Global stabilization of spherical orientation by synergistic hybrid feedback with application to reduced-attitude tracking for rigid bodies

In this paper, we propose a hybrid feedback based on a “synergistic” potential function that achieves global asymptotic stabilization of a desired orientation on the n -sphere with a nominal robustness to measurement disturbances, a task that is not possible by classical feedback–be it smooth, nonsmooth, periodic, or any combination thereof–due to the topological structure of the sphere. We extend this basic result to a tracking controller for the reduced attitude–or pointing direction–of a rigid body and provide a method to remove jumps in the controlled torque by backstepping. The proposed hybrid feedback is compared with a similar smooth feedback in simulation, where it is illustrated that the hybrid feedback overcomes performance limitations inherent to the smooth feedback. We provide two examples of a synergistic potential function–one defined on a general sphere and the other on the unit circle.