  This work proposes a quaternion-based sliding variable that describes
exponentially convergent error dynamics for any forward complete desired
attitude trajectory. The proposed sliding variable directly operates on the
non-Euclidean space formed by quaternions and explicitly handles the double
covering property to enable global attitude tracking when used in feedback.
In-depth analysis of the sliding variable is provided and compared to others in
the literature. Several feedback controllers including nonlinear PD, robust,
and adaptive sliding control are then derived. Simulation results of a rigid
body with uncertain dynamics demonstrate the effectiveness and superiority of
the approach.
