Sufficient conditions for connectivity maintenance and rendezvous in leader–follower networks

In this paper we derive a set of constraints that are sufficient to guarantee maintained connectivity in a leader–follower multi-agent network with a proximity based communication topology. In the scenario we consider, only the leaders are aware of the global mission, which is to converge at a known destination point. Thus, the followers need to stay in contact with the group of leaders in order to reach the goal. In the paper we show that we can maintain the initial network structure, and thereby connectivity, by setting up bounds on the ratio of leaders-to-followers and on the magnitude of the goal attraction force experienced by the leaders. The results are first established for an initially complete communication graph and then extended to an incomplete graph. The results are illustrated by computer simulations.