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

Let X be a smooth quadric of dimension 2m in P2m+1 C 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 sixrevolute serial-link manipulator.

• Type: Journal
• Year: 2010
• Where: AMC
• Authors: Sandra Di Rocco, David Eklund, Andrew J. Sommese, Charles W. Wampler
• Keywords: AMC 2010, Dimension, Homotopy Method, Intersection Points