On topological conditions to maintain leader-follower connectivity in double-integrator multi-agent systems

In this work, a set of sufficient conditions that guarantee consensus towards a pre-specified target state in double-integrator leader-follower proximity-based networks are derived. Since only the leader agents are aware of the global objective and proximity-based communication between agents is considered, the follower agents must not lose contact to the leaders. We establish a connectivity analysis framework which is used to show that the initial network topology is maintained if the ratio of leaders-to-followers and the magnitude of the goal attraction force experienced by the leaders are below certain bounds. Various network topologies are examined, starting from a complete graph and extending to incomplete graphs. The theoretical results are illustrated by simulations.