Autonomous Airborne Refueling: Relative State Estimation

171 Pages·2011·6.72 MB·English

Autonomous Airborne Refueling: Relative State Estimation
by
Anton Johan Runhaar
Thesis presented in partial fulfilment of the requirements for the degree of
Master of Science in Engineering
at the Faculty of Engineering, Stellenbosch University
Supervisor: DrI.K.Peddle
DepartmentElectricalandElectronicEngineering
December 2011
Stellenbosch University http://scholar.sun.ac.za
Declaration
By submitting this thesis electronically, I declare that the entirety of the work contained
therein is my own, original work, that I am the sole author thereof (save to the extent expli-
citly otherwise stated), that reproduction and publication thereof by Stellenbosch University
will not infringe any third party rights and that I have not previously in its entirety or in part
submitteditforobtaininganyqualification.
December2011
Copyright©2011StellenboschUniversity
Allrightsreserved
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Abstract
This thesis presents the development of a state estimation system for use in an Autonomous
AirborneRefueling(AAR)operationthroughthesimulatedimplementationofGPS,monocular
and stereoscopic vision, inertial measurement sensors and boom parameter measurement in
combinationwiththeExtendedKalmanFilter(EKF)andUnscentedKalmanFilter(UKF).
A set of functional criteria for the estimation system was developed through an analysis of
the control system input requirements and associated constraints. The estimation system
is further developed by integrating the sensor configurations into the estimation algorithm
structures through the derivation of the applicable mathematical models. Final sensor con-
figurations are set based on a sensitivity analysis in which the effect of parameters such as
sensor noise, placement and quantity are related to the accuracy with which the states are
estimated.
Uncertainty in the process noise, which is typically approximated, is overcome by adding an
adaptiveelementtotheestimationalgorithmsinwhichthecurrentprocessnoiseisestimated
allowingcompensationforunmodeledprocessnoiseuncertainty.
Finally twelve practical sensor configurations are established utilising unique combinations
of the five sensors. Each configuration is simulated using both estimation algorithms after
which all results are evaluated with respect to one another as well as to the minimum state
accuracy criteria. Conclusions are presented based on the evaluation of the results followed
byrecommendationforfuturedevelopment.
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Opsomming
Dieontwikkelingvan’ntoestandafskattingstelsel,spesifiektoegepasopoutonomebrandstof-
hervulling, word voorgelê in hierdie tesis. Hierdie ontwikkeling behels die implementering
van GPS, monukulêre- en stereo-visie sensors, inersiële sensor eenhede en verbindingsarm-
sensorswatgebruikwordin’nUitgebruideKalmanFilter(ExtendedKalmanFilter)enGeur-
loseKalmanFilter(UnscentedKalmanFilter).
’nVolledigeontledingvandiebeheerstelselsetoevoervereistesengeassosieerdebeperkings
is gebruik om ’n stel beoordelingsmaatstawwe vir die toestandafskatting-stelsel te bepaal.
Die stelsel is verder ontwikkel deur verskillende sensorkonfigurasies met die afskattingsal-
goritmes te kombineer deur die afleiding van toepaslike wiskundinge modelle. Hierdie kon-
figurasiesisverfyndeur’nsensitiwiteitsanalise,waardieverwantskaptussendieeffektevan
sensorruis, sensorligging, hoeveelheid sensors ondersoek is met betrekking tot afskatting-
sakkuraatheid.
Onsekerheid in die stelsel se prosesruis is deur ’n aanpassings substelsel hanteer, wat kom-
pensasievirongemodeleerdeonsekerheidmoontlikmaak. Twaalfpraktiesesensorkonfiguras-
ies is opgestel vanuit unieke kombinasies van die vyf sensore behartig in die projek. Hierdie
konfigurasiesisdeurbeideafskattingsalgoritmesgebruikomsodoendedieakkuraatheidvan
die konfigurasies asook die afskattingsalgoritmes te evalueer met betrekking tot mekaar en
aandiehandvandiebeoordelingsmaatstawwevirdiebeheerstelsel. Dietesisisafgesluitdeur
gevolgtrekkingsasookaanbevelingsvirtoekomstigenavorsing.
