Global exponential attitude tracking for spacecraft with gyro bias estimation

This paper addresses the global exponential attitude tracking of a spacecraft when gyro measurements are corrupted by bias. Based on contraction analysis, an exponentially convergent nonlinear observer is designed first to estimate the gyro bias. Relying on this bias estimator and the quaternion logarithm representation of the tracking error, an exponentially globally convergent controller is devised. This controller stabilizes the unique equilibrium of the closed-loop system, where the tracking error is the unit quaternion. For more energy-efficiency and enhancing the robustness in the presence of measurement noise, a hysteretically switching variable as in [1] is incorporated in the control loop and an unwinding-free globally exponentially convergent tracking controller is obtained. Numeric simulations were done to evaluate its performance in terms of tracking errors and energy-efficiency, as well as the robustness to measurement noise and time-varying bias in gyro sensors.