Passivity design of a VC with dual-sampling-rate fractional derivatives to display tapping motion

This paper studies a design method of a virtual coupling (VC) including fractional derivatives for a haptic interface used in virtual reality technology. In the previous research, parameters of fractional derivatives in the VC were optimized, concerning the passivity property of measured real objects. However, as the sampling rate was fixed to a single value and the characteristics of discretization were restricted, it was difficult to match the passivity in a wide range of frequencies. For this issue, this paper proposed to use discretization with several different sampling rates for fractional derivatives, by combining the discretization terms with the low and high rates, the proposed method can realize adequate passivity through the wide range of frequency. Finally, free fall experiments and human tapping experiments are performed and the results show that the proposed method can generate better behavior than the previous method in a physical repulsion and a more similar haptic expression to a real object in a human tapping motion.