Circular Formation Control with Collision Avoidance Based on Probabilistic Position

In this paper, we study the circular formation problem for the second-order multi-agent systems in a plane, in which the agents maintain a circular formation based on a probabilistic position. A distributed hybrid control protocol based on a probabilistic position is designed to achieve circular formation stabilization and consensus. In the current framework, the mobile agents follow the following rules: 1) the agent must follow a circular trajectory; 2) all the agents in the same circular trajectory must have the same direction. The formation control objective includes two parts: 1) drive all the agents to the circular formation; 2) avoid a collision. Based on Lyapunov methods, convergence and stability of the proposed circular formation protocol are provided. Due to limitations in collision avoidance, we extend the results to LaSalle's invariance principle. Some theoretical examples and numerical simulations show the effectiveness of the proposed scheme.