Three-dimensional formation merging control under directed and switching topologies

This paper concentrates on the formation merging control problem for a leader–follower network. The objective is to control a team of agents called followers such that they are merged with another team of agents called leaders to form a single globally rigid formation. A method based on graph Laplacian is introduced to address this problem. Each follower selects its interaction neighbors and interaction weights according to the given target configuration. The graph modeling the interaction topology of all the agents is directed and time-varying. First, by assuming that the synchronized velocity of the leaders is known to all the followers, a necessary and sufficient condition is derived to ensure uniform asymptotic formation merging. Second, we relax this assumption and consider that the velocity of the leaders is known to only a subset of followers, for which the same necessary and sufficient condition is obtained with the help of an internal model for velocity synchronization.