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

摘要

Let X be a smooth quadric of dimension 2 m in P_C~(2 m + 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.