Distributed Constrained Optimal Formation Matching for Large-Scale Systems

In this article, we investigate a distributed constrained optimal formation matching problem for a large-scale multi-agent system. A distributed formation matching algorithm for a large-scale multi-agent system (DFMA-LSMAS) is proposed. The algorithm employs a distributed continuous-time strategy to deal with a minimal weight bipartite graph matching (MWBGM) problem for the optimal matching relationship between each agent and each hole in the formation configuration. It prevents a centralized structure and the explosion of storage spaces compared with the Kuhn-Munkras algorithm. Additionally, DFMA-LSMAS utilizes a distributed parameter projection approach for the optimal location of the formation configuration subjected to a common state constraint. It reduces the growth of the auxiliary variables with the scale of the multi-agent system. In the special case, an unmatched phenomenon appears which may cause the failure of DFMA-LSMAS. Therefore, a perturbation-based algorithm is provided to eliminate the influence of this phenomenon but does not affect the optimality of the solution. Finally, simulation results are provided to verify the algorithms.