phd-thesis/1-introduction/related-work/2-wearable-haptics.tex

\section{Augmenting Object Perception with Wearable Haptics}
\label{wearable_haptics}

One of the roles of haptic systems is to render virtual interactions and sensations that are \emph{similar and comparable} to those experienced by the haptic sense with real objects, particularly in a visual \VE \cite{maclean2008it,culbertson2018haptics}.
Moreover, a haptic augmentation system should \enquote{modulating the feel of a real object by virtual [haptic] feedback} \cite{jeon2009haptic}, \ie a touch interaction with a real object whose perception is modified by the addition of virtual haptic feedback.
The haptic system should be hand-held or worn, \eg on the hand, and \enquote{not permanently attached to or integrated in the object} \cite{bhatia2024augmenting}.


\subsection{Level of Wearability}
\label{wearability_level}

Different types of haptic devices can be worn on the hand, but only some of them can be considered wearable.
\textcite{pacchierotti2017wearable} classify them into three levels of wearability, as illustrated in the \figref{pacchierotti2017wearable}.
An increasing wearability resulting in the loss of the system's kinesthetic feedback capability.

\begin{subfigs}{pacchierotti2017wearable}{
        Schematic wearability level of haptic devices for the hand \cite{pacchierotti2017wearable}.
    }[
        \item World-grounded haptic devices are fixed on the environment to provide kinesthetic feedback to the user.
        \item Exoskeletons are body-grounded kinesthetic devices.
        \item Wearable haptic devices are grounded on the point of application of the tactile stimulus.
    ]
    \subfigsheight{38mm}
    \subfig{pacchierotti2017wearable_1}
    \subfig{pacchierotti2017wearable_2}
    \subfig{pacchierotti2017wearable_3}
\end{subfigs}

Haptic research comes from robotics and teleoperation, and historically led to the design of haptic systems that are \emph{world-grounded} to an external support in the environment, such as a table (\figref{pacchierotti2017wearable_1}).
These are robotic arms whose end-effector is either held in the hand or worn on a finger and which simulate interactions with a \VE by providing kinesthetic forces and torques feedback (\figref{pacchierotti2015cutaneous}).
They provide high fidelity haptic feedback but are heavy, bulky and limited to small workspaces \cite{culbertson2018haptics}.

More portable designs have been developed by moving the grounded part to the user's body.
The entire robotic system is thus mounted on the user, forming an exoskeleton capable of providing kinesthetic feedback to the finger, \eg in \figref{achibet2017flexifingers}.
However, it cannot constrain the movements of the wrist and the reaction force is transmitted to the user where the device is grounded (\figref{pacchierotti2017wearable_2}).
Such \emph{body-grounded} devices are often heavy and bulky and cannot be considered wearable.

\textcite{pacchierotti2017wearable} defined that : \enquote{A wearable haptic interface should also be small, easy to carry, comfortable, and it should not impair the motion of the wearer}.
An approach is then to move the grounding point very close to the end-effector (\figref{pacchierotti2017wearable_3}): the interface is limited to cutaneous haptic feedback, but its design is more compact, lightweight, comfortable and portable, \eg in \figref{grounded_to_wearable}.
Moreover, as detailed in \secref{object_properties}, cutaneous sensations are necessary and often sufficient for the perception of the haptic properties of an object explored with the hand, as also argued by \textcite{pacchierotti2017wearable}.

\begin{subfigs}{grounded_to_wearable}{
        Haptic devices for the hand with different wearability levels.
    }[
        \item Teleoperation of a virtual cube grasped with the thumb and index fingers each attached to a grounded haptic device \cite{pacchierotti2015cutaneous}.
        \item A passive exoskeleton for fingers simulating stiffness of a trumpet's pistons \cite{achibet2017flexifingers}.
        \item Manipulation of a virtual cube with the thumb and index fingers each attached with the 3-RSR wearable haptic device \cite{leonardis20173rsr}.
    ]
    \subfigsheight{38mm}
    \subfig{pacchierotti2015cutaneous}
    \subfig{achibet2017flexifingers}
    \subfig{leonardis20173rsr}
\end{subfigs}

