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

2002/10/31 by Jean-Claude Hausmann, Hausmann, Jean-Claude
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/0210477

27 pages, in french

arxiv created 2002/10/31 · arxiv updated 2009/11/30

Abstract

For a m-tuple a=(a₁,...,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(z₁,...,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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