Theory Of Applied Robotics: Kinematics, Dynamics, And Control (2nd Edition) / Edition 2

Theory of Applied Robotics: Kinematics, Dynamics, and Control 2E is appropriate for courses in robotics that emphasize kinematics, dynamics, and control.
The contents of this book are presented at a theoretical-practical level. It explains robotics concepts in detail, concentrating on their practical use. Related theorems and formal proofs are provided, as are real-life applications. Students, researchers, and practicing engineers alike will appreciate this user-friendly presentation of a wealth of robotics topics, most notably orientation, velocity, and forward kinematics.
The second edition includes updated and expanded exercise sets and problems, new coverage includes, Components and Mechanisms of a Robotic Systems with actuators, sensors and controllers and updated and expanded material on Kinematics including geometric kinematics, Derivative Kinematics, velocity kinematics, and new coverage on sensing and control including position sensors, speed sensors and acceleration sensors

Table Of Contents:

1 Introduction 1

1.1 Historical Development 2

1.2 Robot Components 3

1.2.1 Link 3

1.2.2 Joint 3

1.2.3 Manipulator 5

1.2.4 Wrist 5

1.2.5 End-effector 6

1.2.6 Actuators 7

1.2.7 Sensors 7

1.2.8 Controller 7

1.3 Robot Classifications 8

1.3.1 Geometry 8

1.3.2 Workspace 13

1.3.3 Actuation 13

1.3.4 Control 13

1.3.5 Application 14

1.4 Introduction to Robot's Kinematics, Dynamics, and Control 15

1.4.1 * Triad 16

1.4.2 Unit Vectors 16

1.4.3 Reference Frame and Coordinate System 17

1.4.4 Vector Function 20

1.5 Problems of Robot Dynamics 20

1.6 Preview of Covered Topics 22

1.7 Robots as Multi-disciplinary Machines 23

1.8 Summary 24

Exercises 25

I Kinematics 29

2 Rotation Kinematics 33

2.1 Rotation about Global Cartesian Axes 33

2.2 Successive Rotation about Global Cartesian Axes 40

2.3 Global Roll-Pitch-Yaw Angles 44

2.4 Rotation about Local Cartesian Axes 46

2.5 Successive Rotation about Local Cartesian Axes 50

2.6 Euler Angles 52

2.7 Local Roll-Pitch-Yaw Angles 62

2.8 Local Axes Versus Global Axes Rotation 63

2.9 General Transformation 65

2.10 Active and Passive Transformation 73

2.11 Summary 77

2.12 Key Symbols 79

Exercises 81

3 Orientation Kinematics 91

3.1 Axis-angle Rotation 91

3.2 * Euler Parameters 102

3.3 * Determination of Euler Parameters 110

3.4 * Quaternions 112

3.5 * Spinors and Rotators 116

3.6 * Problems in Representing Rotations 118

3.6.1 * Rotation matrix 119

3.6.2 * Angle-axis 120

3.6.3 * Euler angles 121

3.6.4 * Quaternion 122

3.6.5 * Euler parameters 124

3.7 * Composition and Decomposition of Rotations 126

3.8 Summary 133

3.9 Key Symbols 135

Exercises 137

4 Motion Kinematics 149

4.1 Rigid Body Motion 149

4.2 Homogeneous Transformation 154

4.3 Inverse. Homogeneous Transformation 162

4.4 Compound Homogeneous Transformation 168

4.5 * Screw Coordinates 178

4.6 * Inverse Screw 195

4.7 * Compound Screw Transformation 198

4.8 * The Plücker Line Coordinate 201

4.9 * The Geometry of Plane and Line 208

4.9.1 * Moment 208

4.9.2 * Angle and Distance 209

4.9.3 * Plane and Line 209

4.10 * Screw and Plücker Coordinate 214

4.11 Summary 217

4.12 Key Symbols 219

Exercises 221

5 Forward Kinematics 233

5.1 Denavit-Hartenberg Notation 233

5.2 Transformation Between Two Adjacent Coordinate Frames 242

5.3 Forward Position Kinematics of Robots 259

5.4 Spherical Wrist 270

