Algorithms and experiments on routing of unmanned aerial vehicles with mobile recharging stations

We study the problem of planning a tour for an energy-limited Unmanned Aerial Vehicle (UAV) to visit a set of sites in the least amount of time. We envision scenarios where the UAV can be recharged at a site or along an edge either by landing on stationary recharging stations or on Unmanned Ground Vehicles (UGVs) acting as mobile recharging stations. This leads to a new variant of the Traveling Salesperson Problem (TSP) with mobile recharging stations. We present an algorithm that finds not only the order in which to visit the sites but also when and where to land on the charging stations to recharge. Our algorithm plans tours for the UGVs as well as determines the best locations to place stationary charging stations. We study three variants for charging: Multiple stationary charging stations, single mobile charging station, and multiple mobile charging stations. As the problems we study are nondeterministic polynomial time (NP)-Hard, we present a practical solution using Generalized TSP that finds the optimal solution that minimizes the total time, subject to the discretization of battery levels. If the UGVs are slower than the UAVs, then the algorithm also finds the minimum number of UGVs required to support the UAV mission such that the UAV is not required to wait for the UGV. Our simulation results show that the running time is acceptable for reasonably sized instances in practice. We evaluate the performance of our algorithm through simulations and proof-of-concept field experiments with a fully autonomous system of one UAV and UGV.