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TLFeBOOK TLFeBOOK SENSING, INTELLIGENCE, MOTION SENSING, INTELLIGENCE, MOTION HOW ROBOTS AND HUMANS MOVE IN AN UNSTRUCTURED WORLD Vladimir J. Lumelsky A JOHN WILEY & SONS, INC., PUBLICATION Copyright 2006 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Lumelsky, Vladimir. Sensing, intelligence motion : how robots and humans move in an unstructured world / Vladimir L. Lumelsky. p. cm. “A Wiley-Interscience publication.” Includes bibliographical references and index. ISBN-13 978-0-471-70740-0 ISBN-10 0-471-70740-6 1. Robots—Motion. 2. Manipulators (Mechanism) I. Title. TJ211.L85 2005 629.8  92—dc22 2005041748 Printed in the United States of America. 10987654321 MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests To Rakhil, Nadya, Michael, and Anna CONTENTS Preface xiii Acknowledgments xxiii 1 Motion Planning—Introduction 1 1.1 Introduction 1 1.2 Basic Concepts 13 1.2.1 Robot? What Robot? 13 1.2.2 Space. Objects 15 1.2.3 Input Information. Sensing 15 1.2.4 Degrees of Freedom. Coordinate Systems 18 1.2.5 Motion Control 20 1.2.6 Robot Programming 21 1.2.7 Motion Planning 24 2 A Quick Sketch of Major Issues in Robotics 27 2.1 Kinematics 29 2.2 Statics 33 2.3 Dynamics 33 2.4 Feedback Control 37 2.5 Compliant Motion 40 2.6 Trajectory Modification 44 2.7 Collision Avoidance 48 2.8 Motion Planning with Complete Information 51 2.9 Motion Planning with Incomplete Information 55 2.9.1 The Beginnings 59 2.9.2 Maze-to-Graph Transition 66 vii viii CONTENTS 2.9.3 Sensor-Based Motion Planning 66 2.10 Exercises 71 3 Motion Planning for a Mobile Robot 73 3.1 The Model 78 3.2 Universal Lower Bound for the Path Planning Problem 80 3.3 Basic Algorithms 84 3.3.1 First Basic Algorithm: Bug1 84 3.3.2 Second Basic Algorithm: Bug2 90 3.4 Combining Good Features of Basic Algorithms 100 3.5 Going After Tighter Bounds 103 3.6 Vision and Motion Planning 104 3.6.1 The Model 106 3.6.2 Algorithm VisBug-21 110 3.6.3 Algorithm VisBug-22 120 3.7 From a Point Robot to a Physical Robot 123 3.8 Other Approaches 124 3.9 Which Algorithm to Choose? 127 3.10 Discussion 130 3.11 Exercises 135 4 Accounting for Body Dynamics: The Jogger’s Problem 139 4.1 Problem Statement 139 4.2 Maximum Turn Strategy 144 4.2.1 The Model 144 4.2.2 Sketching the Approach 146 4.2.3 Velocity Constraints. Minimum Time Braking 148 4.2.4 Optimal Straight-Line Motion 149 4.2.5 Dynamics and Collision Avoidance 152 4.2.6 The Algorithm 154 4.2.7 Examples 157 4.3 Minimum Time Strategy 159 4.3.1 The Model 160 4.3.2 Sketching the Approach 161 4.3.3 Dynamics and Collision Avoidance 164 CONTENTS ix 4.3.4 Canonical Solution 166 4.3.5 Near-Canonical Solution 169 4.3.6 The Algorithm 170 4.3.7 Convergence. Computational Complexity 172 4.3.8 Examples 175 5 Motion Planning for Two-Dimensional Arm Manipulators 177 5.1 Introduction 177 5.1.1 Model and Definitions 183 5.2 Planar Revolute–Revolute (RR) Arm 187 5.2.1 Analysis 189 5.2.2 Algorithm 210 5.2.3 Step Planning 211 5.2.4 Example 212 5.2.5 Motion Planning with Vision and Proximity Sensing 213 5.2.6 Concluding Remarks 218 5.3 Distinct Kinematic Configurations of RR Arm 220 5.4 Prismatic–Prismatic (PP, or Cartesian) Arm 226 5.5 Revolute–Prismatic (RP) Arm with Parallel Links 229 5.6 Revolute–Prismatic (RP) Arm with Perpendicular Links 234 5.7 Prismatic–Revolute (PR) Arm 234 5.8 Topology of Arm’s Free Configuration Space 245 5.8.1 Workspace; Configuration Space 249 5.8.2 Interaction Between the Robot and Obstacles 252 5.8.3 Uniform Local Connectedness 255 5.8.4 The General Case of 2-DOF Arm Manipulators 256 5.9 Appendix 258 5.10 Exercises 267 6 Motion Planning for Three-Dimensional Arm Manipulators 271 6.1 Introduction 271 6.2 The Case of the PPP (Cartesian) Arm 276 6.2.1 Model, Definitions, and Terminology 276 6.2.2 The Approach 283 6.2.3 Topology of W -Obstacles and C-Obstacles 285 6.2.4 Connectivity of C 295 [...]