent to 0.26◦ . Table 2. Comparison of characteristics. Joint

Weight Footprint (kg) (mm)

Cost (e)

Max. Torque (Nm)

95.13

4.54

Current Proposal 0.890

100 × 110 × 168

Proposal [1]

7.2

110 × 110 × 220.5 Unknown 80

Proposal [2]

3.9

115 × 115 × 150

3370.60

333

Despite the difference in torque being significant, the proposal presented is substantially lighter and more affordable than the other existing ones. Consequently, it fills this existing gap. 6.2

Performance Results

The performance results consists on the analysis of the three controller’s behavior to a given reference: PD Position Controller, Cascade PID Controller with Dead Zone Compensation, and PI Speed Controller with Inverse Dynamic Feedforward. Thus, Figs. 9, 10 and 11 demonstrate the controller’s response. Regarding the steady-state behavior, after several experiments, the PD Controller presented an average absolute error of 0.00416 rad and a maximum absolute error of 0.01 rad. In the same tests, the Cascade Controller had an average absolute error of 0.0035 rad and a maximum absolute error of 0.004 rad. In the transient response, the PD controller had a settling time of 650 ms and the cascade controller of 525 ms. Consequently, we can conclude that the performance

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Fig. 9. PD Position Controller response to reference.

Fig. 10. Cascade PID Controller with Dead Zone Compensation(DZC) response to reference.

Fig. 11. PI Speed Controller response to reference.

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of the Cascade Controller with DZC is the best one, given the lower errors and the faster response. About the PI Speed Controller, after several experiments, it was obtained an average absolute error of 0.006124 rad/s and a maximum absolute error of 0.035 rad/s in steady-state. Regarding its transient response, despite presenting an overshoot of 5.2%, it allows to obtain an average settling-time of 425 ms.

7

Conclusion

In this paper, a new approach on how to build a modular robotic joint was proposed. The final result meets the initial requirements, more specifically, low cost, high modularity, easy reconfiguration and control in speed and position incorporated. To develop the prototype, 3D printing was used as a manufacturing method, and the sensors, the actuator and the microcontroller responsible for the control were installed. Results obtained from the dynamic tests validated the proposed prototype. Future work would go through processes such as: weight reduction, increasing structural rigidity and the use of Hermite polynomials for the control references. Acknowledgements. This work is financed by National Funds through the Portuguese funding agency, FCT - Funda¸ca ˜o para a Ciˆencia e a Tecnologia within project UIDB/50014/2020.

References 1. Jia, Q.-X., Sun, H.-X., Song, J., Cheng, T., Zheng, P.: Development of modular robot joint, 2006 IEEE International Conference on Industrial Informatics, INDIN 2006 (2006). https://doi.org/10.1109/INDIN.2006.275669 2. Robot Joints RDrive. https://rozum.com/robotic-joints-by-rozum/ 3. Crispel, S., et al.: Introducing compound planetary gears (C-PGTs): a compact way to achieve high gear ratios for wearable robots. In: Carrozza, M., Micera, S., Pons, J. (eds.) Wearable Robotics: Challenges and Trends. WeRob 2018. Biosystems & Biorobotics, vol. 22, pp. 485–489. Springer, Cham (2019). https://doi.org/10.1007/ 978-3-030-01887-0 94 4. Fruehauf, P.S., Chien, I.-L., Lauritsen, M.D.: Simplified IMC-PID tuning rules, ISA Trans. 33(1), 43–59 (1994). ISSN 0019–0578, https://doi.org/10.1016/00190578(94)90035-3 5. Kaiser, D.: Fundamentals of servo motion control. Motion Syst. Des. 43, 22– 28 (2001). https://www.scopus.com/inward/record.uri?eid=2-s2.0-17944399301& partnerID=40&md5=7afec604117ae23eac145a7eb3a02429 6. Bolton, W.: Instrumentation and Control Systems, Chapter 13 - Control Systems, 2nd edn., pp. 281–302 (2015). https://doi.org/10.1016/B978-0-08-100613-9.00013-4

Section–4: Innovative Design of CLAWAR

The Flatworm-Like Pedal Locomotory Robot WORMESH-II: Fundamental Properties of Pedal Wave Locomotion G. V. C. Rasanga1(B) , R. Hodoshima2 , and S. Kotosaka2 1

Graduate School of Science and Engineering, Saitama University, Department of Mechanical Engineering, Saitama-shi, Saitama 3388570, Japan [email protected] 2 Department of Mechanical Engineering, Saitama University, Saitama-shi, Saitama 338-8570, Japan

Abstract. Inspired by flatworm locomotion, we proposed concept of a novel flatworm like robot named WORMESH. The feature of this robot is its structure, in which the component links are connected in a mesh pattern in the vertical and horizontal directions with joints having multiple degrees of freedom. The entire body of the robot is flexed to create multiple pedal waves simultaneously, to move and work. The second experimental model, WORMESH-II was then developed, with newly designed interlocking double joints. Further, its mobility performance is being verified. This paper discusses pedal wave locomotion of the WORMESH-II and how locomotion behaves under transitioned friction conditions. The simulation results depicted three significant: First, the pedal wave locomotion of WORMESH-II which has constructed by three units of kinematic chain arrangement is not continuous wave motion, and it is a combination of four locomotion steps. Second, there is an average velocity reduction when the robot moves between a lower friction area to a higher friction area. Third, in such a situation, locomotion can be improved by changing the robot’s front and rear joints’ wave parameters. Keywords: Pedal wave locomotion · Bioinspired robotics · WORMESH

1 Introduction Bio-inspired robot is one of the hot topics in robotic research, because of higher adaptability and efficient behavior of living creatures. The limbless robot is an interesting research area, particularly locomotion in an unstructured environment [1]. We have proposed new concept of a robot inspired by the flatworm, named WORMESH, and have been testing it with an experimental robot in order to clarify the characteristics of the robot’s mobile performance and morphology [2]. As illustrated in Fig. 1, it can crawling on a surface (Fig. 1(a)), walking on rough terrain (Fig. 1(b)), carry and manipulate an object (Fig. 1(c) and 1(d), respectively). WORMESH has many degrees of freedom and can exhibit a high degree of flexibility. This allows high terrain adaptability and ability c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 95–107, 2022. https://doi.org/10.1007/978-3-030-86294-7_9

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(a) Crawling

(b) Walking

(c) Transportating

(d) Manipulating

Fig. 1. Concept of flatworm-like pedal wave locomotory Robot

to change its own structure as needed. So those capabilities will lead to developing efficient robot systems for surveillance, disaster and rescue robot applications. The fundamental motion method of the WORMESH is crawling on a surface. When considering the crawling motion of limbless robot system, there are several locomotion gaits related to snake [3], inchworm [4], and caterpillar [5] robot systems. During past two-three decades locomotion of snake-robots has been widely discussed. Serpentine locomotion [6], traveling wave locomotion [7], sidewinding [8], and rolling [9] are some of the main locomotion gaits of snake robots. Serpentine motion generates on supporting plane, and friction forces consequently generate along the normal and tangential direction to the supporting plane, which create driving force [6]. Usually, serpentine locomotion robots need wheels to produce proper directional friction conditions[10], thereby it will cause some adaptability in different environment. On the other hand, traveling wave develops in vertical plane, that is orthogonal to the supporting plane, which has much adaptability to different frictional conditions and uneven surface [7, 11]. Crawling motion of WORMESH generates based on pedal wave (traveling wave) locomotion. The majority of pass researches related to the pedal wave locomotion were focused on snake robots, consist of more than six links [7, 11]. In this study, the construction of WORMESH is entirely different because WORMESH has bilaterally symmetrical construction unlike snake robots. Figure 2 shows prototypes of WORMESH-II and its simulation model. WORMESHII is a modular type robot, constructed by connecting a number of same type modules with accordance to mesh formation. On the other hand, kinematic model of this construction’s can be expressed as a formation of kinematic chains. The dash lines in Fig. 2(a) show kinematic chains. Thereby, WORMESH-II can be represented as three links per one kinematic chain and detailed construction will be explained in following sections. For limbless locomotion on ground, friction behavior at the ground contact point is the fundamental physical parameter. In real-world applications, locomotion in constant friction condition is unlikely to be realistic. Therefore, it is essential to understand how WORMESH behaves under variable frictional conditions. Koopaee [11] discussed sixlink snake robot movement through higher friction surface to lower friction surface for pedal wave locomotion. That result indicated a 20.3% velocity reduction. Nevertheless, it is difficult for robot mechanisms having a three-link kinematic chain, to generate a continuous wave by bending its body. Figure. 3 illustrates link positions along with pedal wave for kinematic chain of higher number of links (14 links in Fig. 3(a)) and three links (Fig. 3(b)). When kinematic chain has several number of links, ground contacts are occurred at the lowest point of the wave (Fig. 3(a)). This

WORMESH-II: Locomotion

(a) Model in a matrix form 3×3

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(b) Prototype of WORMESH-II robot

Fig. 2. WORMESH-II: prototype of flatworm-like pedal wave locomotory Robot

(a) Links pose of a kinematic chain with multiple numbers of links on the travelling wave.

(b) Four different links poses of a three-link kinematic chain on the travelling wave. Fig. 3. Links pose on a travelling wave.

can be viewed as a continuous traveling wave, permitting the robot to achieve smooth locomotion. Figure. 3(b) displays four different poses of three-links kinematic chain along with the wave. Moreover, 1 to 4 positions in Fig. 3(b) depict how those links are positioned on the supporting plane under gravity. It shows that the ground is not contacted at the lowest points of the traveling wave for the minimum number of link situations. Therefore, it implies that the locomotion of the case for three or low number links should significantly differ from the case of complete pedal wave locomotion. This paper discusses the pedal wave locomotion mechanism of three-link kinematic chain and how the WORMESH-II robot moves through the transient friction areas by analyzing the locomotion mechanism. Analyzing the locomotion of a flatworm-like robot with a mesh structure, which is based on a mathematically developed kinematic model is a

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challenging task. Therefore, CoppeliaSim robotic simulator interfacing with MATLAB was adopted in this study for analysis of the WORMESH-II robot locomotion. In this paper, Sect. 2 presents about the construction of WORMESH-II as a flatworm-like robot with a mesh structure. The cyclic pedal wave locomotion mechanism of WORMESH-II is discussed in Sect. 3. Likewise Sect. 4 presents the pedal wave locomotion of WORMESH-II in different environmental conditions and Sect. 5 summarizes the study.

2 WORMESH-II: A Flatworm-Like Robot with a Mesh Structure 2.1

Mechanical Configuration

The structure of WORMESH-II consists of modules that connected by revolute joints (Fig. 4(a)). There are two types modules called “control module” and “joint module”. The mass of each module is 300 g. Control modules include control hardware and power supply units and joint modules are occupied by actuators and sensors. The complete connection between two consecutive control modules is connected by one joint module and two sets of rotational joints; Ji1 (i = 1, 2, ...n) and Ji2 (i: joint module number), (Fig. 4(b)). By three kinds of rotational joints, which can rotate along roll, yaw, and pitch directions, the nearest control modules are connected to each other via two joints (Ji1 or Ji2 in Fig. 4(b)) in a joint module between them. This joint arrangement of the joint module is called a coupled double joint arrangement (Di ), in which each axis of the oppositely installed universal joint operates interconnectedly. These two universal joints are arranged so that they have rotation in yaw and pitch axis directions. Each yaw and pitch axis is coupled, and their rotational motion is generated by two DC motor. Therefore, coupled double joint mechanism actually has a pseudo four degree of freedoms (DOFs), and summation of Ji1 and Ji2 creates the relative angle between the nearest control modules. The whole structure of WORMESH-II comprises of nine control modules(MCi ) and twelve joint modules (MJi ) (Fig. 2). An arrangement of two joint modules seriously connecting in series with three control modules is a kinematic chain. These all modules create six kinematic chains, which are marked in Fig. 2(a) by dash lines accordingly to the mesh formation.

(a) Modular and joint configuration in the sim- (b) Joint configuration between ulation environment. consecutive two control modules. Fig. 4. WORMESH-II: Module and joint arrangement

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Figure 5(a) illustrates a kinematic chain of WORMESH-II during translational motion in simulation environment. MC1 , MC2 , and MC3 are control modules, whilst MJ1 , MJ2 are two joint modules. J11 , J12 , J21 , and J22 is the set of three-DOF joint units. MC1 and MC2 are connected by J11 and J12 . Correspondingly, MC2 and MC3 are connected by J21 and J22 . Pi (i = 1, 2, .., 10) indicates the bottom edges of the relevant modules. These are the ground contact points of one kinematic chain of WORMESH-II during locomotion. Moreover, simplified kinematic chain is displayed by Fig. 5(b). P1 − P2 , P5 − P6 , and P9 − P10 represent MC1 , MC2 , and MC3 , respectively. P3 − P4 , P7 − P8 symbolize MJ1 , and MJ2 , respectively. The ∠R1 Q1 J12 is equals to the summation of ∠Q1 J11 J12 and ∠Q1 J12 J11 ; similarly, ∠ R2 Q2 J22 equals to the summation of ∠Q2 J21 J22 and ∠Q2 J22 J21 . According to the mechanical design of WORMESH-II, ∠Qi Ji1 Ji2 and ∠Qi Ji2 Ji1 (i=1,2) are equal. Apparently this arrangement can be simplified into a kinematic chain of three links, which are connected by two joints. Thereby, P1 − Q1 , Q1 − Q2 , and Q2 − P10 are links. Also, Q1 and Q2 are joints. This arrangement is a three-link kinematic chain.

(a) Modular and Joint terminology of a (b) Three links kinematic chain configuration of kinematic chain. WORMESH-II. Fig. 5. The terminology of modules and joint arrangement a kinematic chain.

2.2 Pedal Wave Generation WORMESH-II can make different locomotion patterns for crawling on a surface [2] though this paper considers only translational motions. As explained in [2], three parallel and synchronous pedal waves that propagate along WORMESH-II creates translational motion. Figure 6 shows how three parallel, synchronous pedal waves propagate along with two different module arrangements of WORMESH-II. Moreover, translational motion is generated by controlling the joint angle of relevant pitch joints. To generate pedal wave locomotion, pitch joint angles (∠Qi Ji j Ji j (i, j =1, 2)) of the relevant kinematic chain of WORMESH-II control according to Eq. 1 [12], where A is the maximum amplitude, ω is the temporal frequency and β is the phase shift between adjacent joints. ∠Qi Ji j Ji j = A sin {ω t + β (i − 1)}

(i = 1, 2, · · · , n)

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(a) Model3×3 .

(b) Model6×3 .

Fig. 6. Pedal wave propagation on broth robot models in translation motion.The black colour dash lines illustrate the pedal wave.

Fig. 7. Links pose of pedal wave locomotion of WORMESH (Model3×3 ) (Fig. 2(a)) robot model and linear velocity at the bottom corners (Pi ) of the modules for horizontal direction for one complete locomotion cycle (Pedal wave parameters;A = π /8, ω = 0.5π , β = 2π /3).

3 Cyclic Pedal Wave Locomotion Mechanism The simulation procedure was carried out as follows to understand the pedal wave locomotion mechanism of WORMESH-II. Two simulations were done for two robot models to identify the difference of locomotion mechanisms when the robot has limited links per kinematic chain. Those robot models were Model3×3 (Fig. 6(a)), which includes three control modules per one kinematic chain and Model6×3 (Fig. 6(b)), which includes six control modules per one kinematic chain along the wave propagation direction. During this simulation, the surface’s friction coefficient was kept at a higher value (0.90) to minimize unnecessary slipping and ensure the ideal condition of locomotion because it helps to identify the ideal sliding and anchoring behavior of ground contact points. Also, pedal wave parameters of both robot models were kept at the same value throughout the simulation, which were temporal frequency (ω ) at 0.5π , phase shift(β ) at 2π /3, and amplitude (A) at π /8. For both models, the position, orientation, and velocity of the ground contact points (Pi ) were determined. Consequently, poses of kinematic chain

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during locomotion were plotted and then calculated the ground reaction force and friction at the relevant Pi points. 3.1 Analysis of Basic Waveform Figure 7 illustrates poses of WORMESH-II (Model3×3 ) of 3 × 3 control module formation and “+” marks of right hand side plot illustrate linear velocities of the bottom edge points (Pi ) of modules towards the propagation direction of pedal wave. The redcolour points indicate the appropriate module locations, which contact ground. The black-colour arrow indicates travelling direction of the pedal wave. Also, these module poses revealed that the locomotion of WORMESH-II can be categorized into quaternary steps, and those were named as quarter Q1 (rear sliding), Q2 , Q3 (front sliding), and Q4 (Fig. 7) to simplify the discussion. Among them, two steps (Q1 and Q3 ) cause the robot move towards the travelling direction and step, Q2 shifts the body shape from Q1 to Q3 . Likewise, step Q4 shifts body shape from Q3 to Q1 . Locomotion Quarter Q1 (rear sliding): According to the links pose shown in Fig. 7, when simulation time equals to 4.25 s, and 7.75 s, the linear velocity towards the wave direction of P1 is positive and higher than the other points (0.02512 m/s and 0.03487 m/s respectively). The area between P6 and P9 results second ground contact points (P8 at time = 4.25 s, P7 at time = 7.75 s). These points show the minimum velocity towards the wave direction, which is almost zero (Fig. 7). That means during locomotion quarter Q1 , the rear side of the robot moves to wave travelling direction while P7 and P8 remain stationary. Therefore, it said that P1 is sliding while P7 and P8 are anchoring. Locomotion Quarter Q2 : The front (P10 ) and rear (P1 ) points contact with the ground. These locations also show the minimum linear velocity, which approximates to zero (When time = 5.10 s, velocity of P1 =-0.0032 m/s and P10 = 0.0017 m/s; Fig. 7). Locomotion step Q2 dose not contribute to robot movement towards the travelling direction but, it transfers the robot pose from Q1 to Q3 . However, when simulation time equals to 4.65 s and 5.55 s, P10 and P1 , respectively move opposite to the wave travelling direction. Nevertheless, these velocities are smaller than of the sliding point’s velocities during step Q1 and step Q3 . Locomotion Quarter Q3 (front sliding): During this step, point P10 and points between P2 and P5 are in contact with the ground (time = 6.00 s; Fig. 7). P10 is the sliding point, which shows the maximum velocity towards the wave direction while P4 and P5 do the anchoring. Locomotion Quarter Q4 : Central area (P5 , P6 ) of the robot contacts the ground. Furthermore, both points have almost zero velocity. This locomotion step also does not contribute to motion towards the wave travelling direction. Similar to quarter Q2 , quarter Q4 transfers the robot pose from Q3 to Q1 . In Fig. 8, blue colour left-hand plots display the mesh-like robot model’s locomotion pose, which has six control modules per one kinematic chain (Model6×3 ) along pedal wave propagation direction. In right-hand plot, “ + ” marks indicate the linear velocity of the bottom points towards the pedal wave travelling direction. This arrangement can generate a complete waveform instead of the three-link kinematic chain. Also, the velocity at the ground contacts points is almost zero and stationary. The locomotion is continuous, and no sliding actions at the ground contact points (Fig. 8). Moreover,

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the velocity distribution along the kinematic chain shows a sinusoidal shape, which is similar to the velocity distribution of rolling wheel. 3.2

Result and Discussion

These results depicted that the locomotion mechanism between WORMESH-II robot model, of a three-link kinematic chain (Model3×3 ) and the mesh-like robot model, which has a high number of links is significantly different. In the scenario of minimum number of modules, Model3×3 module formation could not produce a continuous pedal wave locomotion. It moves towards the travelling direction based on two ground contact point, which cause anchoring and sliding. The critical point of the locomotion of Model3×3 is the behavior of the friction at the ground contact points. In order to create anchoring and sliding action efficiently, there must be adequate frictional difference between anchoring and sliding points. To produce a successful move towards the travelling direction, a higher friction must be at the anchoring point and lower friction at the sliding point. Those friction forces depend on the surface condition and vertical reaction force (RPi (i = 1, 2, .., 10)) at the ground contact point. Hence, Ri at the ground contact points was calculated for all locomotion poses. Figure 9 illustrates RPi at the ground contact points when simulation time = 4.25, 4.65, 5.10, 5.55, 6.00, 6.40, 6.85, 7.30, 7.75 and 8.15 s. the reaction force during locomotion of Q2 shows in red colour boundary in Fig. 9. The contact points are P1 and P10 , and RP1 and RP10 are approximately equal. The black colour boundary in Fig. 9 shows reaction forces during Q4 , where P5 and P6 are contact points. Both RP5 and RP6 are approximately same. The blue and green colour boundary areas show reaction force of steps Q3 and Q1 , respectively. Both of them has a higher difference between reaction forces at the contact points. Therefore, during both Q1 and Q3 quarters, the contact point having a lower reaction force, is sliding, while the contact point with a higher reaction force is anchoring.

