Communication constrained task allocation with optimized local task swaps

Communication constraints dictated by hardware often require a multi-robot system to make decisions and take actions locally. Unfortunately, local knowledge may impose limits that ultimately impede global optimality in a decentralized optimization problem. This paper enhances a recent anytime optimal assignment method based on a task-swap mechanism, redesigning the algorithm to address task allocation problems in a decentralized fashion. We propose a fully decentralized approach that allows local search processes to execute concurrently while minimizing interactions amongst the processes, needing neither global broadcast nor a multi-hop communication protocol. The formulation is analyzed in a novel way using tools from group theory and optimization duality theory to show that the convergence of local searching processes is related to a shortest path routing problem on a graph subject to the network topology. Simulation results show that this fully decentralized method converges quickly while sacrificing little optimality.