Preface v
1 Introduction 1
1.1 Mathematical Modeling of Robots 5
1.2 Robots as Mechanical Devices 7
1.3 Common Kinematic Arrangements 13
1.4 Outline of the Text 18
Problems 27
Notes and References 29
I The Geometry of Robots 33
2 Rigid Motions 35
2.1 Representing Positions 36
2.2 Representing Rotations 38
2.3 Rotational Transformations 44
2.4 Composition of Rotations 48
2.5 Parameterizations of Rotations 52
2.6 Rigid Motions 61
2.7 Chapter Summary 65
Problems 67
Notes and References 73
3 Forward Kinematics 75
3.1 Kinematic Chains 75
3.2 The Denavit-Hartenberg Convention 78
3.3 Examples 87
3.4 Chapter Summary 96
Problems 96
Notes and References 99
4 Velocity Kinematics 101
4.1 Angular Velocity: The Fixed Axis Case 102
4.2 Skew-Symmetric Matrices 103
4.3 Angular Velocity: The General Case 107
4.4 Addition of Angular Velocities 108
4.5 Linear Velocity of a Point Attached to a Moving Frame 110
4.6 Derivation of the Jacobian 111
4.7 The Tool Velocity 119
4.8 The Analytical Jacobian 121
4.9 Singularities 122
4.10 Static Force/Torque Relationships 129
4.11 Inverse Velocity and Acceleration 131
4.12 Manipulability 133
4.13 Chapter Summary 136
Problems 138
Notes and References 140
5 Inverse Kinematics 141
5.1 The General Inverse Kinematics Problem 141
5.2 Kinematic Decoupling 143
5.3 Inverse Position: A Geometric Approach 145
5.4 Inverse Orientation 151
5.5 Numerical Inverse Kinematics 156
5.6 Chapter Summary 158
Problems 160
Notes and References 162
II Dynamics and Motion Planning 163
6 Dynamics 165
6.1 The Euler-Lagrange Equations 166
6.2 Kinetic and Potential Energy 177
6.3 Equations of Motion 181
6.4 Some Common Configurations 184
6.5 Properties of Robot Dynamic Equations 194
6.6 Newton-Euler Formulation 198
6.7 Chapter Summary 209
Problems 211
Notes and References 214
7 Path and Trajectory Planning 215
7.1 The Configuration Space 216
7.2 Path Planning for Q = â2 221
7.3 Artificial Potential Fields 229
7.4 Sampling-Based Methods 245
7.5 Trajectory Planning 252
7.6 Chapter Summary 263
Problems 265
Notes and References 267
III Control of Manipulators 269
8 Independent Joint Control 271
8.1 Introduction 271
8.2 Actuator Dynamics 273
8.3 Load Dynamics 276
8.4 Independent Joint Model 278
8.5 PID Control 281
8.6 Feedforward Control 288
8.7 Drive-Train Dynamics 292
8.8 State Space Design 297
8.9 Chapter Summary 304
Problems 307
Notes and References 309
9 Nonlinear and Multivariable Control 311
9.1 Introduction 311
9.2 PD Control Revisited 313
9.3 Inverse Dynamics 317
9.4 Passivity-Based Control 329
9.5 Torque Optimization 333
9.6 Chapter Summary 337
Problems 341
Notes and References 343
10 Force Control 345
10.1 Coordinate Frames and Constraints 347
10.2 Network Models and Impedance 351
10.3 Task Space Dynamics and Control 355
10.4 Chapter Summary 361
Problems 362
Notes and References 364
11 Vision-Based Control 365
11.1 Design Considerations 366
11.2 Computer Vision for Vision-Based Control 368
11.3 Camera Motion and the Interaction Matrix 378
11.4 The Interaction Matrix for Point Features 379
11.5 Image-Based Control Laws 386
11.6 End Effector and Camera Motions 393
11.7 Partitioned Approaches 394
11.8 Motion Perceptibility 397
11.9 Summary 399
Problems 401
Notes and References 405
12 Feedback Linearization 409
12.1 Background 410
12.2 Feedback Linearization 417
12.3 Single-Input Systems 419
12.4 Multi-Input Systems 429
12.5 Chapter Summary 433
Problems 433
Notes and References 435
IV Control of Underactuated Systems 437
13 Underactuated Robots 439
13.1 Introduction 439
13.2 Modeling 440
13.3 Examples of Underactuated Robots 443
13.4 Equilibria and Linear Controllability 448
13.5 Partial Feedback Linearization 456
13.6 Output Feedback Linearization 461
13.7 Passivity-Based Control 466
13.8 Chapter Summary 474
Problems 476
Notes and References 477
14 Mobile Robots 479
14.1 Nonholonomic Constraints 480
14.2 Involutivity and Holonomy 484
14.3 Examples of Nonholonomic Systems 487
14.4 Dynamic Extension 493
14.5 Controllability of Driftless Systems 495
14.6 Motion Planning 499
14.7 Feedback Control of Driftless Systems 509
14.8 Chapter Summary 519
Problems 520
Notes and References 521
A Trigonometry 523
A.1 The Two-Argument Arctangent Function 523
A.2 Useful Trigonometric Formulas 523
B Linear Algebra 525
B.1 Vectors 525
B.2 Inner Product Spaces 526
B.3 Matrices 528
B.4 Eigenvalues and Eigenvectors 530
B.5 Differentiation of Vectors 533
B.6 The Matrix Exponential 534
B.7 Lie Groups and Lie Algebras 534
B.8 Matrix Pseudoinverse 536
B.9 Schur Complement 536
B.10 Singular Value Decomposition (SVD) 537
C Lyapunov Stability 539
C.1 Continuity and Differentiability 539
C.2 Vector Fields and Equilibria 541
C.3 Lyapunov Functions 545
C.4 Stability Criteria 545
C.5 Global and Exponential Stability 546
C.6 Stability of Linear Systems 547
C.7 LaSalle's Theorem 548
C.8 Barbalat's Lemma 549
D Optimization 551
D.1 Unconstrained Optimization 551
D.2 Constrained Optimization 552
E Camera Calibration 555
E.1 The Image Plane and the Sensor Array 555
E.2 Extrinsic Camera Parameters 556
E.3 Intrinsic Camera Parameters 557
E.4 Determining the Camera Parameters 557
Bibliography 561
Index 576
