Three-dimensional formation merging control of second-order agents under directed and switching topologies

This paper investigates the formation merging problem for a leader-follower network. The objective is to control a group of agents called followers and modeled by double-integrator dynamics so that they are merged with another group of agents called leaders to form a single globally rigid formation. With the assumption that leaders move in a globally rigid formation with their synchronized velocity known to the followers, we show that a globally rigid formation can be merged. Each follower selects its neighbors and control law according to the target configuration and thus it allows directed and time-varying switching topologies. We provide a necessary and sufficient condition such that a globally rigid formation can be merged asymptotically for the leader-follower network in a setup with directed and time-varying graphs.