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Principles of Robot Motion : Theory, Algorithms, and Implementations - Howie M. Choset

Principles of Robot Motion

Theory, Algorithms, and Implementations

Hardcover Published: 4th June 2005
ISBN: 9780262033275
Number Of Pages: 626
For Ages: 18+ years old

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Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, relating low-level implementation details to high-level algorithmic concepts.

Forewordp. xv
Prefacep. xvii
Acknowledgmentsp. xxi
Introductionp. 1
Overview of Concepts in Motion Planningp. 9
Overview of the Bookp. 12
Mathematical Stylep. 13
Bug Algorithmsp. 17
Bug1 and Bug2p. 17
Tangent Bugp. 23
Implementationp. 30
What Information: The Tangent Linep. 31
How to Infer Information with Sensors: Distance and Gradientp. 32
How to Process Sensor Information: Continuation Methodsp. 35
Configuration Spacep. 39
Specifying a Robot's Configurationp. 40
Obstacles and the Configuration Spacep. 43
Circular Mobile Robotp. 43
Two-Joint Planar Armp. 45
The Dimension of the Configuration Spacep. 47
The Topology of the Configuration Spacep. 50
Homeomorphisms and Diffeomorphismsp. 51
Differentiable Manifoldsp. 55
Connectedness and Compactnessp. 58
Not All Configuration Spaces Are Manifoldsp. 59
Embeddings of Manifolds in R[superscript n]p. 59
Matrix Representations of Rigid-Body Configurationp. 60
Parameterizations of SO(3)p. 66
Example Configuration Spacesp. 68
Transforming Configuration and Velocity Representationsp. 69
Potential Functionsp. 77
Additive Attractive/Repulsive Potentialp. 80
Gradient Descentp. 84
Computing Distance for Implementation in the Planep. 85
Mobile Robot Implementationp. 86
Brushfire Algorithm: A Method to Compute Distance on a Gridp. 86
Local Minima Problemp. 89
Wave-Front Plannerp. 90
Navigation Potential Functionsp. 93
Sphere-Spacep. 93
Star-Spacep. 96
Potential Functions in Non-Euclidean Spacesp. 99
Relationship between Forces in the Workspace and Configuration Spacep. 100
Potential Functions for Rigid-Body Robotsp. 101
Path Planning for Articulated Bodiesp. 104
Roadmapsp. 107
Visibility Maps: The Visibility Graphp. 110
Visibility Graph Definitionp. 110
Visibility Graph Constructionp. 113
Deformation Retracts: Generalized Voronoi Diagramp. 117
GVD Definitionp. 118
GVD Roadmap Propertiesp. 119
Deformation Retract Definitionp. 121
GVD Dimension: The Preimage Theorem and Critical Pointsp. 123
Construction of the GVDp. 126
Retract-like Structures: The Generalized Voronoi Graphp. 129
GVG Dimension: Transversalityp. 130
Retract-like Structure Connectivityp. 133
Lyapunov Control: Sensor-Based Construction of the HGVGp. 136
Piecewise Retracts: The Rod-Hierarchical Generalized Voronoi Graphp. 138
Silhouette Methodsp. 141
Canny's Roadmap Algorithmp. 142
Opportunistic Path Plannerp. 151
Cell Decompositionsp. 161
Trapezoidal Decompositionp. 162
Morse Cell Decompositionsp. 168
Boustrophedon Decompositionp. 169
Morse Decomposition Definitionp. 170
Examples of Morse Decomposition: Variable Slicep. 172
Sensor-Based Coveragep. 178
Complexity of Coveragep. 182
Visibility-Based Decompositions for Pursuit/Evasionp. 187
Sampling-Based Algorithmsp. 197
Probabilistic Roadmapsp. 202
Basic PRMp. 203
A Practical Implementation of Basic PRMp. 208
PRM Sampling Strategiesp. 216
PRM Connection Strategiesp. 225
Single-Query Sampling-Based Plannersp. 227
Expansive-Spaces Treesp. 230
Rapidly-Exploring Random Treesp. 233
Connection Strategies and the SBL Plannerp. 238
Integration of Planners: Sampling-Based Roadmap of Treesp. 238
Analysis of PRMp. 242
PRM Operating in R[superscript d]p. 243
([epsilon, alpha, beta])-Expansivenessp. 246
Abstract Path Tilingp. 250
Beyond Basic Path Planningp. 253
Control-Based Planningp. 253
Multiple Robotsp. 254
Manipulation Planningp. 257
Assembly Planningp. 259
Flexible Objectsp. 260
Biological Applicationsp. 262
Kalman Filteringp. 269
Probabilistic Estimationp. 270
Linear Kalman Filteringp. 272
Overviewp. 273
