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Erwan Normand
2024-09-20 16:50:31 +02:00
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1-introduction/related-work/1-haptic-hand.tex
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@@ -194,9 +194,9 @@ This allows us to read Braille~\cite{lederman2009haptic}.
However, the speed of exploration affects the perceived intensity of micro-roughness~\cite{bensmaia2003vibrations}.
To establish the relationship between spacing and intensity for macro-roughness, patterned textured surfaces were manufactured: as a linear grating (on one axis) composed of ridges and grooves, \eg in \figref{lawrence2007haptic_1}~\cite{lederman1972fingertip,lawrence2007haptic}, or as a surface composed of micro conical elements on two axes, \eg in \figref{klatzky2003feeling_1}~\cite{klatzky2003feeling}.
As shown in \figref{lawrence2007haptic_2}, there is a quadratic relationship between the logarithm of the perceived roughness intensity $R$ and the logarithm of the space between the elements $s$ ($a$, $b$ and $c$ are empirical parameters to be estimated)~\cite{klatzky2003feeling}:
As shown in \figref{lawrence2007haptic_2}, there is a quadratic relationship between the logarithm of the perceived roughness intensity $r$ and the logarithm of the space between the elements $s$ ($a$, $b$ and $c$ are empirical parameters to be estimated)~\cite{klatzky2003feeling}:
\begin{equation}{roughness_intensity}
log(R) \sim a \, log(s)^2 + b \, s + c
log(r) \sim a \, log(s)^2 + b \, s + c
\end{equation}
A larger spacing between elements increases the perceived roughness, but reaches a plateau from \qty{\sim 5}{\mm} for the linear grating~\cite{lawrence2007haptic}, while the roughness decreases from \qty{\sim 2.5}{\mm}~\cite{klatzky2003feeling} for the conical elements.
@@ -230,7 +230,7 @@ For grid textures, as illustrated in \figref{delhaye2012textureinduced}, the rat
\lambda \sim \frac{v}{f_p}
\end{equation}
The vibrations generated by exploring natural textures are also very specific to each texture and similar between individuals, making them identifiable by vibration alone~\cite{greenspon2020effect}.
The vibrations generated by exploring natural textures are also very specific to each texture and similar between individuals, making them identifiable by vibration alone~\cite{manfredi2014natural,greenspon2020effect}.
This shows the importance of vibration cues even for macro textures and the possibility of generating virtual texture sensations with vibrotactile rendering.
\fig[0.55]{delhaye2012textureinduced}{Speed of finger exploration (horizontal axis) on grating textures with different periods $\lambda$ of spacing (in color) and frequency of the vibration intensity peak $f_p$ propagated in the wrist (vertical axis)~\cite{delhaye2012textureinduced}.}
@@ -249,7 +249,7 @@ By tapping on a surface, metal will be perceived as harder than wood.
If the surface returns to its original shape after being deformed, the object is elastic (like a spring), otherwise it is plastic (like clay).
When the finger presses on an object (\figref{exploratory_procedures}), its surface will move and deform with some resistance, and the contact area of the skin will also expand, changing the pressure distribution.
When the surface is touched or tapped, vibrations are also transmitted to the skin.
When the surface is touched or tapped, vibrations are also transmitted to the skin~\cite{higashi2019hardness}.
Passive touch (without voluntary hand movements) and tapping allow a perception of hardness as good as active touch~\cite{friedman2008magnitude}.
Two physical properties determine the haptic perception of hardness: its stiffness and elasticity, as shown in \figref{hardness}~\cite{bergmanntiest2010tactual}.
@@ -276,6 +276,10 @@ With finger pressure, a relative difference (the \emph{Weber fraction}) of \perc
However, in the absence of pressure sensations (by placing a thin disc between the finger and the object), the necessary relative difference becomes much larger (Weber fraction of \percent{\sim 50}).
Thus, the perception of hardness relies on \percent{90} on surface deformation cues and \percent{10} on displacement cues.
In addition, an object with low stiffness but high Young's modulus can be perceived as hard, and vice versa, as shown in \figref{bergmanntiest2009cues}.
Finally, when pressing with the finger, the perceived hardness intensity $h$ follows a power law with the stiffness $k$~\cite{harper1964subjective}:
\begin{equation}{hardness_intensity}
h = k^{0.8}
\end{equation}
%En pressant du doigt, l'intensité perçue (subjective) de dureté suit avec la raideur une relation selon une loi de puissance avec un exposant de \num{0.8}~\cite{harper1964subjective}, \ie quand la raideur double, la dureté perçue augmente de \num{1.7}.
%\textcite{bergmanntiest2009cues} ont ainsi observé une relation quadratique d'égale intensité perçue de dureté, comme illustré sur la \figref{bergmanntiest2009cues}.