An Efficient Stochastic Clustering Auction for Heterogeneous Robotic Collaborative Teams

Abstract

Stochastic Clustering Auctions (SCAs) constitute a class of cooperative auction methods that enable improvement of the global cost of the task allocations obtained with fast greedy algorithms. Prior research had developed Contracts Sequencing Algorithms (CSAs) that are deterministic and enable transfers, swaps, and other types of contracts between team members. In contrast to CSAs, SCAs use stochastic transfers or swaps between the task clusters assigned to each team member and have algorithm parameters that can enable tradeoffs between optimality and computational and communication requirements. The first SCA was based on a “Gibbs Sampler” and constrained the stochastic cluster reallocations to simple single transfers or swaps; it is applicable to heterogeneous teams. Subsequently, a more efficient SCA was developed, based on the generalized Swendsen-Wang method; it achieves the increased efficiency by connecting tasks that appear to be synergistic and then stochastically reassigning these connected tasks, hence enabling more complex and efficient movements between clusters than the first SCA. However, its application was limited to homogeneous teams. The contribution of this work is to present an efficient SCA for heterogeneous teams; it is based on a modified Swendsen-Wang method. For centralized auctioning and homogeneous teams, extensive numerical experiments were used to provide a comparison in terms of costs and computational and communication requirements of the three SCAs and a baseline CSA. It was seen that the new SCA maintains the efficiency of the second SCA and can yield similar performance to the baseline CSA in far fewer iterations. The same metrics were used to evaluate the performance of the new SCA for heterogeneous teams. A distributed version of the new SCA was also evaluated in numerical experiments. The results show that, as expected, the distributed SCA continually improves the global performance with each iteration, but converges to a higher cost solution than the centralized SCA. The final discussion outlines a systematic procedure to use SCA in various aspects of the application of multi-robot cooperative systems.