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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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 [...]... “not 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... 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 information, we will use the name Sensing Intelligence Motion (SIM) for motion. .. Manipulator 407 Suggested Course Projects 417 References 421 Index 429 PREFACE We humans are good at moving around in this world of ours If we are serious about the ubiquity of robots help to humankind, we must pass this skill to our robots It also turns out that in some tasks, robots can find their way better than humans This suggests that it is time for humans and robots to join forces Imagine you arrive... information into proper motion trajectories Today there are plenty of such algorithms This setup represents the Intelligence Motion planning paradigm This algorithmic paradigm was formulated right at the beginning of robotics as a field of science and technology, around the mid-1960s Today the Intelligence Motion paradigm boasts a large literature, appearing under such names as motion planning with complete... one doesn’t know which object is going to be where and when, or because of all three In dealing with an environment that has to be taken as is, our robots have a good example to follow: The evolution has taught us humans how to move around in our messy unstructured world We want our robots to leap-frog this process And then there are tasks—especially, as we will see, with motion planning for arm manipulators—where... intelligent automation, asking humans how they do it is not a gratifying experience Similar to some other tasks that humans do well (say, medical diagnostics), we humans cannot explain well how we do it Why did I decide to walk around a table this way and not some other way, and how did this decision fit into my plan to get to the door? I can hardly answer This means that robot motion planning strategies... will see, that often humans are not as good in motion planning as one may think Second, the above example with moving in the dark underlines the importance of sensing hardware Strategies that humans and animals use to realize safe motion in an unstructured environment are intimately tied to the sensing machinery a species possesses When coming from the outside into a dark room, your movement suddenly... robot”—that is, switching sharply from one movement to the other and being oblivious to the surroundings That is not what robots should be and even are today Examples in Chapter 8 will show that when equipped with means for self-awareness and with strategies to use it, robots become sensitive to their surroundings, “pensive,” and even gentle in how they “mind” their movement.1 A nonprofessional reader curious... being the pet project of science fiction writers and philosophers alike The pictures of real-life robots in the media, in which they look as close to a human as, say, a refrigerator, seem to only insult the public’s insistence on how a robot should look How much of “not quite”-ness is or ever will be there is the subject of sometimes fierce arguments It is usually agreed upon that high intelligence is... 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 After all, the physical setting that encompasses this information . 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.,. 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. pass this skill to our robots. It also turns out that in some tasks, robots can find their way better than humans. This suggests that it is time for humans and robots to join forces. Imagine you