Scheduling Spare Drones for Persistent Task Performance under Energy Constraints

This paper considers the problem of enabling persistent execution
of a multi-drone task under energy limitations. The drones are
given a set of locations and their task is to ensure that at least
one drone will be present, for example for monitoring, over each
location at any given time. Because of energy limitations, drones
must be replaced from time to time, and fly back home where their
batteries can be replaced. Our goals are to identify the minimum
number of spare drones needed to accomplish the task while no
drone battery drains, and to provide a drone replacement strategy.
We present an efficient procedure for calculating whether one spare
drone is enough for a given task and provide an optimal replacement strategy. If more than one drone is needed, we aim at finding the minimum number of spare drones required, and extend the replacement strategy to multiple spare drones by introducing a new Bin-Packing variant, named Bin Maximum Item Double Packing (BMIDP). Since the problem is presumably computationally hard, we
provide a first fit greedy approximation algorithm for efficiently solving the BMIDP problem. For the offline version, in which all locations are known in advance, we prove an approximation factor upper bound of 1.5, and for the online version, in which locations are given one by one, we show via extensive simulations, that the approximation yields an average factor of 1.7.