L. Sciavicco and B. Siciliano Modelling and Control of Robot Manipulators Second Edition With 190 Figures Springer
Table of Contents 1. Introduction 1 1.1 Robotics 1 1.2 Industrial Robot 3 1.3 Manipulator Structures 6 1.4 Modelling and Control of Robot Manipulators 14 1.4.1 Modelling 15 1.4.2 Control 15 1.5 Bibliographical Reference Texts 16 2. Kinematics 21 2.1 Position and Orientation of a Rigid Body 21 2.2 Rotation Matrix 22 2.2.1 Elementary Rotations 23 2.2.2 Representation of a Vector 24 2.2.3 Rotation of a Vector 25 2.3 Composition of Rotation Matrices 26 2.4 Euler Angles 30 2.4.1 ZYZ Angles 30 2.4.2 Roll-Pitch-Yaw Angles 32 2.5 Angle and Axis 33 2.6 Unit Quaternion 35 2.7 Homogeneous Transformations 37 2.8 Direct Kinematics 39 2.8.1 Open Chain 41 2.8.2 Denavit-Hartenberg Convention 42 2.8.3 Closed Chain 46 2.9 Kinematics of Typical Manipulator Structures 49 2.9.1 Three-link Planar Arm 49 2.9.2 Parallelogram Arm 51 2.9.3 Spherical Arm 53 2.9.4 Anthropomorphic Arm 54 2.9.5 Spherical Wrist 55 2.9.6 Stanford Manipulator 57 2.9.7 Anthropomorphic Arm with Spherical Wrist 58 2.10 Joint Space and Operational Space 59 2.10.1 Workspace 61
xx Table of Contents 2.10.2 Kinematic Redundancy 63 2.11 Kinematic Calibration 64 2.12 Inverse Kinematics Problem 66 2.12.1 Solution of Three-link Planar Arm 67 2.12.2 Solution of Manipulators with Spherical Wrist 70 2.12.3 Solution of Spherical Arm 71 2.12.4 Solution of Anthropomorphic Arm 72 2.12.5 Solution of Spherical Wrist 73 Problems 74 Bibliography 76 3. Differential Kinematics and Statics* 79 3.1 Geometric Jacobian 79 3.1.1 Derivative of a Rotation Matrix 80 3.1.2 Link Velocity 82 3.1.3 Jacobian Computation 84 3.2 Jacobian of Typical Manipulator Structures 87 3.2.1 Three-link Planar Arm 87 3.2.2 Anthropomorphic Arm 88 3.2.3 Stanford Manipulator 89 3.3 Kinematic Singularities 89 3.3.1 Singularity Decoupling 91 3.3.2 Wrist Singularities 92 3.3.3 Arm Singularities 92 3.4 Analysis of Redundancy 94 3.5 Differential Kinematics Inversion 96 3.5.1 Redundant Manipulators 97 3.5.2 Kinematic Singularities 100 3.6 Analytical Jacobian 100 3.7 Inverse Kinematics Algorithms 104 3.7.1 Jacobian (Pseudo-)Inverse 105 3.7.2 Jacobian Transpose 106 3.7.3 Orientation Error 109 3.7.4 A Comparison Between Inverse Kinematics Algorithms.. 112 3.8 Statics 116 3.8.1 Kineto-statics Duality 118 3.8.2 Velocity and Force Transformation 119 3.8.3 Closed Chain 120 3.9 Manipulability Ellipsoids 121 Problems 127 Bibliography 128 4. Dynamics 131 4.1 Lagrange Formulation 131 4.1.1 Computation of Kinetic Energy 133 4.1.2 Computation of Potential Energy 139 4.1.3 Equations of Motion 140
