Geometry of non-holonomic diffusion

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.

References in corpus (4)

• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization
• Singular cotangent bundle reduction and spin Calogero-Moser systems
• Symmetry reduction of Brownian motion and Quantum Calogero-Moser systems

Cited by in corpus (6)

• Variational Principles for Stochastic Fluid Dynamics
• Momentum Maps and Stochastic Clebsch Action Principles
• Reduction and reconstruction of stochastic differential equations via symmetries
• Dynamics of non-holonomic systems with stochastic transport
• A Hamiltonian interacting particle system for compressible flow
• Dynamics of geodesic flows with random forcing on Lie groups with left-invariant metrics