Perceived Hardness of Virtual Surface: A Function of Stiffness, Damping, and Contact Transient

Haptic rendering of virtual objects requires a model for the object's hardness. The classical spring-damper model is effective in resisting the user's penetration into the virtual surface, while a short vibratory transient signal superimposed at contact increases the user-perceived hardness. In this paper, we are concerned with the combined case: the perceived hardness of a virtual surface rendered by the spring-damper model with a contact transient, in the tool-mediated perception. We report three perceptual experiments conducted to clarify the effects of five rendering parameters - stiffness and damping (spring-damper model); and amplitude, frequency, and decay rate (contact transient). All the parameters except decay rate are shown to have statistically significant effects on the perceived hardness. We also present a psychophysical magnitude function of perceived hardness for the four significant parameters of stiffness, damping, amplitude, and frequency. This mathematical model helps virtual environment designs build the virtual surfaces of desired perceived hardness.