Symbolic Computation of the Lie Algebra se(3) of the Euclidean Group SE(3): An Application to the Infinitesimal Kinematics of Robot Manipulators

Abstract

This paper reports an application of the Lie algebra se(3) of the Euclidean group SE(3), which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic computation of the infinitesimal kinematics allows one to obtain algebraic expressions related to the kinematic characteristics of the end effector of the serial manipulator, while in the case of complex manipulators, numerical computations are preferred owing to the emergence of long terms. The algorithm presented enables the symbolic computation of the velocity and acceleration characteristics of the end effector in serial manipulators in order to allow the compact and efficient modeling of velocity and acceleration analyses of both parallel and serial robotic manipulators. Unlike other algebras, these procedures can be extended without significant effort to higher-order analyses such as the jerk and jounce.