Geometry of non-holonomic diffusion

TL;DR

This paper explores how stochastic perturbations in non-holonomic systems relate to their geometric constraints, providing criteria for preserved measures and applications to noisy robotic motion planning.

Contribution

It introduces a geometric framework linking stochastic properties to non-holonomic constraints and offers a stochastic criterion for preserved measures in G-Chaplygin systems.

Findings

Established a geometric link between stochastic properties and constraint distributions.

Derived a criterion for the existence of smooth preserved measures in G-Chaplygin systems.

Applied results to motion planning problems for noisy robots.

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.