  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.
