Dimensional Reduction for 6D Vibrotactile Display

The human hand detects high-frequency vibrations in all directions but cannot distinguish the direction, which suggests a multi-dimensional vibrotactile stimulus is haptically equivalent to some one-dimensional (1D) stimulus. In this article, we explore how a 6D vibrotactile stimulus rendered at the haptic interaction point (HIP) of a kinesthetic haptic interface, with the stylus held in a precision pen-hold grasp, is mapped to an equivalent 1D stimulus normalized by the detection threshold. We gather a large human-subjects data set in which we determine detection thresholds for 45 distinct combinations of three orthogonal forces and three orthogonal torques rendered at the HIP, at a single frequency of 108 Hz corresponding to the peak sensitivity in our prior study. Using this data set, we find a general quadratic weighting function to predict the 1D normalized stimulus for a given 6D vibrotactile stimulus. We find that including just seven (out of a possible 21) independent parameters in the symmetric weighting matrix is sufficient to capture the non-obvious coupling between forces and torques rendered at the HIP for dimensional reduction from 6D to 1D.