A Comparative Study of the Kinematics of Robots Manipulators by Denavit-Hartenberg and Dual Quaternion

Abstract

This paper presents a comparative study of the kinematics of robot manipulators between Denavit-Hartenberg convention and the Dual Quaternion approach. The kinematics of robot manipulators can be obtained from a traditional form by Denavit-Hartenberg convention. In this way, the posture (position and orientation) of the end-effector is determined from a homogeneous transformation matrix. The dual-quaternion algebra is composed of elements with 8 components and under conditions it represents the posture of a rigid body by a minimal form. The operations and the properties of the dual-quaternion algebra arise from the definitions of elements of a more general algebra: the Clifford algebra that provides the necessary framework to the approach chosen in this paper. In this paper a dual-quaternion algebra is used to model the kinematic equations of robot manipulators in a more compact representation. A numerical robustness analysis is performed and the main characteristics of the dual-quaternion approach and its performance with respect to the Denavit-Hartenberg method will be illustrated in a case study of a 3R robot manipulator.