Modelling and Control of Robot Manipulators Second Edition

L. Sciavicco and B. Siciliano

Modelling and Control of Robot Manipulators Second Edition With 190 Figures

Springer

Table of Contents

1.

Introduction 1.1 Robotics 1.2 Industrial Robot 1.3 Manipulator Structures 1.4 Modelling and Control of Robot Manipulators 1.4.1 Modelling 1.4.2 Control 1.5 Bibliographical Reference Texts

1 1 3 6 14 15 15 16

2.

Kinematics 2.1 Position and Orientation of a Rigid Body 2.2 Rotation Matrix 2.2.1 Elementary Rotations 2.2.2 Representation of a Vector 2.2.3 Rotation of a Vector 2.3 Composition of Rotation Matrices 2.4 Euler Angles 2.4.1 ZYZ Angles 2.4.2 Roll-Pitch-Yaw Angles 2.5 Angle and Axis 2.6 Unit Quaternion 2.7 Homogeneous Transformations 2.8 Direct Kinematics 2.8.1 Open Chain 2.8.2 Denavit-Hartenberg Convention 2.8.3 Closed Chain 2.9 Kinematics of Typical Manipulator Structures 2.9.1 Three-link Planar Arm 2.9.2 Parallelogram Arm 2.9.3 Spherical Arm 2.9.4 Anthropomorphic Arm 2.9.5 Spherical Wrist 2.9.6 Stanford Manipulator 2.9.7 Anthropomorphic Arm with Spherical Wrist 2.10 Joint Space and Operational Space 2.10.1 Workspace

21 21 22 23 24 25 26 30 30 32 33 35 37 39 41 42 46 49 49 51 53 54 55 57 58 59 61

xx

Table of Contents 2.10.2 Kinematic Redundancy 2.11 Kinematic Calibration 2.12 Inverse Kinematics Problem 2.12.1 Solution of Three-link Planar Arm 2.12.2 Solution of Manipulators with Spherical Wrist 2.12.3 Solution of Spherical Arm 2.12.4 Solution of Anthropomorphic Arm 2.12.5 Solution of Spherical Wrist Problems Bibliography

63 64 66 67 70 71 72 73 74 76

3.

Differential Kinematics and Statics* 3.1 Geometric Jacobian 3.1.1 Derivative of a Rotation Matrix 3.1.2 Link Velocity 3.1.3 Jacobian Computation 3.2 Jacobian of Typical Manipulator Structures 3.2.1 Three-link Planar Arm 3.2.2 Anthropomorphic Arm 3.2.3 Stanford Manipulator 3.3 Kinematic Singularities 3.3.1 Singularity Decoupling 3.3.2 Wrist Singularities 3.3.3 Arm Singularities 3.4 Analysis of Redundancy 3.5 Differential Kinematics Inversion 3.5.1 Redundant Manipulators 3.5.2 Kinematic Singularities 3.6 Analytical Jacobian 3.7 Inverse Kinematics Algorithms 3.7.1 Jacobian (Pseudo-)Inverse 3.7.2 Jacobian Transpose 3.7.3 Orientation Error 3.7.4 A Comparison Between Inverse Kinematics Algorithms .. 3.8 Statics 3.8.1 Kineto-statics Duality 3.8.2 Velocity and Force Transformation 3.8.3 Closed Chain 3.9 Manipulability Ellipsoids Problems Bibliography

79 79 80 82 84 87 87 88 89 89 91 92 92 94 96 97 100 100 104 105 106 109 112 116 118 119 120 121 127 128

4.