% Tradeoff realistic and cost + analogy with sound, Hi-Fi costs a lot and is realistic, but 40$ BT headphone is more practical and enough, as cutaneous feedback without kinesthesic could be enough for wearable haptics and far more affordable and comfortable than world- or body-grounded haptics + cutaneous even better than kine for rendering surface curvature and fine manipulation


\subsection{Wearable Haptic Devices for the Hand}
\label{wearable_haptic_devices}

We present an overview of wearable haptic devices for the hand, following the categories of \textcite{pacchierotti2017wearable}.
The rendering of a haptic device is indeed determined by the nature of the actuators employed, which form the interface between the haptic system and the user's skin, and therefore the types of mechanical stimuli they can supply.
Several actuators are often combined in a haptic device to obtain richer haptic feedback.

\subsubsection{Moving Platforms}
\label{moving_platforms}

The moving platforms translate perpendicularly on the skin to create sensations of contact, pressure and edges \cite{pacchierotti2017wearable}.
Placed under the fingertips, they can come into contact with the skin with different forces, speeds and orientations.
The platform is moved by means of cables, \eg in \figref{gabardi2016new}, or articulated arms, \eg in \figref{perez2017optimizationbased}, activated by motors grounded to the nail \cite{gabardi2016new,perez2017optimizationbased}.
The motors lengthen and shorten the cables or orient the arms to move the platform over 3 \DoFs: two for orientation and one for normal force relative to the finger.
However, these platforms are specifically designed to provide haptic feedback to the fingertip in \VEs, preventing interaction with a \RE.

\subsubsection{Pin and Pneumatic Arrays}
\label{array_actuators}

A pin-array is a surface made up of small, rigid pins arranged very close together in a grid and that can be moved individually.
When placed in contact with the fingertip, it can create sensations of edge, pressure and texture.
The \figref{sarakoglou2012high} shows an example of a pin-array consisting of \numproduct{4 x 4} pins of \qty{1.5}{\mm} diameter and \qty{2}{\mm} height, spaced at \qty{2}{\mm} \cite{sarakoglou2012high}.
Pneumatic systems use a fluid such as air or water to inflate membranes under the skin, creating sensations of contact and pressure \cite{raza2024pneumatically}.
Multiple membranes are often used in a grid to simulate edges and textures, as in the \figref{ujitoko2020development} \cite{ujitoko2020development}.
Although these two types of effector can be considered wearable, their actuation requires a high level of mechanical and electronic complexity that makes the system as a whole not portable.

\begin{subfigs}{normal_actuators}{
        Normal indentation actuators for the fingertip.
    }[
        \item A moving platform actuated with cables \cite{gabardi2016new}.
        \item A moving platform actuated by articulated limbs \cite{perez2017optimizationbased}.
        \item Diagram of a pin-array of tactors \cite{sarakoglou2012high}.
        \item A pneumatic system composed of a \numproduct{12 x 10} array of air cylinders \cite{ujitoko2020development}.
    ]
    \subfigsheight{37mm}
    \subfig{gabardi2016new}
    \subfig{perez2017optimizationbased}
    \subfig{sarakoglou2012high}
    \subfig{ujitoko2020development}
\end{subfigs}

\subsubsection{Tangential Motion Actuators}
\label{tangential_actuators}

Similar in design to the mobile platforms, the tangential motion actuators activate a rigid pin or surface in contact with the fingertip under the finger to create shearing sensation on the skin.
An articulated and motorized arm structure moves the effector in multiple directions over 2 \DoFs parallel to the skin, \eg in \figref{leonardis2015wearable} \cite{leonardis2015wearable}.
Some actuators are capable of both normal and tangential motion over 3 \DoFs on the skin and can also make or break contact with the finger, \eg in \figref{schorr2017fingertip} \cite{schorr2017fingertip}.

