Observer-based spacecraft attitude tracking with guaranteed performance bounds

Recently, a sequential Lyapunov technique has been developed for the purpose of determining non-conservative steady-state performance bounds for rigid spacecraft attitude tracking. In particular, given known bounds on disturbance torques and uncertainties in the spacecraft inertia matrix, non-conservative ultimate bounds were obtained for the attitude tracking error assuming that the attitude and angular velocity are measured with known bounds on the measurement errors. In this paper, these results are extended to the case where the attitude and angular velocity are not measured, but estimated using an observer. Specifically, it is shown that given any attitude and angular velocity observer with known ultimate bounds on the estimation errors, the previously developed expressions for the ultimate bounds on the tracking error remain valid with observer-based control, provided the ultimate bounds on the estimation errors are used in place of the previously fixed bounds on the measurement errors. A numerical example of attitude tracking using a gyro and a single vector measurement demonstrates the utility of the proposed technique.