Euclidean-Distance-Based Distributed Constrained Optimal Formation Matching for Open Large-Scale Multiagent Systems

In this article, we investigate a Euclidean-distance-based distributed constrained optimal formation matching (EDCOFM) problem for open large-scale multiagent systems (OLSMASs), where the number of agents is large and variable. To address the open property of the multiagent system, we introduce the concept of a depository, which can provide additional agents or store redundant agents. When the number of agents is sufficient to achieve the formation configuration, a distributed formation matching algorithm for a large-scale multiagent system (DFMA-LSMAS) is proposed to search for the optimal location of the formation configuration within a designed constraint and the optimal matching relationship. Notably, the framework is applicable to open multiagent systems. When the number of agents is smaller than the requirement to achieve the formation configuration, and more than one agent needs to be provided from the depository, an unmatched phenomenon occurs, which results in the failure of the proposed algorithm. To address this, a disturbance-based approach is proposed to eliminate the phenomenon without impacting the optimal solution. When the number of agents is larger than the requirement to achieve the formation configuration, and some agents have to leave the system, a fair competition mechanism is proposed to selectthe remainder and their optimal matching relationship. This mechanism avoids multiple competitions in a centralized manner. Finally, several simulation results are provided to verify the proposed algorithms.