Table Of ContentProbabilistic
Robotics
Probabilistic
Robotics
SebastianThrun
WolframBurgard
DieterFox
TheMITPress
Cambridge,Massachusetts
London,England
©2006MassachusettsInstituteofTechnology
All rights reserved. No part of this book may be reproduced in any form by any
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Typesetin10/13LucidaBrightbytheauthorsusingLATEX2ε.
PrintedandboundintheUnitedStatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Thrun,Sebastian,1967–
Probabilisticrobotics/SebastianThrun,WolframBurgard,DieterFox.
p.cm.–(Intelligentroboticsandautonomousagentsseries)
Includesbibliographicalreferencesandindex.
ISBN-13:978-0-262-20162-9(alk.paper)
1. Robotics. 2. Probabilities. I.Burgard,Wolfram. II.Fox,Dieter. III.Title. IV.In-
telligentroboticsandautonomousagents.
TJ211.T5752005
629.8’92–dc22
2005043346
10 9 8 7 6 5 6 3
Brief Contents
I Basics 1
1 Introduction 3
2 RecursiveStateEstimation 13
3 GaussianFilters 39
4 NonparametricFilters 85
5 RobotMotion 117
6 RobotPerception 149
II Localization 189
7 MobileRobotLocalization: MarkovandGaussian 191
8 MobileRobotLocalization: GridAndMonteCarlo 237
III Mapping 279
9 OccupancyGridMapping 281
10 SimultaneousLocalizationandMapping 309
11 TheGraphSLAMAlgorithm 337
12 TheSparseExtendedInformationFilter 385
13 TheFastSLAMAlgorithm 437
IV PlanningandControl 485
14 MarkovDecisionProcesses 487
15 PartiallyObservableMarkovDecisionProcesses 513
vi BriefContents
16 ApproximatePOMDPTechniques 547
17 Exploration 569
Contents
Preface xvii
Acknowledgments xix
I Basics 1
1 Introduction 3
1.1 UncertaintyinRobotics 3
1.2 ProbabilisticRobotics 4
1.3 Implications 9
1.4 RoadMap 10
1.5 TeachingProbabilisticRobotics 11
1.6 BibliographicalRemarks 11
2 RecursiveStateEstimation 13
2.1 Introduction 13
2.2 BasicConceptsinProbability 14
2.3 RobotEnvironmentInteraction 19
2.3.1 State 20
2.3.2 EnvironmentInteraction 22
2.3.3 ProbabilisticGenerativeLaws 24
2.3.4 BeliefDistributions 25
2.4 BayesFilters 26
2.4.1 TheBayesFilterAlgorithm 26
2.4.2 Example 28
2.4.3 MathematicalDerivationoftheBayesFilter 31
2.4.4 TheMarkovAssumption 33
viii Contents
2.5 RepresentationandComputation 34
2.6 Summary 35
2.7 BibliographicalRemarks 36
2.8 Exercises 36
3 GaussianFilters 39
3.1 Introduction 39
3.2 TheKalmanFilter 40
3.2.1 LinearGaussianSystems 40
3.2.2 TheKalmanFilterAlgorithm 43
3.2.3 Illustration 44
3.2.4 MathematicalDerivationoftheKF 45
3.3 TheExtendedKalmanFilter 54
3.3.1 WhyLinearize? 54
3.3.2 LinearizationViaTaylorExpansion 56
3.3.3 TheEKFAlgorithm 59
3.3.4 MathematicalDerivationoftheEKF 59
3.3.5 PracticalConsiderations 61
3.4 TheUnscentedKalmanFilter 65
3.4.1 LinearizationViatheUnscentedTransform 65
3.4.2 TheUKFAlgorithm 67
3.5 TheInformationFilter 71
3.5.1 CanonicalParameterization 71
3.5.2 TheInformationFilterAlgorithm 73
3.5.3 MathematicalDerivationoftheInformationFilter 74
3.5.4 TheExtendedInformationFilterAlgorithm 75
3.5.5 MathematicalDerivationoftheExtended
InformationFilter 76
3.5.6 PracticalConsiderations 77
3.6 Summary 79
3.7 BibliographicalRemarks 81
3.8 Exercises 81
4 NonparametricFilters 85
4.1 TheHistogramFilter 86
4.1.1 TheDiscreteBayesFilterAlgorithm 86
4.1.2 ContinuousState 87
4.1.3 MathematicalDerivationoftheHistogram
Approximation 89
Contents ix
4.1.4 DecompositionTechniques 92
4.2 BinaryBayesFilterswithStaticState 94
4.3 TheParticleFilter 96
4.3.1 BasicAlgorithm 96
4.3.2 ImportanceSampling 100
4.3.3 MathematicalDerivationofthePF 103
4.3.4 PracticalConsiderationsandPropertiesofParticle
Filters 104
4.4 Summary 113
4.5 BibliographicalRemarks 114
4.6 Exercises 115
5 RobotMotion 117
5.1 Introduction 117
5.2 Preliminaries 118
5.2.1 KinematicConfiguration 118
5.2.2 ProbabilisticKinematics 119
5.3 VelocityMotionModel 121
5.3.1 ClosedFormCalculation 121
5.3.2 SamplingAlgorithm 122
5.3.3 MathematicalDerivationoftheVelocityMotion
Model 125
5.4 OdometryMotionModel 132
5.4.1 ClosedFormCalculation 133
5.4.2 SamplingAlgorithm 137
5.4.3 MathematicalDerivationoftheOdometryMotion
Model 137
5.5 MotionandMaps 140
5.6 Summary 143
5.7 BibliographicalRemarks 145
5.8 Exercises 145
6 RobotPerception 149
6.1 Introduction 149
6.2 Maps 152
6.3 BeamModelsofRangeFinders 153
6.3.1 TheBasicMeasurementAlgorithm 153
6.3.2 AdjustingtheIntrinsicModelParameters 158
6.3.3 MathematicalDerivationoftheBeamModel 162
Description:An introduction to the techniques and algorithms of the newest field in robotics.Probabilistic robotics is a new and growing area in robotics, concerned with perception and control in the face of uncertainty. Building on the field of mathematical statistics, probabilistic robotics endows robots with