Fig. 8. Links pose of Pedal wave locomotion of Model6×3 robot model and linear velocity at the bottom corners of the modules (Pi ) to the horizontal direction (Pedal wave parameters; A = π /8, ω = 0.5π , β = 2π /3).

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Fig. 9. Reaction forces along a kinematic chain at the ground contact points of the WORMESH-II (Model3×3 ) model for an one pedal wave cycle. Q1 , Q2 , Q3 , and Q4 are locomotion quarter. The contacts point shows by Pi (i = 1, 2, .., 10)

Moreover, Fig. 10 shows friction force and its direction at the ground contact points. The red colour arrows indicate the direction of force. Generally, both friction forces act in opposite directions to each other. During locomotion quarter Q1 and Q3 , the difference between friction at anchoring point and sliding point is more than double. For efficient locomotion, the anchoring point must have a higher friction force than the sliding point. In homogeneous surface condition, the frictional difference relies on the geometry of robot pose. Nevertheless, when anchoring point and sliding point are in a significantly different friction conditions, this would be problematic that will be discussed in the following section.

Fig. 10. Friction force at the ground contact points for a one locomotion cycle (friction force is proportional to the arrow’s length).

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Fig. 11. Links pose and velocity at point Pi of the robot when move across the F1 and F2 . The friction coefficient of F1 =0.05 and F2 =0.7. Pedal wave parameters: A = π /10, ω = π , β = 2π /3.

4 Locomotion in Different Environments As discussed in the above section, among the locomotion quarters of Model3×3 , Q1 and Q3 had contributed to positive moves equally under homogeneous friction conditions. This section presents WORMESH-II robot’s locomotion along different friction surfaces as illustrated in Fig. 2(a). The simulation environment has two surface areas denoted by F1 and F2 , which can change friction properties. 4.1

Cyclic Pedal Wave Locomotion in Different Friction Conditions

The friction coefficients of surface F1 , and F2 are 0.05 and 0.7, respectively. Figure 11 illustrates the robot’s pose of locomotion steps while moving from F1 to F2 . The blue colour vertical dashed line shows the boundary line between F1 and F2 . The“ +” symbol displays the horizontal velocity of the each Pi points. During locomotion step Q3 (at simulation time 25.1 s), the ground contact point, P10 has almost zero velocity, whereas other contact points (P4 ) have negative velocities. According to the locomotion on homogeneous friction condition, P10 is supposed to be the sliding point, and the area between P2 and P5 would be the anchoring point (Fig. 7). However, in the middle of different friction conditions, locomotion step Q3 was not successful for positive move towards the travelling direction. For locomotion quarter Q1 , the anchoring point was at the higher friction area and the sliding point was at the lower friction area. Therefore, Q1 generated a better move towards the travelling direction. Furthermore, blue colour plot in Fig. 12 shows the displacement of WORMESHII robot with time. It can identify positive and negative moves towards the travelling directions when robot position varies, where displacement (y) equals 0.73 m-1.21 m. The positive displacement is Q1 while negative displacement is Q3 . It indicates that the movement from higher friction area to lower friction area has a reduction of locomotion performance. Therefore, it needs some improvement in such a situation. The next section suggests a modified pedal wave to improve the locomotion to move across the F1 to F2 . (2) ∠Qi Ji j Ji j = A sin {ω t + β (i − 1)} + ksti f f ens (i = 1, 2, · · · , n)

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Fig. 12. WORMESH-II displacement toward the travelling direction vs time during locomotion from surface F1 to F2 . The friction coefficient of F1 =0.05 and F2 =0.7. Pedal wave parameters:A = π /10, ω = π , β = 2π /3. Red colored plot ksti f f ens = |π /15|.

Fig. 13. Relative angle between MC1 -MC2 (∠R1 Q1 J12 =2∠Q1 J1 j J1 j ) and MC2 -MC3 (∠R2 Q2 J22 = 2∠Q2 J2 j J2 j )

4.2 Adaptive Pedal Wave Locomotion Between the Transition Friction Surface In above section, when the robot moved from lower fiction to a higher friction area, Q3 showed a negative displacement. On the other hand, locomotion quarter Q1 performed well. Therefore, to improve the locomotion across F1 and F2 , it needs to reduce the effect of Q3 and increase the effect of Q1 . In order to reduce locomotion-quarter Q3 ’s negative stroke, positive stiffness (ksti f f ness > 0) was added to revolute joints J21 and J22 . Similarly, to increase the locomotion-quarter Q1 ’s positive stroke, negative stiffness(ksti f f ness < 0) was added to revolute joints J11 and J12 . Figure 13 (a) and (b) show the wave pattern of ∠R1 Q1 J12 and ∠R2 Q2 J22 without stiffness and with stiffness, respectively. Equation 2 shows the modified pedal wave to locomote within different friction areas. Figure 14 displays the robot pose when the robot is locomoted by pedal wave with joint stiffness. In simulation, locomotion quarter Q1 was at 24 s and 25.8 s. Interestingly, there was no locomotion quarter Q3 . Due to the added stiffness, Q3 was removed. The blue colour plot in Fig. 12 shows robot displacement without joint stiffness. Whereas red colour plot shows robot displacement with joint stiffness. The

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Fig. 14. Links pose and velocity at point Pi of the robot when move across the F1 and F2 with modified pedal wave. The friction coefficient of F1 =0.05 and F2 =0.7. Pedal wave parameters:A = π /10, ω = π , β = 2π /3.

robot’s average velocity from displacement (y) of 0.7284 m to 1.069 m for blue and red plot is 0.547 cm/s and 0.700 cm/s, respectively. This result reveals that the proposed method could improve the average velocity by 28% for locomotion across significantly different friction areas.

5 Conclusions This paper discussed the newly introduced WORMESH-II robot’s locomotion, which used multiple pedal waves to make a crawling motion. The paper’s main contribution was to; understand the crawling locomotion mechanism of WORMESH-II, which consists of a three-links kinematic chain and its locomotion under transition frictional condition. This study introduced a stiffness coefficient (ksti f f ness ) for pedal wave locomotion to improve locomotion across the different frictional areas. However, pedal wave locomotion can move WORMESH-II towards the positive direction through a friction boundary, even with a significant frictional difference. Nevertheless, in the real application, the fictional condition is an unknown physical parameter. Therefore, disparagement pattern of the robot (Fig. 12) can be used to identified ground conditions. Future, it is important to understand how to control ksti f f ness to optimize the locomotion, which is not discussed in this paper. Moreover, these simulation results are useful to improve the robot system’s crawling motion, not only WORMESH, but also for the pedal wave locomotion of other modular type robot systems, especially those with a limited number of links.

References 1. Cho, K.J., Wood, R.: Biomimetic robots. In: Siciliano, B., Khatib, O. (eds.) Springer Handbook of Robotics, 2nd ed., vol. 75, no. 1, pp. 544–545. Springer, Berlin (2016) 2. Rasanga, G.V.C., Hodoshima, R., Kotosaka, S.: The flatworm-like pedal locomotory robot WORMESH-I: locomotion based on the combination of pedal waves. In: International Conference on IEEE/SICE International Symposium on System Integrations (SII), pp. 72–77, Iwaki, January 2021

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3. Mori, M., Hirose, S.: Locomotion of 3D snake-like robots - shifting and rolling control of active cord mechanism ACM-R3. J. Robot. Mechatron. 18(5), 521–528 (2006) 4. Gamus, B., Salem, L., Gat, A.D., Or, Y.: Understanding inchworm crawling for soft-robotics. In: IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 1397–1404, April 2020. https:// doi.org/10.1109/LRA.2020.2966407 5. Umedachi, T., Shimizu, M., Kawahara, Y.: Caterpillar-Inspired crawling Robot Using both compression and bending deformations. In: IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 670–676, April 2019. https://doi.org/10.1109/LRA.2019.2893438 6. Wu, X., Ma, S.: CPG-based control of serpentine locomotion of a snake-like robot. Mechatronics 20(2), 326–334 (2010) 7. Koopaee, M.J., Pretty, C., Classens, K., Chen, X.: Dynamical modeling and control of modular snake robots with series elastic actuators for pedal wave locomotion on uneven terrain. J. Mech. Des. 142(3), 032301–1-032301–11 (2020). https://doi.org/10.1115/1.4044691 8. Marvi, H., et al.: Sidewinding with minimal slip: snake and robot ascent of sandy slopes. Science 346(6206), 224–229 (2014). https://doi.org/10.1126/science.1255718 9. Chen, L., Wang, Y., Ma, S., Li, B.: Studies on lateral rolling locomotion of a snake robot. In: IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA 2004, pp. 5070–5074, New Orleans, (2004). https://doi.org/10.1109/ROBOT.2004.1302521 10. Tanaka, M., Matsuno, F.: Control of snake robots with switching constraints: trajectory tracking with moving obstacle. Adv. Robot. 28(5), 415–429 (2014) 11. Koopaee, M.J., Bal, S., Pretty, C., Chen, X.: Design and development of a wheel-less snake robot with active stiffness control for adaptive pedal wave locomotion. J. Bionic Eng. 16(4), 593–607 (2019). https://doi.org/10.1007/s42235-019-0048-x 12. Li, D., Wang, C., Deng, H., Wei, Y.: Motion planning algorithm of a multi-joint snake-like robot based on improved serpenoid curve. IEEE Access 8, 8346–8360 (2020). https://doi. org/10.1109/ACCESS.2020.2964486

Experimental Investigation of Locomotive Efficiency of a Soft Robotic Eel with a Largely Passive Body Dinh Quang Nguyen(B) and Van Anh Ho School of Materials Science, Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan {dinh-nguyen,van-ho}@jaist.ac.jp http://www.jaist.ac.jp/ms/labs/vanho/index-e.html

Abstract. In this paper, the swimming efficiency of a soft elongated robot with a largely passive body was evaluated. The previously developed robot was constituted of a series of soft actuators, and we assumed that half of the soft eel robot’s body was uncontrolled. In this case, only the head segment plays the role of the wave source, and the rest becomes the wave propagation parts. Four values of tail beat frequencies were chosen from 0.83 Hz to 1.67 Hz, while the maximum pressure of head segment was varied from 40 kPa to 75 kPa. The swimming velocity increases corresponding to the rise of the head segment’s inner pressure and reaches a peak at 65 kPa, followed by decrements of the speed. We observed that the soft eel robot performed the best swimming efficiency at 1.0 Hz with the highest velocity of 12.46 cm/s (or 0.235 BL/s (Body Length per second)), with lowest COT (cost of transport) of 9.39. The results in this paper can be utilized to enlarge the working conditions of the soft elongated robot body even when the body is partly damaged.

Keywords: Soft eel robot

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Introduction

Thank to having soft and flexible body structures, soft robots are of interest in the development of devices that require gentle interactions with the surrounding environment especially with soft and fragile objects [1,2]. Among them, bioinspired aquatic soft robots have potential applications and are also a challenge due to the vast variety of swimming strategies of aquatic animals and the complex physical interaction with fluid environment [3–5]. The development of soft aquatic robots not only enlarges categories and characteristics of mobile devices for search and surveillance but also helps with studying the physic of locomotion principle of underwater natural animals. The most popular in a soft aquatic robot is fish-like robots when there are a number of reports on constructing many kinds of soft robots inspired by fish [6,7]. The reason comes partly from the popularity of fish and mainly from the simple swimming strategy that the c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 108–116, 2022. https://doi.org/10.1007/978-3-030-86294-7_10

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tail segment only has to perform the flapping movement for forward swimming [8]. Meanwhile, there are few pieces of research on soft robot inspired by other kinds of species with different swimming strategies such as jellyfish [9], squid [10], anguilliform locomotor [11,12] due to the efficiency and the complex structure and control. Elongated body soft robot performing anguilliform movement requires a complex structure in both robot body and control method. To mimic this kind of movement, a series of soft actuators must be employed and stimulated in sequence to create propagation waves from anterior to posterior part of the robot body. Having a large number of body parts and the complexity in control leads to consuming higher power compared to the aforementioned soft robots (inspired by fish, jellyfish, and squid). However, the flexibility of the body also opens the potential applications for elongated body robots such as performing tasks in complex and narrow spaces. In our previous research, we introduced an tethered soft robotic eel with four pairs of pneumatic soft actuators [14]. To reduce energy consumption or enlarge working conditions of the robot, the robotic eel was evaluated its swimming efficiency with partially body inactivation. Interestingly, with a quarterly passive body, the robot performs better swimming efficiency (i.e., higher velocity and lower COT (cost of transport)) than that with fully-controlled strategy [15]. In this research, we plan to increase the passive degree of the soft eel robot with a passive half body, and evaluate the swimming efficiency of this swimming mode. Our specific goals in this paper are: First, to find the maximum possibility of the passive degree of the robot that relates to energy consumption saving ability and working ability of a partly damaged soft eel robot. Second, working conditions including tail beat frequency and maximum air pressure of remain active parts for the best swimming efficiency (highest velocity and lowest COT) are determined.

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Swimming Strategies of Soft Eel-Inspired Robot Design of the Soft Eel Robot

The soft eel robot employs a series of pneumatic actuators to create wave-like movement from head to tail for forward locomotion. The design and air connection method of the robot body is shown in Fig. 1. Four pairs of pneumatic soft actuators, which have segmented and chamber structure permitting the actuator bend when inflating [13], were used to construct the robot body with a total length of 530 mm and a total weight of 0.68 kg. The details of the design and fabrication of the robot were presented at [14]. 2.2

Swimming Strategies

Each segment of the robot body is fed by air pressure in sequence to create sinusoidal waves from head to tail. In this research, air pressure from the compressor (JUN-AIR, USA) goes through throttle valves (AS2052F, SMC, Japan)

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to adjust the feeding flow rate, after that, solenoid valves (VQD 1121-5L, SMC, Japan) contribute pressure air to actuators orderly (see [14,15] for more detail). Three segments were controlled independently by three solenoid valves that were operated by pulse signals with a suitable shifting phases. Suitable control signal bandwidth for the designed soft actuator drops at a range between 0.83 Hz and 1.67 Hz. The eel robot performed two types of swimming strategies basing on two different pipe connection methods [14,15]. The first one is generated by using the same inflated phase of the head and tail segment. The body gait in this combination creates by the formation and release of a big curve, and the middle segment plays an important role in motion phase transition [14]. In this strategy, the highest efficiency of the robot is at a shifting phase of 100% when the swimming speed is at 0.36 BL/s (Body Length per second) and cost of transport is at the lowest value of 10.72. Meanwhile, with the traditional one, the robotic eel creates propagation waves from head to tail that mimic the natural eels movement. In this movement way, the robot velocity reaches the peak at the control shifting phase from the range of 30% to 50% depending on different tail beat frequencies. At the shifting phase of 90% the robot cannot move forward due to the cancellation resulting from segments’ movement(segments that are next to each other move to opposite sides nearly at the same time). Therefore, to duplicate the anguilliform movement of the natural eel, control signal’s shifting phase from 30% to 50% must be applied. A question arising when developing an elongated body robot is about the swimming efficiency of a robot with a partly damaged body. The question might be a big challenge with the traditional elongated body robots (the rigid ones) which have discontinuous body structures when the bodies are constructed by a series of rigid segments operated by a corresponding number of motors [16]. However, with a soft and continuous body, an elongated body soft robot could be a suitable subject to address this question. Based on the aforementioned analysis on swimming strategies, creating propagation waves from head to tail is an appropriate method for the evaluation of the swimming ability of an elongated body soft robot with a partially damaged body. 2.3

Soft Eel Robot with a Large Passive Body

In our previous research, the swimming efficiency of the soft eel robot with a passive tail segment corresponding to one-fourth of the total body length was evaluated [15]. The result indicated that at a quarterly passive body, the robot

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performed the swimming efficiency better than that of the fully-controlled robot. In this study, to confirm the possibility of enlarging the swimming ability of the soft elongated body robot, the passive degree is increased to half of the total body length, in which, only the head segment constructing by two pairs of the soft actuator is activated. The tail beat frequency is varied from 0.83 Hz to 1.67 Hz, which was suitable for the designed soft actuator in our previous research [14], while the maximum pressure of head segment is varied from 40 kPa to 75 kPa with a step of 5 kPa.

