Cooperative Path Planning of Unmanned Aerial Vehicles

212 Pages·2012·2.13 MB·English

Cooperative Path
Planning of Unmanned
Aerial Vehicles
Cooperative Path Planning of Unmanned Aerial Vehicles
Antonios Tsourdos, Brian White and and Madhavan Shanmugavel
© 2011 John Wiley & Sons, Ltd. ISBN: 978-0-470-74129-0
Aerospace Series List
CooperativePathPlanningofUnmanned Tsourdosetal November2010
AerialVehicles
PrinciplesofFlightforPilots Swatton October2010
AirTravelandHealth:ASystems Seabridgeetal September2010
Perspective
DesignandAnalysisofComposite Kassapoglou September2010
Structures:WithApplicationsto
AerospaceStructures
UnmannedAircraftSystems:UAVS Austin April2010
Design,DevelopmentandDeployment
IntroductiontoAntennaPlacement& Macnamara April2010
Installations
PrinciplesofFlightSimulation Allerton October2009
AircraftFuelSystems Langtonetal May2009
TheGlobalAirlineIndustry Belobaba April2009
ComputationalModellingandSimulation Diston April2009
ofAircraftandtheEnvironment:Volume
1–PlatformKinematicsandSynthetic
Environment
HandbookofSpaceTechnology Ley,Wittmann April2009
Hallmann
AircraftPerformanceTheoryandPractice Swatton August2008
forPilots
SurrogateModellinginEngineering Forrester, August2008
Design:APracticalGuide Sobester,Keane
AircraftSystems,3rdEdition Moir&Seabridge March2008
IntroductiontoAircraftAeroelasticity Wright&Cooper December2007
AndLoads
StabilityandControlofAircraftSystems Langton September2006
MilitaryAvionicsSystems Moir&Seabridge February2006
DesignandDevelopmentofAircraft Moir&Seabridge June2004
Systems
AircraftLoadingandStructuralLayout Howe May2004
AircraftDisplaySystems Jukes December2003
CivilAvionicsSystems Moir&Seabridge December2002
Cooperative Path
Planning of Unmanned
Aerial Vehicles
Antonios Tsourdos, Brian White
and Madhavan Shanmugavel
CranfieldDefenceandSecurity
CranfieldUniversity,UK
A John Wiley and Sons, Ltd., Publication
Thiseditionfirstpublished2011
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LibraryofCongressCataloguing-in-PublicationData
Tsourdos,Antonios.
Cooperativepathplanningofunmannedaerialvehicles/AntoniosTsourdos,
BrianWhite,MadhavanShanmugavel.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-74129-0(cloth)
1.Droneaircraft–Automaticcontrol.2.Guidancesystems(Flight)
3.Airplanes–Piloting–Mathematics.4.Airplanes–Piloting–Planning.
5.Airways–Mathematicalmodels.I.White,Brian,1947June6-
II.Shanmugavel,Madhavan.III.Title.
TL589.4.T782010
629.132’5–dc22
2010026275
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
PrintISBN:978-0-470-74129-0
ePDFISBN:978-0-470-97520-6
oBookISBN:978-0-470-97463-6
ePubISBN:978-0-470-97464-3
Typesetin10/12.5ptPalatinobyLaserwordsPrivateLimited,Chennai,India
Contents
AbouttheAuthors ix
SeriesPreface xi
Preface xii
Acknowledgements xiii
ListofFigures xv
ListofTables xxi
Nomenclature xxiii
1 Introduction 1
1.1 PathPlanningFormulation 2
1.2 PathPlanningConstraints 3
1.2.1 FlyablePaths:CapturingKinematics 4
1.2.2 UAVInertialManoeuvreCoordinates 6
1.2.3 GenerationofSafePathsforPathPlanning 7
1.3 CooperativePathPlanningandMissionPlanning 7
1.4 PathPlanning–AnOverview 10
1.5 TheRoadMapMethod 13
1.5.1 VisibilityGraphs 14
1.5.2 VoronoiDiagrams 14
vi Contents
1.6 ProbabilisticMethods 16
1.7 PotentialField 16
1.8 CellDecomposition 17
1.9 OptimalControl 18
1.10 OptimizationTechniques 18
1.11 TrajectoriesforPathPlanning 19
1.12 OutlineoftheBook 20
References 22
2 PathPlanninginTwoDimensions 29
2.1 DubinsPaths 30
2.2 DesigningDubinsPathsusingAnalyticalGeometry 31
2.2.1 DubinsPath:ExternalTangentSolution 33
2.2.2 DubinsPath:InternalTangentSolution 35
2.3 ExistenceofDubinsPaths 37
2.4 LengthofDubinsPath 39
2.5 DesignofDubinsPathsusingPrinciplesofDifferential
Geometry 39
2.5.1 DubinsPathLength 43
2.6 PathsofContinuousCurvature 45
