Modelling and Control of Robot Manipulators

Transcription

1 L. Sciavicco and B. Siciliano Modelling and Control of Robot Manipulators Second Edition With 190 Figures Springer

2 Table of Contents 1. Introduction Robotics Industrial Robot Manipulator Structures Modelling and Control of Robot Manipulators Modelling Control Bibliographical Reference Texts Kinematics Position and Orientation of a Rigid Body Rotation Matrix Elementary Rotations Representation of a Vector Rotation of a Vector Composition of Rotation Matrices Euler Angles ZYZ Angles Roll-Pitch-Yaw Angles Angle and Axis Unit Quaternion Homogeneous Transformations Direct Kinematics Open Chain Denavit-Hartenberg Convention Closed Chain Kinematics of Typical Manipulator Structures Three-link Planar Arm Parallelogram Arm Spherical Arm Anthropomorphic Arm Spherical Wrist Stanford Manipulator Anthropomorphic Arm with Spherical Wrist Joint Space and Operational Space Workspace 61

3 xx Table of Contents Kinematic Redundancy Kinematic Calibration Inverse Kinematics Problem Solution of Three-link Planar Arm Solution of Manipulators with Spherical Wrist Solution of Spherical Arm Solution of Anthropomorphic Arm Solution of Spherical Wrist 73 Problems 74 Bibliography Differential Kinematics and Statics* Geometric Jacobian Derivative of a Rotation Matrix Link Velocity Jacobian Computation Jacobian of Typical Manipulator Structures Three-link Planar Arm Anthropomorphic Arm Stanford Manipulator Kinematic Singularities Singularity Decoupling Wrist Singularities Arm Singularities Analysis of Redundancy Differential Kinematics Inversion Redundant Manipulators Kinematic Singularities Analytical Jacobian Inverse Kinematics Algorithms Jacobian (Pseudo-)Inverse Jacobian Transpose Orientation Error A Comparison Between Inverse Kinematics Algorithms Statics Kineto-statics Duality Velocity and Force Transformation Closed Chain Manipulability Ellipsoids 121 Problems 127 Bibliography Dynamics Lagrange Formulation Computation of Kinetic Energy Computation of Potential Energy Equations of Motion 140

4 Table of Contents xxi 4.2 Notable Properties of Dynamic Model* Skew-symmetryofMatrixB-2C Linearity in the Dynamic Parameters Dynamic Model of Simple Manipulator Structures Two-link Cartesian Arm Two-link Planar Arm Parallelogram Arm Dynamic Parameter Identification* Newton-Euler Formulation* Link Acceleration Recursive Algorithm Example Direct Dynamics and Inverse Dynamics* Operational Space Dynamic Model* Dynamic Manipulability Ellipsoid* 179 Problems 181 Bibliography Trajectory Planning Path and Trajectory Joint Space Trajectories Point-to-point Motion Path Motion Operational Space Trajectories Path Primitives Position Orientation Dynamic Scaling of Trajectories 209 Problems 211 Bibliography Motion Control The Control Problem Joint Space Control Independent Joint Control Feedback Control Decentralized Feedforward Compensation Computed Torque Feedforward Control Centralized Control* PD Control with Gravity Compensation Inverse Dynamics Control Robust Control Adaptive Control Operational Space Control* General Schemes PD Control with Gravity Compensation Inverse Dynamics Control 254

5 xxii Table of Contents 6.7 A Comparison Between Various Control Schemes* 256 Problems 263 Bibliography Interaction Control* Manipulator Interaction with Environment Compliance Control Impedance Control Force Control Force Control with Inner Position Loop Force Control with Inner Velocity Loop Parallel Force/Position Control Natural Constraints and Artificial Constraints Case Studies Hybrid Force/Position Control 288 Problems 292 Bibliography Actuators and Sensors Joint Actuating System Transmissions Servomotors Power Amplifiers Power Supplies Servomotors Electric Servomotors Hydraulic Servomotors Sensors Position Transducers Velocity Transducers Force Sensors Vision Sensors 315 Problems 319 Bibliography Control Architecture Functional Architecture Programming Environment Teaching-by-showing Robot-oriented Programming Hardware Architecture 329 Problems 332 Bibliography 333 Appendix A. Linear Algebra 335 A.I Definitions 335 A.2 Matrix Operations 337

6 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