MARK W. SPONG has been researching and teaching robotics for over 35 years. He currently serves as a Professor, Excellence in Education Chair, in the Department of Systems Engineering at the University of Texas at Dallas. He has been recognized for outstanding achievements including the John R. Ragazzini Award for Control Education and the IEEE RAS Pioneer in Robotics Award. He is currently a Fellow of both IEEE and IFAC.

SETH HUTCHINSON received his Ph.D. from Purdue University in 1988, and is currently Professor and KUKA Chair for Robotics in the School of Interactive Computing at the Georgia Institute of Technology, where he also serves as Executive Director of the Institute for Robotics and Intelligent Machines. He was the Founding Editor-in-Chief of the IEEE Robotics and Automation Society's Conference Editorial Board, Editor-in-Chief of the IEEE Transactions on Robotics, and is a Fellow of the IEEE. His research in robotics spans the areas of planning, sensing, and control.

MATHUKUMALLI VIDYASAGAR received his Ph.D. in electrical engineering in 1969 from the University of Wisconsin in Madison. During his fifty-year career, he has worked in control theory, machine learning, robotics and cancer biology. Among the many honors he has received are Fellowship in The Royal Society and the IEEE Control Systems Award. At present he is a Distinguished Professor at the Indian Institute of Technology Hyderabad.

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 = 2 221

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