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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.
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Submitted on : Wednesday, November 16, 2016 - 1:31:26 PM
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Simon Hochgerner, Tudor S. Ratiu. Geometry of non-holonomic diffusion. Journal of the European Mathematical Society, European Mathematical Society, 2015, 17 (2), pp.273-319. ⟨10.4171/JEMS/504⟩. ⟨hal-01397852⟩



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