Tuning functions-based output feedback adaptive spacecraft formation flying despite disturbances

Abstract

This article presents a non-linear adaptive satellite formation control system based on the tuning functions design method using output feedback. A leader spacecraft is orbiting in an elliptic orbit, and a follower satellite is in motion around it. It is assumed that unknown periodic disturbance forces as well as random disturbances are acting on the follower spacecraft, and its mass is not known. Furthermore, only the relative position of the follower satellite, with respect to the leader satellite, is measured for feedback. The objective is to design an adaptive controller so that the follower spacecraft remains in a specific formation with respect to the leader spacecraft. For the purpose of design, first a simplified model including only periodic disturbance inputs is considered, and a canonical representation of the non-linear relative dynamics is obtained. Based on this canonical form, filters are designed to obtain the estimate of the relative velocity of the follower spacecraft and an output feedback adaptive law is derived for the relative position trajectory control. Based on the Lyapunov approach, it is shown that the closed-loop system is globally uniformly stable, and that the adaptive law accomplishes global asymptotic tracking of the reference trajectory in the presence of periodic disturbances. For robustness with respect to random forces in the model, a modified form of the adaptation law using σ-modification is synthesized. Simulation results are presented, which show that the designed output feedback control system achieves precise formation control, despite the periodic and random disturbance forces and parameter uncertainty in the model.