Perceived Magnitude Function of Friction Rendered By the Dahl Model

The discrete vectorial Dahl model, proposed by Hayward and Armstrong, is appropriate for haptic friction rendering using a force-feedback interface due to its modeling power of complex frictional behaviors and relatively simple discrete formula favorable for real-time computation. The model has a few parameters that determine the subjective sensations of virtual surface friction, but their perceptual roles have not been clarified. This paper presents the design and results of a perceptual experiment that aimed to quantify the effects of the discrete vectorial Dahl model parameters in the perceived magnitude of friction. It was observed that the maximum magnitude of the sliding friction force has the most critical effect on friction perception. We also fit a nonlinear function between the perceptual magnitude of friction and the maximum sliding friction force in the form of Steven’s power law. This function serves as a psychophysical magnitude function that enables haptic application designers to understand the perceptual strength of virtual friction rendering implemented using the Dahl model.