3 3.1

Results Swimming Velocity

Fig. 2. Experimental setup for measuring swimming velocity and the robot’s midline kinematics

The robot velocity was taken place at a water tank with a dimension of 450 × 450 × 900 mm in length, width, and depth, respectively. Sony’s camera (DSC-RX10M4), which is set on top of the tank as shown in Fig. 2, was utilized to record the robot movement for measuring velocity and extracting midline kinematics. Due to the medium size of the tank, to avoid the bounce-back waves from the tank that might negatively affect the accuracy of the measurement results, the robot was controlled to travel along with the tank one time for each measurement trial. The next trial was only conducted after the water surface was stable. Each measurement was repeated five times (trials), then the average and the standard deviation of the speed were estimated. Figure 3 shows the variation of the robot swimming speed depending on the head segment’s pressurization at four different frequencies. In general, the robot velocity rises significantly before reaching the peak at 65 kPa, then decreases. At 1.67 Hz, the maximum velocity is just over 5 cm/s at 70 kPa. Meanwhile, the velocity at 65 kPa, which is slightly smaller than that at 70 kPa, is just under 5 cm/s. The highest velocity

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is 12.5 cm/s (0.236 BL/s) at operating frequency of 1.0 Hz. The highest speed at 0.83 Hz and 1.25 Hz are 10 cm/s and 9.4 cm/s, respectively. These values are still smaller than the robot velocity at 1.0 Hz with the maximum head segment pressure of 70 kPa that is the second-fastest speed at this working frequency regime (just over 11 cm/s). f = 0.83 Hz

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Fig. 3. The variation of swimming velocity (line graph) and corresponding COT (bar graph) of the eel robot with a one-half passive body versus maximum pressure value at the head segment at four different frequencies.

3.2

Cost of Transport and Swimming Efficiency

To make convenience for comparison, swimming states of the robot are named as Mode 1, Mode 2 and Mode 3, in which, in Mode 1, all segment is actively controlled, in Mode 2, the control of only tail segment is deactivated (passive level 1) (see [15] for more detail of the two modes), and Mode 3 that one-half of the body is deactivated is detail examined in this report. Table 1 shows the values of COT (cost of transport) and average velocity at different working modes (in this table, the data of average velocity and COT of the robot with passive body level 0 and 1 is extracted from our previous research [15] that also revealed detail equation and calculation method for COT, PE (electrical energy), and PA (air pressure energy)). The combination of high velocity and low COT implies high swimming efficiency. It can be seen that the best performance belongs to the swimming modes that have the shifting phase of 40% or 50% and maximum pressure of the head segment of 65 kPa. However, the best COT value (the lowest one) is not corresponding to the highest velocity. This result might

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come from the difference in energy consumption due to the passive level of the robot where higher passive body level using means lower energy consumption. The highest velocity (14.34 cm/s (0.27 BL/s)) drops to robot working at passive level 1 at 1.0 Hz and control shifting phase of 40% with the COT value of 11.06. Meanwhile, the best COT value of 9.39 belongs to the robot swimming at Mode 3 with a tail beat frequency of 1.0 Hz, at this condition, the robot velocity is at 12.46 cm/s (0.235 BL/s). Table 1. Comparison of the highest COT at different Modes Working mode (level-f -s or p)* PE (J) PA (J) Average velocity (cm/s) COT 0 – 1.25 – 50 (s)

5.52

7.94

10.5

18.84

1 – 0.83 – 50 (s)

3.96

6.09

10.51

14.06

1 – 1.00 – 40 (s)

4.18

6.6

14.34

11.06

1 – 1.25 – 40 (s)

4.18

6.91

11.74

13.88

1 – 1.67 – 40 (s)

4.18

7.29

14.12

11.94

2 – 0.83 – 65 (p)

2.64

4.88

10.02

11.05

2 – 1.00 – 65 (p)

2.64

5.32

12.46

9.39

2 – 1.25 – 65 (p)

2.64

5.54

9.39

12.8

2 – 1.67 – 65 (p) 2.64 5.75 4.92 25.09 * level 0: Mode 1, 1: Mode 2, 2: Mode 3, f : tail beat frequency, s: shifting phase, p: head segment pressure Data for Mode 1 and Mode 2 are extracted from [15]

4

Discussion

In this research, the soft eel robot was set to operate with one-half body passively. In most states of the conditions (four tail beat frequencies, and eight maximum values of head segment pressure) the eel robot can swim forward except at a frequency of 1.67 Hz with maximum pressure at head segment smaller than 60 kPa (Fig. 3). In case of the only head segment is activated, the body waves start from this active segment and then passively propagate along with the other segments. Thus, for the forward movement, there are two decisive conditions relating to wave propagation feasibility. The first one is the intensity of the wave source that associate with head segment amplitude. The second one is the flexibility of the passive tail depending on the body properties (structure, material). Based on these reasons, the stay still condition of the robot at 1.67 Hz and low pressure at the head segment can be explained due to the low intensity of the wave source (small head segment amplitude). This phenomenon agrees with the experiment results on deciding the bandwidth of the soft actuator [14] when at 1.67 Hz perform the low response (low bending degree) compare to the others at similar conditions. The increment of head segment pressure associate with the increase of wave source intensity, however, after reach the peak at 65 kPa

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the forward speed of the robot decrease despite the rise of pressure. The going down of velocity, in this case, comes from the large lateral movement of the head segment, which partly prevents the forward movement of the robot. 65-0-0

0.83Hz

1.0Hz

Displacement (BL) -0.2 0 0.2

Displacement (BL) -0.2 0 0.2

65-0-0

0

0.2

0.4 0.6 Position (BL)

0

1.0

0.2

0.4 0.6 Position (BL) 65-0-0

0.8

1.0

1.67Hz

Displacement (BL) -0.2 0 0.2

1.25Hz

Displacement (BL) 0 0.2 -0.2

65-0-0

0.8

0

0.2

0.4 0.6 Position (BL)

0.8

1.0

0

0.2

0.4 0.6 Position (BL)

0.8

1.0

Fig. 4. Midline kinematics of the soft eel robot with one-half passive body with head segment maximum pressure of 65 kPa at four different frequencies.

As aforementioned, the efficiency of swimming can be estimated by examining the robot velocity and its corresponding COT. Figure 3 and Table 1 present the correlation between the robot’s forward velocity and its COT. Because of the small differences in energy consumption among operating modes, the rise of the robot velocity mostly results in the decrease of COT (i.e., higher efficiency). Generally, when the robot performs the highest velocity, it also implies its high efficiency in energy consumption and swimming. The robot has the best COT of 9.39 in Mode 3 at a frequency of 1.0 Hz and the maximum pressure of 65 kPa of the head segment, at which the speed is performed at 0.12 BL. On the other hand, the highest velocity is 14.34 cm/s (0.27 BL/s) in Mode 2 at a frequency of 1.0 Hz, and control shifting phase of 40%, however, the COT in this mode is 11.06 larger 15.1% than the case with the best COT. The analysis of the best COT value and the highest velocity of the robot in various operating modes in this paper can be applied for designing similar robots for long-term and long-haul operation tasks.

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In Mode 3, with an uncontrolled middle and tail segment, the robot did not show efficient swimming performance as in the two other modes. At 1.25 Hz, the robot could only swim at 9.39 cm/s which is slower than that of Mode 1 and 2 (9.93 cm/s and 11.74 cm/s, respectively). The body midline’s kinematics in Fig. 4 also supports this claim, since the displacement amplitude of the tail segment in Mode 3 is much smaller compared to the two others [15]. The low tail beat displacement might come from the inertia of the long passive part of the body at a high frequency (in comparison with frequency bandwidth from 0.83 Hz to 1.67 Hz). However, there is a remarkable point at 1.0 Hz (see Fig. 3), at which the robot reaches the forward speed of 12.46 cm/s (0.235 BL/s). From the data of midline kinematic, swimming gait might strongly affect swimming speed. It can be seen from Fig. 4 that the swimming gait of the robot at 1.0 Hz similar to these at 1.25 Hz when swimming in Mode 1 and 2, in which, the robot performs good swimming efficiency. Swimming posture depends not only on working conditions but also on the robot’s body structure properties. This conclusion might pave the way to optimize the swimming efficiency of the robot by examining both working parameters and robot body structure including actuator and backbone structure and material. However, the result in this research also indicated that the working mode is valuable for designing an untethered design of this robot since it consumes the least energy compared with other modes.

5

Conclusion

In this paper, the soft eel robot swimming with the one-half passive body was examined. In this case, the active head segment was considered as wave source and the other body parts play as wave propagation section passively. The experiment data indicated that different from natural anguilliform locomotor and rigid elongated robot body the soft eel robot is able to perform good swimming efficiently (at some conditions even better than a fully-controlled robot). In conclusion, the research on the soft eel robot swimming with a large passive body part (as much as possible) enlarge the robot swimming mode for different kinds of tasks or continuously working when the body damaged partly. In the next work, we plan to investigate on an untethered soft eel robot working with the three modes for inspection, search and surveillance at underwater narrow spaces.

References 1. Das, A., Nabi, M.: A review on soft robotics: modeling, control and applications in human-robot interaction. In: 2019 International Conference on Computing, Communication, and Intelligent Systems (ICCCIS), Greater Noida, India, 2019, pp. 306–311 (2019) 2. Kim, S., Laschi, C., Trimmer, B.: Soft robotics: a bioinspired evolution in robotics. Trends Biotechnol. 31(5), 287–294 (2013) 3. Sfakiotakis, M., Lane, D.M., Bruce, J., Davies, C.: Review of fish swimming modes for aquatic locomotion. IEEE J. Oceanic Eng. 24(2), 237–252 (1999)

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4. Magnuson, J.J.: Locomotion by Scombrid fishes: hydromechanics, morphology and behavior. Fish Physiol. 7, 239–313 (1978) 5. Gemmell, B.J., et al.: How the bending kinematics of swimming lampreys build negative pressure fields for suction thrust. J. Exp. Biol. 219, 3884–3895 (2016) 6. Chen, B., Jiang, H.: Swimming performance of a tensegrity robotic fish. Soft Rob. 6(4), 520–531 (2019) 7. Katzschmann, R.K., DelPreto, J., MacCurdy, R., Rus, D.: Exploration of underwater life with an acoustically controlled soft robotic fish. Sci. Robot. 3(16) (2018) 8. Jusufi, A., Vogt, D.M., Wood, R.J., Lauder, G.V.: Undulatory swimming performance and body stiffness modulation in a soft robotic fish-inspired physical model. Soft Rob. 4(3), 202–210 (2017) 9. Frame, J., Lopez, N., Curet, O., Engeberg, E.D.: Thrust force characterization of free-swimming soft robotic jellyfish. Bioinspirat. Biomimet. 13(6) (2018) 10. Hou, T., et al.: Design and experiments of a squid-like aquatic-aerial vehicle with soft morphing fins and arms. In: International Conference on Robotics and Automation 2019, Montreal, Canada, May 20–24, 2019 (2019) 11. Christianson, C., Goldberg, N.N., Deheyn, D.D., Cai, S., Tolley, M.T.: Translucent soft robots driven by frameless fluid electrode dielectric elastomer actuators. Sci. Robot. 3(17) (2018). eaat1893 12. Feng, H., Sun, Y., Todd, P.A., Lee, H.P.: Body wave generation for anguilliform locomotion using a fiber-reinforced soft fluidic elastomer actuator array toward the development of the eel-inspired underwater soft robot. Soft Robot. 7(2), 233–250 (2020) 13. Nguyen, D.Q., Ho, V.A.: Kinematic evaluation of a series of soft actuators in designing an eel-inspired robot. In: IEEE/SICE International Symposium on System Intergration (SII), January 12–15, 2020. Honolulu, Hawaii, USA (2020) 14. Nguyen, D.Q., Ho, V.A.: Anguilliform swimming performance of an eel-inspired soft robot. Soft Robot. https://doi.org/10.1089/soro.2020.0093 15. Nguyen, D.Q., Ho, V.A.: Evaluation on swimming efficiency of an eel-inspired soft robot with partially damaged body. In: 4th IEEE International Conference on Soft Robotics (RoboSoft), April 2021, Yale University, USA (2021) 16. Crespi, A., Karakasiliotis, K., Guignard, A., Ijpeert, A.J.: Salamandra Robotica II: an amphibious robot to study salamander-like swimming and walking gaits. IEEE Trans. Robot. 29(2), 308–320 (2013) 17. Ramananarivo, S., Godoy-Diana, R., Thiria, B.: Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming. J. Roy. Soc. Interface 10(88) (2013)

Non-assembly Walking Mechanism for Robotic In-Pipe Inspection George H. Jackson-Mills(B) , Basil A. Shead, James R. Collett, Masego Mphake, Nicholas Fry, Andrew R. Barber, Jordan H. Boyle, Robert C. Richardson, Andrew E. Jackson, and Shaun Whitehead Department of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK [email protected]

Abstract. The manufacture and assembly of small-scale robotics can be expensive and time-consuming using traditional methods; especially when complex mechanisms are involved. By refining current additive manufacturing techniques a micro-scale walking robot can be 3D printed without the need for any complex mechanical assembly. The robot requires only the addition of simple circuitry and 2 motors, one for each of the 1 degree of freedom walking mechanisms before it is capable of being driven wirelessly. Once fully assembled, differential drive of the parallel leg sets allows for locomotion in any direction on a 2-D plane. The robot’s compact size; just 62 mm (x) × 38 mm (y) × 88 mm (z), and leg curvature makes travel possible through borehole/pipe diameters as low as 65 mm. By pushing printer tolerances to the limit, complex mechanisms can work in Non-Assembly at a small scale. Through the Query application of these Non-Assembly techniques to field robots such as those intended for use in the Pipebots project could allow for the production of large swarms of robots quickly and affordably. Keywords: Robot · 3D printing · Walking · In-pipe

1 Introduction Pipebots aims to revolutionise buried pipe infrastructure management with the development of micro-robots designed to work in underground pipe networks and dangerous site. This project will include the analysis of both clean and waste water pipelines in systems that cannot readily be accessed by humans without invasive excavation procedures. Small, tight, in-pipe environments are common in aging waste water systems, such as those in Fig. 1 these spaces are well suited to miniature robots. Capable of allowing human pilots remote operative access, in-pipe environments can be inspected safely using robots without invasive, expensive, and environmentally unfriendly excavation procedures. Inspection of these spaces can require different approaches; access points can often vary in size. One specific robot may be unequipped to deal with all eventualities of the mission. For example it may be too large or have the wrong locomotion method. This type of inaccessible environment scenario can commonly be found in waste water pipelines. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 117–128, 2022. https://doi.org/10.1007/978-3-030-86294-7_11

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Fig. 1. Inaccessible environment scenario cutaway with a 100 mm borehole entrance into an open area.

Additive manufacturing (3D printing) allows rapid fabrication of functional robotic parts and has become popular due to the quick turnaround from model to physical prototype. The relative affordability and accessibility of 3D printing vs. traditional subtractive manufacturing methods, has led to the creation of many Non-Assembly mechanical designs. Non-Assembly printable designs work straight off the printing bed as intended with no fasteners, connectors or glue required. Work has been done on the effectiveness of these techniques in respect to robotic part creation [1], and even in Non-Assembly animal models such as moveable joints in a functional 3D printed elephant [2]. These techniques have been applied to create Non-Assembly versions of historical mechanisms such as slider-cranks and ratchets [3]. Even universal joints have been printed as functional Non-Assembly parts out of stainless steel [4]. Cornell University created an untethered 3D-Printed mechanical insect which utilized 3D printed wing structures [5]. Tufts University capitalized on the use of soft material printing to create a soft robot with full steering control based on the caterpillar of the tobacco hawk moth [6]. Robot hands have been fully printed with shape memory alloy actuation [7], and even origami-based methods have been employed to create Non-Assembly medical gripping arms [8]. By applying these Non-Assembly printing techniques, specially adapted robots can be created rapidly from a library of pre-made designs. If these robots could be printed fully assembled off the print bed, a new robot could be produced and deployed in a matter of hours after the addition of actuation and control systems. In a case such as Fig. 1, a small ( 0 and k2 > 0 are positive (friction) coefficients. Investigations of similar mechanical systems in presents of viscous rolling resistance is considered in works [6,7]. The coefficient of friction was determined for the condition of minimizing the deviation of the simulated trajectory from the experimental one, by analogy with the work [8]. The evolution of the configuration variables is governed by the system ˙ v1 sin ϕ(t) + c2 ϕ(t) , ψ˙ = − c1 cos ϕ(t) + c2 v1 sin ϕ(t) + c2 ϕ(t) ˙ x˙ = v1 cos ψ − c1 sin ψ, c1 cos ϕ(t) + c2 v1 sin ϕ(t) + c2 ϕ(t) ˙ y˙ = v1 sin ψ + c1 cos ψ. c1 cos ϕ(t) + c2

(4)

The angle φ(t) between the platforms is used as a control action. In next section, the influence of the mass-inertia parameters of the platforms and the control parameters on the velocity of propulsion of the Roller Racer are considered.

