A Decentralized Optimal Control Law for Multi-circular Circumnavigation around a Stationary Target

This paper explores the circumnavigation of a stationary target by a group of nonholonomic agents aiming to achieve a desired multi-circular formation. Despite the substantial number of works in the area of cooperative circumnavigation problems, the existing literature lacks an optimal control law that minimizes the deviation of the desired values of agents. Therefore, a two-stage control protocol is proposed in this work to ensure the multi-circular circumnavigation formation. At first, assuming the inaccessibility of the formation parameters to some of the agents, distributed estimators are considered to estimate the parameters. Then, a linear quadratic regulator (LQR) based decentralized optimal control algorithm is proposed to minimize a weighted sum of squared deviations from desired states and control inputs. The effectiveness of the proposed algorithm is demonstrated through numerical simulations.