Closed-loop manipulator control using quaternion feedback

Euler parameters, a form of normalized quaternions, are used to model the hand-orientation errors in resolved-rate and resolved-acceleration control of manipulators. The quaternion formulation simplifies the stability analysis of the orientation error dynamics. Two types of quaternion feedback have been considered. The first type uses only the vector portion of the quaternion error, while the second is based on a Euler rotation representation. The quaternion vector approach leads to a linear feedback control law for which the global asymptotic convergence of the orientation error is readily established. The Euler rotation approach also results in asymptotic error convergence in the large except for a singularity where the hand orientation differs from its desired orientation by a rotation of 180°