\subsubsection{Compression Belts}
\label{belt_actuators}

A simpler alternative approach is to place a belt under the finger, and to actuate it over 2 \DoFs by two motors placed on top of the finger \cite{minamizawa2007gravity}.
By turning in opposite directions, the motors shorten the belt and create a sensation of pressure.
Conversely, by turning simultaneously in the same direction, the belt pulls on the skin, creating a shearing sensation.
The simplicity of this approach allows the belt to be placed anywhere on the hand, leaving the fingertip free to interact with the \RE, \eg the hRing on the proximal phalanx in \figref{pacchierotti2016hring} \cite{pacchierotti2016hring} or Tasbi on the wrist in \figref{pezent2022design} \cite{pezent2022design}.

\begin{subfigs}{tangential_belts}{Tangential motion actuators and compression belts. }[
        \item A skin strech actuator for the fingertip \cite{leonardis2015wearable}.
        \item A 3 \DoF actuator capable of normal and tangential motion on the fingertip \cite{schorr2017fingertip}.
        %\item A shearing belt actuator for the fingertip \cite{minamizawa2007gravity}.
        \item The hRing, a shearing belt actuator for the proximal phalanx of the finger \cite{pacchierotti2016hring}.
        \item Tasbi, a wristband capable of pressure and vibrotactile feedback \cite{pezent2022design}.
    ]
    \subfigsheight{33.5mm}
    \subfig{leonardis2015wearable}
    \subfig{schorr2017fingertip}
    \subfig{pacchierotti2016hring}
    \subfig{pezent2022design}
\end{subfigs}

\subsubsection{Vibrotactile Actuators}
\label{vibrotactile_actuators}

Vibrotactile actuators are the most common and simplest wearable haptic interfaces, and are available as consumer products.
They are small, lightweight and can be placed directly on any part of the hand.
\textcite{choi2013vibrotactile} provided a detailed review.
All vibrotactile actuators are based on the same principle: generating an oscillating motion from an electric current with a frequency and amplitude high enough to be perceived by cutaneous mechanoreceptors.
Several types of vibrotactile actuators are used in haptics, with different trade-offs between size, proposed \DoFs and application constraints.

An \ERM is a \DC motor that rotates an off-center mass when a voltage or current is applied (\figref{precisionmicrodrives_erm}). \ERMs are easy to control, inexpensive and can be encapsulated in a few millimeters cylinder or coin form factor. However, they have only one \DoF because both the frequency and amplitude of the vibration are coupled to the speed of the rotation, \eg low (high) frequencies output at low (high) amplitudes, as shown on \figref{precisionmicrodrives_erm_performances}.

\begin{subfigs}{erm}{Diagram and performance of \ERMs. }[
        \item Diagram of a cylindrical encapsulated \ERM. From Precision Microdrives~\footnotemark.
        \item Amplitude and frequency output of an \ERM as a function of the input voltage.
    ]
    \subfigsheight{45mm}
    \subfig{precisionmicrodrives_erm}
    \subfig{precisionmicrodrives_erm_performances}
\end{subfigs}

\footnotetext{\url{https://www.precisionmicrodrives.com/}}

A \LRA consists of a coil that creates a magnetic field from an \AC to oscillate a magnet attached to a spring, as an audio loudspeaker (\figref{precisionmicrodrives_lra}). They are more complex to control and a bit larger than \ERMs. Each \LRA is designed to vibrate with maximum amplitude at a given resonant frequency, but won't vibrate efficiently at other frequencies, \ie their bandwidth is narrow, as shown on \figref{azadi2014vibrotactile}.
A \VCA is a \LRA but capable of generating vibration at two \DoF, with an independent control of the frequency and amplitude of the vibration on a wide bandwidth. They are larger in size than \ERMs and \LRAs, but can generate more complex renderings.

