USF Libraries
USF Digital Collections

Autonomous vertical autorotation for unmanned helicopters

MISSING IMAGE

Material Information

Title:
Autonomous vertical autorotation for unmanned helicopters
Physical Description:
Book
Language:
English
Creator:
Dalamagkidis, Konstantinos
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Helicopter control
Non-linear model-predictive control
Neural network
Autorotative flight
Safety
Dissertations, Academic -- Computer Science and Engineering -- Doctoral -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Small Unmanned Aircraft Systems (UAS) are considered the stepping stone for the integration of civil unmanned vehicles in the National Airspace System (NAS) because of their low cost and risk. Such systems are aimed at a variety of applications including search and rescue, surveillance, communications, traffic monitoring and inspection of buildings, power lines and bridges. Amidst these systems, small helicopters play an important role because of their capability to hold a position, to maneuver in tight spaces and to take off and land from virtually anywhere. Nevertheless civil adoption of such systems is minimal, mostly because of regulatory problems that in turn are due to safety concerns. This dissertation examines the risk to safety imposed by UAS in general and small helicopters in particular, focusing on accidents resulting in a ground impact. To improve the performance of small helicopters in this area, the use of autonomous autorotation is proposed. This research goes beyond previous work in the area of autonomous autorotation by developing an on-line, model-based, real-time controller that is capable of handling constraints and different cost functions. The approach selected is based on a non-linear model-predictive controller, that is augmented by a neural network to improve the speed of the non-linear optimization. The immediate benefit of this controller is that a class of failures that would otherwise result in an uncontrolled crash and possible injuries or fatalities can now be accommodated. Furthermore besides simply landing the helicopter, the controller is also capable of minimizing the risk of serious injury to people in the area. This is accomplished by minimizing the kinetic energy during the last phase of the descent. The presented research is designed to benefit the entire UAS community as well as the public, by allowing for safer UAS operations, which in turn also allow faster and less expensive integration of UAS in the NAS.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Konstantinos Dalamagkidis.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 128 pages.
General Note:
Includes vita.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 002068399
oclc - 606891644
usfldc doi - E14-SFE0003147
usfldc handle - e14.3147
System ID:
SFS0027463:00001


This item is only available as the following downloads:


Full Text

PAGE 1

AutonomousVerticalAutorotationforUnmannedHelicopters by KonstantinosDalamagkidis Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofComputerScienceandEngineering CollegeofEngineering UniversityofSouthFlorida Co-MajorProfessor:KimonP.Valavanis,Ph.D. Co-MajorProfessor:LesA.Piegl,Ph.D. JayLigatti,Ph.D. AliYalcin,Ph.D. ThomasBieske,Ph.D. DateofApproval: July30,2009 Keywords:HelicopterControl,Non-linearModel-predictiveControl,NeuralNetwork, AutorotativeFlight,Safety c r 2009,KonstantinosDalamagkidis

PAGE 2

Tomyparents.

PAGE 3

TableofContentsListofTables iv ListofFigures v Nomenclature x Abstract xiv Chapter1Introduction 1 1.1Motivation 1 1.2ProblemStatement 2 1.3HistoryandStateoftheArtofAutonomousAutorotation21.4Methodology 4 1.5SummaryofContributions 5 1.6Denitions 6 1.6.1AirTra cControl 6 1.6.2Airworthiness 6 1.6.3FederalAviationRegulations(FAR)61.6.4Flare 6 1.6.5GeneralAviation 7 1.6.6NationalAirspaceSystem 7 1.6.7PublicandCivilAircraft 7 1.6.8SinkRateandAutorotativeSinkRate71.6.9UnmannedAircraftSystem 7 1.7DissertationOutline 8 Chapter2UnmannedAircraftSafetyConsiderations 9 2.1Introduction 9 2.2CurrentCerticationPathsandOperationalGuidelinesintheU.S.102.3EquivalentLevelofSafety 12 2.3.1MannedAviationRequirements12 2.3.1.1Applications 14 2.3.1.2Sacricability 14 2.3.1.3PilotPhysicallyRemovedfromCockpit142.3.1.4Take-o Weight 15 2.3.1.5Payload 15 i

PAGE 4

2.3.2UASAccidentTypes 15 2.3.3DerivationofanELOSforUAS16 2.4GroundImpactRequirements 17 2.4.1UASEquivalentLevelofSafety182.4.2TargetReliabilityLevel 19 2.5Conclusions 23 Chapter3HelicopterDynamicsModel 25 3.1Introduction 25 3.1.1Dynamics 25 3.1.2Control 27 3.2HelicopterFailuresandRecovery 28 3.2.1MainRotorFailures 28 3.2.2TailRotorFailures 28 3.2.3Autorotation 29 3.3HoveringState 30 3.3.1MomentumTheory 31 3.3.2BladeElementTheory 33 3.4VerticalDescent 35 3.4.1VortexRingStateandTurbulentWakeState363.4.2GroundE ect 38 3.4.3InowDynamics 39 3.5VerticalAutorotationModel 40 3.6Remarks 42 Chapter4ControllerDesign 43 4.1PrinciplesofModelPredictiveControl43 4.1.1Fundamentals 43 4.1.2Prediction 45 4.1.3Optimization 45 4.1.4Tuning 46 4.2CollectiveControllerDesign 47 4.2.1InternalVerticalAutorotationModel474.2.2Non-linearOptimizationusingRecurrentNeuralNetworks494.2.3ControllerDerivation 50 4.2.3.1Prediction 50 4.2.3.2Constraints 52 4.2.3.3Non-linearOptimization55 4.2.4DesignSummary 55 4.3VerticalAutorotationController 56 4.3.1Roll / Pitch / YawController 58 4.3.2SensorFusion 59 4.3.3NeuralNetworkFiltering 60 4.3.4VerticalAutorotationControllerBlockDiagram61 ii

PAGE 5

Chapter5SimulationResults 62 5.1OH-58AHERS 63 5.1.1BaselineScenario 63 5.1.1.1CostFunction 67 5.1.1.2Non-linearOptimizationProblemConvexity675.1.1.3ConvergenceCharacteristics685.1.1.4Real-timeOperation69 5.1.2InitialAltitude 71 5.1.3LearningRate 71 5.1.4Noise 73 5.1.5ReactionTime 73 5.1.6SamplingRate 78 5.2X-PlaneSimulation 78 5.3Raptor30v2 82 5.3.1BaselineScenario 82 5.3.1.1CostFunction 83 5.3.1.2Non-linearOptimizationProblemConvexity855.3.1.3ConvergenceCharacteristics865.3.1.4Real-timeOperation87 5.3.2AlternativeCostFunction 89 5.3.3InitialAltitude 89 5.3.4LearningRate 92 5.3.5Noise 92 5.3.6ReactionTime 97 5.3.7SamplingRate 97 5.3.8StricterConstraint 97 Chapter6ConclusionandFutureExtensions 101 6.1ModelPredictionImprovement 102 6.2 n -constraintHandling 103 6.3IntegrationintoanEmergencyLandingSystem1036.4TheIssueofFindingaSuitableLandingLocation1056.5UseinMannedAircraft 106 ListofReferences 108 Appendices 116 AppendixA:CaseStudy 117 AppendixB:GroundFatalityProbabilityModelSensitivityAnalysis120 AbouttheAuthor EndPage iii

PAGE 6

ListofTablesTable2.1FARPart23aircraftclassesandcorrespondingacceptablefailurecondition probabilitybasedonseverityasdenedinAC23-1309-1C.13 Table2.2FatalityratesfromallaccidentsbasedonanalysisofNTSBaccidentdata[62] between1983and2006. 17 Table2.3Fatalityratesforaccidentswhereanin-ightcollisionwithterrainorwater occurred. 19 Table2.4Fatalityratesforaccidentswhereoneoracombinationofin-ightcollision withterrainorwater,hard / forcedlanding,runwayoverrunorditchingoccurred. 19 Table5.1VerticalautorotationmodelparametersforamodiedOH-58Ahelicopter withhighenergyrotorsystem. 64 Table5.2SensornoiselevelsusedinthecaseoftheOH-58Ahelicopter.73Table5.3ModelparametersfortheThundertigerRaptor30v2R / Cmodelhelicopter.83 Table5.4SensornoiselevelsinthecaseoftheThundertigerRaptor30v2simulation.92TableA.1Characteristicsofvexedwingandverotary-wingUASofvarioussizes, usedforthecaseanalysis. 117 TableA.2Theparametersusedforeachtestcaseandadescriptionofapossiblescenariocorrespondingtothatcase. 117 TableA.3Fatalityprobabilityandreliabilityrequirementswithrespecttogroundimpact accidentsfortenUASunderthreedi erentcases.118 TableA.4ThepercentageoftheUSareaoverwhicheachUAScanloiterwithoutviolatingsetTLSrequirement,basedonexhibitedreliability.119 iv

PAGE 7

ListofFiguresFigure2.1Riskreferencesystemforlargemannedaircraft(thegrayedareassignify unacceptablerisk). 13 Figure2.2PrimaryandsecondaryaccidentsthatcanresultfromtheoperationofUAS andtheirpossibleoutcomes. 17 Figure2.3Fatalityratesfromgeneralaviation,commuterandaircarrieraccidentsasa functionoftime. 18 Figure2.4Theprobabilityoffatalityasafunctionofkineticenergyimpactasestimated byWeibel[84]andmodelsderivedinRCC321[67]andRCC323[66].21 Figure2.5Theprobabilityoffatalityasafunctionofkineticenergyimpactfortheproposedmodelwith f = 10 6 J, f = 100Jandforseveralvaluesof f s .23 Figure3.1Thesinglemainrotorwithtailrotorhelicopterdesign.26Figure3.2Helicoptershave6degreesoffreedom. 27 Figure3.3AtypicalhelicopterH-Vcurveliketheoneavailableinhelicoptermanuals.30Figure3.4Theowmodelcreatedbythemainrotorasassumedbymomentumtheory.31Figure3.5Theforcesactingonarotorbladesectionasaresultoflocalairvelocity.33Figure3.6Theforcesactingonarotorbladesectionasaresultoflocalairvelocity duringdescent. 36 Figure3.7Therotorwakecharacteristicsstartingfromaxialclimborhovering(normal workingstate)andmovingthroughthevortexring,turbulentwakeandwind-millbrakestatesasthedescentvelocityincreases.37 Figure3.8Theinducedvelocityproleinthefouroperationalstates.38Figure3.9Theforcesactingonahelicopterduringverticalautorotativedescent.40 v

PAGE 8

Figure4.1Adiagramofthebasicprinciplebehindmodelpredictivecontrol.44Figure4.2Blockdiagramofthepredictionmoduleofthecontroller.52Figure4.3BlockdiagramoftheNN-NMPC. 55 Figure4.4TheNN-NMPCalgorithm. 56 Figure4.5OverviewofthecalculationsintheNN-NMPCloopthatcanruninparallel.57Figure4.6BlockdiagramoftheRPYcontroller. 59 Figure4.7Blockdiagramoftheverticalautorotationcontroller.61Figure5.1Duringtheautorotativedescentthehelicoptertraversesthreedistinctregions ofoperation:free, n -controlledand v H -controlleddescent.63 Figure5.2Thesinkrate,rotorrpmandcontrolinputoftheOH-58Ahelicopterfora descentfromaninitialaltitudeof120m( N s = 10, N c = 5).65 Figure5.3Thesinkrate,rotorrpmandcontrolinputoftheOH-58Ahelicopterfora descentfromaninitialaltitudeof120m( N s = 12, N c = 6).66 Figure5.4ThecostfunctionusedbythecontrollerforautorotationoftheOH-58Ahelicopter. 67 Figure5.5Worst-case N s fordi erentvaluesof v H ,bladepitchwith N c = 6and t s = 50msinthecaseoftheOH-58Ahelicopter.68 Figure5.6Worst-caseandrstoctile N s asafunctionof N c t s inthecaseoftheOH58Ahelicopter. 69 Figure5.7Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfrom freeto n -controlleddescentinthecaseoftheOH-58Ahelicopter.70 Figure5.8Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfrom n -controlledto v H -controlleddescentinthecaseoftheOH-58Ahelicopter.70 Figure5.9Theevolutionoftheoutputoftheneuralnetworkinthelastsecondsbefore touchdowninthecaseoftheOH-58Ahelicopter.70 Figure5.10Theexecutiontimepercontrollerinnerloopiterationasafunctionofpredictionandcontrolhorizon. 71 vi

PAGE 9

Figure5.11Thee ectofdi erentinitialaltitudesontheperformanceoftheOH-58A controller. 72 Figure5.12Thevarianceoftheneuralnetworkoutputwithrespecttotimeandhelicopter sinkrateforfourvaluesofthelearningrateparameterinthecaseoftheOH-58Ahelicopter. 74 Figure5.13ThetrajectoryoftheOH-58Ahelicopterwithandwithoutnoiseunderthe rstnoiselevel. 75 Figure5.14ThetrajectoryoftheOH-58Ahelicopterwithandwithoutnoiseunderthe secondnoiselevel. 76 Figure5.15ThetrajectoryoftheOH-58Ahelicopterwithandwithoutnoiseunderthe thirdnoiselevel. 77 Figure5.16Thee ectofreactiontimeontheOH-58Acontrollerperformance.79 Figure5.17Controllerperformanceusingdi erentsamplingratesinthecaseoftheOH58Ahelicopter. 80 Figure5.18Simulationresultsforanautorotativedescentfrom180mintheX-Plane simulator. 81 Figure5.19Thesinkrate,rotorrpmandcontrolinputoftheThundertigerRaptor30v2for adescentfromaninitialaltitudeof120m( N s = 4, N c = 3).84 Figure5.20ThecostfunctionusedbytheThundertigerRaptor30v2controller.85Figure5.21The5%ofsampleswithlowerworst-case N s fordi erentvaluesof v H and bladepitchinthecaseoftheThundertigerRaptor30v2.86 Figure5.22Worst-caseandrstoctile N s asafunctionof N c t s inthecaseoftheThundertigerRaptor30v2. 87 Figure5.23Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfrom freeto n -controlleddescentinthecaseoftheThundertigerRaptor30v2.88 Figure5.24Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfrom n -controlledto v H -controlleddescentinthecaseoftheThundertigerRaptor 30v2. 88 Figure5.25Theevolutionoftheoutputoftheneuralnetworkduringthelastseconds beforetouchdowninthecaseoftheThundertigerRaptor30v2.88 vii

PAGE 10

Figure5.26AnalternativecostfunctionusedbytheThundertigerRaptor30v2controller.89Figure5.27Thesinkrate,rotorrpmandcontrolinputoftheThundertigerRaptor30v2for adescentfromaninitialaltitudeof120m( N s = 5, N c = 4)usinganalternate costfunction. 90 Figure5.28Thee ectofdi erentinitialaltitudesontheperformanceoftheThundertiger Raptor30v2controller. 91 Figure5.29Thevarianceoftheneuralnetworkoutputwithrespecttotimeandhelicopter sinkrateforfourvaluesofthelearningrateparameterinthecaseoftheThun-dertigerRaptor30v2. 93 Figure5.30ThetrajectoryoftheThundertigerRaptor30v2withandwithoutnoiseunder therstnoiselevel. 94 Figure5.31ThetrajectoryoftheThundertigerRaptor30v2withandwithoutnoiseunder thesecondnoiselevel. 95 Figure5.32ThetrajectoryoftheThundertigerRaptor30v2withandwithoutnoiseunder thethirdnoiselevel. 96 Figure5.33Thee ectofreactiontimeontheperformanceoftheThundertigerRaptor 30v2controller. 98 Figure5.34ThundertigerRaptor30v2controllerperformanceasafunctionofsampling rate. 99 Figure5.35ThundertigerRaptor30v2controllerperformanceusingastricter n constraint. 100 Figure6.1BlockdiagramoftheproposedEmergencyLandingSystem.104Figure6.2BlockdiagramoftheproposedhardwaredesignoftheEmergencyLanding System. 105 FigureB.1Thebiascalculatedforperturbationsofthe x 1 randomvariable,correspondingtothe log 10 E imp asafunctionoftheactualvalueof x 1 .123 FigureB.2Thevariancecalculatedforperturbationsofthe x 1 randomvariable,correspondingtothe log 10 E imp asafunctionoftheactualvalueof x 1 .124 FigureB.3Thebiascalculatedforperturbationsofthe x 2 randomvariable,correspondingtothe log 10 f asafunctionoftheactualvalueof x 2 .125 viii

PAGE 11

FigureB.4Thevariancecalculatedforperturbationsofthe x 2 randomvariable,correspondingtothe log 10 f asafunctionoftheactualvalueof x 2 .126 FigureB.5Thebiascalculatedforperturbationsofthe x 3 randomvariable,correspondingtotheshelteringfactor f s asafunctionoftheactualvalueof x 3 .127 FigureB.6Thevariancecalculatedforperturbationsofthe x 3 randomvariable,correspondingtotheshelteringfactor f s asafunctionoftheactualvalueof x 3 .128 ix

PAGE 12

Nomenclature A Rotordiscarea A cs Aircraftcross-sectionarea C Constraintfunction C d Bladedragcoe cient C d ; 0 Averagebladedragcoe cient C l Bladeliftcoe cient C l ; a Liftcurveslope C P Powercoe cient C Q Torquecoe cient C T Thrustcoe cient D Dragforce E Neuralnetworkepochsize E imp Kineticenergyatimpact F Frequency f Groundfatalityprobabilitymodelparameter f Groundfatalityprobabilitymodelparameter F D Dragforceonblade f e Equivalentunitdragcoe cientarea f g Grounde ectfactor f i Inowvelocityfactor x

PAGE 13

F L Liftforceonblade f r Ratioofmaximumtonominalrotorrpm f s Shelteringfactor g Accelerationofgravity I R Rotormomentofinertia J Jacobianmatrix K Kalmangain L Costfunction l TR Dinstancebetweenmainandtailrotor M Helicoptermass m a Airmass N b Numberofblades N c Controlhorizon N exp Numberofpeopleexposed N s Predictionhorizon P Rotorpower P Kalmanstatecovariancematrix Q Rotortorque Q Modelerrorcovariancematrix R Rotorradius r Non-dimensionalizeddistanceofbladestationfromcenterofrotor R Sensorerrorcovariancematrix S Areaexposedtoanaircraftimpact T Thrust xi

PAGE 14

t d Reactiondelay t f Finaltime t s Samplingperiod u Action v Velocity v H Helicoptersinkrate W Weight w Weightfactor Auxiliaryvector x State y Distanceofbladestationfromcenterofrotor c y Bladechordatstationy z Helicopteraltitude z Measurementvector z 0 Helicopterinitialaltitude GreekLetters Aerodynamicangleofattack r Learningrate T Timeinterval Sensornoise Bladepitchat3 / 4ofitslength Inducedpowercorrectionfactor Inowratio Meanvalue xii

PAGE 15

Modelnoise Airdensity p Populationdensity Rotorsolidityfactor Angleoflocalairvelocity n Rotorspeedofrotation n 0 Nominalrotorspeedofrotation Subscripts f Fatality GI GroundImpact h Athover i Induced M Maximum m Minimum MR Mainrotor op Operational s Steady-state tip Rotortip TR Tailrotor xiii

PAGE 16

AutonomousVerticalAutorotationforUnmannedHelicopters KonstantinosDalamagkidis ABSTRACT SmallUnmannedAircraftSystems(UAS)areconsideredthesteppingstonefortheintegrationofcivilunmannedvehiclesintheNationalAirspaceSystem(NAS)becauseoftheirlowcostandrisk.Suchsystemsareaimedatavarietyofapplicationsincludingsearchandrescue,surveillance,communications,tra cmonitoringandinspectionofbuildings,powerlinesandbridges.Amidst thesesystems,smallhelicoptersplayanimportantrolebecauseoftheircapabilitytoholdaposi-tion,tomaneuverintightspacesandtotakeo andlandfromvirtuallyanywhere.Nevertheless civiladoptionofsuchsystemsisminimal,mostlybecauseofregulatoryproblemsthatinturnareduetosafetyconcerns.ThisdissertationexaminestherisktosafetyimposedbyUASingeneralandsmallhelicoptersinparticular,focusingonaccidentsresultinginagroundimpact.Toimprovetheperformanceofsmallhelicoptersinthisarea,theuseofautonomousautorotationisproposed.Thisresearchgoesbeyondpreviousworkintheareaofautonomousautorotationbydevelopinganon-line,model-based,real-timecontrollerthatiscapableofhandlingconstraintsanddi erentcostfunctions. Theapproachselectedisbasedonanon-linearmodel-predictivecontroller,thatisaugmentedbyaneuralnetworktoimprovethespeedofthenon-linearoptimization.Theimmediatebenetofthiscontrolleristhataclassoffailuresthatwouldotherwiseresultinanuncontrolledcrashandpossibleinjuriesorfatalitiescannowbeaccommodated.Furthermorebesidessimplylandingthehelicopter,thecontrollerisalsocapableofminimizingtheriskofseriousinjurytopeopleinthearea.Thisisaccomplishedbyminimizingthekineticenergyduringthelastphaseofthedescent.ThepresentedresearchisdesignedtobenettheentireUAScommunityaswellasthepublic,byallowingforsaferUASoperations,whichinturnalsoallowfasterandlessexpensiveintegrationofUASintheNAS. xiv

PAGE 17

Chapter1:IntroductionTheeldofroboticshasexpandedgreatlyoverthelastfewdecadesbeyondtheautomatedman-ufacturingeld.Oneoftheadvancesrelatestotheuseofunmannedaircraftthathaverepeatedlydemonstratedmajorpotentialfordiverseapplicationsinthemilitary,civilandpublicdomains.ItisnoteworthythatunmannedaircrafthavealreadyloggedhundredsofthousandsofhoursoverthebattleeldandthattheU.S.Congress,identifyingtheadvantagesofthistechnology,hasmandatedinPublicLaw106-398thatonethirdoftheaircraftintheoperationaldeepstrikeforceshouldbeunmannedby2010.Neverthelessnotallaircraftareequal.Helicopterspresentuniquecharacteristicsthatmakethemparticularlysuitableforanumberofapplications.Thesecharacteristicsincludetheabilitytoho-ver,maneuverintightspacesandthelackofarequirementfortake-o andlandinginfrastructure. Asaconsequence,thereissignicantinterestfortheuseofunmannedhelicoptersindiverseappli-cationsandtasks.1.1MotivationAccordingtopublicopinion,unmannedaircraftingeneralandunmannedhelicoptersinparticulararelesssafethantheirmannedcounterparts.Thisisalsoreectedinrestrictivepublicpolicycur-rentlygoverningunmannedoperations.Furthermore,helicoptersingeneralhavebeendescribedas“ungainly,aerodynamicmavericks”[11],sincetheyexhibitacomplexaerodynamicperformancethatisextremelydi culttoaccuratelypredict.Asaresult,controllingahelicopterrequiressignicante ortandconstantattention.Thisisalsosigniedfromaphrasecommonamongpilots; “Airplaneswanttoy,helicopterswanttocrash”.Severaloftheapplicationsaimedatunmannedhelicoptersconcernurbanenvironments.Thisposesarisktolivesandpropertyinthecaseofon-boardfailures,ifthelatterresultinuncontrolledighttermination.Currentliteraturehasaddressedthisissuebymakingunmannedaircraftfault-tolerant.Thismeansthatifafailureoccursthehelicopterreconguresitscontrolpolicyadaptingtothenewsituation.Dependingonthefailure,itmaycontinuetowardscompletingthenextob-jectiveorreturntobaseforrepairs.Nevertheless,therearefailuresthatcannotbeaccommodatedbyrecongurationalone.Majorfailuresmaynotallowcontinuedightandthehelicopterwillbeforcedtolandimmediately. 1

PAGE 18

Amaneuveravailabletohelicopterpilotstobringahelicoptersafelytothegroundevenafterlossofpowertothemainrotorisautorotation.Thismaneuver,describedinmoredetailinSec-tion3.2.3,reducestheverticalspeedofthehelicopterjustbeforetouchdownandisusableinun-mannedhelicopterstoo,regardlessoftheirsize.Althoughoptimalautorotationtrajectorieshavebeeninvestigatedseveraldecadesago,autono-mousautorotationhasremainedlargelyunexploreduntilveryrecently.Thepossiblebenetsofintroducingthiscapabilityinunmannedhelicoptersisthemaindrivingforcebehindthisresearch.1.2ProblemStatementDependingonthefunctionalityavailabletoanunmannedhelicopterafterafailure,itmaybepos-sibletocontinueightoritmaybenecessarytoterminateightimmediately.Inthelattercaseanuncontrolledcrashisnotnecessarilyinevitable.Undercertainconditionsitmaybepossibletocontrolthehelicopterandlanditsafely.Thefocusofthisdissertationisonhelicopterfailuresthatjeopardizeorcompletelyprecludecon-tinuedightevenundermanualcontrol,butcanbeaccommodatedbyanon-boardemergencyightcontrollerandimmediateighttermination.Suchfailuresincludelossofpowerorcontroltothetailandpossiblymainrotorandinmannedhelicoptersareaddressedusingautorotationtobringthehelicoptersafelytotheground.Thegoalofthisresearchistodevelopanappropriatecontrollerthatcanperformtheautorotationmaneuverautonomously,withoutviolatingperformanceandsafetyrequirements.Thiscontrollercaninthefuturebeintegratedintoaredundantsafetysystemthatcansafelylandanunmannedhelicopterwhenthelattersu ersfailuresthatdonotallowcontinuedight. Thenextsectionreviewscurrentliteratureonunmannedautorotation,startingfromtheearlierworkonautorotationtrajectoryoptimization.Thissetsthebackgroundfortheintroductionoftheapproachusedinthisresearch,whichfollowsinSection1.4.1.3HistoryandStateoftheArtofAutonomousAutorotationAutorotationisaphenomenonthatdistinguisheshelicoptersfromxed-wingaircraftandallowsthemtomaintainliftandcontrolinthecaseofenginefailure[54].Althoughtheconceptofau-torotationwasknownforyears,thepersoncreditedforapplyingautorotationforrecoveryofhe-licoptersisPescara.Histhirdhelicopterdesignwascompletedin1923andincludedfeaturesthatallowedautorotationinthecaseofenginefailure[56].Successfulautorotationshavebeencarriedoutasfarbackas1937,rstbyEwaldRohlfs,thetestpilotoftheFw61andafewmonthslaterbytheBreguet-Dorandcoaxialhelicopter[54,56,60]. 2

PAGE 19

Inthelate1970s,theNASAAmesResearchCenterwasinvolvedinworkonautorotationop-timization.Specicallyin1977,Johnsonderivedanon-linearautorotationmodelthatincludesverticalaswellaslongitudinalmovement[42].Theoptimalcontrolwasderivedusingacostfunc-tionthatminimizedhorizontalandverticalspeedattouchdown.Thederivationofthecontrollawwasbasedoniterativenumericalintegrationforwardsandthenbackwardsbetweenthetwoboundarypointsandupdatingusingthesteepestdescentmethod.Johnsonalsoprovedthattheoptimaltrajectoryafterpowerlossinhoverispurelyvertical.TheresultswerethencomparedwiththeperformanceofamodiedBellOH-58AcarryingaHighEnergyRotorSystem(HERS)duringighttests.Thesetestswereperformedin1976aspartofaBellHelicopterCompanyresearchprojectsponsoredbytheU.S.Army[18].Ayearlater,TalbotandSchroerspublishedtheirownworkondeterminingtheminimumautorotativedescentrateforsinglerotorhelicoptersbasedontheminimumpowerforlevelight[75].Theresultingmodelincludedempiricalcorrectionfactorsaswellasamethodologytoobtainestimatesoftheminimumpowerinlevelight.In1985,inStanford,AllanYeow-NamLeeenhancedJohnson'sworkbyintroducingstatein-equalityconstraintsthatwereconvertedtoequalityusingslackvariables[51].ThecontrollerwasderivedbynumericalparameteroptimizationusingtheSequentialGradientRestorationtechnique(aniterativemethod).LeeobtainedresultsfordescentsbothfromhoverandfromforwardightandcomparedthemwiththeighttestdataoftheHERSprogram.AlthoughJohnsonandLeederivedoptimalautorotationtrajectories,theissueofautonomousau-torotationwasnotaddresseduntilalmosttwodecadeslater,specicallyin2004.InJapan,Hazawaetal.[36]developedtwoautorotationmodels,onenon-linearderivedfromrstprinciplesandonelinear.Theparametersofthelatterwereidentiedusinganeuralnetwork.APIcontrollerwasthenusedtolandasmallunmannedhelicopterinsimulation.InacontinuationoftheworkofJohnsonandLee,Aponsoetal.presentedtheirownmethodtoop-timizethetrajectoryandcontrolinputsforafull-sizehelicopterduringanautorotationlanding[8].ThemodelusedwasthesametothatJohnsonderivedandtheoptimizationproblemwassolvedusingsequentialquadraticprogramming.Thegoaloftheirworkwastoprovideautorotationguid-ancetoensurethesurvivalofsensitivesensorsanddatastoredon-boardthehelicopterinthecaseofnon-catastrophicfailures.Asignicantdrawbackoftheirmethodisthatitpre-calculatesthecontrolinputsandthetrajectorybeforeenteringtheautorotationmaneuverandasaresultisnotrobustwithrespecttomodelingerrorsandoutsideinterference.Becauseofthismismatchbetweenmodelandsimulation,aarelawwasnecessary,thatforcesthearetooccurat30ft.TheirworkwasevaluatedagainstahighdelityBell206simulator.During2008,twogroupspublishedresearchresultsonautonomousautorotation,bothusingma-chinelearningtechniques.Intherstapproach[4],thecontrollerwastrainedusingpre-recordedpilotreferenceautorotationsthatprovidedamodeloftheaircraftandthe“ideal”trajectory.Thelandingitselfwasachievedbyforcingthehelicoptertohoverat0 : 5m.Theperformanceofthe 3

PAGE 20

controllerwasdemonstratedusingasmallunmannedhelicopter(XCellTempest).However,usingahumanpilotasareferencefortrainingcanbeproblematicsincethelimitationsofahumanpilotareincorporatedintothedesignandtheperformancewillbe,atbest,asgoodasahumanpilot.Furthermoreitdoesnotallowfordi erentobjectivesandlargedeviationsfromtheconditions underwhichtheexperimentswererecorded.Thesecondapproachwasastraightforwardapplicationofreinforcementlearningtotrainacon-trollerusingtheJohnsonmodel,costfunctionandexperimentaldata[53].Thenalstate-actionspacehas10dimensionsandwascoveredusingradialbasisfunctionswhoseparameterswereupdatedusingbackpropagation.After9000epochsthenumberofradialbasisfunctionswasabout19,000andthesuccessratearound80%.Inthisapproachtheaccuracyofthesimulationmodelusedisveryimportant.Furthermorethecontrollerneedstoberepeatedlytrainedunderallpossibleconditions.Inaproblemwithhighstatedimensionalitythiscanleadtoalargecomputationalload.1.4MethodologyCurrentproposedmethodsforautonomousautorotationhaveoneormoresignicantdrawbacksthatdonotallowthemtobeincorporatedastheyareincurrentandfutureaircraft.Inordertobeusablebyawiderangeofhelicopters,acompleteautonomousautorotationcontrollerisrequired.Thiscontrollershouldbecapableofreal-timeoperationandberobusttosensorerrorsandenvi-ronmentaldisturbances.Undernormalautorotation,theobjectiveistominimizethehelicoptersinkratejustbeforetouch-down,thusavoidingdamagetotheaircraftandharmingitsoccupants.Nevertheless,inthecaseofunmannedhelicopterstheobjectiveoftheautonomousautorotationcontrollercanbedi erent. Thisisbecause–aswillbediscussedinChapter2–theprimaryconcernistominimizetheriskforhumaninjuriesorfatalities,evenattheexpenseofsignicantdamagetothehelicopteritself.Asaresulttheapproachusedinthisworkwillalsofeaturecongurablecostfunctions.Thesecostfunctionsaretunedtominimizethesinkrateataltitudeshigherthantouchdown.Thiswillgivetimetopeopletoavoidtheaircraftandcleartheareaaswellasreducethekineticenergyonimpactifsomeoneisunabletoevacuatethelandingsite.Otherkeycharacteristicsoftheproposedapproachincludetheuseofaninternalhelicoptermodel,thecapabilityofhandlingconstraintsandindependentoperationfromthenominalcontrolsystem.Theuseofamodel-basedapproachallowseasyrecongurationfordi erenthelicoptertypes, whiletheindependencefromthenominalcontrolsystemincreasesreliability.Theconstrainthan-dlingcapabilityisimportantforoperatingwithinmechanical,structuralandaerodynamictoler-ances,aswellasforachievingsafetygoals.Toachievethecharacteristicsdescribedabove,anon-linearmodelpredictivecontrol(NMPC)approachhasbeenchosen. 4

