Sliding on Manifolds: Geometric Attitude Control with Quaternions
This work addresses attitude control for rigid bodies, such as in robotics or aerospace, by providing a novel geometric approach that handles the non-Euclidean space of quaternions, though it appears incremental as it builds on existing sliding control methods.
The paper tackled the problem of global attitude tracking for rigid bodies by proposing a quaternion-based sliding variable that ensures exponentially convergent error dynamics for any forward complete desired attitude trajectory, and demonstrated its effectiveness and superiority through simulations of a rigid body with uncertain dynamics.
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.