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Contents
Abstract iii
Opsomming iv
List of Figures ix
List of Tables xi
Nomenclature xiii
Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Referenceframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
RelevantShorthand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
VectorNotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
MathOperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Acknowledgments xvi
1 Introduction 1
1.1 AirbusandAutonomousAirborneRefueling . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 ControlResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 EstimationResearch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 LiteratureStudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 EstimationAlgorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 PracticalImplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 ProposedApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Thesislayout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 AAR State Estimation 13
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CONTENTS vi
2.1 TheAARScenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 AircraftConfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Stagesofoperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 TheControlSystemSpecifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 ControlEnvelopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 ControlInputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Minimumcontrolinputaccuracy . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 StateEstimationSystemSpecifications . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 TheStateVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Stateestimateaccuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 InertialMeasurementUnit . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2 RoamingBaseDifferentialGPS . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 Opticalsensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.3.1 Monocular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.3.2 Stereoscopic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.4 Boomparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 ProposedConfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6 EstimationAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 State Estimation Algorithms 35
3.1 Thenon-linearsystemmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 ParticleFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 ExtendedKalmanFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 UnscentedKalmanFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 AlgorithmComparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Processcovarianceadaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 Process and Measurement Model Derivation 54
4.1 ProcessModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.1 AccelerometerandRateGyroscopeMeasurementModels . . . . . . . . . 55
4.1.1.1 Measuredvector,noiseandbias . . . . . . . . . . . . . . . . . . . 55
4.1.1.2 IMUoffsetfromaircraftCG . . . . . . . . . . . . . . . . . . . . . 57
4.1.1.3 Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.2 RelativeAngularRateandAttitudeKinematics . . . . . . . . . . . . . . . 58
4.1.2.1 ErrorAttitudeRepresentations . . . . . . . . . . . . . . . . . . . 60
4.1.2.2 ModifiedRodriguesParameters . . . . . . . . . . . . . . . . . . . 61
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CONTENTS vii
4.1.2.3 ErrorMRPkinematicequation. . . . . . . . . . . . . . . . . . . . 63
4.1.3 RelativePositionandVelocityKinematics . . . . . . . . . . . . . . . . . . . 65
4.1.4 ProcessModelLinearisation . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 MeasurementModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2.1 RoamingBaseDifferentialGPS . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2.2 MonocularVision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.3 StereoscopicVision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.4 Boom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Sensitivity Analysis 78
5.1 ErrorCovarianceAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 ErrorCovariancePropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.3 ErrorCovarianceCorrection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.1 RoamingBaseDGPS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.2 Optical-Monocular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3.3 Optical-Stereoscopic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.4 Boom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4 Non-rigidwingeffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.5 AdditionalMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6 Simulation and results 99
6.1 SimulationScenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 SensorConfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3 Results-Configuration1(RoamingBase-DGPS) . . . . . . . . . . . . . . . . . . . 106
6.3.1 Stateestimateerrorandthe3σ errorbound . . . . . . . . . . . . . . . . . 107
6.3.2 PercentageControlEnvelope . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.3.3 ProcessCovarianceAdaptation . . . . . . . . . . . . . . . . . . . . . . . . 110
6.3.4 EKFvs. UKF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.4 Results-AllConfigurationSummary . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.4.1 RelativePosition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.4.2 RelativeVelocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.4.3 RelativeAttitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.4 Relativeangularrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.5 Percentageofcontrolenvelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.6 AdditionalSimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.6.1 ConfigurationImprovements . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
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CONTENTS viii
7 Conclusions and Recommendations 127
A Vector Notation and Coordinate Frames 132
A.1 Referenceframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.1.1 Inertialreferenceframe,Fi . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.1.2 LocalNEDreferenceframe,Fl . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.1.3 EarthCenteredEarthfixedreferenceframe,Fe . . . . . . . . . . . . . . . 133
