Optimal Multi-Robot Path Planning for Cyclic Tasks using Petri Nets

In this paper, we investigate the problem of optimal multi-robot path planning for a cyclic task represented by a particular type of linear-temporal logic (LTL) formulae. Specifically, the team of robot needs to fulfill a given LTL formula and at the same time, accomplishes some particular tasks infinitely often. To avoid the state-space explosion when the number of robot increases, we use Petri nets to model the team of multi-robot. Our goal is to find an optimal infinite sequence in the prefix-suffix form for each robot such that the average cost per task is minimized. We propose an efficient planning method based on the notion of basis reachability graph (BRG), which is a compact representation of the reachability space of the PN. We demonstrate the computational efficiency of our method through illustrative examples.