  In this paper, we design a hybrid controller that globally exponentially
stabilizes a system evolving on the n-dimensional sphere, denoted by Sn. This
hybrid controller is induced by a synergistic collection of potential functions
on Sn. We propose a particular construction of this class of functions that
generates flows along geodesics of the sphere, providing convergence to the
desired reference with minimal path length. We show that the proposed strategy
is suitable to the exponential stabilization of a quadrotor vehicle.
