COMPUTATIONAL ASPECTS OF THE PRODUCT-OF-EXPONENTIALS FORMULA FOR ROBOT KINEMATICS

In this article we investigate the modeling and computational aspects of the product-of-exponentials (POE) formula for robot kinematics. Whi le its connections with Lie groups and Lie algebras give the POE equat ions mathematical appeal, little is known regarding its usefulness for control and other applications. We show that the POE formula admits a simple global interpretation of an open kinematic chain and possesses several useful device-independent features absent in the Denavit-Hart enberg (DH) representations. Methods for efficiently computing the for ward kinematics and Jacobian using these equations are presented. In p articular, the computational requirements for evaluating the Jacobian from the POE formula are compared to those of the recursive methods su rveyed in Orin and Schrader [5].