Collision-Free Approximate Optimal Control of Spacecraft Formation With Predefined Performance

This article aims to design an approximate optimal control algorithm for spacecraft formations with predefined performance while ensuring collision avoidance. Achieving these control objectives simultaneously is challenging, especially when there is a conflict between predefined performance and collision avoidance. To address this problem, a predefined variable-performance function equipped with an auxiliary system is designed to achieve the formation error constraints. The relaxation effect of the auxiliary system ensures that obstacle avoidance takes precedence, while the spacecraft move toward the target position. Furthermore, by employing an optimal backstepping control method, a collision-free optimal performance index function is formulated through a simple error transformation to derive the optimal controller. An actor–critic neural network is used to estimate the approximate values of unknown terms in the optimal controller. Through Lyapunov stability analysis, it is demonstrated that the consensus error of the system is ultimately uniformly bounded. Finally, the effectiveness of the proposed controller is validated through a set of simulations.