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Robotics, Modelling, Planning and Control.pdf

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    Series Editors’ Foreword
    Preface
    Contents
    1 Introduction
    1.1 Robotics
    1.2 Robot Mechanical Structure
    1.2.1 Robot Manipulators
    1.2.2 Mobile Robots
    1.3 Industrial Robotics
    1.4 Advanced Robotics
    1.4.1 Field Robots
    1.4.2 Service Robots
    1.5 Robot Modelling, Planning and Control
    1.5.1 Modelling
    1.5.2 Planning
    1.5.3 Control
    Bibliography
    Basic textbooks
    Specialized books
    Edited collections on the state of the art of research
    Scientific journals
    Series of international scientific conferences
    2 Kinematics
    2.1 Pose of a Rigid Body
    2.2 Rotation Matrix
    2.2.1 Elementary Rotations
    2.2.2 Representation of a Vector
    2.2.3 Rotation of a Vector
    2.3 Composition of Rotation Matrices
    2.4 Euler Angles
    2.4.1 ZYZ Angles
    2.4.2 RPY Angles
    2.5 Angle and Axis
    2.6 Unit Quaternion
    2.7 Homogeneous Transformations
    2.8 Direct Kinematics
    2.8.1 Open Chain
    2.8.2 Denavit–Hartenberg Convention
    2.8.3 Closed Chain
    2.9 Kinematics of Typical Manipulator Structures
    2.9.1 Three-link Planar Arm
    2.9.2 Parallelogram Arm
    2.9.3 Spherical Arm
    2.9.4 Anthropomorphic Arm
    2.9.5 Spherical Wrist
    2.9.6 Stanford Manipulator
    2.9.7 Anthropomorphic Arm with Spherical Wrist
    2.9.8 DLR Manipulator
    2.9.9 Humanoid Manipulator
    2.10 Joint Space and Operational Space
    2.10.1 Workspace
    2.10.2 Kinematic Redundancy
    2.11 Kinematic Calibration
    2.12 Inverse Kinematics Problem
    2.12.1 Solution of Three-link Planar Arm
    2.12.2 Solution of Manipulators with Spherical Wrist
    2.12.3 Solution of Spherical Arm
    2.12.4 Solution of Anthropomorphic Arm
    2.12.5 Solution of Spherical Wrist
    Bibliography
    Problems
    3 Differential Kinematics and Statics
    3.1 Geometric Jacobian
    3.1.1 Derivative of a Rotation Matrix
    3.1.2 Link Velocities
    3.1.3 Jacobian Computation
    3.2 Jacobian of Typical Manipulator Structures
    3.2.1 Three-link Planar Arm
    3.2.2 Anthropomorphic Arm
    3.2.3 Stanford Manipulator
    3.3 Kinematic Singularities
    3.3.1 Singularity Decoupling
    3.3.2 Wrist Singularities
    3.3.3 Arm Singularities
    3.4 Analysis of Redundancy
    3.5 Inverse Differential Kinematics
    3.5.1 Redundant Manipulators
    3.5.2 Kinematic Singularities
    3.6 Analytical Jacobian
    3.7 Inverse Kinematics Algorithms
    3.7.1 Jacobian (Pseudo-)inverse
    3.7.2 Jacobian Transpose
    3.7.3 Orientation Error
    3.7.4 Second-order Algorithms
    3.7.5 Comparison Among Inverse Kinematics Algorithms
    3.8 Statics
    3.8.1 Kineto-Statics Duality
    3.8.2 Velocity and Force Transformation
    3.8.3 Closed Chain
    3.9 Manipulability Ellipsoids
    Bibliography
    Problems
    4 Trajectory Planning
    4.1 Path and Trajectory
    4.2 Joint Space Trajectories
    4.2.1 Point-to-Point Motion
    4.2.2 Motion Through a Sequence of Points
    4.3 Operational Space Trajectories
    4.3.1 Path Primitives
    4.3.2 Position
    4.3.3 Orientation
    Bibliography
    Problems
    5 Actuators and Sensors
    5.1 Joint Actuating System
    5.1.1 Transmissions
    5.1.2 Servomotors
    5.1.3 Power Amplifiers
    5.1.4 Power Supply
    5.2 Drives
    5.2.1 Electric Drives
    5.2.2 Hydraulic Drives
    5.2.3 Transmission Effects
    5.2.4 Position Control
    5.3 Proprioceptive Sensors
    5.3.1 Position Transducers
    5.3.2 Velocity Transducers
    5.4 Exteroceptive Sensors
    5.4.1 Force Sensors
    5.4.2 Range Sensors
    5.4.3 Vision Sensors
    Bibliography
    Problems
    6 Control Architecture
    6.1 Functional Architecture
    6.2 Programming Environment
    6.2.1 Teaching-by-Showing
    6.2.2 Robot-oriented Programming
    6.3 Hardware Architecture
    Bibliography
    Problems
    7 Dynamics
    7.1 Lagrange Formulation
    7.1.1 Computation of Kinetic Energy
    7.1.2 Computation of Potential Energy
    7.1.3 Equations of Motion
    7.2 Notable Properties of Dynamic Model
    7.2.1 Skew-symmetry of Matrix B − 2C
