STT-CBS: A Conflict-Based Search Algorithm for Multi-Agent Path Finding with Stochastic Travel Times

We present an algorithm for finding optimal paths for multiple stochastic agents in a graph to reach their destinations with a user-specified maximum pairwise collision probability. Our algorithm, called STT-CBS, uses Conflict-Based Search (CBS) with a stochastic travel time (STT) model for the agents. We model robot travel time along each edge of the graph by independent gamma-distributed random variables, and propose probabilistic collision identification and constraint creation methods to robustly handle travel time uncertainty. We show that under reasonable assumptions our algorithm is optimal in terms of expected sum of travel times, while ensuring an upper bound on each pairwise conflict probability. Simulations and hardware experiments show that STT-CBS is able to significantly decrease conflict probability over CBS, while remaining within the same complexity class.