Robust Impedance Control

In impedance control, a robot is regulated to appear the port property similar to that of a physical system so that the wanted interactive performance is accomplished while interaction with the environment occurs. Since the port property of a robot is independent of the environment, impedance control can be synthesized without taking the environment into account. In this paper, we develop an operator approach to model interaction dynamics based on the law of conservation of energy and Newton's third law of motion. Then, interaction stability, as well as its robustness, are rigorously analyzed by using passivity and passivity indices, and, together with the exact linearization, a robust impedance controller is built to implement optimal impedance matching in the \mathscr{H}-{\infty} sense. Finally, the case study is engaged to demonstrate how to conceive the robust impedance controller and to verify the theoretical results introduced in this paper.