Dynamics And Control Of Robotic Systems 1119524830, 9781119524830, 1119524954, 9781119524953

Table of contents :
Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 15
Acknowledgment......Page 17
About the Companion Website......Page 19
1.1 Motivation......Page 21
1.2 Origins of Robotic Systems......Page 25
1.3 General Structure of Robotic Systems......Page 27
1.4.1 Typical Structure of Robotic Manipulators......Page 29
1.4.2.1 Classification by Motion Characteristics......Page 31
1.4.2.4 Classification by Kinematic Structure......Page 32
1.4.3 Examples of Robotic Manipulators......Page 34
1.4.3.1 Cartesian Robotic Manipulator......Page 35
1.4.3.3 SCARA Robotic Manipulator......Page 36
1.4.3.4 Spherical Robotic Manipulator......Page 37
1.4.4 Spherical Wrist......Page 38
1.5.1 Humanoid Robots......Page 40
1.5.2 Autonomous Ground Vehicles......Page 42
1.5.3 Autonomous Air Vehicles......Page 43
1.5.4 Autonomous Marine Vehicles......Page 45
1.6 An Overview of Robotics Dynamics and Control Problems......Page 46
1.6.1 Forward Kinematics......Page 47
1.6.3 Forward Dynamics......Page 48
1.6.4 Inverse Dynamics and Feedback Control......Page 49
1.6.5 Dynamics and Control of Robotic Vehicles......Page 50
1.7 Organization of the Book......Page 51
1.8 Problems for Chapter 1......Page 53
2.1.1 N‐Tuples and M x N Arrays......Page 55
2.1.2 Vectors, Bases and Frames......Page 59
2.1.2.1 Vectors......Page 60
2.1.2.2 Bases and Frames......Page 61
2.2 Rotation Matrices......Page 69
2.3.1 Single Axis Rotations......Page 72
2.3.2.1 Cascade Rotations about Moving Axes......Page 76
2.3.3 Euler Angles......Page 77
2.3.3.1 The 3‐2‐1 Yaw‐Pitch‐Roll Euler Angles......Page 78
2.3.3.2 The 3‐1‐3 Precession‐Nutation‐Spin Euler Angles......Page 82
2.3.4 Axis Angle Parameterization......Page 85
2.4 Position, Velocity, and Acceleration......Page 88
2.5.1 Angular Velocity......Page 97
2.5.2 Angular Acceleration......Page 103
2.6.1 Addition of Angular Velocities......Page 104
2.6.2 Relative Velocity......Page 107
2.6.3 Relative Acceleration......Page 108
2.6.4.1 Cartesian Coordinates......Page 111
2.6.4.2 Cylindrical Coordinates......Page 112
2.6.4.3 Spherical Coordinates......Page 114
2.7.1 Problems on N‐tuples and M x N Arrays......Page 116
2.7.2 Problems on Vectors, Bases, and Frames......Page 117
2.7.3 Problems on Rotation Matrices......Page 118
2.7.4 Problems on Position, Velocity, and Acceleration......Page 122
2.7.6.1 Problems on the Addition of Angular Velocities......Page 124
2.7.7 Problems on Relative Velocity and Acceleration......Page 125
2.7.8 Problems on Common Coordinate Systems......Page 128
3.1 Homogeneous Transformations and Rigid Motion......Page 129
3.2 Ideal Joints......Page 135
3.2.1 The Prismatic Joint......Page 136
3.2.2 The Revolute Joint......Page 137
3.2.3 Other Ideal Joints......Page 139
3.3.1 Kinematic Chains and Numbering in the DH Convention......Page 141
3.3.2 Definition of Frames in the DH Convention......Page 143
3.3.3 Homogeneous Transforms in the DH Convention......Page 144
3.3.4 The DH Procedure......Page 147
3.3.5 Angular Velocity and Velocity in the DH Convention......Page 153
3.4 Recursive O(N) Formulation of Forward Kinematics......Page 158
3.4.1 Recursive Calculation of Velocity and Angular Velocity......Page 160
3.4.2 Efficiency and Computational Cost......Page 163
3.4.3 Recursive Calculation of Acceleration and Angular Acceleration......Page 167
3.5.1 Solvability......Page 180
3.5.2.1 Algebraic Methods......Page 183
3.5.2.2 Geometric Methods......Page 194
3.5.3 Optimization Methods......Page 196
3.5.4 Inverse Velocity Kinematics......Page 204
3.5.4.1 Singularity......Page 205
3.6.1 Problems on Homogeneous Transformations......Page 206
