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Erwan Normand
2024-09-16 09:15:19 +02:00
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1-introduction/related-work/1-haptic-hand.tex
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@@ -253,19 +253,20 @@ When the surface is touched or tapped, vibrations are also transmitted to the sk
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}.
The \emph{stiffness} $k$ of an object is the ratio between the applied force $F$ and the resulting \emph{displacement} $\Delta l$ of the surface:
The \emph{stiffness} $k$ of an object is the ratio between the applied force $F$ and the resulting \emph{displacement} $D$ of the surface:
\begin{equation}
\label{eq:stiffness}
k = \frac{F}{\Delta l}
k = \frac{F}{D}
\end{equation}
The \emph{elasticity} of an object is expressed by its Young's modulus $Y$, which is the ratio between the applied pressure (the force $F$ per unit area $A$) and the resulting deformation $\Delta l / l$ (the relative displacement) of the object:
The \emph{elasticity} of an object is expressed by its Young's modulus $Y$, which is the ratio between the applied pressure (the force $F$ per unit area $A$) and the resulting deformation $D / l$ (the relative displacement) of the object:
\begin{equation}
\label{eq:young_modulus}
Y = \frac{F / A}{\Delta l / l}
Y = \frac{F / A}{D / l}
\end{equation}
\begin{subfigs}{stiffness_young}{Perceived hardness of an object by finger pressure. }[
\item Diagram of an object with a stiffness coefficient $k$ and a length $l$ compressed by a force $F$ on an area $A$ by a distance $\Delta l$.
\item Diagram of an object with a stiffness coefficient $k$ and a length $l$ compressed by a force $F$ on an area $A$ by a distance $D$.
\item Identical perceived hardness intensity between Young's modulus (horizontal axis) and stiffness (vertical axis). The dashed and dotted lines indicate the objects tested, the arrows the correspondences made between these objects, and the grey lines the predictions of the quadratic relationship~\cite{bergmanntiest2009cues}.
]
\subfig[.3]{hardness}
@@ -374,4 +375,4 @@ Haptic perception and manipulation of objects with the hand involves several sim
Exploratory movements of the hand are performed on contact with the object to obtain multiple sensory information from several cutaneous and kinaesthetic receptors.
These sensations express physical parameters in the form of perceptual cues, which are then integrated to form a perception of the property being explored.
It is often the case that one perceptual cue is particularly important in the perception of a property, but perceptual constancy is possible by compensating for its absence with others.
In turn, these perceptions help to guide the grasping and manipulation of the object by adapting the grasp type and the forces applied to the shape of the object and the task to be performed.
In turn, these perceptions help to guide the grasping and manipulation of the object by adapting the grasp type and the forces applied to the shape of the object and the task to be performed.