Distance-Constrained Formation Control of Multi-Agent Systems Using Asymmetric Barrier Lyapunov Function

This paper studies the formation control of a multi-agent system where each agent is considered to have a physical shape, unlike a point mass model representation. For simplicity, we consider that the shape of each agent is characterized by a circular disk of the same radii. Leveraging the inter-center distance or interior-angle information among the neighboring agents, that can be easily measured by low-cost vision sensors, we apply constraint on the distance between the two agents such that they avoid collisions as well as maintain connectivity with the neighboring agents. To achieve these constraints on inter-agent distances, we exploit the idea of asymmetric barrier Lyapunov function from the existing literature, and design the stabilizing control law. We show that the agents asymptotically converge to the desired formation and their distances follow the required constraints. Simulations are provided to illustrate the efficacy of the proposed control law.