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More About This Title Dynamics and Control of Robotic Systems
English
A comprehensive review of the principles and dynamics of robotic systems
Dynamics and Control of Robotic Systems offers a systematic and thorough theoretical background for the study of the dynamics and control of robotic systems. The authors—noted experts in the field—highlight the underlying principles of dynamics and control that can be employed in a variety of contemporary applications. The book contains a detailed presentation of the precepts of robotics and provides methodologies that are relevant to realistic robotic systems. The robotic systems represented include wide range examples from classical industrial manipulators, humanoid robots to robotic surgical assistants, space vehicles, and computer controlled milling machines.
The book puts the emphasis on the systematic application of the underlying principles and show how the computational and analytical tools such as MATLAB, Mathematica, and Maple enable students to focus on robotics’ principles and theory. Dynamics and Control of Robotic Systems contains an extensive collection of examples and problems and:
- Puts the focus on the fundamentals of kinematics and dynamics as applied to robotic systems
- Presents the techniques of analytical mechanics of robotics
- Includes a review of advanced topics such as the recursive order N formulation
- Contains a wide array of design and analysis problems for robotic systems
Written for students of robotics, Dynamics and Control of Robotic Systems offers a comprehensive review of the underlying principles and methods of the science of robotics.
English
Andrew J. Kurdila, PhD, is the W. Martin Johnson Professor of Mechanical Engineering at Virginia Tech. He is the author of Structural Dynamics: An Introduction to Computer Methods from Wiley.
Pinhas Ben-Tzvi, PhD, is Associate Professor of Mechanical Engineering at Virginia Tech. He has expertise in robotics and autonomous systems, bio-inspired robotics, mechatronics, control systems, robotic vision, human-robot interaction, machine learning, and more.
English
Preface
Introduction 1
1.1 Motivation 2
1.2 Origins of Robotic Systems 5
1.3 General Structure of Robotic Systems 7
1.4 Robotic Manipulators 8
1.4.1 Typical Structure of Robotic Manipulators 10
1.4.2 Classification of Robotic Manipulators 13
1.4.2.1 Classification by Motion Characteristics 13
1.4.2.2 Classification by Degrees of Freedom 13
1.4.2.3 Classification by Driver Technology and Drive Power 14
1.4.2.4 Classification by Kinematic Structure 14
1.4.2.5 Classification by Workspace Geometry 16
1.4.3 Examples of Robotic Manipulators 17
1.4.3.1 Cartesian Robotic Manipulator 17
1.4.3.2 Cylindrical Robotic Manipulator 17
1.4.3.3 SCARA Robotic Manipulator 18
1.4.3.4 Spherical Robotic Manipulator 19
1.4.3.5 PUMA Robotic Manipulator 21
1.4.4 Spherical Wrist 22
1.4.5 Articulated Robot 23
1.5 Mobile Robotics 24
1.5.1 Humanoid Robots 24
1.5.2 Autonomous Ground Vehicles 26
1.5.3 Autonomous Air Vehicles 26
1.5.4 Autonomous Marine Vehicles 29
1.6 An Overview of Robotics Dynamics and Control Problems 31
1.6.1 Forward Kinematics 31
1.6.2 Inverse Kinematics 33
1.6.3 Forward Dynamics 34
1.6.4 Inverse Dynamics and Feedback Control 34
