Trajectory Learning for Highly Aerobatic Unmanned Aerial Vehicle Master Thesis Maja Celine ...

87 Pages·2012·1.66 MB·English

UNIVERSITY OF OSLO
Department of Informatics
Trajectory Learning
for Highly Aerobatic
Unmanned Aerial
Vehicle
Master Thesis
Maja Celine
Sevaldson
August 14, 2012

Abstract
Thedynamicsoffixedwingplanesarewellunderstood withinthe conven-
tional flight envelope. The situation is different in the case of aerobatic
maneuverswithalargeangleofattack,suchasperchingandverticalhover.
In such maneuvers the airflows around the plane are unpredictable mak-
ingitdifficulttocreateaccuratedynamicmodels,whichwouldnormallybe
neededforthedesignofconventionalcontrollers. YethumanRCpilotsare
abletoflythesemaneuverswithfixedwingplanes.
Apprenticeship learning provides a promising solution to the problem
of automating highly aerobatic maneuvers. It allows the maneuver to be
learnedfrom demonstration flightsdone by a human RC pilotrather than
relyingonanaccuratedynamicsmodel.
Thefocusofthisthesisisonaspecificissueinapprenticeshiplearning,
namely how to infer the trajectory the pilot intended to fly from a set of
suboptimal demonstration trajectories. Such a trajectory can be used as
a target trajectory for an autonomous controller. A trajectory learning
algorithm that has shown promising results in automation of aerobatic
helicopterflightisappliedtoafixedwingUAVplatform.
The algorithm is tested on two different maneuvers; A straight line of
level flight, and a vertical hover maneuver. In the case of both maneuvers
the algorithm learned the intended trajectory without prior knowledge
aboutthetrajectory.
In order to collect training data for the trajectory learning task, an
appropriate platform and data acquisition system are needed. This thesis
therefore also presents the development of a fixed wing UAV platform for
researchonautomationofaerobaticflight.
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Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thesisoverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Supportingcontributions . . . . . . . . . . . . . . . . . . 2
1.2.2 Thesisoutline . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Relatedwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 StanfordAutonomousHelicopter . . . . . . . . . . . . . 3
1.3.2 Aerobaticmaneuvers . . . . . . . . . . . . . . . . . . . . 4
2 Background 7
2.1 HiddenMarkovModels . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 DiscreteMarkovProcesses . . . . . . . . . . . . . . . . . 7
2.1.2 HiddenMarkovModel. . . . . . . . . . . . . . . . . . . . 8
2.2 Expectation-Maximization. . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 MaximumLikelihoodEstimation . . . . . . . . . . . . . 11
2.2.2 EM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 ExtendedKalmanSmoother. . . . . . . . . . . . . . . . . . . . . 12
2.3.1 DiscreteKalmanfilter . . . . . . . . . . . . . . . . . . . . 12
2.3.2 ExtendedKalmanfilter . . . . . . . . . . . . . . . . . . . 13
2.3.3 Kalmansmoother . . . . . . . . . . . . . . . . . . . . . . 13
2.4 DynamicTimeWarping . . . . . . . . . . . . . . . . . . . . . . . 14
3 TrajectoryLearning 17
3.1 Statemodelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Timealignment . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Thetrajectorylearningalgorithm . . . . . . . . . . . . . . . . . 19
3.2.1 E-stepforhiddentrajectory . . . . . . . . . . . . . . . . 20
3.2.2 M-stepforhiddentrajectory . . . . . . . . . . . . . . . . 20
3.2.3 Timealignment . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 DynamicModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.1 Equationsofmotion . . . . . . . . . . . . . . . . . . . . . 22
3.4 Improvementsofthemodel . . . . . . . . . . . . . . . . . . . . . 23
4 Experimentalplatform 25
4.1 Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.1 Dynamicalpropertiesoftheplane. . . . . . . . . . . . . 27
4.1.2 Modificationstotheairframe . . . . . . . . . . . . . . . 29
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4.1.3 Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.4 RadioControlSystem . . . . . . . . . . . . . . . . . . . . 30
4.2 Microcontrollers,SensorsandDataAcquisition . . . . . . . . 31
4.2.1 ArduPilotMega . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.2 InertialMeasurementUnit . . . . . . . . . . . . . . . . . 32
4.2.3 GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.4 Barometricpressuresensor. . . . . . . . . . . . . . . . . 34
4.2.5 Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.6 PilotInputs . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.7 DataAcquisitionandStorage . . . . . . . . . . . . . . . 37
4.3 Testenvironment . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 AlternativePositioningSystems . . . . . . . . . . . . . . . . . . 39
4.5 Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 ExperimentsandResults 43
5.1 Preliminarytests. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1.1 GPSaccuracy . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1.2 Outdoorflighttests . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Collectingtrainingdata. . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.1 Linearflightandbankedturns . . . . . . . . . . . . . . . 46
5.2.2 Hoveringwithtransitions . . . . . . . . . . . . . . . . . . 47
5.3 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3.1 Selectinggooddemonstrations . . . . . . . . . . . . . . 49
5.3.2 BPMfilteringandcalibration. . . . . . . . . . . . . . . . 49
5.3.3 LocalizationofPositionData . . . . . . . . . . . . . . . . 51
5.3.4 IMUdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3.5 Pilotcontrolinputs . . . . . . . . . . . . . . . . . . . . . . 55
5.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.1 Timealignment . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.2 Straightlineoflevelflight . . . . . . . . . . . . . . . . . . 59
