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arXiv · 1812.08759

Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics

Marceau Coupechoux·Jérôme Darbon·Jean-Marc Kélif·Marc Sigelle
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Abstract

In this paper, we consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). We consider a map 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. We formulate the problem 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, we provide necessary conditions of optimality and propose an Alternating Optimization Algorithm that returns a trajectory satisfying these conditions. The Algorithm is initialized with a Model Predictive Control (MPC) online algorithm. Numerical results show how we improve the trajectory with respect to the MPC solution.

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Marceau Coupechoux, Jérôme Darbon, Jean-Marc Kélif, Marc Sigelle. 2018-12-20. Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics. https://arxiv.org/abs/1812.08759

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