3

Experimental Part

Experimental validation of the proposed model with viscous rolling resistance in case of periodical control action was obtained in [15]. Continuing those studies we consider the prototype of the Roller Racer which allows us to change the mass distribution at each platform or change their axial moments of inertia. The 3D model and fabricated prototype are shown in Fig. 2. The values of the mass-inertia parameters of fabricated prototype used also in simulations are presented in Table 1. As design parameters in this paper we consider the ratio of the axial moments of inertia of the platform J20 /J10 . The mass of the first platform is constant. The mass of second platform is variable by adding loads to the special places located on the second platform. As a control action we use the periodic function: ϕ(t) = α · sin(

2πt ) + ϕ0 , T

(5)

where T is the period of function, α is an amplitude, ϕ0 the vertical of the function shift. For control of the Roller Racer, a control board based on the STM32F303K3C6 microcontroller is developed. To control the angle between of half-frames, a CDS5516 servo drive is used. The servo drive powered by a

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Fig. 2. Prototype the Roller Racer a) 3d model of robot b) picture of prototype with loads Table 1. The values of parameters of Roller Racer Parameter

Value

Maximum amplitude of rotation angle between the platforms ϕ, rad Maximum angular velocity ϕ, ˙ rpm The mass of the first platform (without additional load), kg The mass of the second platform, kg The mass of one load, kg The axial moment of inertia of the first platform I10 (relative to the vertical axis passing through the center of mass of the first platform), kg · m2 The axial moment of inertia of the second platform I20 (relative to the vertical axis passing through the center of mass of the second platform, kg · m2 The distance from the center of mass of the first platform to the point P (c1 − a1 ), m The distance from the center of mass of the second platform to the point P (c2 − a2 ), m Coefficient of viscous friction κ

2.6 30 0.469 0.250 0.066 0.00386

0.00175

0.186 0.0441 0.25

LiPo 2S battery. The servo is connected to the control board via a half-duplex UART. The speed of the serial port of the controller is 1 Mbps, the frequency of updating the status of the servo 250 Hz. The frequency of the update cycle of the robot control system 125 Hz for T = 0.8 s, 67 Hz for T = 1.6 s. There are two types of motion depending on the value of ϕ0 . In case of ϕ0 = 0 the robot moves along a straight line, and if ϕ0 = 0 the trajectory of motion is a curve, which radius is defined by the value of ϕ0 .

Roller Racer

3.1

433

Motion Along a Straight Line

Since the control function has a periodic character the point P oscillates along a trajectory during the robot’s motion. For evaluation of the motion we calculate an average velocity of the Roller Racer over the period of oscillation. The data for calculation of the position and velocity is obtained by the Vicon motion capture system. The capture frequency of the motion capture system 100 Hz, the marker recognition error does not exceed 1 mm.

Fig. 3. A typical graph of the trajectory (a) and the average velocity of movement (b) of the robot. The dashed lines show the speeds obtained experimentally, without taking into account acceleration and deceleration. The solid line shows the average speed of the robot for three experiments with the same initial conditions.

The variability of the average velocity is explained by the influence of manufacturing errors of the robot, non-roughness of the underlying surfaces, etc. [14]. To investigate the theoretical model of the robot’s motion two simulation series were carried out taking into account the mass-inertia parameters of the prototype: 1) the dependence of the average velocity on the ratio of the moments of inertia J20 /J10 for various values of α; 2) the dependence of the average velocity on the amplitude and the period of the control function (5). Each experiment is conducted at least three times. The average speed is calculated as the movement of the point P over the period of the control function T . The statistical analysis of the results consisted of calculating the confidence intervals for the mean-based results. The mean-based results is analysed using the standard equation for 95% confidence level and sample size - 3. For the first experiments the period of the control function was taken T = 1 s, and the values of the amplitude of the rotation of the platform were taken from interval [0; 1.4] by step 0.05. The ratio of axial moments of inertia J20 /J10 was changed by attachment of the additional loads as follows: 0.08; 0.14; 0.17; 0.19; 0.2. Figure 4 shows the results of simulations and experimental investigations with real prototype. The experimental values are marked by the circle. A minor deviation of the experimental values from the theoretical ones confirms the adequacy of the model and its ability to describe the motion by various

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control and inertia parameters. The numerical results of experiments with confidence intervals are shown in the Table 2.

Fig. 4. Average velocity of Roller Racer versus ratio of the moments of inertia and the amplitude of the rotation angle between platforms Table 2. The numerical results for first series of experiments σ J20 /J10 v ± tα,n−1 ∗ √ , m/s vexp , m/s n 0.16 0.1015 ± 0.056 0.1057 0.18

0.1659 ± 0.085

0.1511

0.2

0.2099 ± 0.096

0.1954

In another series of experiments we change the period of control from the interval T = [0.8; 2] s, by step 0.05 and the amplitude α = [0; 1.2] rad by 0.1 rad for the ratio of moments of inertia J20 /J10 = 0.3. The surface of results of the simulation with the experimental data are shown in Fig. 5. The numerical results of experiments with confidence intervals are shown in the Table 3.

Fig. 5. Average velocity of Roller Racer versus period of the control function and the amplitude of the rotation angle between platforms.

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435

Table 3. The numerical results for second series of experiments σ T, s α, rad v ± tα,n−1 ∗ √ , m/s vexp , m/s n 1 0.262 0.0181 ± 0.015 0.027 1

0.524

0.1378 ± 0.046

0.16

1

0.785

0.3473 ± 0.124

0.45

2

0.262

0.0069 ± 0.006

0.011

2

0.524

0.0348 ± 0.024

0.023

2

0.785

0.0536 ± 0.014

0.04

According to the graphs shown in Figs. 5 and 4 we can conclude that the angular velocity of the robot increase when frequency of oscillation 1/T increases as well as the amplitude oscillations increases up to a certain value (about 1 rad, for our prototype). When the value of the amplitude increase more than this value the average velocity decreases first, and then the robot moves in opposite direction. According to the Tables 2 and 3 we can conclude that the simulation results are located within confidence intervals. 3.2

Movement of the Roller Racer Along a Circle

In the case of ϕ0 = 0 the robot moves along a circle. Experiments and simulations were carried out with the same mass-inertia parameters of the prototype as for movement along the straight line and the ratio of moments of inertia was equal 0.3. The values of the ϕ0 = 0 lie within the interval [−π; π]. The trajectories of motion obtained from the experiments and simulations for the values of parameters α = 0.52, T = 1, ϕ0 = [0,0873; 0,174533; 0,261799] are presented in Fig. 6. The experimental data is shown by dashed lines.

Fig. 6. Trajectories of movement with different shift of the control function. Dashed lines present theoretical trajectories. Solid lines present experimental trajectories.

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The sign of the ϕ0 defines the direction of motion. By increasing the value of ϕ0 ∈ [0; π] the radius of curvature of the trajectory of the robot decreases respectively.

4

Conclusions

The paper observed the results of simulations and experimental studies of the Roller Racer. For the developed prototype of the robot, the most optimal control parameters which ensure the maximum average velocity have been found. Combining simple movements along a straight line and a circle trajectories, more complex trajectories can be designed. The results of experiments of the prototype coincide with the results of simulations. In the future, we plan to investigate more detail the curvature of the trajectory from the shift ϕ0 , the amplitude α, the period T and the ratios of moments of inertia J20 /J10 . Acknowledgment. The work of A. A. Kilin (Sect. 2) is carried out in the Ural Mathematical Center. The work of Yefremov K. S. and Karavaev Y. L. (Sect. 3) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (FZZN-2020-0011). The experimental investigations were carried out using the equipment of the Common Use Center of the Udmurt State University.

References 1. Martynenko, Y.G.: Motion control of mobile wheeled robots. J. Math. Sci. (N. Y.) 147(2), 6569–6606 (2007) 2. Bloch, A.: Nonholonomic Mechanics and Control. Springer, Heidelberg, 501p. (2003). https://doi.org/10.1007/b97376 3. Rocard, Y.: L’instabilit´e en m´ecanique: Automobiles, avions, ponts suspendus. Masson, Paris (1954) 4. Bizyaev, I.A.: The inertial motion of a roller racer. Regul. Chaotic Dyn. 22(3), 239–247 (2017) 5. Bizyaev, I.A., Borisov, A.V., Mamaev, I.S.: Exotic dynamics of nonholonomic roller racer with periodic control. Regul. Chaotic Dyn. 23(7–8), 983–994 (2018) 6. Borisov, A.V., Ivanova, T.B., Karavaev, Y.L., Mamaev, I.S.: Theoretical and experimental investigations of the rolling of a ball on a rotating plane (turntable). Eur. J. Phys. 39(6), 065001 (2018) 7. Borisov, A.V., Kilin, A.A., Karavaev, Y.L.: Retrograde motion of a rolling disk. Physics-Uspekhi 60(9), 931–934 (2017) 8. Karavaev, Y.L., Kilin, A.A., Klekovkin, A.V.: The dynamical model of the rolling friction of spherical bodies on a plane without slipping. Russ. J. Nonlinear Dyn. 13(4), 599–609 (2017) 9. Krishnaprasad, P.S., Tsakiris, D.P.: Oscillations, SE (2)-snakes and motion control: a study of the roller racer. Dyn. Syst.: Int. J. 16(4), 347–397 (2001) 10. Fedonyuk, V., Tallapragada, P.: Locomotion of a compliant mechanism with nonholonomic constraints. ASME. J. Mech. Robot. 12, 1–13 (2020). https://doi.org/ 10.1115/1.4046510 11. Bullo, F., Lewis, A.D.: Kinematic controllability and motion planning for the snakeboard. IEEE Trans. Autom. Control 19, 494–498 (2003)

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12. Shammas, E., de Oliveira, M.: Motion planning for the snakeboard. Int. J. Robot. Res. 31(7), 872–885 (2012). https://doi.org/10.1177/0278364912441954 13. Bizyaev, I.A., Borisov, A.V., Mamaev, I.S.: Dynamics of the Chaplygin Sleigh on a cylinder. Regul. Chaotic Dyn. 21(1), 136–146 (2016) 14. Ardentov, A.A., Karavaev, Y.L., Yefremov, K.S.: Euler elasticas for optimal control of the motion of mobile wheeled robots: the problem of experimental realization. Regul. Chaotic Dyn. 24(3), 312–328 (2019). https://doi.org/10.1134/ S1560354719030055 15. Yefremov, K.S., Ivanova, T.B., Kilin, A.A., Karavaev, Y.L.: Theoretical and experimental investigations of the controlled motion of the Roller Racer. In: 2020 International Conference Nonlinearity, Information and Robotics (NIR), pp. 1–5. IEEE (December 2020)

Generation of the Self-motion Manifolds of a Functionally Redundant Robot Using Multi-objective Optimization Ilka Banfield1,2 and Humberto Rodr´ıguez1,2(B) 1

2

Mechanical Engineering Faculty, Universidad Tecnol´ ogica de Panam´ a, Panama City, Panama {ilka.banfield,humberto.rodriguez}@utp.ac.pa LEADS-UTP, Universidad Tecnol´ ogica de Panam´ a, Panama City, Panama http://utp.ac.pa, http://www.leads.utp.ac.pa Abstract. Off-line analysis of path tracking of functionally redundant robot manipulators is essential for effective use of industrial robots. The kinematic redundancy of the robot with respect to specific task can be exploited to optimize a desired criterion. Recently, industrial serial robots of 6 DOF are being widely used for a variety of tasks that only require 5 DOF or less, which is causes functional redundancy. For the case of functional redundancy, where the redundant parameters are within the operational space, once the optimal parameters have been selected, the inverse mapping between the operational space and the joint space often corresponds to a closed solution, which means that there are a finite number of joints configurations. This is the case for the most commonly used non-redundant 6 DoF serial robot manipulators. Moreover, each configuration lies on a specific solution branch into joint space. Due to this characteristic, during the optimization process by means of the Pareto Front technique, a sufficiently diverse set of Pareto Optimum points is not obtained to ensure that a solution close to the best combination of the multiple objectives can be found for a global optimization of the robot path. To overcome this difficulty, in this work, the Pareto Front is used to determine the topology of the selfmotions generated by redundancy and from these to identify the invertible subregions between the operational space and the configuration space. Multi-Objective Genetic Algorithms, MOGA, is used to solve the Inverse Kinematics (IK) for global optimization of functionally redundant robots, for incomplete orientation constrained task. Keywords: Kinematic redundancy · Functional redundancy kinematic · Manifolds · Self-motions · MOGA

1

· Inverse

Introduction

Most non-redundant industrial robot manipulators have 6 degrees of freedom (DoF). However, in many cases 6-DoF is insufficient due to the limited dexterity c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 438–452, 2022. https://doi.org/10.1007/978-3-030-86294-7_39

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that the workspace provides, so it is usual for the robot structure to be augmented with additional degrees of freedom [1,2], which leads to the dimension of the robot configuration space, dim(C) = n, higher than the operational space dim(O) = m, which corresponds to an intrinsic redundancy condition [3]. On the other hand, even though many industrial relevant tasks only require 5-DoF or less, kinematics problem of functionally redundant robots performing tasks with five o less DoF has drawn much less attention than that of intrinsically redundant robots [4]. Functional redundancy is defined as a robot operational space dimension dim(O), being higher than the task space dimension dim(T ) = t. Some industrial task examples include welding [5], drilling [6], milling [7], machining [8], laser cutting [9], spray painting [10], and additive manufacturing [11]. For example, milling tasks require 5-DoF and are typically performed by 6-DoF manipulators. Redundancy resolution analysis of redundant robots can be categorized into two groups: solutions in the velocity domain, and solutions in the position domain [12,13]. In the first group, the instantaneous inverse solution is sought in the linearized velocity domain with use of the Jacobian matrix [3]. In the first group, the most popular approach consists on finding the instantaneous inverse solution in the linearized velocity domain with use of the Jacobian matrix [14]. However, for functional redundant robots the unused DoFs cannot be mapped into the null space of the Jacobian matrix, therefore modifications to the traditional methods have been presented [15]. Huo et al. [3] proposed a twist composition algorithm for reducing the task space by orthogonal decomposition of the end effector twist. Baron et al. [16], in-stead, proposed augmenting the joint space by virtually inserting an additional joint. Other method for the resolution of the functional redundancy are based on the optimization. The optimization can be performed by evaluating the index function on a range of rotation angles around the tool axis [17] or by using the incremental change of the rotation around the tool axis directly to adapt the joint angles [14]. The optimization process can be implemented in the position domain also. Metaheuristics optimization methods such as ant colony optimization, swarm particle optimization and genetic algorithm have also been also used [18]. This approach does not require of inversion of the Jacobian matrix, so any problem related to the matrix inversion is overcome. This document proposes the resolution of functional redundancy by determining the feasible population that provides an overview of the configuration space and its relationship with the operating space, through the exploration of self-motion topology. The objective is the solution of the inverse kinematic problem, in order to implement global optimization approaches. The IK problem is PSPACE-hard [19], highly non-linear and with constraints, which make the feasible subset of the configuration space disconnected. Also, it is surjective but not necessarily injective. These characteristics are the cause of IK cannot be solved in a closed-form expression (in general). However, methods have been developed to model and solve inverse kinematics problems. The most flexible of these methods typically rely on iterative optimization to seek out an

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approximate solution. Several metaheuristic approaches have been proposed to deal with the complexity issue in optimization problems and the methods of solution is supported by a self-organized search in variable space (C-space), as dense as the size of the initial population. This paper proposed selected set of redundant parameters and then solving, for each redundant joint value, a nonredundant IK problem for the remaining joints, using NSGA II. The Non-Sorting Genetic Algorithm (NSGA II) [20] was selected due to the characteristics of the method to address multiobjective optimization problems using Pareto Front. Other works that aims is the kinetic control of redundant robots by exploring self-motion topology are based on the random sampling of joint configurations for discretized end effector poses, [21,22]. This approach generates trees of nodes and edges, where the nodes are the configurations and the edges correspond to two adjacent poses of end effector’s robot. The disadvantage of these methods is that they can not generate dense uniformly spaced samples on the self-motion manifolds due to singularities. In this paper, the kinematic mapping for functionally redundant robot is analyzed from the geometric standpoint generated using Multioptimization Genetic Algorithm (MOGA). Through this approach, the set of feasible solutions related to the objective functions is obtained, which allows some definition of the manifolds related to redundancy and selection of the best compromise between optimization objectives. The latter is the main contribution of this work. In addition, it is discussed in this work that when solving the redundancy problem, the geometric analysis provides a better perspective of the problem, which allows an effective selection of the objective functions that are optimized, the initial search configurations and even the most appropriated search methods.

2

IK of Incomplete Orientation Constraints in a Serial Robot

The non-uniqueness of solution to IK problem occurs for both, redundant and nonredundant serial robots and its manifestations are both, local and global. The IK mapping of a particular pose of the operational space, consist of a finite number of distinct sets of configurations, each set being a manifold in the configuration space, C-space, of dimensionality ri = n − m [3]. However, the above description corresponds only to the definition of intrinsic redundancy. When the orientation in the operational space is not completely restricted, the redundant dimension rf = m − t, appears into the operational space. In this case, as in intrinsic case, there are also an infinite number of solutions to the IK, and these solutions can be grouped into a finite and bounded set of disjoint continuous manifolds, but each pose of redundant manifold maps globally to a finite number, many to one and locally one to one [23], as IK solutions of non-redundant robot, as shown in Fig. 1 The exact number of inverse solution branches or set of configurations depends on several factors including the task space topology and geometry. Several branches correspond to each pose on the path in the O-space. However, the

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(a) Functional Redundancy.

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(b) Intrinsical Redundancy.

