  We solve the stabilization problem on the $n-$sphere in the presence of conic
constraints. We use the stereographic projection to map this problem to the
classical navigation problem on $\mathbb{R}^n$ in the presence of spherical
obstacles. As a consequence, any obstacle avoidance algorithm for navigation in
the Euclidean space can be used to solve the given problem on the $n-$sphere.
We illustrate the effectiveness of the approach using the kinematics of the
reduced attitude model on the $2-$sphere.
