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Centralized and distributed task allocation in multi-robot teams via a stochastic clustering auction

This article considers the problem of optimal task allocation for heterogeneous teams, for example, teams of heterogeneous robots or human-robot teams. It is well-known that this problem is NP-hard and hence computationally feasible approaches must develop an approximate solution. Here, we propose a solution via a Stochastic Clustering Auction (SCA) that uses a Markov chain search process along with simulated annealing. This is the first stochastic auction method used in conjunction with global optimization. It is based on stochastic transfer and swap moves between the clusters of tasks assigned to the various robots and considers not only downhill movements, but also uphill movements, which can avoid local minima. A novel feature of this algorithm is that, by tuning the annealing suite and turning the uphill movements on and off, the global team performance after algorithm convergence can slide in the region between the global optimal performance and the performance associated with a random allocation. Extensive numerical experiments are used to evaluate the performance of SCA in terms of costs and computational and communication requirements. For centralized auctioning, the SCA algorithm is compared to fast greedy auction algorithms. Distributed auctioning is then compared with centralized SCA.