The control design for formation flight about multiple Unmanned Aerial Vehicles.docx

The control design for formation flight about multiple Unmanned Aerial Vehicles.docx

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ThecontroldesignforformationflightaboutmultipleUnmannedAerialVehicles

Abstract:

ThecontroldesignforformationflightaboutmultipleUnmannedAerialVehicles（UAVs）isahighlycomplexquestionbecauseoftheharshrequirementsimposedbymanykindsoftasks.Theproblemisabouttodesignaformation-holdautopilotforthefollowerUAVs,asaresultthepositionsbetweentheleaderandthefollowerscanbedesignedclosetothedesiredvalue.Inthispaper,wefirstgiveaRecedingHorizonControl（RHC）schemewhichmakestheUAVsformationproblemtoasequenceofonlineoptimizationproblemsoveraplanninghorizon.WenextraisedanovelChemicalReactionOptimization（CRO）approachtoseekoptimalcontrolinputsforthefollowerUAVstokeepcoordinatedflightwiththeminimuminputcostinalloftheplanninghorizons.Severalexperimentalcomparisonresultsaregiventoshowthefeasibilityandeffectivenessofourproposedcontrolmethod.

Keywords:

UnmannedAerialVehicles（UAVs）;FormationFlight;ChemicalReactionOptimization

I.Introduction

ModelingandcontrolofformationflightofmultipleUAVsisangrowingtopicofresearchintheaerospacefield,andhasanumberofapplicationsinmilitarymissionssuchasreconnaissanceandsurveillance,taskallocationandtargetdataacquisition,radiojamming,andthesuppressionsofenemyairdefenseaswellasincivilianmissionssuchascropmonitoring,areasearchandrescue.ThemultipleUAVsformationflightproblemaimstoachievedesiredgeometriesbycontrollingtheoverallbehaviorofthegroup.AccuratemaintenanceoftheformationcanoftenaccomplishobjectivesimpossibleforasingleUAVandleadtocertainadvantagessuchasareductionintheformation’sinduceddragandenergysavingfromvortexforcecreatedbytheleadaircraft.DevelopmentofformationcontrolproblemsandnumerousapproachesforUAVsformationcontroldesignhavebeenwelldemonstrated.InRef,R.Sattigerietal.proposedadecentralizedadaptiveoutputfeedbackapproachwhichallowedthevehiclestomaintaintheformationwhileconsideringobstacles.InRef,W.Renetal.developedaleaderlessformationcontrolschemebasedonconsensusalgorithmswhichovercomeasinglepointoffailurefortheformation.InRef,D.Galzietal.proposedHighOrderSlidingMode（HOSM）controllerforaswarmofUAVstoachieveleader/followerscollision-freeformationinthepresenceofunknowndisturbances.InRef,MasayukiSuzukietal.designedathree-dimensionalformationcontrolschemeusingthenewapproachofbifurcatingartificialpotentialfields.InRef,YunfeiZouandPrabhakarR.PagillausedthetheoryofconstraintforcestodeterminethetotalforcerequiredoneveryaircrafttobuildaformationfromarbitraryinitialconditionsforUAVs.Butthesemethodsmaynotbeabletodealwiththeconstraintseasily,suchastheaccelerationofvelocityandangularturnrateconstraints,andcontrolinputsaturationconstraints.Optimization-basedapproachescansolvetheconstraintsofUAVformationcontrolsystemsappropriatelyandhavebeenprovedtoasuccessfulwaytothemultipleUAVsformationproblems.Amongthemostpopularoptimization-basedmethodsisRHCmethod.

II.ProblemFormulation

2.1ModelofUAVflightdynamicsandcontrolsystems

TheequationsofmotiondescribingUAVflightdynamicsaregivenasfollows[23,24]:

Forceequations:

（1）

Kinematicequations:

（2）

Momentequations:

（3）

Navigationequations:

（4）

Inthispaper,wereducedthecomplexmodeltoasimplermodelforthepurposeofguidancelawdesign.Accordingly,first-ordersystemsareadoptedtorepresenttwocontrolchannelsincludingtheUAVflightdynamicsasfollows:

（speedcontrolchannel）（5）

（headinganglecontrolchannel）（6）

Where

arethetimeconstantsand

arethecontrolcommandinputofeachcontrolloop.

2.2RecedingHorizonControl

Recedinghorizoncontrol（RHC）,alsoknownasmodelpredictivecontrol（MPC）,isafeedbackcontrolschemeinwhichafinitehorizonopen-loopoptimizationproblemissolvedateachsamplinginstant[25,26].

TheRHCprocedureworksasshowninFig.1.Attimet,weconsideratimeintervalextendingpstepsintothefuture,t,t+1,…,t+p.Wethencarryoutthefollowingsteps:

（1）Replacealltheuncertainquantitiesoverthepredictionhorizonpwiththeirestimatesusingtheinformationavailableattimettopredictthefuturedynamicbehaviorofthesystem.

（2）Optimizeapredeterminedperformanceobjectivefunctionsubjecttotheestimateddynamicsandconstraints.Theoptimizationresultisaplanofactionforthenextpsteps.

（3）Determinetheinputoveracontrolhorizonmusingtheplanofaction.Atthenexttimestep,theprocessisrepeated,withtheupdatedestimatesofthecurrentstateandfuturequantities.

