Geodesic
Geometry of non-holonomic diffusion
Journal of the European Mathematical Society, Tome 17 (2015) no. 2, pp. 273-319 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/504
Classification : 37-XX, 00-XX, 58-XX, 93-XX
Keywords: Non-holonomic system, symmetry, measure, reduction, diffusion, Brownian motion, generator, Chaplygin system, snakeboard, two-wheeled carriage 
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     title = {Geometry of non-holonomic diffusion},
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Simon Hochgerner; Tudor S. Ratiu. Geometry of non-holonomic diffusion. Journal of the European Mathematical Society, Tome 17 (2015) no. 2, pp. 273-319. doi: 10.4171/jems/504

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