Optimal Path Planning for Multi-Robot Systems Using Petri Nets

This letter deals with the problem of path planning of multi-robot systems within the context of high-level tasks. Specifically, a task comprises logical requirements (conjunctions, disjunctions, and negations) on the trajectories and final states of robots in certain regions of interest. We propose an optimal planning approach that combines offline computation and online planning. First, a simplified Petri net model is proposed to model the multi-robot system. Then, indicating places are designed to implement the logical requirements of the specifications. Building upon this, a compact representation of the state space called extended basis reachability graph is constructed and a real-time online planning algorithm based on integer linear programming is developed to obtain the optimal paths. It is shown that the most burdensome part of the planning procedure may be removed offline, thanks to the construction of the extended basis reachability graph. Finally, series of simulations are conducted to demonstrate the computational efficiency and scalability of our developed method.