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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A New Edition Featuring Case Studies and Examples of the Fundamentals of Robot Kinematics, Dynamics, and Control In the 2nd Edition of Robot Modeling and Control, students will cover the theoretical fundamentals and the latest technological advances in robot kinematics. With so much advancement in technology, from robotics to motion planning, society can implement more powerful and dynamic algorithms than ever before. This in-depth reference guide educates readers in four distinct parts; the first two serve as a guide to the fundamentals of robotics and motion control, while the last two dive more in-depth into control theory and nonlinear system analysis. With the new edition, readers gain access to new case studies and thoroughly researched information covering topics such as: * Motion-planning, collision avoidance, trajectory optimization, and control of robots * Popular topics within the robotics industry and how they apply to various technologies * An expanded set of examples, simulations, problems, and case studies * Open-ended suggestions for students to apply the knowledge to real-life situations A four-part reference essential for both undergraduate and graduate students, Robot Modeling and Control serves as a foundation for a solid education in robotics and motion planning.
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Robot Modeling and Control
Second Edition
Mark W. Spong
Seth Hutchinson
M. Vidyasagar
This edition first published 2020
© 2020 John Wiley & Sons, Ltd
Edition History
John Wiley & Sons, Ltd (1e, 2006)
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Library of Congress Cataloging-in-Publication Data
Names: Spong, Mark W, author. I Hutchinson, Seth, author. I Vidyasagar, M. (Mathukumalli), 1947- author.
Title: Robot modeling and control / Mark W Spong, Seth Hutchinson, and M. Vidyasagar.
Description: Second edition. I Hoboken, NJ: John Wiley & Sons, Inc., 2020. I Includes bibliographical references and index.
Identifiers: LCCN 2019055413 (print) I LCCN 2019055414 (ebook) I ISBN 9781119523994 (hardback) I
ISBN 9781119524076 (adobe pdf) I ISBN 9781119524045 (epub)
Subjects: LCSH: Robots-Control systems. I Robots-Dynamics. I Robotics.
Classification: LCC TJ211.35 .S75 2020 (print) I LCC TJ211.35 (ebook) I DDC 629.8/92-dc23
LC record available at https://lccn.loc.gov/2019055413
LC ebook record available at https://lccn.loc.gov/2019055414
Cover image: © Patrick Palej/EyeEm/Getty Images
Cover design by Wiley
CONTENTS
Cover
Preface:
Chapter 1 Introduction
1.1 Mathematical Modeling of Robots
1.2 Robots as Mechanical Devices
1.3 Common Kinematic Arrangements
1.4 Outline of the Text
Problems
Notes and References
Notes
Part I The Geometry of Robots
Chapter 2 Rigid Motions
2.1 Representing Positions
2.2 Representing Rotations
2.3 Rotational Transformations
2.4 Composition of Rotations
2.5 Parameterizations of Rotations
2.6 Rigid Motions
2.7 Chapter Summary
Problems
Notes and References
Notes
Chapter 3 Forward Kinematics
3.1 Kinematic Chains
3.2 The Denavit–Hartenberg Convention
3.3 Examples
3.4 Chapter Summary
Problems
Notes and References
Chapter 4 Velocity Kinematics
4.1 Angular Velocity: The Fixed Axis Case
4.2 Skew-Symmetric Matrices
4.3 Angular Velocity: The General Case
4.4 Addition of Angular Velocities
4.5 Linear Velocity of a Point Attached to a Moving Frame
4.6 Derivation of the Jacobian
4.7 The Tool Velocity
4.8 The Analytical Jacobian
4.9 Singularities
4.10 Static Force/Torque Relationships
4.11 Inverse Velocity and Acceleration
4.12 Manipulability
4.13 Chapter Summary
Problems
Notes and References
Notes
Chapter 5 Inverse Kinematics
5.1 The General Inverse Kinematics Problem
5.2 Kinematic Decoupling
5.3 Inverse Position: A Geometric Approach
5.4 Inverse Orientation
5.5 Numerical Inverse Kinematics
5.6 Chapter Summary
Problems
Notes and References
Part II Dynamics and Motion Planning
Chapter 6 Dynamics
6.1 The Euler–Lagrange Equations
6.2 Kinetic and Potential Energy
6.3 Equations of Motion
6.4 Some Common Configurations
6.5 Properties of Robot Dynamic Equations
6.6 Newton–Euler Formulation
