Hierarchical Voronoi Graphs: Spatial Representation and Reasoning for Mobile Robots

233 Pages·2010·18.92 MB·English

by  Jan Oliver Wallgrün (auth.)

Hierarchical Voronoi Graphs
Jan Oliver Wallgrün
Hierarchical
Voronoi Graphs
Spatial Representation and Reasoning
for Mobile Robots
Dr.-Ing. Jan Oliver Wallgrün
Cognitive Systems Group
Department of Mathematics and Informatics
University of Bremen
P.O. Box 330 440
28334 Bremen
Germany
[email protected]

This thesis was accepted as doctoral dissertation by the Department of Mathematics and
Informatics, University of Bremen, under the title “Hierarchical Route Graph Repre-
sentations for Mobile Robots Based on Generalized Voronoi Graphs”. Based on this work
the author was granted the academic degree Dr.-Ing.
Date of oral examination: 19 August 2008
Reviewers:
Prof. Christian Freksa, Ph.D. (University of Bremen, Germany)
Prof. Benjamin Kuipers, Ph.D. (University of Texas at Austin, USA)
ISBN 978-3-642-10302-5 e-ISBN 978-3-642-10345-2
DOI 10.1007/978-3-642-10345-2
SpringerHeidelbergDordrechtLondonNewYork
Library of Congress Control Number: 2009941853
ACM Computing Classification (1998): I.2, J.2.
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v
Foreword
Whatisspace?Istherespacewhenthereareobjectstooccupyitoristherespaceonly
when there are no objects to occupy it? Can there be space without objects? These
areoldphilosophicalquestionsthatconcerntheontologyofspaceinthephilosophical
senseof‘ontology’–whatisthenatureofspace?
Cognitive science in general and artificial intelligence in particular are less con-
cernedwiththenatureofthingsthanwiththeirmentalconceptualizations. Inspatial
cognition research we address questions like What do we know about space? How
is space represented? What are the representational entities? What are the repre-
sentational structures? Answers to these questions are described in what is called
ontologies in artificial intelligence. Different tasks require different knowledge, and
different representations of knowledge facilitate different ways of solving problems.
Inthisbook,JanOliverWallgründevelopsandinvestigatesrepresentationalstructures
to support tasks of autonomous mobile robots, from the acquisition of knowledge to
theuseofthisknowledgefornavigation.
The research presented is concerned with the robot mapping problem, the prob-
lem of building a spatial representation of an environment that is perceived by sen-
sorsthatonlyprovideincompleteanduncertaininformation;thisinformationusually
needs to be related to other imprecise or uncertain information. The routes a robot
can take can be abstractly described in terms of graphs where alternative routes are
representedbyalternativebranchesintheseroutegraphs. Theproposedhierarchical
Voronoigraphrepresentationprovidesaconceptualizationofspaceexcellentlysuited
fornavigation,high-levelspatialreasoningaboutenvironments,andagent-agentcom-
municationaboutnavigablespace.TheproblemisthattheVoronoirepresentationsare
rathersensitivetomeasurementerrors;thereforeuniquerepresentationscannoteasily
bederivedinpractice. Inthisbook,JanOliverWallgrünpresentsanumberofsignifi-
cantcontributionstothestateoftheartinrobotmappingbydevelopingtechniquesfor
generatingstableVoronoirepresentationsfromrealsensordata.
RobotmappingandtheconstructionofVoronoigraphscanalsobeseenasaspatial
reasoningprobleminwhichlocalspatialknowledgehastobeconsistentlyintegrated
into global knowledge. On an abstract qualitative level, these kinds of spatial rea-
soning problems are studied in the area of qualitative spatial reasoning. Jan Oliver
Wallgrünsuccessfullybringstogetherthesetwodistinctresearchareas;thisresultsin
amulti-hypothesistrackingframeworkfortopologicalmapping.Fromtheperspective
ofqualitativespatialreasoning, theworkdescribesaninstructiveapplicationdomain
forcomparingspatialcalculi.Italsoprovidesvaluableresultsregardingtheapplicabil-
ityofdirectioninformationandexistingreasoningtechniques.Theresearchpresented
in this book raises significant challenges for the development of spatial calculi and
spatialreasoningsystemsthathavetobeaddressedbyfuturetheoreticalresearch.
