Spare Drone Optimization for Persistent Task Performance with Multiple Homes

In this paper we examine the problem of persistent task performance by a team of multiple drones, where the drones suffer from energy limitations. The drones are required to occupy a set of m locations in order to perform a task, for example surveillance, indefinitely. Since the drones have a limited battery supply, they must be replaced in order to refuel, recharge or change their battery at a fixed set of refueling stations called homes. Therefore, in order to enable the persistent task performance, it is essential to add spare drones to the system that will replace the drones in their task. We examine two problems in this context: determining the minimal number of spare drones that will guarantee that the task will be carried out persistently and indefinitely, and finding a schedule for drone-replacements. The novelty of this work is twofold: (i) Proving that a simple drone replacement schedule is enough with respect to minimizing the number of spare drones, thus reducing the need to cope with O(m
²
) pairwise travel costs of the given m locations to only O(m) travel costs between the m locations and the homes; and (ii) The introduction of an innovative approximation approach for the minimum number of spare drones required, and providing a replacement scheduling strategy by combining a Voronoi tessellation with a Bin-Packing variant (Bin Maximum Item Double Packing-BMIDP) for the Multi-homes problem, which is much harder than the single home problem and is NP-Hard even for a single spare drone.