On the Almost-Global Stabilization of Rigid Bodies Using Exponential Coordinates

This article addresses the attitude stabilization problem of fully actuated rigid bodies such as quadrotors, spacecraft, or satellites. To describe the attitude of the rigid body, we employ the exponential coordinates of rotation. By exploiting the properties of kinematic and dynamic models, we design a nonlinear attitude controller that guarantees almost global exponential stability (aGES) of the closed-loop dynamics. We also consider the case when the attitude dynamics are subject to constant disturbances. To counteract the external disturbance, we modify the attitude control law to include an integral action that rejects the disturbance and achieves aGES. In addition, we show that the stabilization control law can be extended to address the attitude-tracking problem. Using barrier Lyapunov functions, we demonstrate that the proposed control algorithms avoid the singularity of the exponential coordinates during the transient response. We propose strict Lyapunov functions to prove the aGES of the origin of the closed-loop dynamics. Numerical simulations and experimental results performed on a commercial small aerial robot assessed the effectiveness and feasibility of the proposed control laws.