Bremen, ChristianFreksa
July,2009
vii
Preface
Learninganinternalspatialmodelofaninitiallyunknownenvironmentisconsidered
to be one of the fundamental capabilities for an autonomous spatial agent. It is no-
ticeable that—in contrast to what is known about mental spatial representations of
humans—most map learning approaches in robotics employ sensor-near representa-
tionformatsinwhichtheenvironmentisdescribedbyprovidingpreciselocationsof
environmentalfeaturesusingasingleandabsoluteframeofreference. Thequestion
of how the spatial properties of the environment should best be represented in order
to support fundamental tasks like navigation and communication about space is fre-
quently not addressed at all. Instead, the focus is on the problem of how to build
upaspatialmodelfromuncertainsensordataforarepresentationapproachwhichis
assumedasgiven.
One goal of the work described in this book is to take a more general view on
the robot mapping problem, explicitly distinguishing between the spatial representa-
tion perspective and the uncertainty handling perspective: The spatial representation
perspectiveisconcernedwithwhatkindofspatialinformationshouldberepresented
and how this information should be represented in the model in order to adequately
support a broad range of spatial competences. The uncertainty handling perspective
addressesthequestionofhowtodealwiththeinherentuncertaintythatmakeslearning
ofanenvironmentalmodelsuchachallengingproblem.
Themaincontributionsofthisworkaremadewithrespecttooneparticularspa-
tial representation approach, in which the environment is modeled as a hierarchical
route graph based on the generalized Voronoi diagram. From the spatial representa-
tion perspective, this approach is particularly well suited as the core representation
forenvironmentswithaclearroutestructure,suchasmostindoorenvironments. The
mainchallengewithregardtothiskindofrepresentationandthefocusofthisbookis
thedevelopmentoftechniquesthatallowtherobustconstructionofthespatialmodel
underuncertainty.
Oneunderlyingthesisofthisworkisthatthecombinationofratherabstractrepre-
sentations—liketheroutegraphsconsideredhere—withprovenuncertaintyhandling
methods is a promising direction of research. It has the potential of leading to ap-
proacheswhichareatthesametimerobustandwell-suitedtorealizehigh-levelspatial
cognitive abilities. Another concern of this book is to investigate the application of
constraint satisfaction techniques stemming from research on qualitative spatial rea-
soning for consistently integrating local observations into survey knowledge in the
contextofrobotmapping.
Thetechniquesdevelopedinthisbookareconcernedwiththreedifferentaspects
ofthemodelacquisitionprocess: First,theproblemofconstructingtheproposedhi-
erarchical representation from noisy 2D range data is considered, assuming that the
correctdataassociationbetweenperceivedelementsandthecorrespondingelements
in the robot’s internal model is given. The main results are a measure to assess the
viii Preface
relevanceandstabilityofVoronoinodesandthemethodstoautomaticallybuildupthe
hierarchybasedonthismeasure.
Second,thedataassociationproblemisconsideredwiththegoalofachievingre-
liable identification of Voronoi nodes on the local level. A matching approach for
Voronoigraphsisdevelopedwhichtakesintoaccountvariationscausedbysensorlim-
itationsandallowstheincorporationofgeometricconstraints.
Third, to deal with uncertainty on the global level, mapping is formulated as the
problemoffindingaminimalroutegraphmodelthatexplainsthehistoryofobserva-
tionsandactions, anapproachwhichhasbeenproposedbyKuipers. Thedeveloped
solutionconsistsofabest-firstbranchandboundsearchthroughthetreeofpossible
associationsofnodesresultinginasimultaneoustrackingofmultiplemaphypotheses.
Thefocushereisoninvestigatingtheadequacyofqualitativedirectionconstraintsand
theplanarityconstrainttosignificantlyreducethesearchspace.
Besidestheindividualtechniquesdevelopedinthiswork,whichcanbecombined
inmultipleways,anoverallmappingsystemispresentedthatisabletoconstructthe
Voronoi-based hierarchical route graph representation directly from range data. Al-
thoughthedescribedmethodshavebeendevelopedwithregardtothisparticularrep-
resentation,contributionslikethedataassociationapproachandtheresultsconcerning
globalmappingusingqualitativespatialconstraintsaremoregenerallyapplicableand
provideinsightsthatarealsorelevantoutsidetherobotmappingdomain.