PAGE 21

ItshouldbenotedthattheNMPCisdesignedtocontrolonlytheverticalmovementoftheheli-copter.Lateral,longitudinalandangularmotionistobecontrolledbyaseparatecontroller.Thelattercontrollerisresponsibleforkeepingtheaircraftlevelandmaintainingposition,thusensuringverticalightandsafetouchdown.Althoughthenominalcontrollercanbeusedtoachievetherequiredbehavior,itmaybepreferabletouseanindependentsystemforsafetyreasons.Currentapplicationsforunmannedhelicopterstypicallyrequirehoveringatrelativelylowaltitudesofafewhundredmeters.Sincethesinkrateduringautorotationcanbesignicant,thewholemaneuvermaytakeonlyafewsecondstocompletemakingmanualinterventiondi cult,ifnot impossible.Furthermoreon-boardprocessingcapacityofsmallunmannedhelicoptersislimited,whichinturnimposesboundsonthecomputationalcomplexityofthecontrollerifreal-timeop-erationistobeachieved.TomeettheseperformancerequirementstheNMPCisaugmentedbyarecurrentneuralnetworkthatisresponsibleforthenon-linearoptimization.1.5SummaryofContributionsThesolutionpresentedinthisdissertationconcernsthedesignofacontrollerthatcanlandun-mannedhelicoptersusingautorotation.Theproposedcontrollerimprovesoncurrentsolutionsbycombiningthebenetsofmodel-baseddesigns(robustness,congurability,stateconstrainthandling)withthoseusingmachinelearningtechniques(real-timeoperation).Furthermore,thisdissertationalsopresentsamethodologyforanalyzingtheriskstemmingfromgroundimpactaccidentsinvolvingunmannedaircraft.Thismethodologyisusedtoassesstheben-etsofusingautonomousautorotationcapabilitiesandtoderivecostfunctionsthatarecompatiblewithsafetyobjectives.Themajorcontributionofthisresearchisthedevelopmentofanautonomousautorotationsys-temthatcansignicantlydecreasetherisktopeopleonthegroundfromunmannedhelicopteroperations.Thisisachievedbydesigningthecontrollercostfunctionsothatthekineticenergyisappropriatelyminimized.Nevertheless,theaforementionedsystemalsoreducestheprobabilityofdamagestothehelicopteritself.Duetothelowerrisktohumanlife,theunmannedhelicopterreliabilityrequirementscanbelow-eredwithoutcompromisingcurrentsafetylevels.Itisalsopossibletoyoverareaswithhigherpopulationdensitieswithoutviolatingsafetylimits.Asaresult,along-termbenetofthisre-searchisthatitfacilitatesfastandsafeintegrationofunmannedhelicoptersinthenationalairspacesystem.Inadditiontocommercialandmilitaryoperations,thiswillalsobenetalltheareasofunmannedaircraftresearchbyprovidingresearcherswithsaferplatformstoadvancetheirworkwith.Finally,anothercontributionisthattheproposedcontrollerisapplicabletohelicoptersofallsizes.Therefore,itispossibleinthefuturetoadaptthissystemforuseinmannedhelicopters,either 5

PAGE 22

toprovideguidancetothepilotortoperformtheautorotationautonomously.Thiswillleadtoanincreaseinhelicopteroperations'safety,especiallywithrespecttofailureconditionsthataredi culttohandlemanually,suchastailrotorfailures. 1.6DenitionsThissectionincludesdenitionsofcommonlyusedtermsinaviation.1.6.1AirTra cControl AirTra cControl(ATC)isaserviceprovidedunderappropriateauthoritytopromotethesafe, orderlyandexpeditiousowofairtra c[5]. 1.6.2AirworthinessInorderforanyaircrafttoylegallyintheU.S.,airworthinessmustrstbedemonstrated.Ac-cordingtotheFederalAviationAdministration,therearetwoconditionsthatneedtobemetinorderforanaircrafttobeconsideredairworthy;itmustconformtoitstypecerticateincludinganysupplementalcerticates,anditmustbeinaconditionthatensuressafeoperation[25].Foraircraftthatarenottypecertied,compliancewiththesecondconditionisadequate.Besidesstandardcertication,specialairworthinesscerticatesarealsoavailable,usuallyforexperimentalorspecialpurposeaircraft.1.6.3FederalAviationRegulations(FAR)AviationregulationsintheU.S.arecollectedandcodiedintheCodeofFederalRegulations,Ti-tle14,Chap.IandareknownastheFederalAviationRegulation(FAR).TheFARiscomprisedofdi erentpartsrelatedtoairworthinesscerticationfordi erentaircrafttypes(21-39),maintenance (43),registrationandmarking(45-49),pilotcertication(61-67),airspaceclasses(71-77)andoperatingrules(91-99)amongothers.1.6.4FlareFlarereferstotheendoftheautorotationmaneuverjustbeforelanding.Duringarecollectiveisincreasedtolowerthesinkrateandcushionthelanding.Itisalsocommontoincludeanincreaseinpitchtoreduceforwardvelocityifany. 6

PAGE 23

1.6.5GeneralAviationGeneralAviationisatermusedtodescribeallnon-militaryandnon-airlineying,encompassingeverythingfromrecreationalaircrafttoexperimentalaircrafttoprivatelyownedandoperatedbusinessjets[5].1.6.6NationalAirspaceSystemTheNationalAirspaceSystem(NAS)referstothecommonnetworkofU.S.airspace,airnaviga-tionfacilities,equipmentandservices,airportsorlandingareas[5].1.6.7PublicandCivilAircraftAircraftarecategorizedbasedontheirownershipaspublicorstatewhentheyareownedandoperatedbypublicentitieslikefederalagenciesorlocallawenforcement,andcivilwhentheyareownedbyindustryorprivateparties[37].1.6.8SinkRateandAutorotativeSinkRateThevelocitywithwhichahelicopterdescentsisknownasthesinkrate.Highsinkratesattouch-downcandamagethelandingsystemandcauseinjuriestopeopleon-board.Theautorotativesinkratereferstothesinkratewherenoenergyisaddedorsubtractedfromthemainrotorandisafunctionofrotorrpm.Ifthesinkrateincreasesbeyondtheautorotativevaluecorrespondingtothecurrentrotorrpm,therotorrpmwillalsoincreaseandviceversa.1.6.9UnmannedAircraftSystemThetermUAVorUnmannedAerialVehiclehasbeenusedforseveralyearsbutrecentlytheU.S.DepartmentofDefense,followedbytheFederalAviationAdministrationandtheEuropeanAvi-ationSafetyAgency,adoptedthetermUASorUnmannedAircraftSystem.ThiswasmeanttosignifythatUASareaircraftandassuch,airworthinesswillneedtobedemonstratedandthattheyarealsosystemsconsistingofgroundcontrolstations,communicationlinksandlaunchandretrievalsystemsinadditiontotheaircraftitself.TheFAAhasdenedanUnmannedAircraftorUAas[29]: Adeviceusedorintendedtobeusedforightintheairthathasnoonboardpilot.Thisincludesallclassesofairplanes,helicopters,airships,andtranslationallift 7

PAGE 24

aircraftthathavenoonboardpilot.Unmannedaircraftareunderstoodtoincludeonlythoseaircraftcontrollableinthreeaxesandtherefore,excludetraditionalballoons. ItshouldbenotedthatthetermUASdoesnotnecessarilymeananautonomoussystem.Itisactu-allymorecommonforUAStoberemotelyoperated,oftenbyapersonthatisaqualiedpilotforthattypeofaircraft.1.7DissertationOutlineThedissertationbeginswithanaccountofsafetyconsiderationssurroundingUASoperations.Thisprovidesthebackgroundmotivationbehindtheresearchcarriedout.Itisfollowedbyachap-terontheaerodynamicsofverticalhelicopterightwhichcloseswithafundamentalmodelofverticalautorotation.ThismodelisusedasthebasisforamodelpredictivecontrollerdiscussedinChapter4.TheresultsofextensivesimulationtestingoftheaforementionedcontrolleristhesubjectofChapter5.Thelastchapterofthisdissertationpresentstheconclusionsderivedfromtheresearchandfutureimprovementsuggestions. 8

PAGE 25

Chapter2:UnmannedAircraftSafetyConsiderationsThischapterpresentssafetyconsiderationsregardingUnmannedAircraftSystems(UAS)op-erations.Currentpublicpolicyreectsareluctanceofnationalaviationagenciesinintegratingunmannedaircraftwithmannedairtra c.Thisismostlyduetoconcernsonthesafetyofpeople andpropertythatarenotsu cientlyaddressedbycurrenttechnology.Asaresultanddespitethe factthatUAShaveseveralpotentialapplications,theiruseisseverelylimited.ThersthalfofthischapterdescribesthecurrentstatusofunmannedaircraftpolicyfocusingontheU.S.ItpresentsthecurrentsafetyrecordofmannedaviationandhowthatcanbethebasisofasafetyevaluationofUAS.Thesecondhalfinvestigatesinmoredetailgroundimpactaccidents.Thereductionoftheseverityandthepossibledamagesfollowingthelatterprovidesthemotivationforproposinganemergencysystemforunmannedhelicopters,whichisthesubjectofthisdisserta-tion.2.1IntroductionIntheUnitedStates,federallawgivestheSecretaryofTransportationandtheAdministratoroftheFederalAviationAgency(FAA)theresponsibilityoftheeconomicandsafetyregulationoftheaviationindustry.Tofulllthisobligation,theyaregiventheauthoritytoconductinvestigations,prescriberegulations,standards,andprocedures,andissueorders[1].Federallawassignssafetyandsecuritythehighestprioritiesinaircommerceasstatedin[3].Regardingthesafetyimplica-tionsofnewtechnologies,thestatutorymandateoftheFAArequires[2]: ...beforeauthorizingnewairtransportationservices,evaluatingthesafetyimplicationsofthoseservices;andpreventingdeteriorationinestablishedsafetypro-cedures,recognizingtheclearintent,encouragement,anddedicationofCongresstofurtherthehighestdegreeofsafetyinairtransportationandaircommerce,andtomaintainthesafetyvigilancethathasevolvedinairtransportationandaircommerceandhascometobeexpectedbythetravelingandshippingpublic. OverthelastdecadetheinterestforcivilaswellaspublicUASoperationshassteadilyincreased.StakeholdersarerequestingNationalAirspaceSystem(NAS)accesswithrulessimilartothoseformannedaviation.Ontheotherhandsafetyconcernsareworkingagainstaquickintegrationof 9

PAGE 26

UASintheNAS.ThefollowingexcerptfromatalkofMr.N.A.Sabatini,AssociateAdministra-torforAviationSafetybeforetheHouseaviationsubcommittee[22]isindicativeoftheconcernsofallaviationauthorities: ...thereisamissinglinkintermsoftechnologytodaythatpreventstheseaircraft fromgettingunrestrictedaccesstotheNAS... Despitetheseproblems,manycountrieshaveestablishedpreliminaryoperationalguidelinesthatallowlimitedoperationsintheirrespectiveNAS.ForsafetyreasonsUASightiscurrentlyseg-regatedfromtherestoftheairtra cwiththeuseofNoticestoAirmen(NOTAM)[31].Atthe sametime,nationalaviationauthoritiesincooperationwithindustry,academiaandinternationalorganizationsarepreparingroadmaps,airworthinessanddesignstandardsaswellaspolicy.2.2CurrentCerticationPathsandOperationalGuidelinesintheU.S.Currently,ightofpublicUASintheU.S.isauthorizedonaper-casebasisandafteraCerticateofAuthorization(COA)applicationisledatleast60dayspriortocommencementofoperations.TheCOAisissuedaftersubmissionofrequireddocumentationandananalysisperformedbytheFAAAirTra cDivisiontodeterminethatanEquivalentLevelofSafety(ELOS)withthatof mannedaviationisachieved.COAapplicationsforpublicUASareapprovedbasedoncompliancewithMIL-HDBK-516“Airworthinesscerticationcriteria”orotherapprovedpolicieslistedin[29]andarenormallye ectiveforuptooneyear.Itshouldbenotedthatthecerticationbasisis theresponsibilityofthepublicagencyoperatingtheUAS[76].ItisalsonoteworthythataCOAistypicallyissuedforaspecicregionofoperations,UASandoperationtype.NeverthelessanexceptiontothatrulewasmadewithanationalCOAthatwasissuedtotheUnitedStatesAirForceforoperatingGlobalHawkintheNAS,primarilyfortrainingpurposes[79].AccordingtocurrentFAApolicy,COAapplicationsareacceptedonlyforpublicUAS.CivilUAScaninsteadgetaspecialcerticateundertheexperimentalcategory,apolicyprototypedin2007[76].Currentlyexperimentalcerticatesareavailableforresearchanddevelopment,crewtrainingandmarketsurveypurposesandareissuedbasedonOrder8130.34[27].Accordingtothatorder,theapplicationmustbeaccompaniedbyaprogramletter,asafetychecklist,chartsoftheareaofoperations,trainingmanuals,pilotandmedicalcerticates.Theprogramletterdetailsthecharac-teristicsoftheUAS,thepurposeandtypeofoperations,theareaofoperations,safetymeasurestaken,etc.Beforeissuanceofthecerticate,FAApersonnelwillconductasafetyevaluationofthedocumentationprovided,followedbyanon-siteinspection.OperationsunderanexperimentalcerticatearepossibleforuptooneyearandaresubjecttothesamerestrictionsimposedforthatcategoryinFederalAviationRegulations(FAR)Part21[26]andpossiblyadditionalprovisionssetbytheFAA,specifyingotheroperationalrequirements 10

PAGE 27

[37].ItshouldbenotedthattheFAAconsidersboththeCOAandspecialairworthinesscerticateprocessesasinterimmeasures[68].Despitetheregulatoryproblems,asignicantinterestfortheuseofUASwasdemonstratedwiththenumberofCOAapplications.In2005theFAAissued50COAandmorethan100wereissuedin2006[15,92].Atthesametimeandbyearly2008,28specialairworthinesscerticateshadbeenissued[69]andseveralmorearepending[16].Neverthelessduetothehighload,theFAAdecidedin2007toreducethenumberofspecialairworthinesscerticatesissued,tofourperyear[76].UASoperationsarealsopossiblewithoutaCOAoranexperimentalairworthinesscerticateforoperatorsthathaveaccesstorestrictedairspace.Thiskindofoperationscantakeplaceincoordinationwiththeauthorityresponsibleforcontrollingthatairspaceandunderanyrestrictionsdeemednecessary.AllUASoperationsaresubjecttotheguidelinesestablishedinthe“InterimOperationalApprovalGuidance08-01”[29].ArequirementofmajorimportancetotheFAAconcernswhatisknownas“see-and-avoid”whichiscrucialinavoidingmid-aircollisionswithotheraircraft.Currentguidancepresentsthreealternatives;segregationofoperations,thepresenceofqualiedobserversunlessoperatingininstrumentightrules(IFR)conditionsoradequateon-boardseeandavoid(S&A)capability.Observerscanbeeitheronthegroundoron-boardachaseaircraft,butmustmaintainconstantcommunicationwiththeUASoperatorandassurecollisionavoidance.Inaddi-tiontothat,radiocommunicationwithAirTra cControl(ATC)shouldbeavailabletotheUAS operator.Arecommendationisalsomadeonavoidingyingovertra ckedroadsandopen-air assemblieswhileightoverpopulatedareasisallowedonlyindisasterrelieforotheremergencysituations.Toenhancesafety,guidelinesrequirethepresenceofafacilityallowingthepilottotakeovercontrol,su cientsystemredundancyorwhennotpossibleaightterminationsystem,as wellasofprovisionstorecovertheUASinthecaseoflossofthecommunicationslink.SeveralaviationagencieshavealsopreparedguidelinesforlightUAS,aircraftwithlowmaximumtake-o weight.Althoughtheweightlimitdi ersbetweencountries,theoperatingrestrictions aretypicallymorerelaxedbecauseofthelowerperceivedrisk.Suchsystemsareconsideredtheentrypointforcivilcommercialapplicationsinthefuturebecauseoftheirlowcost,portabilityandsmallerassociatedrisks[81].IntheU.S.thisprocesshasstartedwiththeformationofthesmallUASaviationrulemakingcommitteeinAprilof2008[28].AyearlaterthecommitteepublishedasetofrecommendationsforsmallUAS[30].ItwasrecommendedthatsmallUASincludeaircraftupto55lbsor25kgandshouldbedividedintofourclasseswithdi erentoperationalrequirements.Itshouldalsobenotedthatthecommitteedidnotreachconsensusonanumberofmatters[30]andasaresultitmaytakesometimebeforeitsworkisintroducedintotheFAR. 11

PAGE 28

2.3EquivalentLevelofSafetyAlthoughthegoalofassuringsafetyofoperationsisclear,specifyingthisgoalintermsofde-signandoperationrequirementshasproveddi cult.AccordingtotheJAA / EUROCONTROL UASTaskForceaswellastheEASA,oneoftheguidingprinciplesforUASregulationshouldbe“equivalence”,andbasedonthat,theyassertthefollowing[20,44]: RegulatoryairworthinessstandardsshouldbesettobenolessdemandingthanthosecurrentlyappliedtocomparablemannedaircraftnorshouldtheypenalizeUASsys-temsbyrequiringcompliancewithhigherstandardssimplybecausetechnologyper-mits. Thisprinciplehasbeenadoptedbymostnationalaviationagenciesworldwideandisknownasthe“EquivalentLevelofSafety”orELOSrequirement.Neverthelessthereisalsosomecriticismaimedattheusefulnessofthisprinciple,becauseofthedi cultyinquantifyingwhatexactlythe ELOSrequiremententails.Inanycase,todenetheELOS,requirementsofcurrentregulationsformannedaviationneedrstbeinvestigated.2.3.1MannedAviationRequirementsMannedaviationallovertheworldisregulatedthroughacodeofrequirements.Theserequire-mentsusuallytaketheformofstandardsforvariousaircraftsubsystemsandforallstagesofde-sign,manufactureandoperationthenalsystemmustadhereto[34].UseofstandardsensuresthatthecomponentsofthesystemarereliableenoughsothatthewholesystemiscompliantwithsetTargetLevelofSafety(TLS).Neverthelesscurrentregulationsalsocontainsafetytargetsfoundinparagraph1309ofcurrentCerticationSpecications(CS)orthecorrespondingAcceptableMeansofCompliance(AMC)sections.Thesetargetsaretypicallypresentedasarisksystemthatcategorizeseventsbasedontheirseverityandassignsamaximumrateofoccurrenceforeacheventcategory.Figure2.1presentstherisksystemproposedinthe1309AMCsectionofEASACS25.Therisksysteminquestiondenesfailureconditionsthatincludeinjuriesand / orfatalitiesashazardous whilethoseresultinginmultiplefatalitiesascatastrophic[21].Itthenassignsamaximumaccept-ablefrequencyofoccurrenceof10 7 h 1 and10 9 h 1 totheformerandlatterrespectively[21]. TheriskreferencesystempresentedinFigure2.1doesnotapplytoallaircraft.Variationsexistforsmallerordi erenttypesofaircraft.Thisisbecauseitwasfoundthatapplyingcertication standardsdevelopedfortransportcategoryaircrafttosmallerones,leadtounrealisticallyhighequipmentreliabilityrequirements[24].Inadditiontothat,theresultsofaccidentinvestigationsshowedthatthemaincauseofmannedaviationaccidentsispiloterror.Assuch,highequipment 12

PAGE 29

Catastrophic Hazardous Major Minor Probable > 10 5 h 1 Remote < 10 5 h 1 Extremelyremote < 10 7 h 1 ExtremelyImprobable < 10 9 h 1 Figure2.1:Riskreferencesystemforlargemannedaircraft(thegrayedareassignifyunacceptablerisk).Source:[21]reliabilitywouldhaveonlyaminore ectonoverallaviationsafety.In1999theFAAissuedAC 23.1309-1CthatcontainsAMCforaircraftcertiedbasedonFARPart23.Withthisdocument,fourclassesofaircraftwithinthatcategorywheredened,eachwithdi erentacceptableprobabilitiesforfailureconditions,asshowninTable2.1.Table2.1:FARPart23aircraftclassesandcorrespondingacceptablefailureconditionprobabilitybasedonseverityasdenedinAC23-1309-1C.Source:[24] AircraftclassMinorMajorHazardousCatastrophic ClassI( < 2 ; 720kg,SRE)10 3 h 1 10 4 h 1 10 5 h 1 10 6 h 1 ClassII( < 2 ; 720kg,STE,MRE)10 3 h 1 10 5 h 1 10 6 h 1 10 7 h 1 ClassIII( > 2 ; 720kg,SRE,MRE,STE,MTE)10 3 h 1 10 5 h 1 10 7 h 1 10 8 h 1 ClassIV(commuter)10 3 h 1 10 5 h 1 10 7 h 1 10 9 h 1 UseoftheriskreferencesystememployedinmannedaviationforUASisnotstraightforwardbecauseofthewiderangeofUASsizesandcharacteristics.Inadditiontothat,UASdependontheon-boardightcontrolsystemand / orthecommunicationlinktooperate,introducingadditional failuremodesthatmayincreasethetotalnumberofaccidentsforthesamereliabilityrequirement.Nevertheless,evenifsaidrequirementsareadaptedastheyaretoanumberofUASclasses,theymaystillleadtounnecessarilyhighreliabilityrequirements.ThisisduetothefactthatUASdonotcarrypassengersand,asaresult,theprobabilityofinjuriesandfatalitiesafteranaccidentisgreatlyreduced,comparedwiththatofgeneralaviationortransportaircraft.Theaveragenumberandseverityofinjuriesperaccidentisalsoexpectedtobelower.Thefollowingsectionsdetailsomeofthedi erencesbetweenUASandmannedaircraftthatneedbetakenintoaccountwhen deningtheELOSrequirement. 13

PAGE 30

2.3.1.1ApplicationsTraditionally,safetylevelshavebeenconsideredundertheassumptionthatthevastmajorityofmannedaircraftyinpoint-to-pointoperationstransportingpeopleorgoods.Thisimpliesthatasignicantportionoftheirighttimeisspentoverlessdenselypopulatedareas.Thisassumptionhasbeentakenintoaccountforaviationsafetyregulationsloweringtherequiredreliabilitylevels[20],butdoesnotholdforUAS.Thisisespeciallytrueforsurveillance / patrollingapplications, whereUASarerequiredtoloiteroverspecicareas.Itisobviousthatifsuchareasundercon-siderationhaveverylowpopulation(borders,forests,etc.),then,thesafetylevelrequirementobtainedformannedaviationwouldbeover-conservative;onthecontrary,iftheUASisrequiredtoloiteroverametropolitanarea,thissafetylevelwouldbeinadequate.2.3.1.2SacricabilityEarly,abnormalighttermination,regardlessofwhetheritiscontrolledornot,isamajorconcernformannedaviationduetothehighprobabilityoffatalitiesassociatedwithit.Anyfailurecon-ditionthatcanleadtosuchanaccidentistypicallyconsideredcatastrophicandthelowestprob-abilityofoccurrenceneedstobedemonstrated.Thisalsoentailsimposingthestrictestreliabilityrequirementsonrelatedequipment.InthecaseofUASanuncontrolledgroundimpactmaystillbeconsideredacatastrophicaccident.Neverthelessitisacceptable–andpossiblydesirable–toallowaUAStocrashinacontrolledmanner,ifthatwouldminimizetherisktopeopleandproperty.2.3.1.3PilotPhysicallyRemovedfromCockpitAnaircraftpilotisintimatelyawareofthesurroundingsaswellastheperformanceoftheaircraft.Vibrations,smells,noise,controllerfeelandotherindicatorsofpossiblefailuresareavailable.Thepilotisalsotheultimateauthorityoftheaircraft,beingabletoassumefullcontrolofeveryaspectofitsoperation.OntheotherhandaUASoperator,beingphysicallyremovedfromthecockpit,haslimitedpercep-tionoftheaircraftstate.ThisisbecauseonereliesonlyondatasentbackfromtheUAS,whichmaynotprovideimportantorneededinformationandlacktheaforementionedsensoryindicators[7,35].ForremotelyoperatedUAS,thisseparationhastheaddedside-e ectthattheremaybe alagbetweentheUASsensingsomethingandexecutingacorrection,sinceinformationmustberelayedtothegroundcontrolstationandback. 14

PAGE 31

Furthermore,ithasbeensuggestedthatsincethepilotisinasafeenvironmentandlife-threateningconsequencesfrommistakesarenotexpected,piloterrorsmaybemorefrequent[39].Similarly,maintenancepersonnelmaybecomecomplacentandnegligentintheirduties[39].Finally,removalofthepilotgeneratesadditionalrequirementsonthesafetyofthegroundcontrolstation,whichisavitalpartofaUAS,replacingtheroleofthecockpitinmannedaircraft.Asaresultthegroundcontrolstationandthelinkbetweenitandtheaircraftmustbesecuredfromnaturaldisasters,interferenceandotherdisruptions.2.3.1.4Take-o Weight Mannedaircrafthaveawiderangeoftake-o weights,startingatabout100kgforultralight,unpoweredvehiclesandabouttwicethatforpowered.Generalaviationaircraftaretypicallyseveraltimesheavierandthelargesttransportaircrafthavereached600tinthecaseoftheAirbusA380.Ontheotherhand,UASspantheentirespectrumfromafewgramsandupto–currently–12t.ThismeansthatUAScoveranumberofcurrentmannedaviationaircraftclassesandseveralFARparts.Inaddition,thereisaclassofvehicles,lighterthan100kg,forwhichthereisnoequivalentmannedaviationregulation,besidestheAC21-97forwhichFAAhasalreadydeclaredthatitisapplicabletorecreationalR / CmodelingonlyandnottoUAS. 2.3.1.5PayloadInsteadofcargo,severalUASapplicationslikeweathermonitoring,communicationsrelayingandlawenforcementwillrequiretheuseofsophisticatedsensors,communicationdevicesorotherequipment.Thispayloadmaybeintricatelyconnectedtotheightcontrolsystemandcapableofchanginghighlevelmissioncommandsorgeneratingnewwaypoints.Asaresultnewhazardsemergebecauseofthepossiblecontrolfailureinducedbythepayload[35].Ontheotherhand,thepayloadmayalsobeusedtoprovideredundancyformainaircraftsensorsthusmitigatingotherhazards[35].2.3.2UASAccidentTypesSincefailurefrequencyrequirementsprescribedformannedaircraftofthesamesizecannotbeuseddirectly,othermeanstoderivesuchrequirementsforUASneedbeemployed.Adi erentapproachfrequentlyusedinsafetyengineeringistodenesafetyconstraintsforaspecicaccidentbasedonthedesiredlikelihoodoftheworstpossibleoutcome[66],whichcaninturnbeusedtodeterminemaximumfailurefrequency.ThisrequiresaninvestigationofthehazardsinherentinUASoperationsandthetypesofaccidentsthatmayoccur.Specicallythreeprimaryaccidents 15

PAGE 32

canbeidentied:unintendedorabnormalsystemmobilityoperation[78],mid-aircollision,andearlyighttermination[14].UnintendedorabnormalmobilityoperationreferstoaccidentsthatoccurwhentheUASisstillontheground.InthiscasetheUASmaymoveunexpectedly,potentiallyseriouslyinjuringgroundcrewmembers.SuchaccidentsusuallyhappenbecauseofoperatorerrorandmayoccurwhentheUASoperatordoesnothaveaviewoftheUASandincorrectlyassumesthateveryonehasclearedthearea.Mid-aircollisionsmayoccurbetweentwoUASorbetweenaUASandamannedaircraft.De-pendingonthenatureofthecollisiontheycanresultinthelossofoneorbothoftheaircraft.Asecondaryaccidentusuallyfollowingmid-aircollisions,isgroundimpactofdebristhatmayinjurepeopleanddamageproperty.Finally,earlyighttermination,eithercontrolledoruncontrolled,willresultingroundorwaterimpact.Undercontrolledightterminationitmaybepossibletoselectthepointofimpactandpossiblythespeedandorientationoftheaircraft,thusreducingtheprobabilityoffatalitiesaswellasdamagestopropertyandtheaircraftitself.Potentialdamagesresultingfromtheseaccidentsincludeinjuryorfatalityofpeopleonthegroundoron-boardanotheraircraft,damageorlossofthevehicleanddamagetoproperty.Anindirectdamageisenvironmentalpollutioneitherfromthepayloadoftheaircraftorasaresultoffuelleakageand / orrefollowingtheaccident.ThisisespeciallyimportantforUASthatwillcarry chemicalstoxictohumanbeings,forexamplethoseusedinagriculturalapplications.Apossibledamagethatisoftenignoredisthatofsocietalrejectionoroutragethatmaydisruptfutureoperations.Thiscanoccurasaconsequenceofahighaccidentrate(evenifnoinjuriesoc-cur)oriftheaccidentinvolvescultural / societalsensitiveareaslikenationalparksormonuments, schoolsandchurches.Figure2.2summarizespossibleaccidentsandcorrespondingdamagesstemmingfromtheoperationofUASintheNAS.2.3.3DerivationofanELOSforUASAsmentionedintheprevioussection,theELOSforUASshouldbebasedontheworstpossibleoutcomewhichistheoccurrenceofoneormorefatalities.Currentmannedaviationregulationdoesnotimposelimitsonthefrequencyoffatalitiesasitdoesforaccidents.Nevertheless,astatisticalanalysisofhistoricaldatacanprovidevaluableinsightonthefatalityratesofmannedaviationandbethebasisfordeningtheELOSforUAS.AnanalysisofaccidentdatafromtheNationalTransportationandSafetyBoard(NTSB)rangingfrom1983to2006ispresentedinTable2.2.Itshouldbenotedthattheexactnumbersmayvarydependingonthetypeofaviation(general,regional / commuter,aircarrier)andtheperiodoverwhichthedataare 16

PAGE 33

Ground Impact Unintented Movement Mid-air Collision Falling Debris and / or Impacton environment Impacton society Damage / Loss ofsystem Damageto property Injuryor fatality PrimaryAccidentsSecondaryAccidents Figure2.2:PrimaryandsecondaryaccidentsthatcanresultfromtheoperationofUASandtheirpossibleoutcomes.averaged[13].Thisispartlyduetosignicantvariationinthenumberofaccidentsfromyeartoyear,asshowninFigure2.3.Table2.2:FatalityratesfromallaccidentsbasedonanalysisofNTSBaccidentdata[62]between1983and2006. RatesperhourAirCarrierCommuterGeneralAviationTotal Accident2 : 43 10 6 h 1 2 : 37 10 5 h 1 8 : 05 10 5 h 1 5 : 05 10 5 h 1 Fatalitiesaboard8 : 68 10 6 h 1 1 : 64 10 5 h 1 2 : 77 10 5 h 1 2 : 06 10 5 h 1 Groundfatalities3 : 37 10 7 h 1 8 : 30 10 6 h 1 6 : 54 10 7 h 1 1 : 31 10 6 h 1 2.4GroundImpactRequirementsAlthoughthereareothertypesofaccidents,theautonomousautorotationsystemisdesignedtore-ducetheriskofgroundimpactaccidents.Intheprevioussectionthefatalityratefollowingmannedaviationaccidentswasinvestigated.AssuminganequivalentrisklevelforUAS,appropriaterelia-bilitylevelscanbedetermined.Toaccomplishthisafatalityprobabilitymodelwillrstneedtobederived.Thismodelwillalsoprovidenecessaryinsightonthedesignoftheautorotationcontroller 17

PAGE 34

n rrn nnnnn Figure2.3:Fatalityratesfromgeneralaviation,commuterandaircarrieraccidentsasafunctionoftime.BasedonanalysisofNTSBaccidentdata[62]between1983and2006.sothattheriskoffatalitiesisreduced.ThefollowingsectionspresentwhatanequivalentlevelofsafetyforUASis,followedbyamethodologyondeterminingappropriatereliabilitylevelsusingafatalityprobabilitymodel.2.4.1UASEquivalentLevelofSafetyIndeterminingthefatalityraterequirementaftergroundimpacts,specialconsiderationshouldbegiventothefactthatUASareunmanned.Thismeansthatonlythenumberoffatalitiesonthegroundaretobetakenintoaccount.AccordingtoTable2.2thisnumberrepresentsonlyaverysmallpercentageofthetotalfatalities,about6%.Thegroundfatalityratecalculatedisintheorderof10 6 h 1 ,althoughamoreconservativeELOScanbederivedbasedonthegroundfatalityrate ofaircarrierswhichisintheorderof F f = 10 7 h 1 ItshouldbenotedthatTable2.2considersallaccidents.Analternativeanalysiscanbeusedbyconsideringonlyaccidentswhereanin-ightcollisionwithterrainorwateroccurred(approxi-mately35%ofthetotal).TheupdatedfatalityratesbasedonNTSBdatafortheperiod1983to2006,arepresentedinTable2.3.InthiscasetheproposedELOSwouldbeintheorderof F f = 10 8 h 1 ,althoughitdoesnotincludefatalitiesafteremergencylandings,ditchingandothersituations.Ifthelatterareincluded,theELOSiscloserto F f = 10 7 h 1 asshowninTable2.4. Forthesubsequentanalysisthe F f = 10 7 h 1 isgoingtobeused.Howeveritshouldbenoted thatlowerorhigheracceptablefatalityrateshavealsobeenproposed.In[84],althoughanELOS 18

