The rolling problem overview and challenges

Yacine Chitour (1) , Mauricio Godoy Molina (2) , Petri Kokkonen (1)

1 L2S - Laboratoire des signaux et systèmes
2 Georg-August-University = Georg-August-Universität Göttingen

In the present paper we give a historical account -ranging from classical to modern results-of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory-have employed the rolling problem.

Domaines: Mathématiques [math]

Yacine Chitour, Mauricio Godoy Molina, Petri Kokkonen. The rolling problem overview and challenges. Meeting on Geometric Control Theory and Sub-Riemannian Geometry, May 2012, Cortona, Italy. ⟨10.1007/978-3-319-02132-4_7⟩. ⟨hal-02320829⟩