6.7 Chapter Summary
Problems
Notes and References
Chapter 7 Path and Trajectory Planning
7.1 The Configuration Space
7.2 Path Planning for
7.3 Artificial Potential Fields
7.4 Sampling-Based Methods
7.5 Trajectory Planning
7.6 Chapter Summary
Problems
Notes and References
Notes
Part III Control of Manipulators
Chapter 8 Independent Joint Control
8.1 Introduction
8.2 Actuator Dynamics
8.3 Load Dynamics
8.4 Independent Joint Model
8.5 PID Control
8.6 Feedforward Control
8.7 Drive-Train Dynamics
8.8 State Space Design
8.9 Chapter Summary
Problems
Notes and References
Notes
Chapter 9 Nonlinear and Multivariable Control
9.1 Introduction
9.2 PD Control Revisited
9.3 Inverse Dynamics
9.4 Passivity-Based Control
9.5 Torque Optimization
9.6 Chapter Summary
Problems
Notes and References
Notes
Chapter 10 Force Control
10.1 Coordinate Frames and Constraints
10.2 Network Models and Impedance
10.3 Task Space Dynamics and Control
10.4 Chapter Summary
Problems
Notes and References
Notes
Chapter 11 Vision-Based Control
11.1 Design Considerations
11.2 Computer Vision for Vision-Based Control
11.3 Camera Motion and the Interaction Matrix
11.4 The Interaction Matrix for Point Features
11.5 Image-Based Control Laws
11.6 End Effector and Camera Motions
11.7 Partitioned Approaches
11.8 Motion Perceptibility
11.9 Summary
Problems
Notes and References
Notes
Chapter 12 Feedback Linearization
12.1 Background
12.2 Feedback Linearization
12.3 Single-Input Systems
12.4 Multi-Input Systems
12.5 Chapter Summary
Problems
Notes and References
Notes
Part IV Control of Underactuated Systems
Chapter 13 Underactuated Robots
13.1 Introduction
13.2 Modeling
13.3 Examples of Underactuated Robots
13.4 Equilibria and Linear Controllability
13.5 Partial Feedback Linearization
13.6 Output Feedback Linearization
13.7 Passivity-Based Control
13.8 Chapter Summary
Problems
Notes and References
Note
Chapter 14 Mobile Robots
14.1 Nonholonomic Constraints
14.2 Involutivity and Holonomy
14.3 Examples of Nonholonomic Systems
14.4 Dynamic Extension
14.5 Controllability of Driftless Systems
14.6 Motion Planning
14.7 Feedback Control of Driftless Systems
14.8 Chapter Summary
Problems
Notes and References
Note
Appendix A Trigonometry
A.1 The Two-Argument Arctangent Function
A.2 Useful Trigonometric Formulas
Appendix B Linear Algebra
B.1 Vectors
B.2 Inner Product Spaces
B.3 Matrices
B.4 Eigenvalues and Eigenvectors
B.5 Differentiation of Vectors
B.6 The Matrix Exponential
B.7 Lie Groups and Lie Algebras
B.8 Matrix Pseudoinverse
B.9 Schur Complement
B.10 Singular Value Decomposition (SVD)
Appendix C Lyapunov Stability
C.1 Continuity and Differentiability
C.2 Vector Fields and Equilibria
C.3 Lyapunov Functions
C.4 Stability Criteria
C.5 Global and Exponential Stability
C.6 Stability of Linear Systems
C.7 LaSalle’s Theorem
C.8 Barbalat’s Lemma
Appendix D Optimization
D.1 Unconstrained Optimization
D.2 Constrained Optimization
Appendix E Camera Calibration
E.1 The Image Plane and the Sensor Array
E.2 Extrinsic Camera Parameters
E.3 Intrinsic Camera Parameters
E.4 Determining the Camera Parameters
Note
Bibliography
Index
End User License Agreement
List of Tables
Chapter 3
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Chapter 5
Table 5.1
Chapter 7
Table 7.1
Chapter 8
Table 8.1
Chapter 13
Table 13.1
Chapter 14
Table 14.1
Guide
Cover
Table of Contents
Preface
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To my wife Lila – MWSTo my wife Wendy – SHTo my grandson Niyuddh Anand – MV
Preface
This text is a second edition of our book, Robot Modeling and Control, John Wiley & Sons, Inc., 2006, which grew out of the earlier text, M.W. Spong and M. Vidyasagar, Robot Dynamics and Control, John Wiley & Sons, Inc., 1989. The second edition reflects some of the changes that have occurred in robotics and robotics education in the past decade. In particular, many courses are now treating mobile robots on an equal footing with robot manipulators. As a result, we have expanded the discussion on mobile robots into a full chapter. In addition, we have added a new chapter on underactuated robots. We have also revised the material on vision, vision-based control, and motion planning to reflect changes in those topics.
