Geometry of non-holonomic diffusion

  • Simon Hochgerner

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
  • Tudor S. Ratiu

    Ecole Polytechnique Fédérale de Lausanne, Switzerland


We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.

Cite this article

Simon Hochgerner, Tudor S. Ratiu, Geometry of non-holonomic diffusion. J. Eur. Math. Soc. 17 (2015), no. 2, pp. 273–319

DOI 10.4171/JEMS/504