Formation Merging Control in 3D under Directed and Switching Topologies

The paper studies the formation merging problem for a leader-follower network. That is, how to control a team of agents called followers so that they are merged with a team of agents called leaders to form a larger globally rigid formation. Under the premise that a group of leaders move in a globally rigid formation with their synchronized velocity known to the followers, we show that the followers can asymptotically merge themselves to the formation for arbitrarily initial configurations. Each follower selects its neighbors and also its control law according to the target formation they aim to achieve and thus it allows directed and time-varying switching topologies. It is shown that a globally rigid formation can be merged asymptotically for the leader-follower network in a setup with directed and time-varying graphs if and only if every follower frequently has a joint path from at least a leader.