Drake does not yet offer a joint impedance controller, which would use feedback to shape the stiffness, damping, and inertia of the closed-loop system.
We do however offer JointStiffnessController which uses feedback to shape the closed-loop stiffness and damping. Most modern control stacks, such as the JointImpedanceControl mode on Kuka's iiwa and Franka's Panda, are actually better modeled as stiffness control (unless one is also modeling the details of the elastic joints and rotor-interia shaping).
See https://manipulation.csail.mit.edu/force.html for more details.
#include <drake/systems/controllers/joint_stiffness_controller.h>