Energy-saving deployment algorithms of UAV swarm for sustainable wireless coverage

Recent years have witnessed increasingly more uses of Unmanned Aerial Vehicle (UAV) swarms for rapidly providing wireless coverage to ground users. Each UAV is constrained in its energy storage and wireless coverage, and it consumes most energy when flying to the top of the target area, leaving limited leftover energy for hovering at its deployed position and keeping wireless coverage. The literature largely overlooks this sustainability issue of deploying UAV swarm deployment, and we aim to maximize the minimum leftover energy storage among all the UAVs after their deployment. Our new energy-saving deployment problem captures that each UAV's wireless coverage is adjustable by its service altitude, and also takes the no-fly-zone (NFZ) constraint into account. Despite of this, we propose an optimal energy-saving deployment algorithm by jointly balancing heterogeneous UAVs' flying distances on the ground and final service altitudes in the sky. We show that a UAV with larger initial energy storage in the UAV swarm should be deployed further away from the UAV station. Moreover, when $n$ homogeneous UAVs are dispatched from different initial locations, we first prove that any two UAVs of the same initial energy storage will not fly across each other, and then design an approximation algorithm of complexity $n \log \frac{1}{\epsilon}$ to arbitrarily approach the optimum with error $\epsilon$. Finally, we consider that UAVs may have different initial energy storages, and we prove this problem is NP-hard. Despite of this, we successfully propose a heuristic algorithm to solve it by balancing the efficiency and computation complexity well.