PAGE 35

Table2.3:Fatalityratesforaccidentswhereanin-ightcollisionwithterrainorwateroccurred.BasedonanalysisofNTSBaccidentdata[61]between1983and2006. RatesperhourAirCarrierCommuterGeneralAviationTotal Accident2 : 06 10 7 h 1 9 : 33 10 6 h 1 2 : 84 10 5 h 1 1 : 77 10 5 h 1 Fatalitiesaboard4 : 71 10 6 h 1 1 : 32 10 5 h 1 2 : 16 10 5 h 1 1 : 55 10 5 h 1 Groundfatalities9 : 84 10 8 h 1 2 : 86 10 8 h 1 4 : 46 10 8 h 1 5 : 99 10 8 h 1 Table2.4:Fatalityratesforaccidentswhereoneoracombinationofin-ightcollisionwithterrainorwater,hard / forcedlanding,runwayoverrunorditchingoccurred.BasedonanalysisofNTSB accidentdata[61]between1983and2006. RatesperhourAirCarrierCommuterGeneralAviationTotal Accident5 : 64 10 7 h 1 1 : 56 10 5 h 1 5 : 18 10 5 h 1 3 : 21 10 5 h 1 Fatalitiesaboard4 : 85 10 6 h 1 1 : 46 10 5 h 1 2 : 41 10 5 h 1 1 : 71 10 5 h 1 Groundfatalities1 : 01 10 7 h 1 7 : 63 10 8 h 1 8 : 43 10 8 h 1 8 : 89 10 8 h 1 of10 7 h 1 wasderived,atargetof10 8 h 1 isproposedtoaccountforthefactthatthebenets ofUASoperationsarenotevidenttothegeneralpublicandasaresultthetoleranceforfatalitieswillbelower.In[14]analysisisbasedonmultipleacceptablefatalitylikelihoodsrangingfrom10 6 h 1 to10 9 h 1 .TheRangeSafetyCriteriaforUASproposedafatalityrateof10 6 h 1 or lessbasedonaU.S.Navyaccidentsurvey[66],buttheirrequirementsareformilitaryoperationsthatallowhigherfatalityrates.FinallyNATOadoptedaTLSof10 6 h 1 forcatastrophicUAS accidents[43],whichcorrespondstoanequalorhigherfatalityrate.Althoughstricterrequirementsmaybeattractive,theycanseriouslyimpedecommercializationofUASaswellastheirintegrationintheNAS.Therefore,aconservativeevaluationoftheriskfromemerginghazardsispreferable,sinceitcanbelateraccommodatedasighthoursaccumulateandcondenceinriskestimatesimproves.2.4.2TargetReliabilityLevelSincetheELOShasbeendened,theTLScanbedeterminedasthemaximumacceptablefre-quencyofagroundimpactaccident F GI basedontheexpectedrateoffatalities( F f )andthe expectednumberoffatalitiesgivenagroundimpact,as:(2.1) F GI = E (fatalities j groundimpact) 1 F f In(2.1)the E (fatalities j groundimpact)termhastobecalculated.Thistermisafunctionofseveral parameters,includingthenumberofpeopleatthecrashsiteandtheenergyoftheimpact.The 19

PAGE 36

expectednumberoffatalitiesafteranaircraftgroundimpactcanbedeterminedbasedontheprob-abilityofafatalinjuryforpeopleexposedtothecrash,using:(2.2) E (fatalities j groundimpact) = N exp P (fatality j exposure) where N exp isthenumberofpeopleexposedtothatimpact. Assumingauniformpopulationdensity, N exp canbecalculatedastheproductofthepopulation density( p )bythesurfaceoftheareaa ectedbythecrash( S ): (2.3) N exp = S p Thereareseveralwaystodetermine S basedonimpactcharacteristics.Foraverticalcrash,this areamaybeapproximatedbythefrontalareaoftheaircraftaugmentedbyasmallbu ertoaccountforthewidthofanaveragehumanbeing,typicallydenedas0 : 6m[65].Foraglidingdescentitcanbeapproximatedby(2.4),wherethewingspanandlengthoftheaircrafthavealsobeenincreasedbythewidthofanaverageperson[14]:(2.4) S = Width aircraft Length aircraft + Height person sin( glideangle ) # Inthediscussionthatfollows,theminimumrequiredtimebetweengroundimpacts( T GI ; min )will beusedinsteadofthefrequencyofgroundimpactaccidents.Thisisbecause,liketheMeanTimeBetweenFailures(MTBF),itrepresentsamoreintuitivemeasureofrequiredreliability. T GI ; min istheinverseofthegroundimpactaccidentfrequencyandcanbecalculatedaftercombining(2.1)and(2.2),obtaining: T GI ; min = F GI 1 ; max = S p P (fatality j exposure) F f (2.5)Asaresult,whenthenumberofpeopleexposedtothecrashisknown,thefatalityprobabilitygiventheexposureneedstobecalculated.Theprobabilityoffatalitycanbeestimatedasafunc-tionofthekineticenergyonimpact,althoughotherparametersmayalsoinuenceit.Unfortu-nately,thereisnoagreementorconsensusintheliteratureonhowthisrelationship / functionisbest dened.AccordingtostudyresultspresentedinRCC323[66],a1lbsobjectwithkineticenergyof50Jhasaprobabilityofcausingafatalityof10%,whileformorethan200Jthatprobabilityrisestoabove 20

PAGE 37

90%.AccordingtostudyresultspresentedinRCC321[67],thecorrespondingkineticenergyes-timatesforanimpactofa1 ; 000lbsobjecttothetorsoareapproximately1 : 2kJand3 : 5kJ,respectively,adi erenceofatleastanorderofmagnitudefromthepreviousmodel.Thesedi erences canbeattributedtothefactthatkineticenergydoesnotcorrelatewellwithfatalityprobabilitiesestimatedfromaccidentdata[67].Asaresult,impactofobjectsofdi erentmasscanhavedifferente ects,evenifthekineticenergyimpartedatimpactisthesame.Nevertheless,alogistic curvebasedonthekineticenergyimpactisgenerallyconsideredagoodmodelforfatalityrateestimation[67].Additionally,averyconservativelimitisproposedin[67]of15Jfordirectimpactofdebristhatisconsideredtocorrespondtozerofatalityprobability.Itisalsostatedthataforementionedmodelsarebasedondirectimpactofanobjecttoapersonwithouttakingintoaccountthatduringanimpact,someoftheimpactenergymaybeabsorbedbybuildings,trees,vehiclesorotherobstacles.In[84]theprobabilityoffatalityisgivenasapenetrationfactorthatdependsonthecharacteristicsoftheUASandtakesintoaccountshelter-ing.ButobservingthefourexamplepenetrationfactorsgivenbyWeibel[84]asillustratedinFigure2.4forcomparisonpurposes,itcanbearguedthatWeibel'sestimateforsmallervehiclesisoverconservative,sinceafatalityprobabilityof5%isassignedtoavehiclethatweighslessthan100g,while,atthesametime,themodelunderestimatesthelethalityoflargervehicles.Nomethodisprovidedtoconsistentlyestimatethepenetrationfactor(parameter)forotherUAS. 0 0 : 2 0 : 4 0 : 6 0 : 8 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9ProbabilityofFatalityKineticEnergyinJoules RCC323RCC321 Weibel Figure2.4:TheprobabilityoffatalityasafunctionofkineticenergyimpactasestimatedbyWeibel[84]andmodelsderivedinRCC321[67]andRCC323[66].Consideringallpreviousjusticationsandobservations,andbasedontheformofthefatalitycurvesderivedin[66,67],avariationofthelogisticgrowthmodelisproposedtoestimatethe 21

PAGE 38

probabilityoffatality( P (fatality j exposure))asafunctionofkineticenergyatimpact( E imp )that alsotakesintoaccountsheltering:(2.6) P (fatality j exposure) = 1 1 + q f f f E imp 1 4 f s Themodelpresentedin(2.6)growsasafunctionof E imp similarlytotheexistingmodelsin[66, 67],butalsoincludesaparametertoincreaseordecreasetherateofgrowth.Thisparameteriscalledtheshelteringfactor f s 2 (0 ; 1]anddetermineshowexposedthepopulationistoanimpact. Itisafunctionoftheamountofobstaclesinthecrashtrajectoryoftheaircraftthatcanabsorbimpactenergyordeectdebris,aswellastheabilityofpeopletotakeshelterbehindsuchobsta-cles.Highervaluesmeanbettershelteringandalowerprobabilityoffatalityforthesamekineticenergy.The f parameteristheimpactenergyrequiredforafatalityprobabilityof50%with f s = 0 : 5andthe f parameteristheimpactenergythresholdrequiredtocauseafatalityas f s goesto zero.Forsmallvaluesof f s andappropriatelychosen f ,(2.6)approximatesaccuratelythecurves in[66,67].Figure2.5presentsthecurvesgeneratedfromtheproposedmodelforvariousvaluesofthe f s parameter. ThekineticenergyatimpactisafunctionofimpactspeedthatmayvarydependingontheUASandthedescentcharacteristics.Ausefulconservativeestimateoftheimpactspeedisterminalvelocity.Thekineticenergyatterminalvelocityiscalculatedbyequalizingthedragforcewiththegravitationalforce[17],andisgivenby:(2.7) E imp = M 2 g p A cs C d In(2.7),the A cs andthe C d parametersarenotalwaysavailablebecausetheyvarywiththeorientationoftheaircraftduringadescent.Theequationabovealsoassumesafreefallandasaresultacorrectionneedstobemadeforthethrustprovidedbytheenginesiftheyarestilloperational.In[20,34,44],theuseofthemaximumoperatingvelocity( v op )increasedby40%isproposedto simplifycalculations,asshownin(2.8):(2.8) E imp = Mv op 2 InAppendixAacasestudyispresented,wheretheTLSwithrespecttogroundimpactofvarioustypesofUASiscalculatedbasedonthemodelpresentedabove.Abriefinvestigationofthesensi-tivityofthemodelwithrespecttoparameterchangeisavailableinAppendixB.ThemethodologyaboveresultsinaTLSforgroundimpactaccidentsthatconcernstheentireplatform.Todeterminethereliabilityrequirementsforeachsystem,subsystemandcomponent, 22

PAGE 39

0 0 : 2 0 : 4 0 : 6 0 : 8 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9ProbabilityofFatalityKineticEnergyinJoulesf s = 0 : 1fs= 0 : 4f s = 0 : 5fs= 0 : 6 Proposed RCC323RCC321 Weibel Figure2.5:Theprobabilityoffatalityasafunctionofkineticenergyimpactfortheproposedmodelwith f = 10 6 J, f = 100Jandforseveralvaluesof f s .Forcomparisonpurposesthe estimatesofWeibel[84]aswellasthemodelsofRCC321[67]andRCC323[66]aregiven.thevariousfailuremodesneedtobeidentied,theirprobabilitiesofoccurrencecalculatedandtheTLSmappedbacktoeachofthem.ThisproceduredependsheavilyontheexactcharacteristicsoftheUASinquestionandassuchnogeneralestimatescanbegiven.2.5ConclusionsToensureanappropriatelevelofsafetyinUASoperationsthereareseveralmeasuresthatcanbetaken.Theobvioussolutionistoincreasereliabilitysothatfailuresaresu cientlyinfrequent. NeverthelessthismaysignicantlyincreasecostsandmayevenbeimpossibleforsmallUASthathavelimitedpayloadcapacity.ThealternativeisforUAStofailgracefully.TheFAAdenesacontinuedsafeightandlandingrequirementformannedaircraftundernoncatastrophicfailuresas[23]: “Thecapabilityforcontinuedcontrolledightandlandingatasuitableairport,pos-siblyusingemergencyprocedures,butwithoutrequiringexceptionalpilotskillorstrength.Someairplanedamagemaybeassociatedwithafailurecondition,duringightoruponlanding” ItisverylikelythatthisrequirementwillbeusedforUASaswell.Inadditiontoamandateforfaulttoleranceinightcontrolsystemsthiswillalsodemandtheuseofappropriatetechnologytoallowgracefulfailures.Thiscanbeaccomplishedbycontrollingightterminationinsucha 23

PAGE 40

waythattheaircraftlandssafelyorifthatisnotpossibleatleastminimizestheriskofinjuriestopeopleontheground.Thelattercanbeachievedbytryingtoavoidpeopleand / orreducethe kineticenergyatimpacttolevelsthatcanbeconsideredsu cientlysafe. Asaresulttheintroductionofautonomousautorotationinunmannedhelicoptersisexpectedtoallowcompliancewiththecontinuedsafeightandlandingrequirement.ThisinturncanpavethewayforgreaterpenetrationofsuchsystemsintheNAS. 24

PAGE 41

Chapter3:HelicopterDynamicsModelBeforethederivationofthecontrolleritself,amodelofhelicopterautorotationisrequired.Thischapterwillbeginwithanoverviewofthebasicdynamicsandcontrolofhelicopters,followedbyananalysisofaxialightaerodynamics.Forwardightandmaneuveringwillbeomittedsincetheyarenotofinterestinthecaseofverticalautorotation.Afterthebasicsofaxialightarepre-sented,thecaseofverticalautorotationwillbeinvestigatedandthemajorfactorsthata ectthe performanceofthehelicopterafterlossofmainrotorpowerwillbemodeled.Thischaptercon-cludeswithagenericmodelofverticalautorotation.Underverticalautorotation,nolongitudinalorlateralmovementisexhibitedbythehelicopter.Asaresult,theframeofreferencewillbebasedonasingleaxiswithpositivepointingtowardstheground.3.1IntroductionHelicopteraerodynamicsarecomplexanddi culttomodelcomparedtothedynamicsofxed wingaircraft.Thisisbecauseoftwomajorfactors;theuseofasingleactuatortocontrolmove-mentandbecausehelicoptersoperateclosetowake.Inxed-wingaircrafteachdesiredmovement(up-down,left-right)isaccomplishedwiththeuseofaseparateactuatorsurfaceonthewingsandonthetailn.Inthecaseofhelicopters,themainrotorisresponsibleforlongitudinal,lateralaswellasverticalmovement.Furthermore,duringtheightofxed-wingaircraftthewakegener-atedbytheaerodynamicsurfacesisleftbehind,whileinhelicopterstherotoroperatesveryclosetoitsownwakeandinsomecasesevenwithinit.Thisresultsinvariationsinliftanddragonthebladesthatinuencehelicopterperformance.Asaresult,typicalhelicoptermodelsarebasedonamixtureofanalyticalaerodynamicequationsandempiricalrelationshipsandcorrectionfactorsthatmaybevalidonlyundercertainassump-tionsorincertainoperatingregions.3.1.1DynamicsThehelicopterachievesliftbyimpartingadownwardvelocitytoalargemassofair.Thisisac-complishedbyrotatingblades,thatconstitutethemainrotor.Thepowerrequiredtomovethe 25

PAGE 42

air,iscalledinducedpower.Toachieveverticalmotion,itispossibletovarythespeedofthemainrotor,thusinducingahigherorlowerairvelocitychange.Unfortunatelyrotorinertiamakesaccuratecontrolofliftusingthismechanismimpossible[83].Normallyverticalmovementisachievedbychangingtheangleofattackoftheblades.Thisoccursbymountingthebladesontherotorwithbearingsthatallowsthemtoturn,amechanismknownasfeathering[83].Astheangleofattackincreases,theliftincreases,untilitreachesapointwheretheairowaroundthebladeseparatesandliftislost[83].Itshouldalsobenotedthatinincreasedanglesofattack,thepowerrequiredtorotatethebladesishigherduetoincreaseddrag.Thisisknownastheprole-dragpowerrequirement.Inordertoachievetranslationalmovement,itispossibletoapplyacyclicvariationontheblade'sangleofattack.Allowingthebladestooscillatesinusoidallyatthesamefrequencyastherotorturns,resultsinanincreaseinliftononesideoftherotoranddecreaseintheother,whichinturnmakestherotordisktiltandthehelicoptertoaccelerateintheappropriatedirection[83].Move-mentofthefuselagethroughtheairresultsindragthatcorrespondstoathirdpowercomponent,knownasparasitepower.Drivingtherotorresultsinaturningmomentinducedonthehelicopterfuselage.Thisproblemcanbesolvedusingdi erentdesignmethodologies.Inthetypicalhelicoptercongurationof Figure3.1thetail-rotorisusedtocounterthetorque.Anotherpopulardesignistohavetwomainrotorsspinninginoppositedirections.Althoughthemainrotorinducesonlyaturningmoment,theo -centerpositionofthetail-rotorresultsalsoinasidewaysmovementcalledtail-rotordrift[83]. Thetail-rotorisdesignedsimilarlytothemainrotorandallowscontrolofthecollectivealthoughnotthecyclic[83].Achangeinthetail-rotorcollective(alsoknownastail-rotorpitch)allowsthepilottorotatethehelicopterfuselagewithrespecttoaverticalaxispassingthroughthecenteroftherotordisk. Tailrotor Mainrotor Figure3.1:Thesinglemainrotorwithtailrotorhelicopterdesign.Ithastwocontrolsurfaces,themainandtailrotors.Otherhelicoptertypesmaynothaveatailrotorormayhavemorethanonemainrotor. 26

PAGE 43

3.1.2ControlHelicoptercontrolvectorsaretypicallycomprisedoffourcomponents:collective,lateralcyclic,longitudinalcyclicandtailrotorpitch(orpedal)[19].Itshouldbenotedthatinsomecasesthephysicalactuatorsthatcorrespondtoeachoftheaforementionedcontrolinputsarenotpresentandinsteadthecontrolise ectedindirectly,bythecombinationoftwoormoreactuatorswhichin turncana ectmorethanonecontrolinputatthesametime[19]. Verticalcontrolisachievedbyadjustingthecollectivepitchorthemainrotorrpm,althoughthelatterisnormallykeptconstantthroughouttheight.Directionalcontrol(controlofthehelicopter'srotationaroundtheverticalaxis)isachievedbyadjustingthetail-rotorpitch.Finally,lateralandlongitudinalcontrolisachievedbytherespectivecyclicactuatorsthattilttherotorplane,andasaresultthethrustvector,inthedirectionoftheintendedmovement.Thefourcontrolvectorsarenotuncoupled.Forexample,anincreaseordecreaseincollectivepitch,requiresacorrectionofthetail-rotorpitchtoaccountforthechangeintheturningmomentduetothechangeinrotorthrust[33].Afterachangeinthetail-rotorpitch,achangeinlateralcol-lectiveisalsoneededtoaccountforthechangeindrift[83].ThecouplingofthecontrolvectorsisvisualizedinFigure3.2,whichshowsthe6degreesoffreedomofthehelicopterandwhichcontrolisa ectingmotionineachoneofthem. Lateralcyclic,Tail-rotorpitch,Collective Longitudinalcyclic Lateralcyclic Tail-rotorpitch,Collective Collective,Longitudinalcyclic,Lateralcyclic LongitudinalcyclicCollective Figure3.2:Helicoptershave6degreesoffreedom.Motionineachoneistypicallyinuencedbymorethanonecontrolinput. 27

PAGE 44

3.2HelicopterFailuresandRecoveryAlthoughthereisawiderangeofpossiblefailuresahelicoptercansustain,thisresearchfocusesonproblemsinthemaincontrolsurfaces.Asaresultthenexttwosectionswillprovideabriefoverviewofthefailureconditionsa ectingthemainandtailrotors.Thiswillbefollowedbya descriptionofautorotation,arecoverymaneuverusedbyhelicopterpilotstolandtheiraircraftinthecaseofseriousproblems.3.2.1MainRotorFailuresAsmentionedinSection3.1,helicoptersrelyonthemainrotorbothtoachieveliftaswellasforlateralandlongitudinalcontrol.Asaresult,afailureinthatsystemcanresultinacatastrophicaccident.Mainrotorfailurescanbeseparatedintodi erentcategoriesdependingontheire ects.Onecategoryconcernsfailuresresultingfromdamagetothemainrotorbladesusuallyafteracollisionwithanobstacle.Thistypicallyresultsinanuncontrolledightterminationsincebothliftandthrustvectorcontrolisessentiallylost.Safeightterminationisalsounlikelyinthecasewhenthecon-trollineshavebeensevered.Thiscanoccurduetomaterialfatigueorfaultsinothersubsystemsandresultsinlimitedornocontroloftheaircraft.Amanageablefailurecategoryrelatestolossofthrust.Thismaymanifestasalossofrotorrpmeitherduetoenginefailureorbecauseofaprobleminthetransmissionsystem.Inthiscasecon-tinuedightisnolongerpossibleandthehelicopterwillquicklylosealtitude.Neverthelessthisfailuretypecanbeaccommodatedandthehelicoptercansafelylandusingautorotation,providedthatcollectiveandcycliccontrolisnota ected. 3.2.2TailRotorFailuresTailrotorfailuresaremanifestedviatwomainmechanisms;afailureinthetailrotordriveorasacontrolfailure[70].Theformeristypicallyattributedtofatigueorexternalimpact,whilethelatteraremoreoftenduetoseveredcontrollinesandusuallyresultinpartialortotallossoftailrotorthrustcontrol.Intermsofdynamics,tailrotorfailurescanbecategorizedbasedonthethrustproducedafterthefailureasstuckoructuatingpitch.Stuckpitchfailurescanbefurthersubdividedintolow,trimandhighpitch.Completelossoftailrotorthrustduetodrivefailurecanbeconsideredasanextremecaseofalowpitchstuckfailure. 28

PAGE 45

Thee ectoftailrotorfailurescanbedividedinthreephases:(a)transientthatisinvolvedwith theinitiale ectsofthefailureconditionandtherecoverytosafeight,(b)maneuveringand(c) landing[70].Inthecaseofcompletelossoftailrotorthrust,thehelicopterwillstartturningtotheright.Ifthehelicopterwashoveringoryingatlowairspeeds,signicantpositiveyawrateswillappear.Ontheotherhand,iftherewasforwardspeed,thenalthoughrightyawmayremainsmall,positiverollandnegativepitchwillalsobeexperienced.Inthecaseofmanualoperation,afterthepilotcompensatesfortheroll,thehelicopterwillexperienceleftside-slip.Forhighairspeeds,theside-slipmaybecomesevereenoughtocauselossofcontrolora ectthestructuralintegrityofthe aircraft.Whenastucktailrotorpitchfailureoccurs,thee ectdependsonthetailrotorthrustatthetime ofthefailure.Ifthepitchisstuckhigh,thehelicopterwillexperiencenegativeyawratesandsuc-cessfulrecoveryisdi cult,whileifitisstucklowthee ectsaresimilartolossoftailrotorthrust althoughsignicantlylesspronouncedbecausethetailrotorstillprovidessomecompensationformainrotortorque.Themostbenigncaseiswhenthetailrotorpitchisstuckatornearthetrimsetting.Itshouldbenotedthoughthatinanycasemaneuverabilitywillbedeteriorated,sinceyawcontrolise ectivelylost. Thereareseveralwaystoovercomethee ectsofatailrotorfailure.Thepilotmayincreaseforwardvelocity,decreasemainrotorrpmordecreasecollective.Allofthesemeasurescanreducethetorquinge ect.Nevertheless,itisstillnecessarytodetermineasuitablelandinglocationand landassoonaspossible.Autorotationisusuallyemployedforlandingbyswitchingthemainrotoro toreduceyawingduringtouchdown. 3.2.3AutorotationDuetotheaerodynamicsofthemainrotor,evenwhennopowerissuppliedtoit,itisstillpossibletomaintainasteadyrateofdescent.Thisisaccomplishedbyusingtheairowingthroughtherotordisktorotatethemainrotor-thereverseprocessfromnormalight.Inthiscasethemainrotoractsasaparachute,breakingthehelicoptersinkrateandallowingsafeightterminationwithoutpower.Thisisknownasautorotativeightorsimplyautorotation.Autorotationcanbeusedasanemergencymaneuvertobringahelicopterthathassu eredan enginefailuresafelytotheground.Duringthismaneuverthehelicopterislefttoglidedownwards.Asitmovestheairpassingthroughtherotordiskisutilizedtomaintainrotorrpm.Justbeforetouchdowntherotorrpmisexchangedforareductioninthedescentratethusallowingtheheli-coptertolandsafely.Somegroundspeedistypicallypreferredtoavoidthevortexringstateandmaintainsightofthelandingarea. 29

PAGE 46

Helicoptermanualsnormallyprovideaheight-velocitydiagramintheirperformancesectionswhichillustratestheoperatingregionswhereitispossibletosafelyperformanautorotationland-ing,followingapowerfailure.Atypicalheight-velocitydiagram,alsoknownasanH-VcurveisdepictedinFigure3.3. OperationinshadedareasshouldbeavoidedHeightaboveterrainIndicatedairspeed Recommended take-o prole Figure3.3:AtypicalhelicopterH-Vcurveliketheoneavailableinhelicoptermanuals.3.3HoveringStateAtanytimeahelicoptermayoperateinoneofseveralstates,eachfeaturingdi erentcharacteristics.Takingintoaccountonlyverticalmovement,thehelicoptermaybehovering(i.e.maintainingaltitude),climbingordescending.Althoughinthecaseofhelicopterautorotationonlythedescent-ingmodeisofinterest,thehoveringstatewillrstbedescribed.Thisisbecausesomederivationsrequiredformodelingtheautorotativestatearetypicallymadewithrespecttothehoveringstate.Thissectionconcernsthemodelingofthehoveringstate,whileSection3.4isconcernedwiththedynamicsofverticaldescent.Bothsectionsarebasedonthehelicopteraerodynamicstreatiseof[54]andusethesamenomenclaturewiththeexceptionofthechangeinthe z axisandinstances whereitwouldleadtoambiguity. 30

PAGE 47

3.3.1MomentumTheoryInthehoveringstatethemainrotorimpartsenergyontheairforcingittomovedownwards,pro-ducingenoughthrusttobalancetheweightofthehelicopter.Arstapproximationoftheheli-copterperformancecanbebasedonMomentumTheory(MT).Thisisdonebyapplyingthemass,momentumandenergyconservationlaws,undertheassumptionofone-dimensional,quasi-steady,incompressibleandinviscidowthroughtherotor[54],asshowninFigure3.4.Therotoritselfismodeledasazerothicknessactuatordisk,whereasuddenjumpinairpressureoccurs. v 0 v 1 v 2 v 1 Figure3.4:Theowmodelcreatedbythemainrotorasassumedbymomentumtheory.Duetomassconservation,themassowrateateachstationinFigure3.4mustbethesame:(3.1) m a = A 1 v 1 = A 2 v 2 = Av i = A 1 v 1 where A and v i istheareaoftherotordiskandthevelocityoftheairstreamattherotor,respectively.Thelatterisknownastheinducedvelocity.Fromuidmomentumconservationthechangeinairmomentumisequaltotherotorthrust:(3.2) T = m a v 0 m a v 1 Fromenergyconservation,theworkdoneontheairbytherotormustequalthechangeinkineticenergy:(3.3) Tv i = 1 2 v 21 31

PAGE 48

Assumingthattheairvelocityhighabovetherotoriszero,i.e. v 0 = 0andcombining(3.1)to (3.3),thefollowingrelationshipbetweenrotorthrustandinducedvelocityisderived:(3.4) T = 2 Av i 2 whereitfollowsthattheinducedvelocityathover( v i ; h )is: (3.5) v i ; h = s T 2 A or s W 2 A ,sinceinhovering T = W Atthispointitneedsbementionedthatitiscommontousenon-dimensionalquantitiesinheli-copterdynamicsanalysis,bydividinglengthsbytheradius R oftherotorandvelocitiesbythetip velocity( v tip =n R ).Asaresult,thefollowingquantitiesareintroduced: C T = T AR 2 n 2 (thrustcoe cient) (3.6) C Q = Q AR 3 n 2 (torquecoe cient) (3.7) C P = P AR 3 n 3 (powercoe cient) (3.8) = v i v H R n (inowratio) (3.9) and = bladearea diskarea (solidityfactor) (3.10) wheretheinowratioisusedtodeterminethenetairowthroughtherotordisk.Itshouldbenotedthatbecause P = Q n ,itfollowsthat C P = C Q Usingthenon-dimensionalformulation,(3.4)becomes:(3.11) C T = 2 h 2 andthepowerrequiredtomaintainhoverisgivenby:(3.12) C P = C T 3 = 2 p 2 Inpracticeithasbeenfoundthatthepowerisactuallyhigher,sincetheassumptionofquasi-steady,one-dimensional,incompressibleandinviscidowdoesnothold.Asaresultaninducedpower 32

PAGE 49

correctionfactor isintroducedin(3.12),withvaluestypicallyintherangeof1.1to1.25,to accountforthelackofexactmodelingoftheuidow[54].3.3.2BladeElementTheoryTheanalysisusedintheprevioussectionconcernsonlytheinducedpoweranddidnottakeintoaccounttheprolepower,i.e.thepowerexpendedinovercomingbladeproledraggeneratedbytheirrotationthroughtheair.Totakethise ectintoaccount,itisnecessarytoinvestigatethe localphenomenaateachblade.Thisisaccomplishedbydividingeachbladeintosmallersections,derivingthedynamicsateachsectionandthenintegratingoverthewholeblade.TheapproachdescribedisknownasBladeElementTheoryorBET.Thelocalvelocityoftheairstreamontheblade( v )isasumoftwocomponents;acomponentdue torotation v '; r =n y andacomponentduetotheinowwhichisthesumoftheinducedvelocity andtheverticalvelocityofthehelicopter, v '; z = v i v H .Theangleofthelocalairvelocityis = tan 1 v '; z v '; r .Fromgeometry,itisevidentthat = where isthebladepitchand the aerodynamicangleofattack(AoA).Theforceappliedtoeachbladeelementbytheair( F )canbedividedintotwocomponents;a lift F L andadrag F D asshowninFigure3.5.Theseforcesarecalculatedbasedonthegeometric characteristicsofthebladeelementasfollows: dF L = 1 2 v 2' c y C l dy (3.13) dF D = 1 2 v 2' c y C d dy (3.14)where c y isthebladechordatdistance y fromthecenteroftherotor. n Figure3.5:Theforcesactingonarotorbladesectionasaresultoflocalairvelocity. 33

PAGE 50

Projectingthesetwoforcesontherotorplaneandthe z axis,thethrustandtorquecontributionof eachelementwillbegivenby: dT = N b cos dF L N b sin dF D (3.15) dQ = N b y sin dF L + N b y cos dF D (3.16)where N b isthenumberofbladesoftherotor. Integrating(3.15)and(3.16)overthewholebladewillgivethetotalthrustproducedbytherotorandthetorquerequiredtoovercomethedragofthebladesalsoknownasproledrag.Undertheassumptionthattheinowangleissmall,(sin = andcos = 1)andthatthee ect ofthedragforceonthethrustisnegligiblecomparedtotheliftforce,(3.15)and(3.16)canbesimpliedto: dT = N b dF L ) dC T = N b AR 2 n 2 1 2 v 2' c y C l dy = 1 2 N b c y R C l v 2' R 2 n 2 d y R = 1 2 N b c y R C l y 2 R 2 d y R = 1 2 N b c y R C l r 2 dr (3.17)and dQ = N b dF L + N b dF D ) dC Q = N b 1 2 v 2' c y C l ydy + N b 1 2 v 2' c y C d ydy AR 3 n 2 = 1 2 N b c y R ( C l + C d ) v 2' y R 3 n 2 d y R = 1 2 N b c y R ( C l + C d ) r 3 dr (3.18)where r isthenon-dimensionalizeddistanceofthecurrentbladestation.Furthermore,the N b c y R termcorrespondstothefractionofthebladesurfacetothatoftherotorandisknownassolidityfactor( ). 34

PAGE 51

Iftheinowisuniformandthebladeislinearlytwistedwithconstantchord,integrating(3.17)gives:(3.19) C T = 1 2 C l ; a : 75 3 2 where : 75 isthebladepitchat3 / 4ofitslength. Similarlyintegrationof(3.18)yields:(3.20) C Q = C T + 1 8 C d ; 0 Itshouldbenotedthatinmanyhelicoptercongurationsthetail-rotorispoweredfromthesameengine.Asaresulttondthetotalpowerrequiredinaxialight,thepowerconsumptionofthetail-rotorneedstobeaddedtotheinducedandprolepowerconsumption.Specicallythethrustofthetail-rotorshouldcounterthetorquegeneratedbythemain-rotor.Asaresultthethrustofthetail-rotorisgivenby:(3.21) T TR = Q MR l TR where l TR isthedistancebetweenthetailandmainrotor. 3.4VerticalDescentDuringdescent,theowthroughtherotorisreversedandtheforcesoneachbladeelementareoftheformdepictedin3.6.Asaresult(3.17)and(3.18)become: dC T = 1 2 N b c y R C l r 2 dr (3.22) dC Q = 1 2 N b c y R ( C l + C d ) r 3 dr (3.23)Sinceinthiscase = ,integrationoftheseequationsyields(3.19)and(3.20). Theinducedvelocityduringverticaldescentcanbecalculatedusingmomentumtheoryfrom:(3.24) T = 2 A ( v i v H ) v i Assumingthesamethrustindescentandhoverandcombiningwith(3.4)gives:(3.25) v i ; h 2 + v i 2 v i v H = 0 35