1.6.5 Dynamics and Control of Robotic Vehicles 35
1.7 Organization of the Book 37
1.8 Problems for Chapter (1), Introduction 38
2 Fundamentals of Kinematics 41
2.1 Bases and Coordinate Systems 41
2.1.1 N-Tuples and M_N Arrays 42
2.1.2 Vectors, Bases and Frames 46
2.1.2.1 Vectors 47
2.1.2.2 Bases and Frames 48
2.2 Rotation Matrices 55
2.3 Parameterizations of Rotation Matrices 59
2.3.1 Single Axis Rotations 59
2.3.2 Cascades of Rotation Matrices 63
2.3.2.1 Cascade Rotations about Moving Axes 63
2.3.2.2 Cascade Rotations about Fixed Axes 64
2.3.3 Euler Angles 65
2.3.3.1 The 3-2-1 Yaw-Pitch-Roll Euler Angles 66
2.3.3.2 The 3-1-3 Precession-Nutation-Spin Euler Angles 70
2.3.4 Axis-Angle Parameterization 73
2.4 Position, Velocity, and Acceleration 77
2.5 Angular Velocity and Angular Acceleration 86
2.5.1 Angular Velocity 86
2.5.2 Angular Acceleration 92
2.6 Theorems of Kinematics 92
2.6.1 Addition of Angular Velocities 93
2.6.2 Relative Velocity 96
2.6.3 Relative Acceleration 97
2.6.4 Common Coordinate Systems 100
2.6.4.1 Cartesian Coordinates 101
2.6.4.2 Cylindrical Coordinates 101
2.6.4.3 Spherical Coordinates 103
2.7 Problems for Chapter 2, Kinematics 106
2.7.1 Problems on N-tuples and M_N Arrays 106
2.7.2 Problems on Vectors, Bases, Frames 107
2.7.3 Problems on Rotation Matrices 108
2.7.4 Problems on Position, Velocity, Acceleration 113
2.7.5 Problems on Angular Velocity 116
2.7.6 Problems on the Theorems of Kinematics 116
2.7.6.1 Problems on the Addition of Angular Velocities 116
2.7.7 Problems on Relative Velocity and Acceleration 117
2.7.8 Problems on Common Coordinate Systems 120
3 Kinematics of Robotic Systems 121
3.1 Homogeneous Transformations and Rigid Motion 121
3.2 Ideal Joints 127
3.2.1 The Prismatic Joint 128
3.2.2 The Revolute Joint 130
3.2.3 Other Ideal Joints 131
3.3 The Denavit-Hartenberg (DH) Convention 134
3.3.1 Kinematic Chains, Numbering in the DH Convention 134
3.3.2 Definition of Frames in the DH Convention 136
3.3.3 Homogeneous Transforms in the Denavit-Hartenberg Convention 137
3.3.4 The DH Procedure 139
3.3.5 Angular Velocity and Velocity in the DH Convention 147
3.4 Recursive O(N) Formulation of Forward Kinematics 151
3.4.1 Recursive Calculation of Velocity and Angular Velocity 154
3.4.2 Efficiency and Computational Cost 157
3.4.3 Recursive Calculation of Acceleration and Angular Acceleration 161
3.5 Inverse Kinematics 175
3.5.1 Solvability 176
3.5.2 Analytical Methods 179
3.5.2.1 Algebraic Methods 179
3.5.2.2 Geometric Methods 190
3.5.3 Optimization Methods 194
3.5.4 Inverse Velocity Kinematics 202
3.5.4.1 Singularity 202
3.6 Problems for Chapter 3, Kinematics of Robotic Systems 203
3.6.1 Problems on Homogeneous Transformations 203
3.6.2 Problems on Ideal Joints and Constraints 206
3.6.3 Problems on Denavit-Hartenberg Convention 207
3.6.4 Problems on Angular Velocity and Velocity for Kinematic Chains 208
3.6.5 Problems on Inverse Kinematics 212
4 Newton-Euler Formulations 215
4.1 Linear Momentum of Rigid Bodies 215
4.2 Angular Momentum of Rigid Bodies 222
4.2.1 First Principles 222
4.2.2 Angular Momentum and Inertia 228
4.2.3 Calculation of the Inertia Matrix 234
4.2.3.1 The Inertia Rotation Transformation Law 235
4.2.3.2 Principal Axes of Inertia 238
4.2.3.3 The Parallel Axis Theorem 241
4.2.3.4 Symmetry and Inertia 245
4.3 The Newton-Euler Equations 250
