Safe Proximity Operation to Rotating Non-Cooperative Spacecraft with Complex Shape Using Gaussian Mixture Model-Based Fixed-Time Control

Abstract

This paper studies the safety control problem for rotating spacecraft proximity maneuver in presence of complex shaped obstacles. First, considering the attitude change of the target spacecraft, a dynamic model of close-range relative motion in a body-fixed coordinate system is derived using a novel approach. Then, the Gaussian mixture model (GMM) is utilized to reconstruct the complex shape of the spacecraft, and a novel GMM-based artificial potential function (APF) is proposed to represent the collision avoidance requirement. By combining GMM-based APF with fixed-time stability methodology, a fixed-time control (FTC) is designed for close-range proximity operation to a rotating spacecraft having a complex shape. The presented GMM-FTC scheme can guarantee the convergence of relative state errors, and ensure that no collision occurs. Finally, simulation results are provided to illustrate the feasibility of the proposed control approach.