Joint-Based Robotic Impedance Control Transformations: An Experimental Study

We present an experimental study in this paper to illustrate the effect of the Cartesian damping matrix on modulating the dynamic response of a robotic manipulator in impedance control. We first derive the transformation of the matrices of impedance control between the Cartesian and joint spaces using differential mathematics. Through experiments conducted on a redundant Franka Panda robot, it is demonstrated that the coupling term between damping and stiffness in impedance control derived from theoretical analysis, when transforming between the Cartesian and joint spaces, is important in stabilizing the dynamic response of the joints. We apply a methodology to modulate the dynamic response of a robot performing impedance control that allows us to study and select diagonal and off-diagonal elements of the Cartesian damping matrix according to the damping ratios and natural frequencies of the system in the modal space. In addition, we explain and show that an arbitrary selection of damping is counter-productive for robots to perform tasks under impedance control, and may lead to instability and out-of-range torques at the joints of the robotic manipulator.