Fig. 1. The forward (FK) and inverse (IK) kinematic mapping. (a) Functional redundancy where the local inverse mapping is from one pose to one configuration. (b) Intrinsic redundancy with a local inverse mapping from one pose to infinite configurations.

number always is finite and relatively small [24]. Common industrial designs with 6-DoF have at maximum eight (8) solutions of IK and the maximum number of solutions for a general 6-DoF serial robot is sixteen (16) [25]. To solve the IK of intrinsically redundant robots, these are reduced to nonredundant ones by selecting a set of joints, denoted as redundant joints, and their joint variables are parameterized [26]. Once these joints have been identified, several analytical closed-form methods can be applied to non-redundant serial robots. The selection of the redundant variable is relatively simple when there are unconstrained orientations in the task space, which is a common case of functional redundancy. The parametrization of the unconstrained orientations and the subsequent solution of the IK allows to obtain the discretized map of the workspace in orientation for the task and the sets of configurations with the optimal values of some performance indices relative to the task. 2.1

Kinematical Redundancy and Self Motion

The topological structure of the redundant robot kinematics problem shows that the one-to-one inverse map between the set of solution branches and the discretized set of redundant parameters leads to effective methods to approximate the IK function. It also gives us the option of optimizing the performance of the robot’s task with its restrictions under a generalized framework that avoids tailored solutions. In this section concepts related to about topology are briefly reviewed. Readers may refer to [23–26] for detailed definitions and proofs. The C-space, of a n-revolute joint serial robot, n − R manipulator, is a product space formed by n-times product of the individual joint manifold, that results in a compact manifold n-torus, T n as follows, C = S 1S 1 . . . S 1 = T n

(1)

The Figs. 2(a) and 2(b) show a 2-torus configuration space of 2 − R planar manipulator, The 2-torus is usually defined as the quotient space of the unit

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Fig. 2. The Two-link Planar Manipulator and the 2-torus configuration space

square as shown in Fig. 2(c). This transformation is useful for a 3-torus configuration space that cannot be directly visualized in 3-dimensional space, but it is possible to describe the 3-torus as a quotient space of 3-dimensional space, R3 . Since the forward kinematics function is a smooth function which maps C, a compact manifold, O, the solution of IK of a redundant serial robot for a reachable pose, must be an r-dimensional sub-manifold in C. However, the sub-manifold may be divided into more than one disjoint manifold. These rdimensional sub-manifold in the inverse kinematics solution is defined as selfmotion manifold [24]. A self-motion is the subspace described by the continuous motion of a serial robot which leaves end-effector motion less. Each self-motion can be parametrized by a set of r independent parameters γ = {γ1 , γ2 , . . . , γr }. An n-revolute joint redundant manipulator does not have no more selfmotions than the maximum number of IK solutions of a non-redundant of the same class. Consider a 3 − R planar manipulator redundant with joint coordinates, T T q = [q1 , q2 , q3 ] , and end effector position and orientation xee = [x, y, ψ] , 3 in R . The task requires to constrain x and y, therefore the orientation ψ is the redundant parameter. The self-motions of the 3 − R planar manipulator are determined using the IK solution for a set of discrete values of the parameter ψ, in its feasible range, [−π, π]. There are two possible sets of joint angles, which physically correspond to “elbow down” and “elbow up” self-motions. The Fig. 3 shows self-motions manifolds for a radial path with five equidistant points. The inverse map of points A, B and C, Fig. 3(b), produce two continuous branches each, or disjoint self-motions manifolds that correspond with “elbow down” and “elbow up” of sub-chain 2 − R of the 3 − R manipulator for the same complete end effector pose, see Fig. 3(c). Also, the points D and E produce two

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(b)

(a)

(c)

(d)

Fig. 3. The Three-link Planar Manipulator, l1 = l2 = 1.0 y l3 = 0.5 (a) Straight line path P = [0.5 : 0.25 : 1.5], configurations optimized with joint limited in ±1.2π (b) Self-motions generates for each pose and redundant parameter ψ in Quotient space of 3-dimensional space R3 (c) “Elbow down” and “elbow up” sets of configurations. (d) Discontinues in generation of self-motions.

disjoint manifolds each, separated by the two discontinuities, where the sub-chain 2 − R is in singularity, often denoted as a constraint singularity, see Fig. 3(d). On both case the value of q2 = 0, that is, the first two links are collinear. The IK of each position of the path P are one dimensional self-motions diffeomorphic to the circle, S 1 , but the points D and E mapping, does not contain a 2π rotation of the redundant parameter ψ. The manifolds are both, the C-space and the O-space are differentiable manifolds, and the mapping between them is smooth (infinitely differentiable).

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Population 1

Population 2

Objetive Space

Mapping from Parameter Space to Objetive Space

Population 3

Pareto Optimal Front

Fig. 4. Decision variable space to Objective functions space mapping. The solutions that lie in the Pareto Front are the IK solutions for each pose corresponding to the value of the redundancy parameter.

3

Topology of Kinematic Map Using MOGA

Multi Objective Evolutionary Algorithms (MOEA) have become one of the mainstream algorithms for solving multi-objective optimization problems and are very suitable for solving IK problems [12]. The goal of these evolutionary algorithms is the Pareto Front, the surface on which the set of non-dominated solutions lies. This work uses the robot configurations that generate the Pareto Front, which corresponds to the sets of optimal solutions from in inverse mapping of the range of feasible values of the redundant parameter, Fig. 4. The search for the optimum is carried out for each feasible value of the redundant parameter, therefore the search space is circumscribed only by a finite number of solutions to the IK of the robot. The result is a framework to represent global features of the kinematic map for a redundant manipulator. The MOGA approach is presented as a general global framework for solving IK using a densely sample the self-motion. Also easy to implement in the sense that it only requires a proper constraint formulation of the problem and allows the easy inclusion of all kinds of restrictions in the workspace and the configuration space. In particular, the NSGA II, is a method with characteristics of a non-dominated and diverse selection, which guarantees the exploration of the domain, and the determination of the solutions in each self-motions manifolds. The adequate selection of objectives and the diversity preservation developed in the NSGA II algorithm, allows to configure the search for the feasible and finite IK solutions.

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3.1

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Generation of Self-motions

Consider the 3 − R redundant manipulator previously analyzed. The joint T coordinates are q = [q1 , q2 , q3 ] ; end effector position and orientation are T T xee = [x, y, ψ] , in R3 , and the task space coordinates are xt = [x, y] , and the redundant dimension is one, rf = m − t = 3 − 2 = 1. One comparative approach for the generation of self-motion manifolds is the solution of the following set of non-linear Eqs. 2, [22], f (q, xt ) = 0

(2)

First, the serial chain is reduced to non-redundant one and the redundant parameter in C-space, q3 , is swept. Then it is discretized, clustered and mapped. This work proposes to solve the following the multicriteria optimization problem: minimize (f1 (q), f2 (q), . . . , fk (q)) q

subject to

f (q, xt ) = 0,

(3)

qj− ≤ qj ≤ qj+ for j = 1, 2, . . . , n where f1 (q), f2 (q), . . . , fk (q) are the objectives functions or performances indices, f (q, xt ) = 0, is the IK of a non-redundant robot and qj− ≤ qj ≤ qj+ are n-constraints joint limits. The natural parameter redundant parameter in T O-space, ψ, is swepted, then is defined each xee = [x, y, ψ] as points of a path where x and y are constant. 3.2

Objective Functions

For the purposes of this study, the selection of objectives is important not only to achieve the best performance of any given task, but also to achieve a set of representative solutions for each disjoint continuous manifold in the C-space. Robotic drilling is a good example of an industrial task where a point to point motion is required. Due to the symmetry axis of the rotating drill, this orientation is unconstrained. When the robot approaches to a singularity, jerking movement of the joint may occur, and the accuracy decreases [27], hence avoiding singularity is essential. Manipulability index [28], and joint limit avoidance, were proposed in this work as performance indexes. Since additional task requirements are a smooth and continuous motion in the C-space and in the O-space, another criteria was considered: the 2-norm of angular joint displacements. Finally, to obtain the limits of the disjoint self-motion manifolds, the objective of avoiding the limits of the joints is used. The values of the objective functions obtained from the Pareto Front are optimal values, however, the three objectives considered are maximized and minimized in two combinations and in two stages of the optimization process.

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Manipulability. Yosikawa’s manipulability index for non-redundant robot is used in this work, (4) f1 = μ = |det(J(q))| where, J is the Jacobian matrix and q is the generalized coordinates vector. This performance index takes advantage of the global search to ensure that the disjoints self-motion manifolds and singularity free sub-spaces are obtained. Avoiding Joints Limits. For joint limit criteria, when the angle value of the joint is close to limits, the objective value is close to one and, when the angle is in the middle of the range, the objective value is zero. Therefore, the objective function is as follows,  2 (qi− +qi+ ) n q −  i 2 1 f2 =  2 n i=1 (qi− +qi+ ) − − q i 2

for i = 1, 2, . . . n

(5)

Similarly, to the manipulability index, the character of this objective function is glob-al and strengthens the search in this sense and in a different way than the index of manipulability. Furthermore, by maximizing this objective we can determine the limit values of each disjoint self-motion manifold. 2-Norm of Joint Displacement. The 2-norm of the displacement is used in this work as an optimization objective, which does not propose smoothness directly, but rather looks for the shortest stroke in joint displacements. It is a solution that avoids large changes in the robot configuration. To implement the minimization of joint displacement, the function is as follows, f3 = qi − qi−1 

(6)

The 2-norm of the displacement objective allows for the definition of one disjoint self-motion, because a local and differentiable search, allows the complete generation of a manifold. However, considering that the generation in term of this target is a function of the initial search configuration and that the IK function is a local difeomorphism [26], and therefore the self-motion manifolds must be locally difeomorphic to the redundant space, the generation of configurations far from optimal solutions is encouraged. But it is important to highlight that, the exact global geometry of manifolds depends on several factors. As mentioned above, optimization is carried out in two stages. The first stage is the search for solutions that maximizes manipulability, maximizes the distance to the joint limits and y minimizes the norm of joint displacements. In the second stage, the manipulability and the distance to the joints limits are mini-mized, while the norm of the joints displacement is maximized. The second stage ensures that less favorable options are found, but that nonetheless they can offer a better overall compromise of the objectives.

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Fig. 5. Self-motion manifold of 3−R manipulator in P trajectory in a) generated using IK analytical model, b) using MOGA. c) Two disjoint manifolds of the x = 1.5 and y = 1.5 generate only maximization of function 2-norm of angular displacements, f3 d) The same two disjoint but it is adding the manifold generated with minimization of objective function, f3 .

3.3

3 − R Planar Manipulator Self-motions Generated with MOGA

In Sect. 3.1 the path and the discretization of ψ was defined for a 3 − R manipulator. The optimization was carried out with a NSGA II algorithm under the following configuration parameters: Initial population of 600 to obtain a dense resolution of solutions, e−10 optimality tolerances, heuristic crossover function with radio = 2, phenotype distance crowding. By selecting these parameters, the goal is to obtain diversity in the variable space. The Fig. 5 shows the generations of self-motion manifold with IK, Fig. 5(a) has a density of 260642 different configurations in a cube bounded by the joint limits. MOGA generations, in Fig. 5(b) has 1004027 different configurations, approximately. Also, the definition of the boundaries of disjoint manifold is more precise with MOGA, which guarantees better results for subsequent clustering. The use of minimum and maximum values of objectives must be analyzed for

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Denavit-Hartenberg Parameters of NACHI MZ04 Joint

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Fig. 6. NACHI MZ04 model robot, Denavit-Hartenberg parameters, and values of limits of joints.

improves the results. The maxf3 , produces solutions of both disjoint manifolds, as shown in Fig. 5(c), however minf3 generates solutions in one disjoint manifold where the initial configuration of the optimization process is located, as shown in Fig. 5(d), the red circles are solutions of minf3 and the blue circles are solutions of maxf3 .

4

Analysis, Modeling and Optimization with NACHI Robot

In this section, a 6-DoF NACHI MZ04, industrial robot is used, (see Fig. 6. The case where the application does not require control of the angle of rotation around the tool is studied. The tool is symmetrical with respect to the tool axis. Most of the examples of industrial applications correspond to this case. Moreover, two types of motions are necessary to execute the task, a continuous and smooth path and other point to point path. T The NACHI robot joint vector in C-space is q = [q1 , q2 , q3 , q4 , q5 , q6 ] . The T end effector vector in O-space is xee = [x, y, z, φ, θ, ψ] and the task vector T in T -space is xt = [x, y, z, φ, θ] , therefore the redundancy is one dimensional. The parameters shown in Fig. 6 are used for kinematic modelling of the robot. Homogeneous transformations, bn T = b T1 1 T2 . . . n−1 Tn are commonly used to

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define of the kinematics model, where n is the number of links, Ti is the link transformation of the ith joint frame with respect to the i − 1th joint frame, and b n T is the homogeneous transformation of n-joint (end-effector) relative to the base frame. The NACHI MZ04 is modeled as an articulated arm with spherical wrist. The positions of its wrist axis intersection are determined by the first three joints, q1 , q2 , q3 and the IK has a closed-form with eight (8) different solutions. For a spherical wrist robot, due the frames of the last three joints q4 , q5 , q6 , intersect the same point, its non-redundant Jacobian matrix can be expressed as follow,   J00 03×3 (7) J= J10 J11 Since the redundancy parameter is orientation and this space is used to optimize performance, we can define the manipulability index as follow, f1 = |detJ11 (q)|

(8)

where J1 1 is the sub-matrix that refers to angular velocities. Because the analysis can be sectioned into the translational motion and the rotational motion, in spherical wrist robot, it is possible to visualize the selfmotions of the last three joints where the self-motion manifolds related with redundancy are generated. The trajectory is P (t) = [0.5, t, 0.5 + t] and the tool orientation is expected to be always perpendicular to the surface of the object. The orientation constrain is the axis of rotation tˆ = [1, 0, 0] with respect to the inertial frame. For the selfmotion generation, three (3) equidistant points from the path P (t) are selected, T T T p1 = [0.5, 0.1, 0.6] , p2 = [0.5, 0.0, 0.5] and p3 = [0.5, −0.1, 0.4] meters. Then, the rotation matrix is defined as, ⎛ ⎞ 0 0 1 R(ψ) = ⎝cos(ψ) −sin(ψ) 0⎠ (9) sin(ψ) cos(ψ) 0 where the swept in redundant orientation is ψ = [−π, π] radians. The Fig. 7(a) shows a 3D view of the different self-motion manifolds of the three points of the path. In the other two figures, Fig. 7(b) y Fig. 7(c), plane views, the manifolds appear continuous, but they are in fact discontinuous due to singularities, mostly due to joint boundaries. However, these views present the continuous form of the manifolds for unlimited joints. Only the point T p1 = [0.5, 0.1, 0.6] , has a degenerative critical point corresponding to wrist singularity.

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(a) Pose

(b)

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(c)

Fig. 7. NACHI MZ04 with incomplete constrained orientation in the red circles. a) 3D view of self-motion manifolds for 3 positions of the path. b) q4 − q5 plane view and c) q5 − q6 plane view. Each branch has two colors because of two step of search of set of solutions.

5

Conclusion

A method to obtain the self-motion manifolds for functional redundant robots has been presented. The method consists of using multi-objective optimization genetic algorithm to solve the inverse kinematics for the robot. The Pareto Front values of the multiobjective optimization are used to visualize the self-motion manifolds at each point of the operational space. The main advantage of the proposed method is that it can be applied to any robot structure, redundant or not, as long as the necessary constraints are considered. The collected data may find multiple possible applications, such as deep learning, control, design optimization, and global optimization of a trajectory by using other objective functions. On the other hand, the method has had the disadvantage of being time-consuming. The computation time used to collect the data is a function of the required density. In addition, the objective functions used to generate the self-motion manifolds must be carefully selected so that the topology is well defined. Future work will be the use of the data for a global optimization of the trajectory with parallel acceleration of search algorithm.

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17. Farouki, R., Shiqiao, L.: Optimal tool orientation control for 5-axis CNC milling with ball-end cutters. Comput. Aided Geom. Des. 30, 226–239 (2013). https://doi. org/10.1016/j.cagd.2012.11.003 18. Rokbani, N., Alimi, A.M.: Inverse kinematics using particle swarm optimization, a statistical analysis. Procedia Eng. 64, 1602–1611 (2013). https://doi.org/10.1016/ j.proeng.2013.09.242 19. Madhav, M., Harry, I., Richard, S., Venkatesh, V.: Approximation algorithms for PSPACE-hard hierarchically and periodically specified problems. SIAM J. Comput. 27, 1237–1261 (1998). https://doi.org/10.1137/S0097539795285254 20. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017 21. L¨ uck, C.L.: Self-motion representation and global path planning optimization for redundant manipulators through topology-based discretization. J. Intell. Robot. Syst. 19, 23–38 (1997). https://doi.org/10.1023/A:1007989214364 22. Peidr´ o, A., Reinoso, O., Gil, A., Mar´ın, J.M., Pay´ a, L.: A method based on the vanishing of self-motion manifolds to determine the collision-free workspace of redundant robots. Mech. Mach. Theory 128, 84–109 (2018). https://doi.org/10. 1016/j.mechmachtheory.2018.05.013 23. Demers, D.E.: Learning to invert many-to-one mappings. Ph.D. thesis. University of California at San Diego, La Jolla, CA, USA (1993) 24. DeMers, D., Kreutz-Delgado, K.: Issues in learning global properties of the robot kinematic mapping. In: Proceedings of the 1993 IEEE International Conference on Robotics and Automation, pp. 205–212 (1993). https://doi.org/10.1109/ROBOT. 1993.291984 25. DeMers, D., Kreutz-Delgado, K.: Canonically parameterized families of inverse kinematic functions for redundant manipulators. In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation, pp. 1881–1886 (1994). https://doi.org/10.1109/ROBOT.1994.351187 26. DeMers, D., Kreutz-Delgado, K.: Inverse kinematics of dextrous manipulators. In: Neural Systems for Robotics, pp. 75–116 (2012). https://doi.org/10.1016/B978-008-092509-7.50008-7 27. Wenlei, X., Henning, S., Torsten, L., Hans-Werner, H., J¨ urgen, H.: Closed-form inverse kinematics of 6R milling robot with singularity avoidance. Prod. Eng. 5, 103–110 (2011). https://doi.org/10.1007/s11740-010-0283-9 28. Yoshikawa, T.: Manipulability of robotic mechanisms. Int. J. Robot. Res. 4(2), 3–9 (1985). https://doi.org/10.1177/027836498500400201

Section–10: Wearable Devices and Assistive Robotics

Evaluation Method of Gait Motion of a Patient Received Total Knee Arthroplasty Using Correlation Between Measurement Data and Evaluation Score Koji Makino1(B) , Masahiro Nakamura2 , Ryo Hagihara1 , Hidenori Omori2 , Yoshinobu Hanagata2 , Kohei Shirataki2 , Shohei Ueda2 , and Hidetsugu Terada1 1

2

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Abstract. It is important to evaluate a gait motion in a walking rehabilitation using the simple method. This paper describes the relation between the measurement of the gait motion of the patient received Total Hip Arthroplasty (THA) and the evaluation score by the physical therapist based of the implicit knowledge. And the evaluation method using the correlation coefficient is proposed newly. The evaluation score by the physical therapist is recorded using the check sheet, and the gait motion of the patient is measured using our developed three-dimensional measurement system. The correlation coefficient between the measurement data and the evaluation score is calculated. We confirm that the multiplication between the measurement data and the correlation coefficient is useful to evaluation of the condition of the gait motion. Keywords: Gait motion

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Introduction

One of the reasons that the elderly person becomes bedridden is disorder of the leg. To prevent it, they are often given a surgery of a hip joint, a knee joint, a lumbus joint and etc. Total Hip Arthroplasty (THA) is a surgical operation to replace the hip joint to the artificial joint as shown in Fig. 1, and it is effective to improve the condition [1,2]. The number of the patients receiving the surgery of THA is over 30 thousand in 2017 in Japan, and is increased every year [3]. The patients should receive rehabilitation for walking to reform the gait motion, since they have a habit in undesirable gait motion before the surgery. The other joints of the leg become damage, if the patient walks in undesirable gait motion. To perform the effective rehabilitation, it is important to evaluate the condition of the gait motion of the patient, properly. There are many studies and many measurement devices to evaluate the condition. To evaluate the condition, it is necessary to observe the motion of the c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 455–464, 2022. https://doi.org/10.1007/978-3-030-86294-7_40

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(a) before a surgery (b) after a surgery

Fig. 1. A X-ray photographs of Total Hip Arthroplasty (THA).

patients. For example, a VICON, a force plate, some high speed cameras and etc. [4,5] are widely used to represent the gait motion by the highly accurate and reliable numerical information. The gait motion have been evaluated by a lot of studies [6–9] using various measurement devices. And, there are some studies of the gait motion of the patients of THA [10–13]. It is difficult to evaluate the gait motion, since the gait motion includes the many factors. In the fact, the physical therapist often analyzes and evaluates the condition of the patient based on the implicit knowledge, since complex and continuous factors are included in the walking. We studies the analysis of the implicit knowledge of walking after the surgery of Total Knee Arthroplasty [14–16]. In this paper, the evaluation method of the gait motion of the patient that receives the surgery of THA is proposed based on the implicit knowledge of the physical therapist. The reason to limit to the THA is to simplify the problem, and to removal the complex factors. First, to consider the implicit knowledge of the physical therapist in the gait motion, the subjective evaluation using the numerical score is performed in Sect. 2. And it is shown that the evaluation score is related with the period from the days that the patient receives the surgery. Second, the relation between the gait motion and the period of the hospitalization is investigated using measurement of some position at leg and hip using our developed three–dimensional measurement devise in Sect. 3. Next, the correlation between the measurement data and evaluation score is investigated, and the valuation method using the correlation is proposed newly in Sect. 4. Section 5 is conclusion.