3.6.3 Problems on the DH Convention......Page 208
3.6.4 Problems on Angular Velocity and Velocity for Kinematic Chains......Page 210
3.6.5 Problems on Inverse Kinematics......Page 215
4.1 Linear Momentum of Rigid Bodies......Page 217
4.2.1 First Principles......Page 223
4.2.2 Angular Momentum and Inertia......Page 228
4.2.3.1 The Inertia Rotation Transformation Law......Page 234
4.2.3.2 Principal Axes of Inertia......Page 238
4.2.3.3 The Parallel Axis Theorem......Page 241
4.2.3.4 Symmetry and Inertia......Page 244
4.3 The Newton–Euler Equations......Page 249
4.4 Euler's Equation for a Rigid Body......Page 253
4.5.1 The General Strategy......Page 255
4.5.2 Free Body Diagrams......Page 256
4.6.1 Differential Algebraic Equations (DAEs)......Page 278
4.6.2 Ordinary Differential Equations (ODEs)......Page 280
4.7.0 Recursive Calculation of Forces and Moments......Page 282
4.8 Recursive Derivation of the Equations of Motion......Page 291
4.9.1 Problems on Linear Momentum......Page 294
4.9.2 Problems on the Center of Mass......Page 297
4.9.3 Problems on the Inertia Matrix......Page 299
4.9.4 Problems on Angular Momentum......Page 301
4.9.5 Problems on the Newton–Euler Equations......Page 302
5.1.1 Generalized Coordinates......Page 305
5.1.2 Functionals and the Calculus of Variations......Page 308
5.1.3 Hamilton's Principle for Conservative Systems......Page 312
5.1.4 Kinetic Energy for Rigid Bodies......Page 319
5.2 Lagrange's Equations for Conservative Systems......Page 323
5.3.1 Virtual Work Formulations......Page 327
5.4.1 Natural Systems......Page 342
5.4.2 Lagrange's Equations and the Denavit–Hartenberg Convention......Page 346
5.5 Constrained Systems......Page 349
5.6.1 Problems on Hamilton's Principle......Page 354
5.6.2 Problems on Lagrange's Equations......Page 357
5.6.3 Problems on Hamilton's Extended Principle......Page 359
5.6.4 Problems on Constrained Systems......Page 365
6.1 The Structure of Control Problems......Page 367
6.1.1 Setpoint and Tracking Feedback Control Problems......Page 368
6.1.3 Linear and Nonlinear Control......Page 369
6.2 Fundamentals of Stability Theory......Page 370
6.3 Advanced Techniques of Stability Theory......Page 377
6.4 Lyapunov's Direct Method......Page 378
6.5 The Invariance Principle......Page 381
6.6 Dynamic Inversion or Computed Torque Control......Page 386
6.7 Approximate Dynamic Inversion and Uncertainty......Page 396
6.8 Controllers Based on Passivity......Page 409
6.9.1 Electric Motors......Page 413
6.9.2 Linear Actuators......Page 420
6.10 Backstepping Control and Actuator Dynamics......Page 424
6.11.1 Problems on Gravity Compensation and PD Setpoint Control......Page 427
6.11.2 Problems on Computed Torque Tracking Control......Page 432
6.11.3 Problems on Dissipativity Based Tracking Control......Page 433
7.1.1 Perspective Projection and Pinhole Camera Models......Page 435
7.1.2 Pixel Coordinates and CCD Cameras......Page 438
7.1.3 The Interaction Matrix......Page 439
7.2 Image Based Visual Servo Control......Page 443
7.2.1 Control Synthesis and Closed Loop Equations......Page 444
7.2.2 Calculation of Initial Conditions......Page 447
7.3 Task Space Control......Page 461
7.4 Task Space and Visual Control......Page 467
7.5 Problems for Chapter 7......Page 479
A.1 Fundamentals of Linear Algebra......Page 485
A.1.1 Solution of Matrix Equations......Page 487
A.1.2 Linear Independence and Rank......Page 488
A.1.4 Least Squares Approximation......Page 490
A.2 The Algebraic Eigenvalue Problem......Page 495
A.2.1 Self‐adjoint Matrices......Page 496
A.2.2 Jordan Canonical Form......Page 498
A.3 Gauss Transformations and LU Factorizations......Page 499
References......Page 505
Index......Page 509
EULA......Page 517