A Scalable Algorithm for the Optimal Trajectory of a Massive Swarm of UAV Base Stations Using Lagrangian Mechanics

In this paper, we consider multiple Unmanned Aerial Vehicles (UAV) serving as flying Base Stations (BS) of a wireless network and the problem of jointly optimizing their trajectory with respect to a running cost. This cost accounts for the consumed energy related to the vehicle velocity and for the amount of data traffic collected or served by the UAVs. The data traffic is supposed to be spatially distributed around a hotspot and is equivalent to a potential in Physics. Using the principles of Lagrangian Mechanics, we derive a scalable algorithm able to optimize the trajectory of thousands of drones in milliseconds on a off-the-shelf laptop. Our model allows to control the distance between the UAVs to avoid collisions by using a coupling between the drone trajectories.