Multi-Robot Path Planning With Boolean Specification Tasks Under Motion Uncertainties

This paper studies the path planning problem of multi-robot systems under motion uncertainties with high-level tasks that are expressed as Boolean specifications. The specification imposes logical constraints on robot trajectories and final states. First, a global Markov decision process model of the multi-robot system is constructed to provide its current state. In order to tackle the state explosion problem, at each stage, we construct a local Markov decision process for every individual agent in sequence to compute the local optimal movement strategy and update the global Markov decision process accordingly (i.e., compute locally and update globally). Next, we propose a heuristic reward function design method that provides different rewards for visiting different task points by introducing the estimated distance to complete the global task. Finally, a series of numerical experiments are conducted to demonstrate the computational efficiency and scalability of our developed approach.