On Homogeneous Transforms, Quaternions, and Computational Efficiency

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