Piezoelectric actuators deform a solid material when a voltage is applied. They are very small and thin, and allow two \DoFs of amplitude and frequency control. However, they require high voltages to operate thus limiting their use in wearable devices.

\begin{subfigs}{lra}{Diagram and performance of \LRAs. }[
        \item Diagram. From Precision Microdrives~\footnotemarkrepeat.
        \item Force generated by two \LRAs as a function of sine wave input with different frequencies: both their maximum force and resonant frequency are different \cite{azadi2014vibrotactile}.
    ]
    \subfigsheight{50mm}
    \subfig{precisionmicrodrives_lra}
    \subfig{azadi2014vibrotactile}
\end{subfigs}


\subsection{Modifying Perceived Haptic Roughness and Hardness}
\label{tactile_rendering}

Tactile rendering of haptic properties consists in modelling and reproducing virtual tactile sensations comparable to those perceived when interacting with real objects \cite{klatzky2013haptic}.
By adding such tactile rendering as feedback to the touch actions of the hand on a real object \cite{bhatia2024augmenting}, the perception of the object's haptic property can be modified.
The integration of the real and virtual sensations into a single property perception is discussed in more details in \secref{sensations_perception}.
%, both the real and virtual haptic sensations are integrated into a single property perception, as presented in \secref{sensations_perception}, \ie the perceived haptic property is modulated by the added virtual feedback.
In particular, the visual rendering of a touched object can also influence the perception of its haptic properties, \eg by modifying its visual texture in \AR or \VR, as discussed in the \secref{visuo_haptic}.

\textcite{bhatia2024augmenting} categorize the haptic augmentations into three types: direct touch, touch-through, and tool mediated.
In \emph{direct touch}, the haptic device does not cover the interior of the hand to not impair the user to interact with the \RE, and is typically achieved with wearable haptics.
In touch-through and tool-mediated, or \emph{indirect feel-through} \cite{jeon2015haptic}, the haptic device is interposed between the hand and the \RE.
%We are interested in direct touch augmentations with wearable haptics (\secref{wearable_haptic_devices}), as their integration with \AR is particularly promising for free hand interaction with visuo-haptic augmentations.
Many haptic augmentations were first developed with touch-through devices, and some (but not all) were later transposed to direct touch augmentation with wearable haptic devices.
%We also focus on tactile augmentations stimulating the mechanoreceptors of the skin (\secref{haptic_sense}), thus excluding temperature perception, as they are the most common existing haptic interfaces.

As we chose in \secref{object_properties} to focus on the haptic perception of the roughness and hardness of objects, we overview bellow the methods to modify the perception of these properties.
Of course, wearable haptics can also be used in direct touch context to modify the perceived friction \cite{konyo2008alternative,salazar2020altering}, weight \cite{minamizawa2007gravity}, or local deformation \cite{salazar2020altering} of real objects, but they are rare \cite{bhatia2024augmenting} and will not be detailed here.

% \cite{klatzky2003feeling} : rendering roughness, friction, deformation, temperatures
% \cite{girard2016haptip} : renderings with a tangential motion actuator

\subsubsection{Roughness}
\label{texture_rendering}

To modify the perception of haptic roughness (or texture, see \secref{roughness}) of a real object, vibrations are typically provided to the skin by the wearable haptic device when running the finger over the surface.
This is because running the finger or a tool on a textured surface generates pressures and vibrations (\secref{roughness}) at frequencies that are too high for rendering capabilities of most haptic devices \cite{campion2005fundamental,culbertson2018haptics}.
Two main approaches are used to render virtual textures: \emph{simulation models} and \emph{data-driven models} \cite{klatzky2013haptic,culbertson2018haptics}.

\paragraph{Simulation Models}

Simulations of virtual textures are based on the physics of the interaction between the finger and the surface, and are used to generate the vibrations that the user feels when running the finger over the surface.

Early renderings of virtual textures consisted of modelling the surface with a periodic function

As more traditional force feedback systems are unable to accurately render such micro-details on a simulated surface, vibrotactile devices attached to the end effector instead generate vibrations to simulate interaction with the virtual texture \cite{campion2005fundamental,culbertson2018haptics}.
High-fidelity force feedback devices can reproduce patterned textures with great precision and provide similar perceptions to real textures, but they are expensive, have a limited workspace, and impose to hold a probe to explore the texture \cite{unger2011roughness}.

