Distributed Formation Control via Mixed Barycentric Coordinate and Distance-Based Approach

We present a distributed control strategy for a team of agents to autonomously achieve a desired planar formation. Our control strategy is based on combining the barycentric coordinate-based (BCB) and the distance-based (DB) approach. In the BCB approach, the almost global convergence of the agents to the desired formation shape is guaranteed, however, the formation scale cannot be controlled. In the DB method, the scale of the achieved formation is controlled, however, the convergence is local and in general stable undesired equilibria exist. By combining these methods via imposing a timescale separation between their respective dynamics, our proposed control strategy retains the advantages of each approach and avoids their shortcomings. We analyze the stability properties of the proposed control and prove that the desired formation is an almost globally stable equilibrium. We provide simulations to typify the theoretical results and compare our method with a leader-follower BCB (LF-BCB) approach that can be used to control the formation scale in the BCB strategy. In particular, we demonstrate that unlike the LF-BCB approach, our method is far more robust to measurement inaccuracies.