    7.2.2 Linearity in the Dynamic Parameters
    7.3 Dynamic Model of Simple Manipulator Structures
    7.3.1 Two-link Cartesian Arm
    7.3.2 Two-link Planar Arm
    7.3.3 Parallelogram Arm
    7.4 Dynamic Parameter Identification
    7.5 Newton–Euler Formulation
    7.5.1 Link Accelerations
    7.5.2 Recursive Algorithm
    7.5.3 Example
    7.6 Direct Dynamics and Inverse Dynamics
    7.7 Dynamic Scaling of Trajectories
    7.8 Operational Space Dynamic Model
    7.9 Dynamic Manipulability Ellipsoid
    Bibliography
    Problems
    8 Motion Control
    8.1 The Control Problem
    8.2 Joint Space Control
    8.3 Decentralized Control
    8.3.1 Independent Joint Control
    8.3.2 Decentralized Feedforward Compensation
    8.4 Computed Torque Feedforward Control
    8.5 Centralized Control
    8.5.1 PD Control with Gravity Compensation
    8.5.2 Inverse Dynamics Control
    8.5.3 Robust Control
    8.5.4 Adaptive Control
    8.6 Operational Space Control
    8.6.1 General Schemes
    8.6.2 PD Control with Gravity Compensation
    8.6.3 Inverse Dynamics Control
    8.7 Comparison Among Various Control Schemes
    Bibliography
    Problems
    9 Force Control
    9.1 Manipulator Interaction with Environment
    9.2 Compliance Control
    9.2.1 Passive Compliance
    9.2.2 Active Compliance
    9.3 Impedance Control
    9.4 Force Control
    9.4.1 Force Control with Inner Position Loop
    9.4.2 Force Control with Inner Velocity Loop
    9.4.3 Parallel Force/Position Control
    9.5 Constrained Motion
    9.5.1 Rigid Environment
    9.5.2 Compliant Environment
    9.6 Natural and Artificial Constraints
    9.6.1 Analysis of Tasks
    9.7 Hybrid Force/Motion Control
    9.7.1 Compliant Environment
    9.7.2 Rigid Environment
    Bibliography
    Problems
    10 Visual Servoing
    10.1 Vision for Control
    10.1.1 Configuration of the Visual System
    10.2 Image Processing
    10.2.1 Image Segmentation
    10.2.2 Image Interpretation
    10.3 Pose Estimation
    10.3.1 Analytical Solution
    10.3.2 Interaction Matrix
    10.3.3 Algorithmic Solution
    10.4 Stereo Vision
    10.4.1 Epipolar Geometry
    10.4.2 Triangulation
    10.4.3 Absolute Orientation
    10.4.4 3D Reconstruction from Planar Homography
    10.5 Camera Calibration
    10.6 The Visual Servoing Problem
    10.7 Position-based Visual Servoing
    10.7.1 PD Control with Gravity Compensation
    10.7.2 Resolved-velocity Control
    10.8 Image-based Visual Servoing
    10.8.1 PD Control with Gravity Compensation
    10.8.2 Resolved-velocity Control
    10.9 Comparison Among Various Control Schemes
    10.10 Hybrid Visual Servoing
    Bibliography
    Problems
    11 Mobile Robots
    11.1 Nonholonomic Constraints
    11.1.1 Integrability Conditions
    11.2 Kinematic Model
    11.2.1 Unicycle
    11.2.2 Bicycle
    11.3 Chained Form
    11.4 Dynamic Model
    11.5 Planning
    11.5.1 Path and Timing Law
    11.5.2 Flat Outputs
    11.5.3 Path Planning
    11.5.4 Trajectory Planning
    11.5.5 Optimal Trajectories
    11.6 Motion Control
    11.6.1 Trajectory Tracking
    11.6.2 Regulation
    11.7 Odometric Localization
    Bibliography
    Problems
    12 Motion Planning
    12.1 The Canonical Problem
    12.2 Configuration Space
    12.2.1 Distance
    12.2.2 Obstacles
    12.2.3 Examples of Obstacles
    12.3 Planning via Retraction
    12.4 Planning via Cell Decomposition
    12.4.1 Exact Decomposition
    12.4.2 Approximate Decomposition
    12.5 Probabilistic Planning
    12.5.1 PRM Method
    12.5.2 Bidirectional RRT Method
    12.6 Planning via Artificial Potentials
    12.6.1 Attractive Potential
    12.6.2 Repulsive Potential
    12.6.3 Total Potential
    12.6.4 Planning Techniques
    12.6.5 The Local Minima Problem
    12.7 The Robot Manipulator Case
    Bibliography
    Problems
    Appendices
    A Linear Algebra
    A.1 Definitions
    A.2 Matrix Operations
    A.3 Vector Operations
    A.4 Linear Transformation
    A.5 Eigenvalues and Eigenvectors
    A.6 Bilinear Forms and Quadratic Forms
    A.7 Pseudo-inverse
    A.8 Singular Value Decomposition
    Bibliography
    B Rigid-body Mechanics
    B.1 Kinematics
    B.2 Dynamics
    B.3 Work and Energy
    B.4 Constrained Systems
    Bibliography
