\section{User Study}
\label{method}

Providing haptic feedback during free-hand manipulation in \AR is not trivial, as wearing haptic devices on the hand might affect the tracking capabilities of the system.
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Moreover, it is important to leave the user capable of interacting with both virtual and real objects, avoiding the use of haptic interfaces that cover the fingertips or palm.
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For this reason, it is often considered beneficial to move the point of application of the haptic rendering elsewhere on the hand.% (\secref{haptics}).

This second experiment aims to evaluate whether a visuo-haptic hand rendering affects the performance and user experience of manipulation of virtual objects with bare hands in \AR.
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The chosen visuo-haptic hand renderings are the combination of the two most representative visual hand renderings established in the first experiment, \ie Skeleton and None, described in \secref[visual_hand]{hands}, with two contact vibration techniques provided at four delocalized positions on the hand.

\subsection{Vibrotactile Renderings}
\label{vibration}

The vibrotactile hand rendering provided information about the contacts between the virtual object and the thumb and index fingers of the user, as they were the two fingers most used for grasping in our first experiment.
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We evaluated both the delocalized positioning and the contact vibration technique of the vibrotactile hand rendering.

\subsubsection{Vibrotactile Positionings}
\label{positioning}

\fig[0.30]{method/locations}{%
  Experiment \#2: setup of the vibrotactile devices.
  %
  To ensure minimal encumbrance, we used the same two motors throughout the experiment, moving them to the considered positioning before each new experimental block (in this case, on the co-located proximal phalanges, \emph{Prox}).
  %
  Thin self-gripping straps were placed on the five considered positionings during the entirety of the experiment.
}

\begin{itemize}
  \item \textit{Fingertips (Tips):} Vibrating actuators were placed right above the nails, similarly to \cite{ando2007fingernailmounted}. This is the positioning closest to the fingertips.
    %
  \item \textit{Proximal Phalanges (Prox):} Vibrating actuators were placed on the dorsal side of the proximal phalanges, similarly to \cite{maisto2017evaluation, meli2018combining, chinello2020modular}.
    %
  \item \textit{Wrist (Wris):} Vibrating actuators providing contacts rendering for the index and thumb were placed on ulnar and radial sides of the wrist, similarly to \cite{pezent2019tasbi, palmer2022haptic, sarac2022perceived}.
    %
  \item \textit{Opposite fingertips (Oppo):} Vibrating actuators were placed on the fingertips of contralateral hand, also above the nails, similarly to \cite{prattichizzo2012cutaneous, detinguy2018enhancing}.
    %
  \item \textit{Nowhere (Nowh):} As a reference, we also considered the case where we provided no vibrotactile rendering.
\end{itemize}

\subsubsection{Contact Vibration Techniques}
\label{technique}

When a fingertip contacts the virtual cube, we activate the corresponding vibrating actuator.
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We considered two representative contact vibration techniques, \ie two ways of rendering such contacts through vibrations:
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\begin{itemize}
  \item \textit{Impact (Impa):} a \qty{200}{\ms}--long vibration burst is applied when the fingertip makes contact with the object; the amplitude of the vibration is proportional to the speed of the fingertip at the moment of the contact.
  \item \textit{Distance (Dist):} a continuous vibration is applied whenever the fingertip is in contact with the object; the amplitude of the vibration is proportional to the interpenetration between the fingertip and the virtual cube surface.
\end{itemize}
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The implementation of these two techniques have been tuned according to the results of a preliminary experiment.
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Three participants were asked to carry out a series of push and grasp tasks similar to those used in the actual experiment.
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Results showed that 95~\% of the contacts between the fingertip and the virtual cube happened at speeds below \qty{1.5}{\m\per\s}.
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We also measured the perceived minimum amplitude to be 15~\% (\qty{0.6}{\g}) of the maximum amplitude of the motors we used.
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For this reason, we designed the Impact vibration technique (Impa) so that contact speeds from \qtyrange{0}{1.5}{\m\per\s} are linearly mapped into \qtyrange{15}{100}{\%} amplitude commands for the motors.
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Similarly, we designed the distance vibration technique (Dist) so that interpenetrations from \qtyrange{0}{2.5}{\cm} are linearly mapped into \qtyrange{15}{100}{\%} amplitude commands for the motors, recalling that the virtual cube has an edge of \qty{5}{\cm}.

