An Emergent Synchronization Property in a Set of Non-Competing Multi-Agent Systems

This letter investigates an emergent synchronization property within a set of non-competing multi-agent systems. The primary objective is to develop behavioral mathematical models that enable multiple groups of agents to adhere to predetermined paths while concurrently achieving consensus among corresponding members within each group. In this pursuit, the inherent coordination challenge is addressed while acknowledging absence of communication channels between the different agent groups but requiring a centralized and omniscient authority that assigns suitable and prescribed reference curves to track for each swarm. As a further assumption, the described emergent synchronization property is achieved by exploiting a complete communication graph, with an all-to-all communication topology in each multi-agent system. The proposed solution exploits a diffeomorphic mapping to translate the task into two independent and simpler problems: the first one relates to reaching the curve of interest and the second to moving on it while maintaining the synchronization condition between couple of agents.