PAGE 52

n Figure3.6:Theforcesactingonarotorbladesectionasaresultoflocalairvelocityduringdescent.ordividingwith v i ; h 2 : (3.26) v i v i ; h 2 v H v i ; h v i v i ; h + 1 = 0 Thequadratic(3.26)hastwosolutions,butonlyonehasaphysicalmeaning:(3.27) v i v i ; h = v H 2 v i ; h s v H 2 v i ; h 2 1 Includingtheinducedpowercorrectionfactor,(3.27)canbeusedtodetermineaninducedvelocityfactor f i = v i v i ; h ,thatrelatestheinducedvelocitywiththeidealinducedvelocityathover. 3.4.1VortexRingStateandTurbulentWakeStateItshouldbenotedthattheuniforminowassumptionandasaconsequence(3.27)doesnotholdforsmalldescentrates.Thisisbecauseundertheseconditionsthewakecanbeupwardsordown-wardsdependingonthebladestationwhichresultsinrecirculationandturbulence.SpecicallytheairowcharacteristicsgothroughthreedistinctstatesasshowninFigure3.7.Atverysmallratesofdescent v H < v i ; h thehelicopterisintheVortexRingstateandasthedescentrateincreases itenterstheTurbulentWakestate( v i ; h > v H > 2 v i ; h ).Whentheverticalvelocityincreasesfurther ( v H > 2 v i ; h )thentheairowbecomesuniformagainand(3.27)isapplicable.Thisstateiscalled theWindmillBrakestate.InthecaseoftheVortexRingandTurbulentWakestatesonlyan“e ective”inducedvelocitycan becalculatedbasedonexperimentaldatabymeasuringtheperformanceofthehelicopterandcalculatingtheinducedvelocitytoachievethisperformanceundertheassumptionofuniformwake.Thereareseveralempiricalmodelstocalculatetheinducedvelocityinthesetwostates.A 36

PAGE 53

n r n r r nn r Figure3.7:Therotorwakecharacteristicsstartingfromaxialclimborhovering(normalworkingstate)andmovingthroughthevortexring,turbulentwakeandwindmillbrakestatesasthedescentvelocityincreases.linearapproximationisgivenby[54]:(3.28) f i = v i v i ; h = 8>>>>>>>>><>>>>>>>>>: + 0 : 75 v H v i ; h 0 v H v i ; h 8 4 + 1 7 3 v H v i ; h 8 4 + 1 v H v i ; h 2 where istheinducedpowercorrectionfactorintroducedinSection3.3.1. Aquarticthatappliesinthewholeregion0 v H v i ; h 2isgivenby[54]: (3.29) f i = v i v i ; h = + k 1 v H v i ; h + k 2 v H v i ; h 2 + k 3 v H v i ; h 3 + k 4 v H v i ; h 4 where k 1 = 1 : 125, k 2 = 1 : 372, k 3 = 1 : 718, k 4 = 0 : 655, 37

PAGE 54

Theproleof v i v i ; h withrespectto v H v i ; h forthevariousoperatingstatesisgiveninFigure3.8. 0 0 : 5 1 1 : 5 2 2 : 5 3 2 101234v i = v i ; hv H = v i ; h NormalworkingstateVortexringstate Turbulentwakestate Windmillbrakestate Figure3.8:Theinducedvelocityproleinthefouroperationalstates.ForoperationintheTurbulentWakeandVortexRingstates,themomentumandbladeelementtheoriesnolongerapplyandtwoempiricalmodelsareprovidedbasedonlinearandpolynomialttingofexperimentaldata(dashedanddottedlinesrespectively).3.4.2GroundE ect Anadditionalcorrectionfactorisrequiredforhoveringneartheground,duetoaphenomenoncalledgrounde ect.Becausetherotorwakemeetsthegroundthepressurebelowtherotorrises [72].Thisincreaseinpressureresultsinhigherthrustgenerationforthesamepower,cushion-ingthetouchdownespeciallyinunpoweredlandings[33].Thereareseveralempiricalmodelsofgrounde ect,onesuchmodelisgivenby[54]: (3.30) T T 1 # P = const = 1 1 C l ; a i 4 C T R 4 z 2 orassumingnegligiblebladeloadinge ects: (3.31) T T 1 # P = const = 1 1 R z 2 Itshouldbenotedthatthepreviousequationsassumehoveringight.Ifthehelicopterisinfor-wardight,thewakemayincluderecirculationandvorticesnearthegroundandthee ectson 38

PAGE 55

performancearemorecomplex.Ingeneralthough,thebenetsofthegrounde ectarequickly lostevenforsmallforwardvelocities.3.4.3InowDynamicsTheresponseoftheinducedvelocitytothrustchangesisnotinstantaneousbutexhibitsadynamicbehavior.Thisbehaviorcanbemodeledusinganinertiamodelwithanapparentmassequalto63.7%thatofasphereofairwiththesameradiusasthatoftherotor( m a = 0 : 637 4 3 R 3 )[54]. Asaresultthethrustwillbegivenby[54]: T = m a v i + 2 Av i ( v i v H ) = 0 : 849 AR v i + 2 Av i ( v i v H ) (3.32) Insteady-stateconditionsthethrustisgivenby(3.24)whichwhencombinedwith(3.32)pro-duces: 2 A ( v H + v i ; s ) v i ; s = 0 : 849 AR v i + 2 Av i ( v i v H ) ( v H + v i ; s ) v i ; s = 0 : 4245 R v i + v i ( v i v H ) v i = 2 : 356 R v i ( v i v H ) v i ; s ( v i ; s v H ) v i = 2 : 356 R v i v i ; s v i + v i ; s v H (3.33)where v i ; s isthesteadystateinducedvelocitycalculatedfrom(3.27)and(3.28)or(3.29)asa functionof v H .Itisobviousthatthederivedequationhastwopossiblesteadystatesolutions; v i = v i ; s and v i = v H v i ; s althoughonlytheformerisofinterest.Toovercomethisproblem, itisassumedthat v i v H v i ; s v H andasaresultthenalinducedvelocitymodelisgivenby: (3.34) v i = 2 : 356 R v i 2 v i ; s 2 Asimplermodelhasbeenemployedin[42],basedonthelinearizationof(3.32)aroundthethrust,rotorrpmandinducedvelocityathover,resultingin:(3.35) 0 : 21 n 0 v i + v i = v i ; h f i f g where f g isafactormodelingthegrounde ect. 39

PAGE 56

3.5VerticalAutorotationModelDuringverticalautorotationtherearethreeforcesactingonthehelicopter,thethrustofthemainrotor,theaerodynamicdragfrommovingthroughtheairandtheweightofthevehicleitself,asshowninFigure3.9. TW D Figure3.9:Theforcesactingonahelicopterduringverticalautorotativedescent.Applyingabalanceofforcesonthedescentinghelicopter,theverticalaccelerationcanbecalcu-latedas: M v H = W T D v H = g 1 M T 1 M D (3.36)where g istheaccelerationofgravity.Thethrustcanbecalculatedusingbladeelementtheory from(3.19)andthedragisgivenby:(3.37) D = 1 2 f e v H 2 where f e istheequivalentareaofasurfacewithunitdragcoe cient.Asaresult(3.36)becomes: v H = g 1 M T 1 M D = g AR 2 n 2 M C T f e 2 M v H 2 = g AR 2 n 2 2 M C l ; a : 75 3 2 f e 2 M v H 2 (3.38)Atorquebalanceonthemainrotorgives: 40

PAGE 57

n= 1 I R Q = AR 3 n 2 I R C Q = AR 3 n 2 I R C T + 1 8 C d ; 0 # = AR 3 n 2 I R v i v H R n C l ; a : 75 3 2 AR 3 n 2 8 I R C d ; 0 (3.39)Finally,theODEmodelingtheheight z ofthehelicopterisgivenby: (3.40) z = v H Therearetwoalternativesindeningtheinputtothemodel;thebladepitchandthethrustcoef-cient,eachwithitownadvantagesanddisadvantages.Naturallybothapproachesareequivalentsinceforanygivenstateitispossibletodeterminetheappropriatecollectivepitchtoachievetherequiredthrustandviceversausing(3.19).Thethrustcoe cientiscommonlyusedastheinputtothemodelsinceitallowsforsimplermodel equations.Furthermoretheuppercollectivelimitdependsonthebladestalllimitwhichinturnisnormallyexpressedwithrespecttothethrustcoe cient.Inadditiontothat,thereisnoneed totakeintoaccountthegrounde ectinthemodelsinceitonlya ectstherelationshipbetween thrustandcollectivepitch.Inthecasewhereonlypositivethrustcoe cientsareconsidered,then anissuearisesbecauseatzerothrustthehelicopterrotorislosingenergy.Thiswillresultintheremainingenergynearthegroundbeinginsu cienttoperformtheare. Theadvantageofusingthebladepitchisthatitdirectlymapstothephysicalactuator.Asaresultupperandlowerlimitsareimmediatelyavailablealthoughtheupperlimitmaybeinsidethebladestallregion.Inthisworkthebladepitchwillbeusedasthecontrolinputandasaresultthenalmodelwillbeexpressedwithrespectto Puttingeverythingtogether,themodelequationsforverticalautorotationare: v H = g AR 2 n 2 2 M f g C l ; a 3 v i v H 2 n R f e 2 M v H 2 (3.41) z = v H (3.42) n= AR 3 n 2 I R v i v H R n f g C l ; a 3 v i v H 2 n R AR 3 n 2 8 I R C d ; 0 (3.43) v i = 2 : 356 R v i 2 v i ; s 2 (3.44) 41

PAGE 58

3.6RemarksThemodelderivedintheprevioussectionrepresentsahighlynon-linear,under-actuatedsystem.AnalyticalsolutionofthisprobleminvolvessolvingtheHamilton-Jacobi-Bellmanequation,whichispossibleforonlyasmallsubsetofnon-linearproblems.Asecondalternativeistointroduceanon-linearfeedbackcontrollawthatlinearizesthesystem.Nevertheless,thisrequiresachangeofvariablesthatisnotpossibleinthiscase.Asaresultmodelpredictivecontrolwaschosen,atechniquethatpredictsthefuturestatetrajectoryanddeterminesthecontrolsequencewhichmin-imizesacostfunctionandallowsforstateandcontrolconstraintenforcement.Thistechniqueisapproximatebecausethepredictiondoesnotincludethewholemaneuveruntilthehelicopterhaslanded,butratheraxedhorizonaheadofthecurrentstate.Thefollowingchapterpresentsthecontrollerdesignindetail. 42

PAGE 59

Chapter4:ControllerDesignTheautorotationcontrollerisbasedonthemodelpredictivecontrolapproach,asdiscussedinChapter1.Beforegoingintothespecicsofthedesignedcontroller,theprinciplesofmodelpre-dictivecontrolwillbegiven.Thenthedesignofthecollectivecontrollerispresented,followedbythedesignoftheentireverticalautorotationcontroller.4.1PrinciplesofModelPredictiveControlBesidesthetraditionalPID,modelpredictivecontrol(MPC)istheonlyothercontrolmethodologythathasbeenwidelyacceptedinprocesscontrol[38,41,50].OneofthekeyadvantagesofMPCisconstrainthandling.Specically,MPCiscapableofhandlinginput,outputandstateconstraints,whichdirectlymaptoquality,e ciencyandsafetyinproductionenvironments[50].Itisalso possibletouserateofchangeconstraintstobettermapactuatorphysicallimitations[38].Otheradvantagesincludegoodperformanceinmultivariatecontrol[50],abilityforrecongurationbychangingtheinternalmodel[45]andtheavailabilityofMPCcommercialtoolstodevelopmodelsanddesigncontrollers[64].4.1.1FundamentalsTheideabehindMPCistostartwithaxedpredictionhorizon( N s ),usingthecurrentstateofthe plantastheinitialstate.Anoptimalcontrolsequenceoflength N c ( N s N c )isthenobtained thatminimizesacostfunctionoverthepredictionhorizon,whileatthesametimesatisfyingposedconstraints.When N c < N s ,forpredictionbeyondthecontrolhorizon,thelastcomputedvalue ofthecontrolisused[38].Afterapplyingtherstelementofthatsequenceasaninputtotheplant,thenewstateisobserved.Thepredictionhorizonisthenmovedonestepforwardandtheprocessisrepeated.BecauseoftheconstantmovingofthepredictionhorizonMPCisalsoknownasrecedinghorizoncontrol.ThisprocedureisdepictedinFigure4.1.Theproblemofdeterminingtheoptimalcontrolsequencecanbeexpressedasaconstrainedopti-mizationproblem,specically: min L ( u ; x )s : t : C ( u ; x ) 0 (4.1) 43

PAGE 60

PastFuture t 0 t 0 + 1 t 0 + 2 t 0 + N s t 0 + 1 + N s x (0) ˆ x (1) x (1) StateControl Figure4.1:Adiagramofthebasicprinciplebehindmodelpredictivecontrol.Attime t 0 the systemhasreachedstate x (0).Basedonthecurrentstate,anoptimalcontrolsequenceandthe correspondingfuturestatetrajectoryisdetermined(dashedlines).Therstelementofthecontrolsequenceisexecutedandthenewstate x (1)isobservedwhichmaynotbethesameasthe predictedone(ˆ x (1)).Anewcontrolsequenceandfuturestatetrajectoryiscalculated(dottedlines) repeatingtheprocess.whereacontrolsequence u isdeterminedthatminimizesthecostfunction L andsatisestheinequalityconstraints C .Althoughthe L functioncantakeanyform,itiscommontouseaquadratic form.ThisisespeciallytrueinprocessengineeringwhereMPCisusedtorejectdisturbancesandthecostfunctionmodelsthedeviationfromthesetpoint[38].Theoptimizationproblemdescribedaboveneedstobesolvedeachtimeanewstateisobservedwhichmayresultinsignicantcomputationaldemand–especiallyiflargepredictionandcontrolhorizonsareused.AsaresulttheearlyapplicationsofMPCwerelimitedtoprocesscontrolofplantswithslowdynamicsthatallowedsamplingtimesintheorderofminutes.NeverthelessfastercomputershaveallowedtheuseofMPCinothereldsincludingaviation.MPChasbeenappliedtothecontrolofanF-16[9],aswellasofaBoeing747freighteraircraftunderfailures[45].Additionally,KeviczkyandBalasproposedanMPCforguidancecontrolofaUAS[48],whileSlegersetalusedMPCtocontrolanunmannedparafoilandanautonomousglider[73].An-otherapplicationrelatingtounmannedaircraftwhereMPChasalsobeenproposed,istrajectoryplanningunderconstraintsanddisturbances[49].AlthoughcurrentlymostMPCapplicationsutilizelinearplantmodels,someprocessesexhibitsignicantnon-linearity.Inthiscase,anon-linearpredictionmodelisrequiredwhichleadstonon-linearmodelpredictivecontrol(NMPC)problems.AlthoughNMPChasthesameadvantagesasthelinearMPC,on-linesolutioncanbechallenging.Thisisbecauseateachsamplingperiod,a 44

PAGE 61

non-linearoptimizationproblem(alsoknownasanonlinearprogrammingproblem)needstobesolved.Suchproblemscanbecomputationallyintensiveandsignicantlymoredi culttosolve duetobeingnon-convex,non-quadraticandpossiblymulti-modal[50].Thismeansthatreal-timerequirementsaredi culttobesatisedwhileatthesametimenoguaranteeisgiventhatan optimalsolutionwillbefound.4.1.2PredictionNMPCproblemscanbecategorizedaccordingtothetypeofpredictionmodelusedandthewaytheoptimizationproblemissolved.Basedonthechoiceofpredictionmodeltherstcategorycorrespondstoonesderivedusingrstprinciplestechniques.Thisapproachisoflimiteduseinpracticesincesuchmodelsareexpensivetoderiveandmaintaininindustrialsettings[64].Alternativelyblackandgrayboxapproachesarealsoavailable,wheretheplantismodeledbasedonempiricaldataoracombinationofsuchdataandrstprinciplederivations.Blackboxap-proachestypicallyusecommonfeedforwardneuralnetworksforpredictionorforbothpredictionandoptimization.InthelattercasetheyimplementthecompleteMPCasin[6,82].UseofneuralnetworksisverypopularinMPCproblemsasevidencedbyasurveycarriedoutin1999byHus-sain[41].Thissurveydocumentedcloseto20di erentapplicationsofneuralnetworksforMPC invariousprocesscontrolproblems.Althoughmulti-layered,feedforwardnetworksarethemostpopularchoice,otherapproacheshavealsobeenproposed.MiaoandWangusedsupportvectorregressiontoimproveaccuracy[58],whileSayyar-Rodsarietal.proposedextrapolatinggain-constrainedneuralnetworkstoimprovemodelperformanceinregionswherenotrainingdataisavailable[71].Adi erentapproachwas adoptedbyKamalabadyandSalashoorthatproposedtheuseofadaptivegrowingandpruningneuralnetworksforonlineidentication[46].Thestructureofthepredictionmodelcanalsobeselectedinsuchawaythatthesolutionoftheoptimizationproblemisfacilitated.Forexample,theuseofsecondorderVolterraseriesmodelsreducesproblemcomplexityandcanbederivedusingeitherthenonlinearfundamentalmodelorplantdata[55].Alternativelytheuseofpolynomialautoregressivewithexogenousinputmodelsmaylead,afterappropriatetransformation,toproblemsreadilysolvablewithglobaloptimizationtechniques[74].4.1.3OptimizationForthesolutionoftheoptimizationproblemanumberofalternativeshavebeenproposedintheliterature.Onepossibledivisionisbetweentechniquesthatsolvetheproblemexactlyandthosethatuseapproximatesolutions[91]byreducingorlinearizingtheproblem.Oneapproachtore45

PAGE 62

ducingthesizeoftheproblemiscalculatingfuturecontroleitherwithoutconstraintsorapprox-imately[91].Sincethefuturecontrolisnotgoingtobeapplied,itisassumedthatthee ecton controllerperformancewillbesmall.OtherapproachesrelyonrstorderTaylorexpansion[10]orlinearizationaroundaspecictrajectoryoroperatingpointandtheirapplicabilityandperformancemaydependonthestructureoftheplant.Asimilarapproachistosuccessivelylinearizethemodelaroundthecurrentoperatingpointeachtimeanewstateisobserved[38].Itisalsopossibletosplitthemodelintoalinearandnon-linearpart.In[64]anon-linearmodelwasderivedbasedonempiricaldata,whilealinearmodelwasbuiltfromsteptestexperiments.Thetwomodelswerethencombinedusinggainscheduling.Similarlytheuseofalinearizedmodelplantwithnon-linearfreetrajectoryisdiscussedin[50].Atechniquethatprovidesexactsolutionsisthatoffeedbacklinearization.Joostenetal.proposedarecongurableightcontroller,thatusesfeedbacklinearizationtolinearizethemodelusinganappropriatelydesignednon-linearfeedbackcontrollaw[45].Theoptimizationcanthenbeaccom-plishedusingcommonlineartechniques.Neverthelessfeedbacklinearizationcanbedi cultor impossibletoimplementincertainsystems,especiallyunder-actuatedones.Anothercategoryofoptimizationtechniquesinvolvesdirectlysolvingthenon-linearproblemalthoughthismayresultinunwantedcomputationalburdenandconvergenceproblemsfornon-convexproblems.Forexamplein[9],asequentialquadraticprogrammingalgorithmwasusedbutreal-timerequirementscouldnotbemet.Insteadofestimatingthegradientonline,ifaneuralnet-workwasusedtomodeltheprocess,itsstructurecanbeexploitedtodeterminethecostgradientfaster[77].4.1.4TuningAnyNMPCimplementation,inadditiontoanyparametersusedbythenon-linearoptimizationscheme,hasthreeparametersthatcanbetunedtoimproveperformance.Theseparametersare N s N c and t s andtheire ectoncontrollerperformanceisdi culttopredictbeforehand[38]. Neverthelessgeneralguidelinesontuningtheseparametershavebeendiscussedintheliterature.Ingenerallowersamplingintervalsincreasecomputationaldemandbutcancaptureprocessdy-namicsbetterandmayevenberequiredwhenthemodelingerrorislarge[57].Underaconstantpredictionhorizon,decreasingthecontrolhorizonmayreducecomputationalloadbutwillalsore-sultinmoresluggishandconservativecontrol[57].Thee ectofdecreasingthepredictionhorizon issimilar. 46

PAGE 63

4.2CollectiveControllerDesignTherststepinthedesignofthecontrolleristhederivationofanappropriatemodelforverticalautorotation.Althoughsuchamodelhasalreadybeenderived,directuseof(3.41)–(3.44)presentsproblems.ThisisbecausewhenappliedinanMPCsetting,itwouldrequirethemeasurementofstatesthatarenotnormallyavailable.ThefollowingsectiondescribestheinternalmodelusedbytheMPC.4.2.1InternalVerticalAutorotationModelTheuseoftheautorotationmodelderivedinSection3.5isnotpossiblewithoutcertainmodi-cations.Sincetheinowdynamicsaregenerallynotmeasurableduringight,themodelusedinternallybythecontrollerwillbesimpliedtoincludeonlytheobservablestates,namely v H ; z and n .Asaresult,thecontrollerassumesasteady-stateinowvelocity,thatis: (4.2) v i = v i ; s = v i ; h f i wheretheterm v i ; h iscalculatedusing(3.5),as: (4.3) v i ; h = s Mg 2 A TocalculatetheinowratiointheturbulentwakeandthevortexringstatestheuseofthequarticapproximationgiveninSection3.4.1waschosen.Thisisbecausethelinearapproximationresultsinnon-continuousderivativewhichinturnwasresponsiblefordeterioratingcontrollerperfor-mance.Using(3.26)and(3.29),theinowratioisgivenby:(4.4) f i = 8>>>>>><>>>>>>: v H 2 v i ; h s v H 2 v i ; h 2 1 ; 2 v H v i ; h + k 1 v H v i ; h + k 2 v H v i ; h 2 + k 3 v H v i ; h 3 + k 4 v H v i ; h 4 ; otherwise Inadditiontothatandinordertokeepthemodelequationsrelativelysimpleandthecomputa-tionalcomplexitylow,thegrounde ectisconsiderednegligible,i.e. f g = 1.Asaresultthe 47

PAGE 64

verticalautorotationmodelusedforthecontrollerisgivenby: v H = g AR 2 n 2 2 M C l ; a 3 v i v H 2 n R f e 2 M v H 2 (4.5) z = v H (4.6) n= AR 3 n 2 I R v i v H R n C l ; a 3 v i v H 2 n R AR 3 n 2 8 I R C d ; 0 (4.7)Toavoidnumericalissues,scalingisnecessary.Specicallythecontrolinputisscaledtothe[0 ; 1] range,whilethemodelequationsarenon-dimensionalizedusingthenominalrotorangularveloc-ity n 0 andtherotorradius R andthenscaled: = n 0 t 100 ) d d t = n 0 100 d d (4.8) x 1 = 100 v H n 0 R ) v H = n 0 R 100 x 1 (4.9) x 2 = z 10 R ) z = 10 Rx 2 (4.10) x 3 = n n 0 ) n=n 0 x 3 (4.11) x 4 = 100 v i ; s n 0 R ) v i ; s = n 0 R 100 x 4 (4.12) u = + min max min ) = u ( max min ) + min (4.13)Thenalcontrollermodelequationsare:(4.14) x 1 = 10 4 n 0 2 R g f e R 2 M x 21 + 25 AR C l ; a M x 3 ( x 4 x 1 ) 29 : 1 AR C l ; a min M x 23 29 : 1 AR C l ; a ( max min ) M x 23 u (4.15) x 2 = 1 10 x 1 (4.16) x 3 = 100 AR 3 C d ; 0 8 I R x 23 + AR 3 C l ; a 400 I R ( x 4 x 1 ) 2 2 : 91 AR 3 C l ; a min 10 3 I R ( x 4 x 1 ) x 3 2 : 91 AR 3 C l ; a ( max min ) 10 3 I R ( x 4 x 1 ) x 3 u 48

PAGE 65

4.2.2Non-linearOptimizationusingRecurrentNeuralNetworksApplicationareaslikeaviationhavestrictreal-timerequirementsthatmaybedi culttosatisfy withtraditionalgradientdescentorglobaloptimizationmethods.Ontheotherhandaneuralnet-workcanbeimplementede ectivelyinhardwarewhichallowshighprocessingspeeds[90].This approachwasadoptedtosolvethenon-linearoptimizationproblem.Tosolvesuchproblems,Xiaetalhaveproposedaseriesofrecurrentneuralnetworks[86–90].Thesenetworksarecapableofsolvingconvex,non-linearoptimizationproblemswithlinear[90]ornon-linear[89]constraints.Theconstraintsthemselvescanbemodeledasinequality[87–89],equality[90]orboth[86].Furthermoreinthelateriterations,therequirementforconvexitywasrelaxedandconvergencewasguaranteedforaclassofnon-convexproblemsaswell.TheideabehindtheirapproachistobuildaneuralnetworkthatmodelsanODEwhoseequilib-riumpointistheoptimalsolutiontotheproblem(4.1).Thisapproachhasthreemajoradvantages;norestrictionsareimposedontheinitialpoint,guaranteedconvergenceinthecaseofconvexprob-lemsandveryfastexecutionspeedwhenusinghardwarethatcanperformparallelcomputations.Thestateequationoftheneuralnetworkisgivenby[87]:(4.17) d 0BBBBB@ u 1CCCCCA = r 0BBBBB@ u + u d L d u d C d u + + C ( u ) + 1CCCCCA andtheoutputisgivenby u In(4.17) r isalearningrateconstant,( ) + isanactivationfunctionand isanauxiliaryvector withsizeequaltothenumberofconstraints.Theauxiliaryvectorisresponsibleforcapturingtheviolationofconstraintsandissubsequentlyusedtomovetheoutputoftheneuralnetworkaccordingly.Sincetheotheroperationsareelementary,thecomputationalcomplexitydependsonthecalcula-tionof d L d u C ( u )and d C d u In[87],Xiaetal.provedthatiftheproblemisconvex,thatis d 2 L d u 2 ispositivesemi-denite,then theoutputofthenetworkconvergesgloballytotheoptimalsolutionofthenon-linearoptimiza-tionproblem.Furthermoretheconvergencerateisproportionaltothedesignconstant r .Additionallyitwasprovedthatasu cientconditiontoguaranteeconvergencewasconvexityofthe Lagrangian:(4.18) d 2 L d u 2 + n X i = 1 i C i ( u ) 0 Thisisamorerelaxedcriterionsinceitallowsfornon-convex L functions. 49

PAGE 66

4.2.3ControllerDerivationTheverticalautorotationmodeldescribedby(4.5)–(4.7)canbeexpressedasageneralSIMO,non-linear,a neinthecontrolproblemgivenby: x = f ( x ) + g ( x ) u (4.19) min u 2 U Z t f 0 L ( x ; u ) (4.20) SinceNMPCrequiresadiscretetimeinput-outputmodel,theproblemabovemustbediscretized.ThiscanbeaccomplishedbyTaylorseriesexpansion[47].ToavoidincreasingthecomputationalcomplexitytheTaylorserieswastruncatedintherstterm,resultingin: x ( t + 1) = x ( t ) + t s f ( x ( t )) + t s g ( x ( t )) u ( t ) (4.21) min u ( i ) 2 U t f X i = 0 L ( x ( i ) ; u ( i )) (4.22) Tondtheoptimalsequenceusingtherecurrentneuralnetworkof(4.17),the d L d u C ( u )and d C d u quantitiesneedrstbecalculated.Inordertodothatthefuturestatesequenceanditsderivativewithrespecttothecontrolsequenceisrequired.Thisisaccomplishedinthepredictionstepwherethe d L d u isalsocalculated.Thepredictionstepisfollowedbytheconstrainthandlingstepwhich isresponsibleforthecalculationof C ( u )and d C d u .Itshouldbenotedthatthisdistinctionismade onlyforpresentationpurposessinceitispossibletohandletheconstraintsinparallelwiththeprediction,asvaluesbecomeavailable.4.2.3.1PredictionThestatesequenceisobtaineddirectlyfrom(4.21).Di erentiating(4.21)withrespecttoacontrol action u ( i ): d x ( k + 1) d u ( i ) = d x ( k ) d u ( i ) + t s J f ( x ( k )) d x ( k ) d u ( i ) + t s J g ( x ( k )) d x ( k ) d u ( i ) u ( k ) + t s g ( x ( k )) d u ( k ) d u ( i ) = h I + t s J f ( x ( k )) + t s J g ( x ( k )) u ( k ) i d x ( k ) d u ( i ) + t s g ( x ( k )) d u ( k ) d u ( i ) (4.23)Actionscanonlya ectfuturestates: (4.24) d x ( k ) d u ( i ) = 0 ; 8 x ( k ) ; u ( i ): i k 50

PAGE 67

anddonotdependonpastorfutureactions:(4.25) d u ( k ) d u ( i ) = 8>>><>>>: 1if i = k 0otherwise Using(4.23)andtakingintoaccount(4.24)and(4.25),thefollowingupdateruleforcalculatingthe d x ( t ) d u ( i ) fromthepreviouspredictionstepisobtained: (4.26) d x ( k + 1) d u ( i ) = 8>>>>>>><>>>>>>>: 0if k + 1 < i t s g ( x ( k ))if k + 1 = i h I + t s J f ( x ( k )) + t s J g ( x ( k )) u ( k ) i d x ( k ) d u ( i ) otherwise Acostfunctionthatseparatesthecontributionofthecontrolsequencefromthatofthestateofthehelicopterisassumed: L = N s X j = 1 L ( x ( j )) + w u T u (4.27)where L isafunctionofthestateand w isapositiveweightfactor.Thelattermodelstheweight ofthecontrole ortonthecostfunctionandistypicallyasmallvalue. Thederivativeofthecostfunctionisthengivenby:(4.28) d L d u = N s X i = 1 @ L @ x ( i ) d x ( i ) d u + 2 w u Figure4.2showsablockdiagramofthepredictionmoduleofthecontroller.Onthelefttheinitialstateandthecontrolsequenceareusedtodeterminefuturestatesandtheirderivativeswithrespecttothecontrolsequenceinacascadeofmodelevaluations.Althoughthispartcanbeparallelizedwithrespecttothecontrolsequence,eachstepinthestatepredictiondimensionrequirestheprevi-oustobecompleted.Nevertheless,observing(4.26),itisevidentthatthe d x d u isatriangularmatrix andasaresultsomecomputationscanbeeasilyskipped.Furthermoreasthederivativesarecalcu-latedtheyarealsousedtoupdatethevalueofthe d L d u 51

PAGE 68

M M M x 0 u u (0) u (1) u (2) x (1) x (2) x ( N s ) x (1) d x ( N s ) d u d x (1) d u d x (2) d u @ L @ x (1) @ L @ x (2) @ L @ x (3) x d x d u d L d u Figure4.2:Blockdiagramofthepredictionmoduleofthecontroller.Onthelefthalfacascadedconnectionisusedtocalculate d x ( i ) d u from d x ( i 1) d u .Thesummationblockisinitializedtothevalueof 2 w u 4.2.3.2ConstraintsTherearethreetypesofconstraintsimposedonthecontroller.Therstconcernsthephysicallimitsoftheactuator:(4.29) min max ) 0 u 1 Thistypeofconstraintiseasilyhandledbyappropriatedesignoftheneuralnetworkactivationfunction.Inthiscasetheactivationfunctionisasaturationfunctionthatlimitstheinputtotherange[0 ; 1],sothatthecontrolsequenceisalwayswithintheactuatorlimits: (4.30)( ) + = min(1 ; max( ; 0)) Thesecondconstraintisincorporatedtoavoidbladestall.Assumingthatthethrustrequiredtokeepthehelicopterintheareaisconstant,astherpmdropsthebladepitchneedstobeadjustedtocompensate.Neverthelessthereisalimitafterwhichtheairowseparatesandliftislost.Thisistypicallymodeledusingthebladeloadingcoe cient( C T )whichcantakevaluesupto0 : 12–0 : 14 withoutstalling[54].Inthiscaseaconservativelimitof0 : 125waschosen: (4.31) C T 8 ) 1 2 C l ; a 1 3 u ( max min ) + 1 3 min 1 200 x 4 ( i ) x 1 ( i ) x 3 ( i ) 8 52

PAGE 69

Thelastconstraintisdesignedtoprotectthemainrotorfrommechanicalstress.Thisisbecauseforverylowbladepitchtherotorangularvelocitymayincreaseabovenominal,possiblydam-agingtherotorassembly.Theconstraintistypicallyexpressedasafunctionofthenominalrotorrpm.(4.32) n f r n 0 ) x 3 f r wherefromliterature f r typicallytakesvaluesbetween1 : 05and1 : 25[8,52]. Theconstraintsinthevectorformrequiredbytherecurrentneuralnetworkaregivenby:(4.33) C ( u ) = 266666666666666664 h C T ( i ) 8 i 1 i N c n ( j ) f r n 0 1 j N c 377777777777777775 or(4.34) C ( u ) = 266666666666666664 C l ; a ( max min ) 6 u + min max min 3 4 1 max min 1 C l ; a 3 400 1 max min x 4 ( i ) x 1 ( i ) x 3 ( i ) 1 i N c x 3 ( j ) f r 1 j N c 377777777777777775 Finallydi erentiating(4.34)withrespecttothecontrolsequencegives d C d u : (4.35) d C d u = 2666666666666666666664 C l ; a ( max min ) 6 [ I ] N c N c C l ; a 800 d x 4 ( i ) d x 1 ( i ) 1 x 3 ( i ) d x 1 ( i ) d u ( j ) x 4 ( i ) x 1 ( i ) x 23 ( i ) d x 3 ( i ) d u ( j ) # 1 i N c 1 j N c h d x 3 ( i ) d u ( j ) i 1 i N c 1 j N c 3777777777777777777775 Itshouldbenotedthatthereisanissuewiththeuseoftheconstraintsasmodeledabove.Thisissueoccurswhenthehelicopter'ssinkrateexceedstheautorotativesinkrate,thatisthesinkratewherenoenergyisaddedorsubtractedfromthemainrotor.Atthisstateifcollectiveissuddenlyincreasedtherotorrpmwillshowanincreaseinsteadofdecreasing.Thereasonisthattheinowratiowillbenegativeandthecollectivedependentterminthetorquebalancewillbepositiveandhigherthanthetorquelosses.Thisresultsina d C d u thathaselementswithpositivesign.Asthemain rotorapproachestherpmlimit,thecontrollerwillaccuratelypredicttheviolationoftheconstraint,butthecommandedactionwillbetodecreasecollectiveinsteadofincreasingit.Theaforementionedproblemcanbeaccommodatedinvariousways.Onealternativeistoputaconstraintonthesinkrate.Thisconstraintwillensurethatthehelicopterdoesnotexceedthe 53

