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.
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Simon Hochgerner, Tudor S. Ratiu, Geometry of non-holonomic diffusion. J. Eur. Math. Soc. 17 (2015), no. 2, pp. 273–319DOI 10.4171/JEMS/504