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Contrôle des bras articulés et transformations de Moebius (Control of robot arms and Moebius transformations)

Jean-Claude Hausmann
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Abstract

For a m-tuple a=(a_1,...,a_m) of positive real numbers, the robot arm of type a in R^d is the map f^a:(S^{d-1})^m -> R^d defined by f^a(z_1,...,z_m) to be the sum of the a_jz_j's. Our aim is to attack the inverse problem via the horizontal liftings for the distribution Delta^a orthogonal to the fibers of f^a. One shows that the connected components by horizontal curves are the orbits of an actiion on (S^{d-1})^m by a product of groups of Moebius transformations. In several cases, the holonomy orbits of the distribution Delta^a are also described.

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Jean-Claude Hausmann. 2002-10-31. Contrôle des bras articulés et transformations de Moebius (Control of robot arms and Moebius transformations). https://arxiv.org/abs/math/0210477

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