Dynamics 4.1 Lagrange Formulation 4.1.1 Computation of Kinetic Energy 4.1.2 Computation of Potential Energy 4.1.3 Equations of Motion

131 131 133 139 140

Table of Contents 4.2

4.3

4.4 4.5

4.6 4.7 4.8

Notable Properties of Dynamic Model* 4.2.1 Skew-symmetryofMatrixB-2C 4.2.2 Linearity in the Dynamic Parameters Dynamic Model of Simple Manipulator Structures 4.3.1 Two-link Cartesian Arm 4.3.2 Two-link Planar Arm 4.3.3 Parallelogram Arm Dynamic Parameter Identification* Newton-Euler Formulation* 4.5.1 Link Acceleration 4.5.2 Recursive Algorithm 4.5.3 Example Direct Dynamics and Inverse Dynamics* Operational Space Dynamic Model* Dynamic Manipulability Ellipsoid* Problems Bibliography

xxi 141 142 143 148 148 149 161 164 166 168 169 172 175 176 179 181 182

5.

Trajectory Planning 5.1 Path and Trajectory 5.2 Joint Space Trajectories 5.2.1 Point-to-point Motion 5.2.2 Path Motion 5.3 Operational Space Trajectories 5.3.1 Path Primitives 5.3.2 Position 5.3.3 Orientation 5.4 Dynamic Scaling of Trajectories Problems Bibliography

185 185 186 187 192 202 203 207 208 209 211 212

6.

Motion Control 6.1 The Control Problem 6.2 Joint Space Control 6.3 Independent Joint Control 6.3.1 Feedback Control 6.3.2 Decentralized Feedforward Compensation 6.4 Computed Torque Feedforward Control 6.5 Centralized Control* 6.5.1 PD Control with Gravity Compensation 6.5.2 Inverse Dynamics Control 6.5.3 Robust Control 6.5.4 Adaptive Control 6.6 Operational Space Control* 6.6.1 General Schemes 6.6.2 PD Control with Gravity Compensation 6.6.3 Inverse Dynamics Control

213 213 215 217 218 227 231 234 236 238 240 246 250 251 252 254

xxii

Table of Contents 6.7

A Comparison Between Various Control Schemes* Problems Bibliography

256 263 268

7.

Interaction Control* 7.1 Manipulator Interaction with Environment 7.2 Compliance Control 7.3 Impedance Control 7.4 Force Control 7.4.1 Force Control with Inner Position Loop 7.4.2 Force Control with Inner Velocity Loop 7.4.3 Parallel Force/Position Control 7.5 Natural Constraints and Artificial Constraints 7.5.1 Case Studies 7.6 Hybrid Force/Position Control Problems Bibliography

271 271 272 276 280 280 281 282 285 287 288 292 292

8.

Actuators and Sensors 8.1 Joint Actuating System 8.1.1 Transmissions 8.1.2 Servomotors 8.1.3 Power Amplifiers 8.1.4 Power Supplies 8.2 Servomotors 8.2.1 Electric Servomotors 8.2.2 Hydraulic Servomotors 8.3 Sensors 8.3.1 Position Transducers 8.3.2 Velocity Transducers 8.3.3 Force Sensors 8.3.4 Vision Sensors Problems Bibliography

295 295 296 297 299 300 300 300 304 307 307 310 311 315 319 319

9.

Control Architecture 9.1 Functional Architecture 9.2 Programming Environment 9.2.1 Teaching-by-showing 9.2.2 Robot-oriented Programming 9.3 Hardware Architecture Problems Bibliography

321 321 326 327 328 329 332 333

Appendix A. Linear Algebra A.I Definitions A.2 Matrix Operations

335 335 337

Table of Contents A.3 A.4 A.5 A.6 A.7 A.8

Vector Operations Linear Transformations Eigenvalues and Eigenvectors Bilinear Forms and Quadratic Forms Pseudo-inverse Singular Value Decomposition Bibliography

xxiii 341 344 345 345 347 348 349

Appendix B. Rigid Body Mechanics B.I Kinematics B.2 Dynamics B.3 Work and Energy B.4 Constrained Systems Bibliography

351 351 353 356 356 359

Appendix C. Feedback Control C.I Control of Single-input/Single-outputLinear Systems C.2 Control of Nonlinear Mechanical Systems C.3 Lyapunov Direct Method Bibliography

361 361 366 368 369

Index

371