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现代机器人学:机械、规划和控制-Modern Robotics: Mechanics, Planning, and Control

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标题(title):Modern Robotics: Mechanics, Planning, and Control
现代机器人学:机械、规划和控制
作者(author):Frank C. Park; Kevin M. Lynch
出版社(publisher):Cambridge University Press
大小(size):7 MB (7344604 bytes)
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This introduction to robotics offers a distinct and unified perspective of the mechanics, planning and control of robots. Ideal for self-learning, or for courses, as it assumes only freshman-level physics, ordinary differential equations, linear algebra and a little bit of computing background. Modern Robotics presents the state-of-the-art, screw-theoretic techniques capturing the most salient physical features of a robot in an intuitive geometrical way. With numerous exercises at the end of each chapter, accompanying software written to reinforce the concepts in the book and video lectures aimed at changing the classroom experience, this is the go-to textbook for learning about this fascinating subject.
Table of contents :
Foreword by Roger Brockett ix
Foreword by Matthew Mason xi
Preface xiii
1 Preview 1
2 Configuration Space 11
2.1 Degrees of Freedom of a Rigid Body . . . . . . . . . . . . . . . . 12
2.2 Degrees of Freedom of a Robot . . . . . . . . . . . . . . . . . . . 15
2.2.1 Robot Joints . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Gr¨ubler’s Formula . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Configuration Space: Topology and Representation . . . . . . . . 23
2.3.1 Configuration Space Topology . . . . . . . . . . . . . . . . 23
2.3.2 Configuration Space Representation . . . . . . . . . . . . 25
2.4 Configuration and Velocity Constraints . . . . . . . . . . . . . . . 29
2.5 Task Space and Workspace . . . . . . . . . . . . . . . . . . . . . 32
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.7 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Rigid-Body Motions 59
3.1 Rigid-Body Motions in the Plane . . . . . . . . . . . . . . . . . . 62
3.2 Rotations and Angular Velocities . . . . . . . . . . . . . . . . . . 68
3.2.1 Rotation Matrices . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 Angular Velocities . . . . . . . . . . . . . . . . . . . . . . 76
3.2.3 Exponential Coordinate Representation of Rotation . . . 79
3.3 Rigid-Body Motions and Twists . . . . . . . . . . . . . . . . . . . 89
3.3.1 Homogeneous Transformation Matrices . . . . . . . . . . 89
3.3.2 Twists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.3.3 Exponential Coordinate Representation of Rigid-BodyMotions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.4 Wrenches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.6 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.7 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4 Forward Kinematics 137
4.1 Product of Exponentials Formula . . . . . . . . . . . . . . . . . . 140
4.1.1 First Formulation: Screw Axes in the Base Frame . . . . 141
4.1.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.1.3 Second Formulation: Screw Axes in the End-E↵ector Frame148
4.2 The Universal Robot Description Format . . . . . . . . . . . . . 152
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.4 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.5 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 160
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5 Velocity Kinematics and Statics 171
5.1 Manipulator Jacobian . . . . . . . . . . . . . . . . . . . . . . . . 178
5.1.1 Space Jacobian . . . . . . . . . . . . . . . . . . . . . . . . 178
5.1.2 Body Jacobian . . . . . . . . . . . . . . . . . . . . . . . . 183
5.1.3 Visualizing the Space and Body Jacobian . . . . . . . . . 185
5.1.4 Relationship between the Space and Body Jacobian . . . 187
5.1.5 Alternative Notions of the Jacobian . . . . . . . . . . . . 187
5.1.6 Looking Ahead to Inverse Velocity Kinematics . . . . . . 189
5.2 Statics of Open Chains . . . . . . . . . . . . . . . . . . . . . . . . 190
5.3 Singularity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.4 Manipulability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.6 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.7 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6 Inverse Kinematics 219
6.1 Analytic Inverse Kinematics . . . . . . . . . . . . . . . . . . . . . 221
6.1.1 6R PUMA-Type Arm . . . . . . . . . . . . . . . . . . . . 221