4.4 Euler’s Equation for a Rigid Body 255
4.5 Equations of Motion for Mechanical Systems 257
4.5.1 The General Strategy 257
4.5.2 Free Body Diagrams 258
4.6 Structure of Governing Equations: Newton-Euler Formulations 281
4.6.1 Differential-Algebraic Equations (DAEs) 281
4.6.2 Ordinary Differential Equations (ODEs) 283
4.7 Recursive Newton-Euler Formulations 285
4.7.1 Recursive Calculation of Forces and Moments 285
4.8 Recursive Derivation of the Equations of Motion 293
4.9 Problems for Chapter 4, Newton-Euler Equations 296
4.9.1 Problems on Linear Momentum 296
4.9.2 Problems on the Center of Mass 300
4.9.3 Problems on the Inertia matrix 303
4.9.4 Problems on Angular Momentum304
4.9.5 Problems on the Newton-Euler Equations 305
5 Analytical Mechanics 309
5.1 Hamilton’s Principle 309
5.1.1 Generalized Coordinates 309
5.1.2 Functionals and the Calculus of Variations 312
5.1.3 Hamilton’s Principle for Conservative Systems 316
5.1.4 Kinetic Energy for Rigid Bodies 324
5.2 Lagrange’s Equations for Conservative Systems 329
5.3 Hamilton’s Extended Principle 333
5.3.1 Virtual Work Formulations 333
5.4 Lagrange’s Equations for Robotic Systems 349
5.4.1 Natural Systems 350
5.4.2 Lagrange’s Equations and the Denavit-Hartenberg Convention 354
5.5 Constrained Systems 357
5.6 Problems for Chapter 5, Analytical Mechanics 362
5.6.1 Problems on Hamilton’s Principle 362
5.6.2 Problems on Lagrange’s Equations 366
5.6.3 Problems on Hamilton’s Extended Principle 368
5.6.4 Problems on Constrained Systems 374
6 Control of Robotic Systems 377
6.1 The Structure of Control Problems 377
6.1.1 Setpoint and Tracking Feedback Control Problems 378
6.1.2 Open Loop and Closed Loop Control 379
6.1.3 Linear and Nonlinear Control 379
6.2 Fundamentals of Stability Theory 381
6.3 Advanced Techniques of Stability Theory 388
6.4 Lyapunov’s Direct Method 389
6.5 The Invariance Principle 392
6.6 Dynamic Inversion or Computed Torque Control 398
6.7 Approximate Dynamic Inversion and Uncertainty 407
6.8 Controllers Based on Passivity 421
6.9 Actuator Models 426
6.9.1 Electric Motors 426
6.9.2 Linear Actuators 433
6.10 Backstepping Control and Actuator Dynamics 438
6.11 Problems for Chapter (6), control of Robotic Systems 442
6.11.1 Problems on Gravity Compensation and PD setpoint control 442
6.11.2 Problems on Computed Torque Tracking Control 446
6.11.3 Problems on Dissipativity Based Tracking Control 447
7 Image-Based Control of Robotic Systems 451
7.1 The Geometry of Camera Measurements 451
7.1.1 Perspective Projection and Pinhole Camera Models 452
7.1.2 Pixel Coordinates and CCD Cameras 454
7.1.3 The Interaction Matrix 456
7.2 Image-Based Visual Servo Control 460
7.2.1 Control Synthesis and Closed Loop Equations 460
7.2.2 Calculation of Initial Conditions 464
7.3 Task Space Control 473
7.4 Task Space and Visual Control 480
7.5 Problems for Chapter (7) 499
8 Appendices 505
8.1 Fundamentals of Linear Algebra 505
8.1.1 Solution of Matrix Equations 507
8.1.2 Linear Independence and Rank 509
8.1.3 Invertibility and Rank 510
8.1.4 Least Squares Approximation 511
8.1.5 Rank Conditions and the Interaction Matrix 516
8.2 The Algebraic Eigenvalue Problem 516
8.2.1 Self-Adjoint Matrices 518
8.2.2 Jordan Canonical Form 520
8.3 Gauss Transformations and LU Factorizations 521
Index 527
References 534
Index 537
