  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.
