Resumen: In this article, 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 every point to be constantly revisited. 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 with 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. Idioma: Inglés DOI: 10.1177/0278364919882082 Año: 2019 Publicado en: International Journal of Robotics Research 38, 14 (2019), 1674-1694 ISSN: 0278-3649 Factor impacto JCR: 4.703 (2019) Categ. JCR: ROBOTICS rank: 5 / 28 = 0.179 (2019) - Q1 - T1 Factor impacto SCIMAGO: 3.212 - Applied Mathematics (Q1) - Artificial Intelligence (Q1) - Software (Q1) - Mechanical Engineering (Q1) - Modeling and Simulation (Q1) - Electrical and Electronic Engineering (Q1)