Unwinding-Free Attitude Control Based on Fully Actuated Systems: Transformation, Design, and Analysis

The unit quaternion is one of the most commonly utilized attitude representations because of its global representation and singularity-free properties. Nevertheless, the double cover property caused by the quaternion representation, which provides two sets of quaternions to describe an orientation, may lead to the occurrence of the unwinding phenomenon. This phenomenon implies that the rotation angles exceed 180°. In the past several decades, numerous methods have been proposed to address the unwinding phenomenon. For instance, introducing switching logic variables with hysteresis, combining sliding mode control technologies with switching functions, constructing different attitude error functions, designing antiunwinding potential functions, etc. Most reported unwinding-free controllers are designed based on the state-space framework; therefore, introducing additional operations is generally inevitable. Contrary to this, the present work is based on a fully actuated system framework. Since the special structure of the fully actuated system controllers, they are immune to the effects of the double cover property of the quaternion representation. This implies that the proposed attitude controllers can be unwinding-free, and no additional operations need to be introduced to prevent the occurrence of the unwinding phenomenon. Theoretical analyses and numerical simulations verify both the stability of the controlled system and the unwinding-free property of the proposed controllers.