Casimir based impedance control

This paper proposes a new impedance control principle for mechanical systems which have driving systems whose control input is not the torque any more. It is shown how to transform such mechanical systems with driving systems into another systems with the desired mechanical impedance. Also it is proved that the proposed principle achieves a robustness in the presence of parameter perturbations. First, we propose a new state space expression of mechanical systems with driving systems based on a natural Casimir function. Second, we propose an impedance control using an artificial Casimir function as well as the natural Casimir function. Third, we analyze a robustness not on the closed-loop stability but on the closed-loop structure. Finally, the validity of the proposed method is confirmed by numerical simulations. Remarkably, the closed-loop system keeps the mechanical impedance structure robustly and thus achieves a robust behavior.