In this paper we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring to constantly revisit every point. As a first step, our solution finds a partition of the environment where the amount of work for each robot, weighted by the importance of each point, is equal. This is achieved using a power diagram and finding an equitable partition through a provably correct distributed control law on the power weights. Compared to other existing partitioning methods, our solution considers a continuous environment formulation with non-convex obstacles. In the second step, each robot computes a graph that gathers sweep-like paths and covers its entire partition. At each planning time, the coverage error at the graph vertices is assigned as weights of the corresponding edges. Then, our solution is capable of efficiently finding the optimal open coverage path through the graph with respect to the coverage error per distance traversed. Simulation and experimental results are presented to support our proposal.

翻译：本文研究使用机器人团队持续覆盖复杂非凸环境的问题。我们考虑覆盖质量随时间衰减的场景，这要求系统持续重新访问每个点。作为第一步，我们提出一种环境划分方法，使每个机器人所需完成的工作量（按各点重要度加权）达到均衡。该划分通过功率图实现，并利用功率权值上的可证明收敛分布式控制律寻找公平划分。与现有其他划分方法相比，我们的方案考虑了含非凸障碍物的连续环境建模。第二步中，每个机器人构建一个汇集类似扫描路径的图，并覆盖其整个划分区域。在每个规划时刻，将图顶点的覆盖误差分配为对应边的权值。随后，我们的方案能够基于每单位路径长度的覆盖误差，高效找到通过该图的最优开环覆盖路径。仿真与实验结果验证了所提方法的有效性。