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Chapter 1 Introduction1

1 Brief History1

2 Multifingered Hands and Dextrous Manipulation8

3 Outline of the Book13

3.1 Manipulation using single robots14

3.2 Coordinated manipulation using multifingered robot hands15

3.3 Nonholonomic behavior in robotic systems16

4 Bibliography18

Chapter 2 Rigid Body Motion19

1 Rigid Body Transformations20

2 Rotational Motion in R322

2.1 Properties of rotation matrices23

2.2 Exponential coordinates for rotation27

2.3 Other representations31

3 Rigid Motion in R334

3.1 Homogeneous representation36

3.2 Exponential coordinates for rigid motion and twists39

3.3 Screws：a geometric description of twists45

4 Velocity of a Rigid Body51

4.1 Rotational velocity51

4.2 Rigid body velocity54

4.3 Velocity of a screw motion58

4.4 Coordinate transformations59

5 Wrenches and Reciprocal Screws61

5.1 Wrenches61

5.2 Screw coordinates for a wrench65

5.3 Reciprocal screws66

6 Summary70

7 Bibliography72

8 Exercises73

Chapter 3 Manipulator Kinematics81

1 Introduction81

2 Forward Kinematics83

2.1 Problem statement83

2.2 The product of exponentials formula85

2.3 Parameterization of manipulators via twists91

2.4 Manipulator workspace95

3 Inverse Kinematics97

3.1 A planar example97

3.2 Paden-Kahan subproblems99

3.3 Solving inverse kinematics using subproblems104

3.4 General solutions to inverse kinematics problems108

4 The Manipulator Jacobian115

4.1 End-effector velocity115

4.2 End-effector forces121

4.3 Singularities123

4.4 Manipulability128

5 Redundant and Parallel Manipulators129

5.1 Redundant manipulators130

5.2 Parallel manipulators132

5.3 Four-bar linkage135

5.4 Stewart platform139

6 Summary144

7 Bibliography146

8 Exercises147

Chapter 4 Robot Dynamics and Control155

1 Introduction155

2 Lagrange’s Equations156

2.1 Basic formulation157

2.2 Inertial properties of rigid bodies160

2.3 Example：Dynamics of a two-link planar robot164

2.4 Newton-Euler equations for a rigid body165

3 Dynamics of Open-Chain Manipulators168

3.1 The Lagrangian for an open-chain robot168

3.2 Equations of motion for an open-chain manipulator169

3.3 Robot dynamics and the product of exponentials formula175

4 Lyapunov Stability Theory179

4.1 Basic definitions179

4.2 The direct method of Lyapunov182

4.3 The indirect method of Lyapunov184

4.4 Examples185

4.5 Lasalle’s invariance principle188

5 Position Control and Trajectory Tracking190

5.1 Problem description190

5.2 Computed torque191

5.3 PD control193

5.4 Workspace control196

6 Control of Constrained Manipulators199

6.1 Dynamics of constrained systems200

6.2 Control of constrained manipulators202

6.3 Example：A planar manipulator moving in a slot203

7 Summary206

8 Bibliography207

9 Exercises208

Chapter 5 Multifingered Hand Kinematics211

1 Introduction to Grasping211

2 Grasp Statics214

2.1 Contact models214

2.2 The grasp map218

3 Force-Closure223

3.1 Formal definition223

3.2 Constructive force-closure conditions224

4 Grasp Planning229

4.1 Bounds on number of required contacts229

4.2 Constructing force-closure grasps232

5 Grasp Constraints234

5.1 Finger kinematics234

5.2 Properties of a multifingered grasp237

5.3 Example：Two SCARA fingers grasping a box240

6 Rolling Contact Kinematics243

6.1 Surface models243

6.2 Contact kinematics248

6.3 Grasp kinematics with rolling253

7 Summary256

8 Bibliography257

9 Exercises259

Chapter 6 Hand Dynamics and Control265

1 Lagrange’s Equations with Constraints265

1.1 Pfaffian constraints266

1.2 Lagrange multipliers269

1.3 Lagrange-d’Alembert formulation271

1.4 The nature of nonholonomic constraints274

2 Robot Hand Dynamics276

2.1 Derivation and properties276

2.2 Internal forces279

2.3 Other robot systems281

3 Redundant and Nonmanipulable Robot Systems285

3.1 Dynamics of redundant manipulators286

3.2 Nonmanipulable grasps290

3.3 Example：Two-fingered SCARA grasp291

4 Kinematics and Statics of Tendon Actuation293

4.1 Inelastic tendons294

4.2 Elastic tendons296

4.3 Analysis and control of tendon-driven fingers298

5 Control of Robot Hands300

5.1 Extending controllers300

5.2 Hierarchical control structures302

6 Summary311

7 Bibliography313

8 Exercises314

Chapter 7 Nonholonomic Behavior in Robotic Systems317

1 Introduction317

2 Controllability and Frobenius’ Theorem321

2.1 Vector fields and flows322

2.2 Lie brackets and Frobenius’ theorem323

2.3 Nonlinear Controllability329

3 Examples of Nonholonomic Systems332

4 Structure of Nonholonomic Systems339

4.1 Classification of nonholonomic distributions340

4.2 Examples of nonholonomic systems，continued341

4.3 Philip Hall basis344

5 Summary346

6 Bibliography347

7 Exercises349

Chapter 8 Nonholonomic Motion Planning355

1 Introduction355

2 Steering Model Control Systems Using Sinusoids358

2.1 First-order controllable systems：Brockett’s system358

2.2 Second-order controllable systems362

2.3 Higher-order systems：chained form systems363

3 General Methods for Steering366

3.1 Fourier techniques367

3.2 Conversion to chained form369

3.3 Optimal steering of nonholonomic systems371

3.4 Steering with piecewise constant inputs375

4 Dynamic Finger Repositioning382

4.1 Problem description382

4.2 Steering using sinusoids383

4.3 Geometric phase algorithm384

5 Summary389

6 Bibliography390

7 Exercises391

Chapter 9 Future Prospects395

1 Robots in Hazardous Environments396

2 Medical Applications for Multifingered Hands398

3 Robots on a Small Scale：Microrobotics399

Appendix A Lie Groups and Robot Kinematics403

1 Differentiable Manifolds403

1.1 Manifolds and maps403

1.2 Tangent spaces and tangent maps404

1.3 Cotangent spaces and cotangent maps405

1.4 Vector fields406

1.5 Differential forms408

2 Lie Groups408

2.1 Definition and examples408

2.2 The Lie algebra associated with a Lie group410

2.3 The exponential map412

2.4 Canonical coordinates on a Lie group414

2.5 Actions of Lie groups415

3 The Geometry of the Euclidean Group416

3.1 Basic properties416

3.2 Metric properties of SE（3）422

3.3 Volume forms on SE（3）430

Appendix B A Mathematica Package for Screw Calculus435

Bibliography441

Index449