PAGE 70

autorotativesinkratecorrespondingtotherpmupperlimit.Inthiscaseaconstraintonrotorrpmisnolongernecessarysincerpmwillslowlyincreaseuntilitreachestheupperlimit.Thedisadvan-tageofthisapproachisthattheenergyavailableonthemainrotorduringarecanbesignicantlylowerdependingontheinitialdelaytodetectthefailureandthealtitudeatwhichthefailureoc-curred.Thisisbecauseuntilthefailureisdetectedandcollectiveisloweredtherotorisquicklybleedingrpmandtheremaynotbeenoughtimetorecoverthelostrpm.Asecondapproachandtheoneusedinthisworkistointroduceaninequalityconstraintontherpmrateofchange.Specicallywhentherpmapproachestherpmupperlimit,therateofchangeisrestrictedtozeroornegativevalues.Asaconsequencethecontrollerneedstoraisethecol-lectiveandreducethehelicoptersinkratetotheautorotativevalue.Inthiscase(4.33)–(4.35)become:(4.36) C ( u ) = 266666666666666664 h C T ( i ) 8 i 1 i N c h n ( j ) i 1 j N c 377777777777777775 (4.37) C ( u ) = 266666666666666666664 k 1 u + min max min 3 4 1 max min 1 C l ; a 3 400 1 max min x 4 ( i ) x 1 ( i ) x 3 ( i ) 1 i N c k 2 ( x 4 ( j ) x 1 ( j )) x 3 ( j ) u + min max min 0 : 859 max min x 4 ( j ) x 1 ( j ) x 3 ( j ) + 4295 max min x 3 ( j ) x 4 ( j ) x 1 ( j ) 1 j N c 377777777777777777775 (4.38) d C d u = 266666666666666666666666666666666666666666666666666664 k 1 [ I ] N c N c C l ; a 800 d x 4 ( i ) d x 1 ( i ) 1 x 3 ( i ) d x 1 ( i ) d u ( j ) x 4 ( i ) x 1 ( i ) x 23 ( i ) d x 3 ( i ) d u ( j ) # 1 i N c 1 j N c 26666666666666666666666666666664 k 2 d x 4 ( i ) d x 1 ( i ) 1 x 3 ( i ) d x 1 ( i ) d u ( j ) ( x 4 ( i ) x 1 ( i )) d x 3 ( i ) d u ( j ) u + min max min + 1 1 x 3 ( i ) d x 3 ( i ) d u ( j ) + d x 4 ( i ) d x 1 ( i ) 1 x 4 ( i ) x 1 ( i ) d x 1 ( i ) d u ( j ) + 8590 max min x 3 ( i ) d x 3 ( i ) d u ( j ) d x 4 ( i ) d x 1 ( i ) 1 x 3 ( i ) d x 1 ( i ) d u ( j ) ( x 4 ( i ) x 1 ( i )) d x 3 ( i ) d u ( j ) 1 : 718 max min ( x 4 ( i ) x 1 ( i )) d x 4 ( i ) d x 1 ( i ) 1 d x 1 ( i ) d u ( j ) d x 4 ( i ) d x 1 ( i ) 1 x 3 ( i ) d x 1 ( i ) d u ( j ) ( x 4 ( i ) x 1 ( i )) d x 3 ( i ) d u ( j ) 37777777777777777777777777777775 1 i N c 1 j N c 377777777777777777777777777777777777777777777777777775 where k 1 = C l ; a ( max min ) 6 and k 2 = 2 : 91 AR 3 C l ; a ( max min ) 10 3 I R 54

PAGE 71

Calculate d C d u ( ) + ( ) + Calculate C ( u ; x ) rr RR + + + + Prediction d x d u d L d u x x 0 u Figure4.3:BlockdiagramoftheNN-NMPC.Theleftpartconcernsthemodel-basedprediction,whileontherightarecurrentneuralnetworkisusedfornon-linearoptimization.Withtheexceptionofthepredictionblock,theotheroperationscanberuninparallel.4.2.3.3Non-linearOptimizationAfterthe d L d u C ( u )and d C d u quantitiesarecalculated,theyarefedtotherecurrentneuralnetwork. TheblockdiagramoftheentireNN-NMPCisprovidedinFigure4.3.AfterthepredictionblockdetailedinFigure4.2hascompleteditscalculations,theconstraintanditsderivativewithrespecttothecontrolsequencearecalculated.Eachelementoftheconstraintvectoraswellasthecon-straintderivativematrixcanbecalculatedindependently,allowingparallelization.TherightpartoftheNN-NMPCimplementstherecurrentneuralnetworkusedfornon-linearoptimization.Thetoppathupdatesthecontrolsequencewhilethelowerisusedtoupdatetheauxiliaryvector mapping theconstraints.FromFigure4.3,thenumberofoperationsintheneuralnetworkare N c 2 + 3 N c multiplications, N c 2 + 9 N c additionsand4 N c comparisonswhichindicatesanexecutiontimeof O ( N c 2 ).Neverthelessinthecaseofspecializedhardwarethatallowsparallelization,thesameoperationscanbeaccomplishedin O ( N c ).Furthermorethetimeconstantcanalsobereducedbyexecutingthe updateof u and inparallelandtakingintoaccountthatthe d C d u matrixistriangular,wherebythe numberofoperationsinthedotproductblockaresignicantlyreduced.4.2.4DesignSummaryThealgorithmsummarizingthecollectivecontrollerisgiveninFigure4.4.Theinnerloopcorre-spondstotheNN-NMPCcalculationstodeterminetheoptimalcontrolsequence,whiletheouterloopexecuteswhenanewstateisobserved.Insidetheinnerloop,asmallerpredictionloopisexecutedthatcalculatesincrementallythe x d x d u d L d u C ( u )and d C d u quantities.Thisapproachwas 55

PAGE 72

chosentolowertheamountofmemoryrequiredtoexecutethecalculations.Specicallyonlythemostcurrentvalueof x d x d u and d L d u iskept. Itshouldalsobenotedthatthenumberofrepetitionsoftheinnerloopisnotnecessarilyconstant.Analternativedesignmaybeusedthatcontinuouslyupdatesthecontrolsequenceuntilanewstateisobservedortheneuralnetworkhasconverged.foreach Newsensordata( z )received do Outerloop Filter( z )usingEKFtoobtainanestimateoncurrentstate x (0) for k 0 to E 1 do Innerloop d L d u w u T u for i 0 to N s do for j 0 to N c 1 do Calculate d x ( i ) d u ( j ) endCalculate x ( i + 1)from x ( i ) d L d u d L d u + d L d x d x ( i ) d u Calculate C ( i ) // C T constraint Calculate C ( N c + i ) // n constraint for j 1 to N c 1 do Calculate d C ( i ) d u ( j ) // C T constraint Calculate d C ( N c + i ) d u ( j ) // n constraint end end + r h + C ( u ) + i u u + r u + u d L d u d C d u + endSendcollectivecommand u (0) u [ u (1) u (2) ::: u ( N c 1) u ( N c 1) ] endFigure4.4:TheNN-NMPCalgorithm.Online3insteadofhavingaxedepochsize,theupdatingmaybeallowedtocontinueuntilnewsensordataareavailableorthenetworkhasconverged.Asmentionedintheprevioussections,severalofthecalculationsrequiredcanbeexecutedinparallelthusallowinghigherupdaterates.Figure4.5providesanoverviewofhowthealgorithmofFigure4.4canbeexecutedonspeciallydesignedhardware.4.3VerticalAutorotationControllerItshouldbenotedthatalthoughtheNN-NMPCisthecentralpartoftheverticalautorotationcon-troller,itrequiresothercomponentstooperatee ciently.Sincetheothercomponentsareintrinsic 56

PAGE 73

1 2 3 4 5 6 7 8 9 1 x (1) 2 x (2) d x (1) d u 3 x (3) d x (2) d u @ L @ x (1) d x (1) d u C (0) C ( N c ) d C (0) d u d C ( N c ) d u ::: N c + 1 x ( N c + 1) d x ( N c ) d u @ L @ x ( N c 1) d x ( N c 1) d u C ( N c 1) C (2 N c 1) d C ( N c 1) d u d C (2 N c 1) d u N c + 2 x ( N c + 2) d x ( N c + 1) d u @ L @ x ( N c ) d x ( N c ) d u ::: N s x ( N s ) d x ( N s 1) d u @ L @ x ( N s 2) d x ( N s 2) d u N s + 1 d x ( N s ) d u @ L @ x ( N s 1) d x ( N s 1) d u N s + 2 @ L @ x ( N s ) d x ( N s ) d u N s + 3 u Figure4.5:OverviewofthecalculationsintheNN-NMPCloopthatcanruninparallel.Eachboxcanbeexecutedin O (1)time.Columnssignifycomputationsrunninginparallel,specicallynine parallelcomputationstreams.Toexecutethecomputationsofeachrow,theresultsofthepreviousrowmustrstbeavailable.Thismeansthattheentirelooprequires O ( N s )time. toitsoperationtheyshouldnotjeopardizethecapabilityforreal-timeoperationbyimposingsig-nicantcomputationaloverhead.SincetheNN-NMPCprovidesonlythecollectivepitch,oneoftheaforementionedrequiredcom-ponentsisacontrollerthatdeterminesthecyclicandtailrotorpitchcommandsnecessarytokeeptheaircraftlevelandwithconstantheading.Thiscontrollercaneitherbethenominalightcon-trollerofthehelicopteroranindependentmoduleimplementedintheverticalautorotationcon-troller.Ineithercase,henceforthitwillbereferredtoastheRPYcontroller.Furthermore,andbeforesensormeasurementsareusedbytheNN-NMPCforpredictionanddeterminingtheoptimalcontrolsequence,theyneedtobeappropriatelylteredtoremovenoise.Thefollowingsectionspresentthesetwocomponentsaswellasanoptionalcomponentthatlterstheoutputoftheneuralnetwork.Thelatterprovidesdiagnosticinformationontheconvergence 57

PAGE 74

behavioroftheneuralnetworkandcanbealsousedtoprovideabetterestimateoftheoptimalcontrolactioninthecasewheretheneuralnetworkdidnotsuccessfullyconverge.4.3.1Roll / Pitch / YawController TheRPYcontrollerisusedtokeeptheroll,pitchandyawratesnearzeroduringdescent.ThisensuresthatallofthemainrotorthrustisusedtokeepthehelicoptersinkrateincheckandasaresulttheaccuracyofthemodeldescribedinSection4.2.1doesnotdeteriorate.Inadditiontothat,itisresponsibleformaintainingzerolateralandlongitudinalvelocity,e ectivelyensuringa verticalautorotation.Inthisworkafuzzycontrollerdescribedin[32]wasusedtoimplementtheRPYcontroller.Theoriginalcontrollerconsistedoffourindependentfuzzyinferencesystems,oneforeachoftheaforementionedcontroloutputsandoneforcontrollingthecollective.Thepitchandrollcon-trollersareusedunchanged.Eachhasfourinputs,oneoutputand375rules.Thetailrotorpitchcontrollerhastwoinputs,theheadingerrorandtheyawrate.Theoutputalsoincorporatedabiasdesignedtocounterthehelicopterturningmomentduetothemainrotor.Thiscontrollerwasmodiedtotakeintoaccountthechangeinthemomentinducedbythemainro-torafterthefailureoccurs.Specicallytheinternalbiaswasremovedandtheoutputgivestherequiredtailrotorpitchassumingnotorquingfromthemainrotor.Anexternalbiasisthenin-troducedthatcalculatestherequiredtailrotorthrustandfromthatthetailrotorpitchtoexactlycounterthemainrotor.Therequiredbiasiscalculatedusing(3.21): Q MR T TR l TR = 0 A MR n MR 2 R MR 2 C Q MR A TR n TR 2 R TR 2 C T TR l TR = 0 C T TR = n MR 2 R MR 5 n TR 2 R TR 4 C Q MR l TR (4.39)Themainrotortorquecoe cientiscalculatedbasedon(3.20)andthenusedin(4.39)tocalculate therequiredtailrotorthrustcoe cienttocountertheturningmomentoftherotor.Afterthelatter isobtained,itisconvertedtotailrotorpitchusing(3.19).AnoverviewofthedesignoftheRPYcontrollerisgiveninFigure4.6.Thethreefuzzyinferencesystemsreceiverelevantsensorinformationafterrequiredpreprocessingtocalculateerrorsandconvertvelocitiesfromthelocaltotheglobalframe. 58

PAGE 75

Lon.ErrorLon.Vel.Lon.Accel. Pitch Lon.Cyclic Lat.ErrorLat.Vel.Lat.Accel. Roll Lat.Cyclic YawerrorYawrate Tailpitch Localtoglobalframe transformation d d t d d t LongitudeLongitudesetpointPitchLatitudeLatitudesetpointRollLocalLon.Vel.LocalLat.Vel.YawHeadingsetpointYawrate + + + Tailpitchbias calculation Figure4.6:BlockdiagramoftheRPYcontroller.4.3.2SensorFusionTheinformationfromthesensorsislteredusinganExtendedKalmanFilter(EKF)thatutilizestheinternal,non-linearmodelofverticalautorotation.Thisallowstheremovalofsensornoise,whilereusingthecalculationscarriedoutinthepredictionstepoftheNN-NMPC.AsaresultofthelatterthecontributionoftheEKFtothetimerequiredforacompleteloopisminimal.ThestatetransitionandobservationequationsusedfortheEKFaregivenby: x ( k + 1) = x ( k ) + t s f ( x ( k )) + t s g ( x ( k )) u ( k ) + ( k ) (4.40) z ( k + 1) = x ( k + 1) + ( k ) (4.41) wherethe ( t )and ( t )representzeromeangaussiannoisewithcovariancematrices Q and R respectively.TheoperationoftheEKFistypicallyseparatedintotwosteps,thepredictionandtheupdate.Thepredictionsteprstcalculatesthepredictednewstate x ( k + 1)ofthehelicopterbasedonthe previousstateandthecontrolactionfrom(4.21).Itthenupdatesthecovariancematrix P using: (4.42) P h I + t s J f ( x ( k )) + t s J g ( x ( k )) u ( k ) i P h I + t s J f ( x ( k )) + t s J g ( x ( k )) u ( k ) i T + Q 59

PAGE 76

Intheupdatestep,thepredictionsarecorrectedbasedontheactualnewstateofthehelicopterasmeasuredbythesensors z ( k + 1).TheKalmangainiscalculatedby: (4.43) K = P ( P + R ) 1 Thepredictednewstateisthenupdatedusing:(4.44) x ( k + 1) x ( k + 1) + K [ z ( k + 1) x ( k + 1) ] andthecorrectedcovariancematrix P isgivenby: (4.45) P ( I K ) P IntheequationsabovethesloweststepisthematrixinversionrequiredforcalculatingtheKalmangainin(4.43).ThisisaccomplishedusingLUfactorizationandbacksubstitutionofunitvectors,althoughdirectcalculationisalsopossiblesincethematrixisonlyofsize3.4.3.3NeuralNetworkFilteringAlthoughnotnecessaryfortheperformanceoftheNN-NMPC,anadditionalmodulewasintro-ducedintheoutputoftheneuralnetwork.Itisusedfordiagnosticpurposesandsimulationresultanalysisbyprovidinginsightonhowwelltheneuralnetworkhasconverged.Specically,thismodulekeepsarecordoftheaverageandvarianceofthenetwork'soutputduringthelast20%oftheepoch.Toconserveonmemorybothvaluesareevaluatediterativelybasedonthepreviousvalue.Themeanisgivenby[85]:(4.46) n = n 1 n n 1 + 1 n u n whilethevarianceiscalculatedbyadaptingtheiterativecalculationofcorrectedsumsin[85]asfollows:(4.47) 2n = 2n 1 + n 1 n 2 ( u n n 1 ) 2 wherethesubscriptdenotesthenumberofentriestakenintoaccount.Forexampleifthevaluestobeaveragedaregivenby x i i = 1 ; 2 ;:::; n : (4.48) n 1 n n X i = 1 x i 60

PAGE 77

Anotheruseofthismoduleistoprovidethemeanvaluerecordedasthecontroloutputtothehe-licopter.Thismaybebenecialwhenthereisaconcernonwhethertheneuralnetworkconvergedornot,butwillnothaveanye ectifconvergencewasachievedearly. 4.3.4VerticalAutorotationControllerBlockDiagramTheblockdiagramoftheverticalautorotationcontrollerisgiveninFigure4.7.Therearetwodistinctloopsinthecontroller.TherstisinternaltotheNN-NMPCandisusedtooptimizethecontrolsequenceforthecurrentstate.Theupdaterateusedisdeterminedbytheepochsizeparam-eter( E )whichcorrespondstothenumberofiterationsoftheneuralnetwork.Inthesimulations detailedinChapter5,itisexecutedwithratesupto3kHz. u u (1) Extended KalmanFilter u (2) ; u (3) ;:::; u ( N c 1) ; u ( N c 1) Helicopter NN-NMPC ˆ x RPYController Pitch RollYawColl Averaging Filter Figure4.7:Blockdiagramoftheverticalautorotationcontroller.ThecontrolleriscomprisedoftheNN-NMPCwhichisresponsibleforcollective,theRPY-Controllerforroll,pitchandyawaswellasanEKFtoltertheinformationsentbythesensors.Thesecondlooprunsatasignicantlylowerrate(10–20Hz)andincludesthehelicopter.Ineachiterationoftheouterloopitrstsamplesthestateoftheneuralnetworkwhichcorrespondstothe(near-)optimalcontrolsequence.Therstelementofthatsequenceissenttothehelicopter,whiletherestisfedbackastheinitialneuralnetworkstateforthenextoptimizationepoch.Atthesametimethenewstateofthehelicopterisobserved,lteredusingtheEKFandfedbacktothepredictionblockoftheNN-NMPC. 61

PAGE 78

Chapter5:SimulationResultsTheNN-NMPCisimplementedasaClibrarytoallowtestingwithdi erentsimulatorsandenvironments.Todetermineitsperformance,aswellasthee ectofvariousparametersonaccuracy andconvergencespeed,severalsimulationswerecarriedoutmodelingdi erentscenarios.The resultsofthesetestsarepresentedintwosections,therstconcerningthecaseoftheOH-58AhelicopterwithhighenergyrotorsystemandthesecondtheThundertigerRaptor30v2.ThesimulationswerecarriedoutusingasimulatordevelopedinC ++ thatimplementsthemodel describedinSection3.5.Theupdaterateusedis1kHzwhiletheNN-NMPCupdateratecanbesetindependently.Thesimulatoracceptsarangeofcommand-lineoptionsthatincludehelicopterselection,initialhelicopterstateandNN-NMPCparameters.Duringexecution,thesimulationtime,convergenceprogressaswellasboththeactualandmeasuredstatepresentedtothecon-trolleraresavedinaletoallowlateranalysis.Inadditiontotheuseoftheaforementionedsimulator,experimentsweredoneintheX-Planesim-ulator.Thisparticularsimulatoro ershighprecisionandtheabilitytointerfacewithcontrollers locatedlocallyoronthenetworkusingtheUDPprotocol.Italsoo erssuperiorvisualization capabilitiesaswellasvideocapturing.FortheX-Planesimulations,agraphicaluserinterfacewasdevelopedfortheNN-NMPCusingQt / C ++ .TheuserinterfaceallowseasymonitoringofthestateofthehelicopterinX-Planeaswell assettingparametersandset-points.ThecommunicationisimplementedusingUDPonalocalnetworkatanupdaterateof10Hz.SpecicallytheX-Planesendsinformationonthestateofthehelicopterandsimulatorandreceivesfourcommands,thelongitudinalandlatercyclicintherange[0 ; 1]andthecollectiveandtailrotorpitchindegrees.ThissoftwarealsoimplementstheRPY controllerasaseparatemodule.ThelatteriscapableofreadingfuzzyinferencesystemdenitionsproducedbythefuzzytoolboxofMatlabandstoringtheminmemory.Itthencalculatesthecyclicandtailrotorpitchcommandstakingintoaccountthebiasfrom(4.39).Beforediscussingtheresults,threeregionsofoperationareidentiedasshowninFigure5.1whichdepictsthesinkrateand n trajectoriesforadescentstartingat120m.Thedistinctionbetween theseregionswillbeusedextensivelyinthischapterbecausethee ectofcertainparameterson controllerperformancechangesfromonetoanother.Eachregionischaracterizedbythethevari-ablethatgovernstheoutputofthecontroller.Specicallywhereasintherstregion,theheli62

PAGE 79

copterdescentsfreely,atonepointtherotorrpmapproachesthemaximumallowedandthenthen -controlledregionisentered.Inthelaststageofthedescent( v H -controlledregion)thesinkrate israpidlyreducedandmaintainedatalowvalueuntilthehelicoptertouchestheground.Itshouldbenotedthatwhentheinitialaltitudeissu cientlysmall,thehelicoptermayneverenterthe n controlledregion. 0 5 10 15 20 0 20 40 60 80 100 120Sinkrate(ms 1 )z inmFreedescentn -controlleddescent v H -controlleddescent0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 0 20 40 60 80 100 120RPMratio( n = n 0 )z inmFreedescentn -controlleddescent v H -controlleddescent Figure5.1:Duringtheautorotativedescentthehelicoptertraversesthreedistinctregionsofoperation:free, n -controlledand v H -controlleddescent. 5.1OH-58AHERSTheOH-58Aisasingleenginehelicopterusedmainlyinmilitaryobservationapplicationsmod-iedwithahighenergyrotorsystem(HERS).ItwasinitiallydevelopedbyBellhelicopterinthelate1960sbasedonthedesignoftheBell206Jetranger.In1976theU.S.ArmyMobilityResearchandDevelopmentLaboratoryawardedacontracttotheBellHelicopterTextroncompanytitled“IncreasedAircraftAgilitywithHighEnergyRotorSystem”[18].Thecompanymodiedthebladesaddingtipweightstoincreaseinertiaandperformedightteststotalling21 : 9h[18]. TheresultswerelaterusedbyLee[51]andotherresearcherstotestoptimalautorotationtrajectoryoptimizationalgorithms.TheparametersusedforthesimulationsaresummarizedinTable5.1.5.1.1BaselineScenarioThebaselinecaseagainstwhichthetestedscenariosarecomparedinvolvesadescentfromaninitialaltitudeof120musingperfectsensorinformation.Thecontrollerobjectiveistomaintainasinkrateof0 : 5ms 1 duringthelast3mofthedescent.Thesimulationisperformedatanupdate rateof1kHzwhilethecontrollerisrunat10Hz.Theneuralnetworkparametersare E = 150and r = 0 : 08. 63

PAGE 80

Table5.1:VerticalautorotationmodelparametersforamodiedOH-58Ahelicopterwithhighenergyrotorsystem.Source:[18,51]. Helicoptermass( M )1 ; 360kg Mainrotormomentofinertia( I R )1 ; 822kgm 2 Solidityfactor( )0 : 048 Mainrotordiscradius( R )5 : 37m Mainrotormeandragcoe cient( C d ; 0 )0 : 0087 Mainrotorliftcoe cient( C l ; a )5 : 73rad 1 Equivalentunitdragcoe cientarea( f e )2 : 32m 2 Inducedpowercorrectionfactor( )1 : 13 Nominalmainrotorspeed( n 0 )354rpmor37rads 1 Airdensity( )1 : 225kgm 3 Distancebetweentailandmainrotor5 : 94m Nominaltailrotorspeed( n 0 TR )2 ; 620rpmor274 : 4rads 1 Tailrotordiscradius( R TR )0 : 82m Tailrotorliftcoe cient( C l ; a TR )5 : 04rad 1 Tailrotorsolidityfactor( TR )0 : 094 Minimummainrotorpitch 2 Maximummainrotorpitch16 Maximummainrotorrpm1 : 15 n 0 Theresultingsinkrate,rotorrpmandcontrolinputtrajectoriesfor N s = 10and N c = 5are presentedinFigure5.2.Thesametrajectoriesforlargerpredictionandcontrolhorizons,namely N s = 12and N c = 6areshowninFigure5.3. Theresultsshowthatthehelicopteraccomplishedthestatedobjective,withoutviolatingthethrustcoe cientandrpmconstraints.Thewholemaneuverlastsforabout14s,althoughabouthalf ofitcorrespondstothelast4mofthedescent.Thesuddenjumpinbladepitchatanaltitudeofabout60misduetothebigdroprequiredinthesinkratesothatthe n -constraintisnotviolated. Asmoothertransitionisalsopossible,butattheexpenseofeitherviolatingtheconstraintorre-quiringalongerpredictionhorizon.Itshouldalsobenotedthatalthoughasinkrateof0 : 5ms 1 isachieved,towardstheendofthe maneuveranincreaseinthesinkrateisobserved.Thisisduetotherapidlossofinertialenergyintherotorandtheonsetofstallinthebladesthatrequirescheckingtherateofincreaseofthebladepitch.Nevertheless,anddespitetheincrease,thevelocityattouchdownremainswithinmechanicaltolerancesofthelandinggear,sincethelatteristypicallydesignedforsinkratesupto3ms 1 Bothoftheaforementionedguresalsopresenttheresultingtrajectoriesfor E = 1500.Itis obviousthatdespitethetenfoldincreaseinthetimeavailabletotheneuralnetwork,theoutputisnotsignicantlydi erentandtheresultsarecomparable. 64

PAGE 81

0 5 10 15 20 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 12 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 12 2 0 2 4 6 8 10 12 14 16 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 12 4 2 0 2 4 6 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 12 0 5 10 15 20 5 8 11 14Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 4 0 : 1 1 10 100 5 8 11 14z inmTimetotouchdownins 0 1 2 3 4 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 Figure5.2:Thesinkrate,rotorrpmandcontrolinputoftheOH-58Ahelicopterforadescentfromaninitialaltitudeof120m( N s = 10, N c = 5).Theshadedregionsrepresenttheposedconstraints. Thescaleontherightsideofthegraphshasbeenalteredtoshowthelaststageofthedescentinhigherdetail. 65

PAGE 82

0 5 10 15 20 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 12 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 12 2 0 2 4 6 8 10 12 14 16 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 12 4 2 0 2 4 6 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 12 0 5 10 15 20 5 8 11 14Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 4 0 : 1 1 10 100 5 8 11 14z inmTimetotouchdownins 0 1 2 3 4 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 Figure5.3:Thesinkrate,rotorrpmandcontrolinputoftheOH-58Ahelicopterforadescentfromaninitialaltitudeof120m( N s = 12, N c = 6).Theshadedregionsrepresenttheposedconstraints. Thescaleontherightsideofthegraphshasbeenalteredtoshowthelaststageofthedescentinhigherdetail. 66

PAGE 83

5.1.1.1CostFunctionThecostfunction,chosenbytrialanderror,isgivenby:(5.1) L = 0 : 05 ( max( v H ; 5 : 5) 0 : 5 ) 2 e 1 1 : 25min( z ; 1) andisvisualizedinFigure5.4.Thisfunctionwasdesignedtointroducelargepenaltiesforsinkratesawayfrom0 : 5ms 1 during thelast3mofthedescent.Tokeepthecostfunctionfromincreasingtoomuch,thesinkrateinputissaturatedto5 : 5ms 1 .Similarlyanexponentialtermisusedtomakethetransitiontoloweraltitudessmootherandavoidlargederivatives.Finallythescalingconstantwasdeterminedthroughtrialanderrortoensurederivativeswithappropriateorderofmagnitude.Sinkrate(ms 1)Altitude(m) 2 0 2 4 6 8 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1PenaltyFigure5.4:ThecostfunctionusedbythecontrollerforautorotationoftheOH-58Ahelicopter.5.1.1.2Non-linearOptimizationProblemConvexityToevaluatethepossibilityofthehelicopterenteringregionswheretheproblemisnon-convex,randomsamplingwasusedtodeterminethemaximumallowablepredictionhorizon.Specically28 ; 000samplesweretakenovertheentirestate-actionspaceandfordi erentcontrolhorizons andcontrollersamplingtimes.Foreachsamplethehighestvalueof N s (upto100)wherethe d 2 L d u 2 remainspositivedenitewasrecorded.This N s representsaconservativelimitonthelongest predictionhorizonavailable.Thisisbecauseitispossiblethatevenaftermomentarilyenteringanon-convexregion,atthenextepochtheproblemwillbeconvexagain.FurthermoreasdiscussedinSection4.2.2,theneuralnetworkiscapableofglobalconvergenceforaclassofnon-convexproblemsaswell. 67

PAGE 84

The5%ofthesamplesexhibitingthelowerallowable N s arepresentedinFigure5.5.Theseresults wereobtainedusing N c = 6and t s = 50ms.Itisevidentthathighsinkratesmayjeopardizethe convexityoftheproblem.Thisisexacerbatedbycorrespondinglyhighactionvaluesthatwouldnormallyviolatethethrustcoe cientconstraint.Inanycasetheworst-case N s wasfoundtobe20 andlessthan2%ofthesampleshad N s < 40. 2 0 2 4 6 8 10 12 14 16 05101520max( u 1 ; u 2 )(degrees)Sinkrate(ms 1 ) Figure5.5:Worst-case N s fordi erentvaluesof v H ,bladepitchwith N c = 6and t s = 50msinthe caseoftheOH-58Ahelicopter.Thelowestvaluesoccurforhighsinkratesandaretypicallycombinedwithhighinputactions.Thee ectofdi erentvaluesof N c and t s ontheworst-casepredictionhorizonisfoundinFigure5.6.Thisgureshowsthatthecontrolhorizonhasasignicantlymorepronouncede ectthan thesamplingtimeused.Forlow t s theproblemisconvexevenwithpredictionhorizonsapproaching40.Inthecaseof t s = 50msthatwaschosenforthesimulations,theworstcase N s varies between8and20dependingonthecontrolhorizon.Neverthelessitshouldbenotedthattherstoctileis100withtheexceptionof N c = 10.Ingeneralapredictionhorizonupto0 : 5saheadisnot expectedtocauseconvergenceproblemsduetoproblemnon-convexity.5.1.1.3ConvergenceCharacteristicsTheoutputoftheneuralnetworkduringeachepochofthebaselinesimulationandfordi erent stagesofthedescentispresentedinFigures5.7to5.9.Thetransitionfromfreeto n -controlled descentispresentedinFigure5.7.Theoscillationsinepochs39and40arebecauseofthesuddenjumpinrequiredoutputandtheassociatedlearningrate.Theycouldhavebeenavoidedatthecostofaslowertransitionandthepossibilityofviolatingtherpmconstraint.Usingahigherupdateratemayalsohelptoalleviatethisissuesinceitallowsfornercontrol.Thetransitionfrom n -controlledto v H -controlleddescentissmootherandispresentedinFigure5.8.Oscillationsarealsoevidentinepoch71thatarealsoattributedtothesuddenjumpin 68

PAGE 85

4 5 6 7 8 9 10 1030507090110130150ControlhorizonControllertimestep(ms) 46,10067,10017,10012,1007,646,567,406,38 100,10015,1008,1009,7510,698,426,336,35 100,10027,10020,1007,799,597,427,365,31 60,10014,10010,10017,724,528,406,376,30 23,10026,1009,10013,684,5414,399,338,29 52,10020,1008,10010,6114,489,385,344,27 46,10031,1008,9214,606,4710,366,327,29 Figure5.6:Worst-caseandrstoctile N s asafunctionof N c t s inthecaseoftheOH-58A helicopter.TherstoctilewascalculatedusingtheM&Mmethod[59].requiredoutput.Incontrast,thelearningratewasinsu cienttoallowconvergenceinepoch72. ThenalstageofthedescentincludingthetouchdownispresentedinFigure5.9.Inthiscasetherotorrpmhasdecayedsignicantlyandthehelicopteristryingtomaintainthrustwithoutenteringstall.Thisresultsinsomeoscillationsinthelastfewepochs,thatareneverthelessofverysmallamplitudeanddonotinuencethesuccessfulcompletionofthemaneuver.5.1.1.4Real-timeOperationAnadditionalparameterthatisimportantinthisproblemistheexecutionspeedofthecontroller.Todeterminethis,theexecutiontimeofasingleiterationwascalculatedfordi erentprediction andcontrolhorizons.Sinceasingleiterationisveryfast,itsexecutiontimewasestimatedbymeasuringthetotaltimerequiredfor2 ; 000iterations.ThetestswerecarriedoutusingasinglecoreAthlonXP3200 + (modelof2005)CPU,throttledtoafrequencyof1GHzrunninga32bitversionofDebianLinux.Noparallelizationoro -lineoptimizationwasusedtoimprovethe executiontime.ThecostoftheEKFwasalsocalculatedunderthesameconditionsandwasfoundtobeapproximately128 s. TheresultsofthesetestsarepresentedinFigure5.10asafunctionofpredictionhorizon.For N s = 10and N c = 5acontrolleriterationrequired0 : 88mswhereasfor N s = 12and N c = 6thistime increasedto1 : 23ms.Ifanupdaterateof10Hzischosen,undertheaforementionedconditionsthe maximumepochlengthis113and81respectively.Forhigherpredictionandcontrolhorizonthenumberofpossibleiterationsdropsconsiderably,downto30for N s = 20and N c = 10. 69

