Optimal Patrolling Trajectory Design for Multi-UAV Wireless Servicing and Battery Swapping

In terrestrial cellular networks, cell-edge users often suffer from poor channel conditions due to their long distances from ground base station. Unmanned Aerial Vehicle (UAV) patrolling can help to enhance the channel conditions of cell-edge users by flying close to them to provide wireless service. As a UAV's wireless coverage is limited and can only serve users closely, appropriate patrolling trajectory may significantly shorten the communication distance and thus is crucial for high-capacity performance. Existing work on UAV patrolling trajectory design overlooks the limit of UAV's patrolling time due to its limited battery capacity, and we should jointly design UAVs' trajectories and battery swapping at the station to serve cell-edge users for achieving sustainable patrolling. The design becomes more challenging for multi-UAV scenario and we study the problem of minimizing the maximum idle time for serving any cell-edge user. By partitioning the cell-edge into uniform arcs patrolled separately by individual UAV in a back and forth fashion, we present two patrolling algorithms, in which one restricts UAV to make round trip for battery swapping (round trip swapping) and the other performs better since it benefits from UAV flying from one endpoint of the arc to the other endpoint (closed loop swapping) by using battery swapping station as a relay. Further, we evenly distribute all UAVs and allow each UAV to fly in the same direction along the cell-edge and thus present a cyclic-based algorithm. We prove the lower bound of idle time for our problem, and show that partition algorithm based on closed loop swapping and cyclic-based algorithm can both achieve optimal idle time. Finally, we validate the theoretical results by simulations.