Geometry of non-holonomic diffusion
Mathematical Physics
2019-11-14 v1 math.MP
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 -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
@article{arxiv.1204.6438,
title = {Geometry of non-holonomic diffusion},
author = {Simon Hochgerner and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:1204.6438},
year = {2019}
}