PAGE 86

0 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5 3637383940414243444546474849505152535455NeuralnetworkoutputNeuralnetworkepoch Figure5.7:Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfromfreeton -controlleddescentinthecaseoftheOH-58Ahelicopter.Thetransitioniscompletewithin5 epochsor0 : 5s. 0 : 2 0 : 3 0 : 4 0 : 5 0 : 6 0 : 7 0 : 8 6667686970717273747576777879808182838485NeuralnetworkoutputNeuralnetworkepoch Figure5.8:Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfromn -controlledto v H -controlleddescentinthecaseoftheOH-58Ahelicopter. 0 : 8 0 : 9 123124125126127128129130131132133134135136137138139140141142NeuralnetworkoutputNeuralnetworkepoch Figure5.9:TheevolutionoftheoutputoftheneuralnetworkinthelastsecondsbeforetouchdowninthecaseoftheOH-58Ahelicopter. 70

PAGE 87

0 0 : 5 1 1 : 5 2 2 : 5 3 3 : 5 4 4 : 5 891011121314151617181920Time(ms)Predictionhorizon N c 141210 86 Figure5.10:Theexecutiontimepercontrollerinnerloopiterationasafunctionofpredictionandcontrolhorizon.5.1.2InitialAltitudeTheinitialaltitudecaninuencethestateofthehelicopteratthenalstageofthedescentandspecicallytherotationalenergyavailableintherotortoreducethesinkrate.Forinitialaltitudesexceeding90mthehelicopterwillhavetimetoreachthelimitoftheallowablerotorrpm.Asaresultineachcaseitwillreachthearealtitudewith n 1 : 15 n 0 and v H 15ms 1 Converselyintheoccasionsweretheinitialaltitudeislowerthan90m,thekineticenergystoredintherotorwillbelower.Thesinkratecanbelowerthan15ms 1 ifthehelicopterfailedatavery lowaltitude( < 10m)orhigherforintermediatealtitudes.Figure5.11presentsthetrajectoriesfor threesimulationsthatfeatureaninitialaltitudeof120m,60mand30m.Inthelastinstanceandalthoughtheoutputofthecontrollerdoesnotdeviatesignicantlyfromthatoftheothersimula-tions,thetargetsinkrateisachievedonlycentimetersabovetheground.Thisisbecauseofthethrustcoe cientconstraintandthelowerenergystoredintherotor.Toimprovetheperformance inthiscase,eitherthepredictionhorizonwouldneedtobeincreasedorthethrustcoe cientconstraintberelaxed.5.1.3LearningRateHighervaluesoftheneuralnetworklearningrateparameteraretypicallyusedtoimprovetheconvergencespeed.Ontheotherhand,suchvaluescanleadtoover-correctionsandoscillations.Thisisexacerbatedbyconstraintenforcementandresultsinproducingtheoppositeofthedesirede ect.Theinuenceofthee ectofthecontrollerdesignparameter r wasevaluatedusingthe varianceintheneuralnetworkoutputduringthelast20%oftherepetitionsofeachcycle.The 71

PAGE 88

0 5 10 15 20 30 50 70 90 110Sinkrate(ms 1 )Altitude(m) 0 2 4 6 8 10 12 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )Altitude(m) 0 2 4 6 8 10 12 2 0 2 4 6 8 10 12 14 16 30 50 70 90 110Bladepitch(degrees)Altitude(m) 0 2 4 6 8 10 12 4 2 0 2 4 6 30 50 70 90 110Thrustcoe cientAltitude(m) 0 2 4 6 8 10 12 0 5 10 15 20 5 8 11 14Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 4 0 : 1 1 10 100 5 8 11 14z inmTimetotouchdownins 0 1 2 3 4 z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 120m z 0 = 60m z 0 = 30m Figure5.11:Thee ectofdi erentinitialaltitudesontheperformanceoftheOH-58Acontroller. 72

PAGE 89

variancewascalculatedusingthemoduledescribedinSection4.3.3.Iftheneuralnetworkhasconverged,lowoutputvarianceisexpected.TheresultssummarizedinFigure5.12showthathighvarianceisexhibitedmainlyinregionswherethehelicoptertransitionsfromonemodetoanother.Thisisexpectedbecausethecostandconstraintderivativestaketheirhighervaluesthere.Additionallyforlearningrates0 : 12andabove, varianceisexhibitedrstintheregionofdecelerationandthenintheentirevelocity-controlledregion.5.1.4NoiseToinvestigatetheimpactofsensornoiseoncontrollerperformance,threesimulationswerecarriedoutusingthreedi erentnoiselevels.Inallcasesthenoiseisconsideredtobezero-mean,gaussian withvaryingstandarddeviation.ThenoiselevelsaresummarizedinTable5.2.Table5.2:SensornoiselevelsusedinthecaseoftheOH-58Ahelicopter. Standarddeviation Level1Level2Level3 Sinkrate(ms 1 )0.10.20.5 Altitude(m)0.10.250.75Rotorspeed(RPM)3.5710.5 Figure5.13showsthesimulationresultsfortherstnoiselevelscenario.Thetrajectoryisnotsignicantlychangedandtheonlythinga ectedisthecontrolleroutputduringthe n -controlled descent.ThelatteroccursbecauseofthedesignofthecontrollerthattriestomaintainconstantrpmandbecomesmorepronouncedasthenoiseintherpmmeasurementsincreasesasshowninFigure5.14.Asthenoiselevelincreasesthe v H -controlledregionstartstogeta ectedaswell. Thisisbecausethecontrollerisrequiredtomaintainaconstantvelocityinthefaceofnoisymea-surements.Neverthelesseveninthecaseofthethirdnoiselevel,thetrajectoryisnotsignicantlya ected.Itshouldbenotedthatinthelastcasethesimulationisterminatedearly.Thisisbecause accordingtotheinformationavailabletothecontroller,thehelicopterhasreachedtheground.Toalleviatethisprobleminanactualimplementationthecontrollercanbeallowedtocontinuegivingcommandsevenafterthersttimethealtitudesensorindicatesatouchdown.5.1.5ReactionTimeReactiontimecanplayanimportantroleinthesuccessofanautorotationmaneuver.Therequiredmaximumpilotreactiontimetoaneventis2s,buthighworkloadmaynegativelyinuencethat[70].Althoughanautomatedsystemisexpectedtoallowsub-seconddetectionofafailure,the 73

PAGE 90

C Tr = 0 : 04C Tr = 0 : 12C Tr = 0 : 08C Tr = 0 : 16 0 2 4 6 8 10 12 14 16 18 0246810121416v H (ms 1 )Time(s) 10 2 10 3 0 2 4 6 8 10 12 14 16 18 024681012v H (ms 1 )Time(s) 10 2 10 3 0 2 4 6 8 10 12 14 16 18 0246810121416v H (ms 1 )Time(s) 10 2 10 3 0 2 4 6 8 10 12 14 16 18 024681012v H (ms 1 )Time(s) 10 2 10 3 Figure5.12:ThevarianceoftheneuralnetworkoutputwithrespecttotimeandhelicoptersinkrateforfourvaluesofthelearningrateparameterinthecaseoftheOH-58Ahelicopter.Largercirclesmeanlargervariancewhilevariancessmallerthan10 4 arenotshown.Forcomparison purposesthethrustcoe cientatthecorrespondingtimeisalsoprovided. 74

PAGE 91

0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3Abs.Error 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3Abs.Error 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03Abs.Error 4 2 0 2 4 6Thrustcoe cient0 5 10 15 20 02468101214Sinkrate(ms 1 )Time(s) 0 : 1 1 10 100 02468101214Altitude(meter)Time(s) 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 02468101214RPMratio( n = n 0 )Time(s) 2 0 2 4 6 8 10 12 14 16 02468101214Pitch(degrees)Time(s) Withnoise Nonoise Withnoise Nonoise Withnoise Nonoise Figure5.13:ThetrajectoryoftheOH-58Ahelicopterwithandwithoutnoiseundertherstnoiselevel.Thecrossescorrespondtothemeasurementsgivenbythecorrespondingsensor. 75

PAGE 92

0 : 4 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5Abs.Error 0 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8Abs.Error 0 : 05 0 : 04 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03 0 : 04Abs.Error 4 2 0 2 4 6Thrustcoe cient0 5 10 15 20 02468101214Sinkrate(ms 1 )Time(s) 0 : 1 1 10 100 02468101214Altitude(meter)Time(s) 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 02468101214RPMratio( n = n 0 )Time(s) 2 0 2 4 6 8 10 12 14 16 02468101214Pitch(degrees)Time(s) Withnoise Nonoise Withnoise Nonoise Withnoise Nonoise Figure5.14:ThetrajectoryoftheOH-58Ahelicopterwithandwithoutnoiseunderthesecondnoiselevel.Thecrossescorrespondtothemeasurementsgivenbythecorrespondingsensor. 76

PAGE 93

1 : 5 1 0 : 5 0 0 : 5 1 1 : 5Abs.Error 2 : 4 1 : 2 0 1 : 2 2 : 4Abs.Error 0 : 1 0 : 05 0 0 : 05 0 : 1Abs.Error 4 2 0 2 4 6Thrustcoe cient0 5 10 15 20 02468101214Sinkrate(ms 1 )Time(s) 0 : 1 1 10 100 02468101214Altitude(meter)Time(s) 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 02468101214RPMratio( n = n 0 )Time(s) 2 0 2 4 6 8 10 12 14 16 02468101214Pitch(degrees)Time(s) Withnoise Nonoise Withnoise Nonoise Withnoise Nonoise Figure5.15:ThetrajectoryoftheOH-58Ahelicopterwithandwithoutnoiseunderthethirdnoiselevel.Thecrossescorrespondtothemeasurementsgivenbythecorrespondingsensor. 77

PAGE 94

controllerwastestedfor1,2and3sdelaybetweenonsetoffailureanddetection.Duringthistimeintervalthecontrollertriestohoverthehelicopterusingthesamecollectiveasbeforethefailureoccurred.Thisresultsinrapidlossofrpm,closeto20%inthecaseof3sdelay.ThesimulationresultsareshowninFigure5.16.Itisevidentthatthedelaytimehasasimilare ectwithstartingfromalowerinitialaltitude.For delaysof1and2stherotorspeedreachesmaximumallowedrpmandthetrajectoriesduringtheareareveryclose.Ontheotherhandwitha3sdelaythehelicopterreachesarewithlowerrpmandhighersinkrate,thusreachingthegoalof v H = 0 : 5ms 1 slightlydelayed. 5.1.6SamplingRateThecontrollerwasalsotestedtodeterminethee ectofthesamplingrateusingratesdoubleand tripletheoneusedinthebaselinecase,namely20Hzand30Hz.HighersamplingratesallowtheNN-NMPCtohavenercollectivecontrol.Additionallyitimprovesperformancewhenforanyreasontheneuralnetworkdidnotconverge,sincenewerstatesareobservedmoreoftenandthecontrolisupdatedaccordingly.ThisisevidentinFigure5.17whereforhighersamplingratesthedipinsinkratefromfreedescentto n -controlleddescentissmaller.Neverthelessthetrajectories forhighersamplingratesareverysimilar,especiallywhencomparingthosefor20Hzand30Hzwhichindicatesthatnosignicantbenetscanbeexpectedfromfurtherincrease.Increasingthesamplingratemayalsodeterioratetheperformanceofthecontroller.Forexampleifthesamplingrateisdoubled,thetimeavailabletotheneuralnetworktoconvergeisreducedbyafactoroftwo.Thismeansthatitmaynotbepossibletomaintainepochsizesashighas150.5.2X-PlaneSimulationToassesstheperformanceofthecompleteautonomousautorotationcontroller,theX-Planesimu-latorwasused.Thissimulatorallowsthedenitionofnewaircraftmodels,bydeningtheshapesandtypesoftheaerodynamicsurfaces,aswellasengineandrotorcharacteristics.SincetheOH-58Amodeldoesnotexistintheaircraftmodeldatabase,theBell207helicoptermodelwasusedinstead.Thelatterwasmodiedtoaddweightsatthetipsoftherotorstoincreasetherotorinertiaandthetotalmassofthehelicopterwasadjustedto1 ; 360kg. Totestthecontrolleranenginefailurewassimulatedatanaltitudeofabout180m.Thefailureisdetectedapproximately2slaterandthecontrollertakesover.TheresultsofthesimulationarepresentedinFigure5.18.Itisevidentthatthetargetof0 : 5ms 1 wasachievedatanaltitudeof4m andthehelicoptermaintainedthatvelocityforapproximately7suntilitlanded.Inthesesimulationresultsthetailrotorpitchtrajectoryisalsopresented.Beforethefailure,thetailrotorpitchisabout15 .ItthenrapidlydropsbecausetheRPYcontrollertriestomaintain 78

PAGE 95

0 5 10 15 20 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 12 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 12 2 0 2 4 6 8 10 12 14 16 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 12 4 2 0 2 4 6 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 12 0 5 10 15 20 5 8 11 14Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 4 0 : 1 1 10 100 5 8 11 14z inmTimetotouchdownins 0 1 2 3 4 t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s Figure5.16:Thee ectofreactiontimeontheOH-58Acontrollerperformance.Betweenonsetof failureanddetection,thehelicopterishoveringinplace. 79

PAGE 96

0 5 10 15 20 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 12 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 12 2 0 2 4 6 8 10 12 14 16 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 12 4 2 0 2 4 6 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 12 0 5 10 15 20 5 8 11 14Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 4 0 : 1 1 10 100 5 8 11 14z inmTimetotouchdownins 0 1 2 3 4 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz Figure5.17:Controllerperformanceusingdi erentsamplingratesinthecaseoftheOH-58A helicopter.Althoughtherearesomechangesinthecontrolleroutput,especiallyafteranincreasefrom10Hzto20Hz,thehelicoptertrajectoryitselfisnotsignicantlya ected. 80

PAGE 97

0 5 10 15 20 60 120 180Sinkrate(ms 1 )z inm 0 5 10 15 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 60 120 180RPMratio( n = n 0 )z inm 0 5 10 15 0 5 10 15 20 8 12 16 20Sinkrate(ms 1 )Timetotouchdown(s) 0 2 4 6 0 : 1 1 10 100 8 12 16 20z (m)Timetotouchdown(s) 0 2 4 6 2 0 2 4 6 8 10 12 8 12 16 20Mainrotorbladepitch(degrees)Timetotouchdown(s) 0 2 4 6 5 0 5 10 15 8 12 16 20Tailrotorbladepitch(degrees)Timetotouchdown(s) 0 2 4 6 Figure5.18:Simulationresultsforanautorotativedescentfrom180mintheX-Planesimulator. 81

PAGE 98

theoriginalheadingusingthewrongbiassincethetorquee ectofthemainrotorissignicantly reduced.Afterthefailureisdetectedthetailpitchbiasiscorrected,thepitchismaintainedat3 : 8 andtheyawrateofthehelicopterisnearzero.Duringthearethebiaschangesagainbecauseoftheincreaseincollective.ItshouldbenotedthatthereissignicantdiscrepancybetweentheinternalmodelofthecontrollerandthatofX-Plane.ThisisbothduetotheuseofthemodiedBell207helicoptermodelinsteadofanaccurateOH-58AmodelaswellasbecausetheX-Planesimulatormodelsaerodynamicinteractionsbetweentherotor,thefuselageandthegroundthatarenottakenintoaccountinthecontrollermodel.Furthermore,becauseofthewaytheenginefailureismodeledinX-Plane,thetorqueprovidedtothemainrotordoesnotinstantlydroptozero.Nevertheless,anddespitethesediscrepancies,theautorotationcontrollerperformedwellandtheobjectivewasachieved.5.3Raptor30v2TheThundertigerRaptor30v2isapopular,gas-powered,remotecontrolledhelicopter.Ithasapayloadcapacityofmorethan1kgandrun-timeofabout10–20mindependingonpayloadandighttype(hovering,way-pointnavigationoraggressivemaneuvering).Thishelicopterandothersofsimilarsizeandcharacteristicsareoftenusedforroboticresearchanddevelopment.Despiteitssmallsizeitcanstillpossessasignicantamountofkineticenergyonimpacttoposearisktopeople.SpecicallyusingthemethodologypresentedinSection2.4.2,theprobabilityoffatalityfollowingagroundimpactisover5%( f = 10 6 ; f = 10 2 ; f s = 0 : 5).Neverthelessbecauseofitssmallsizeitispossibletosatisfyeventhestrictestkineticenergy criterionofSection2.4.2ifthesinkratecanbecontrolled.Specicallyifthehelicoptersinkrateatthetimeofimpactwithapersonislessthan3ms 1 ,thenthekineticenergyimpartedisless than15J,whichreducestheprobabilityoffatalitytozero.Asaresultinthissection,theobjectiveofthecontrollerwillbetoreducethekineticenergyduringthelast2 : 5mofthedescentbelowtheaforementionedthreshold.Additionallyasecondaryobjectiveistoachievealowersinkrateatthemomentoflandingof0 : 5ms 1 .Simulationresultsfor di erentscenariosandparametervaluesarepresentedinthesectionsthatfollow.TheThundertigerRaptor30v2modelparametersusedforthesimulationsaresummarizedinTable5.3.5.3.1BaselineScenarioThebaselinecaseagainstwhichthetestedscenariosarecomparedisthesameasthatfortheOH-58Ahelicopter.Itinvolvesadescentfromaninitialaltitudeof120musingperfectsensorinfor-mation.Thesimulationisperformedatanupdaterateof1kHzwhilethecontrollerisrunat10Hz.Theneuralnetworkparametersare E = 150and r = 0 : 05.Theresultingtrajectoryfor N s = 4and 82

PAGE 99

Table5.3:ModelparametersfortheThundertigerRaptor30v2R / Cmodelhelicopter.The parameterswerederivedusingdirectmeasurement,manufacturerdataandexpertestimates. Helicoptermass( M )3kg Mainrotormomentofinertia( I R )0 : 03kgm 2 Solidityfactor( )0 : 0455 Mainrotordiscradius( R )0 : 62m Mainrotormeandragcoe cient( C d ; 0 )0 : 0085 Mainrotorliftcoe cient( C l ; a )5 : 84rad 1 Equivalentunitdragcoe cientarea( f e )0 : 03m 2 Inducedpowercorrectionfactor( )1 : 15 Nominalmainrotorspeed( n 0 )1 ; 800rpmor188 : 5rads 1 Airdensity( )1 : 225kgm 3 Minimummainrotorpitch 6 Maximummainrotorpitch12 Maximummainrotorrpm1 : 2 n 0 N c = 3ispresentedinFigure5.19.Thepredictionhorizonwaschosentobesmallersince,because ofthelowerrotorinertia,thehelicopterresponsetocontrolinputisfaster.Inthebeginningthehelicopterfreefalls,butquicklyreachestherpmlimitandthecontrollerre-ducesthesinkratetotheautorotativevalueforthatrpmofabout8 : 5ms 1 .The v H -controlledregionisenteredatanaltitudeof10m,atwhichpointcollectiveisincreased.Thehelicopterreachesthe3ms 1 sinkratelimitatanaltitudeofapproximately2 : 6mand3slatertouchesdownwith asinkrateof0 : 5ms 1 .Noneoftheconstraintsareviolated,althoughduringthelast0 : 5mthe helicopterincreasesitssinkratefromabout0 : 1ms 1 to0 : 5ms 1 becausethethrustcoe cient limithasbeenreached.Theaforementionedgurealsopresentstheresultingtrajectoriesusing E = 1500forcomparison purposes.Theincreaseintimeavailableforconvergenceresultedindi erencesonlyduringthe transitionbetweenthe n -controlledand v H -controlledphasesofthedescent.Thisisbecauseatthe sinkratesexperiencedduringthetransition,evensmallincreasesinbladepitchhavesignicante ectwhichinturnmakesconvergencemoredi cult. 5.3.1.1CostFunctionThecostfunctionchosenisgivenby:(5.2) L = 8>>><>>>: 0 : 1( v H 1 : 25 z 0 : 1) 2 v H 1 : 25 z 0 : 1 0 0otherwise 83

PAGE 100

0 2 4 6 8 10 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 6 4 2 0 2 4 6 8 10 12 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 2 1 0 1 2 3 4 5 6 7 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 0 2 4 6 8 10 6 9 12 15Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 0 : 1 1 10 100 6 9 12 15z inmTimetotouchdownins 0 1 2 3 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 Figure5.19:Thesinkrate,rotorrpmandcontrolinputoftheThundertigerRaptor30v2foradescentfromaninitialaltitudeof120m( N s = 4, N c = 3).Thebottomtwographsshowthesink rateandaltitudeasafunctionoftimetotouchdown.Theshadedregionsrepresenttheposedconstraints.Thescaleontherightsideofthegraphshasbeenalteredtopresentthelaststageofthedescentinhigherdetail. 84

PAGE 101

andisvisualizedinFigure5.20.Thisfunctionwasdesignedtointroducelargepenaltiesforhighsinkratesduringthelastphaseofthedescent.Specicallythepenaltyisintroducedwhenthenumericvalueofthesinkrateinms 1 ishigherthanthatofthealtitudeinmwhenthelatteris increasedby25%.Ine ectthisshouldreducethesinkratetoabout3ms 1 atanaltitudeof2 : 5m andto0 : 1ms 1 duringtouchdown.Thescalingconstantwasaddedaftertrialanderrortoreduce themagnitudeofthecostandconstraintderivatives.Sinkrate(ms 1 )Altitude(m) 0 2 4 6 2 4 6 0 0 : 2 0 : 4 0 : 6 0 : 8 1PenaltyFigure5.20:ThecostfunctionusedbytheThundertigerRaptor30v2controller.5.3.1.2Non-linearOptimizationProblemConvexitySinceitispossibleforthehelicoptertoenterregionswheretheproblemisnon-convex,randomsamplingwasusedtodeterminethemaximumallowablepredictionhorizon.AsinthecaseoftheOH-58A,28 ; 000samplesweretakenovertheentirestate-actionspaceandfordi erentcontrol horizonsandcontrollersamplingtimes.Foreachsamplethehighestvalueof N s (upto100)where the d 2 L d u 2 remainspositivedenitewasrecorded.This N s representsaconservativelimitonthe longestpredictionhorizonavailable.Thisisbecauseitispossiblethatevenaftermomentarilyenteringanon-convexregion,atthenextepochtheproblemwillbeconvexagain.FurthermoreasdiscussedinSection4.2.2,theneuralnetworkiscapableofglobalconvergenceforaclassofnon-convexproblemsaswell.Figure5.21showstheworst5%ofpredictionhorizonsrecordedusing N c = 3and t s = 50ms. Itisevidentthathighsink-ratesmayresultinanon-convexproblem.Thisisexacerbatedbycor-respondinglyhighactionvaluesthatwouldnormallyviolatethethrustcoe cientconstraint.In 85

PAGE 102

anycasetheworst-case N s wasfoundtobe5whichishigherthanthepredictionhorizonused. Furthermorelessthan2%ofthesampleshad N s < 10. 6 4 2 0 2 4 6 8 10 12 0246810max( u 1 ; u 2 )(degrees)Sinkrate(ms 1 ) Figure5.21:The5%ofsampleswithlowerworst-case N s fordi erentvaluesof v H andblade pitchinthecaseoftheThundertigerRaptor30v2.Thesimulationwasdoneusing N c = 3and t s = 50ms.Thelowestvaluesoccurforhighinputactionsandaretypicallycombinedwithhigh sink-rates.Thee ectofdi erentvaluesof N c and t s ontheworst-casepredictionhorizonisfoundinFigure5.22.Thisgureshowsthatthesamplingtimeisthemaininuenceofconvexityratherthanthecontrolhorizon.Thiscanbeattributedtothefasterresponsetimesofthesmallerhelicopterandthelargererrorsresultingfromuseofhigh t s .If t s = 10msisusedtheproblemisconvex evenwithpredictionhorizonsof10orhigher.Inthecaseof t s = 50msthatwaschosenforthe simulations,theworstcase N s isreducedto4althoughtherstoctileishigherthan10.Foreven highervaluesof t s theworstcase N s remainsat4,althoughanincreasingnumberofsampleshave N s lowerthan10. 5.3.1.3ConvergenceCharacteristicsTheoutputoftheneuralnetworkduringeachepochofthebaselinesimulationandfordi erent stagesofthedescentispresentedinFigures5.23to5.25.Thetransitionfromfreeto n -controlled descentispresentedinFigure5.23.Althoughtheneuralnetworkdidnotconvergeduringepoch53,theproblemiscorrectedinepoch54.Thenon-convergenceispartlyduetotheneedforasuddenincreaseinbladepitchatahighsinkrate,whichresultsinlargederivativesofthestatewithrespecttocontrol. 86

PAGE 103

2 3 4 5 6 7 8 1030507090110130150ControlhorizonControllersamplingperiod(ms) 17,1008,1005,445,164,104,84,74,6 29,1005,495,234,124,94,74,64,6 18,1006,404,174,114,94,74,64,6 16,1005,304,154,105,94,74,64,6 13,1007,305,154,104,84,74,64,6 9,1005,264,145,105,94,74,74,6 12,1006,244,144,114,84,74,64,6 Figure5.22:Worst-caseandrstoctile N s asafunctionof N c t s inthecaseoftheThundertiger Raptor30v2.TherstoctilewascalculatedusingtheM&Mmethod[59].Similarlythetransitionfrom n -controlledto v H -controlleddescentalsofeaturesconvergence issuesinepochs130to134.Thesecanbeaccommodatedbyhigherlearningrates,atthecostofpossiblygeneratingconvergenceproblemsinotherregions.ThenalstageofthedescentthatincludesthetouchdownispresentedinFigure5.25.Theneu-ralnetworkconvergesfastandwithoutproblemsinallepochsshownbesidesthelast3.Thisisbecauseatthatpointtherotorrpmhasdecreasedtothepointofimminentstall.Neverthelessthisdoesnota ectthesuccessfullandingsincethehelicopterisalreadyonlyafewcentimetersfrom theground.5.3.1.4Real-timeOperationAsinthecaseoftheOH-58A,theexecutionspeedofthecontrollerwasmeasuredtodetermineifreal-timeoperationispossible.ThemethodologyusedisthesameasthatemployedinthecaseoftheOH-58Ahelicopter.Specicallyasingle-coreAthlonXP3200 + (modelof2005)CPU, throttledtoafrequencyof1GHzrunninga32-bitversionofDebianLinuxwasused.Theresultwasobtainedbycalculatingthetimerequiredtorun100 ; 000iterationsoftheneuralnetworkto accountforitsverylowvalue.Theexecutiontimemeasuredis190 speriterationwhichissignicantlylowerthanthatofthe OH-58A.Thisismostlyduetothesmallerpredictionhorizonalthoughthesimplercostfunctionmayhavecontributedaswell.Basedontheresultabove,atacontrollerupdaterateof10Hz,morethan5 ; 000iterationsarepossible.Similarlyif E = 150,amaximumupdaterateof35Hzcanbe achieved.ThecostoftheEKFdidnotchangesincethemodelisofthesamedimensionality. 87

PAGE 104

0 0 : 05 0 : 1 4647484950515253545556575859606162636465NeuralnetworkoutputNeuralnetworkepoch Figure5.23:Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfromfreeton -controlleddescentinthecaseoftheThundertigerRaptor30v2.Thetransitioniscomplete within5epochsor0 : 5s. 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5 0 : 6 126127128129130131132133134135136137138139140141142143144145NeuralnetworkoutputNeuralnetworkepoch Figure5.24:Theevolutionoftheoutputoftheneuralnetworkduringthetransitionfromn -controlledto v H -controlleddescentinthecaseoftheThundertigerRaptor30v2. 0 : 7 0 : 8 0 : 9 1 155156157158159160161162163164165166167168169170171172173174175NeuralnetworkoutputNeuralnetworkepoch Figure5.25:TheevolutionoftheoutputoftheneuralnetworkduringthelastsecondsbeforetouchdowninthecaseoftheThundertigerRaptor30v2. 88

PAGE 105

5.3.2AlternativeCostFunctionTheuseofothercostfunctionstoaccomplishdi erentobjectivesispossible.Ifforexampleit ispermissibleordesirabletoallowthesinkratetoincreaseforaltitudesbetween3mandtouch-down,thenthefollowingcostfunctioncanbeused:(5.3) L = 8>>>>>>><>>>>>>>: 0 : 1 ( max( v H ; 3 : 5) 0 : 5 ) 2 e 9 3 z y 3 0 : 1 ( max( v H ; 3 : 5) 0 : 5 ) 2 e 2 : 5 z 9 3 > y 1 : 5 0 : 1 ( max( v H ; 3 : 5) 0 : 5 ) 2 e 3 z otherwise ThisfunctionisvisualizedinFigure5.26.Largepenaltiesareintroducedforsinkratesawayfrom0 : 5ms 1 atanaltitudeofabout3mandjustbeforetouchdown.Ofcoursehighsinkratescloseto thegroundmaybeproblematicsincetheactualsinkrateattouchdownmaybemoresensitivewithrespecttonoiseandotherparameters.Theresultsforadescentfrom120musingthecostfunctionabovearegiveninFigure5.27.Sinkrate(ms 1)Altitude(m) 0 2 4 6 2 4 6 0 0 : 2 0 : 4 0 : 6 0 : 8 1PenaltyFigure5.26:AnalternativecostfunctionusedbytheThundertigerRaptor30v2controller.5.3.3InitialAltitudeTheinitialaltitudecaninuencethestateofthehelicopteratthenalstageofthedescentandspecicallytherotationalenergyavailableintherotortoreducethesinkrate.Threesimulationswerecarriedoutusinginitialaltitudesof60m,30mand10m.Forinitialaltitudesexceeding 89

PAGE 106

0 2 4 6 8 10 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 6 4 2 0 2 4 6 8 10 12 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 2 1 0 1 2 3 4 5 6 7 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 0 2 4 6 8 10 6 9 12 15Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 0 : 1 1 10 100 6 9 12 15z inmTimetotouchdownins 0 1 2 3 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 E = 150 E = 1500 Figure5.27:Thesinkrate,rotorrpmandcontrolinputoftheThundertigerRaptor30v2foradescentfromaninitialaltitudeof120m( N s = 5, N c = 4)usinganalternatecostfunction.The bottomtwographsshowthesinkrateandaltitudeasafunctionoftimetotouchdown.Theshadedregionsrepresenttheposedconstraints.Thescaleontherightsideofthegraphshasbeenalteredtoshowthelaststageofthedescentinhigherdetail. 90

PAGE 107

60mthehelicopterwillhavetimetoreachthelimitoftherotorrpmallowableandasaresultthetrajectoryafterwardswillbethesame.Converselyinsituationsweretheinitialaltitudeislowerthan60mthehelicopterwillenterthev H -controlledregiondirectlyfromthefreedescentone.Figure5.28presentsthetrajectoriesfor thethreesimulationsdescribedabove,aswellasthebaselinedescentfrom120mforcompari-sonpurposes.Ineachcasethetrajectoryofthehelicopterisdi erentonlyinitially.Afterapoint allthetrajectoriesconvergeandtheobjectiveoflowsinkrateatlowaltitudesisachieved.Itisnoteworthythatinthecasewherethehelicopterwasinitiallyat10m,thesinkratefrom7muntiltouchdownisessentiallyidenticaltothecaseswherethehelicopterstartedfromhigheraltitudes.Neverthelessbecauseofthelowerrpmavailableontherotor,thestalllimitisreachedearlierandthesinkrateiscloseto1ms 1 attouchdown. 0 2 4 6 8 10 30 50 70 90 110Sinkrate(ms 1 )Altitude(m) 0 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )Altitude(m) 0 2 4 6 8 10 6 4 2 0 2 4 6 8 10 12 30 50 70 90 110Bladepitch(degrees)Altitude(m) 0 2 4 6 8 10 0 1 2 3 4 5 6 30 50 70 90 110Thrustcoe cientAltitude(m) 0 2 4 6 8 10 z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 10m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 10m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 10m z 0 = 120m z 0 = 60m z 0 = 30m z 0 = 10m Figure5.28:Thee ectofdi erentinitialaltitudesontheperformanceoftheThundertigerRaptor 30v2controller. 91

