  Unmanned aerial vehicles (UAVs) can be used to provide wireless network and
remote surveillance coverage for disaster-affected areas. During such a
situation, the UAVs need to return periodically to a charging station for
recharging, due to their limited battery capacity. We study the problem of
minimizing the number of UAVs required for a continuous coverage of a given
area, given the recharging requirement. We prove that this problem is
NP-complete. Due to its intractability, we study partitioning the coverage
graph into cycles that start at the charging station. We first characterize the
minimum number of UAVs to cover such a cycle based on the charging time, the
traveling time, and the number of subareas to be covered by the cycle. Based on
this analysis, we then develop an efficient algorithm, the cycles with limited
energy algorithm. The straightforward method to continuously cover a given area
is to split it into N subareas and cover it by N cycles using N additional
UAVs. Our simulation results examine the importance of critical system
parameters: the energy capacity of the UAVs, the number of subareas in the
covered area, and the UAV charging and traveling times.We demonstrate that the
cycles with limited energy algorithm requires 69%-94% fewer additional UAVs
relative to the straightforward method, as the energy capacity of the UAVs is
increased, and 67%-71% fewer additional UAVs, as the number of subareas is
increased.