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There are two methods to evaluate the gait motion; a quantitative method and a qualitative method. First, the quantitative method is shown. The patient walks 10 m, and the number of the steps and the interval time are measured. It is known as the ten meters walking test. The walking ability can be measured, however the condition of the patient after the surgery of THA may not be expressed. Second, the qualitative method is explained. The doctor and the physical therapist evaluate the gait motion by the visual observation, and the evaluation is based on the implicit knowledge.

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The evaluation using the score is introduced to find out the points for evaluation of the gait motion in this paper. The eight items that are decided by the discussion of the doctor and the physical therapists that are cooperated with our experiments are shown in Fig. 2. The score of each item is checked among the number from 1 to 10. And the score of 7 means that the patient obtains the walking ability that is enough to discharge from the hospital. The physical therapist evaluates each item, subjectively. walking ability enough to discharge from the hospital

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every weeks later after the surgery. The score of each patient is shown in Fig. 3. The scores on one week later after the surgery become lower than the scores before the surgery, temporary. After that, the scores become higher if the days are passed.

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The physical therapist observes the gait motion of the patient, and evaluates the condition. Therefore, we guess that the condition can be evaluated using the movie camera images, since the motion contains the factors for the evaluation. First, the measurement system is described. In the measurement system, the patient walks on the flat floor using the walking caster as shown in Fig. 4. The markers are attached to the leg and the trochanter major as shown in Fig. 4(a) to calculate the position in three–dimensional space using two cameras or more. The gait motion of the patient is recorded by eight cameras as shown in Fig. 4(b). The reason using more than two cameras is to prevent from occlusion problems.

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Next, the subjective score of gait motion is described. The physical therapists guess that the motions of pelvis are related with the condition of the gait motion. The four kinds of the motions of the pelvis is measured on as shown in Fig. 5; lateral movement, declination, horizontal fluctuation, longitudinal inclination.

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And two kinds of the leg motions also are addressed to investigate the motion of the hip joint as shown in Fig. 6 : flexion, extension, adduction (Add), abduction (Abd). Here, flexion means the maximum angle of the hip joint as shown in Fig. 6(a). And extension means the angle when the patients stretches the leg to front direction as shown in Fig. 6(b). The patients cannot stretch the leg completely because of pain and /or habit of walking, though the healthy subject can stretch it completely in general. Adduction and abduction as shown in Fig. 6(c),(d) are the maximum angle in swing phase and the minimum angle in stance phase, respectively. The patient often swings the leg to inner direction. The physical therapists know that these motions often occur based on the implicit knowledge, however it is unclear whether the prediction is correct or not.

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Some examples of the result of the measurement is illustrated. Figure 7(a) show the time sequence data of the angle of longitudinal inclination after 1 week and 3 weeks. The difference of the angle are approximate 20◦ and 16◦ respectively. Figure 7(b) show the time sequence data of the angle of extension of each leg. The difference of the angle are about 25◦ and 28◦ , respectively. In this paper, the values of the measurement are not read exactly, and rough values are used. The reason is that the patients cannot walk at constant cycle and many times, since they feel the pain. In following discussion, the rough values are adapted. Finally, to analyze the trend of the condition of the gait motion of each patient, each measurement value of the item evaluated by the physical therapist at every measurement day are illustrated. Figure 8 shows the data of each patient. In the desirable trend, the measurement values increase if the week is passed. However, almost items are not corresponding with the desirable trend. It is clear that the condition of the gait motion cannot be expressed by only one item, and that the physical therapist evaluates it using combination of some data.

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In Sect. 2, it is shown that the evaluation of the physical therapist is according with the desirable trend. On the other hand, in Sect. 3, it is shown that the measurement values obtained using movie camera images are not related with

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the period in the hospital. However, we assume that some measurement values are correlated with the evaluation of the physical therapist. The correlation between the measurement values and the evaluation of the physical therapist is analyzed, first. Second, the high correlation coefficients are selected, and the new values to evaluate the condition of the gait motion is proposed.

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All correlation coefficients between the measurement values and the evaluation scores are shown in Fig. 9. The items of the very strong correlation (over 0.7 or under −0.7) is expressed as pink cell in the table. And items of the strong and weak correlation (over 0.4 or under −0.4 and over 0.3 or under −0.2) are expressed as yellow and blue cells, respectively.

Fig. 9. All correlation coefficients between the measurement values and the evaluation scores.

First, the pink cells (very strong correlation) are focused on. We analyze following factors: – There are many cells in items of declination and flexion of affected side. – There are some cells in item of extension of affected side. – There are not cells in items of lateral movement, longitudinal inclination, and Add & Abd . It is clear that the items of declination and extension and flexion of affected side are related with the evaluation of the physical therapist. The measurement results of the three items are shown in Fig. 10 that is a part of Fig. 8. These graphs have the desirable trend though the same values are expressed. However, it is difficult to evaluate the condition of the gait motion, since the difference of the items on each day is small. Second, the leg motions (lateral movement, longitudinal inclination, and Add & Abd) are addressed. All items are weak correlation or no correlation. Especially, it is a surprise result since the physical therapists guess that Add & Abd are related with the condition of the gait motion of the patient before the surgery of THA. Therefore, the unexpected results were obtained. This is a part of implicit knowledge.

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The correlation coefficient expresses the relation between the measurement data and the evaluation score. We assume that there is relation between the correlation coefficient and importance of the measurement item. First, multiplication between each item and each correlation coefficient is calculated as shown in Fig. 11

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On the other hand, the average of three items using correlation coefficient as shown in Fig. 11 are shown in Fig. 12(b). In the case of usage of the correlation coefficient, the desirable trend is obtained after the surgery. We confirm that the multiplication between the measurement data and the correlation coefficient is useful to evaluation of the condition of the gait motion. Furthermore, the condition of the gait motion of the patient before the surgery are worst if this evaluation is used. On the other hand, the evaluation of the physical therapist is not bad, rather is better as shown in Sect. 2. We discuss the difference. We guess that the evaluation of the condition of the patient before the surgery by the physical therapist is influenced by the completely different items that are used in this paper. For example, the pain of the patient before the surgery is small, and the walking motion is smooth though the motion is not desirable. In case that the motion of pelvis and the hip joint are focused on, the condition of the patient before the surgery may be worse than the condition after the surgery in fact. If this hypothesis is right, the result is useful to developed the automatic evaluation system.

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This paper describes the relation between the measurement of the gait motion of the patient received Total Hip Arthroplasty (THA) and the evaluation score by the physical therapist based on the implicit knowledge, and proposes the new evaluation method using the correlation coefficient. First, the evaluation of the gait motion by the physical therapist is shown. Especially, the subjective evaluation of the physical therapist based on the implicit knowledge is addressed. And, the evaluation score is employed to investigate the relation between the evaluation of the physical therapist and the measurement data. We confirm that the score becomes higher if the days are passed. Second, the measurement system to measure the three–dimensional positions of leg and hip is described. In this system, some motions of the hip and leg are analyzed. However, the almost measurement data are not corresponding with the evaluation score. Third, all correlation coefficients between the measurement values and evaluation scores are considered. It is clear that the data of declination, extension and flexion is related with the evaluation of the physical therapist. However, the unexpected results were obtained though the physical therapists guess that adduction and abduction are related with the condition of the gait motion of the patient before the surgery of THA. We think that this result is a one of the implicit knowledges. And, the multiplication between the measurement values such that each item and each correlation coefficient is calculated, and three data of high correlation coefficient are averaged. As a result, we confirm that the multiplication is useful to evaluation of the condition of the gait motion. Furthermore, the condition of the gait motion of the patient before the surgery are worst if this evaluation is used. The pain of the patient before the surgery is small, and the walking motion is smooth though the motion is not desirable. Therefore, the evaluation score may become good. We guess that the condition of the patient before the

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surgery may be worse than the condition after the surgery in fact in case of focusing on the motion of only hip joint. The result is useful to developed the automatic evaluation system, if this hypothesis is right. In the future works, the hypothesis will be verified using a lot of clinical data. And the automatic evaluation system will be developed.

References 1. McKee, G.K., Watson-Farrar, J.: Replacement of artiritic hips by the McKee-Farrar prosheesis. J. Bone Joint Surg. Br. 48(2), 245–259 (1966) 2. Siopack, J.S., Jergesen, H.E.: Total hip arthroplasty. West. J. Med. 162(3), 243– 249 (1995) 3. Anual report 2017, The Japanese Society for Replacement Arthroplasty. https:// jsra.info/pdf/2017.pdf 4. Gadotti, I.C., Vieira, E.R., Magee, D.J.: Importance and clarification of measurement properties in rehabilitation. Rev. Bras. Fisioter. 10(2), 137–146 (2006) 5. K¨ u¸cu ¨kdeveci, A.A., Tennant, A., Grimby, G., Franchignoni, F.: Strategies for assessment and outcome measurement in physical and rehabilitation medicine: an educational review. J. Rehabil. Med. 43(8), 661–672 (2011) 6. Kadaba, M.P., Ramakrishnan, H.K., Wootten, M.E.: Measurement of lower extremity kinematics during level walking. J. Orthop. Res. 8(3), 383–392 (1990) 7. Yoo, J.H.: Extracting human gait signatures by body segment properties. In: Proceedings of Fifth IEEE Southwest Symposium on Image Analysis and Interpretation, pp. 35–39 (2002) ´ 8. Josi´ nski, H., Swito´ nski, A., J¸edrasiak, K., Kostrzewa, D.: Human identification based on gait motion capture data. In: Proceedings of the International MultiConference of Engineers, vol. 1, pp. 454–457 (2012) 9. Okusa, K., Kamakura, T.: Gait Parameter and Speed Estimation from the Frontal View Gait Video Data Based on the Gait Motion and Spatial Modeling 10. Perron, M., Malouin, F., Moffet, H., McFadyen, B.J.: Three-dimensional gait analysis in women with a total hip arthroplasty. Clin. Biomech. 15(7), 504–515 (2000) 11. Queen, R.M., Butler, R.J., Watters, T.S., Kelley, S.S., Attarian, D.E., Bolognesi, M.P.: The effect of total hip arthroplasty surgical approach on postoperative gait mechanics. J. Arthroplasty 26, 66–71 (2011) 12. Gerhardt, D.M.J.M., Mors, T.G.T., Hannink, G., Susante, J.L.C.V.: Resurfacing hip arthroplasty better preserves a normal gait pattern at increasing walking speeds compared to total hip arthroplasty. Acta Orthopaedica 90(3), 231–236 (2019) 13. Ricciardi, C., Gerhardt, D.M.J.M., Mors, T.G.T., Hannink, G., Susante, J.L.C.V.: Improving prosthetic selection and predicting BMD from biometric measurements in patients receiving total hip arthroplasty acta orthopaedica. Diagnostics 10(10), 815–817 (2020) 14. Makino, K., Omori, H., Nakamura, M., Terada, H.: Gait analysis using gravitycenter fluctuation of the sole at walking based on self-organizing map. In: The 24th IEEE International Symposium on Industrial Electronics, pp. 964–969 (2015) 15. Makino, K., et al.: Evaluation method of the gait motion based on self-organizing map using the gravity center fluctuation on the sole. J. Autom. Comput. 14, 603– 614 (2017) 16. Liu, Z., et al.: Analysis of eye tracking of physiotherapist during walk rehabilitation. In: 45th Annual Conference of the IEEE Industrial Electronics Society(IECON2019), pp. 6702–6707 (2019)

Lightweight Locomotion Assistant for People with Mild Disabilities Gon¸calo Neves1 , Jo˜ ao S. Sequeira1(B) , and Cristina Santos2 1

Instituto Superior T´ecnico, University of Lisbon, 1049-001 Lisbon, Portugal {goncalomneves,joao.silva.sequeira}@tecnico.ulisboa.pt 2 Universidade do Minho, Braga, Portugal [email protected] Abstract. With the current increase of the elderly population, locomotion disabilities cases are growing, and hence there is a need for lightweight, minimally intrusive, locomotion aiding devices. Bulky devices, often used in hospitals and domestic environments, namely during recovering and rehabilitation phases, tend to create difficulties to the users. This paper describes a robotic cane to assist people with mild locomotion disabilities, e.g., in the final stages of rehabilitation processes, helping users to maintain and recover balance in standing and walking situations. Moreover, the lightweight characteristics of the device enable its use in tight spaces (as often found in domestic environments). The device has unicycle kinematics and adapts its movement to the state of the user. The mathematical model, control, and hardware are detailed in the paper. Performance is assessed through experiments with real users with and without mobility impairments. The results obtained strongly confirm the viability of the concept. Keywords: Robot cane · Locomotion assistance Full-state feedback · Unicycle

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The ability to walk upright is one of the most important factors that define human beings. Alongside the massive brain (homo sapiens) and the ability to make tools (homo habilis), it is one of the distinctive features that separates the human species and its ancestors (homo erectus) from the rest of the animals [1]. Alongside that, being able to walk brings not only physical well-being but also psychological, social and economical well-being, since that such inability removes a major portion of the patient’s freedom and lowers the performance at most activities of daily living [2]. Due to low levels of physical strength resulting from muscular weaknesses and/or other comorbidities, elderly people tend to suffer the most from movement restrictions. As the elderly population is growing, a shortage of young people for nursing care can become a problem [3], and robotic devices are seen as an interesting contribution to alleviate the efforts by healthcare professionals. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 465–476, 2022. https://doi.org/10.1007/978-3-030-86294-7_41

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Robotics based walking-aiding devices are becoming objects of extreme importance to regenerate the ability to walk of impaired users. Moreover, as more sophisticated robot features are included, the stress arising from constant supervision by healthcare professionals may be reduced, hence contributing to general well-being. Studies have been made on Smart Walkers (SWs) for clinical evaluation and assistance of people with decreased locomotion capabilities, ([4–10]). However, these robotized walker devices present bulky and complex designs that reduce the possibility of its use outside of clinical and hospital environments. Therefore, a Smart Cane (SC), i.e., a lightweight robotized cane, is claimed to be more adequate for domestic and unsupervised usage. Moreover, by including monitoring features that can send remotely warnings on relevant events, constant (possibly remote) supervision by medical staff can be used more effectively. Among the works on these types of devices are [11–17] or [18]. The device proposed in this paper is highly mobile and less intrusive than standard walk-aiding devices. The specific dynamics, akin to an inverted pendulum, where stability is a key feature, makes it more appropriate to people that still hold some control over their locomotion. Control strategies help maintaining or correcting their locomotion gait. It can be used also as a second stage for people recovering from ataxic problems or other gait problems that have already been evaluated and rehabilitated with the help of a Smart Walker (SW) in a clinical environment in a first stage, and now are able to go home and continue recovering using a small, lightweight, and less intrusive device. Even though the SC’s in the literature are relatively small devices, most of them are still too big to provide a comfortable usage in tight/cluttered places and/or require sensors to be physically connected to the user. The device described in this paper has a smaller footprint and requires no sensors connected to the user, presenting a simple and easy to use application. The paper is organized as follows. Section 2 details implementation aspects. Section 3 describe tests with real users. Finally, Sect. 4 points to conclusions and future work.

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Implementation

In order to minimize the footprint that the robot will have, the cane has only one wheel connected to the rod, on which the user grabs, as in Fig. 1. With only one moving part, the robot becomes less mechanically complex, the weight is reduced, since only one motor and wheel are needed. With the reduction of the footprint of the device, the user has more space to move his lower limbs, preventing situations where the user would hit the cane or vice-versa. The wheel used is a simple wheel which implies that the cane can only move with unicycle kinematics. Compared to a traditional walking cane, the transversal behaviour will be the same, being manually adjusted by the user, while the longitudinal movement is automatically managed by the robot. Still, it is enough to create a point of contact with the ground that acts as a support for a light cane. Also, it

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reduces the possibility of the cane to slip sideways, simplifying also the movement of the robot and becoming more predictable for the user.

