On Modeling A Dynamic Hybrid System with Constraints: Computing Aircraft Landing

Konstantin Artiouchine

Description

Niveau: Supérieur
On Modeling A Dynamic Hybrid System with Constraints: Computing Aircraft Landing Trajectories Konstantin Artiouchine Thales TRT, Domaine de Corbeville, 91404 Orsay CEDEX, France and LIX, Ecole Polytechnique, 91128 Palaiseau, France, Philippe Baptiste LIX, Ecole Polytechnique, 91128 Palaiseau, France, Juliette Mattioli Thales TRT, Domaine de Corbeville, 91404 Orsay CEDEX, France, We study the problem of computing trajectories of a set of aircraft in their final descent, right before landing. Trajectories must be compatible with aircraft dynamics while keeping distance between aircraft large enough. Our objective is to determine the order in which aircraft land as well as their exact trajectories in order to minimize the maximal landing time. We study a highly simplified version of this hybrid problem where time and space are discretized. A constraint based model relying on several specific global constraints is introduced. Computational experiments are reported. Key words: Air-Traffic Control, Scheduling, Constraint Programming 1

• can stay


• between aircraft


• air-traffic control


• initial variables


• landing times


• control theory


• inter-distance constraints

Sujets

• Thalès
• Baptiste
• Variables
• École polytechnique
• Mattioli
• Air traffic control
• Control theory

Informations

• Publié par: chaeh
• Nombre de lectures: 11
• Langue: English

Extrait

OnModelingADynamicHybridSystemwith Constraints:ComputingAircraftLanding Trajectories KonstantinArtiouchine ThalesTRT,DomainedeCorbeville,91404OrsayCEDEX,FranceandLIX,Ecole Polytechnique,91128Palaiseau,France,[e-mail] PhilippeBaptiste LIX,EcolePolytechnique,91128Palaiseau,France,[e-mail] JulietteMattioli ThalesTRT,DomainedeCorbeville,91404OrsayCEDEX,France, [e-mail] Westudytheproblemofcomputingtrajectoriesofasetofaircraftintheir finaldescent,rightbeforelanding.Trajectoriesmustbecompatiblewith aircraftdynamicswhilekeepingdistancebetweenaircraftlargeenough.Our objectiveistodeterminetheorderinwhichaircraftlandaswellastheir exacttrajectoriesinordertominimizethemaximallandingtime.Westudy ahighlysimplifiedversionofthishybridproblemwheretimeandspace arediscretized.Aconstraintbasedmodelrelyingonseveralspecificglobal constraintsisintroduced.Computationalexperimentsarereported. Keywords:Air-TrafficControl,Scheduling,ConstraintProgramming 1

1.Introduction Systemsareoftenmodeledbydifferentialequationsderivedfromphysical lawsthatcapturethedynamicsofthesystem.Controltheoryisdevotedto thisfieldofresearch.Hybridsystemsarecharacterizedbytheinteraction ofcontinuousanddiscretemodels(e.g.,thesystemismodeledbyvariables takingvaluesfromacontinuoussetandvariablestakingvaluesfromadiscrete .)eno Motivatedbylongtermindustrialapplicationsof Thales ,westudya hybridsystemwhereaircrafttrajectorieshavetobecomputedwhenaircraft reachthefinaldescentintheTerminalRadarApproachCONtrolarea( tra- con ).Trajectoriesmustbecompatiblewithaircraftdynamicswhilekeeping thedistancebetweenaircraft,atanytime,largerthansomepredefinedvalue. Moreover,thereisminimumdelaybetweenanytwoconsecutivelandingson thesamerunway,underwhichsafetyisnotgranted.Ourobjectiveisto determinetheorderinwhichaircraftlandaswellastheirexacttrajectories inordertominimizethemaximallandingtime. Similarproblemshavebeenstudiedintheliterature.Inthe“static” versionstudieninArtiouchine,Baptiste,andDu¨rr(2004),Beasleyetal. (2000)allpossibletrajectoriesareprecomputedforeachaircrafttakenin- dependentlyfromothers.Fromthiscomputation,asetofpossiblelanding timesisassociatedtoeachaircraft.Theproblemofsequencingaircrafton therunway,whilemeetingoneofthepossiblelandingtimes,isthensolved asastandardschedulingproblem.Oncethelandingtimesareknown,cor- respondingaircraftflightplanscanbecomputed.Notethatthisprocess, describedinBayenandTomlin(2003)doesnotensurethattrajectoriesdo notconflicteachothersinceinter-distanceconstraintscanbeviolated.This drawbackcomesfromthefactthattheschedulingproblemandthetrajectory 2