\subsection{Experimental Design}
\label{design}

\begin{subfigs}{tasks}{The two manipulation tasks of the user study. }[
    Both pictures show the cube to manipulate in the middle (\qty{5}{\cm} and opaque) and the eight possible targets to reach (\qty{7}{\cm} cube and semi-transparent).
    Only one target at a time was shown during the experiments.
  ][
  \item Pushing a virtual cube along a table toward a target placed on the same surface.
  \item Grasping and lifting a virtual cube toward a target placed on a \qty{20}{\cm} higher plane.
  ]
  \subfig[0.23]{method/task-push}
  \subfig[0.23]{method/task-grasp}
\end{subfigs}

\begin{subfigs}{push_results}{Results of the grasp task performance metrics. }[
    Geometric means with bootstrap 95~\% \CI for each vibrotactile positioning (a, b and c) or visual hand rendering (d)
    and Tukey's \HSD pairwise comparisons: *** is \pinf{0.001}, ** is \pinf{0.01}, and * is \pinf{0.05}.
  ][
  \item Time to complete a trial.
  \item Number of contacts with the cube.
  \item Mean time spent on each contact.
  \item Mean time spent on each contact.
  ]
  \subfig[0.24]{results/Push-CompletionTime-Location-Overall-Means}
  \subfig[0.24]{results/Push-Contacts-Location-Overall-Means}
  \subfig[0.24]{results/Push-TimePerContact-Location-Overall-Means}
  \subfig[0.24]{results/Push-TimePerContact-Hand-Overall-Means}
\end{subfigs}

We considered the same two tasks as in Experiment \#1, described in \secref[visual_hand]{tasks}, that we analyzed separately, considering four independent, within-subject variables:

\begin{itemize}
  \item \emph{{Vibrotactile Positioning}:} the five positionings for providing vibrotactile hand rendering of the virtual contacts, as described in \secref{positioning}.
  \item \emph{Contact Vibration Technique}: the two contact vibration techniques, as described in \secref{technique}.
  \item \emph{visual Hand rendering}: two visual hand renderings from the first experiment, Skeleton (Skel) and None, as described in \secref[visual_hand]{hands}; we considered Skeleton as it performed the best in terms of performance and perceived effectiveness and None as reference.
  \item \emph{Target}: we considered target volumes located at NW and SW during the Push task, and at NE, NW, SW, and SE during the Grasp task (\figref{tasks}); we considered these targets because they presented different difficulties.
\end{itemize}

To account for learning and fatigue effects, the positioning of the vibrotactile hand rendering (positioning) was counter-balanced using a balanced \numproduct{10 x 10} Latin square.
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In these ten blocks, all possible Technique \x Hand \x Target combination conditions were repeated three times in a random order.
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As we did not find any relevant effect of the order in which the tasks were performed in the first experiment, we fixed the order of the tasks: first, the Push task and then the Grasp task.

This design led to a total of 5 vibrotactile positionings \x 2 vibration contact techniques \x 2 visual hand rendering \x (2 targets on the Push task + 4 targets on the Grasp task) \x 3 repetitions $=$ 420 trials per participant.

\subsection{Apparatus and Protocol}
\label{apparatus}

Apparatus and protocol were very similar to the first experiment, as described in \secref[visual_hand]{apparatus} and \secref[visual_hand]{protocol}, respectively.
%
We report here only the differences.