The perceived roughness of real surfaces can be then modified when touched by a tool with a vibrotactile actuator attached \cite{culbertson2014modeling,ujitoko2019modulating} or directly with the finger wearing the vibrotactile actuator \cite{asano2015vibrotactile}, creating a haptic texture augmentation.
Of course, the fingertip skin is not deformed by the virtual texture and only vibrations are felt, but it has been shown that the vibrations produced on the fingertip skin running over a real surface are texture specific and similar between individuals \cite{delhaye2012textureinduced,manfredi2014natural}.
A common method vibrotactile rendering of texture is to use a sinusoidal signal whose frequency is modulated by the finger position or velocity \cite{asano2015vibrotactile,friesen2024perceived,strohmeier2017generating,ujitoko2019modulating}.

\paragraph{Data-driven Models}

Because simulations of virtual textures can be very complex to design and to render in real-time, direct capture of real textures have been used instead to model the produced vibrations \cite{culbertson2018haptics}.

\textcite{okamura1998vibration} first dragged a stylus over sandpapers and patterned surfaces to measure the vibrations produced by the interaction.
They found that the contact vibrations with patterns could be modelled as exponential decaying sine waves (\eqref{contact_transient}) that depend on the normal force and scanning velocity of the stylus on the surface.
This technique was employed by \textcite{ando2007fingernailmounted} to augment a smooth sheet of paper with a virtual patterned texture: With a \LRA mounted on the nail, they rendered the virtual contacts of the finger with \qty{20}{\ms} vibration impulses at \qty{130}{\Hz} (\figref{ando2007fingernailmounted}).
Participants matched the virtual textures to real ones, with \qty{0.25}{\mm} height and \qtyrange{1}{10}{\mm} width, but systematically overestimated the virtual width to be \qty{4}{\mm} longer.

More models have been developed to capture "natural" (such as sandpapers) textures \cite{guruswamy2011iir} with many force and speed measures while staying compact and capable of real-time rendering \cite{romano2012creating,culbertson2014modeling}.
Such models are capable from the user's measurements of velocity and force as inputs to interpolate and generate a virtual texture to render as vibrations (\secref{vibrotactile_actuators}).
This led the release of the Penn Haptic Texture Toolkit (HaTT) database, a public set of stylus records and models of 100 haptic textures \cite{culbertson2014one}.
A similar database but captured directly from the fingertip was released very recently \cite{balasubramanian2024sens3}.
One limitation of these data-driven models is that they can render only isotropic textures: their capture does not depend on the position of the measure, and the rendering is the same whatever the direction of the movement.
Alternative models have been proposed to both render isotropic and patterned textures \cite{chan2021hasti}.

When comparing real textures felt through a stylus with their virtual models rendered with a voice-coil actuator attached to the stylus (\figref{culbertson2012refined}), the virtual textures were found to accurately recreated roughness perception, but hardness and friction were not rendered properly \cite{culbertson2014modeling}.
\textcite{culbertson2015should} further showed that the perceived realism of the virtual textures, and similarity to the real textures, depended mostly on the user's speed but not on the user's force as inputs to the model, \ie respond to velocity is sufficient to render isotropic virtual textures.

\begin{subfigs}{textures_rendering_data}{Augmentating haptic texture perception with voice-coil actuators. }[
        \item Increasing and decreasing the perceived roughness of a real patterned texture in direct touch \cite{asano2015vibrotactile}.
        \item Comparing real patterned texture with virtual texture augmentation in direct touch \cite{friesen2024perceived}.
        \item Rendering virtual contacts in direct touch with the virtual texture \cite{ando2007fingernailmounted}.
        \item Rendering an isotropic virtual texture over a real surface while sliding a hand-held stylus on it \cite{culbertson2012refined}.
    ]
    \subfigsheight{35mm}
    \subfig{asano2015vibrotactile}
    \subfig{friesen2024perceived}
    \subfig{ando2007fingernailmounted}
    \subfig{culbertson2012refined}
\end{subfigs}


\subsubsection{Hardness}
\label{hardness_rendering}

The perceived hardness (\secref{hardness}) of a real surface can be modified by rendering forces or vibrations.

