Hybrid impedance control of redundant manipulators: An approach to decouple task space and null space motions

In this paper, an approach to resolve the kinematic redundancy and to control the motion/force of redundant manipulators is presented using the concept of a quasi-coordinate. Using this factorization, we can transform the joint space dynamics into a new decoupled form with dimensional consistency. Then by extracting the minimal null-motion component to control the internal motion of redundant manipulator, inertial decoupling of the task space and null-space motions for redundant manipulator is achieved. Combining the extracted null-motion component and task space variables, an extended Jacobian is constructed and using this extended Jacobian, we devise a new hybrid impedance controller for redundant manipulator. The unique feature of this controller is the ability to directly control the null space motion which is known to have strong effect on performance of task space motion. Some numerical examples are given to demonstrate the performance of the proposed control method.