PAGE 108

5.3.4LearningRateAsalreadymentioned,althoughhighlearningratesaredesirabletoimproveconvergencespeed,theycanhaveadversee ectsandmayevenresultintheneuralnetworknotconvergingatall. AsinSection5.1.3,theinuenceofthee ectofthedesignparameter r wasevaluatedusingthe varianceintheneuralnetworkoutputduringthelast20%oftherepetitionsofeachcycle.ThevariancewascalculatedusingthemoduledescribedinSection4.3.3.TheresultssummarizedinFigure5.29showthatthevariancesaregenerallysmallerthanthoseofSection5.1.3.Varianceisexhibitedmainlyinregionswherethehelicoptertransitionsfromonemodetoanother.Forhigherlearningratesvarianceisalsoexhibitedintheentireregionwherethesinkrateisreducedfromtheautorotativevaluetoabout3ms 1 5.3.5NoiseThee ectofsensornoiseoncontrollerperformanceisinvestigatedusingthreesimulationscarried outusingthreedi erentnoiselevels.Inallcasesthenoiseisconsideredtobezero-mean,Gaussianwithvaryingstandarddeviation.ThenoiselevelsaresummarizedinTable5.4.Table5.4:SensornoiselevelsinthecaseoftheThundertigerRaptor30v2simulation. Standarddeviation Level1Level2Level3 Sinkrate(ms 1 )0.10.20.5 Altitude(m)0.10.250.75Rotorspeed(RPM)91827 Figure5.30showsthesimulationresultsfortherstnoiselevelscenario.Thenaltrajectoryisalmostthesamewiththeexceptionofthearewherethe v H and z errorsresultinalotofcontrollercorrection.ForhighernoiselevelsshowninFigure5.31,thecontrolleroutputduringthen -controlleddescentisalsoa ected.Thelatteroccursbecauseofthedesignofthecontroller thattriestomaintainconstantrpmandbecomesmorepronouncedasthenoiseintherpmmea-surementsincreasesasshowninFigure5.32.Additionallythecontrolleroutputduringthearealsoworsensbecauseofthesensors'inabilitytoaccuratelypinpointthealtitudeandsinkrate.Neverthelesseveninthecaseofthethirdnoiselevel,thetrajectoryisnotsignicantlya ected. Itshouldbenotedthatalthoughthesimulationterminatesearlythatdoesnotmeanthehelicoptercrashed.Thisisanissueofthedesignofthesimulator,whichterminatesassoonasthesensorsindicatenegativealtitude. 92

PAGE 109

C Tr = 0 : 02C Tr = 0 : 08C Tr = 0 : 05C Tr = 0 : 11 0 1 2 3 4 5 6 7 8 9 10 024681012141618v H (ms 1 )Time(s) 10 2 10 3 0 1 2 3 4 5 6 7 8 9 10 024681012141618v H (ms 1 )Time(s) 10 2 10 3 0 1 2 3 4 5 6 7 8 9 10 024681012141618v H (ms 1 )Time(s) 10 2 10 3 0 1 2 3 4 5 6 7 8 9 10 024681012141618v H (ms 1 )Time(s) 10 2 10 3 Figure5.29:ThevarianceoftheneuralnetworkoutputwithrespecttotimeandhelicoptersinkrateforfourvaluesofthelearningrateparameterinthecaseoftheThundertigerRaptor30v2.Largercirclesmeanlargervariancewhilevariancessmallerthan10 5 arenotshown.For comparisonpurposesthethrustcoe cientatthecorrespondingtimeisalsoprovided. 93

PAGE 110

0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3Abs.Error 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3Abs.Error 0 : 02 0 : 015 0 : 01 0 : 005 0 0 : 005 0 : 01 0 : 015 0 : 02Abs.Error 4 2 0 2 4 6Thrustcoe cient0 2 4 6 8 10 0246810121416Sinkrate(ms 1 )Time(s) 0 : 1 1 10 100 0246810121416Altitude(meter)Time(s) 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 0246810121416RPMratio( n = n 0 )Time(s) 5 0 5 10 0246810121416Pitch(degrees)Time(s) Withnoise Nonoise Withnoise Nonoise Withnoise Nonoise Figure5.30:ThetrajectoryoftheThundertigerRaptor30v2withandwithoutnoiseundertherstnoiselevel.Thecrossescorrespondtothemeasurementsgivenbythecorrespondingsensor. 94

PAGE 111

0 : 4 0 : 2 0 0 : 2 0 : 4Abs.Error 0 : 4 0 : 2 0 0 : 2 0 : 4Abs.Error 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03Abs.Error 4 2 0 2 4 6Thrustcoe cient0 2 4 6 8 10 0246810121416Sinkrate(ms 1 )Time(s) 0 : 1 1 10 100 0246810121416Altitude(meter)Time(s) 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 0246810121416RPMratio( n = n 0 )Time(s) 5 0 5 10 0246810121416Pitch(degrees)Time(s) Withnoise Nonoise Withnoise Nonoise Withnoise Nonoise Figure5.31:ThetrajectoryoftheThundertigerRaptor30v2withandwithoutnoiseunderthesecondnoiselevel.Thecrossescorrespondtothemeasurementsgivenbythecorrespondingsensor. 95

PAGE 112

1 0 : 5 0 0 : 5 1Abs.Error 1 0 : 5 0 0 : 5 1Abs.Error 0 : 04 0 : 02 0 0 : 02 0 : 04Abs.Error 4 2 0 2 4 6Thrustcoe cient0 2 4 6 8 10 0246810121416Sinkrate(ms 1 )Time(s) 0 : 1 1 10 100 0246810121416Altitude(meter)Time(s) 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 0246810121416RPMratio( n = n 0 )Time(s) 5 0 5 10 0246810121416Pitch(degrees)Time(s) Withnoise Nonoise Withnoise Nonoise Withnoise Nonoise Figure5.32:ThetrajectoryoftheThundertigerRaptor30v2withandwithoutnoiseunderthethirdnoiselevel.Thecrossescorrespondtothemeasurementsgivenbythecorrespondingsensor. 96

PAGE 113

5.3.6ReactionTimeThedelaybetweenfailureonsetanddetectioncansignicantlyimpacttherotorenergyavailableduringtheare.Althoughpilotreactiontimetosucheventsistypicallyintherangeof1–2s,healthmonitoringsystemscanreducethisintervaltosub-secondduration.Totestthee ectofthisdelay,threesimulationsarecarriedoutusing1,2and3sdelays.During theperiodbetweenfailureonsetanddetection,thecontrollermaintainsthebladepitchrequiredforhovering,resultinginrapidlossofrpm.TheresultsareshowninFigure5.33.Theresultsshowthatthedelaytimehasasimilare ectwithstartingfromalowerinitialaltitude. Therotorspeedreachesmaximumallowedrpmatloweraltitudesdependingonthedelay.Never-thelessthetrajectoriesafterthatanduntiltouchdownarealmostidentical.5.3.7SamplingRateThecontrollerwasalsotestedtodeterminetheperformanceimprovementofhigherupdaterates.Specicallythebaseline10Hziscomparedtothetrajectoriesobtainedusing20Hzand30Hz.Itisobviousthattheincreaseinupdateratehasminimale ectandonlyinthetransitionfromthe n controlledtothe v H -controlledregion.Thisisbecausethehigherrateallowsmorefrequentsensor measurementsinaregionofoperationwherethedynamicsarefast.Althoughhigherupdateratesreducetheamountoftimeavailabletothenetworktoconverge,inthiscaseitisnotasignicantproblemsinceepochsofsize150canbeachievedevenunder30Hz.5.3.8StricterConstraintThe n -constraintusedintheprevioussimulationsmaybeconsideredtoorelaxed.Asaresulta stricterconstraintwasalsotestedthatallowstherotortomaintainlessenergy.Specicallytherpmisallowedtoreach105%thenominalvalueinsteadof120%.Inaddition,aninitialdelayoffailuredetectionof2swasused.Theresults,summarizedinFigure5.35showthatdespitethestricterconstraint,thetrajectoryofthehelicopterisnota ected.Specicallythetwotrajectoriesmeetatanaltitudeof6mand arealmostidenticaluntiltouchdown.Neverthelessthesinkrateattouchdownisincreasedfrom0 : 5ms 1 to0 : 9ms 1 ,sincethestalllimitisreachedalittlesooner.Alsobecauseofthelowersink ratesallowed,theentiremaneuvertakes3smoretocomplete.Finally,thedelaydoesnothaveane ectsincethemaximumrpmisreached. 97

PAGE 114

0 2 4 6 8 10 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 2 1 0 1 2 3 4 5 6 7 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 2 1 0 1 2 3 4 5 6 7 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 0 2 4 6 8 10 6 9 12 15 18Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 0 : 1 1 10 100 6 9 12 15z inmTimetotouchdownins 0 1 2 3 t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s t d = 1s t d = 2s t d = 3s Figure5.33:Thee ectofreactiontimeontheperformanceoftheThundertigerRaptor30v2 controller.Betweenonsetoffailureanddetection,thehelicopterishoveringinplace. 98

PAGE 115

0 2 4 6 8 10 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 6 4 2 0 2 4 6 8 10 12 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 2 1 0 1 2 3 4 5 6 7 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 0 2 4 6 8 10 6 9 12 15Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 0 : 1 1 10 100 6 9 12 15z inmTimetotouchdownins 0 1 2 3 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz 10Hz20Hz30Hz Figure5.34:ThundertigerRaptor30v2controllerperformanceasafunctionofsamplingrate. 99

PAGE 116

0 2 4 6 8 10 30 50 70 90 110Sinkrate(ms 1 )z inm 0 2 4 6 8 10 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 30 50 70 90 110RPMratio( n = n 0 )z inm 0 2 4 6 8 10 6 4 2 0 2 4 6 8 10 12 30 50 70 90 110Bladepitch(degrees)z inm 0 2 4 6 8 10 2 1 0 1 2 3 4 5 6 7 30 50 70 90 110Thrustcoe cientz inm 0 2 4 6 8 10 0 2 4 6 8 10 6 10 14 18Sinkrate(ms 1 )Timetotouchdownins 0 1 2 3 0 : 1 1 10 100 6 10 14 18z inmTimetotouchdownins 0 1 2 3 f r = 1.2 f r = 1.05 f r = 1.2 f r = 1.05 f r = 1.2 f r = 1.05 f r = 1.2 f r = 1.05 f r = 1.2 f r = 1.05 f r = 1.2 f r = 1.05 Figure5.35:ThundertigerRaptor30v2controllerperformanceusingastricter n constraint. 100

PAGE 117

Chapter6:ConclusionandFutureExtensionsThisdissertationpresentedanovelcontroldesignforperformingautonomousautorotationwithunmannedhelicopters.TheresultspresentedinChapter5demonstratethatautonomousautorota-tioncanbeusedtosafelylandanunmannedhelicopterfollowingseverefailures.Furthermore,byappropriatelycontrollingthesinkrateduringthedescent,itispossibletoreducetherisktopeopleontheground.Specicallysimulationtestingshowedsuccessfulautorotationoftwoverydi erent typesofhelicoptersunderdisturbancesandmodeluncertainty.Resultswerealsorepeatablewiththehighaccuracyblack-boxsimulationmodelinX-Plane.Thecontrollerpresented,featuresuniquecharacteristicsthatcontributetotheareaofautonomousautorotationandautorotationoptimization.Thesecharacteristicsincludecongurability,real-timeoperationandconstrainthandlingusinganaerodynamics-basedinternalmodelofthehelicopter.Anadditionalnoveltyistheuseofcostfunctionsthataredesignedforreducingtherisktopeo-pleonthegroundratherthanthehelicopteritself.Thisapproachwaschosenbyrealizingthatunmannedaircraft,incontrasttotheirmannedcounterparts,aresacricableandassuchhumanlivestakepriority.Anothersignicantcontributionofthisresearchisthereductionofthereliabilityrequirementsofunmannedhelicopters.UsingthemethodologypresentedinSection2.4,itispossibletocalculatetherequiredreliabilitywithandwithoutautonomousautorotationcapability.ThederivationsthatfollowwillbebasedonthecharacteristicsoftheOH-58Ahelicopter.Additionallythefollowingfatalityprobabilitymodelparametersareassumed f s = 0 : 5, f = 1 10 6 and f = 100. Itshouldbenotedthatnotallfailuresthatleadtoagroundimpactcanbeaccommodatedbyau-tonomousautorotation.Toimproveclarityoftheanalysisthatwillfollow,twotypesoffailureswillbeidentied.Therstcorrespondstofailuresthattypicallyresultinanuncontrolledgroundimpactandwhichwillbehenceforthbereferredtoascatastrophic.Asubsetofthesefailurescanbeaccommodatedusinganautonomousautorotationsystem.Thesewillbereferredtoasconformable.Assumingthatnoautorotationcapabilityispresent,theprobabilityoffatalitygivenagroundimpactinthecaseoftheOH-58Ahelicopterisapproximately45%.Assuming p = 200ppl = km 2 therequiredreliabilityis T GI = 98 ; 235hfor F f = 1 10 7 h 1 .Ifautorotationisused,the velocityatimpactcanbereducedto1ms 1 orlower.Asaresultthekineticenergyisalsolower 101

PAGE 118

andtheprobabilityoffatalitywilldroptoabout2.5%.Thismeansthat,ifonly10%ofthetimeacatastrophicfailureisalsoconformable,thenthe T GI requirementdropsto88 ; 957h.Furthermore,ifinhalfoftheotherwisecatastrophicfailuresautonomousautorotationcanbeusedthen T GI = 51 ; 846h. Analternativeanalysiscanbeusedtodemonstratetheincreasedareaofoperationsavailabletosystemswithautonomousautorotationcapability.Giventhatthehelicopterhasareliabilityof T GI = 1 10 5 h,itisonlycapableofloiteringoverareasof p = 200ppl = km 2 withoutviolating thetargetsafetylevelposedinSection2.4.1.Foraircraftequippedwithanautonomousautorota-tionsystem,ightispossibleoverareaswith p = 225ppl = km 2 and p = 385ppl = km 2 ,if10%or 50%respectivelyofcatastrophicfailuresareconformable.TheresultsforthecaseoftheThundertigerRaptorR30helicopteraresimilaralthoughinthiscasethefatalityprobabilityfollowingconformablefailuresiszero.Theanalysispresentedaboveindicatesthatintroductionofautonomousautorotationinunmannedhelicopterscansignicantlya ecttheirperformanceintermsofsafety.Thiscanbeusedasthe basisforasafetyargumenttoaviationauthoritiestowardsobtainingoperatingpermits.Inthelong-termthepresenceofanemergencylandingsystemmaybeconsideredsu cientforoperating undercertainsituationsormayberequiredasanadditionalsafetymeasureinothers.Inanycaseitisanticipatedthatsuchsystemswillfacilitatequick,easierandsafeintegrationofunmannedhelicoptersintheNAS.Ofcoursethisdoesnotmeanthatthereisnoroomforimprovementandinfactitishopedthatthisdissertationwillbethebasisforfurtherresearchintothisareaandwilleventuallyleadtohardwareimplementationofautonomousautorotationandincreasedsafetyofhelicopteroperations.TherestofthischapterpresentspossibilitiesonfutureresearchanddevelopmentbasedontheautorotationcontrollerpresentedinChapter4.Thersttwosectionsareconcernedwithimprovementsonthecontrolleritself,whiletherestdiscusstheintegrationofautonomousautorotationcapabilityonlargersystemsmannedandunmannedandprovidingcompleteemergencyhandling.6.1ModelPredictionImprovementSpecializedhardware,increasedcomputingavailabilityinnewerplatformsandsoftwareoptimiza-tionscanimprovetheexecutionspeedoftheNN-NMPC.NeverthelessthereisalsothepossibilityforimprovingthespeedofthepredictionstepoftheNN-NMPC–whichiswherethemajorityofthecomputationtakesplace–usingadi erentalgorithmicapproach.Specically,thiscan beaccomplishedbychangingthepredictionmodelfromthecurrentaerodynamicsmodeltoaproperlydesignedblack-boxmodule.Theaforementionedmodulecanthenbedesignedtoallowcomputingthewholepredictionhori-zoninparallel.Thiscanbeachievedwiththeuseofaneuralnetworkthatistrainedusingan 102

PAGE 119

autorotationmodel.Sinceneuralnetworksarecapableofaccuratelycapturingnon-linearsystemdynamics,theincreasedexecutionspeedisobtainedonlyatthecostofhavingtoretraintheneuralnetworkwhenmodelparameterschange.Alternativelyadi erentpredictionmodulemaybeusedtoguaranteeconvergencebyensuring thatthenon-linearoptimizationproblemisconvex.Thismaybepossibleusingpolynomialau-toregressivemodelswhichwithappropriatevariabletransformationcanbesolvedusingglobaloptimizationtechniques[74].6.2 n -constraintHandling AsdiscussedinSection4.2.3.2,enforcingthe n constraintmaypresentproblemswhenthehelicopterhasexceededitsautorotativesinkrate.Thisproblemwasovercomebyimposingalimitonthetimederivativeof n .Althoughthissolutiondidprovidetherequiredfunctionality,ithasmade thecontrollermoresensitivewithrespecttonoise.Thisisbecausetheerrorfromboththe v H and the n estimationcontributetothecalculationoftheconstraintvectoranditsassociatedderivative. Thisproblemmaybeexacerbatedwhentheavailablesensorsarelimitedeitherbecauseofpayloadlimitationsorbecauseofmalfunctions.Thisisbecausethestateofthehelicopterinthatsituationwouldhavetobesurmisedusingstateobserversthatmayintroduceadditionalerror.Apossiblesolutiontothisproblemistocontrol n bycontrollingthesinkrateofthehelicopter. Inthatcaseasthehelicopterapproachestheupper n limit,thecollectivewillbecommanded toriseuntilthesinkrateisequaltotheautorotativesinkrate.Neverthelessthisapproachcouldpossiblyallowovershootingandevenviolationoftheconstraintiftheautorotativesinkrateandtheactualsinkratecannotbeestimatedwithaccuracy.Amorecompleteapproachwouldrequireputtingconstraintsonrpm,itsderivativeandthesinkrateandintroducinghigherlevelintelligenceonhowtocombinethemthroughanexpertsystem.Althoughthelatterapproachcouldhandledisturbancesandsensornoisemoree ectively,therewouldbesignicantcomputationaloverhead. 6.3IntegrationintoanEmergencyLandingSystemAlthoughevenbyitselfanautonomousautorotationcontrollerisasignicantsafetyenhancementforunmannedhelicopters,inthelong-termanintegratedEmergencyLandingSystem(ELS)isenvisioned.TheELSimplementsanintegratedapproachofhandlingemergenciesfromdetectiontoplanningandexecution,forfailuresthatrequirefast,andpermitsafeighttermination.Whenthehelicopterisyingfailure-free,theELSismonitoringthesensorsandthecommandsissuedbythenominalightcontroller.Faultdetectiontechniqueslikeerrorresidualsbetweentheinternalmodelandtheinformationofthesensorsareusedtodeterminetheonsetofpossiblefailures.Whenafailureisdetected,theELSoverridesthenominalcontrollerandassumescontrol 103

PAGE 120

oftheaircraft.Moreover,thenominalcontrollermayalsosurrendercontrolvoluntarilytotheELSiftheformerdetectedaproblemoritreceivedsuchacommandfromthegroundcontrolstation.ToaccomplishrequiredfunctionalitytheELSisconnectedtothesensorsandactuatorsaboardthehelicopterinordertobeabletoyitinthecaseoftheaforementionedfailures.Inadditiontotheautorotationcontroller,theELSalsofeaturesafaultdetectionandidentication(FDI)andahighlevelContingencyPlanning(CP)module.TheFDImoduleisresponsibleforisolatingfailuresthatrequireanemergencylandingandiscapableofbothindependentoperationaswellascommuni-catingwithotherhealthmonitoringserviceson-boardthehelicopter.TheCPmoduleontheotherhandisresponsiblefordeterminingtheremainingfunctionalityofthehelicopterandselectinganappropriateplanofaction.Severalalternativesareavailableinthecaseofemergencies;immediateverticalautorotation,delayedautorotationafterndingasuitablelandinglocation,controlledcrashorreturningtobase.Tosafelyexecutethesecondandthirdalternatives,asystemisrequiredthatcandobasicway-pointnavigationunderfailuresanddeterminesuitablelandinglocationsorcrashsites.Thelatterisdiscussedinmoredetailedinthesectionthatfollows.AblockdiagramoftheELSthatcontainsalloftheaforementionedmodulesispresentedinFigure6.1. FDI MasterFlightControlComputer (NominalController,HealthMonitoringSystem) Sensors ActuatorsCP Sensor Fusion OverrideSwitch Vision System Way-pointNavigation Controller Autonomous AutorotationController Figure6.1:BlockdiagramoftheproposedEmergencyLandingSystem.TheContingencyPlanningmoduleiscentralinintegratingtheinformationfromthevisionsystem,othersensorsandtheFDIaswellasdeningway-pointsandallocatingcontroltotheemergencycontrollers.Theway-pointnavigationcontrollercanbeimplementedinvariousways.Perhapsthesimplestisasacollectionofemergencycontrollersdesignedtoaccommodatedi erentfailures.Thisallows fastoperationwithminimaloverheadbyallowingtheCPtoselectthemostappropriatecontrollerforeachsituation.Thedrawbackofthisapproachishandlingfailuresthatwerenotanticipated 104

PAGE 121

andforwhichnosuitablecontrollerexists.InthiscasetheELSwouldneedtoresorttoimmediateautorotationevenifbetteralternativesmayexist.Othermethodologiesthato eron-lineidenticationofthenewdynamicsandcontrollerrecongurationmayo ersuperiorperformance,butatthe expenseofsignicantcomputationalburdenimposedontheELSCPU.AsignicantcharacteristicoftheELSistheindependencefromthenominalightcontrolarchi-tecture.Althoughthisrequiresthepresenceofadditionalhardware,asmallboardshouldbesuf-cienttoimplementallrequiredfunctionalitywithoutsignicantlyinuencingavailablepayload.Specically,theELSisdesignedasanindependenthardwaresystemwithitsownCPU,memoryandpowersupplyasshowninFigure6.2.ThiswilleliminatetheriskoffailuresoriginatinginthenominalightcontrolarchitectureinuencingtheELS. SignalConditioning ADC DigitalI / O SRAM Vcc Clock MasterFlightControlComputer (NominalController,HealthMonitoringSystem) Sensors ActuatorsCPU EEPROM Warning LED OverrideSwitch Independent PowerSupply Figure6.2:BlockdiagramoftheproposedhardwaredesignoftheEmergencyLandingSystem.TheCPUcanbeageneric Processororitcanbedesignedtosupportparalleloperationsto improveperformance.AdditionallyasecondCPUmaybeintroducedtohandletheRPY-controllerandsensorfusiontasks.6.4TheIssueofFindingaSuitableLandingLocationToperformasafelanding,asuitablelandinglocationneedstobedetermined.Furthermoreifthehelicopterhassu eredamajorfailureandisalreadyonanautorotativetrajectory,thetime availableforndingthislocationisseverelylimited.Therearethreeapproachestosolvingthis 105

PAGE 122

problem;(a)landimmediatelywithoutattemptingtondasuitablelocation,(b)useGPSdataandpredeterminedsafeareas,and(c)useavisionsystemtoassistwithlanding.Therstalternativeissimple,requiresnoadditionalhardwareoron-boardprocessingandmaybetheonlyalternativeifthehelicoptersu ersamajorfailurewhileyingatalowaltitude.Thedisadvantageobviouslyisthatthehelicoptermaydoanapproachtoanunsuitablelocationincreasingtheriskofinjurytothirdpartiesanddamagetotheaircraftitself.Thesecondalternativerequirestheon-boardstorageofthecoordinatesofsafelocationsthathavebeendeterminedo -line.Itcansignicantlyincreasethesurvivabilityofhelicopters,especially whenthelatterdonotneedtolandimmediately.Ontheotherhandinthecasewheretheterrainhaschangedorthehelicopterisnotabletoreachthepredeterminedsafeareas,noimprovementinsafetyisachieved.Thenalapproachistouseavisionsystem.Thevisionsystemcanprovideup-to-date,dynamicinformationonthesurroundingareaandallowstheselectionofasuitablelandinglocationavoid-ingpeopleorotherdynamicobstacles.Ontheotherhandthisalternativehasamajordrawbackofrequiringsignicantprocessingpower,additionalsensorsandsophisticatedalgorithmsthatcurrentlyareeitherunavailableornotalwaysreliable.Anadditionaldisadvantageisthattheper-formanceofopticalsensorsdependsonthelightconditionswhichmaynotalwaysbesuitable.Forsmallunmannedhelicopterstherstapproachissu cientsincetheyaretypicallyconsidered expendable.Ontheotherhandforlargersystemsandespeciallyformannedaircraftane ort needstobemadetoensurethemaximumprobabilityofsuccess,evenattheexpenseofhardwareoverhead.6.5UseinMannedAircraftTheuseofanautonomousautorotationsysteminmannedhelicoptersisasensitivematterbecauseofthepresenceofthepilot.Pilotsaretypicallytrainedtohandleemergenciesandarecapableofperformingtheautorotationmaneuvertosavetheaircraft.Furthermoretheymaynotbewillingtotrustanautomatedsystemtotakeovertheiraircraftunderlifethreateningconditions.AsaresultanEmergencyAutorotationAssistance(EA 2 )systemthatdoesnotoverridethepilotincommand isamoresuitablesolution.TheoperatingcharacteristicsoftheEA 2 willbedi erentdependingonthestateofthehelicopter duringtheautorotation.Undernominalightthesystemindependentlymonitorsthehealthofthehelicopterbasedonthesensorinformationavailabletoit.Itdoesnotinterferewithightorwiththepilot'sworkload.Attheonsetoffailurethesystemcanwarnthepilotofapotentialproblem,sinceinsomecasetheinitialresponsetransientsafterthefailurecanbeslowandnoteasytodetect.Iftheroll,pitchoryawincreasebeyondsafelimitsthesystemwillintervenetostabilizethehelicopter.Finallyinthe 106

PAGE 123

caseoftailrotorfailurethesystemwillstabilizepitchandrollwhileslowlyincreasingaltitudeandreducingyawratebyapplyingforwardvelocity.NeverthelesstheEA 2 willrelinquishcontrolto thepiloteitherpartially(maintainingpitch / rollstabilization)orfullyassoonasthepilotrequires it.Otherwiseinthecaseofmainrotorfailure,ifthepilotdoesnotlowercollectiveandmainrotorrpmdropssignicantly,thenthesystemwillalsoreducecollective.DuringdescenttheEA 2 willonlyinterferewithcollectivecontrolinthecasewherethesinkrate ormainrotorrpmincreasebeyondsafeoperatinglimitsasdeterminedbythehelicoptermanufac-turer.Ifthehelicopterhasreachedthearealtitudeandthepilotdidnotinthemeantimeassumecontroloftheaircraft,theEA 2 willalsobecapableofperformingtheareandsafelylandingthe helicopter. 107

PAGE 124

ListofReferences [1]“Administrative.generalauthority.”Title49U.S.Code,§40113(a),2006.[2]“Policy.economicregulation.”Title49U.S.Code,§40101(a),2006.[3]“Policy.safetyconsiderationsinpublicinterest.”Title49U.S.Code,§40101(d),2006.[4]P.Abbeel,A.Coates,T.Hunter,andA.Y.Ng,“AutonomousautorotationofanRC helicopter,”in Proc.11thInternationalSymposiumonExperimentalRobotics ,Jul.2008. [5]AirTransportAssociation(ATA),“Learningcenter,”Jun.2008.Online:http: // learningcenter.airlines.org / [6]B.M.kessonandH.T.Toivonen,“Aneuralnetworkmodelpredictivecontroller,” Journal ofProcessControl ,vol.16,no.9,pp.937–946,2006. [7]S.Anand,“Domesticuseofunmannedaircraftsystems:Evaluationofpolicyconstraintsand theroleofindustryconsensusstandards,” JournalofEngineeringandPublicPolicy ,vol.11, 2007. [8]B.Aponso,E.Bachelder,andD.Lee,“Automatedautorotationforunmannedrotorcraft recovery,”PresentedatAHSInternationalSpecialists'MeetingonUnmannedRotorcraft,2005. [9]R.Bhattacharya,G.J.Balas,M.A.Kaya,andA.Packard,“Nonlinearrecedinghorizon controlofanF-16aircraft,” JournalofGuidance,ControlandDynamics ,vol.25,no.5,pp. 924–931,2002. [10]M.A.BottoandJ.S.daCosta,“Acomparisonofnonlinearpredictivecontroltechniques usingneuralnetworkmodels,” JournalofSystemsArchitecture ,vol.44,no.8,pp.597–616, 1998. 108

PAGE 125

[11]R.Carlson,“Helicopterperformance-transportation'slatestchromosome:The31stannual alexandera.nikolskylecture,” JournalofTheAmericanHelicopterSociety ,vol.47,no.1, Jan.2002. [12]CenterforInternationalEarthScienceInformationNetwork(CIESIN),Columbia UniversityandCentroInternacionaldeAgriculturaTropical(CIAT),“GriddedPopulationoftheWorldVersion3(GPWv3):PopulationDensityGrids,”Palisades,NY:SocioeconomicDataandApplicationsCenter(SEDAC),ColumbiaUniversity,2005.Online:http: // sedac.ciesin.columbia.edu / gpw [13]R.ClothierandR.Walker,“DeterminationandevaluationofUAVsafetyobjectives,”in Proc. 21stInternationalUnmannedAirVehicleSystemsConference ,2006,pp.18.1–18.16. [14]R.Clothier,R.Walker,N.Fulton,andD.Campbell,“Acasualtyriskanalysisforunmanned aerialsystem(UAS)operationsoverinhabitedareas,”in Proc.12thAustralianInternational AerospaceCongressand2ndAustralasianUnmannedAirVehiclesConference ,2007. [15]K.D.Davis,“Federalaviationadministration:UASprogramo ce,” UnmannedAircraft Systems,TheGlobalPerspective2007 / 2008 ,p.51,May2007. [16]K.D.Davis,“Unmannedaircraftinthenationalairspacesystem-thecerticationpath,” PresentedattheWorkshoponUAV,Feb.2008. [17]W.S.Diehl, Engineeringaerodynamics .TheRonaldpresscompany,1928. [18]L.W.DooleyandR.D.Yeary,“Flighttestevaluationofthehighinertiarotorsystem,”Bell HelicopterTextron,Finalreportforperiod21September1976-February1979USARTL-TR-79-9,Jul.1979. [19]G.R.Drozeski,B.Saha,andG.J.Vachtsevanos,“Afaultdetectionandrecongurablecontrol architectureforunmannedaerialvehicles,”in Proc.IEEEAerospaceConference ,2005,pp. 1–9. [20]EuropeanAviationSafetyAgency(EASA),“A-NPA,No.16 / 2005,policyforunmanned aerialvehicle(UAV)certication,”2005. [21]EuropeanAviationSafetyAgency(EASA),“Certicationspecication25(CS25),” Amendment3,2007. [22]L.Ewing,“Thequestforthemissinglink,sense-and-avoidtechnologyedgesforward,” UnmannedSystems ,vol.25,no.5,pp.18–21,2007. 109

PAGE 126

[23]FederalAviationAdministration,“Systemdesignandanalysis,”AC25.1309-1A,Jun.1988.[24]FederalAviationAdministration,“Equipment,systemsandinstallationsinpart23airplanes,” AC23.1309-1C,Mar.1999. [25]FederalAviationAdministration,“Airworthinesscerticationofaircraftandrelatedproducts,” Order8130.2F,Nov.2004. [26]FederalAviationAdministration,“Unmannedaircraftsystems(UAS)questionsandanswers,” Nov.2007.Online:http: // www.faa.gov / aircraft / air_cert / design_approvals / uas / uas_faq [27]FederalAviationAdministration,“Airworthinesscerticationofunmannedaircraftsystems,” Order8130.34,Mar.2008. [28]FederalAviationAdministration,“Smallunmannedaircraftsystemaviationrulemaking committee,”Order1110.150,Apr.2008. [29]FederalAviationAdministration,“UnmannedaircraftsystemsoperationsintheU.S.national airspacesystem,”InterimOperationalApprovalGuidance08-01,Mar.2008. [30]FederalAviationAdministration,“ComprehensivesetofrecommendationsforsUAS regulatorydevelopment,”Smallunmannedaircraftsystemaviationrulemakingcommittee,Apr.2009. [31]FSFeditorialsta ,“Seewhat'ssharingyourairspace,” FlightSafetyDigest ,vol.24,no.5,pp. 1–26,May2005. [32]R.D.Garcia,“Designinganautonomoushelicoptertestbed:Fromconceptionthrough implementation,”Ph.D.dissertation,UniversityofSouthFlorida,2008. [33]A.GessowandG.C.Myers, Aerodynamicsofthehelicopter .F.UngarPub.Co.,1967. [34]D.R.HaddonandC.J.Whittaker,“Aircraftairworthinesscerticationstandardsforcivil UAVs,”UKCivilAviationAuthority,pp.79–86,Aug.2002. [35]K.J.Hayhurst,J.M.Maddalon,P.S.Miner,M.P.Dewalt,andG.F.Mccormick,“Unmanned aircrafthazardsandtheirimplicationsforregulation,”in Proc.25thIEEE / AIAADigital AvionicsSystemsConference ,2006,pp.1–12. [36]K.Hazawa,J.Shin,D.Fujiwara,K.Igarashi,D.Fernando,andK.Nonami,“Autonomous autorotationlandingofsmallunmannedhelicopter,” TransactionsoftheJapanSocietyof MechanicalEngineersC ,vol.70,no.698,pp.2862–2869,2004. 110