\paragraph{Modulating Forces}

When tapping or pressing a real object, the perceived stiffness $\tilde{k}$ of its surface can be modulated with force feedback \cite{jeon2015haptic}.
This was first proposed by \textcite{jeon2008modulating} who augmented a real surface tapped in 1 \DoF with a grounded force-feedback device held in hand (\figref{jeon2009haptic_1}).
When the haptic end-effector contacts the object at time $t$, the object's surface deforms by displacement $x_r(t)$ and opposes a real reaction force $f_r(t)$.
The virtual force of the device $\tilde{f_r}(t)$ is then controlled to:
\begin{equation}{stiffness_augmentation}
    \tilde{f_r}(t) = f_r(t) - \tilde{k} x_r(t)
\end{equation}
A force sensor embedded in the device measures the reaction force $f_r(t)$.
The displacement $x_r(t)$ is estimated with the reaction force and tapping velocity using a pre-defined model of various materials, as described by \textcite{jeon2011extensions}.
As shown in \figref{jeon2009haptic_2}, the force $\tilde{f_r}(t)$ perceived by the user being modulated, but not the displacement $x_r(t)$, the perceived stiffness is $\tilde{k}(t)$.
This stiffness augmentation technique was then extended to enable tapping and pressing with 3 \DoFs \cite{jeon2010stiffness}, to render friction and weight augmentations \cite{jeon2011extensions}, and to grasping and squeezing the real object with two contact points \cite{jeon2012extending}.

\begin{subfigs}{stiffness_rendering_grounded}{Augmenting the perceived stiffness of a real surface with a hand-held force-feedback device. }[%
        \item Diagram of a user tapping the surface \cite{jeon2009haptic}.
        \item Displacement-force curves of a real rubber ball (dashed line) and when its perceived stiffness $\tilde{k}$ is modulated \cite{jeon2009haptic}.
    ]
    \subfig[0.38]{jeon2009haptic_1}
    \subfig[0.42]{jeon2009haptic_2}
\end{subfigs}

\textcite{detinguy2018enhancing} transposed this stiffness augmentation technique with the hRing device (\secref{belt_actuators}): While pressing a real piston with the fingertip by displacement $x_r(t)$, the belt compressed the finger by a virtual force $\tilde{k}\,x_r(t)$ where $\tilde{k}$ is the added stiffness (\eqref{stiffness_augmentation}), increasing the perceived stiffness of the piston (\figref{detinguy2018enhancing}).
%This enables to \emph{increase} the perceived stiffness of the real piston up to \percent{+14}.
More importantly, the augmentation proved to be robust to the placement of the device, as the increased stiffness was perceived the same on the fingertip, the middle phalanx and the proximal.
Conversely, the technique allowed to \emph{decrease} the perceived stiffness by compressing the phalanx prior the contact and diminish the belt pressure as the user pressed the piston \cite{salazar2020altering}.
\textcite{tao2021altering} proposed instead to restrict the deformation of the fingerpad by pulling a hollow frame around it to decrease perceived stiffness (\figref{tao2021altering}): it augments the finger contact area thus the perceived Young modulus of the object (\secref{hardness}).

\begin{subfigs}{stiffness_rendering_wearable}{Modifying the perceived stiffness with wearable pressure devices. }[%
        \item Modify the perceived stiffness of a piston by pressing the finger during or prior the contact \cite{detinguy2018enhancing,salazar2020altering}.
        \item Decrease perceived stiffness of hard object by restricting the fingerpad deformation \cite{tao2021altering}.
    ]
    \subfigsheight{35mm}
    \subfig{detinguy2018enhancing}
    \subfig{tao2021altering}
\end{subfigs}


