Normal and tangential forces combine to convey contact pressure during dynamic tactile stimulation

Abstract

Humans need to accurately process the contact forces that arise as they perform everyday haptic interactions such as sliding the fingers along a surface to feel for bumps, sticky regions, or other irregularities. Several different mechanisms are possible for how the forces on the skin could be represented and integrated in such interactions. In this study, we used a force-controlled robotic platform and simultaneous ultrasonic modulation of the finger-surface friction to independently manipulate the normal and tangential forces during passive haptic stimulation by a flat surface. To assess whether the contact pressure on their finger had briefly increased or decreased during individual trials in this broad stimulus set, participants did not rely solely on either the normal force or the tangential force. Instead, they integrated tactile cues induced by both components. Support-vector-machine analysis classified physical trial data with up to 75% accuracy and suggested a linear perceptual mechanism. In addition, the change in the amplitude of the force vector predicted participants' responses better than the change of the coefficient of dynamic friction, suggesting that intensive tactile cues are meaningful in this task. These results provide novel insights about how normal and tangential forces shape the perception of tactile contact.

Figure 1

(a) The experimental apparatus used to independently modulate the normal force (NF) and tangential force (TF) that are applied on the index fingertip. (b) Upper: TF is modulated during sliding by vibrating the contact surface at an ultrasonic frequency (39 kHz) to create a microscale air film between the surface and the skin (squeeze film effect), hence reducing the finger-surface friction. Lower: diagram of the proportional-integral (PI) controller that enables the robotic platform to modulate NF according to a commanded pattern. (c) Illustration of the modulation of the contact-force vector when changes are induced compared to the pre-modulation NF and TF. TF is parallel to the contact surface, and NF is orthogonal to it. (d) Typical trials representative of the three normal force conditions: the briefly decreased normal force with ∆NF =  − 0.3 N (purple), the constant normal force of 1.0 N (gray), and the briefly increased normal force with ∆NF =  + 0.3 N (green). The setpoints are represented by the dashed lines. (e) Typical trials representing the six levels of change in TF. Three conditions start with no ultrasonic vibration, and the other three start with a constant 1.5 µm ultrasonic vibration. The changes in the intensity of the ultrasonic vibration and their impact on the finger-surface TF are displayed in the table on the right. One color is associated with each ultrasonic condition.

Figure 2

(a) The average tangential force (TF) and average normal force (NF) during the pre-modulation interval for all eleven participants in each condition, plus summary statistics (mean ± SD). (b) The change in TF and NF averaged across all participants for the 18 conditions of the experiment (c) The averaged answers across participants in the 18 conditions of the experiment (mean ± SD) Left: the conditions in which TF increased or stayed constant at a lower level during the modulated interval. Right: the conditions in which TF decreased or stayed constant at its natural higher level during the modulated interval.

Figure 3

(a) The induced NF and TF changes during the modulated interval for all trials of the study and the classification line of the binary logistic regression. (b) Results for the linear kernel SVM with the addition of the 95% confidence interval boundaries. (c) Results for the Gaussian kernel SVM. (d) Results for the polynomial kernel SVM (degree = 3). (e) The receiver operator characteristic (ROC) curves obtained from the implemented classifiers.

Figure 4

(a) Changes across TF conditions for the two metrics. Individual points represent the averaged change for one participant in a given condition. Lines connect conditions from the same participant with identical baseline and variation of normal force. (b) Same plot for the change across NF conditions. Lines connect conditions from the same participant with identical baseline and ultrasonic vibration.

Figure 5

(a) Histogram of the number of answers with respect to the percentage change of the contact force vector amplitude (A). (b) Same histogram for the percentage change in the coefficient of dynamic friction (µ). (c) Receiver operator characteristic (ROC) curve for the change in A across all participants. (d) Same ROC curve for the change in µ.