Sliding on Manifolds: Geometric Attitude Control with Quaternions

TL;DR

This paper introduces a quaternion-based sliding variable for attitude control that ensures exponential convergence and global tracking on the non-Euclidean quaternion space, with robust controllers validated through simulations.

Contribution

It presents a novel sliding variable operating directly on quaternion space, explicitly handling double covering for global attitude tracking, and develops various feedback controllers.

Findings

Demonstrates exponential convergence of attitude error dynamics.

Shows effectiveness of controllers in simulations with uncertain dynamics.

Provides a comparison with existing methods in the literature.

Abstract

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.