A comparative study of three methods for robot kinematics

Three methods for the formulation of the kinematic equations of robots with rigid links are presented in this paper. The first and most common method in the robotics community is based on 4x4 homogeneous matrix transformation, the second one is based on Lie algebra, and the third one on screw theory expressed via dual quaternions algebra. These three methods are compared in this paper for their use in the kinematic analysis of robot arms. The basic theory and the transformation operators, upon which every method is based, are referenced. Three analytic algorithms are presented for the solution of the direct kinematic problem corresponding to each method, and the geometric significance of the transformation operators and parameters is explained. Finally, a comparative study on the computation and storage requirements for the three methods is worked out.