A Class of Axis-Angle Attitude Control Laws for Rotational Systems

We introduce a new class of attitude control laws for rotational systems, which generalizes the use of the Euler axis-angle representation beyond quaternion-based formulations. Using basic Lyapunov's stability theory and the notion of extended $K_{\infty}$ functions, we developed a method for determining and enforcing the global asymptotic stability of the single fixed point of the resulting closed-loop (CL) scheme. In contrast with traditional quaternion-based methods, the proposed generalized axis-angle approach enables greater flexibility in the design of the control law, which is of great utility when employed in combination with a switching scheme whose transition state depends on the angular velocity of the controlled rotational system. Through simulation and real-time experimental results, we demonstrate the effectiveness of the proposed approach. According to the recorded data, in the execution of high-speed tumble-recovery maneuvers, the new method consistently achieves shorter stabilization times and requires lower control effort relative to those corresponding to the quaternion-based and geometric-control methods used as benchmarks.