On the Use of Dual- Matrix Exponentials in Robotic Kinematics

Abstract

This paper sets forth an approach to robotic kinematics that brings together the use of matrix exponentiation and dual numbers. Working from first principles, it is shown that a screw displacement can be represented by the exponential of a dual skew-symmetric matrix; a product of two such matri ces will suffice to specify the relationship between a pair of link coordinate frames. An example problem, dealing with the kinematics of the Rhino XR-2, illustrates how the approach immediately identifies those groups of joint variables that tend to cluster together.