  In this paper we propose a periodic solution to the problem of persistently
covering a finite set of interest points with a group of autonomous mobile
agents. These agents visit periodically the points and spend some time carrying
out the coverage task, which we call coverage time. Since this periodic
persistent coverage problem is NP-hard, we split it into three subproblems to
counteract its complexity. In the first place, we plan individual closed paths
for the agents to cover all the points. Second, we formulate a quadratically
constrained linear program to find the optimal coverage times and actions that
satisfy the coverage objective. Finally, we join together the individual plans
of the agents in a periodic team plan by obtaining a schedule that guarantees
collision avoidance. To this end, we solve a mixed integer linear program that
minimizes the time in which two or more agents move at the same time.
Eventually, we apply the proposed solution to an induction hob with mobile
inductors for a domestic heating application and show its performance with
experiments on a real prototype.
