Local minimization behavior of weighted kinematically decoupled joint space decomposition for redundant manipulators

Kinematically redundant manipulators have been studied because of its usefulness of kinematic redundancy. It is natural that the kinematic redundancy induces a kind of control redundancy. By using the weighted kinematically decoupled joint space decomposition, we unify the control redundancy and the kinematic redundancy parameterized by the joint space weighting matrix. Concentrating to the particular component of each decomposition, we can describe the local minimization behavior of the control weighted quadratic by each weighted decomposition. The result extends the conventional results on general setting, and should be of interest in understanding the motion behavior of kinematically redundant manipulators.