PAGE 127

[37]D.Hempe,“UnmannedaircraftsystemsintheUnitedStates,”PresentedtotheUS / Europe InternationalSafetyConference,Jun.2006. [38]M.A.Henson,“Nonlinearmodelpredictivecontrol:currentstatusandfuturedirections,” Computers & ChemicalEngineering ,vol.23,no.2,pp.187–202,1998. [39]A.HobbsandS.Herwitz,“Humanfactorsinthemaintenanceofunmannedaircraft,”in UnmannedAerialVehiclesHumanFactorsProgramReview ,W.K.Krebs,Ed.Federal AviationAdministration,O ceoftheChiefScientistforHumanFactors,2005,pp.3–8. [40]J.M.Holtzman,“Onusingperturbationanalysistodosensitivityanalysis:derivativesvs di erences,”in Proc.28thIEEEConferenceonDecisionandControl(CDC'89) ,Dec.1989. [41]M.A.Hussain,“Reviewoftheapplicationsofneuralnetworksinchemicalprocesscontrol– simulationandonlineimplementation,” ArticialIntelligenceinEngineering ,vol.13,no.1, pp.55–68,1999. [42]W.Johnson,“Helicopteroptimaldescentandlandingafterpowerloss,”AmesResearch Center,NationalAeronauticsandSpaceAdministration,NASATM73244,May1977. [43]JointCapabilityGrouponUnmannedAerialVehicles,“STANAG4671-UnmannedAerial VehicleSystemsAirworthinessRequirements(USAR),”NATONavalArmamentsGroup,draft,Mar.2007. [44]JointJAA / EurocontrolInitiativeonUAVs,“Aconceptforeuropeanregulationsforcivil unmannedaerialvehicles(UAV),”FinalReport,May2004. [45]D.A.JoostenandT.J.J.vandenBoom,“Computationallye cientuseofMPCanddynamic inversionforrecongurableightcontrol,”in Proc.AIAAGuidance,NavigationandControl ConferenceandExhibit ,2008. [46]A.KamalabadyandK.Salahshoor,“Newsisoandmisoadaptivenonlinearpredictive controllersbasedonselforganizingrbfneuralnetworks,”in Proc.3rdInternational SymposiumonCommunications,ControlandSignalProcessing,(ISCCSP2008) ,Mar.2008, pp.703–708. [47]N.Kazantzis,K.T.Chong,J.H.Park,andA.G.Parlos,“Control-relevantdiscretization ofnonlinearsystemswithtime-delayusingtaylor-lieseries,”in Proc.AmericanControl Conference ,vol.1,Jun.2003,pp.149–154. 111

PAGE 128

[48]T.KeviczkyandG.J.Balas,“Software-enabledrecedinghorizoncontrolforautonomous unmannedaerialvehicleguidance,” JournalofGuidance,ControlandDynamics ,vol.29, no.3,pp.680–694,2006. [49]Y.Kuwata,T.Schouwenaars,A.Richards,andJ.How,“Robustconstrainedrecedinghorizon controlfortrajectoryplanning,”in Proc.AIAAGuidance,NavigationandControlConference andExhibit ,2005. [50]M.Lawry nczuk,“Afamilyofmodelpredictivecontrolalgorithmswitharticialneural networks,” InternationalJournalofAppliedMathematicsandComputerScience ,vol.17, no.2,pp.217–232,2007. [51]A.Y.-N.Lee,“Optimallandingofahelicopterinautorotation,”Ph.D.dissertation,Department ofAeronauticsandAstronautics,StanfordUniversity,Jul.1985. [52]A.Y.-N.Lee,“Optimalautorotationaldescentofahelicopterwithcontrolandstateinequality constraints,” JournalofGuidance,ControlandDynamics ,vol.13,no.5,pp.922–924,Sep. 1990. [53]D.J.Lee,H.Bang,andK.Baek,“Autorotationofanunmannedhelicopterbyareinforcement learningalgorithm,”in Proc.AIAAGuidance,NavigationandControlConferenceand Exhibit ,Aug.2008. [54]J.G.Leishman, PrinciplesofHelicopterAerodynamics ,2nded.,ser.CambridgeAerospace Series.CambridgeUniversityPress,2006. [55]B.R.Maner,F.J.Doyle,B.A.Ogunnaike,andR.K.Pearson,“Nonlinearmodelpredictive controlofasimulatedmultivariablepolymerizationreactorusingsecond-ordervolterramodels,” Automatica ,vol.32,no.9,pp.1285–1301,1996. [56]S.S.McGowen, Helicopters:anillustratedhistoryoftheirimpact .ABC-CLIO,2005. [57]E.MeadowsandJ.B.Rawlings,“Modelpredictivecontrol,”in Nonlinearprocesscontrol M.A.HensonandD.E.Seborg,Eds.PrenticeHall,1997,ch.5. [58]Q.MiaoandS.-F.Wang,“Nonlinearmodelpredictivecontrolbasedonsupportvector regression,”in Proc.InternationalConferenceonMachineLearningandCybernetics ,vol.3, 2002,pp.1657–1661. [59]D.S.MooreandG.P.McCabe, IntroductiontothePracticeofStatistics ,4thed.W.H. Freeman,2002. 112

PAGE 129

[60]K.Munson, Germanwarbirds:FromWorldWar1toNATOally .SterlingPubCoInc,1986. [61]NationalTransportationSafetyBoard(NTSB),“Accidentdatabaseandsynopses,”Online, Jun.2008.Online:http: // www.ntsb.gov / ntsb / query.asp [62]NationalTransportationSafetyBoard(NTSB),“Aviationaccidentstatistics,”Online,Jun. 2008.Online:http: // www.ntsb.gov / aviation / Stats.htm [63]A.PapoulisandS.U.Pillai, Probability,RandomVariables,andStochasticProcesses ,4thed. Mc-GrawHill,2002. [64]S.Pich,B.Sayyar-Rodsari,D.Johnson,andM.Gerules,“Nonlinearmodelpredictivecontrol usingneuralnetworks,” IEEEControlSystemsMagazine ,vol.20,no.3,pp.53–62,Jun.2000. [65]RangeSafetyGroup,RangeCommandersCouncil,“Rangesafetycriteriaforunmannedair vehicles,”Document323-99,Dec.1999. [66]RangeSafetyGroup,RangeCommandersCouncil,“Rangesafetycriteriaforunmannedair vehicles-rationaleandmethodologysupplement,”Supplementtodocument323-99,Dec.1999. [67]RangeSafetyGroup,RangeCommandersCouncil,“Commonriskcriteriastandardsfor nationaltestranges:Supplement,”Supplementtodocument321-07,Jun.2007. [68]N.Sabatini,“AssuringthesafeintegrationofUAS,” UnmannedAircraftSystems,TheGlobal Perspective2007 / 2008 ,p.11,May2007. [69]N.Sabatini,“Progressonthesafeintegrationofunmannedaircraftsystems,” UASYearbook 2008 / 2009,UVSInternational ,p.9,May2008. [70]SafetyRegulationGroup,“CAAPAPER2003 / 1helicoptertailrotorfailures,”UKCivil AviationAuthority,Nov.2003. [71]B.Sayyar-Rodsari,E.Hartman,E.Plumer,K.Liano,andC.Schweiger,“Extrapolating gain-constrainedneuralnetworks-e ectivemodelingfornonlinearcontrol,”in Proc.43rd IEEEConferenceonDecisionandControl(CDC) ,vol.5,Dec.2004,pp.4964–4971. [72]J.Seddon, Basichelicopteraerodynamics ,ser.AIAAeducationseries.BlackwellScientic Publications,1990. 113

PAGE 130

[73]N.Slegers,J.Kyle,andM.Costello,“Nonlinearmodelpredictivecontroltechniquefor unmannedairvehicles,” JournalofGuidance,ControlandDynamics ,vol.29,no.5,pp. 1179–1188,2006. [74]G.R.SriniwasandY.Arkun,“Aglobalsolutiontothenonlinearmodelpredictivecontrol algorithmsusingpolynomialarxmodels,” Computers & ChemicalEngineering ,vol.21,no.4, pp.431–439,1997. [75]P.D.TalbotandL.G.Schroers,“Asimplemethodforestimatingminimumautorotative descentrateofsinglerotorhelicopters,”AmesResearchCenter,NationalAeronauticsandSpaceAdministration,NASATM78452,Mar.1978. [76]B.Tarbert,“UASairworthiness,certicationandaccesstotheairspace,”Presentedatthe ICASWorkshoponUAVAirworthiness,certicationandaccesstotheairspace,Sep.2007. [77]P.TatjewskiandM.Lawry nczuk,“Softcomputinginmodel-basedpredictivecontrol,” InternationalJournalofAppliedMathematicsandComputerScience ,vol.16,no.1,pp. 7–26,2006. [78]U.S.DepartmentofDefense,“UnmannedsystemssafetyguideforDoDacquisition,”First Edition(Version.96),Jan.2007. [79]U.S.DepartmentofDefense.O ceoftheSecretaryofDefense,“Airspaceintegrationplan forunmannedaviation,”Nov.2004. [80]U.S.DepartmentofDefense.O ceoftheSecretaryofDefense,“Unmannedaircraftsystems roadmap2005-2030,”Report,2005. [81]R.WalkerandL.F.Gonzalez,“Australianresearchcentreforaerospaceautomation,” UnmannedAircraftSystems,TheGlobalPerspective2007 / 2008 ,pp.17–18,May2007. [82]L.-X.WangandF.Wan,“Structuredneuralnetworksforconstrainedmodelpredictive control,” Automatica ,vol.37,no.8,pp.1235–1243,2001. [83]J.Watkinson, Artofthehelicopter .ElsevierButterworth-Heinemann,2004. [84]R.E.WeibelandR.J.Hansman,“Safetyconsiderationsforoperationofdi erentclasses ofUAVsintheNAS,”in Proc.AIAA4thAviationTehcnology,IntegrationandOperations ForumandAIAA3rdUnmannedUnlimitedTechnicalConference,WorkshopandExhibit 2004. 114

PAGE 131

[85]B.P.Welford,“Noteonamethodforcalculatingcorrectedsumsofsquaresandproducts,” Technometrics ,vol.4,no.3,pp.419–420,1962. [86]Y.Xia,G.Feng,andM.Kamel,“Developmentandanalysisofaneuraldynamicalapproachto nonlinearprogrammingproblems,” IEEETransactionsonAutomaticControl ,vol.52,no.11, pp.2154–2159,Nov.2007. [87]Y.Xia,G.Feng,andJ.Wang,“Anovelrecurrentneuralnetworkforsolvingnonlinear optimizationproblemswithinequalityconstraints,” IEEETransactionsonNeuralNetworks vol.19,no.8,pp.1340–1353,Aug.2008. [88]Y.Xia,H.Leung,andJ.Wang,“Aprojectionneuralnetworkanditsapplicationtoconstrained optimizationproblems,” IEEETransactionsonCircuitsandSystems—PartI:Fundamental TheoryandApplications ,vol.49,no.4,pp.447–458,Apr.2002. [89]Y.XiaandJ.Wang,“Arecurrentneuralnetworkfornonlinearconvexoptimizationsubject tononlinearinequalityconstraints,” IEEETransactionsonCircuitsandSystems—PartI: RegularPapers ,vol.51,no.7,pp.1385–1394,Jul.2004. [90]Y.XiaandJ.Wang,“Arecurrentneuralnetworkforsolvingnonlinearconvexprograms subjecttolinearconstraints,” IEEETransactionsonNeuralNetworks ,vol.16,no.2,pp. 379–386,Mar.2005. [91]A.Zheng,“Acomputationallye cientnonlinearmpcalgorithm,”in Proc.AmericanControl Conference ,vol.3,Jun.1997,pp.1623–1627. [92]T.J.Zinser,“ObservationsonFAA'soversightofaviationsafety,”StatementoftheActing InspectorGeneral,USDOTbeforetheCommiteeonTransportationandInfrastructure,SubcommitteeonAviation,USHouseofRepresentatives,Sep.2006. 115

PAGE 132

Appendices 116

PAGE 133

AppendixA:CaseStudyUsingthemethodologypresentedinSection2.4itispossibletoderivethereliabilityrequirementswithrespecttogroundimpact,forvarioustypesofUASandunderdi erentscenarios.Threecases wereinvestigatedusingtenUAS,vexed-wingandverotary-wing.ThesystemswerechosentospanallsizesandtheirbasiccharacteristicsareshowninTableA.1.AdescriptionofeachcaseandtheparametersusedisprovidedinTableA.2.Inallthecasesthe f and f parameterswhere givenaveragevaluesof10 6 and10 2 respectively.TheresultsforeachUASandcasearesummarizedinTableA.3.TableA.1:Characteristicsofvexedwingandverotary-wingUASofvarioussizes,usedforthecaseanalysis.Source:[31,80] Weight(kg)Dimensions(m)Op.Speed(ms 1 )Op.Altitude(ft) RQ-4AGlobalHawk11,61235.4(wingspan)17765,000MQ1Predator1,02114.8(wingspan)7020,000RQ-2Pioneer2055.2(wingspan)4115,000Neptune362.1(wingspan)438,000Aerosonde152.9(wingspan)4212,000RQ-6FireScout1,1578.4(rotordiameter)6520,000CL-327Guardian3504.0(rotordiameter)4418,000RmaxIIG943.12(rotordiameter)5.6500VarioXLV222.5(rotordiameter)16500MaxiJoker281.8(rotordiameter)20 a 400 a guesstimated TableA.2:Theparametersusedforeachtestcaseandadescriptionofapossiblescenariocorrespondingtothatcase. CasePop.Density (ppl = km 2 ) f s Description 1-Easy500.6Lowpopulationdensityarea,whereitisassumed thatpeoplecanbetrainedtoavoidortakecoverwhenrequired,e.g.insurveillanceofremotemilitaryinstallation. 2-Average2000.5Thepopulationdensityisequaltothestandard populationdensityof200ppl = km 2 [20].Thisscenario correspondstooperationsinsuburbanregions. 3-Hard5,0000.4Highpopulationdensityandlowshelteringfactor.This casecorrespondstothescenarioofasearchandrescueoperationinametropolitanarea,whereseveralpeopleareinopenareaspreoccupiedwithothertasks. 117

PAGE 134

AppendixA:(continued)TableA.3:FatalityprobabilityandreliabilityrequirementswithrespecttogroundimpactaccidentsfortenUASunderthreedi erentcases. UAS P (fatality j GI) T GI inhours ModelEasyAverageHardEasyAverageHard RQ-4AGlobalHawk84.4%95.0%99.2%236,3771,064,28127,781,594MQ1Predator55.7%76.8%93.4%43,916242,0827,358,637RQ-2Pioneer39.2%59.7%83.8%7,15243,5881,528,834Neptune24.1%38.8%64.2%1,2237,879325,514Aerosonde11.1%17.1%30.5%6954,291191,553RQ-6FireScout47.3%68.9%89.5%16,19994,2413,062,423Guardian28.3%45.2%71.3%2,47515,798623,337RmaxtypeIIG10.6%16.3%29.0%6003,685164,090VarioXLV5.1%7.0%11.0%1981,08642,955MaxiJoker4.1%5.4%8.0%9348918,336 Althoughtheresultsaresubjecttotheuncertaintiesinherentintheparametersandthemodelitself,theyshouldbeaccurateintermsoforderofmagnitudeandforcomparingdi erentUAS. Ontheotherhand,derivationofmoredetailedmodelsandespeciallyvalidationofsuchmodelscanbequitedi cultbecauseofthescarcityofaccidentdata.Nevertheless,conservativemodels andestimateshavebeenusedinallcasestudies.Consideringthatcurrentmannedaviationaccidentratesareintheorderof10 7 h 1 foraircarriers and10 5 h 1 forgeneralaviation(Table2.3),itisobviousthatforoperationsinhighpopulation densityareas,UASwillneedtoexceedthisperformance.AsimilaranalysiscanbedonetodetermineregionsthatcanbesafelyoverowngiventheUASreliability.ResultsofsuchananalysisaregiveninTableA.4.ItisnoteworthythatalargeUASliketheRQ-4AGlobalHawkcansafelyloiteroveronly38.8%oftheU.S.areaandtherewillstillbe20%ofthatareathatwouldbeunreachableevenifitreachestheaccidentrateofgeneralaviation.SmallersystemsliketheRQ-2PioneerandtheRQ-6Firescoutarealsolimited,sinceeveniftheyreachthe100,000 T GI limit,manyareas,mostlyinand aroundmajorcities,remainout-of-bounds.Ontheotherhand,smallUASwillbesafetooperateovermostareaswithouthighreliabilityrequirements.ItisnoteworthythatwithevenrelativelylowreliabilityalargepercentageoftheareaoftheU.S.,EuropeandAustraliawillbeavailabletothesesystems.Nevertheless,althoughlowreliabilitymaybepermissibleintermsofsecurity,itisunacceptableduetootherfactorslikecost. 118

PAGE 135

AppendixA:(continued)TableA.4:ThepercentageoftheUSareaoverwhicheachUAScanloiterwithoutviolatingsetTLSrequirement,basedonexhibitedreliability.Theboldcolumnrepresentsthereliabilityofmannedgeneralaviation.Populationdensitydata:[12]. T GI inhours 10 2 10 3 10 4 10 5 10 6 RQ-4AGlobalHawk0.4%7.1%38.8% 79.5% 96.6% MQ1Predator2.5%25.6%64.2% 93.8% 99.0% RQ-2Pioneer14.7%52.9%90.3% 98.3% 100.0% Neptune43.8%83.9%97.2% 99.9% 100.0% Aerosonde53.2%90.4%98.3% 100.0% 100.0% RQ-6FireScout7.7%40.8%81.4% 96.8% 99.8% Guardian32.7%72.4%95.5% 99.5% 100.0% RmaxtypeIIG55.9%91.5%98.5% 100.0% 100.0% VarioXLV79.1%96.5%99.7% 100.0% 100.0% MaxiJoker89.4%98.1%100.0% 100.0% 100.0% 119

PAGE 136

AppendixB:GroundFatalityProbabilityModelSensitivityAnalysisInSection2.4,thefollowingmodelwasproposedtocalculatetheprobabilityoffatalitygivenagroundimpact:(B.1) P (fatality j exposure) = 1 1 + q f f f E imp 1 4 f s Inthissectionasensitivityanalysiswillbecarriedouttoevaluatethee ectofperturbationsofthe modelinputsandparameters.Typicallysuchananalysisassumesthatmodelinputsandparam-etersarerandomvariables.Itisthenpossibletodeterminethejointdistributionoftheserandomvariablesandconsequentlythedistributionofthemodeloutputasafunctionofthecharacteris-ticsoftherandomvariables.Alternativelyeachparameterandinputcanbeevaluatedseparately,consideringtherestknown.Assumingafunction g ( x )ofarandomvariable x withadistributionfunction f ( x ),thenitsexpectedvalueof g ( x )isgivenby[63]: (B.2) E g ( x ) = Z + 1 1 g ( x ) f ( x )d x Usingtheexpectationof g ( x ),itispossibletocalculatethebiasas: (B.3) Bias g ( x ) = g ( ) E g ( x ) where isthetruevalueofx,andthevariancefrom: (B.4) Var g ( x ) = E h g 2 ( x ) i E g ( x ) 2 Nevertheless,thefunctionalformofthemodelmakesananalyticalderivationofitsexpectedvaluedi cult.Thisisregardlessoftheassumedprobabilitydistributionfunctionsfortheparametersand inputandwhethertheyareconsideredseparatelyortogether.Analternativeapproachistoconsidersmallperturbationsofeachparameterandinputandcal-culatetheirimpactonthemodel.Thismethod,knownasinnitesimalperturbationanalysisistypicallycarriedoutbytakingaTaylorseriesapproximationofthefunction g ( x ).Assumingthat f ( x )isnegligibleoutsideaninterval( "; + ), E g ( x ) canbeapproximatedas[63]: 120

PAGE 137

AppendixB:(continued)(B.5) E g ( x ) g ( ) + g 00 ( ) 2 2 andthevarianceis:(B.6) Var g ( x ) g 0 ( ) 2 2 Holtzman[40]proposedtheuseofdi erencesinsteadofderivatives.Althoughdi erencesprovide lessaccuracyforapproximationpurposes,Holtzmanassertsthattheuseofdi erencesisadvantageousforsensitivityanalysis,sincederivativesonlyallowforverysmallchangeswithoutallowingonetodenehowsmall.Asaresultheprovedthatusingdi erencesa ordshigheraccuracy,even forhighvaluesofstandarddeviation.Usingasecondordercentraldi erenceapproximationinsteadoftheTaylorexpansion,theexpectedvalueof g ( x )canbeapproximatedfrom[40]: (B.7) E g ( x ) g ( ) + 1 2 g ( + h ) 2 g ( ) + g ( h ) h 2 2 where and arethemeanandvarianceofthe x randomvariable.Thebiasandvarianceof g ( x ) canthenbecalculatedfrom(B.5)and(B.6).Inthisinvestigation,theperturbationanalysiswillbecarriedoutforthefollowingthreerandomvariables: x 1 = log 10 E imp x 2 = log 10 f and x 3 = f s .Eachofthesevariablesisconsideredtobe normallydistributedwithmean i andvariance i .Parameter f isgoingtobeconsideredxed, withavalueof100.Asaresult,bysubstitutingin(B.1),thefunctiontobeanalyzedisgivenby:(B.8) g ( x 1 ; x 2 ; x 3 ) = 1 1 + 10 x 2 2 2 + 2 x 1 4 x 3 In(B.7)avaluefor h needstobechosen.Forthisanalysisthevalueof p 3 i usedin[40]isselected.Foreachrandomvariable,(B.7)isgivenby:(B.9) E h g ( x i j x j ; j i ) i g ( i ) + g ( i + p 3 i ) 2 g ( i ) + g ( i p 3 i ) 6 Ingeneralbiaseslessthan0.01andvarianceslessthan5 10 3 canbeconsideredtohavenegligiblee ectonthenalvalue. 121

PAGE 138

AppendixB:(continued)Fortherstcase x 1 N ( 1 ; 0 : 152)wasassumed.Thiscorrespondsto80%certaintythat 1 0 : 5 < x 1 < 1 + 0 : 5orthatthekineticenergyatimpactestimateiswithinanorderofmagnitude fromtheactual.ThebiasispresentedinFigureB.1andthevarianceinFigureB.2.Itisobviousthatthereissignicantbiasforlowkineticenergies,low f andlowshelteringfactors,especiallyfor f s < 0 : 3and E imp < 1kJ.Nevertheless,itquicklydisappearsforhigher f .The variancecanbesignicantupto f s of0.5,butonlyfor E imp < 1kJandlow f Ingeneralthemodelbehaveswellwithrespecttoperturbationsofthe E imp for f 10 5 and kineticenergiesofatleast100J.Fortheanalysisofparameter f itwasassumedthat x 2 N ( 2 ; 0 : 609).Thistranslatesinto80% certaintythat 2 1 < x 2 < 2 + 1orthattheestimateof f haslessthanoneorderofmagnitude error.ThebiasispresentedinFigureB.3andthevarianceinFigureB.4.Somenegativebiaswasexhibitedforaboveaverageshelteringfactors, f upto10 5 andlowkineticenergiesbutitdidn'texceed0.03.Thevarianceinthesecaseswasalsosignicantapproach-ing0.015.Finallytheshelteringfactorwasalsoconsideredtobenormallydistributed,morespecically x 3 N ( 3 ; 0 : 014).Thismeansthatfor x 3 3 0 : 15 < x 3 < 3 + 0 : 15istrue.Thebiasispresentedin FigureB.5andthevarianceinFigureB.6.Lowkineticenergyincombinationwithalowvalueof f resultedinsomebiaswithrespectto perturbationsoftheshelteringfactor,neverthelesswithin0.01.Thevariancewasalsoverysmallandingenerallessthan10 3 Theperturbationanalysispresentedcannotbeusedtomakeacaseonwhetherthemodelaccu-ratelyrepresentsreality.Athoroughmodelvalidationwouldrequireawealthofexperimentalresults,someofwhicharedi cultifnotimpossibletoobtain.Nevertheless,itshouldbenoted thatthismodelisproposedforthecalculationofanorderofmagnitudeforUAS T GI andnotan exactvalue.Asaresultthebiasesexhibitedwillonlyhaveaminimale ectonthenaloutcome sought.Withtheabovestatedgoalinmindsomeconclusionsonthebehaviorofthemodelcanbedrawn.Althoughthevariancechosenforeachrandomvariablewassignicant,themodelwasingeneralwellbehaved,withperturbationsgenerallyresultinginsmallbiasesandvariance.Anexceptiontothiswasthecombinationofsmallkineticenergyandlowvalueof f and / or f s .Thisisexpected becauseinthiscasethemodelcurveissteepandparameterandinputperturbationscanresultinsignicantchangesinthemodeloutput. 122

PAGE 139

AppendixB:(continued) 0 : 1 0 : 05 0 0 : 05 0 : 1Biasf = 1 10 3 f = 1 10 5 f s = 0.1 f = 1 10 7 0 : 1 0 : 05 0 0 : 05 0 : 1Biasf s = 0.3 0 : 1 0 : 05 0 0 : 05 0 : 1Biasf s = 0.5 0 : 1 0 : 05 0 0 : 05 0 : 1Biasf s = 0.7 0 : 1 0 : 05 0 0 : 05 0 : 1 1234567Biaslog E imp 1234567 log E imp 1234567 f s = 0.9 log E imp FigureB.1:Thebiascalculatedforperturbationsofthe x 1 randomvariable,correspondingtothe log 10 E imp asafunctionoftheactualvalueof x 1 .Theresultsaregivenfordi erentvaluesof f and f s 123

PAGE 140

AppendixB:(continued) 0 0 : 02 0 : 04 0 : 06 0 : 08 0 : 1Variancef = 1 10 3 f = 1 10 5 f s = 0.1 f = 1 10 7 0 0 : 005 0 : 01 0 : 015 0 : 02 0 : 025 0 : 03 0 : 035 0 : 04Variancef s = 0.3 0 0 : 005 0 : 01 0 : 015 0 : 02Variancef s = 0.5 0 0 : 005 0 : 01 0 : 015 0 : 02Variancef s = 0.7 0 0 : 005 0 : 01 0 : 015 0 : 02 1234567Variancelog E imp 1234567 log E imp 1234567 f s = 0.9 log E imp FigureB.2:Thevariancecalculatedforperturbationsofthe x 1 randomvariable,correspondingto the log 10 E imp asafunctionoftheactualvalueof x 1 .Theresultsaregivenfordi erentvaluesof f and f s 124

PAGE 141

AppendixB:(continued) 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03BiasE imp = 1 10 3 E imp = 1 10 6 f s = 0.1 E imp = 1 10 9 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03Biasf s = 0.3 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03Biasf s = 0.5 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03Biasf s = 0.7 0 : 03 0 : 02 0 : 01 0 0 : 01 0 : 02 0 : 03 34567Biaslog f 34567 log f 34567 f s = 0.9 log f FigureB.3:Thebiascalculatedforperturbationsofthe x 2 randomvariable,correspondingtothe log 10 f asafunctionoftheactualvalueof x 2 .Theresultsaregivenfordi erentvaluesof E imp and f s 125

PAGE 142

AppendixB:(continued) 0 0 : 005 0 : 01 0 : 015Variancef s = 1 10 3 f s = 1 10 6 f s = 0.1 f s = 1 10 9 0 0 : 005 0 : 01 0 : 015Variancef s = 0.3 0 0 : 005 0 : 01 0 : 015Variancef s = 0.5 0 0 : 005 0 : 01 0 : 015Variancef s = 0.7 0 0 : 005 0 : 01 0 : 015 34567Variancelog f 34567 log f 34567 f s = 0.9 log f FigureB.4:Thevariancecalculatedforperturbationsofthe x 2 randomvariable,correspondingto the log 10 f asafunctionoftheactualvalueof x 2 .Theresultsaregivenfordi erentvaluesof E imp and f s 126

PAGE 143

AppendixB:(continued) 0 : 01 0 0 : 01Biasf = 1 10 3 f = 1 10 5E imp = 1 10 3f = 1 10 7 0 : 01 0 0 : 01Bias E imp = 1 10 4 0 : 01 0 0 : 01Bias E imp = 1 10 5 0 : 01 0 0 : 01Bias E imp = 1 10 6 0 : 01 0 0 : 01 0 : 20 : 40 : 60 : 8Biasf s 0 : 20 : 40 : 60 : 8 f s 0 : 20 : 40 : 60 : 8E imp = 1 10 7f s FigureB.5:Thebiascalculatedforperturbationsofthe x 3 randomvariable,correspondingtothe shelteringfactor f s asafunctionoftheactualvalueof x 3 .Theresultsaregivenfordi erentvalues of f and E imp 127

PAGE 144

AppendixB:(continued) 10 0 10 3Variancef = 1 10 3 f = 1 10 5E imp = 1 10 3f = 1 10 7 10 0 10 3Variance E imp = 1 10 410 0 10 4Variance E imp = 1 10 510 0 10 4Variance E imp = 1 10 610 0 10 4 0 : 20 : 40 : 60 : 8Variancef s 0 : 20 : 40 : 60 : 8 f s 0 : 20 : 40 : 60 : 8E imp = 1 10 7f s FigureB.6:Thevariancecalculatedforperturbationsofthe x 3 randomvariable,correspondingto theshelteringfactor f s asafunctionoftheactualvalueof x 3 .Theresultsaregivenfordi erent valuesof f and E imp 128

PAGE 145

AbouttheAuthorKonstantinosDalamagkidisreceivedhisDiplomainChemicalEngineeringfromtheNationalUniversityofAthens,Greecein2001.Histhesiswasonaggregatingsensormeasurementsforevaluatingphotovoltaicpanelperformance.In2003hereceivedhisM.Sc.inElectronicsandComputerEngineeringfromtheTechnicalUni-versityofCrete,Greece.Histhesiswasonenergyconservationandthermalcomfortinbuildingsusingreinforcementlearningcontrol.Inparallel,heworkedasacomputerscienceinstructorwiththeTechnicalEducationalInstituteofCrete.Followingthat,hedidhismilitaryserviceassecondlieutenantinlogistics.TowardstheendofhisserviceheparticipatedinEU-fundedresearch,de-velopingasolargreenhousethermalmodelandcontrollermodules.In2005heenteredthePh.D.inComputerScienceandEngineeringprogramintheUniversityofSouthFlorida.HeworkedasagraduateresearcherfortheUnmannedSystemsLabaswellasateachingassistant.Mr.Dalamagkidishaspublishedabook,onebookchapter,vejournalandsixconferencepapers.Hehasalsopreparedseveraltechnicalreports,presentationsandotherdocuments.


xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam 2200409Ka 4500
controlfield tag 001 002068399
005 20100413133543.0
007 cr bnu|||uuuuu
008 100413s2009 flu s 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0003147
035
(OCoLC)606891644
040
FHM
c FHM
049
FHMM
090
TK7885 (Online)
1 100
Dalamagkidis, Konstantinos.
0 245
Autonomous vertical autorotation for unmanned helicopters
h [electronic resource] /
by Konstantinos Dalamagkidis.
260
[Tampa, Fla] :
b University of South Florida,
2009.
500
Title from PDF of title page.
Document formatted into pages; contains 128 pages.
Includes vita.
502
Dissertation (Ph.D.)--University of South Florida, 2009.
504
Includes bibliographical references.
516
Text (Electronic dissertation) in PDF format.
3 520
ABSTRACT: Small Unmanned Aircraft Systems (UAS) are considered the stepping stone for the integration of civil unmanned vehicles in the National Airspace System (NAS) because of their low cost and risk. Such systems are aimed at a variety of applications including search and rescue, surveillance, communications, traffic monitoring and inspection of buildings, power lines and bridges. Amidst these systems, small helicopters play an important role because of their capability to hold a position, to maneuver in tight spaces and to take off and land from virtually anywhere. Nevertheless civil adoption of such systems is minimal, mostly because of regulatory problems that in turn are due to safety concerns. This dissertation examines the risk to safety imposed by UAS in general and small helicopters in particular, focusing on accidents resulting in a ground impact. To improve the performance of small helicopters in this area, the use of autonomous autorotation is proposed. This research goes beyond previous work in the area of autonomous autorotation by developing an on-line, model-based, real-time controller that is capable of handling constraints and different cost functions. The approach selected is based on a non-linear model-predictive controller, that is augmented by a neural network to improve the speed of the non-linear optimization. The immediate benefit of this controller is that a class of failures that would otherwise result in an uncontrolled crash and possible injuries or fatalities can now be accommodated. Furthermore besides simply landing the helicopter, the controller is also capable of minimizing the risk of serious injury to people in the area. This is accomplished by minimizing the kinetic energy during the last phase of the descent. The presented research is designed to benefit the entire UAS community as well as the public, by allowing for safer UAS operations, which in turn also allow faster and less expensive integration of UAS in the NAS.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Co-advisor: Kimon P. Valavanis, Ph.D.
Co-advisor: Les A. Piegl, Ph.D.
653
Helicopter control
Non-linear model-predictive control
Neural network
Autorotative flight
Safety
690
Dissertations, Academic
z USF
x Computer Science and Engineering
Doctoral.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.3147