Robust attitude tracking with exponential convergence

Abstract

This study addresses robust attitude tracking of a spacecraft without unwinding by considering external disturbances and uncertain inertia parameters. Quaternion is used to represent the relative attitude for attitude tracking, thus the closed-loop system has two equilibria. A desired equilibrium is determined from them according to the sign of the initial relative attitude quaternion such that less rotation is required for attitude tracking. A backstepping scheme based on similar skew-symmetric structure is adopted to design the attitude controller. Two compensation terms are introduced to deal with the uncertainties. A parametric condition is provided to guarantee that the attitude tracking has an exponentially convergent speed without unwinding. The related parametric regulation is addressed for response speed, robustness and disturbance attenuation. It is shown that arbitrarily fast response and any specified tracking precision can both be achieved by regulating the related parameters of the proposed controller. Compared with the related research, a variable gain term is included in the proposed controller. Accordingly, the controller has relatively slower gain in the system response, thus large control amplitude is avoided. Furthermore, the controller has much higher gain in the steady state such that much higher control precision can be obtained for a given control amplitude when compared with other attitude tracking controllers. Simulations are carried out to validate the effectiveness of the proposed attitude controller.