On homogeneous transforms, quaternions, and computational efficiency

Abstract

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using 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 as, more compact than, 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>