Observer-based attitude control with measurement uncertainties

The robust spacecraft attitude tracking is addressed with uncertainties in state estimates, inertia matrices, and disturbances. Instead of designing new control laws, this paper considers the simple yet classical quaternion controller consisting of a proportional-derivative feedback plus some feedforward (PD+). First, the closed-loop stability is analyzed when attitude and velocity estimates are algebraically extracted from direct sensor measurements. By a sequential Lyapunov technique, a convergent sequence of analytical, successively tighter upper bounds on the steady-state tracking error is derived from known bounds of measurement errors and modeling uncertainties. Moreover, a numerical algorithm is constructed to obtain less conservative performance bound predictions. These results are then extended to the case when state estimates are generated from any stand-alone observers yielding uniformly ultimately bounded estimation errors. Given known ultimate bounds on the estimation errors, the same algorithm can be used to derive bounds on the ultimate tracking error. Our analyses not only establish a separation principle between the quaternion PD+ controller and a broad class of observers but facilitate gain selection given steady-state performance bounds. Numerical examples demonstrate the utility of the proposed theory.