机器人手臂的控制和Moebius变换
Contrôle des bras articulés et transformations de Moebius (Control of robot arms and Moebius transformations)
摘要：
对于m元组a=（a_1，...，a_m）的正实数，R^d中的类型a的机器人手臂是由f^a（z_1，.，z_m）为a_jz_j的和。我们的目标是通过对分布Delta^a与f^a的纤维正交的水平提升来解决逆问题。其中一个证明了水平曲线的连通分量是（S^{d-1}）^m上的一个活动的轨道，它是Moebius变换群的乘积。在几种情况下，也描述了分布Δ ^a的完整轨道。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
