Afrika Matematika

, Volume 24, Issue 2, pp 169–178 | Cite as

Une Approche Dynamique pour l’Optimisation des Trajectoires de n Véhicules à Guidage Automatique

  • Salimata Guèye Diagne
  • André Langevin
  • Youssou Gningue
Article
  • 84 Downloads

Abstract

We propose an analytic method based on dynamic programming for determining optimal trajectories in a rather delicate problem of transport: by Automated Guided Vehicles (AGV). These are driverless electric vehicles used in many fields including industry. Langevin et al. (Int J Flex Manuf Syst 8(3):247–262, 1996) showed how to determine the optimal solution in the case of two vehicles. Our method generalizes them with some modifications to not generate an exorbitant number of states. For a given state and a mission we offer a single successor instead of n and we prove that the states, in considerable number, that we exclude are not in the optimal trajectory.

Keywords

Dynamic programming AGV Automated guided vehicles Analytic solution Scheduling Dispatching Conflict free routing 

Résumé

Nous proposons une méthode analytique basée sur la programmation dynamique pour la détermination des trajectoires optimales dans un problème de transport relativement complexe : celui par AGV(Automated Guided Vehicles ou Véhicules à Guidage Automatique). Ce sont des véhicules électriques sans conducteur ou robots utilisés dans plusieurs domaines et particulièrement dans l’industrie. Langevin et al. (Int J Flex Manuf Syst 8(3):247–262, 1996) ont montré comment on détermine la solution optimale dans le cas de deux véhicules. Notre méthode généralise la leur avec certaines modifications pour ne pas générer un nombre exorbitant d’états. Pour un état et une mission donnés nous proposons un seul successeur au lieu de n et démontrons que les états, en nombre considérable, que nous écartons n’appartiennent pas à la trajectoire optimale.

Mots clés

Programmation dynamique AGV Solution analytique Ordonnancement Répartition Routage sans conflit 

Mathematics Subject Classification (2000)

90C25 

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Copyright information

© African Mathematical Union and Springer-Verlag 2011

Authors and Affiliations

  • Salimata Guèye Diagne
    • 1
  • André Langevin
    • 2
  • Youssou Gningue
    • 3
  1. 1.Université C.A.D de DakarDakarSenegal
  2. 2.Ecole Polytechnique de MontréalMontrealCanada
  3. 3.Université Laurentienne SudburySudburyCanada

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