An Optimized Circulating Vector Field Obstacle Avoidance Guidance for Unmanned Aerial Vehicles

122 Pages·2017·5.96 MB·English

by  Garrett S. Clem

AnOptimizedCirculatingVectorFieldObstacleAvoidanceGuidanceforUnmanned
AerialVehicles
Athesispresentedto
thefacultyof
theRussCollegeofEngineeringandTechnologyofOhioUniversity
Inpartialfulfillment
oftherequirementsforthedegree
MasterofScience
GarrettS.Clem
August2018
©2018GarrettS.Clem. AllRightsReserved.
2
Thisthesistitled
AnOptimizedCirculatingVectorFieldObstacleAvoidanceGuidanceforUnmanned
AerialVehicles
by
GARRETTS.CLEM
hasbeenapprovedfor
theDepartmentofMechanicalEngineering
andtheRussCollegeofEngineeringandTechnologyby
JayP.Wilhelm
AssistantProfessorofMechanicalEngineering
DennisIrwin
Dean,RussCollegeofEngineeringandTechnology
3
bstract
A
CLEM,GARRETTS.,M.S.,August2018,MechanicalEngineering
AnOptimizedCirculatingVectorFieldObstacleAvoidanceGuidanceforUnmanned
AerialVehicles
DirectorofThesis: JayP.Wilhelm
Unmanned Aerial Vehicles (UAVs) conventionally navigate by following a series
of pre-planned waypoints. When encountering an obstacle in flight, such as no-fly zones
or other aircraft, the vehicle’s path or waypoints may need to be re-planned. Waypoint
guidancecanbeusedtoavoidobstacles,whicharetypicallygeneratedoff-lineandrelayed
to the UAV requiring active communications. Vector Fields (VFs) that are generated
based on a desired path can provide guidance around a newly discovered obstacle without
the need for a re-plan. VF convergence and circulation components were optimized
to minimize deviation from a desired path when guiding around a circular obstacle.
Results indicated that the developed VF obstacle avoidance optimizer provides similar
path deviation performance as waypoints without the need for re-planning. Lookup tables
for GVF circulation and decay radius were constructed allowing for real time obstacle
avoidance without the need to re-plan mission waypoints. Experimental flight tests were
conducted using a indoor quadcopter with imposed turn rate constraints, emulating a fixed
wing UAV. Deviation from the planned path for simulation and experimentation were
compared.
4
cknowledgments
A
Throughout my graduate studies I have had the privilege of working with many
unique and sophisticated people. First and foremost, I would like to thank my advisor Dr.
JayWilhelmforhisseeminglylimitlessacademicsupport. Withouthisleadershipthiswork
would not have been completed. I would like to also thank my committee members, Dr.
Casbeer, Dr. Williams, and Dr. Uijt de Haag for their time, suggestions, and stimulating
discussionsinregardstothecontentsofthisresearch.
Tomyfirstlabcolleague,Gina,yourmentoringandfriendshipwereinvaluableand
I cannot see myself completing this program without your support and humor. Hunter and
Travis,yourassistancewithdebuggingthecontrolsoftwarewasvitaltothesuccessofthis
project. My roommates, Sean, Justin, and Jacob, you all provided welcome distractions.
To my mother, who I grew closer with over the past few years, this is for you. Lastly, I
would like to thank my best friend Emily whose love and support constantly reminded me
whyIcontinuedmyeducationtobettermyself.
