General task execution of redundant manipulators with explicit null-motion control

In this work, a hybrid impedance control scheme of redundant manipulators for a general class of task execution is addressed. To simplify the primary task, a constraint frame is introduced and a target impedance is expressed in the constraint frame. Additionally, the kinematic null-motion component is extracted explicitly. Using the kinematic relation and null-motion expression, an extended task space formulation is presented. Embedding this in the hybrid impedance control frame, it can be possible to control both the motion and force of an end-effector as well as the null-motion. This scheme also shows the capability of repeatable joint motion. Numerical examples are given to demonstrate the performance of the proposed controller.