Hyperbolic normal forms for manipulator kinematics

Abstract

We study the kinematics of robotic manipulators around singular configurations of Corank 1. Sufficient conditions are derived under which the kinematics become equivalent to a hyperbolic normal form. These conditions are illustrated with examples of nonredundant and redundant manipulator kinematics. New normal forms provide a better understanding of the singular behavior of robotic manipulators and are instrumental in solving the singular inverse kinematic problem within the normal form approach.