Acknowledgements
Writing this book would not have been possible without the support and input from
numerouspeopleIhadthepleasureofmeetingoverthelastfewyearsduringmytime
asadoctoralcandidate. IamdeeplygratefulforalltheassistanceIreceived.
First and foremost, I would like to thank my advisor, Christian Freksa, for his
continuous encouragement and guidance. I appreciate that he gave me the freedom
toexploreandpursuemyownideas. Atthesametime,healwaysprovidedvaluable
adviceandfeedbackwhenIneededitandhasbeentremendouslysupportive.Iamsin-
cerelygratefulforthegreattimeIhadinhisgroupandtheinspiringinterdisciplinary
researchenvironmenthehascreated.
I also want to express my gratitude to Benjamin Kuipers for his willingness to
reviewmythesisandfortakinginterestinmyresearch. Hispioneeringworkandin
particularhiscourseattheISCSIinBadZwischenahnin2003hadamajorimpacton
thiswork.
I also owe many thanks to my colleagues and friends at the Cognitive Systems
groupattheUniversitätBremenforcountlessdiscussionsandhelpfulsuggestionswith
regardtomyworkandforgenerallycreatingaverycomfortableandentertainingwork-
ingenvironment.Inparticular,IwouldliketothankDiedrichWolterforbeingmyfirst
addresstodiscussnewideasandforprovidinginvaluableadvice. Specialthanksalso
gototheothermembersoftheR3-[Q-Shape]project,FrankDylla,LutzFrommberger,
Preface ix
andReinhardMoratz. Thecollectiveprojectworkhasbeenhighlyenjoyableandhad
ahugeimpactonmyownresearch.
Severalpeopledirectlycontributedtothisworkanddeservemygratitude: Cyrill
StachnissprovidedtheFastSLAMimplementationsusedfortheevaluationpartofthis
work. IalsoutilizedtwoexplorationdatasetsmadepublicallyavailablebyNickRoy
andDirkHähnel. MartinHeld’ssoftwareVroniwasusedinthesoftwareimplemen-
tations of some of the ideas described here. Stefan Dehm, Lutz Frommberger, Kai-
FlorianRichter,ChristophSippel,HolgerSchultheis,andThorstenTimmallhelpedto
improvethistextbyprovidingfeedbackonearlierversionsandbyproofreadingit.
Financial support of my research by the German Research Foundation (DFG)
within the scope of the Spatial Inference project of the SPP Raumkognition and the
R3-[Q-Shape]projectoftheSFB/TR8SpatialCognitionisgratefullyacknowledged.
Finally,Iwanttoexpressmygratitudetomyfamilyfortheirconstantencourage-
ment, love, and support, especially during the last months of intensive writing. This
bookisdedicatedtoyou.
Bremen, JanOliverWallgrün
July,2009
xi
Contents
1 Introduction 1
1.1 TheRobotMappingProblem . . . . . . . . . . . . . . . . . . . . . . 2
1.2 TheSpatialRepresentationPerspective. . . . . . . . . . . . . . . . . 3
1.3 TheUncertaintyHandlingPerspective . . . . . . . . . . . . . . . . . 3
1.4 CombiningRepresentationandUncertaintyHandling . . . . . . . . . 4
1.5 RouteGraphsBasedonGeneralizedVoronoiDiagrams . . . . . . . . 5
1.6 Theses,Goals,andContributionsofThisBook . . . . . . . . . . . . 6
1.7 OutlineofThisBook . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 RobotMapping 11
2.1 ASpatialModelforWhat? . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 SystematicExploration . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Communication. . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Correctness,Consistency,andCriteria . . . . . . . . . . . . . . . . . 17
2.2.1 ExtractabilityandMaintainability . . . . . . . . . . . . . . . 18
2.2.2 InformationAdequacy . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 EfficiencyandScalability . . . . . . . . . . . . . . . . . . . 18
2.3 SpatialRepresentationandOrganization . . . . . . . . . . . . . . . . 19
