Calibration of Virtual Haptic Texture Algorithms

Abstract

Calibrating displays can be a time-consuming process. We describe a fast method for adjusting the subjective experience of roughness produced by different haptic texture synthesis algorithms. Efficiency results from the exponential convergence of the “modified binary search method” (MOBS) to a point of subjective equivalence between two virtual haptic textures. The method was applied to calibrate the modulation of the normal interaction force component against modulating a tangential friction force component. A table establishing the perceptual equivalence between parameters having different physical dimensions was found by testing 10 subjects. The method is able to overcome significant individual differences in the subjective judgement of roughness because roughness itself never needs to be directly estimated. A similar method could be applied to other perceptual dimensions provided that the controlling parameter be monotonically related to a subjective estimate.

Reprinted from Gianni Campion and Vincent Hayward, “Fast Calibration Of Haptic Texture Synthesis Algorithms.”IEEE Transaction on Haptics, Volume 2, Number 2, 85–93, 2009.

Appendix: Appendix: Characteristic Numbers

9.1.1 9.8.1 Algorithm A

The Jacobian matrix of the force field is

$$ {\mathbf{J}_{\!\boldsymbol{f}}}_{\!\mbox{\scriptsize{\textsf{\textbf{A}}}}}(p) = -\kappa_0 \left[\begin{array}{c@{\quad}c} 0 & 0\\[4pt] -{h'_{\mbox{\scriptsize{\textsf{\textbf{A}}}}} (p^x)}& 1\end{array}\right].$$

(9.4)

Its norm is

$$\|{\mathbf{J}_{\!\boldsymbol{f}}}_{\!\mbox{\scriptsize{\textsf{\textbf{A}}}}}\|_2 = {\kappa}_{\mbox {\scriptsize{\textsf{\textbf{A}}}}} = \kappa_0 \sqrt{1+[{h'_{\mbox{\scriptsize{\textsf{\textbf{A}}}}} (p^x)}]^2 }$$

(9.5)

which gives

$$q_{\mbox{\scriptsize{\textsf{\textbf{A}}}}} = \max{\kappa}_{\mbox {\scriptsize{\textsf{\textbf{A}}}}} / \kappa_0 = \sqrt{1+[2\pi A/L]^2}$$

(9.6)

when${h_{\mbox{\scriptsize{\textsf{\textbf{A}}}}} (p^{x})}=A\sin (2 \pi p^{x} /L)$.

9.1.2 9.8.2 Algorithm F

The Jacobian matrix of the force field is

$${\rm J}_{f_{\rm F} } (p) = - \kappa _0 \left[ {\begin{array}{*{20}c} {\mu \frac{{p^z }}{{d_{\max }^x }}(\frac{{{\rm d}dx}}{{{\rm d}px}} - h_{\rm F} (p^x )\frac{{{\rm d}d^x }}{{{\rm d}p^x }} - h'(p^x ))} & {\mu [1 - h_{\rm F} (p^x )]\frac{{d^x }}{{d_{\max }^x }}} \\ 0 & 1 \\ \end{array}} \right].$$

(9.7)

In the worst case and according to [10], (9.7) becomes:

$$ {\mathbf {J}}_{f_{\mathbf {F}} } (p) = - \kappa _0 \left[ {\begin{array}{*{20}c} {2\mu p^z (1/d_{\max }^x + \pi /L)} & {2\mu } \\ 0 & 1 \\ \end{array}} \right]. $$

(9.8)

For${h_{\mbox{\scriptsize{\textsf{\textbf{F}}}}} (p^{x})}=\sin(2\pi p^{x} /L)$,$q_{\mbox{\scriptsize{\textsf{\textbf{F}}}}} =\max \| {\mathbf{J}_{\!\boldsymbol{f}}}_{\!\mbox{\scriptsize{\textsf{\textbf{A}}}}}\|_{2} / \kappa_{0}$ can be quickly numerically computed since the value ofp ^z must be clamped to a maximum$d^{z}_{\mathrm{max}}$.