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 multiagent system. A distributed formation matching algorithm for a large-scale multiagent system (DFMA-LSMAS) is proposed. The algorithm employs a distributed continuous-time strategy to deal with a minimal weight bipartite graph matching 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 multiagent 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.