Hybrid global exponential stabilization on SO(3)

We propose a central synergistic hybrid approach for global exponential stabilization on the Special Orthogonal group SO(3). We introduce a new switching concept relying on a central family of (possibly) non-differentiable potential functions that enjoy the following properties: (1) being quadratic (as well as their gradients) with respect to the Euclidean attitude distance, and (2) being synergistic with respect to the gradient's singular and/or critical points. The proposed approach is used to solve the attitude tracking problem, leading to global exponential stability results.