Trajectory-Tracking-Control-of-a-Quadrotor-Unmanne

AmericanInstituteofAeronauticsandAstronautics1TrajectoryTrackingControlofaQuadrotorUnmannedMini-HelicopterZongyuZuo*TheSeventhResearchDivision,BeijingUniversityofAeronauticsandAstronautics,Beijing,China,100191NationalKeyLaboratoryofScienceandTechnologyonHolisticControlMingZhu†SchoolofAeronauticsandEngineering,BeijingUniversityofAeronauticsandAstronautics,Beijing,China,100191ZeweiZheng‡TheSeventhResearchDivision,BeijingUniversityofAeronauticsandAstronautics,Beijing,China,100191NationalKeyLaboratoryofScienceandTechnologyonHolisticControlInthispaper,therelationshipbetweenattitudeandlinearaccelerationofthequadrotorunmannedmini-helicopterisbuiltandtwotrajectorytrackingcontroldesignmethodologiesbasedontherelationshipareproposed:classicalinner/outer-loopcontroldesignapproachandanewcommandfilteredbacksteppingdesignstrategy.Variousnumericalsimulationsdemonstratethevalidityofthecontroldesign.Finally,wediscussthetwodesignmethodsandarriveataconclusionviacomparison.NomenclatureGa=gyroscopictorquesg=gravityaccelerationIf=momentofinertiamatrixIr=rotormomentofinertialk,b=rotorforceparametersm=quadrotormassp=positionvectorofquadrotorcenterofmassp,q,r=roll,pitch,yawrateQi=reactivetorqueactsonrotoriR=rotationmatrixv=linearvelocityvectorofthequadrotorcenterofmassx,y,z=positioncomponentsaboutinertialframeΩ=angularratevectorΘ=Euleranglesvectorφ,θ,ψ=roll,pitch,yawτa=controltorqueωi=rotorispeedThisworkwaspartiallysupportedbyResearchFoundationforKeyDisciplinesofBeijngMunicipalCommissionofEducation(XK100060422).*Ph.DCandidate,Room205,No.1KeyanSouthBuilding,BeijingUniversityofAeronauticsandAstronautics,100191,[e-mail]†Instructor,Room202,No.1KeyanSouthBuilding,BeijingUniversityofAeronauticsandAstronautics,100191,Beijing.‡Ph.DCandidate,Room205,No.1KeyanSouthBuilding,BeijingUniversityofAeronauticsandAstronautics,100191,Beijing.48thAIAAAerospaceSciencesMeetingIncludingtheNewHorizonsForumandAerospaceExposition4-7January2010,Orlando,FloridaAIAA2010-948Copyright©2010bytheauthors.PublishedbytheAmericanInstituteofAeronauticsandAstronautics,Inc.,withpermission.AmericanInstituteofAeronauticsandAstronautics2I.IntroductionUADROTORmini-helicopter,consistingoffourindividualrotorsof“X”arrangement,isanexcellent,novelverticaltake-offandlandingUnmannedAerialVehicle(UAV)forbothmilitaryandcivilianusages.Inordertocompensatetheeffectofthereactivetorques,thefourrotorsaredividedintotwopairsof(1,3)and(2,4)turninginoppositedirection,asshowninFig.1.Soaquadrotormini-helicopterissuitableforhoverandpseudo-staticflight.Thequadrotormini-helicopterisatypicalunder-actuated,nonlinearcoupledsystem,andthetable1showsthequadrotorflightmechanism:verticalmotioncreatedbycollectivelyincreasinganddecreasingthespeedofallfourrotors;pitchorrollmotionisachievedbythedifferentialspeedofthefront-rearsetortheleft-rightsetofrotors,coupledwithlateralmotion;yawmotionisrealizedbythedifferentreactivetorquesbetweenthe(1,3)and(2,4)rotors.Thusthenumberofindividualmanipulatingvariablescannotinstantaneouslysettheaccelerationsinalldirectionsoftheconfigurationspace.Inspiteofthefourrotors,thequadrotorisstillanunder-actuatedandnonlinearcoupledsystem.Table1QuadrotorUnmannedMini-HelicopterRotorSpeedControlRotor1Rotor2Rotor3Rotor4Up↑↑↑↑Pitch↑ˉ↓ˉRollˉ↑ˉ↓Yaw↓↑↓↑McKerrow1andHamel2studiedthedynamicalmodelofthefour-rotorVTOLintheirliterature,Tayebi3etalmadeaslightmodificationofthegyroscopictorqueexpressiononthedynamicalmodelinRef.1and2,anddesignedtheattitudestabilizationPD2controllerbasedonunitquaternionframethatiscommonlyemployedbytheattitudecontrolproblem4,5ofarigidbody.Bouabdallah6appliedtheclassicalPIDandLQalgorithmrespectivelytoquadrotorattitudestabilization.However,thequadrotorflightconditionanditsunder-actuatedandstrongcoupledpropertiesrenderthetrajectorytrackingcontrolmuchmorechallenging.InRef.7,Bouabdallaachievedthequadrotortrajectorytrackingbycombiningclassicalinner/outerloopwithbacksteppingandsliding-modetechniquesrespectively,butthetwo-timescaleseparationassumptionneedslargeinner-loopgaintoguaranteeclosed-loopstability8.Madani10,11etaldividedthequadrotordynamicsintothreesubsystemsusingthesamemethodologytotrackthedesiredtrajectoryviafullstatebacksteppingapproach.Inviewoftheuncertaintyandtheunknowndynamics,WashlandandHoffmann9designedanintegralslidingmodecontrollerandareinforcementlearningcontrolschemerespectivelytomakeacomparison,andtheresultsdemonstratedgoodrobustnessofthetwocontrollers.Itiswellknownthatthemotionequationsofarigidbodycontaintranslationandrotationoftwocomponents,andsatisfythestrictfeedbackform.Thatiswhybacksteppingtechnique11,16issopopularinflightcontrolsystems.However,analyticderivativeexpressionsofpseudocontrolvariablesareusuallyoverlycomplicatedorunknownespeciallyforthehighordersystemsandtheuncertainsystems,whichlimitthebacksteppingtechniqueinpracticalapplications.Thisworkadoptscommandfilteredbacksteppingtechnique13tostabilizethequadrotorattitudewithoutcalculatingpseudocontrolsignalderivative,andtodecreasethedependentdegreeonanalyticmodel.Thetrajectorytra