Analysis of orientation representations by Lie algebra in robotics

A number of conventional orientation representation methods that are often used in kinematics and control system design are reviewed. Unlike position, orientation is relatively hard to represent by a three-dimensional vector to reflect its three degrees of freedom. A detailed analysis based on the original conceptions of kinematics and Lie algebra is presented and used to explore a unified representation method for both position and orientation. A set of formulas and relations between the old and new orientation representations are developed