Geometry of non-holonomic diffusion

Simon Hochgerner (1) , Tudor S. Ratiu (2)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 CIB - Bernouilli Center [Lausanne]

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 G-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.

Domaines: Mathématiques [math]

Simon Hochgerner, Tudor S. Ratiu. Geometry of non-holonomic diffusion. Journal of the European Mathematical Society, 2015, 17 (2), pp.273-319. ⟨10.4171/JEMS/504⟩. ⟨hal-01397852⟩