Nonsingular Fixed-Time Attitude Tracking Control for Rigid Spacecraft

In this article, the nonsingular fixed-time control (NFTC) and unwinding problem for rigid spacecraft attitude tracking are investigated. By introducing dynamic powers, a class of sliding functions and a class of NFTC laws are proposed. In particular, dynamic powers in the developed sliding functions are constructed by the elements of the quaternion, and dynamic powers in the presented control laws are composed of the norm of the sliding function. Specifically, a sliding function is developed to ensure that the sliding surface has exactly one equilibrium point. Correspondingly, a nonsingular controller is proposed to guarantee that the obtained closed-loop system is almost globally fixed-time stable. In order to handle the unwinding problem, another sliding function is presented such that the sliding surface contains two stable equilibria. Accordingly, an antiunwinding fixed-time attitude tracking controller is developed such that the set of two stable equilibria is almost globally fixed-time stable. Moreover, adjustable subsets of the attraction regions of two stable equilibria are provided. Finally, numerical simulations are performed to validate the significance of the designed control laws.