6.1.2 Stanford-Type Arms . . . . . . . . . . . . . . . . . . . . . 225
6.2 Numerical Inverse Kinematics . . . . . . . . . . . . . . . . . . . . 226
6.2.1 Newton–Raphson Method . . . . . . . . . . . . . . . . . . 227
6.2.2 Numerical Inverse Kinematics Algorithm . . . . . . . . . 227
6.3 Inverse Velocity Kinematics . . . . . . . . . . . . . . . . . . . . . 232
6.4 A Note on Closed Loops . . . . . . . . . . . . . . . . . . . . . . . 234
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
6.6 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
6.7 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 236
6.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
7 Kinematics of Closed Chains 245
7.1 Inverse and Forward Kinematics . . . . . . . . . . . . . . . . . . 247
7.1.1 3⇥RPR Planar Parallel Mechanism . . . . . . . . . . . . . 247
7.1.2 Stewart–Gough Platform . . . . . . . . . . . . . . . . . . 249
7.1.3 General Parallel Mechanisms . . . . . . . . . . . . . . . . 251
7.2 Di↵erential Kinematics . . . . . . . . . . . . . . . . . . . . . . . . 252
7.2.1 Stewart–Gough Platform . . . . . . . . . . . . . . . . . . 252
7.2.2 General Parallel Mechanisms . . . . . . . . . . . . . . . . 254
7.3 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
7.5 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 262
7.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
8 Dynamics of Open Chains 271
8.1 Lagrangian Formulation . . . . . . . . . . . . . . . . . . . . . . . 272
8.1.1 Basic Concepts and Motivating Examples . . . . . . . . . 272
8.1.2 General Formulation . . . . . . . . . . . . . . . . . . . . . 277
8.1.3 Understanding the Mass Matrix . . . . . . . . . . . . . . 279
8.1.4 Lagrangian Dynamics vs. Newton–Euler Dynamics . . . . 281
8.2 Dynamics of a Single Rigid Body . . . . . . . . . . . . . . . . . . 283
8.2.1 Classical Formulation . . . . . . . . . . . . . . . . . . . . 283
8.2.2 Twist–Wrench Formulation . . . . . . . . . . . . . . . . . 288
8.2.3 Dynamics in Other Frames . . . . . . . . . . . . . . . . . 290
8.3 Newton–Euler Inverse Dynamics . . . . . . . . . . . . . . . . . . 291
8.3.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
8.3.2 Newton-Euler Inverse Dynamics Algorithm . . . . . . . . 294
8.4 Dynamic Equations in Closed Form . . . . . . . . . . . . . . . . . 294
8.5 Forward Dynamics of Open Chains . . . . . . . . . . . . . . . . . 298
8.6 Dynamics in the Task Space . . . . . . . . . . . . . . . . . . . . . 300
8.7 Constrained Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 301
8.8 Robot Dynamics in the URDF . . . . . . . . . . . . . . . . . . . 303
8.9 Actuation, Gearing, and Friction . . . . . . . . . . . . . . . . . . 303
8.9.1 DC Motors and Gearing . . . . . . . . . . . . . . . . . . . 305
8.9.2 Apparent Inertia . . . . . . . . . . . . . . . . . . . . . . . 310
8.9.3 Newton–Euler Inverse Dynamics Algorithm Accounting
for Motor Inertias and Gearing . . . . . . . . . . . . . . . 312
8.9.4 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
8.9.5 Joint and Link Flexibility . . . . . . . . . . . . . . . . . . 314
8.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
8.11 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
8.12 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 320
8.13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
9 Trajectory Generation 325
9.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
9.2 Point-to-Point Trajectories . . . . . . . . . . . . . . . . . . . . . 326
9.2.1 Straight-Line Paths . . . . . . . . . . . . . . . . . . . . . 326
9.2.2 Time Scaling a Straight-Line Path . . . . . . . . . . . . . 328
9.3 Polynomial Via Point Trajectories . . . . . . . . . . . . . . . . . 334
9.4 Time-Optimal Time Scaling . . . . . . . . . . . . . . . . . . . . . 336
9.4.1 The (s, s˙) Phase Plane . . . . . . . . . . . . . . . . . . . . 339
9.4.2 The Time-Scaling Algorithm . . . . . . . . . . . . . . . . 341
9.4.3 A Variation on the Time-Scaling Algorithm . . . . . . . . 342
9.4.4 Assumptions and Caveats . . . . . . . . . . . . . . . . . . 344
9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
9.6 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
9.7 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 347
9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
10 Motion Planning 353
10.1 Overview of Motion Planning . . . . . . . . . . . . . . . . . . . . 353
10.1.1 Types of Motion Planning Problems . . . . . . . . . . . . 354
10.1.2 Properties of Motio
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