5
able of ontents
T C
Page
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
ListofSymbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
ListofAcronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1 MotivationandProblemStatement . . . . . . . . . . . . . . . . . . . . . . 14
1.2 MethodsOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 PhaseI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 PhaseII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 PhaseIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6 SummaryofObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 LiteratureReviewIntroduction . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 UnmannedAerialVehicles . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 GroundStations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Autopilot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 DubinsVehicleModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 UAVGuidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.1 PotentialField . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2 LyapunovVectorFields . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 PathPlanningVectorFields . . . . . . . . . . . . . . . . . . . . . 32
2.4.4 GradientVectorField . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 LiteratureReviewSummary . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1 IntroductiontoMethodology . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 PhaseI:GradientVectorFieldSingularityDetection . . . . . . . . . . . . . 40
3.2.1 PathFollowingVectorFieldGuidance . . . . . . . . . . . . . . . . 41
3.2.2 ConstructinganAvoidanceVectorField . . . . . . . . . . . . . . . 43
3.2.3 SummedGuidanceandSingularityDefinition . . . . . . . . . . . . 46
6
3.3 PhaseII:OptimizationofObstacleField . . . . . . . . . . . . . . . . . . . 50
3.3.1 VehicleandObstacleDefinition . . . . . . . . . . . . . . . . . . . 51
3.3.2 ObstacleonPlannedPath . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.3 OptimalAvoidanceRouteforStraightPath . . . . . . . . . . . . . 61
3.3.4 AvoidancePathandWaypoints . . . . . . . . . . . . . . . . . . . . 62
3.3.5 CirculationandDecayLookupTables . . . . . . . . . . . . . . . . 63
3.4 PhaseIII:Flighttests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.1 ExperimentalOverview . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.2 Crazyflie2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4.3 PythonGuidanceandControlGroundStation . . . . . . . . . . . . 71
3.5 PythonGuidanceValidation . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 SummaryofMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.1 IntroductiontoResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 PhaseI&II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3 WorstCaseAvoidanceScenario . . . . . . . . . . . . . . . . . . . . . . . 77
4.4 FourAvoidanceScenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.5 PhaseIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.6 Summaryofresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
AppendixA:MethodologyPhaseI . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
AppendixB:MethodologyPhaseIII . . . . . . . . . . . . . . . . . . . . . . . . . . 103
AppendixC:Appendix-ResultsPhaseIII . . . . . . . . . . . . . . . . . . . . . . . 105
AppendixD:OptimizationMATLABsourcecode . . . . . . . . . . . . . . . . . . . 109
AppendixE:VectorFieldConstructionsourcecode . . . . . . . . . . . . . . . . . . 115
7
ist of ables
L T
Table Page
2.1 ComparisonofUAVGuidanceMethods . . . . . . . . . . . . . . . . . . . . . 38
3.1 InvestigatedWeightingMethods . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 TunedPIDGainsforRoll,Pitch,YawRate,andThrustController . . . . . . . 72
4.1 GVFAvoidanceScenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 ExperimentalScenariosConductedforCrazyflieQuadcopter . . . . . . . . . . 84
4.3 SimulationandExperimentalCostComparisonTableforScenarios1-4 . . . . 89
8
ist of igures
L F
Figure Page
2.1 FixedWingUAV(a)andMultirotorUAV(b) . . . . . . . . . . . . . . . . . . 20
2.2 GroundStationSoftwarePlanningaWaypointBasedMission . . . . . . . . . 21
2.3 Autopilot’sNavigation,Guidance,andControlArchitecture . . . . . . . . . . 22
2.4 SingleObstaclePotentialFieldGradient[36] . . . . . . . . . . . . . . . . . . 24
2.5 VirtualForceFieldHistogramGuidingaMobileRobot[38] . . . . . . . . . . 25
2.6 PotentialFieldLocalMinimum[36] . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 PotentialFieldLocalMinimum[36] . . . . . . . . . . . . . . . . . . . . . . . 27
2.8 ObstacleClusteringtoPreventLocalMinimum[36] . . . . . . . . . . . . . . . 27
2.9 UAVAvoidingObstaclewithVFFGuidance . . . . . . . . . . . . . . . . . . . 28
2.10 LyapunovVectorFieldforStraightLineandCircularPrimitives[17] . . . . . . 29
2.11 StraightPathFollowinginUrbanEnvironment[17]usingLyapunovVectorField 30
2.12 LyapunovVectorFieldApproachCurvedPath[13] . . . . . . . . . . . . . . . 31
