A comparative study of two methods for forward kinematics and Jacobian matrix determination

In this paper, a comparative study of two methods are presented to determine the forward kinematics and Jacobian matrix for any serial manipulator, based on product of exponentials formula and unit dual quaternion algebra. This comparison is qualitative and particularly quantitative taken into account computational costs and memory requirements that are very critical in the manipulator control and real-time algorithms. For the first time the computational cost in determining the Jacobian matrix by using these two algorithms is compared. The two algorithms are applied to the 7-DOF Kuka Lightweight Robot using MATLAB and compared.