Pareto optimal multi-robot motion planning

This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to identify the Pareto optimal solutions where no robot can unilaterally reduce its traveling time without extending others'. The consistent approximation of the algorithm in the epigraphical profile sense is guaranteed using set-valued numerical analysis. Experiments on an indoor multi-robot platform and computer simulations show the anytime property of the proposed algorithm; i.e., it is able to quickly return a feasible control policy that safely steers the robots to their goal regions and it keeps improving policy optimality if more time is given.