Table of Contents xxi 4.2 Notable Properties of Dynamic Model* 141 4.2.1 Skew-symmetryofMatrixB-2C 142 4.2.2 Linearity in the Dynamic Parameters 143 4.3 Dynamic Model of Simple Manipulator Structures 148 4.3.1 Two-link Cartesian Arm 148 4.3.2 Two-link Planar Arm 149 4.3.3 Parallelogram Arm 161 4.4 Dynamic Parameter Identification* 164 4.5 Newton-Euler Formulation* 166 4.5.1 Link Acceleration 168 4.5.2 Recursive Algorithm 169 4.5.3 Example 172 4.6 Direct Dynamics and Inverse Dynamics* 175 4.7 Operational Space Dynamic Model* 176 4.8 Dynamic Manipulability Ellipsoid* 179 Problems 181 Bibliography 182 5. Trajectory Planning 185 5.1 Path and Trajectory 185 5.2 Joint Space Trajectories 186 5.2.1 Point-to-point Motion 187 5.2.2 Path Motion 192 5.3 Operational Space Trajectories 202 5.3.1 Path Primitives 203 5.3.2 Position 207 5.3.3 Orientation 208 5.4 Dynamic Scaling of Trajectories 209 Problems 211 Bibliography 212 6. Motion Control 213 6.1 The Control Problem 213 6.2 Joint Space Control 215 6.3 Independent Joint Control 217 6.3.1 Feedback Control 218 6.3.2 Decentralized Feedforward Compensation 227 6.4 Computed Torque Feedforward Control 231 6.5 Centralized Control* 234 6.5.1 PD Control with Gravity Compensation 236 6.5.2 Inverse Dynamics Control 238 6.5.3 Robust Control 240 6.5.4 Adaptive Control 246 6.6 Operational Space Control* 250 6.6.1 General Schemes 251 6.6.2 PD Control with Gravity Compensation 252 6.6.3 Inverse Dynamics Control 254
xxii Table of Contents 6.7 A Comparison Between Various Control Schemes* 256 Problems 263 Bibliography 268 7. Interaction Control* 271 7.1 Manipulator Interaction with Environment 271 7.2 Compliance Control 272 7.3 Impedance Control 276 7.4 Force Control 280 7.4.1 Force Control with Inner Position Loop 280 7.4.2 Force Control with Inner Velocity Loop 281 7.4.3 Parallel Force/Position Control 282 7.5 Natural Constraints and Artificial Constraints 285 7.5.1 Case Studies 287 7.6 Hybrid Force/Position Control 288 Problems 292 Bibliography 292 8. Actuators and Sensors 295 8.1 Joint Actuating System 295 8.1.1 Transmissions 296 8.1.2 Servomotors 297 8.1.3 Power Amplifiers 299 8.1.4 Power Supplies 300 8.2 Servomotors 300 8.2.1 Electric Servomotors 300 8.2.2 Hydraulic Servomotors 304 8.3 Sensors 307 8.3.1 Position Transducers 307 8.3.2 Velocity Transducers 310 8.3.3 Force Sensors 311 8.3.4 Vision Sensors 315 Problems 319 Bibliography 319 9. Control Architecture 321 9.1 Functional Architecture 321 9.2 Programming Environment 326 9.2.1 Teaching-by-showing 327 9.2.2 Robot-oriented Programming 328 9.3 Hardware Architecture 329 Problems 332 Bibliography 333 Appendix A. Linear Algebra 335 A.I Definitions 335 A.2 Matrix Operations 337
Table of Contents xxiii A.3 Vector Operations 341 A.4 Linear Transformations 344 A.5 Eigenvalues and Eigenvectors 345 A.6 Bilinear Forms and Quadratic Forms 345 A.7 Pseudo-inverse 347 A.8 Singular Value Decomposition 348 Bibliography 349 Appendix B. Rigid Body Mechanics 351 B.I Kinematics 351 B.2 Dynamics 353 B.3 Work and Energy 356 B.4 Constrained Systems 356 Bibliography 359 Appendix C. Feedback Control 361 C.I Control of Single-input/Single-outputLinear Systems 361 C.2 Control of Nonlinear Mechanical Systems 366 C.3 Lyapunov Direct Method 368 Bibliography 369 Index 371