Event-Triggered Multi-Agent System Rendezvous with Graph Maintenance in Varied Hybrid Formulations: A Comparative Study

This paper explores the rendezvous problem for a multi-agent system (MAS) with distance-limited, intermittent communication and sensing. Unlike previous works that provide specific event-triggered controllers, we provide a framework that characterizes a family of distributed event-triggered controllers leveraging non-singular edge-potentials to achieve approximate rendezvous while maintaining the initial distance-limited graph. The proposed framework excludes the possibility of Zeno behavior and accommodates the development of self-triggered controllers. The combination of continuous and impulsive dynamics results in a hybrid system, where the closed-loop dynamics of the MAS are presented and analyzed using hybrid differential inclusions. In particular, three distinct hybrid system formulations are presented, where the advantages and disadvantages of each construction are discussed in terms of their solution spaces. The approximate rendezvous problem is recast into a set stabilization problem and sufficient conditions of the rendezvous set are obtained through a Lyapunov-based analysis. Simulation results are provided to validate the development, where a specific instance of an event trigger mechanism satisfying the requirements of the proposed design achieves approximate rendezvous while preserving the edges of an initially connected communication graph.