Fig.1ProcedureofRecedingHorizonControl

2.3Leader-followerformationflightmodel

Inthispaper,wemainlyfocusonmultipleUAVsformationproblemonahorizontalplane.Thehorizontalformationgeometricparametersaretheforwardclearance

andthelateralclearance

asdefinedinFig.2.ThereferencepositionforthefollowerUAVcanbecalculatedusingthefollowingrelationship:

（7）

where

representthefollower’sdesiredposition,

and

representthepositionandtheheadingangleoftheleaderUAV.

and

areexpressedas:

（8）

（9）

Fig.2HorizontalFormationGeometry

Weformulatearecedinghorizoncontrolschemebasedonthecostfunction.Attimek,thecontrollerpredictsacontrolsequencefromtimektotime（k+p）,whichcanberepresentedby

…,

.Usingthiscontrolsequenceandthecurrentstateofthesystem

thestateattimek+1,…,k+p,whicharerepresentedby

…,

canbeobtained.Thefitnessfunctionattimekcanbedefinedas:

（10）

subjectto

（11）

whereQandRarepositive-definiteweightedmatrices.

isreferencestateoffollowerUAVsattimek.

isthestateoffollowerUAVsattimek+joverthepredictionhorizon.

isthesamplingtime.

Fig.3RecedingHorizonControlScheme

Minimizingthisfitnessfunctionyieldsanoptimalcontrolsequence,thenthefirstmcontrolactionsinthissequenceisappliedtotheformationflightsystem.Attimek+m,repeatsampling,predicting,optimizationandimplementing.ThisprocedurecanbedescribedasFig.3.

III.PrinciplesofthebasicCROalgorithm

ChemicalReactionOptimization（CRO）isarecentlyestablishedmetaheuristicsforoptimization,inspiredbythenatureofchemicalreactions.Inmicroscopicview,achemicalreactionstartswithsomeunstablemoleculeswithexcessiveenergy.Themoleculesinteractwitheachotherthro-ughasequenceofelementaryreactions.Attheend,theyareconvertedtothosewithminimumenergytosupporttheirexistence.ThispropertyisembeddedinCROtosolveoptimizationproblems.

Ingeneral,theprinciplesofchemicalreactionsaregovernedbythefirsttwolawsofthermodynamics.Thefirstlaw（conservationofenergy）saysthatenergycannotbecreatedordestroyed;energycantransformfromoneformtoanotherandtransferfromoneentitytoanother.Thesecondlawsaysthattheentropyofasystemtendstoincrease,whereentropyisthemeasureofthedegreeofdisorder.Potentialenergyistheenergystoredinamoleculewithrespecttoitsmolecularconfiguration.Whenitisconvertedtootherforms,thesystembecomesmoredisordered.Allreactingsystemstendtoreachthestateofequilibrium,whosepotentialenergydropstoaminimum.InCRO,wecapturethephenomenonbyconvertingpotentialenergytokineticenergyandbygraduallylosingtheenergyofthechemicalmoleculestothesurroundings.

3.1Themanipulatedagent

CROisamulti-agentalgorithmandthemanipulatedagentsaremolecules.Eachmoleculehasseveralattributes,someofwhichareessentialtothebasicoperationsofCRO.Theessentialattributesinclude:

themolecularstructure（ω）;thepotentialenergy（PE）;thekineticenergy（KE）;thenumberofhits（NumHit）;theminimumstructure（Min-Struct）;theminimumPE（MinPE）;andtheminimumhitnumber（MinHit）.

3.2Elementaryreactions

Achemicalchangeofamoleculeistriggeredbyacollision.Therearetwotypesofcollisions:

uni-molecularandinter-molecularcollisions.Weconsiderfourkindsofelementaryreactions:

on-wallineffectivecollision,decomposition,inter-molecularineffectivecollision,andsynthesis.Thetwoineffectivecollisionsimplementlocalsearch（intensification）whiledecompositionandsynthesisgivetheeffectofdiversification.Anappropriatemixtureofintensificationanddiversificationmakesaneffectivesearchoftheglobalminimuminthesolutionspace.

3.2.1On-wallIneffectiveCollision

Anon-wallineffectivecollisionoccurswhenamoleculehitsthewallandthenbouncesback.Somemolecularattributeschangeinthiscollision,andthus,themolecularstructurevariesaccordingly.Asthecollisionisnotsovigorous,theresultantmolecularstructureshouldnotbetoodifferentfromtheoriginalone.Supposethecurrentmolecularstructureisω.Themoleculeintendstoobtainanewstructureω`=Neighbor（ω）initsneighborhoodonthePESinthiscollision.Thechangeisallowedonlyif

PEω+KEω≥PEω`

Weget

KEω`=（PEω+KEω–PEω`）×q

whereq∈[KELossRate,1],and（1−q）representsthefractionofKElosttotheenvironmentwhenithitsthewall.KELossRateisasystemparameterwhichlimitsthemaximumpercentageofKElostatatime.Thelostenergyisstoredinthecentralenergybuffer.Thestoredenergycanbeusedtosupportdecomposition.Ifitdoesnothold,thechangeisprohibitedandthemoleculeretainsitsoriginalω,PEandKE.

3.2.2Decomposition

Decompositionr