Global stabilization of similar formation via edge-based clique addition

In this paper, the focus is on distributed similar formation stabilization, which aims to design a distributed controller to stabilize a group of agents to a desired formation, allowing for arbitrary translations, rotations, and scaling. While existing literature has produced fruitful results in this area, current approaches often rely on restrictive conditions regarding the inter-agent interaction graph. This paper introduces a novel approach using a clique-based control law, along with the concept of “edge-based clique addition”, which offers a more lenient graphical condition compared to previous clique-based methods. By concentrating on a single clique with the new controller, the paper establishes a necessary and sufficient condition for determining the clique shape uniquely, a novel contribution to the field. Furthermore, the paper proposes the graph construction method “edge-based clique addition”, which ensures that the multi-agent system achieves global similar formation stabilization. Similar to distance-based formation control, the proposed controller only necessitates each agent to capture the relative positions from neighbors in its local coordinate frame, without the need for coordinate system alignment or wireless communications. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control strategy.