# On The Continuous Coverage Problem for a Swarm of UAVs

## TL;DR

This paper addresses the challenge of maintaining continuous coverage with UAV swarms by analyzing the problem's complexity, characterizing optimal cycles, and proposing an efficient algorithm that significantly reduces the number of additional UAVs needed.

## Contribution

It proves the NP-completeness of the continuous coverage problem, characterizes minimal UAV cycles, and introduces the cycles with limited energy algorithm for efficient coverage.

## Key findings

- The problem is NP-complete.
- The proposed algorithm reduces UAV requirements by up to 94%.
- Simulation shows effectiveness across various parameters.

## Abstract

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.