Fig. 1. 3D render of the final vision of the cane

2.1

Model of the Robotic Cane

The model is based on an unicycle, with only one actuated degree of freedom. A simple schematic of the model can be seen in Fig. 2 and the model variables are detailed in Table 1. The values of each parameter can be observed in Sect. 2.3, Table 2.

Fig. 2. Schematic of the model.

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G. Neves et al. Table 1. Variable Terminology. θ[rad]

Angle of the rod

x[m]

Position of the wheel

mp [kg]

Rod mass

mr [kg]

Wheel mass

2

g[m /s]

Gravitational force

r[m]

Wheel radius

l[m]

Rod length

lc [m]

Length from axle to rod center of mass

δ[N · m · s/rad] Viscous friction coefficient u

Control input (voltage supplied to motors)

Analysing the forces applied horizontally to the wheel and perpendicularly to the rod, the linear space state model of the cane can be obtained, resulting in the matrices in (1). ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡0 1 0 0 0 x˙ x mp l ⎥ ⎢x˙ ⎥ ⎢ r1 ⎥ 0 0 − mr +m ⎥ ⎢0 ⎢x p⎥ ⎥ ⎢ mr +mp ⎥ ⎢ ¨⎥ = ⎢ ⎥⎢ ⎥ u, 0 0 1 ⎣φ⎦ + ⎢ ⎣φ˙ ⎦ ⎢ ⎣0 ⎣ 0 ⎦ ⎦ mp gl mr r 1 φ˙ φ¨ 1 0 − 1 m2 l2 − 1 m2 l2 − 1 mδ l2 2 3 mp l p p p 3 3 3 ⎡ ⎤   x x˙ ⎥ 0 1000 ⎢ ⎢ ⎥ + u. y= 0 0 0 1 0 ⎣φ⎦ φ˙

(1)

The system is controllable and observable, and is controlled using full-state feedback control (Eq. (2)), which gain K is obtained by minimizing the quadratic cost function in Eq. (3)[19]. Since the motors have low torque, state and control weights are set to Q = C T C and R = 0.0001, making the control input weight in the cost function almost zero, and increasing the state weight. u = −KX

J(u) =

∞

(x Qx + u Ru)dt

(2) (3)

0

2.2

Robot Components

The list of components is limited to a controller, two motors, one motor driver, one inertial measurement unit (IMU), one encoder, two batteries, a Bluetooth module and two force sensitive resistors (component datasheets and full wiring diagram can be accessed at [20]).

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The controller used is an Arduino Uno. In order to obtain the angle of the cane, an IMU was used. The controller receives data from the sensor and calculates the control signal that it has to send to the motors. As a direct connection between the controller and the motors is not feasible, because not only the output currents of the controller are insufficient for the motors, but the electrical noise generated by the motors can damage the controller, a motor driver had to be used. Two force sensitive resistors on the handle measure the forces applied by the user on the device, and a Bluetooth module allows data to be obtained without a cable connecting the cane to a computer. The whole prototype is powered by two batteries, separating the power circuits of the motors and the microcontroller. A Kalman filter is used to clean and combine the signals from the gyro and the accelerometer, with parameters Qangle = 0.001 and Qbias = 0.003 corresponding to the process noise variance for the accelerometer and the gyro bias, respectively, and Rmeasure = 0.03 corresponding to the measurement noise variance. Controller and data acquisition sampling rates are both approximately 142 Hz. 2.3

Robot Prototype

The average mass that an elderly person (60+ years old) can lift, from the hip to the shoulder, in 4 consecutive repetitions, is 20.2 kg for men and 13.2 kg for women [21]. In order to add a comfort gap, reducing the fatigue caused by transporting the cane in situations where it has to be raised repeatedly, a limit of 7 kg has been placed on the mass it should have (similar to [15]), corresponding to approximately half of the lowest value previously mentioned.

Fig. 3. Aluminium prototype of the robot.

A prototype, shown in Fig. 3, was created in order to test the concept with real users. The structure is made of aluminum, increasing the integrity and robustness of the robot, while maintaining mass at small values compatible with elderly/impaired people physical strength. The complete prototype has a mass

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just over 800 g. The batteries are placed at the bottom end of the rod, Fig. 4, lowering the center of mass. It’s predicted that this prototype can work continuously for 16 h at maximum power.

Fig. 4. Location of the battery.

The two force sensors in the handle were positioned separate from each other, as shown in Fig. 5, allowing the analysis of the grasp techniques of users.

Fig. 5. Positioning of force sensors on the handle.

This prototype was tested under the supervision of a medical team. Due to the small variations occurring in the grasps, mostly in an unconscious way, mainly in old ages where problems like Parkinson’s arise, a band of ±5◦ around the vertical position was implemented of this prototype where the gain of the controller is reduced by 80%, making the use of the cane more comfortable and smooth. The parameters of this prototype can be seen in Table 2. Table 2. Parameters of the prototype. Rod mass [kg]

0.810

Wheel mass [kg]

0.060

Wheel radius [m]

0.08

Rod length [m]

0.780

Length from axle to rod center of mass [m] 0.20 Viscous friction coefficient [N · m · s/rad]

0.25

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Tests and Results

The prototype was subjected to several tests in order to assess the operation in real situations. These include real users with and without reduced mobility capabilities. Tuning of the prototype involved tests with 7 individuals without mobility difficulties. In each test, the user moved 4 m forward, then turned around and advanced again to the starting point. The results showed that the way one uses the cane varies significantly from person to person. Younger individuals tend to keep the cane on their side and moved alongside it, keeping it fairly vertical. On the other hand, older people tend to keep the cane in front of the body, close to 20◦ , further reporting that this was the position in which they felt most supported, behaving similarly with classic walking canes. The way users grasp the cane also changed from case to case, but in all cases most of the force was applied over the back force sensor. Two tests were carried out with users with reduced mobility, the first being a case recovering locomotion capabilities and the second a case maintaining them. The first user is recovering from a bone fracture, and thus showed some initial apprehension when seeing the cane, but then used it without any issue, only needing some support from another person in the beginning, while getting used to the device. The second case, an user suffering from rheumatoid arthritis, showed immediate willingness to use the cane, and used it without any help. Both users referred that the support provided by the cane was not enough in some situations where they applied a higher force. At the end of the tests, the first user still preferred a traditional cane, while the second user preferred the robotic cane.

(a) User recovering (b) User with from a fracture. rheumatoid arthritis.

Fig. 6. Tests with users with reduced mobility.

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In both cases, users instinctively placed the cane in front of them, at a 20◦ angle as shown in Fig. 6 and 7, as what older subjects did in the tests with individuals without mobility difficulties. Observing the dynamics of a person standing, it is better understood why these users feel safer with the cane in front of them. Since the human body has only two contact surfaces with the ground (as bipedal), it results in an unstable system if not properly controlled, requiring a third contact point to become stable in these cases. The success of the control depends on the agility, balance and cognitive fitness of each individual. As mentioned in [22] and [23], aging and a sedentary lifestyle lead to these capacities being reduced, worsening the control of the body to remain stable while standing and walking, thus increasing the risk of unbalance and falling.

(a) User recovering from a fracture.

(b) User with rheumatoid arthritis.

Fig. 7. System angle and forces applied on the tests with users with reduced mobility.

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The balance of a standing person is based on the ability to maintain the projection of the center of mass on the ground within the polygon formed by the points in contact with the ground, that is, within the support polygon [24]. If the balance control is degraded due to age or other pathologies, the best solution is to counter this lack of control of the position of the center of mass by increasing the area of the polygon where it can be. In addition, the support polygon, this way, is extended in front of the user, which is the direction most propitious to unbalance since it corresponds to the direction of movement. In Fig. 8 the support polygons are represented when the individual does not use a cane, when he uses it at his side and when he uses it in front of him.

Fig. 8. Support polygons in no cane (left), cane at side (middle) and cane at front (right) situations.

Thus, the reason for instinctively placing the cane in front of older users is justified. However, as younger users do not feel the need to increase the support polygon, they unconsciously place the cane beside them closer to vertical, thus helping to support part of the weight that would otherwise be placed on the lower limbs. Lastly, two tests, with young and elder users, were carried to compare the behaviour of the cane with a traditional cane. This cane had the same handle as the robotic cane, equipped with the IMU and force sensors. As previously mentioned, the way young and elder people use the robotic cane is completely distinct, as confirmed in Fig. 9 and 10. However, when compared to the traditional cane, the robotic cane presents a more constant behaviour in both cases, with less angle variations and a more consistent support of the user. This results from the lack of need to pick up and swing the cane at every step, allowing a more fluid motion of the cane and support for the user during most of its movement.

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(a) Traditional Cane.

(b) Robotic Cane.

Fig. 9. Behaviour of traditional and robotic cane with young user.

(a) Traditional Cane.

(b) Robotic Cane.

Fig. 10. Behaviour of traditional and robotic cane with elder user.

4

Conclusions

The evidence collected from the experiments with real users suggest that the robotic cane developed in this study has a strong potential for success. The behaviour of the system is very smooth and worked very well with the intended applications for the device. Its usage is very intuitive, making it natural for the user during their movement. Despite the limitations of the prototype built, its benefits in supporting the user throughout his movement, and the support of the user to regain balance in fall situations were proven with performance above expectations. The feedback from the test subjects and the medical team was very helpful and positive, thus confirming the viability of the concept. As future work, the motor will be changed to a motor with higher torque, to improve the amount of support the cane can supply to the user. The control will be further adjusted to optimise the behaviour of the system for different situations, and an algorithm to calculate the reference from the force sensors of the handle will be created. A controller using Machine Learning will also

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be tested, allowing continuous improvement of control as the device is used, as well as a faster adaptation of the control to the user. Outdoor tests will also be conducted to verify the performance of the device in situations were the user has more space and freedom of movement. Additionally, the aesthetic of the device will be subject to further developments, in order to become more attractive to users, encouraging its use. Acknowledgements. This research was partially supported by project LARSyS-FCT Project UIDB/50009/2020, Servi¸cos Partilhados do Minist´erio da Sa´ ude (SPMS), and Agrupamento de Centros de Sa´ ude Loures-Odivelas (ACES Loures-Odivelas).

References 1. Lovejoy, C.O.: Evolution of human walking. Sci. Am. 259(5), 118–125 (1988) 2. Winter, D.A.: Biomechanics and Motor Control of Human Movement. 4th (edn) John Wiley & Sons, Hoboken (2009) 3. Fukuda, T., Huang, J., Di, P., Sekiyama, K.: Motion control and Fall Detection of Intelligent Cane Robot. Springer Tracts in Advanced Robotics (2015). https:// doi.org/10.1007/978-3-319-12922-8 12 4. Moreira, R., Alves, J., Matias, A., Santos, C.: Smart and assistive walker - asbgo: rehabilitation robotics: a smart-walker to assist ataxic patients. Adv. Exp. Med. Biol. 1170, 37–68 (2019) 5. Ohnuma, T., Lee, G., Chong, N.Y.: Particle filter based feedback control of JAIST active robotic walker. In: Proceedings - IEEE International Workshop on Robot and Human Interactive Communication, pp. 264–269 (2011) 6. Rentschler, A.J., Simpson, R., Cooper, R.A., Boninger, M.L.: Clinical evaluation of Guido robotic walker. J. Rehabil. Res. Dev. 45(9), 1281–1294 (2008) 7. Neto, A.F., Elias, A., Cifuentes, C., Rodriguez, C., Bastos, T., Carelli, R.: Intelligent Assistive Robots, vol. 106 (2015) 8. Grondin, S.L., Li, Q.: Intelligent control of a smart walker and its performance evaluation. In: IEEE International Conference on Rehabilitation Robotics, pp. 1–6 (2013) 9. Jun, H.G., et al.: Walking and sit-to-stand support system for elderly and disabled. In: IEEE International Conference on Rehabilitation Robotics (2011) 10. Schraft, R.D., Schaeffer, C., May, T.: Care-O-botTM : the concept of a system for assisting elderly or disabled persons in home environments. IECON Proc. (Ind. Electron. Conf.) 4, 2476–2481 (1998) 11. Naeem, M.A., Assal, S.F.: Development of a 4-DOF cane robot to enhance walking activity of elderly. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 0(0), 1–19 (2019) 12. Shim, I., Yoon, J.: A human robot interaction system RoJi. IEEE/ASME Int. Conf. Adv. Intell. Mech. AIM, 2, 723–728 (2003) 13. Spenko, M., Yu, H., Dubowsky, S.: Robotic personal aids for mobility and monitoring for the elderly. IEEE Trans. Neural Syst. Rehabil. Eng. 14, 344–351 (2006) 14. Wang, H., Sun, B., Wu, X., Wang, H., Tang, Z.: An intelligent cane walker robot based on force control. In: 2015 IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems, IEEE-CYBER 2015, pp. 1333–1337 (2015)

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15. Van Lam, P., Fujimoto, Y.: Completed hardware design and controller of the robotic cane using the inverted pendulum for walking assistance. In: IEEE International Symposium on Industrial Electronics, pp. 1935–1940 (2017) 16. Stramel, D.M., Carrera, R.M., Rahok, S.A., Stein, J., Agrawal, S.K.: Effects of a person-following light-touch device during overground walking with visual perturbations in a virtual reality environment. IEEE Robot. Autom. Lett. 4(4), 4139– 4146 (2019) 17. Trujillo-Le´ on, A., Ady, R., Reversat, D., Bachta, W.: Robotic cane controlled to adapt automatically to its user gait characteristics. Front. Robot. AI 7(8), 1–13 (2020) 18. Ady, R., Bachta, W., Bidaud, P.: Development and control of a one-wheel telescopic active cane. In: Proceedings of the IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics, pp. 461–466 (2014) 19. Lemos, J.M.: Controlo No Espa¸co De Estados. 1 edn. IST Press, Hamilton (2019) 20. Neves, G.: Lightweight locomotion assistant for people - Technical Report. Technical report (2020). https://drive.google.com/file/d/1ejZNiFQvWk5BZtg 9TfmJOETJh-o PnYe/view?usp=sharing. Accessed 27 Dec 2020 21. Matheson, L.N., Verna, J., Dreisinger, T.E., Leggett, S., Mayer, J.: Age and gender normative data for lift capacity. Work 49(2), 257–269 (2014) 22. Barbieri, F.A., Vitorio, R.: Locomotion and Posture in Older Adults: The Role of Aging and Movement Disorders (2017) 23. Iosa, M., Fusco, A., Morone, G., Paolucci, S.: Development and decline of upright gait stability. Front. Aging Neurosci. 6(2), 1–12 (2014) 24. Vadakkepat, P., Goswami, D.: Biped locomotion: stability, analysis and control. Int. J. Smart Sens. Intell. Syst. 1(1), 187–207 (2008)

Possibility of Getting On/Off Public Vehicle by Manual Wheelchair with 4 Degrees of Freedom Contact Arm Mechanism Fumiaki Takemori(B) and Ryoga Hayashi Department of Engineering, Graduate School of Sustainability Science, Tottori University, 4-101 Koyama Minami, Tottori, Japan [email protected] Abstract. This paper proposes an elevating mechanism and its control rules for wheelchair users to get on and off public transportation vehicles by themselves. It is shown that it is possible to move up and down with a wheelchair by applying the grounding function with a 4-degree-of-freedom arm to a vehicle environment with two stages at the entrance. We apply an automatic arm grounding judgment method that applies a disturbance observer as a method for detecting whether the arm touches the floor. Its control availability is shown in getting off/on experiment for a railcar. Keywords: Wheelchair Disturbance observer

1

· Public vehicle · Stride over gap and step ·

Introduction

Currently, wheelchair users need assistance to get on and off public transportation vehicles. Assistance in this study means the installation of slopes and the pushing/pulling out of wheelchairs. Because this assistance act requires the operation of a public transportation company, it may cause an increase in the burden on employees of the company or delayed operation. In recent years, unmanned stations have been promoted by railway companies, and the ratio is increasing year by year [1], but on the other hand, unmanned stations also have the disadvantage that is not available for on-demand assistance for passengers who need the assistance in getting on and off. Furthermore there are also reports that wheelchair users hesitate to request assistance by feeling “feeling uncomfortable” with others [2]. According to [1], the unmanned rate of stations is higher on local lines than in urban areas. Since there are many non-electrified routes on local routes, many of the vehicles operated are diesel trains. A diesel railcar is well known a vehicle that uses a diesel engine as a drive source, and because the engine is mounted under the floor of the bogie, it has a floor structure with a step at the entrance and exit. Therefore, as shown in Fig. 1, for getting on and off the diesel railcar, in addition to the gap from the station platform to the vehicle entrance/exit and c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 477–488, 2022. https://doi.org/10.1007/978-3-030-86294-7_42

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F. Takemori and R. Hayashi How wheelchair get on/off independently public vehicle with inner step ? inner step

Platform

(a) Feature of a diesel railcar “Kiha121” in which there is inner step

Train with inner step

(b) Problem presentation on getting on/off by wheelchair

Fig. 1. Traveling issues in getting on/off railway vehicle. Table 1. Expected values in Fig. 2

Platform

Train

Dp Hp Ds Hs

130 ∼ 170 mm 25 ∼ 90 mm 330 mm 170 ∼ 220 mm

Fig. 2. llustration of the gap and step with platform and railway vehicle.

the first step, there is a second step from the entrance/exit step to the inside of the vehicle. It is usually impossible for a standard wheelchair to move on such a two-step structure single-handedly. As a step climbing mobility, a moving body featuring a deformed crawler mechanism [3] and a leg-type four-wheel mechanism [4] has been proposed. Although these have excellent ability to move on rough terrain, because they are dedicated machines, they are not necessarily the optimum solutions desired by wheelchair users in terms of the complexity of the mechanism and control, and the costs associated with them. Therefore, in this research, we focus on getting on and off railway vehicles with wheelchairs and initially sort out the issues, and secondly propose a wheelchair mechanism that enables people to get on and off railway vehicles without the assistance of others. Specifically, this paper presents that a contact arm mechanism with four degrees of freedom is required for a wheelchair to realize movement in an environment where there are nonnegligible gap and two steps. And the possibility of getting on and off the railway vehicle is shown by experiments using the proposed mechanism.

