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1、MultipleAircraftDeconflictedPathPlanningwithWeatherAvoidanceConstraintsJessicaJ.Pannequin∗AlexandreM.Bayen†UniversityofCaliforniaatBerkeley,CA94720UniversityofCaliforniaatBerkeley,CA94720IanM.Mitchell‡UniversityofBritishColumbia,Vancouver,BC,CanadaV6T1Z4HoamChung§ShankarSastry¶Univers
2、ityofCaliforniaatBerkeley,CA94720UniversityofCaliforniaatBerkeley,CA94720Wepresentamodelpredictivecontrolbasedalgorithmforaircraftmotionplanningthatwillapplytoconvergingflowsofaircraftgoingthroughconvectiveweatherintheenrouteairspace.Thecostfunctionassociatedwiththemodelpredictivecont
3、roloptimizationproblemisobtainedbysolvingtheHamilton-Jacobiequation,anon-linearpartialdifferentialequation.Foragivenwindprofile,convectiveweatherconditionsandaircraftdestination,thesolutiontotheHamilton-Jacobiequationprovidesavaluefunctionthatcorrespondstotheminimumtraveltimefromanypoi
4、ntintheNAStothespecifieddestination.Theoptimalcontrolsequenceisthencomputedoverafixedhorizonbyminimizingtheaircraftcostfunction,subjecttoaircraftseparationconstraintsandboundsonaircraftturningrates.Thisalgorithmresultsinaircrafttrajectoriescorrespondingtoalocallyoptimalsolutionoftheopt
5、imizationprograminvolvingthesetofaircraftconsidered.NomenclatureTModelPredictiveControlhorizonlength,(units:seconds)∆tModelPredictiveControltimestep,(units:seconds)nModelPredictiveControlnumberofstepsinhorizonNTotalnumberofaircraftconsideredxi,jxpositionofaircraftiattimej,(units:mete
6、rs)yi,jypositionofaircraftiattimej,(units:meters)θi,jHeadingofaircraftiattimej,(units:radians)ui,jTurningrateofaircraftiattimej,(units:radians/second)x[x1,1,...,x1,n,...,xN,1,...,xN,n]Aircraftxpositionvector,(units:meters)y[y1,1,...,y1,n,...,yN,1,...,yN,n]Aircraftypositionvector,(uni
7、ts:meters)θ[θ1,1,...,θ1,n,...,θN,1,...,θN,n]Aircraftheadingvector,(units:radians)u[u1,1,...,u1,n,...,uN,1,...,uN,n]Aircraftturningratevector,(units:radians/second)ViValuefunctionofaircrafti,encodingtheminimumtimetoreachdestinationi,(units:seconds)vAircraftvelocity,(units:meters/secon
8、d)hAircrafta
