Optimal passivity design of a virtual coupling including FIR-type fractional derivatives for a haptic interface

Abstract

This paper describes a haptic interface with a virtual coupling, including fractional derivatives. A haptic interface is a force feedback technology in virtual reality that takes advantage of the human sense of touch. In a haptic interface, virtual impedance, that is called virtual coupling (VC), is commonly used between the virtual and real objects to calculate reaction force. VC generally consists of a virtual stiffness and damper, but the stiffness has to be set low in a system with long sampling periods. In order to increase the virtual stiffness, this paper considers a VC including fractional derivatives approximated by an FIR approximation. First, we theoretically analyse effects of a single fractional derivative term by using the passivity analysis, but the result shows that its effects depend on the occurred frequency. This paper, therefore, proposes a method to combine multiple fractional derivative terms in a VC and a method to optimize parameters in each fractional derivative term. Finally, experiments are performed to measure the maximum value of the stiffness to illustrate the effects of the proposed method.