Unwinding-Free Attitude Control via Fully Actuated System Approach

Quaternion representation is widely used to describe the attitude motions of rigid bodies because it provides a global representation and is free from singularities. Nevertheless, the double cover property of the representation can result in the unwinding phenomenon, where the rotation angles exceed pi radians. The present work proposes a fundamental attitude control law via the fully actuated system approach. The fundamental control law, without the need for additional operations, can avoid the unwinding phenomenon. Based on the fundamental control law, external disturbances and input saturation are considered. Consequently, an unwinding-free controller is proposed for the attitude control of rigid bodies. Lyapunov's direct method is used to verify the stability of the system. Numerical simulations demonstrate the validity of both the fundamental control law and the proposed controller.