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Proceedingsofthe41slIEEEConferenceonDecisionandControlLasVegas,NevadaUSA,December2002ThM02-1CooperativePathPlanningforMultipleUAVsinDynamicandUncertainEnvironmentsJohnS.Bellingham,MichaelTillerson,MehdiAlighanbari’,andJonathanP.How3MITDepartmentofAeronauticsandAstronauticsAbstractThispaperaddressestheproblemofcooperativepathplanningforafleetofUAVs.Thepat.hsareoptimizedtoaccountforuncertaintylad\iersariesintheenviron-mentbymodelingtheprobabilityofUAVloss.TheapproachextendspriorworkbycouplingthefailureprobabilitiesforeachUAVtotheselectedmissionsforallotherUAVs.Inordertomaximizetheexpect.edmis-sionscore,thisstochasticformulationdesignscoordina-tionplansthatoptimallyexploitthecouplingeffectsofcooperationbetweenUAVstoimprovesurvivalproba-bilities.Thisallocationisshowntorecoverreal-worldairoperationsplanningstrategies,andtoprovidesig-nificantimprovementsoverapproachesthatdonotcor-rectlyaccountforUAVattrition.Thealgorithmisim-plementedinanapproximatedecompositionapproachthatusesstraight-linepathstoestimatethetime-of-flightandriskforeachmission.ThetaskallocationfortheUAVsisthenposedasamixed-integerlinearprogram(BIILP)thatcanhesolvedusingCPLEX.1IntroductionThecapabilitiesandrolesofUAVsareevolvingandrequirenewconceptsfortheircontroljl,21.Forexam-ple,today’sU.4Vstypicallyrequireseveraloperators,butfutureUAVswillhedesignedtomaketacticalde-cisionsautonomouslyandwillbeintegratedintoteamsthatcooperatetoachievehigh-levelgoals,therebyal-lowingoneoperatortocontrolafleetofUAVs.Newmethodsinplanningandexecutionarerequiredtocwordinatetheoperationofthesefleets.Real-worldairoperationsplannersemploycooperationbetweenaircraftinordertomanagetheriskofattrition.Llissionsarescheduledsothatonegroupofaircraftopensacorridorthroughanti-aircraftdefensesbeforeafollow-ongroupattackshighervalueta.rgets,preservingbheirsurvival.\VheneachUAVcanperformmultiplefunctions(e.g.,bothdestroyanti-aircraftdefensesandattackhighvaluetargets)itisverychallengingtoplanmissionstoexploittheintegratedcapabilitiesoftheteam.Notethatcooperationisnotjustdesirable;itiscrucialfordesigningsuccessfulmissionsinheavilyde-’FundedhyMICADARPAcontractN6601-01-C-8075’AssociateProfessor,jhowQmit.eduResearchAssistant,mehdiaQmit.edufendedenvironments.Asuccessfulmethodofperform-ingtheallocationcannotsimplyassumethemissionwillalwaysbeexecutedasdesigned,givenanadver-saryintheenvironmentwhoisactivelyattemptingtocausefailure.Simulationsarepresentedtoshowt.hatignoringtheprobabilityofUAVlossresultsinmissionplansthatarequitelikelytofail.Furthermore,tech-niquesthatmodelthisprobability[8,91,butignoreitscouplingtoeachUAV’smissioncanresultinverypoorperformanceofthefleet.Clearly,aUAVmissionplanningformulationmustrec-ognizetheimportanceofmanagingUAVattribution,andhavethecapabilitytousethesamestrategiesasreal-worldairoperationsplanners.Thenewformu-lationinthispaperapproachesthisbycapturingnotonlythevalueofthewaypointsthateachUAVvisitsandofreturningtheUAVsafelytoitsbase,but,alsobycapturingtheprobabilityoftheseevents.Inor-dertomaximizemissionscoreasanexpectation,thisstochasticformulationdesignscoordinationplansthatoptimallyexploitthecouplingeffectsofcooperationbe-tweenUAVstoimprovesurvivalprobabilities.Thisallocationisshowntorecoverplanningstrategiesforairoperahionsandtoprovidesignificantimprovementsoverpriorapproaches[8,91.ThepaperbrieflypresentsthedecompositionmethodforsolvingtheUAVcoordi-nationandcontrolproblem.Itisthenshownhowtoextendthatformulationtocapturethestochasticef-fectsoftheenvironment.Threesolutionmethodsarediscussedandthencomparedonasimulationexample.Theoptimalfleetcoordinationproblemincludesteamcompositionandgoalassignment,resourceallocation,andtrajectoryoptimization.ThesearecomplicatedoptimizationproblemsforscenarioswithmanyUAVs,obstacles,andtargets.Furthermore,theseproblemsarestronglycoupled,andoptimalcoordinationplanscannotbeachievedifthiscouplingisignored[4,51.Figure1showsanapproximatemethodforsolvingtheUAVcoordinationandcontrolproblems,whichoffersmuchfastersolutiontimes,butcouldyieldsuboptimalresults[4].Thecostfunctionusedistheoverallmis-sioncompletiontimeplusasmallweightingonthein-dividualUAVfinishingtimes.Thecostsareestimatedbasedonthefinishingtimesfoundusingstraight-linepathapproximations.Notethatsignificantpruningof0-7803-7516-5/02/$17.0002002IEEE2816Authorizedlicenseduselimitedto:NANJINGUNIVERSITYOFAERONAUTICSANDASTRONAUTICS.DownloadedonAugust07,2010at15:27:33UTCfromIEEEXplore.Restrictionsapply.EachWaypointcombinationDesignDetailedUAVTrajectoriesFig.1:Stepsindecompositionalgorithm[4]thepossiblemissionscenarioscanbeperformedatsev-eralstagesofthealgorithmtoreducethesizeofthetaskoptimizationproblem.Withtheseapproximatefinishingtimesavailable,thetaskassignmentproblemcanbeperformedtominimizetheapproximatecost,whichisposedasaMILPopti-mizationandsolvedusingCPLEX.TheobjectiveistoassignapermutationtoeachUAVthatiscombinedintothemissionplansuchthatthecostofthemissionisminimizedandthewaypointsvisited(ofNiv)meettheconstraints.Definingf=maxpevt,,theproblemisgivenbycymin~1=t+-~j~j(1)Nvjs
本文标题:5 动态未知环境下 多机协同航迹规划
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