On the number of leaders needed to ensure network connectivity

In this paper we examine the leader-to-follower ratio needed to maintain connectivity in a leader-follower multi-agent network with proximity based communication topology. In the scenario we consider, only the leaders are aware of the global mission, which is to converge to a known destination point. Thus, the objective of the leaders is to drag the team to the desired goal. In the paper we obtain bounds on the number of leaders needed to complete the task while guaranteeing that connectedness of the communication graph is maintained. The results are first established for an initially complete communication graph and then extended to the incomplete case. The results are illustrated by computer simulations.