On Homogeneous Transforms, Quaternions, and Computational Efficiency

Abstract

Threedimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. In this paper, an alternate approach, employing quaternion/Vector pairs as spatial operators, is compared with homogeneous transforms in terms of computational efficiency and storage economy. The conclusion drawn is that quaternion/vector pairs are as efficient, more compact, and more elegant than their matrix counterparts. A robust algorithm for converting rotational matrices into equivalent unit quaternions is described, and an efficient quaternion-based inverse kinematics solution for the Puma 560 robot arm is presented. © 1990 IEEE