5.4.3 Verticalhover . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.4 ModelPredictionError . . . . . . . . . . . . . . . . . . . 64
6 Conclusion 67
6.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.1 Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.2 Timealignment . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1.3 Trajectorylearning . . . . . . . . . . . . . . . . . . . . . . 68
6.2 Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
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List of Figures
2.1 ThreestateMarkovmodeloftheweather . . . . . . . . . . . . . 9
2.2 HiddenMarkovModelofcrazysodadispenser . . . . . . . . . 9
2.3 Dynamictimewarping. Thefigureisadaptedfrom[31]. . . . . 14
2.4 Dynamic time warping distance matrix. The figure is
borrowedfrom[40]. . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Modeloftherelationbetweenthehiddentrajectoryandone
ofthedemonstrations. Thecolourednodesareunobserved. . 19
3.2 Model of the state when τk is fixed. Coloured nodes are
j
unobserved.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1 Expertpilotflyingtheplaneinverticalhover. . . . . . . . . . . 25
4.2 ElectriflyYak543D . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Reinforcementofthemotormount . . . . . . . . . . . . . . . . 30
4.4 Measuredthrustasafunctionofcontrolinput. . . . . . . . . . 30
4.5 7channelFutabaRCsystem . . . . . . . . . . . . . . . . . . . . . 31
4.6 DiagramofDAQsystem . . . . . . . . . . . . . . . . . . . . . . . 32
4.7 Electronicsmountedontheplane . . . . . . . . . . . . . . . . . 33
4.8 ArduPilotMegaboard . . . . . . . . . . . . . . . . . . . . . . . . 34
4.9 MicroStrain3DM-GX3IMU . . . . . . . . . . . . . . . . . . . . . 34
4.10 MediaTek3329GPS . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.11 Bosch Sensortech BMP085 digital pressure sensor inside
plasticenclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.12 Maxbotixultrasonicrangefindersonar . . . . . . . . . . . . . . 36
4.13 Outdoortestspace. . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.14 IndoorflightintheCEPSUMgym. . . . . . . . . . . . . . . . . . 38
4.15 TheStingerDomeofConcordiaUniversityinMontreal . . . . 38
4.16 Principleofstereocomputervision . . . . . . . . . . . . . . . . 39
4.17 2Dtrackingbasedoncolourtresholding . . . . . . . . . . . . . 40
5.1 On ground GPS test at McGill downtown campus. The red
line marks the actual path travelled, while the yellow line
showstheloggedGPSdata. . . . . . . . . . . . . . . . . . . . . . 43
5.2 ComparisonofGPSandBPMaltitudedata . . . . . . . . . . . . 44
5.3 InairtestsofDAQsystemandGPSlogging. . . . . . . . . . . . 45
5.4 Handlaunchoftheplaneforatrainingdatacollectionflight
intheStingerDome. . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.5 Mark-upoftheStingerDomefieldforcollectingtrainingdata. 47
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5.6 VerticalhoverintheStingerDome. . . . . . . . . . . . . . . . . 48
5.7 Verticalhover. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.8 East-Northplotofagoodlinearflightdemonstration. . . . . 49
5.9 Positionplotandpitchanglefromagoodhoverdemonstration 50
5.10 BPMdataisfilteredusinga3rdorderButterworth low-pass
filterwith1Hzcut-offfrequency. . . . . . . . . . . . . . . . . . . 50
5.11 UncalibratedBPMdataandSonarreferencesignal . . . . . . . 51
5.12 Uncalibrated BPM data and Sonar reference at the two
regionswherecalibrationpointswereselected. . . . . . . . . . 51
5.13 CalibratedBPMdataandSonarreferencesignal . . . . . . . . 52
5.14 Zoomedinviewofthetwocalibrationregionsaftercalibration 52
5.15 IMUframeandbodyframeoftheplane. . . . . . . . . . . . . . 53
5.16 Ailerondeflectionasafunctionofinputpulsewidth . . . . . . 55
5.17 Elevatordeflectionasafunctionofinputpulsewidth . . . . . 56
5.18 Rudderdeflectionasafunctionofinputpulsewidth . . . . . . 56
5.19 ThrustinNewtonsvsPWMcommand . . . . . . . . . . . . . . 57
5.20 Linearvelocities(n˙e˙d˙)fromthelinearflight. . . . . . . . . . . 58
5.21 AngularVelocitiesaroundtheplanez-axis(r). . . . . . . . . . . 58
5.22 East-Northpositionoflevelflight(meters) . . . . . . . . . . . . 59
5.23 Positionandlinearvelocityoftheplaneduringastraightline
oflevelflight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.24 Orientationduringlevelflight(EulerAngles). . . . . . . . . . . 60
5.25 Angularvelocitiespqr (rad/sec),levelflight.. . . . . . . . . . . 61
5.26 Controlinputs,levelflight. . . . . . . . . . . . . . . . . . . . . . 61
5.27 Hovermaneuver. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.28 Hovermaneuver-Linearvelocitiesandposition. . . . . . . . . 63
5.29 AngularVelocities,hoverflight(rad/sec). . . . . . . . . . . . . 63
5.30 Orientationduringhover(Eulerangles). . . . . . . . . . . . . . 63
5.31 Controlinputs,hovermaneuver. . . . . . . . . . . . . . . . . . . 64
5.32 Model prediction error inlinearaccelerations (u˙v˙w˙) during
straightflight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.33 Modelpredictionerrorinangularaccelerations(p˙q˙r˙)during
straightflight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.34 Model prediction error inlinearaccelerations (u˙v˙w˙) during
thehovermaneuver. . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.35 Modelpredictionerrorinangularaccelerations(p˙q˙r˙)during
thehovermaneuver. . . . . . . . . . . . . . . . . . . . . . . . . . 65
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List of Tables
4.1 Detailedweightbreakdownoftheexperimentalplatform . . . 27
4.2 MomentsandproductsofinertiaofYak54withData Acqui-
sitionsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Parameters used in calculation of rotational damping mo-
ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
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