A scalable multi-robot goal assignment algorithm for minimizing mission time followed by total movement cost

Abstract

We study a variant of the multi-robot goal assignment problem where a unique goal for each robot needs to be assigned while minimizing the largest cost of movement among the robots, called makespan, and then minimizing the total movement cost of all the robots without exceeding the optimal makespan. A significant step in solving this problem is to find the cost associated with each robot-goal pair, which requires solving several complex path planning problems, thus, limiting the scalability. We present an algorithm that solves the multi-robot goal assignment problem by computing the paths for a significantly smaller number of robot-goal pairs compared to state-of-the-art algorithms, leading to a computationally superior mechanism to solve the problem. We perform theoretical analysis to establish the correctness and optimality of the proposed algorithm, as well as its worst-case polynomial time complexity. We extensively evaluate our algorithm for hundreds of robots on randomly generated and standard workspaces. Our experimental results demonstrate that the proposed algorithm achieves a noticeable speedup over two state-of-the-art baseline algorithms.