2.3.1 BasicSpatialRepresentationApproaches . . . . . . . . . . . 19
2.3.2 Coordinate-BasedRepresentations . . . . . . . . . . . . . . . 20
2.3.3 RelationalRepresentations . . . . . . . . . . . . . . . . . . . 26
2.3.4 OrganizationalForms. . . . . . . . . . . . . . . . . . . . . . 31
2.4 UncertaintyHandlingApproaches . . . . . . . . . . . . . . . . . . . 36
2.4.1 IncrementalApproaches . . . . . . . . . . . . . . . . . . . . 37
2.4.2 Multi-passApproaches . . . . . . . . . . . . . . . . . . . . . 41
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 Voronoi-BasedSpatialRepresentations 45
3.1 VoronoiDiagramandGeneralizedVoronoiDiagram. . . . . . . . . . 45
3.2 GeneralizedVoronoiGraphandEmbeddedGeneralizedVoronoiGraph 47
3.3 AnnotatedGeneralizedVoronoiGraphs . . . . . . . . . . . . . . . . 49
xii Contents
3.4 HierarchicalAnnotatedVoronoiGraphs . . . . . . . . . . . . . . . . 50
3.5 PartialandLocalVoronoiGraphs. . . . . . . . . . . . . . . . . . . . 51
3.6 AnInstanceoftheHAGVG. . . . . . . . . . . . . . . . . . . . . . . 53
3.7 StabilityProblemsofVoronoi-BasedRepresentations . . . . . . . . . 54
3.8 StrengthsandWeaknessesoftheRepresentation . . . . . . . . . . . . 55
4 SimplificationandHierarchicalVoronoiGraphConstruction 59
4.1 RelevanceMeasuresforVoronoiNodes . . . . . . . . . . . . . . . . 60
4.2 ComputationofRelevanceValues . . . . . . . . . . . . . . . . . . . 64
4.3 VoronoiGraphSimplification . . . . . . . . . . . . . . . . . . . . . . 69
4.4 HAGVGConstruction . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5 AdmittingIncompleteInformation . . . . . . . . . . . . . . . . . . . 73
4.6 ImprovingtheEfficiencyoftheRelevanceComputation. . . . . . . . 75
4.7 IncrementalComputation . . . . . . . . . . . . . . . . . . . . . . . . 80
4.8 ApplicationScenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.8.1 IncrementalHAGVGConstruction. . . . . . . . . . . . . . . 82
4.8.2 RemovalofUnstableParts . . . . . . . . . . . . . . . . . . . 82
4.8.3 AutomaticRouteGraphGenerationfromVectorData. . . . . 82
5 VoronoiGraphMatchingforDataAssociation 85
5.1 TheDataAssociationProblem . . . . . . . . . . . . . . . . . . . . . 85
5.1.1 DataAssociationsandtheInterpretationTree . . . . . . . . . 86
5.1.2 DataAssociationApproaches . . . . . . . . . . . . . . . . . 88
5.2 AGVGMatchingBasedonOrderedTreeEditDistance . . . . . . . . 90
5.2.1 OrderedTreeMatchingBasedonEditDistance . . . . . . . . 92
5.2.2 OverallEditDistance . . . . . . . . . . . . . . . . . . . . . . 97
5.2.3 ModelingRemovalandAdditionCosts . . . . . . . . . . . . 98
5.2.4 Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2.5 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3 IncorporatingConstraints . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3.1 UnaryConstraintsBasedonPoseEstimatesandNodeSimilarity101
5.3.2 BinaryConstraintsBasedonRelativeDistance . . . . . . . . 104
5.3.3 TernaryAngleConstraints . . . . . . . . . . . . . . . . . . . 106
5.4 MapMergingBasedonaComputedDataAssociation. . . . . . . . . 109
6 GlobalMapping: MinimalRouteGraphsUnderSpatialConstraints 113
6.1 TheoreticalProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2 BranchandBoundSearchforMinimalModelFinding . . . . . . . . 123
6.2.1 SearchThroughtheInterpretationTree . . . . . . . . . . . . 124
6.2.2 Best-FirstBranchandBoundSearchBasedonSolutionSize . 126
6.2.3 ExpandandUpdateOperations . . . . . . . . . . . . . . . . 128
6.2.4 TwoVariantsoftheMinimalModelFindingProblem . . . . . 134
6.3 PruningBasedonSpatialConstraints. . . . . . . . . . . . . . . . . . 136