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

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

2002-10-31

arxiv.org/abs/math/0210477v1

Mathematics

Differential Geometry

27 pages, in french

Scientific paper

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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