A comparison of transforms and quaternions in robotics

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 discussed and analyzed. Sequential and parallel algorithms for some of the common spatial operations are given for both homogeneous transforms and quaternion/vector pairs and compared in terms of computational efficiency. The two approaches are shown to be essentially equivalent in the absence of the need for frequent renormalization of rotational operators