Angle-Based Shape Determination Theory of Planar Graphs with Application to Formation Stabilization

This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between segments uniquely up to translations, rotations, scalings and reflections. The proposed angle rigidity theory is applied to the formation stabilization problem, where multiple single-integrator modeled agents cooperatively achieve an angle-constrained formation. During the formation process, the global coordinate system is unknown for each agent and wireless communications between agents are not required. Moreover, by utilizing the advantage of high degrees of freedom, we propose a distributed control law for agents to stabilize a target formation shape with desired orientation and scale. Simulation examples are performed for illustrating the effectiveness of the proposed control strategies.