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Directed Formation Control with Controllable Interaction Weights

In this paper, we consider a formation control model whereby there is a directed graph specifying the underlying network topology of the multi-agent system, and the motion of each agent is governed by the interaction weights between itself and its outgoing neighbors. In this formation model, we steer the multi-agent system by controlling the interaction weights among agents. We focus on the strength and limit of this formation control model by investigating its controllability. We show in this paper that this model is (approximately path) controllable almost everywhere as long as the underlying digraph satisfies some mild assumptions. In the proof, we will explore the relations among the geometry of formations, the structure of the network topology and the controllability of the control system.