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We study the control system of a Riemannian manifold $M$ of dimension $n$rolling on the sphere $S^n$. The controllability of this system is described interms of the holonomy of a vector bundle connection which, we prove, isisomorphic to the Riemannian holonomy group of the cone $C(M)$ of $M$.  Using Berger's list, we reduce the possible holonomies to a few families. Inparticular, we focus on the cases where the holonomy is the unitary and thesymplectic group. In the first case, using the rolling formalism, we constructexplicitly a Sasakian structure on $M$; and in the second case, we construct a3-Sasakian structure on $M$.

Rolling against a sphere: The non transitive case