    C Feedback Control
    C.1 Control of Single-input/Single-output Linear Systems
    C.2 Control of Nonlinear Mechanical Systems
    C.3 Lyapunov Direct Method
    Bibliography
    D Differential Geometry
    D.1 Vector Fields and Lie Brackets
    D.2 Nonlinear Controllability
    Bibliography
    E Graph Search Algorithms
    E.1 Complexity
    E.2 Breadth-first and Depth-first Search
    E.3 A* Algorithm
    Bibliography
    References
    Index
    Advanced Textbooks in Control and Signal Processing
    Series Editors Professor Michael J. Grimble, Professor of Industrial Systems and Director Professor Michael A. Johnson, Professor Emeritus of Control Systems and Deputy Director Industrial Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde, Graham Hills Building, 50 George Street, Glasgow G1 1QE, UK Other titles published in this series: Genetic Algorithms K.F. Man, K.S. Tang and S. Kwong Introduction to Optimal Estimation E.W. Kamen and J.K. Su Discrete-time Signal Processing D. Williamson Neural Networks for Modelling and Control of Dynamic Systems M. Nørgaard, O. Ravn, N.K. Poulsen and L.K. Hansen Fault Detection and Diagnosis in Industrial Systems L.H. Chiang, E.L. Russell and R.D. Braatz Soft Computing L. Fortuna, G. Rizzotto, M. Lavorgna, G. Nunnari, M.G. Xibilia and R. Caponetto Statistical Signal Processing T. Chonavel Discrete-time Stochastic Processes (2nd Edition) T. Söderström Parallel Computing for Real-time Signal Processing and Control M.O. Tokhi, M.A. Hossain and M.H. Shaheed Multivariable Control Systems P. Albertos and A. Sala Control Systems with Input and Output Constraints A.H. Glattfelder and W. Schaufelberger Analysis and Control of Non-linear Process Systems K.M. Hangos, J. Bokor and G. Szederkényi Model Predictive Control (2nd Edition) E.F. Camacho and C. Bordons Principles of Adaptive Filters and Self- learning Systems A. Zaknich Digital Self-tuning Controllers V. Bobál, J. Böhm, J. Fessl and J. Macháček Control of Robot Manipulators in Joint Space R. Kelly, V. Santibáñez and A. Loría Receding Horizon Control W.H. Kwon and S. Han Robust Control Design with MATLAB® D.-W. Gu, P.H. Petkov and M.M. Konstantinov Control of Dead-time Processes J.E. Normey-Rico and E.F. Camacho Modeling and Control of Discrete-event Dynamic Systems B. Hrúz and M.C. Zhou
    Bruno Siciliano • Lorenzo Sciavicco Luigi Villani • Giuseppe Oriolo Robotics Modelling, Planning and Control 123
    Bruno Siciliano, PhD Dipartimento di Informatica e Sistemistica Università di Napoli Federico II Via Claudio 21 80125 Napoli Italy siciliano@unina.it Luigi Villani, PhD Dipartimento di Informatica e Sistemistica Università di Napoli Federico II Via Claudio 21 80125 Napoli Italy lvillani@unina.it Lorenzo Sciavicco, DrEng Dipartimento di Informatica e Automazione Università di Roma Tre Via della Vasca Navale 79 00146 Roma Italy sciavicco@uniroma3.it Giuseppe Oriolo, PhD Dipartimento di Informatica e Sistemistica Università di Roma “La Sapienza” Via Ariosto 25 00185 Roma Italy oriolo@dis.uniroma1.it e-ISBN 978-1-84628-642-1 ISSN 1439-2232 ISBN 978-1-84628-641-4 DOI 10.1007/978-1-84628-642-1 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2008939574 © Springer-Verlag London Limited 2010 MATLAB® is a registered trademark of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760- 2098, USA. http://www.mathworks.com Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudioCalamar, Figueres/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
    to our families
    Series Editors’ Foreword The topics of control engineering and signal processing continue to flourish and develop. In common with general scientific investigation, new ideas, concepts and interpretations emerge quite spontaneously and these are then discussed, used, discarded or subsumed into the prevailing subject paradigm. Sometimes these innovative concepts coalesce into a new sub-discipline within the broad subject tapestry of control and signal processing. This preliminary battle be- tween old and new usually takes place at conferences, through the Internet and in the journals of the discipline. After a little more maturity has been acquired by the new concepts then archival publication