Algebraic C*-actions and inverse kinematics
(English)Manuscript (preprint) (Other academic)
Let X be a smooth quadric of dimension 2m in P2m+1C and let Y,Z X be subvarietiesboth of dimension m which intersect transversely. In this paper we give an algorithm forcomputing the intersection points of Y Z based on a homotopy method. The homotopyis constructed using a C*-action on X whose fixed points are isolated, which inducesthe so-called Bialynicki-Birula decompositions of X into locally closed invariant subsets.Notably, the homotopy has the optimal number of solution paths. As an applicationwe present a new solution to the inverse kinematics problem of a general six-revoluteserial-link manipulator.
IdentifiersURN: urn:nbn:se:kth:diva-26112OAI: oai:DiVA.org:kth-26112DiVA: diva2:370137
QC 201011152010-11-152010-11-152010-11-15Bibliographically approved