The control design for formation flight about multiple Unmanned Aerial VehiclesWord格式文档下载.docx

The control design for formation flight about multiple Unmanned Aerial VehiclesWord格式文档下载.docx

《The control design for formation flight about multiple Unmanned Aerial VehiclesWord格式文档下载.docx》由会员分享，可在线阅读，更多相关《The control design for formation flight about multiple Unmanned Aerial VehiclesWord格式文档下载.docx（20页珍藏版）》请在冰豆网上搜索。

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.

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