Table Of Content

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 mechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval) 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 Choset-79066 book February23,2005 13:40 Toourfamilies Choset-79066 book February23,2005 13:40 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 Choset-79066 book February23,2005 13:40 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 Choset-79066 book February23,2005 13:40 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 Choset-79066 book February23,2005 13:40 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 Choset-79066 book February23,2005 13:40 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