Cooperative route planning of multiple fuel-constrained Unmanned Aerial Vehicles with recharging on an Unmanned Ground Vehicle

Multiple small, low cost, multi-rotor Unmanned Aerial Vehicles (UAVs) are ideal for aerial surveillance over large areas. However, their limited battery capacity restricts them to areas in proximity of stationary recharging depots. One solution is to use an Unmanned Ground Vehicle (UGV) to provide a moving recharging depot. The problem is then to find the time-or energy-optimal paths for the multiple fuel-constrained UAVs to visit a set of mission points while being recharged by stopping at the UGV, whose path also needs to be determined. This is a combinatorial optimization problem that is computationally challenging, but may be solved relatively fast using heuristics. In this paper, we present two-level optimization that involves, (1) finding a UGV path by fixing waypoints using K-means and then formulating and solving a traveling salesman problem (TSP), and (2) finding paths for the multiple UAVs using a vehicle routing problem (VRP) formulation with capacity constraints, time windows, and dropped visits. We used constraint programming to solve these problems in less than a minute on a standard desktop computer for up to 25 mission points and 4 UAVs. Our main observation is that increasing the number of UAVs decreases the mission time and refueling stops, but does not decrease the total distance covered or total time taken.