An intrinsic formulation of the rolling manifolds problem

الأصل · EN

We present an intrinsic formulation of the kinematic problem of two n-dimensional manifolds rolling one on another without twisting or slipping. We determine the configuration space of the system, which is an n(n+3)2-dimensional manifold. The conditions of no-twisting and no-slipping are decoded by means of a distribution of rank n. We compare the intrinsic point of view versus the extrinsic one. We also show that the kinematic system of rolling the n-dimensional sphere over Rⁿ is controllable. In contrast with this, we show that in the case of SE(3) rolling over se(3) the system is not controllable, since the configuration space of dimension 27 is foliated by submanifolds of dimension 12.