A coupled nonlinear spacecraft attitude controller/observer with an unknown constant gyro bias

A nonlinear control scheme for attitude control of a spacecraft is combined with a nonlinear gyro bias observer for the case of constant gyro bias. A persistency of excitation analysis shows the observer bias estimates converge to the true bias values exponentially fast. The resulting coupled, closed loop dynamics are proven by a Lyapunov analysis to be globally stable, with asymptotically perfect tracking. The analysis is extended to consider the effects of noise in addition to the gyro bias. A simulation of the proposed observer-controller design is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.