Path Planning of Cooperative Mobile Robots Using Discrete Event Models

228 Pages·2020·6.107 MB·English

by  Cristian Mahulea, Marius Kloetzer, Ramon Gonzalez

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PathPlanningofCooperativeMobileRobotsUsingDiscrete
EventModels
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Path Planning of Cooperative Mobile Robots
Using Discrete Event Models
Cristian Mahulea
University of Zaragoza, Spain
Marius Kloetzer
“Gheorghe Asachi” Technical University of Iasi, Romania
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Ramón González
Robonity, Spain
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Contents
Foreword xi
Preface xv
Acknowledgments xvii
Acronyms xix
1 Introduction 1
1.1 Historicalperspectiveofmobilerobotics 1
1.2 Pathplanning.Definitionandhistoricalbackground 4
(cid:2) 1.3 Motioncontrol.Definitionandhistoricalbackground 9 (cid:2)
1.4 Motivationforexpressivetasks 11
1.5 Assumptionsofthismonograph 14
1.6 Outlineofthismonograph 14
2 RobotMotionToolbox 17
2.1 Introduction 17
2.2 Generaldescriptionofthesimulator 20
2.3 Pathplanningalgorithms 25
2.4 Robotkinematicmodels 26
2.5 Motioncontrolalgorithms 29
2.5.1 Purepursuitalgorithm 29
2.5.2 PIcontroller 32
2.6 Illustrativeexamples 33
2.6.1 Examplesaboutpathplanningaspects 33
2.6.2 Examplesaboutmotioncontrolaspects 35
2.6.3 Examplesaboutmulti-robotsystemsandhigh-leveltasks 37
2.7 Conclusions 40
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viii Contents
3 CellDecompositionAlgorithms 41
3.1 Introduction 41
3.2 Celldecompositionalgorithms 42
3.2.1 Hypothesis 42
3.2.2 Trapezoidaldecomposition 45
3.2.3 Triangulardecomposition 46
3.2.4 Polytopaldecomposition 49
3.2.5 Rectangulardecomposition 52
3.3 Implementationandextensions 53
3.3.1 Extensions 53
3.3.2 Implementedfunctions 55
3.4 Comparativeanalysis 58
3.4.1 Qualitativecomparison 58
3.4.2 Quantitativecomparison 61
3.5 Conclusions 70
4 DiscreteEventSystemModels 71
4.1 Introduction 71
4.2 Environmentabstraction 72
4.3 Transitionsystemmodels 75
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4.3.1 Singlerobotcase 75
4.3.2 Multi-robotcase 79
4.4 Petrinetmodels 83
4.5 Petrinetsinresourceallocationsystemsmodels 90
4.6 High-levelspecifications 96
4.7 Lineartemporallogic 100
4.8 Conclusions 106
5 PathPlanningbyUsingTransitionSystemModels 109
5.1 Introduction 109
5.2 Two-stepplanningforasinglerobotandreachabilityspecification 110
5.3 Quantitativecomparisonoftwo-stepapproaches 115
5.4 Recedinghorizonapproachforasinglerobotandreachability
specification 119
5.5 Simulationsandanalysis 123
5.6 PathplanningwithanLTL specification 126
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5.7 Collisionavoidanceusinginitialdelay 132
5.7.1 Problemdescription 132
5.7.2 SolutionforProblem5.1(decentralized) 135
5.7.3 SolutionforProblem5.2(centralized) 137
5.8 Conclusions 139
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Contents ix
6 PathandTaskPlanningUsingPetriNetModels 141
6.1 Introduction 141
6.2 Boolean-basedspecificationsforcooperativerobots 144
6.2.1 Problemdefinitionandnotations 144
6.2.2 LinearrestrictionsforBoolean-basedspecifications 146
6.2.3 Solutionforconstraintsonthefinalstate 147
6.2.4 Solutionforconstraintsontrajectoryandfinalstate 149
6.2.5 Discussionontheabovesolutions 151
6.2.6 Suboptimalsolution 152
6.2.7 Simulationexamples 154
6.3 LTLspecificationsforcooperativerobots 157
6.3.1 Problemdefinitionandsolution 157
6.3.2 Simulationexamples 167
6.4 Asequencingproblem 170
6.4.1 Problemstatement 170
6.4.2 Solution 175
6.5 Taskgatheringproblem 180
6.5.1 Problemformulation 180
6.5.2 Solution 181
6.6 Deadlockpreventionusingresourceallocationmodels 185
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6.7 Conclusions 192
7 ConcludingRemarks 193
Bibliography 195
Index 211
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Foreword
ThepathplanningapproachbasedonDiscreteEventSystem(DES)modelsisan
important–butachallenging–problem.Ithasbeenstudiedforanumberofyears
intheDEScommunityinthefieldofautomatedguidedvehicle(AGV)systems.In
thiscase,themainissueistocomputecollision-freepathsforanAGVfromastart-
ingconfigurationtoagoalone.Formulti-agentsystems,anadditionalproblemis
to avoid deadlocks that could result if waiting modes are introduced. The main
solutionsobtainedarebasedontheresultsofdeadlockpreventionandavoidance
fromResourceAllocationSystemsthatallowonetouseaDESstructuretoobtain
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deadlock-free trajectories of AGVs. Even if the complexity of these approaches
ishigh,researchershaveidentifiedsomecomputationallytractablesolutionsfor
someparticularclasses.
This book is a step forward from the classical AGV navigation problem, by
assuminghigh-levelspecificationsforateamofcooperativerobots.Therefore,the
problemisnottoreachonlysomegoalconfigurations,buttoaccomplishamore
complicatedtaskcombininglogicandtemporaloperatorsonsomeregionsofthe
environment, called regions of interest. This problem appeared some years ago
intheformalmethodcommunity,whereso-calledsymbolicapproachesareused
tosolveit.Mainly,itssolutionconsistsinobtainingamodelforarobotteamand
amodelforspecifications,combiningtheminasmartwayandthencomputing
robottrajectories.Initially,themodeloftheteamisobtainedbyusingtransition
systems that, in the case of teams with more than 2 or 3 robots, suffer from a
so-calledstatespaceexplosionproblem,i.e.thenumberofdiscretestatesgrows
exponentiallywiththenumberofrobots,makingthisapproachimpractical.
Inordertoavoidthisstatespaceexplosionproblem,twoalternativeapproaches
havebeenproposed.Oneapproachconsistsindividingahigh-levelspecification
into(local)subformulasthatcanbeexecutedinparallel,andthen,foreachlocal
formula, a special model is constructed allowing distribution of the fulfillment
of the task among robots. Another approach, which is presented in this book,
tackles the state explosion problem by using Petri net models and optimization
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