Sample greedy based task allocation for multiple robot systems

This paper addresses in-schedule dependent task allocation problems for multi-robot systems. One of the main issues with those problems is the inherent NP-hardness of combinatorial optimisation. To handle this issue, this paper develops a decentralised task allocation algorithm by leveraging the submodularity concept and a sampling process of task sets. Our theoretical analysis reveals that the proposed algorithm can provide an approximation guarantee of 1/2 of the optimal solution for the monotone submodular case and 1/4 for the non-monotone submodular case, both with polynomial time complexity. To examine the performance of the proposed algorithm and validate the theoretical analysis, we introduce two task allocation scenarios and perform numerical simulations. The simulation results confirm that the proposed algorithm achieves a solution quality which is comparable to state-of-the-art algorithms in the monotone case and much better quality in the non-monotone case with significantly lower computational complexity.