5.5 Assembling Kinematics 280

5.6 * Coordinate Transformation Using Screws 292

5.7 * Non Denavit-Hartenberg Methods 297

5.8 Summary 305

5.9 Key Symbols 307

Exercises 309

6 Inverse Kinematics 325

6.1 Decoupling Technique 325

6.2 Inverse Transformation Technique 341

6.3 * Iterative Technique 357

6.4 * Comparison of the Inverse Kinematics Techniques 361

6.4.1 * Existence and Uniqueness of Solution 361

6.4.2 * Inverse Kinematics Techniques 362

6.5 * Singular Configuration 363

6.6 Summary 367

6.7 Key Symbols 369

Exercises 371

7 Angular Velocity 381

7.1 Angular Velocity Vector and Matrix 381

7.2 * Time Derivative and Coordinate Frames 393

7.3 Rigid Body Velocity 403

7.4 * Velocity Transformation Matrix 409

7.5 Derivative of a Homogeneous Transformation Matrix 417

7.6 Summary 425

7.7 Key Symbols 427

Exercises 429

8 Velocity Kinematics 437

8.1 * Rigid Link Velocity 437

8.2 Forward Velocity Kinematics 442

8.3 Jacobian Generating Vectors 452

8.4 Inverse Velocity Kinematics 465

8.5 Summary 473

8.6 Key Symbols 475

Exercises 477

9 Numerical Methods in Kinematics 485

9.1 Linear Algebraic Equations 485

9.2 Matrix Inversion 497

9.3 Nonlinear Algebraic Equations 503

9.4 * Jacobian Matrix From Link Transformation Matrices 510

9.5 Summary 518

9.6 Key Symbols 519

Exercises 521

II Dynamics 525

10 Acceleration Kinematics 529

10.1 Angular Acceleration Vector and Matrix 529

10.2 Rigid Body Acceleration 538

10.3 * Acceleration Transformation Matrix 541

10.4 Forward Acceleration Kinematics 549

10.5 Inverse Acceleration Kinematics 552

10.6 * Rigid Link Recursive Acceleration 556

10.7 Summary 567

10.8 Key Symbols 569

Exercises 571

11 Motion Dynamics 581

11.1 Force and Moment 581

11.2 Rigid Body Translational Kinetics 586

11.3 Rigid Body Rotational Kinetics 588

11.4 Mass Moment of Inertia Matrix 599

11.5 Lagrange's Form of Newton's Equations 611

11.6 Lagrangian Mechanics 620

11.7 Summary 627

11.8 Key Symbols 629

Exercises 631

12 Robot Dynamics 641

12.1 Rigid Link Newton-Euler Dynamics 641

12.2 * Recursive Newton-Euler Dynamics 661

12.3 Robot Lagrange Dynamics 669

12.4 * Lagrange Equations and Link Transformation Matrices 690

12.5 Robot Statics 700

12.6 Summary 709

12.7 Key Symbols 713

Exercises 715

III Control 725

13 Path Planning 729

13.1 Cubic Path 729

13.2 Polynomial Path 735

13.3 * Non-Polynomial Path Planning 747

13.4 Manipulator Motion by Joint Path 749

13.5 Cartesian Path 754

13.6 * Rotational Path 759

13.7 Manipulator Motion by End-Effector Path 763

13.8 Summary 777

13.9 Key Symbols 779

Exercises 781

14 Time Optimal Control 791

14.1 * Minimum Time and Bang-Bang Control 791

14.2 * Floating Time Method 801

14.3 * Time-Optimal Control for Robots 811

14.4 Summary 817

14.5 Key Symbols 819

Exercises 821

15 Control Techniques 827

15.1 Open and Closed-Loop Control 827

15.2 Computed Torque Control 833

15.3 Linear Control Technique 838

15.3.1 Proportional Control 839

15.3.2 Integral Control 839

15.3.3 Derivative Control 839

15.4 Sensing and Control 842

15.4.1 Position Sensors 843

15.4.2 Speed Sensors 843

15.4.3 Acceleration Sensors 844

15.5 Summary 845

15.6 Key Symbols 847

Exercises 849

References 853

A Global Frame Triple Rotation 863

B Local Frame Triple Rotation 865

C Principal Central Screws Triple Combination 867

D Trigonometric Formula 869

Index 873

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Theory of Applied Robotics