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Arm 1

Arm 2

Platform

Arm 3

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Arm 3

Arm 4

Arm 1

Railcar Gap

Platform

(a) From initial configuration, arm1/arm2 functions support leg, while arm3 functions swing leg for straddling the gap. Arm 2

Arm 2

Arm 4

Arm 4

Caster

Platform

Railcar Gap

Railcar Platform

Gap

Platform

(b) After arm3 is used as a support leg on 1st step, arm4 is used as a free leg to ride on the second step. Arm2 is used to to straddle the gap again, and finally it contacts on 1st step.

Fig. 3. Sequence of striding over gap and step with four contact arms.

2

Sorting Out Problems on Railcar

In this chapter, we summarize the problems when a wheelchair gets on and off a diesel railcar without installing a slope. Since the diesel railcar has an engine mounted under the floor of the bogie, the entrance/exit has two steps. As shown in Fig. 2, assume Dp is the gap between platform and railcar, and Hp is the height from the platform to the entrance/exit step, and likewise Ds and Hs are step going and height of inside the railcar. These expected values are given in Table 1. We consider that four grounding arms are required to stably realize the movement of the environment where such a gap and two steps exist. The conceptual diagram is illustrated in Fig. 3. Based on this figure, the following mechanistical restraints are put together; (a) First, two contact arms, arm1 (or arm2) and arm3, are required to serve as support legs and swing legs for straddling the gap. (b) Next, arm3 is used as a support leg on 1st step, and arm4 is required as a free leg to ride on the second step. (c) Furthermore, in order for the terminal leg to straddle the gap again, it is necessary to make arm2 function as a swing leg while grounding with arm1 as a support leg. Based on the above considerations, this paper assumes that a 4-degree-offreedom contact mechanism is required for getting on and off railway vehicles. In the next chapter, we propose a model in which a 4-degree-of-freedom arm mechanism is added to an existing wheelchair and describe its effectiveness.

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Linear actuator 4 Subwheel

Linear actuator 1 Linear actuator 2 Linear actuator 3 Subwheel

Fig. 4. Wheelchair which adds on contact arms atcuated by linear actuator. Linear actuator 1 Encoder and gear A

Subwheel motor1

Linear actuator 2

gear B

Fig. 5. Detail pictures of front and side view.

3

4DOF Arm Mechanism Added on Existing Wheelchair

The outline of the 4-degree-of-freedom contact arm mechanism proposed in this study is shown in Fig. 4, and the detailed photographs of each part are shown in Fig. 5 and Fig. 6. Each of the four arms can rotate by the expansion and contraction motion of an independent linear actuator. The reason for adopting a linear actuator is that it has an excellent load capacity even though the operating speed is slow, and it also has a mechanism for holding the arm angle in the unlikely event that the control signal is interrupted. The angle of each arm is measured by the encoder via the gear. The front end arm and the rear end arm have sub-wheels for independent running. In other words, as a whole, it is a 5-channel input/output system consisting of 4 arms and running motion. 3.1

Selection of Linear Actuator

This section describes the selection of linear actuators required to achieve ascent and descent in the assumed step environment. As an example, each parameter is defined in Fig. 7. Consider the rear arm as a calculation example. First, locate the origin of the coordinates on the reference plane. Let the arm rotation axis coordinates be A4 (xa , ya ), the arm length be L, and the sub-wheel radius be r, then the height of the lowest point of the sub wheel is y4 = ya + L sin θ4 − r

(1)

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Encoder and gear A

Linear actuator 4

gear B

Linear actuator 3

Subwheel motor2

Fig. 6. Detail pictures of rear devices. In this device, the encoder is installed to measure the angle of rear arm.

, y b) B 4(x b

z4 L

y

A2

d

B2

 C2 y2

r



C4(xc, yc) y4 A4(xa,ya)

z2 O

x

Fig. 7. Parameters definition of devices.

Solving θ4 for Eq.(1),

y4 − ya + r (2) L where, the sign of θ is positive with the horizontal line as the reference. Equation (2) means the solution of the arm angle for the sub-wheel to touch the ground on the step of height yh . Then, setting B4 (xb , yb ) and C4 (xc , yc ) as the coordinates of the endpoints on both sides of the linear actuator respectively, the 4th link length is as follows;  (3) z4 = (xc − xb )2 + (yc − yb )2 θ4 = sin−1

Here, the coordinate B4 is a fixed point, but if the relative quantity from the coordinate A4 is used, xb = xa + Δx, yb = ya + Δy

(4)

can be defined. Since the coordinates C4 are variable with respect to θ, assuming A4 C4 = d, the coordinates of C4 are given by the following equation. xc = xa + d cos θ4 , yc = ya + d sin θ4

(5)

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F. Takemori and R. Hayashi Table 2. Length of arm unit [mm]. ya

Δx

Δy

−155

Front arm 1

d[mm] L

15 160

r

250 50

Front arm 2 215 −245 −25 160

315 62.5

Rear arm 3

215 −135 −20 165

243 32.5

Rear arm 4

215

−20

445 165

10

310 62.5

600 front z2

0

rear z4

550

Length z2 and z4 [mm]

Angle 2 and 4 [deg]

-10 -20 -30 -40 -50 -60 front z2

-70 -80 -200

126 500

450

400

73

350

rear z4

-150

-100

-50

0

50

100

150

200

300 -200

-150

Wheel height y 2 and y4 [mm]

(a) Amount of angle change of θ2 , θ4

-100

-50

0

50

100

150

200

Wheel height y 2 and y4 [mm]

(b) Amount of stroke change of z2 , z4

Fig. 8. An example of linear actuator stroke in case that step depths are y2 = −180 ∼ 30 mm and y4 = −40 ∼ 200 mm.

Therefore, from Eqs. (2) ∼ (5), the required stroke of the link length is determined according to the assumed step height. The stroke of the front arm is also calculated by Eq. (6) by the same process  (6) z2 = (xc − xb )2 + (yc − yb )2 where, (xb , yb ), (xc , yc ) are the coordinates of the front arm nodes B2 and C2 shown in Fig. 7. An example of selection is shown below. Set the coordinate parameter values of the arm unit shown in the Table 2. Under this condition, the height difference of the step is assumed by the following numerical values, y2 = −180 ∼ 30 [mm]

(7)

y4 = −40 ∼ 200 [mm]

(8)

and the stroke of the actuator that realizes these is calculated. Figure 8(a) shows the arm angle that realizes the Eq. (7) and Eq.(8), and Fig. 8(b) shows the change in the stroke of the linear actuator that realizes this change in angle. From these results, it can be seen that Δz2 = 73 mm and Δz4 = 126 mm. Therefore, in this study, a type with a required stroke of 100 mm or more for the linear actuator in arm unit 2 and 150 mm or more for arm unit 4 is selected.

Possibility of Getting On/Off Public Vehicle by Manual Wheelchair

Bevel gear

DC motor

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DC motor

Subwheel

Subwheel

Fig. 9. Detail pictures of subwheel devices. Front subwheel is driven by DC motor thought bevel gear, and Rear subwheel is also driven by DC motor through parallel axis.

3.2

Subwheel Mechanism

When the main wheel of a wheelchair gets out of bed, a drive mechanism for autonomous movement is required. Therefore, in this study, one sub-wheel for autonomous movement is added to each of the front and rear arms. The mechanism photograph is shown in Fig. 9. The front and rear sub-wheels move forward and backward by operating the joystick at hand.

4 4.1

Control Method for Getting On/off Step Detection by Disturbance Observer

The purpose of this paper is to realize step movement without the need for human visual inspection or intervention of operation in raising and lowering the wheelchair. In order to achieve this, in this study, we apply the elevating control to a step with an unknown height proposed by the author in [5]. When the arm touches down from the initial state, the rear or front arm of the occupant becomes a blind spot. Therefore, performing the ascending movement only by the occupant’s operation is due to erroneous operation due to multi-stage operation and accumulation of wasted time. Hence, such manual operation cannot be said to be useful. Therefore, in this section, we apply an automatic arm grounding judgment method that applies a disturbance observer as a method for detecting whether the arm touches the floor. The disturbance detection system is summarized in Fig. 10 (for details, refer to Reference [5]). In the figure, ‘Reference function’is set as the target value function for the arm grounding mode and lift-up mode, and this is switched by the grounding detection parameter d. In addition, the target value tracking control system is incorporated by ‘PI controller’. In this paper, if this disturbance estimate is equal to or greater than an arbitrary threshold value of γ, it is regarded as arm grounding.

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Arm unit

PI controller

Reference function

1/0

Collision detector

Fig. 10. Arm control system with collision detection by disturbance observer. Inverce kinematics Eq.(15)

+

-

PI controller

Contact arm unit

Fig. 11. Lift up control system.

4.2

Inverse Kinematics Model Considering Postural Maintenance

This section describes the control of the wheelchair body after the arm touches the ground. First, let the estimated step height by grounding detection incorpoˆ Next, rated in the previous section be yˆ, and the arm angle at that time be θ. assume Δθ is the amount of change in the arm angle required to virtually change the wheel lowest point by Δy, the height of the i arm lowest point is given by Eq. (9). (9) yˆi + Δy = yia + Li sin(θˆi + Δθi ) − ri Here, note that sign of Δy is defined as negative for downward and positive for upward, so if Δy < 0 is given while the arm is in contact with the ground, the wheelchair body will rise (lift up). Solving the formula (9) explicitly for Δθi , Δθi = sin−1

yˆi + Δy − yia + ri ˆ − θi Li

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can be obtained. Hence by cooperatively giving the same lift-up amount Δy to the two arms that are in contact with the ground, wheelchair body posture can be moved horizontally. In this study, as shown in Fig. 11, we implement a liftup/down motion system in which the angle calculated by Eq. (10) is the target value of the arm unit.

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Fig. 12. Figure of simulated platform and railcar and their admeasurement.

5

Experiment

In this chapter, we verify whether the proposed mechanism can move the environment that simulates the entrance and exit of the actual diesel railcar shown in Fig. 12. The verification experiment is conducted on board an adult. In the environment shown in Fig. 12, the following actual station and vehicle dimensions are set. Dp = 130 mm, Hp = 90 mm, Ds = 330 mm, Hs = 175 mm In the experiment, the wheelchair passenger made the height of the step unknown, and after visually confirming that he has encountered each step, he presses the trigger key to start control of each phase. Firstly, unknown step detectability is verified by disturbance observer. Figures 13(a) ∼ (c) show the disturbance response when the arm touches the 2

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ground at the vehicle boarding gate, inside the vehicle, and on the station platform, respectively. Figure 14 shows the lowest point of the arm corresponding to Fig. 13. From these results, the height of the following steps can be estimated. ˆ p = 86 mm, H ˆ s = 181 mm, yˆ2 = 2 mm H 160

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Fig. 15. Captures in getting on the simulated railcar.

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Fig. 16. Captures in getting off the simulated train.

ˆ s − Hs | = 6 mm, it Although the maximum value of these estimation errors is |H is judged that there is no effect on the subsequent step up and down. Next, the results of implementing the boarding sequence and the disembarking sequence are shown in Fig. 15 and Fig. 16, respectively. The lift-up ˆ p − 10 mm, amount of the vehicle height in the Fig. 15(4) is given by Δy1 = −H ˆ s − 10 mm. On the other hand, The lift-up amount of the vehicle Δy4 = −H ˆ p − 90 mm, Δy4 = −10 mm. As a height in the Fig. 16(4) is given by Δy1 = −H result of these experiments, it is confirmed that a wheelchair with a person on board can get on and off the simulated vehicle by itself.

6

Conclusion

In this study, we have proposed an elevating mechanism and its control rules for wheelchair users to get on and off public transportation vehicles by themselves.

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It was shown that it is possible to move up and down with a wheelchair by applying the grounding function with a 4-degree-of-freedom arm to a vehicle environment with two stages at the entrance. Future tasks include seamlessness and time reduction of each sequence.

References 1. Ministry of Land, Infrastructure, Transport and Tourism. https://www.mlit.go.jp/ tetudo/content/001371424.pdf. (in Japanese). Accessed 1 Mar 2021 2. Takahashi, K., Inoue, N., Kodama, Y.: Supportive and hindering factors affecting the will to continue home care in the case of elderly couples? With a focus on the mindset of the care-giving spouse. Japan J. Nurs. Sci. 26(3), 58–66 (2006). (in Japanese) 3. Sugahara, Y., Yonezawa, N., Kosuge, K.: A Stair-climbing wheelchair with wheeled transformable four-bar linkages. J. Rob. Soc. Japan 29(7), 599–608 (2011). (in Japanese) 4. Nakajima, S.: Evaluation of the mobility performance of a personal mobility vehicle for steps. IEEE Access 5(1), 9748–9756 (2017) 5. Takemori, F.: Development of wheelchair that can acsend and descend unknown height step by using disturbance observer. Trans. JSME 87(895), 20–00376 (2021). (in Japanese)

Author Index

A Anvo, Richard, 154 Anvo, Richard N’zebo, 165 Arykantsev, Vladimir V., 295 Asano, Fumihiko, 37, 242, 262, 274

G Gabdrahmanov, Ruslan, 408 Gallegos Garrido, Gabriela, 165 Goldman, Daniel I., 213 Golubev, Yury F., 192

B Bai, Yang, 408 Banfield, Ilka, 438 Barber, Andrew R., 117 Berns, Karsten, 24 Billeschou, Peter, 69 Bordyugov, Denis V., 421 Boyle, Jordan H., 117 Briskin, Eugene S., 286, 421

H Hagihara, Ryo, 455 Haji, Keigo, 229 Hakamada, Sho, 203 Hanagata, Yoshinobu, 455 Hashimoto, Hiroshi, 54, 369 Hayashi, Ryoga, 477 Hitomi, Takehiro, 348 Ho, Van Anh, 108 Hodoshima, R., 95 Hutter, Marco, 179

C Chernyshev, Vadim V., 295 Chugo, Daisuke, 54, 369 Collett, James R., 117 Costa, Paulo, 81, 303 D Diaz, Kelimar, 213 Do, Cao D., 69 E Echeverría, Octavio, 317 F Fedorov, Andrey V., 3 Foster, James Paul, 129 Fry, Nicholas, 117

I Inagaki, Katsuhiko, 43, 369 Isaka, Keita, 337 Ito, Fumio, 143, 348 Ivanova, Tatiana B., 396 J Jackson, Andrew E., 117 Jackson-Mills, George H., 117 Jatsun, A. S., 3 Jatsun, Sergey F., 3, 255 Jones, William, 229 K Kalinin, Yaroslav V., 295 Karavaev, Yuriy, 428

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 D. Chugo et al. (Eds.): CLAWAR 2021, LNNS 324, pp. 489–491, 2022. https://doi.org/10.1007/978-3-030-86294-7

490 Karavaev, Yury L., 396 Kaur, Aman, 154 Kaur, Aman Preet, 165 Kilin, Alexander, 428 Kilin, Alexander A., 396 Koizumi, Yusuke, 229 Kormushev, Petar, 129 Koryanov, Victor V., 192 Kotosaka, S., 95 Kurasawa, Kazushi, 369 Kurihara, Koki, 229 Kurumaya, Shunichi, 143 L Larsen, Jørgen C., 69 Li, Longchuan, 37, 242, 262, 274 Lima, José, 81, 303 M Magid, Evgeni, 408 Makino, Koji, 455 Malchikov, Andrei V., 255 Manoonpong, Poramate, 69 Markham, Karen, 165 Marques, Vitor, 165 Melkumova, Elena V., 192 Mikami, Sadayoshi, 203 Montes, Héctor, 317 Moro, Seiya, 357 Mphake, Masego, 117 Muramatsu, Satoshi, 43, 54, 369 N Nakamura, Masahiro, 455 Nakamura, Taro, 143, 329, 337, 348 Neves, Gonçalo, 465 Nguyen, Dinh Quang, 108 Nomura, Kenzi, 357 O Okui, Manabu, 329, 337 Omori, Hidenori, 455 P Pechurin, Alexander S., 3 Perez, Víctor, 317 Pinto, Vítor H., 81, 303 Platonov, Vitalu N., 286 Postolniy, Alexey A., 255

Author Index R Rasanga, G. V. C., 95 Ribeiro, Warley F. R., 229 Richardson, Robert C., 117 Rocha, Marco, 81 Rodríguez, Humberto, 317, 438 Routledge, Peter, 165 S Santos, Cristina, 465 Saputra, Roni Permana, 129 Sato, Hiroto, 143 Sattar, Tariq P., 154, 165 Sekine, Satoharu, 357 Sequeira, João S., 465 Sharonov, Nikolay G., 295, 421 She, Jin-Hua, 54 Shead, Basil A., 117 Shirataki, Kohei, 455 Siriwattanalerd, Thawanrat, 43 Smirnaya, Liliya D., 286 Soares, Inês N., 303 Soto, Daniel, 213 Strand, Marcus, 383 Sugihara, Tomomichi, 13 Sugimoto, Ryosuke, 43 Sugiyama, Hyouga, 369 Svinin, Mikhail, 408 T Takemori, Fumiaki, 477 Terada, Hidetsugu, 455 Tokoi, Ryosuke, 329, 337 Tokuda, Isao, 262 Toyama, Wataru, 329, 337 Tsoy, Tatyana, 408 Tsumura, Kazuki, 329, 337 U Uchida, Hiroaki, 357 Uchiyama, Kosuke, 143 Ueda, Shohei, 455 Uno, Kentaro, 179, 229 V Valsecchi, Giorgio, 179 Vonwirth, Patrick, 24 W Waidner, David, 383 Wang, Ke, 129 Watanabe, Tomoki, 329, 337 Whitehead, Shaun, 117

Author Index Y Yamada, Shunsuke, 54 Yamamoto, Takanobu, 13 Yamanaka, Yuta, 348 Yan, Cong, 37, 274 Yatsun, Andrey S., 255 Yefremov, Kirill, 428

491 Yokota, Sho, 54 Yoshida, Hiroshi, 329, 337 Yoshida, Kazuya, 179, 229 Z Zheng, Yanqiu, 37, 242, 274