Distributed Optimal Deployment on a Circle for Cooperative Encirclement of Autonomous Mobile Multi-Agents

A distributed encirclement points deployment scheme for a group of autonomous mobile agents is addressed in this paper. Herein, each agent can measure its own azimuth related to the common target and can at least communicate with its two adjacent neighbors. Given its space-cooperative character, the encirclement points deployment problem is formulated as the coverage control problem on a circle. The measurement range of azimuth sensor is taken into consideration when doing problem formulation, which is closer to the facts in real-world applications. Then, the fully distributed control protocols are put forward based on geometric principle and the convergence is proved strictly with algebraic method. The proposed control protocols can steer the mobile agents to distribute evenly on the circle such that the coverage cost function is minimized, and meanwhile the mobile agents' spatial order on the circle is preserved throughout the systems' evolution. A noteworthy feature of the proposed control protocols is that only the azimuths of a mobile agent and its two adjacent neighbors are needed to calculate the mobile agent's control input, so that the control protocols can be easily implemented in general. Moreover, an adjustable feedback gain is introduced, and it can be employed to improve the convergence rate effectively. Finally, numerical simulations are carried out to verify the effectiveness of the proposed distributed control protocols.