Algebraic C∗-actions and the inverse kinematics of a general 6R manipulator

摘要

Let X be a smooth quadric of dimension 2m in PC2m+1 and let Y,Z⊂X be subvarieties both of dimension m which intersect transversely. In this paper we give an algorithm for computing the intersection points of Y∩Z based on a homotopy method. The homotopy is constructed using a C∗-action on X whose fixed points are isolated, which induces Bialynicki-Birula decompositions of X into locally closed invariant subsets. As an application we present a new solution to the inverse kinematics problem of a general six-revolute serial-link manipulator.