... quite”-ness is a jerky motion sold as robot motion in Hollywood movies and by young people imitating a robot on street corners Whatever future improvements the public is willing to grant the field, a smooth motion and a less-than- wooden personality are not among them A robotics Sensing, Intelligence, Motion, by Vladimir J Lumelsky Copyright  2006 John Wiley & Sons, Inc 1 2 MOTION PLANNING—INTRODUCTION... continuous sensor-based motion planning PREFACE xvii Hence the names of approaches to motion planning in an unstructured environment that one finds in the literature are: motion planning with incomplete information, or sensor-based motion planning Another good name comes from the crucial role that this paradigm assigns to sensing: Similar to the phrase Intelligence Motion for motion planning with complete... choices A typical structure that covers ideas and computational schemes of the sensorbased motion planning paradigm will include Chapters 1, 2, 3, 5, and 6 (Motion Planning—Introduction, A Quick Sketch of Major Issues in Robotics, Motion Planning for a Mobile Robot, Motion Planning for Two-Dimensional Arm Manipulators, Motion Planning for Three-Dimensional Arm Manipulators) Let us call this sequence the... professionals From the standpoint of motion planning, the input information that the robot needs in order to generate the desired motion is available before the motion starts What is needed is appropriate algorithms for transforming this information into proper motion trajectories Today there are plenty of such algorithms This setup represents the Intelligence Motion planning paradigm This algorithmic... Intelligence Motion paradigm boasts a large literature, appearing under such names as motion planning with complete information, or model-based motion planning, or the Piano Mover’s model The symbolism behind the latter term is that when movers set out to move a piano, they can first sit down and figure out the whole sequence of moves and turns and raisings and lowerings, before they start the actual motion. .. two complementary groups—(1) motion planning with complete information and (2) motion planning with incomplete information—is tied in a one-to-one fashion to still another classification, along the scientific tools in the foundation of those approaches Namely, strategies for motion planning with complete information rely exclusively on geometric tools, whereas strategies for motion planning with incomplete... a deeper understanding of the effects of robot PREFACE xix dynamics on motion planning, covered in Chapter 4, plus a cursorial review of principles of design of sensing devices necessary for realizing sensor-based motion planning strategies, Chapter 8 Any group can benefit from Chapter 7, which is devoted to human performance in motion planning and spatial reasoning tasks A two-semester sequence will... fiction-maintained myth Many robot applications—car painting is a good example—require smooth motion and simply cannot tolerate sharp turns Today’s industrial robots can generate a motion that is so smooth and delicate that it may be the envy of “Swan Lake” ballerinas For those who know calculus, what dancer can promise, for example, a motion so smooth that both its derivatives have guaranteed continuity! PREFACE... reasons, in spite of its great theoretical interest and an immense practical potential, the literature on the sensor-based motion planning paradigm is small, especially for arm manipulators In fact, today there are no textbooks devoted to it Our goals in this book are as follows: (a) Formulate the problem of sensor-based motion planning We want to explore why the relevant issues are so hard—so much... such a strategy is, for example, one where the motion has to be repeated over and over again in exactly the same workspace, precisely as it happens on the car assembly line or in a car body painting booth Here complete information about all objects in the robot environment is collected beforehand and passed to the motion planning software The computed motion is then tried and optimized via special . TLFeBOOK TLFeBOOK SENSING, INTELLIGENCE, MOTION SENSING, INTELLIGENCE, MOTION HOW ROBOTS AND HUMANS MOVE IN AN UNSTRUCTURED WORLD Vladimir J sensor- based motion planning paradigm will include Chapters 1, 2, 3, 5, and 6 (Motion Planning—Introduction, A Quick Sketch of Major Issues in Robotics, Motion Planning for a Mobile Robot, Motion Planning. professionals. From the standpoint of motion planning, the input information that the robot needs in order to generate the desired motion is available before the motion starts. What is needed is appropriate