2.7 ProducingFlyableClothoidPaths 46
2.8 ProducingFlyablePythagoreanHodographPaths(2D) 56
2.8.1 DesignofFlyablePathusing2DPHcurve 61
References 62
3 PathPlanninginThreeDimensions 65
3.1 DubinsPathsinThreeDimensionsUsingDifferential
Geometry 67
3.2 PathLength–Dubins3D 72
3.3 PythagoreanHodographPaths–3D 72
3.3.1 SpatialPHCurves 73
3.4 DesignofFlyablePathsUsingPHCurves 74
3.4.1 DesignofFlyablePaths 75
References 78
4 CollisionAvoidance 81
4.1 ResearchintoObstacleAvoidance 83
4.2 ObstacleAvoidanceforMappedObstacles 85
4.2.1 LineIntersectionDetection 86
Contents vii
4.2.2 LineSegmentIntersection 90
4.2.3 ArcIntersection 94
4.3 ObstacleAvoidanceofUnmappedStaticObstacles 103
4.3.1 SafetyCircleAlgorithm 104
4.3.2 IntermediateWaypointAlgorithm 104
4.4 AlgorithmicImplementation 106
4.4.1 DubinsPathModification 107
4.4.2 ClothoidPathModification 107
4.4.3 PHPathModification 110
4.4.4 ObstacleAvoidancein3D 112
References 115
5 Path-FollowingGuidance 119
5.1 PathFollowingtheDubinsPath 120
5.2 LinearGuidanceAlgorithm 124
5.3 NonlinearDynamicInversionGuidance 126
5.4 DynamicObstacleAvoidanceGuidance 132
5.4.1 UAVDirectionControl 135
5.4.2 MultipleConflictResolution 142
References 145
6 PathPlanningforMultipleUAVs 147
6.1 ProblemFormulation 149
6.2 SimultaneousArrival 151
6.3 PhaseI:ProducingFlyablePaths 152
6.4 PhaseII:ProducingFeasiblePaths 152
6.4.1 MinimumSeparationDistance 153
6.4.2 Non-IntersectionPaths 154
6.4.3 OffsetCurves 155
6.5 PhaseIII:EqualizingPathLengths 156
6.6 MultiplePathAlgorithm 156
6.7 AlgorithmApplicationforMultipleUAVs 157
6.7.1 2DDubinsPaths 157
6.7.2 2DClothoidPaths 160
6.8 2DPythagoreanHodographPaths 162
6.9 3DDubinsPaths 165
6.10 3DPythagoreanHodographPaths 169
References 174
viii Contents
AppendixA DifferentialGeometry 175
A.1 Frenet–SerretEquations 177
A.2 ImportanceofCurvatureandTorsion 178
A.3 MotionandFrames 179
References 181
AppendixB PythagoreanHodograph 183
B.1 PythagoreanHodograph 184
References 185
Index 187
About the Authors
Antonios Tsourdos was appointed Head of the Autonomous Systems
Group at Cranfield University in 2007. He obtained a PhD on Nonlinear
Robust Flight Control Design and Analysis from Cranfield University in
1999. He was a member of the Team Stellar, the winning team for the UK
MoDGrandChallenge(2008).HehasservedasanEditorialBoardMember
for the Proceedings of the Institution of Mechanical Engineers, Part G: Journal
ofAerospaceEngineering,theInternationalJournalofSystemsScience,theIEEE
Transactions on Instrumentation and Measurement, the International Journal on
Advances in Intelligent Systems and the international journal Mathematics in
Engineering, Science and Aerospace (MESA). He is a member of the A|D|S
Autonomous Systems Strategy Group and the A&D KTN National Techni-
cal Committee on Autonomous Systems. He is also a member of the IFAC
Technical Committee on Aerospace Control, the IFAC Technical Commit-
tee on Networked Systems, the AIAA Technical Committee on Guidance,
Control&Navigation,theIEEEControlSystemSocietyTechnicalCommittee
onAerospaceControl(TCAC)andtheIEEETechnicalCommitteeonAerial
RoboticsandUnmannedAerialVehicles.
Brian White obtained a BSc degree in Engineering from the University of
Leicester, followed by an MSc and PhD from UMIST, Manchester, in 1974.
HehasworkedintheaerospaceindustryforthecompanyMBDA,working
onnovelguidancetechniquesformissilesystems,includingoneofthefirst
developmentsofKalmanfiltersforintegrationintoguidancesystems.Hehas
since beenafaculty memberofthe Schoolof Engineeringat the University
of Bath and at Cranfield University, where for many years he was Head
of the Department of Aerospace, Power and Sensors. While in the post, he
builtupastrongdepartmentinAerospaceSystemsandalsoledtheControl