Multiple-priority impedance control

Impedance control is well-suited to robot manipulation applications because it gives the designer a measure of control over how the manipulator to conforms to the environment. However, in the context of end-effector impedance control when the robot manipulator is redundant with respect to end-effector configuration, the question arises regarding how to control the impedance of the redundant joints. This paper considers multi-priority impedance control where a second-priority joint space impedance operates in the null space of a first-priority Cartesian impedance at the end-effector. A control law is proposed that realizes both impedances while observing the priority constraint such that a weighted quadratic error function is optimized. This control law is shown to be a generalization of several motion and impedance control laws found in the literature. The paper makes explicit two forms of the control law. In the first, parametrization by passive inertia values allows the control law to be implemented without requiring end-effector force measurements. In the second, a class of parametrizations is introduced that makes the null space impedance independent of end-effector forces. The theoretical results are illustrated in simulation.