Organization of the Text
After the introductory first chapter, which introduces the terminology and history of robotics and discusses the most common robot design and applications, the text is organized into four parts. Part I consists of four chapters dealing with the geometry of rigid motions and the kinematics of manipulators.
Chapter 2 presents the mathematics of rigid motions; rotations, translations, and homogeneous transformations.
Chapter 3 presents solutions to the forward kinematics problem using the Denavit–Hartenberg representation, which gives a very straightforward and systematic way to describe the forward kinematics of manipulators.
Chapter 4 discuses velocity kinematics and the manipulator Jacobian. The geometric Jacobian is derived in the cross product form. We also introduce the so-called analytical Jacobian for later use in task space control. We have reversed the order of our treatment of velocity kinematics and inverse kinematics from the presentation in the first edition in order to include a new section in Chapter 5 on numerical inverse kinematics algorithms, which rely on the Jacobian for their implementation.
Chapter 5 deals with the inverse kinematics problem using the geometric approach, which is especially suited for manipulators with spherical wrists. We show how to solve the inverse kinematics in closed form for the most common manipulator designs. We also discuss numerical search algorithms for solving inverse kinematics. Numerical algorithms are increasingly popular because of both the increasing power of computers and the availability of open-source software for numerical algorithms.
Part II deals with dynamics and motion planning and consists of two chapters.
Chapter 6 is a detailed account of robot dynamics. The Euler–Lagrange equations are derived from first principles and their structural properties are discussed in detail. The recursive Newton–Euler formulation of robot dynamics is also presented.
Chapter 7 is an introduction to the problems of path and trajectory planning. Several of the most popular methods for motion planning and obstacle avoidance are presented, including the method of artificial potential fields, randomized algorithms, and probabilistic roadmap methods. The problem of trajectory generation is presented as essentially a problem of polynomial spline interpolation. Trajectory generation based on cubic and quintic polynomials as well as trapezoidal velocity trajectories are derived for interpolation in joint space.
Part III deals with the control of manipulators.
Chapter 8 is an introduction to independent joint control. Linear models and linear control methods based on PD, PID, and state space methods are presented for set-point regulation, trajectory tracking, and disturbance rejection. The concept of feedforward control, including the method of computed torque control, is introduced as a method for nonlinear disturbance rejection and for tracking of time-varying reference trajectories.
Chapter 9 discusses nonlinear and multivariable control. This chapter summarizes much of the research in robot control that took place in the late 1980s and early 1990s. Simple derivations of the most common robust and adaptive control algorithms are presented that prepare the reader for the extensive literature in robot control.
Chapter 10 treats the force control problem. Both impedance control and hybrid control are discussed. We also present the lesser known hybrid impedance control method, which allows one to control impedance and regulate motion and force at the same time. To our knowledge this is the first textbook that discusses the hybrid impedance control approach to robot force control.
Chapter 11 is an introduction to visual servo control, which is the problem of controlling robots using feedback from cameras mounted either on the robot or in the workspace. We present those aspects of vision that are most useful for vision-based control applications, such as imaging geometry and feature extraction. We then develop the differential kinematics that relate camera motion to changes in extracted features and we discuss the main concepts in visual servo control.
Chapter 12 is a tutorial overview of geometric nonlinear control and the method of feedback linearization of nonlinear systems. Feedback linearization generalizes the methods of computed torque and inverse dynamics control that are covered in Chapters 8 and 9. We derive and prove the necessary and sufficient conditions for local feedback linearization of single-input/single-output nonlinear systems, which we then apply to the flexible joint control problem. We also introduce the notion of nonlinear observers with output injection.
Part IV is a completely new addition to the second edition and treats the control problems for underactuated robots and nonholonomic systems.
