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arXiv · 1204.6438

Geometry of non-holonomic diffusion

Simon Hochgerner·Tudor S. Ratiu
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Abstract

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.

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Simon Hochgerner, Tudor S. Ratiu. 2012-04-28. Geometry of non-holonomic diffusion. https://doi.org/10.4171/jems%2F504

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