A.1.4 Body-fixedreferenceframe,Fb . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.1.5 Body-carriedreferenceframe,Fc . . . . . . . . . . . . . . . . . . . . . . . 134
A.2 VectorNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B Attitude Representations 138
B.1 Eulerangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
B.2 Quaternions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
C Stereoscopic Vision Measurement Transformation 142
D Simulation Configurations 144
D.1 Thetankerandreceiveraircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
D.2 Sensornoisecovariance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
D.2.1 InertialMeasurementUnit . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
D.3 RoamingBaseDifferentialGPS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
D.3.1 Optical-MonocularandStereoscopic . . . . . . . . . . . . . . . . . . . . . 147
D.3.2 Boomparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
D.4 Errorcovariancepropagation-Chapater5 . . . . . . . . . . . . . . . . . . . . . . 148
D.5 Errorcovariancecorrection-Chapter5. . . . . . . . . . . . . . . . . . . . . . . . 149
D.6 FinalSimulation-Chapter6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
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List of Figures
1.1 AARtankerandreceiveraircraftwithflyingboomrefuelingconfiguration . . . . . . 2
2.1 TankerConfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 BoomJointConfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 ReceiverConfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 ControlEnvelopesasafunctionoftheallowableboomparameterdeflection . . . . 18
2.5 PositionControlInput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 VelocityControlInput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 Estimationenvelopechosentobe10%ofthecontrolenvelope . . . . . . . . . . . . 21
2.8 Estimationenvelopeandtheresultsoftheupstreamerroranalysis . . . . . . . . . . 25
2.9 Estimation envelope and area of position control input uncertainty due to state es-
timateuncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.10RoamingBaseDifferentialGPSasitappliedtotheAARscenario . . . . . . . . . . . 29
2.11IRBeaconarrayviewvs. filteredmeasurementpointarrayofopticalsensorCj . . . 30
2.12Estimationalgorithmflowadaptedfrom[1] . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 PropagationofParticleFilterparticlesthroughanon-linearfunction . . . . . . . . . 40
3.2 The propagation of the state mean and covariance based on function linearisation
intheEKF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 UnscentedKalmanFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 MeanandCovariancepropagationexample . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Propagationofmeansandcovariancesinasimplified2Daircraftkinematicsexample50
4.1 RoamingBaseDifferentialGPSmeasurementvectors . . . . . . . . . . . . . . . . . 68
4.2 Monocularvisionmeasurementvectorandcoordinateprojection . . . . . . . . . . . 70
4.3 PinholeCameraModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 Stereoscopic vision configuration with two measurements of a particular beacon,
eachobtainedviatheidealpinholecameramodel . . . . . . . . . . . . . . . . . . . . 73
4.5 Stereoscopicvisionsubsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.6 Measuredboomparametersandtherelativepositionvector . . . . . . . . . . . . . . 76
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LISTOFFIGURES x
5.1 Velocityerrorcovariancepropagation. . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 Attitudeerrorcovariancepropagation . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3 Variation in the roaming GPS receiver position on the tanker fuselage from config-
urationpositionsAtoB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 ChangeinpositionandattitudeerrorcovarianceasafunctionofGPSsensorposition88
5.5 Change in velocity and angular velocity error covariance as a function of DGPS
roamingreceiverposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.6 Variation in the IR beacon position on the tanker fuselage from configuration posi-
tionsAtoB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.7 ChangeinpositionandattitudeerrorcovarianceasafunctionofIRbeaconposition 92
5.8 Fracional change in position and attitude error covariance a function of measure-
mentquantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.9 Change in velocity and angular velocity covariance as a function of GPS sensor
position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1 True position of the tanker CG relative to the receiver CG coordinated in the re-
ceiverreferenceframetobeestimated . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 TruerelativevelocitybetweentankerandreceiverCGscoordinatedinthereceiver
referenceframetobeestimated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3 AttitudeofthetankerrelativetothereceiverinEulerangles . . . . . . . . . . . . . 101
6.4 Angular rate of the tanker body axis relative to the receiver coordinated in the
tankerreferenceframseastobeestimated . . . . . . . . . . . . . . . . . . . . . . . 102
6.5 TankervelocityinthelocalNEDreferenceframe . . . . . . . . . . . . . . . . . . . . 102
6.6 TankerattitudeinthelocalNEDreferenceframe . . . . . . . . . . . . . . . . . . . . 103
6.7 Tanker velocity and attitude in the local NED reference frame as well as angular
ratesrelativetoinertialspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.8 Tanker aircraft with representation of the sensor layout applicable to the each of
thesensorconfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.9 Receiver aircraft with representation of the sensor layout applicable to the each of
thesensorconfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.10Relativepositionestimateerror,3σ boundandaverage3σ bound . . . . . . . . . . 107
6.11Relativevelocityestimateerror,3σ boundandaverage3σ bound . . . . . . . . . . . 108
6.12Relativeattitudeestimateerror,3σ boundandaverage3σ bound . . . . . . . . . . 109
6.13Relativeangularvelocityestimateerror,3σ boundandaverage3σ bound . . . . . . 109
6.14Averaged3σ errorvs. Minimumstateestimateaccuracylimits . . . . . . . . . . . . 110
6.15RoamingBaseDGPSpercentageofcontrolenvelope . . . . . . . . . . . . . . . . . . 111
6.16Processcovarianceadaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.17ComparisonbetweentheresultsobtainedfromtheEKFandUKF . . . . . . . . . . . 113