Persistent coverage aims to maintain a certain coverage level over time in an environment where such level deteriorates. This level can be associated to temperature, dust or sensor information. We propose an algorithmic solution in which each robot locally finds the best paths and coverage actions to keep the desired coverage level over the whole environment. Using Fast Marching Methods, optimal paths are computed in terms of coverage quality, while keeping a safety distance to obstacles. Additionally, our solution enables a computationally efficient evaluation of a list of potential trajectories, allowing us to choose the goal that improves the most the coverage along the whole path. The combination of this algorithm with a Dynamic Window navigation makes our approach more flexible and robust to changing environments than existing solutions. Finally, we also propose a coverage action controller, locally computed and optimal, that makes the robots maintain the coverage level of the environment significantly close to the objective. Simulations and real experiments validate the whole approach and prove a significant improvement with respect to previous works.