Principles of Robot Motion: Theory, Algorithms, and Implementations

616 Pages·2005·6.04 MB·English

by  Choset H.

Choset-79066 book February23,2005 13:40

Principles
of
Robot
Motion
Choset-79066 book February23,2005 13:40
IntelligentRoboticsandAutonomousAgents
RonaldC.Arkin,editor
Behavior-BasedRobotics,RonaldC.Arkin,1998
RobotShaping:AnExperimentinBehaviorEngineering,MarcoDorigoandMarco
Colombetti,1998
LayeredLearninginMultiagentSystems:AWinningApproachtoRoboticSoccer,Peter
Stone,2000
EvolutionaryRobotics:TheBiology,Intelligence,andTechnologyofSelf-Organizing
Machines,StefanoNolfiandDarioFloreano,2000
ReasoningaboutRationalAgents,MichaelWooldridge,2000
IntroductiontoAIRobotics,RobinR.Murphy,2000
StrategicNegotiationinMultiagentEnvironments,SaritKraus,2001
MechanicsofRoboticManipulation,MatthewT.Mason,2001
DesigningSociableRobots,CynthiaL.Breazeal,2001
IntroductiontoAutonomousMobileRobots,RolandSiegwartandIllahR.Nourbakhsh,2004
PrinciplesofRobotMotion:Theory,Algorithms,andImplementations,HowieChoset,Kevin
Lynch,SethHutchinson,GeorgeKantor,WolframBurgard,LydiaKavrakiandSebastian
Thrun,2005
Choset-79066 book February23,2005 13:40
Principles
of
Robot Motion
Theory, Algorithms,
and Implementation
HowieChoset,KevinLynch,SethHutchinson,
GeorgeKantor,WolframBurgard,LydiaKavraki,
andSebastianThrun
ABradfordBook
TheMITPress
Cambridge,Massachusetts
London,England
Choset-79066 book February23,2005 13:40
©2005MassachusettsInstituteofTechnology
Allrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicor
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withoutpermissioninwritingfromthepublisher.
MITPressbooksmaybepurchasedatspecialquantitydiscountsforbusinessorsales
promotionaluse.Forinformation,pleaseemailspecial [email protected]
SpecialSalesDepartment,TheMITPress,5CambridgeCenter,Cambridge,MA02142.
ThisbookwassetinLATEX2ebyInteractiveCompositionCorporationandwasprintedand
boundintheUnitedStatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Principlesofrobotmotion:theory,algorithms,andimplementation/HowieChoset[etal.].
p.cm. (Intelligentroboticsandautonomousagents)
“ABradfordbook.”
Includesbibliographicalreferencesandindex.
ISN0-262-03327-5(alk.paper)
1.Robots—Motion.I.Choset,HowieM.II.Series.
TJ211.4.P752004
629.8(cid:1)92—dc22 2004044906
10987654321
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Toourfamilies
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Contents
Foreword xv
Preface xvii
Acknowledgments xxi
1 Introduction 1
1.1 OverviewofConceptsinMotionPlanning 9
1.2 OverviewoftheBook 12
1.3 MathematicalStyle 13
2 BugAlgorithms 17
2.1 Bug1andBug2 17
2.2 TangentBug 23
2.3 Implementation 30
2.3.1 WhatInformation:TheTangentLine 31
2.3.2 HowtoInferInformationwithSensors:Distance
andGradient 32
2.3.3 HowtoProcessSensorInformation:
ContinuationMethods 35
3 ConfigurationSpace 39
3.1 SpecifyingaRobot’sConfiguration 40
3.2 ObstaclesandtheConfigurationSpace 43
3.2.1 CircularMobileRobot 43
3.2.2 Two-JointPlanarArm 45
3.3 TheDimensionoftheConfigurationSpace 47
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viii Contents
3.4 TheTopologyoftheConfigurationSpace 50
3.4.1 HomeomorphismsandDiffeomorphisms 51
3.4.2 DifferentiableManifolds 55
3.4.3 ConnectednessandCompactness 58
3.4.4 NotAllConfigurationSpacesAreManifolds 59
3.5 EmbeddingsofManifoldsinRn 59
3.5.1 MatrixRepresentationsofRigid-BodyConfiguration 60
3.6 ParameterizationsofSO(3) 66
3.7 ExampleConfigurationSpaces 68
3.8 TransformingConfigurationandVelocity
Representations 69
4 PotentialFunctions 77
4.1 AdditiveAttractive/RepulsivePotential 80
4.2 GradientDescent 84
4.3 ComputingDistanceforImplementationinthePlane 85
4.3.1 MobileRobotImplementation 86
4.3.2 BrushfireAlgorithm:AMethodtoComputeDistance
onaGrid 86
4.4 LocalMinimaProblem 89
4.5 Wave-FrontPlanner 90
4.6 NavigationPotentialFunctions 93