\paragraph{Vibrations Augmentations}

\textcite{okamura2001realitybased} measured impact vibrations $Q(t)$ when tapping on real objects and found they can be modelled as exponential decaying sine wave:
\begin{equation}{contact_transient}
    Q(t) = A \, |v_{in}| \, e^{- \tau t} sin(2 \pi f t)
\end{equation}
With $A$ the amplitude slope, $\tau$ the sine decay rate and $f$ the sine frequency, which are measured material properties, and $v_{in}$ the impact velocity.
It has been shown that these material properties perceptually express the stiffness (\secref{hardness}) of real \cite{higashi2019hardness} and virtual surface \cite{choi2021perceived}.
Therefore, when contacting or tapping a real object through an indirect feel-through interface that provide such vibrations (\figref{choi2021augmenting_control}) using a voice-coil (\secref{vibrotactile_actuators}), the perceived stiffness can be increased or decreased \cite{kuchenbecker2006improving,hachisu2012augmentation,choi2021augmenting}, \eg sponge feeling stiffer or wood feeling softer (\figref{choi2021augmenting_results}).
A challenge with this technique is to provide the vibration feedback at the right time, to be felt simultaneous with the real contact \cite{park2023perceptual}.

\begin{subfigs}{contact_vibrations}{Augmenting perceived stiffness using vibrations when touching a real surface \cite{choi2021augmenting}. }[%
        %\item Experimental setup with a voice-coil actuator attached to a touch-through interface.
        \item Voltage inputs (top) to the voice-coil for soft, medium and hard vibrations, with the corresponding displacement (middle) and force (bottom) outputs of the actuator.
        \item Perceived intensity of stiffness of real sponge ("Sp") and wood ("Wd") surfaces without added vibrations ("N") and modified by soft ("S"), medium ("M") and hard ("H") vibrations.
    ]
    %\subfig[.15]{choi2021augmenting_demo}
    \subfigsheight{50mm}
    \subfig{choi2021augmenting_control}
    \subfig{choi2021augmenting_results}
\end{subfigs}

Vibrations on contact have been employed with wearable haptics but, to the best of our knowledge, only to render \VOs \cite{pezent2019tasbi,teng2021touch,sabnis2023haptic}.
We describe them in the \secref{vhar_haptics}.

%A promising alternative approach
%\cite{kildal20103dpress}

%\begin{subfigs}{vibtration_grains}{Augmenting perceived stiffness of a real surface with vibrations. }
%    \subfigsheight{35mm}
%    \subfig{sabnis2023haptic_device}
%    \subfig{sabnis2023haptic_control}
%\end{subfigs}

%\textcite{choi2021perceived} combined and compared these two rendering approaches (spring-damper and exponential decaying sinusoids) but to render purely virtual surfaces.
%They found that the perceived intensity of the virtual hardness $\tilde{h}$ followed a power law, similarly to \eqref{hardness_intensity}, with the amplitude $a$, the %frequency $f$ and the damping $b$ of the vibration, but not the decay time $\tau$.
%\cite{park2023perceptual}

%\subsubsection{Friction}
%\label{friction_rendering}

%\cite{konyo2008alternative}
%\cite{provancher2009fingerpad}
%\cite{smith2010roughness}
%\cite{jeon2011extensions}
%\cite{salazar2020altering}
%\cite{yim2021multicontact}

%\subsubsection{Weight}
%\label{weight_rendering}

%\cite{minamizawa2007gravity}
%\cite{minamizawa2008interactive}
%\cite{jeon2011extensions}
%\cite{choi2017grabity}
%\cite{culbertson2017waves}


\subsection{Conclusion}
\label{wearable_haptics_conclusion}

%, unlike most previous actuators that are designed specifically for fingertips and would require mechanical adaptation to be placed on other parts of the hand.
% thanks to the vibration propagation and the sensory capabilities distributed throughout the skin, they can be placed without adaption and on any part of the hand