We employed the same vibrotactile device used by \cite{devigne2020power}.
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It is composed of two encapsulated Eccentric Rotating Mass (ERM) vibration motors (Pico-Vibe 304-116, Precision Microdrive, UK).
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They are small and very light (\qty{5}{\mm} \x \qty{20}{\mm}, \qty{1.2}{\g}) actuators capable of vibration frequencies from \qtyrange{120}{285}{\Hz} and
amplitudes from \qtyrange{0.2}{1.15}{\g}.
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They have a latency of \qty{20}{\ms} that we partially compensated for at the software level with slightly larger colliders to trigger the vibrations very close the moment the finger touched the cube.
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These two outputs vary linearly together, based on the tension applied.
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They were controlled by an Arduino Pro Mini (3.3 V) and a custom board that delivered the tension independently to each motor.
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A small \qty{400}{mAh} Li-ion battery allowed for 4 hours of constant vibration at maximum intensity.
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A Bluetooth module (RN42XV module, Microchip Technology Inc., USA) mounted on the Arduino ensured wireless communication with the HoloLens~2.

To ensure minimal encumbrance, we used the same two motors throughout the experiment, moving them to the considered positioning before each new block.
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Thin self-gripping straps were placed on the five positionings, with an elastic strap stitched on top to place the motor, as shown in \figref{method/locations}.
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The straps were fixed during the entirety of the experiment to ensure similar hand tracking conditions.
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We confirmed that this setup ensured a good transmission of the rendering and guaranteed a good hand tracking performance, that was measured to be constant (\qty{15}{\ms}) with and without motors, regardless their positioning.
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The control board was fastened to the arm with an elastic strap.
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Finally, participants wore headphones diffusing brown noise to mask the sound of the vibrotactile motors.

We improved the hand tracking performance of the system by placing on the table a black sheet that absorbs the infrared light as well as placing the participants in front of a wall to ensure a more constant exposure to the light.
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We also made grasping easier by adding a grasping helper, similar to UltraLeap's Physics Hands.\footnoteurl{https://docs.ultraleap.com/unity-api/Preview/physics-hands.html}.
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When a phalanx collider of the tracked hand contacts the virtual cube,
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a spring with a low stiffness is created and attached between the cube and the collider.
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The spring pulls gently the cube toward the phalanxes in contact with the object so as to help maintain a natural and stable grasp.
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When the contact is lost, the spring is destroyed.
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Preliminary tests confirmed this approach.

\subsection{Collected Data}
\label{metrics}

During the experiment, we collected the same data as in the first experiment, see \secref[visual_hand]{metrics}.
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At the end of the experiment, participants were asked if they recognized the different contact vibration techniques.
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They then rated the ten combinations of Positioning \x Technique using a 7-item Likert scale (1=Not at all, 7=Extremely):
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\emph{(Vibration Rating)} How much do you like each vibrotactile rendering? %
\emph{(Workload)} How demanding or frustrating was each vibrotactile rendering? %
\emph{(Usefulness)} How useful was each vibrotactile rendering? %
\emph{(Realism)} How realistic was each vibrotactile rendering?
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Finally, they rated the ten combinations of Positioning \x Hand on a 7-item Likert scale (1=Not at all, 7=Extremely): %
\emph{(positioning \x Hand Rating)} How much do you like each combination of vibrotactile location for each visual hand rendering?

\subsection{Participants}
\label{participants}

Twenty subjects participated in the study (mean age = 26.8, SD = 4.1; 19~males, 1~female).
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One was left-handed, while the other nineteen were right-handed. They all used their dominant hand during the trials.
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They all had a normal or corrected-to-normal vision.
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Thirteen subjects participated also in the previous experiment.

Participants rated their expertise (\enquote{I use it more than once a year}) with \VR, \AR, and haptics in a pre-experiment questionnaire.
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There were twelve experienced with \VR, eight experienced with \AR, and ten experienced with haptics.
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VR and haptics expertise were highly correlated (\pearson{0.9}), as well as \AR and haptics expertise (\pearson{0.6}).
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Other expertise correlations were low ($r<0.35$).