Chapter 13 deals with underactuated serial-link robots. Underactuation arises in applications such as bipedal locomotion and gymnastic robots. In fact, the flexible-joint robot models presented in Chapters 8 and 12 are also examples of underactuated robots. We present the ideas of partial feedback linearization and transformation to normal forms, which are useful for controller design. We also discuss energy and passivity methods to control this class of systems.
Chapter 14 deals primarily with wheeled mobile robots, which are examples of systems subject to nonholonomic constraints. Many of the control design methods presented in the chapters leading up to Chapter 14 do not apply to nonholonomic systems. Thus, we cover some new techniques applicable to these systems. We present two fundamental results, namely Chow’s theorem and Brockett’s theorem, that provide conditions for controllability and stabilizability, respectively, of mobile robots.
Finally, the appendices have been expanded to give much of the necessary background mathematics to be able to follow the development of the concepts in the text.
A Note to the Instructor
This text is suitable for several quarter-long or semester-long courses in robotics, either as a two- or three- course sequence or as stand-alone courses. The first five chapters can be used for a junior/senior-level introduction to robotics for students with at least a minimal background in linear algebra. Chapter 8 may also be included in an introductory course for students with some exposure to linear control systems. The independent joint control problem largely involves the control of actuator and drive-train dynamics; hence most of the subject can be taught without prior knowledge of Euler–Lagrange dynamics.
A graduate-level course on robot dynamics and control can be taught using all or parts of Chapters 6 through 12.
Finally, one or more special topics courses can be taught using Chapters 9 through 14. Below we outline several possible courses that can be taught from this book:
Course 1: Introduction to Robotics
Level: Junior/Senior undergraduate
For a one quarter course (10 weeks):
Chapter 1:
Introduction
Chapter 2:
Rigid Motions and Homogeneous Transformations
Chapter 3:
Forward Kinematics
Chapter 4:
Velocity Kinematics and Jacobians
Chapter 5:
Inverse Kinematics
For a one semester course (16 weeks) add:
Chapter 7:
Motion Planning and Trajectory Generation
Chapter 8:
Independent Joint Control
Course 2: Robot Dynamics and Control
Level: Senior undergraduate/graduate
For a one quarter course (10 weeks):
Chapters 1–5:
Rapid Review of Kinematics (selected sections)
Chapter 6:
Dynamics
Chapter 7:
Path and Trajectory Planning
Chapter 9:
Nonlinear and Multivariable Control
Chapter 10:
Force Control
For a one semester course (16 weeks) add:
Chapter 11:
Vision-Based Control
Chapter 12:
Feedback Linearization
Course 3: Advanced Topics in Robot Control
Level: Graduate
For a one semester course (16 weeks):
Chapter 6:
Dynamics
Chapter 7:
Motion Planning and Trajectory Generation
Chapter 9:
Nonlinear and Multivariable Control
Chapter 11:
Vision-Based Control
Chapter 12:
Feedback Linearization
Chapter 13:
Underactuated Robots
Chapter 14:
Mobile Robots
The instructor may wish to supplement the material in any of these courses with additional material to delve deeper into a particular topic. Also, either of the last two chapters can be covered in Course 2 by eliminating the Force Control chapter or the Vision-Based Control chapter.
Acknowledgements
We would like to offer a special thanks to Nick Gans, Peter Hokayem, Benjamin Sapp, and Daniel Herring, who did an outstanding job of producing most of the figures in the first edition, and to Andrew Messing for figure contributions to the current edition. We would like to thank Francois Chaumette for discussions regarding the formulation of the interaction matrix in Chapter 11 and to Martin Corless for discussion on the robust control problem in Chapter 9. We are indebted to several reviewers for their very detailed and thoughtful reviews, especially Brad Bishop, Jessy Grizzle, Kevin Lynch, Matt Mason, Eric Westervelt. We would like to thank our students, Nikhil Chopra, Chris Graesser, James Davidson, Nick Gans, Jon Holm, Silvia Mastellone, Adrian Lee, Oscar Martinez, Erick Rodriguez, and Kunal Srivastava, for constructive feedback on the first edition.
We would like to acknowledge Lila Spong for proofreading the manuscript of the second edition, and also the many people who sent us lists of typographical errors and corrections to the first edition, especially Katherine Kuchenbecker and her students, who provided numerous corrections.
Mark W. Spong
Seth Hutchinson
M. Vidyasagar
