Tracking Controller Design for Satellite Attitude Under Unknown Constant Disturbance Using Stable Embedding

TL;DR

This paper introduces a robust attitude tracking control law for satellites with unknown constant disturbances, utilizing stable embedding of quaternion dynamics and Lyapunov stability to ensure convergence and robustness.

Contribution

It presents a novel stable embedding technique for quaternion dynamics enabling Lyapunov-based control design under unknown disturbances.

Findings

Control law achieves robust tracking despite disturbances

Numerical simulations demonstrate high performance in challenging scenarios

Stable embedding facilitates Lyapunov analysis in Euclidean space

Abstract

We propose a tracking control law for the fully actuated rigid body system in the presence of any unknown constant disturbance by employing quaternions with the stable embedding technique and Lyapunov stability theory. The stable embedding technique extends the attitude dynamics from the set of unit quaternions to the set of quaternions, which is a Euclidean space, such that the set of unit quaternions is an invariant set of the extended dynamics. Such a stable extension of the system dynamics to a Euclidean space allows us to employ well studied Lyapunov techniques in Euclidean spaces such as LaSalle-Yoshizawa's theorem. A robust tracking control law is proposed for the attitude dynamics subject to unknown constant disturbance and the convergence properties of the tracking control law is rigorously proven. It is demonstrated with the help of numerical simulations that the proposed control law has a remarkable performance even in some challenging situations.