A Simple Observerp. 274
Observing with Probability Distributionsp. 277
The Kalman Filterp. 282
Kalman Filter Summaryp. 284
Example: Kalman Filter for Dead Reckoningp. 285
Observability in Linear Systemsp. 287
Extended Kalman Filterp. 289
EKF for Range and Bearing Localizationp. 290
Data Associationp. 292
EKF for Range-Only Localizationp. 294
Kalman Filter for SLAMp. 294
Simple SLAMp. 294
Range and Bearing SLAMp. 296
Bayesian Methodsp. 301
Localizationp. 301
The Basic Idea of Probabilistic Localizationp. 302
Probabilistic Localization as Recursive Bayesian Filteringp. 304
Derivation of Probabilistic Localizationp. 308
Representations of the Posteriorp. 310
Sensor Modelsp. 322
Mappingp. 328
Mapping with Known Locations of the Robotp. 328
Bayesian Simultaneous Localization and Mappingp. 337
Robot Dynamicsp. 349
Lagrangian Dynamicsp. 349
Standard Forms for Dynamicsp. 353
Velocity Constraintsp. 357
Dynamics of a Rigid Bodyp. 361
Planar Rotationp. 362
Spatial Rotationp. 363
Trajectory Planningp. 373
Preliminariesp. 374
Decoupled Trajectory Planningp. 374
Zero Inertia Pointsp. 378
Global Time-Optimal Trajectory Planningp. 384
Direct Trajectory Planningp. 384
Optimal Controlp. 385
Nonlinear Optimizationp. 389
Grid-Based Searchp. 392
Nonholonomic and Underactuated Systemsp. 401
Preliminariesp. 402
Tangent Spaces and Vector Fieldsp. 405
Distributions and Constraintsp. 407
Lie Bracketsp. 409
Control Systemsp. 414
Controllabilityp. 416
Local Accessibility and Controllabilityp. 419
Global Controllabilityp. 422
Simple Mechanical Control Systemsp. 424
Simplified Controllability Testsp. 425
Kinematic Reductions for Motion Planningp. 434
Simple Mechanical Systems with Nonholonomic Constraintsp. 438
Motion Planningp. 440
Optimal Controlp. 440
Steering Chained-Form Systems Using Sinusoidsp. 444
Nonlinear Optimizationp. 445
Gradient Methods for Driftless Systemsp. 446
Differentially Flat Systemsp. 447
Cars and Cars Pulling Trailersp. 450
Kinematic Reductions of Mechanical Systemsp. 462
Other Approachesp. 465
Mathematical Notationp. 473
Basic Set Definitionsp. 475
Topology and Metric Spacesp. 478
Topologyp. 478
Metric Spacesp. 479
Normed and Inner Product Spacesp. 480
Continuous Functionsp. 481
Jacobians and Gradientsp. 483
Curve Tracingp. 487
Implicit Function Theoremp. 487
Newton-Raphson Convergence Theoremp. 488
Representations of Orientationp. 489
Euler Anglesp. 489
Roll, Pitch, and Yaw Anglesp. 491
Axis-Angle Parameterizationp. 492
Quaternionsp. 494
Polyhedral Robots in Polyhedral Worldsp. 499
Representing Polygons in Two Dimensionsp. 499
Intersection Tests for Polygonsp. 502
Configuration Space Obstacles in Q = R[superscript 2]: The Star Algorithmp. 507
Configuration Space Obstacles in Q = SE(2)p. 508
Computing Distances between Polytopes in R[superscript 2] and R[superscript 3]p. 509
Analysis of Algorithms and Complexity Classesp. 513
Running Timep. 513
Complexity Theoryp. 515
Completenessp. 520
Graph Representation and Basic Searchp. 521
Graphsp. 521
A* Algorithmp. 527
Basic Notation and Assumptionsp. 530
Discussion: Completeness, Efficiency, and Optimalityp. 531
Greedy-Search and Dijkstra's Algorithmp. 532
Example of A* on a Gridp. 533
Nonoptimistic Examplep. 535
D* Algorithmp. 536
Optimal Plansp. 546
Statistics Primerp. 547
Distributions and Densitiesp. 548
Expected Values and Covariancesp. 550
Multivariate Gaussian Distributionsp. 551
Linear Systems and Controlp. 552
State Space Representationp. 552
Stabilityp. 554
LTI Control Systemsp. 557
Observing LTI Systemsp. 559
Discrete Time Systemsp. 562
Stabilityp. 562
Controllability and Observabilityp. 563
Bibliographyp. 565
Indexp. 597
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780262033275
ISBN-10: 0262033275
Series: Intelligent Robotics and Autonomous Agents series
Audience: Professional
For Ages: 18+ years old
Format: Hardcover
Language: English
Number Of Pages: 626
Published: 4th June 2005
Publisher: MIT Press Ltd
Country of Publication: US
Dimensions (cm): 22.9 x 20.3  x 3.8
Weight (kg): 1.32