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.

中文翻译：

---

基于稳定嵌入的未知恒定扰动下卫星姿态跟踪控制器设计

我们通过采用具有稳定嵌入技术和李雅普诺夫稳定性理论的四元数，在存在任何未知恒定扰动的情况下，为完全驱动的刚体系统提出了一种跟踪控制律。稳定嵌入技术将姿态动力学从单位四元数集扩展到四元数集，这是一个欧几里德空间，使得单位四元数集是扩展动力学的不变集。系统动力学到欧几里得空间的这种稳定扩展使我们能够在欧几里得空间中使用经过充分研究的李雅普诺夫技术，例如拉萨尔-吉泽定理。针对未知恒定扰动下的姿态动力学提出了一种鲁棒的跟踪控制律，并严格证明了跟踪控制律的收敛性。