2.13 Elliptical VF Produced by Non-linear Coordinate Transformations a) [5] and
b)[45] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.14 TangentPlusLyapunovVectorFieldsforShortestPathTargetTracking[47] . . 32
2.15 RRT*PathPlannerwithaVFUsedasaTaskSpecification[49] . . . . . . . . 33
2.16 VectorFieldWithinaSetofDelaunayTriangles[50] . . . . . . . . . . . . . . 33
2.17 TangentHyperbolicFunctionforObstacleDecayin[21] . . . . . . . . . . . . 37
3.1 IntersectionofPlanesDefinedbyImplicitSurfaceFunctions . . . . . . . . . . 42
3.2 IntersectionofaCylinderandPlaneDefinedbyImplicitSurfaceFunctions . . 45
→−
3.3 SummedFieldsWithoutTotalNormalization V withNullCirculation . . . . . 47
g
3.4 SummedFieldsWithoutTotalNormalization . . . . . . . . . . . . . . . . . . 48
3.5 GVFConvergingandCirculatingaCircularPath . . . . . . . . . . . . . . . . 49
3.6 SingularityinSummedFieldwithEqualMagnitudeConvergenceandCirculation 50
3.7 FixedWingConvergingandFollowingaPathSimulation . . . . . . . . . . . . 52
3.8 FixedWingConvergingandFollowingaPath . . . . . . . . . . . . . . . . . . 53
3.9 LateralErrorforFixedWingGuidedbyGVFGuidanceofMultipleCirculations 53
3.10 CircularObstacleAlongPlannedPath . . . . . . . . . . . . . . . . . . . . . . 54
3.11 UAV Encountering a Circular Obstacle Centered on Pre-planned Path, No
Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.12 UAV Encountering a Circular Obstacle Centered on Pre-planned Path with
Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.13 HeatmapofCostasFunctionofk and H . . . . . . . . . . . . . . . . . . . . 58
o
3.14 CostFunctionReductioninfmincon()MATLABFunction . . . . . . . . . . . 59
3.15 UAVPathFromOptimizedGVF . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.16 OptimalKinematicPathAroundCircularObstacle . . . . . . . . . . . . . . . 62
3.17 ObstacleDiversionWaypoints . . . . . . . . . . . . . . . . . . . . . . . . . . 63
9
3.18 CostImpactVersusNumberofWaypoints . . . . . . . . . . . . . . . . . . . . 63
3.19 ObstacleCirculationLookupTable,SmoothedbyInterpolation . . . . . . . . . 64
3.20 ObstacleDecayRadiusLookupTable,SmoothedbyInterpolation . . . . . . . 65
3.21 ObstacleCirculationLookupTablewithInterpolationPoints . . . . . . . . . . 66
3.22 ObstacleDecayRadiusLookupTablewithInterpolationPoints . . . . . . . . . 66
3.23 CostofUAVObstacleAvoidanceUsingInterpolatedandOptimizedParameters 67
3.24 MicroQuadcopterCrazyflie2.0byBitcraze . . . . . . . . . . . . . . . . . . . 69
3.25 IndoorQuadcopterFlightExperimentalLayout . . . . . . . . . . . . . . . . . 70
3.26 CrazieflieClientRadioCommunicationSoftware . . . . . . . . . . . . . . . . 70
3.27 CrazyflieGuidanceandControlSoftwareFramework . . . . . . . . . . . . . . 71
3.28 CrazyflieGuidanceandControlSoftwareFramework . . . . . . . . . . . . . . 72
3.29 ValidationofPythonStraightPathGuidanceOverlaidwithMATLAB . . . . . 73
3.30 ValidationofPythonSummedGuidanceOverlaidwithMATLAB . . . . . . . 74
3.31 ValidationofPythonDubinsUAVRouteOverlaidwithMATLAB . . . . . . . 74
4.1 PathofUAVGuidedbyGuidanceMethods . . . . . . . . . . . . . . . . . . . 78
4.2 CostPerformanceforVariousUAVGuidanceMethods . . . . . . . . . . . . . 78
4.3 CenteredObstacleWithSmallRadiusAvoidedbyDubin’sUAVinSimulation . 80
4.4 CenteredObstaclewithLargeRadiusAvoidedbyDubin’sUAVinSimulation . 81
4.5 OffCenteredObstaclewithSmallRadiusAvoidedbyDubin’sUAVinSimulation 82
4.6 OffCenteredObstaclewithLargeRadiusAvoidedbyDubin’sUAVinSimulation 83
4.7 Simulated and Experimental UAV Routes for Path Centered Obstacle with
SmallRadius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.8 UAVSpeedVersusTimeDuringFlightExperimentofScenario1 . . . . . . . . 85
4.9 StateResponsePlotsforScenario1 . . . . . . . . . . . . . . . . . . . . . . . 86
4.10 SimulatedandExperimentalUAVRoutesforOffCenteredObstaclewithSmall
Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.11 Simulated and Experimental UAV Routes for Path Centered Obstacle with
LargeRadius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.12 SimulatedandExperimentalUAVRoutesforOffCenteredObstaclewithLarge
Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
A.1 GVF Circular Attractive Field without Normalization (a) and with Normaliza-
tion(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.2 RepulsiveCircularFieldwithLargeRadius . . . . . . . . . . . . . . . . . . . 100
A.3 RepulsiveCircularFieldwithSmallRadius . . . . . . . . . . . . . . . . . . . 100
A.4 CircularGVFwithoutNormalization(a)andwithNormalization(b) . . . . . . 101
A.5 RepulsiveGVFa)NoCirculation H = 0andb)withCirculation H = 1 . . . . 102
o o
B.1 ValidationofPythonObstacleGuidanceOverlaidwithMATLAB . . . . . . . 103
B.2 ValidationofPythonObstacleDecayGuidanceOverlaidwithMATLAB . . . . 104
C.1 ExperimentalScenario2UAVSpeedandControllerResponse . . . . . . . . . 106
10
C.2 ExperimentalScenario3UAVSpeedandControllerResponse . . . . . . . . . 107
C.3 ExperimentalScenario4UAVSpeedandControllerResponse . . . . . . . . . 108