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Chapter 1 Introduction 1

1 Brief History 1

2 Multifingered Hands and Dextrous Manipulation 8

3 Outline of the Book 13

3.1 Manipulation using single robots 14

3.2 Coordinated manipulation using multifingered robot hands 15

3.3 Nonholonomic behavior in robotic systems 16

4 Bibliography 18

Chapter 2 Rigid Body Motion 19

1 Rigid Body Transformations 20

2 Rotational Motion in R3 22

2.1 Properties of rotation matrices 23

2.2 Exponential coordinates for rotation 27

2.3 Other representations 31

3 Rigid Motion in R3 34

3.1 Homogeneous representation 36

3.2 Exponential coordinates for rigid motion and twists 39

3.3 Screws：a geometric description of twists 45

4 Velocity of a Rigid Body 51

4.1 Rotational velocity 51

4.2 Rigid body velocity 54

4.3 Velocity of a screw motion 58

4.4 Coordinate transformations 59

5 Wrenches and Reciprocal Screws 61

5.1 Wrenches 61

5.2 Screw coordinates for a wrench 65

5.3 Reciprocal screws 66

6 Summary 70

7 Bibliography 72

8 Exercises 73

Chapter 3 Manipulator Kinematics 81

1 Introduction 81

2 Forward Kinematics 83

2.1 Problem statement 83

2.2 The product of exponentials formula 85

2.3 Parameterization of manipulators via twists 91

2.4 Manipulator workspace 95

3 Inverse Kinematics 97

3.1 A planar example 97

3.2 Paden-Kahan subproblems 99

3.3 Solving inverse kinematics using subproblems 104

3.4 General solutions to inverse kinematics problems 108

4 The Manipulator Jacobian 115

4.1 End-effector velocity 115

4.2 End-effector forces 121

4.3 Singularities 123

4.4 Manipulability 128

5 Redundant and Parallel Manipulators 129

5.1 Redundant manipulators 130

5.2 Parallel manipulators 132

5.3 Four-bar linkage 135

5.4 Stewart platform 139

6 Summary 144

7 Bibliography 146

8 Exercises 147

Chapter 4 Robot Dynamics and Control 155

1 Introduction 155

2 Lagrange’s Equations 156

2.1 Basic formulation 157

2.2 Inertial properties of rigid bodies 160

2.3 Example：Dynamics of a two-link planar robot 164

2.4 Newton-Euler equations for a rigid body 165

3 Dynamics of Open-Chain Manipulators 168

3.1 The Lagrangian for an open-chain robot 168

3.2 Equations of motion for an open-chain manipulator 169

3.3 Robot dynamics and the product of exponentials formula 175

4 Lyapunov Stability Theory 179

4.1 Basic definitions 179

4.2 The direct method of Lyapunov 182

4.3 The indirect method of Lyapunov 184

4.4 Examples 185

4.5 Lasalle’s invariance principle 188

5 Position Control and Trajectory Tracking 190

5.1 Problem description 190

5.2 Computed torque 191

5.3 PD control 193

5.4 Workspace control 196

6 Control of Constrained Manipulators 199

6.1 Dynamics of constrained systems 200

6.2 Control of constrained manipulators 202

6.3 Example：A planar manipulator moving in a slot 203

7 Summary 206

8 Bibliography 207

9 Exercises 208

Chapter 5 Multifingered Hand Kinematics 211

1 Introduction to Grasping 211

2 Grasp Statics 214

2.1 Contact models 214

2.2 The grasp map 218

3 Force-Closure 223

3.1 Formal definition 223

3.2 Constructive force-closure conditions 224

4 Grasp Planning 229

4.1 Bounds on number of required contacts 229

4.2 Constructing force-closure grasps 232

5 Grasp Constraints 234

5.1 Finger kinematics 234

5.2 Properties of a multifingered grasp 237

5.3 Example：Two SCARA fingers grasping a box 240

6 Rolling Contact Kinematics 243

6.1 Surface models 243

6.2 Contact kinematics 248

6.3 Grasp kinematics with rolling 253

7 Summary 256

8 Bibliography 257

9 Exercises 259

Chapter 6 Hand Dynamics and Control 265

1 Lagrange’s Equations with Constraints 265

1.1 Pfaffian constraints 266

1.2 Lagrange multipliers 269

1.3 Lagrange-d’Alembert formulation 271

1.4 The nature of nonholonomic constraints 274

2 Robot Hand Dynamics 276

2.1 Derivation and properties 276

2.2 Internal forces 279

2.3 Other robot systems 281

3 Redundant and Nonmanipulable Robot Systems 285

3.1 Dynamics of redundant manipulators 286

3.2 Nonmanipulable grasps 290

3.3 Example：Two-fingered SCARA grasp 291

4 Kinematics and Statics of Tendon Actuation 293

4.1 Inelastic tendons 294

4.2 Elastic tendons 296

4.3 Analysis and control of tendon-driven fingers 298

5 Control of Robot Hands 300

5.1 Extending controllers 300

5.2 Hierarchical control structures 302

6 Summary 311

7 Bibliography 313

8 Exercises 314

Chapter 7 Nonholonomic Behavior in Robotic Systems 317

1 Introduction 317

2 Controllability and Frobenius’ Theorem 321

2.1 Vector fields and flows 322

2.2 Lie brackets and Frobenius’ theorem 323

2.3 Nonlinear Controllability 329

3 Examples of Nonholonomic Systems 332

4 Structure of Nonholonomic Systems 339

4.1 Classification of nonholonomic distributions 340

4.2 Examples of nonholonomic systems，continued 341

4.3 Philip Hall basis 344

5 Summary 346

6 Bibliography 347

7 Exercises 349

Chapter 8 Nonholonomic Motion Planning 355

1 Introduction 355

2 Steering Model Control Systems Using Sinusoids 358

2.1 First-order controllable systems：Brockett’s system 358

2.2 Second-order controllable systems 362

2.3 Higher-order systems：chained form systems 363

3 General Methods for Steering 366

3.1 Fourier techniques 367

3.2 Conversion to chained form 369

3.3 Optimal steering of nonholonomic systems 371

3.4 Steering with piecewise constant inputs 375

4 Dynamic Finger Repositioning 382

4.1 Problem description 382

4.2 Steering using sinusoids 383

4.3 Geometric phase algorithm 384

5 Summary 389

6 Bibliography 390

7 Exercises 391

Chapter 9 Future Prospects 395

1 Robots in Hazardous Environments 396

2 Medical Applications for Multifingered Hands 398

3 Robots on a Small Scale：Microrobotics 399

Appendix A Lie Groups and Robot Kinematics 403

1 Differentiable Manifolds 403

1.1 Manifolds and maps 403

1.2 Tangent spaces and tangent maps 404

1.3 Cotangent spaces and cotangent maps 405

1.4 Vector fields 406

1.5 Differential forms 408

2 Lie Groups 408

2.1 Definition and examples 408

2.2 The Lie algebra associated with a Lie group 410

2.3 The exponential map 412

2.4 Canonical coordinates on a Lie group 414

2.5 Actions of Lie groups 415

3 The Geometry of the Euclidean Group 416

3.1 Basic properties 416

3.2 Metric properties of SE（3） 422

3.3 Volume forms on SE（3） 430

Appendix B A Mathematica Package for Screw Calculus 435

Bibliography 441

Index 449