Connectivity-preserving rendezvous in discrete-time multi-agent systems via relative neighborhood proximity graph

In this paper, we focus on the rendezvous problem of discrete-time multi-agent systems. Each agent is equipped with the same sensing, computing, and motion-control capabilities to achieve rendezvous based on the neighbors’ states. First, a convex hull combination algorithm (CHCA) is designed, in which each agent solves a convex problem composed of perceived neighbors in the sensing region and chooses an optimal control strategy to move to the next position with guaranteed connectivity under low-density network topologies. Second, the relative neighborhood graph is incorporated into the CHCA (RNCHCA) as the constraint set to adapt to the high-density network topologies. The convergence and connectivity of the proposed algorithms are proved based on the geometric concept and case analyses. Finally, a large number of simulation results show that under the initially connected topologies with different densities, the RNCHCA can achieve a higher rendezvous speed than that achieved by the traditional circumcenter algorithm, particularly under high-density network topologies.