4.6.1 Sphere-Space 93
4.6.2 Star-Space 96
4.7 PotentialFunctionsinNon-EuclideanSpaces 99
4.7.1 RelationshipbetweenForcesintheWorkspaceand
ConfigurationSpace 100
4.7.2 PotentialFunctionsforRigid-BodyRobots 101
4.7.3 PathPlanningforArticulatedBodies 104
5 Roadmaps 107
5.1 VisibilityMaps:TheVisibilityGraph 110
5.1.1 VisibilityGraphDefinition 110
5.1.2 VisibilityGraphConstruction 113
5.2 DeformationRetracts:GeneralizedVoronoiDiagram 117
5.2.1 GVDDefinition 118
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Contents ix
5.2.2 GVDRoadmapProperties 119
5.2.3 DeformationRetractDefinition 121
5.2.4 GVDDimension:ThePreimageTheorem
andCriticalPoints 123
5.2.5 ConstructionoftheGVD 126
5.3 Retract-likeStructures:TheGeneralized
VoronoiGraph 129
5.3.1 GVGDimension:Transversality 130
5.3.2 Retract-likeStructureConnectivity 133
5.3.3 LyapunovControl:Sensor-BasedConstruction
oftheHGVG 136
5.4 PiecewiseRetracts:TheRod-HierarchicalGeneralized
VoronoiGraph 138
5.5 SilhouetteMethods 141
5.5.1 Canny’sRoadmapAlgorithm 142
5.5.2 OpportunisticPathPlanner 151
6 CellDecompositions 161
6.1 TrapezoidalDecomposition 162
6.2 MorseCellDecompositions 168
6.2.1 BoustrophedonDecomposition 169
6.2.2 MorseDecompositionDefinition 170
6.2.3 ExamplesofMorseDecomposition:Variable
Slice 172
6.2.4 Sensor-BasedCoverage 178
6.2.5 ComplexityofCoverage 182
6.3 Visibility-BasedDecompositionsforPursuit/Evasion 187
7 Sampling-BasedAlgorithms 197
7.1 ProbabilisticRoadmaps 202
7.1.1 BasicPRM 203
7.1.2 APracticalImplementationofBasicPRM 208
7.1.3 PRMSamplingStrategies 216
7.1.4 PRMConnectionStrategies 225
7.2 Single-QuerySampling-BasedPlanners 227
7.2.1 Expansive-SpacesTrees 230
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x Contents
7.2.2 Rapidly-ExploringRandomTrees 233
7.2.3 ConnectionStrategiesandtheSBLPlanner 238
7.3 IntegrationofPlanners:Sampling-BasedRoadmap
ofTrees 238
7.4 AnalysisofPRM 242
7.4.1 PRMOperatinginRd 243
7.4.2 ((cid:1),α,β)-Expansiveness 246
7.4.3 AbstractPathTiling 250
7.5 BeyondBasicPathPlanning 253
7.5.1 Control-BasedPlanning 253
7.5.2 MultipleRobots 254
7.5.3 ManipulationPlanning 257
7.5.4 AssemblyPlanning 259
7.5.5 FlexibleObjects 260
7.5.6 BiologicalApplications 262
8 KalmanFiltering 269
8.1 ProbabilisticEstimation 270
8.2 LinearKalmanFiltering 272
8.2.1 Overview 273
8.2.2 ASimpleObserver 274
8.2.3 ObservingwithProbabilityDistributions 277
8.2.4 TheKalmanFilter 282
8.2.5 KalmanFilterSummary 284
8.2.6 Example:KalmanFilterforDeadReckoning 285
8.2.7 ObservabilityinLinearSystems 287
8.3 ExtendedKalmanFilter 289
8.3.1 EKFforRangeandBearingLocalization 290
8.3.2 DataAssociation 292
8.3.3 EKFforRange-OnlyLocalization 294
8.4 KalmanFilterforSLAM 294
8.4.1 SimpleSLAM 294
8.4.2 RangeandBearingSLAM 296
9 BayesianMethods 301
9.1 Localization 301
9.1.1 TheBasicIdeaofProbabilisticLocalization 302
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Contents xi
9.1.2 ProbabilisticLocalizationasRecursiveBayesian
Filtering 304
9.1.3 DerivationofProbabilisticLocalization 308
9.1.4 RepresentationsofthePosterior 310
9.1.5 SensorModels 322
9.2 Mapping 328
9.2.1 MappingwithKnownLocations
oftheRobot 328
9.2.2 BayesianSimultaneousLocalizationand
Mapping 337
10 RobotDynamics 349
10.1 LagrangianDynamics 349
10.2 StandardFormsforDynamics 353
10.3 VelocityConstraints 357
10.4 DynamicsofaRigidBody 361
10.4.1 PlanarRotation 362
10.4.2 SpatialRotation 363
11 TrajectoryPlanning 373
11.1 Preliminaries 374
11.2 DecoupledTrajectoryPlanning 374
11.2.1 ZeroInertiaPoints 378
11.2.2 GlobalTime-OptimalTrajectoryPlanning 384
11.3 DirectTrajectoryPlanning 384
11.3.1 OptimalControl 385
11.3.2 NonlinearOptimization 389
11.3.3 Grid-BasedSearch 392
12 NonholonomicandUnderactuatedSystems 401
12.1 Preliminaries 402
12.1.1 TangentSpacesandVectorFields 405
12.1.2 DistributionsandConstraints 407
12.1.3 LieBrackets 409
12.2 ControlSystems 414