as a scientific or engineering monograph may occur. A new concept in control and signal processing is known to have arrived when sufficient material has evolved for the topic to be taught as a specialised tutorial workshop or as a course to undergraduate, graduate or industrial engineers. Advanced Textbooks in Control and Signal Processing are designed as a vehicle for the systematic presentation of course material for both popular and innovative topics in the discipline. It is hoped that prospective authors will welcome the opportunity to publish a structured and systematic presentation of some of the newer emerging control and signal processing technologies in the textbook series. Robots have appeared extensively in the artistic field of science fiction writing. The actual name robot arose from its use by the playwright Karel ˇCapek in the play Rossum’s Universal Robots (1920). Not surprisingly, the artistic focus has been on mechanical bipeds with anthropomorphic person- alities often termed androids. This focus has been the theme of such cine- matic productions as, I, Robot (based on Isaac Asimov’s stories) and Stanley Kubrick’s film, A.I.; however, this book demonstrates that robot technology is already widely used in industry and that there is some robot technology which is at prototype stage rapidly approaching introduction to commercial use. Currently, robots may be classified according to their mobility attributes as shown in the figure.
    viii Series Editors’ Foreword The largest class of robots extant today is that of the fixed robot which does repetitive but often precise mechanical and physical tasks. These robots pervade many areas of modern industrial automation and are mainly con- cerned with tasks performed in a structured environment. It seems highly likely that as the technology develops the number of mobile robots will signif- icantly increase and become far more visible as more applications and tasks in an unstructured environment are serviced by robotic technology. What then is robotics? A succinct definition is given in The Chamber’s Dic- tionary (2003): the branch of technology dealing with the design, construction and use of robots. This definition certainly captures the spirit of this volume in the Advanced Textbooks in Control and Signal Processing series entitled Robotics and written by Bruno Siciliano, Lorenzo Sciavicco, Luigi Villani and Giuseppe Oriolo. This book is a greatly extended and revised version of an earlier book in the series, Modelling and Control of Robot Manipulators (2000, ISBN: 978-1-85233-221-1). As can be seen from the figure above, robots cover a wide variety of types and the new book seeks to present a unified approach to robotics whilst focusing on the two leading classes of robots, the fixed and the wheeled types. The textbook series publishes volumes in support of new disciplines that are emerging with their own novel identity, and robotics as a subject certainly falls into this category. The full scope of robotics lies at the intersection of mechanics, electronics, signal processing, control engineer- ing, computing and mathematical modelling. However, within this very broad framework the authors have pursued the themes of modelling, planning and control. These are, and will remain, fundamental aspects of robot design and operation for years to come. Some interesting innovations in this text include material on wheeled robots and on vision as used in the control of robots. Thus, the book provides a thorough theoretical grounding in an area where the technologies are evolving and developing in new applications. The series is one of textbooks for advanced courses, and volumes in the series have useful pedagogical features. This volume has twelve chapters cov- ering both fundamental and specialist topics, and there is a Problems section at the end of each chapter. Five appendices have been included to give more depth to some of the advanced methods used in the text. There are over twelve pages of references and nine pages of index. The details of the citations and index should also facilitate the use of the volume as a source of reference as
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