In this paper we study multi-robot path planning for persistent monitoring tasks. We consider the case where robots have a limited battery capacity with a discharge time $D$. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum allowable time between robot visits, called the latency. The objective is to find the minimum number of robots that can satisfy these latency constraints while also ensuring that the robots periodically charge at a recharging depot. The decision version of this problem is known to be PSPACE-complete. We present a $O(\frac{\log D}{\log \log D}\log \rho)$ approximation algorithm for the problem where $\rho$ is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show empirically that it typically provides higher quality solutions than the approximation algorithm. We extend our results to provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. We evaluate our algorithms on large problem instances in a patrolling scenario and in a wildfire monitoring application. We also compare the algorithms with an existing solver on benchmark instances.

翻译：本文研究持久监控任务中的多机器人路径规划问题。我们考虑机器人电池容量有限且放电时间为$D$的情形。将待监控区域表示为加权图的顶点，每个顶点对机器人两次访问之间的最大允许时间间隔存在约束（称为延迟）。目标是在确保机器人定期在充电站充电的同时，寻找满足延迟约束所需的最少机器人数量。该问题的判定版本已知为PSPACE完全问题。我们提出一种$O(\frac{\log D}{\log \log D}\log \rho)$近似算法，其中$\rho$为最大与最小延迟约束的比值。同时提出基于定向越野的启发式算法进行求解，实验表明该算法通常能提供比近似算法更优的解。我们将结果扩展至固定机器人数量下最小化最大加权延迟的问题。在巡逻场景与野火监控应用的大规模问题实例上评估算法性能，并在基准实例上将所提算法与现有求解器进行比较。