https://hal.telecom-paris.fr/hal-02288564Coupechoux, MarceauMarceauCoupechouxRMS - Réseaux, Mobilité et Services - LTCI - Laboratoire Traitement et Communication de l'Information - IMT - Institut Mines-Télécom [Paris] - Télécom ParisINFRES - Département Informatique et Réseaux - Télécom ParisTechDarbon, JérômeJérômeDarbonKélif, Jean-MarcJean-MarcKélifOrange Labs [Lannion] - France TélécomSigelle, MarcMarcSigelleLTCI - Laboratoire Traitement et Communication de l'Information - IMT - Institut Mines-Télécom [Paris] - Télécom ParisOptimal Trajectories of a UAV Base Station Using Lagrangian MechanicsHAL CCSD2019[INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]HAL, TelecomParis2019-09-14 18:56:572021-11-03 08:16:452019-09-14 18:56:57enConference papers1This paper considers the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). A map is considered, characterized by a traffic intensity of users to be served. The UAV BS must travel from a given initial location at an initial time to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. The problem is formulated using the framework of Lagrangian mechanics. When the traffic intensity is quadratic (single-phase), we derive closed-form formulas for the optimal trajectory. When the traffic intensity is bi-phase, necessary conditions of optimality are provided and an Alternating Optimization Algorithm is proposed, that returns a trajectory satisfying these conditions. The Algorithm is initialized with a Model Predictive Control (MPC) online algorithm. Numerical results show how the trajectory is improved with respect to the MPC solution.