A comparison of transforms and quaternions in robotics

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 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>