A Trajectory Model for Desktop-Scale Hand Redirection in Virtual Reality

Abstract

In Virtual Reality, visuo-haptic illusions such as hand redirection introduce a discrepancy between the user's hand and its virtual avatar. This visual shift can be used, for instance, to provide multiple virtual haptic objects through a single physical proxy object. This lowcost approach improves the sense of presence, however, it is unclear how these illusions impact the hand trajectory and if there is a relationship between trajectory and the detection of illusion. In this paper, we present an empirical model predicting the hand trajectory as a function of the redirection. It relies on a cubic Bézier curve with 4 control points. We conduct a two alternative forced choice (2AFC) experiment to calibrate and validate our model. Results show that (1) our model predicts well the hand trajectory of each individual using a single parameter; (2) the hand trajectory better explains the detection of the illusion than the amplitude of the redirection alone; (3) a user specific calibration allows to predict per-user redirected trajectories and detection probabilities. Our findings provide a better understanding of visuo-haptic illusions and how they impact the user's movements. As such they may provide foundations to design novel interaction techniques, e.g. interacting in a scene with multiple physical obstacles.

Generalizing the Hand Redirection Function in Virtual Reality

“…This implementation can be seen on the left panel of figure 1. In an other implementation, the virtual hand position is set by rotating the virtual hand around the starting position using the angle formed by the real target, the starting position and the virtual target [24,35]. This implementation can be seen on the right panel of figure 1.…”

“…Different experimental protocols have been used to determine the detection threshold. The most common is the 2 Alternative Forced Choice (2AFC) [3,12,17,24,27,35]: for each trial, the participant is exposed to the illusion for a given parameter value. At the end of the trial, the participant is asked to indicate in which direction their virtual hand is compared to their real hand.…”

“…We focus on second-order polynomials illustrated in figure 3. The experimental protocol is similar to Lebrun et al [24] and Zenner et al [35] where participants realize a pointing task in VR. After each repetition, participants select a Two Alternative Forced Choice (2AFC) about the direction of redirection (Left or Right) as well as if they detected the illusion (Yes or No).…”

Généralisation de la Fonction de Redirection de la Main en Réalité Virtuelle

“…On vérifie que lorsque 𝑑 = 𝐷 (c.a.d lorsque la main réelle est à l'Origine), les mains virtuelle et réelle sont à la même position (Δ 𝑀 = 0). Certains travaux [23,32] décrivent le décalage entre la main réelle et la main virtuelle en fonction de l'angle créé par les cibles réelle et virtuelle autour de la position de départ, plutôt que 𝐷 et ì 𝜆. Cependant les deux formalisations sont équivalentes (comme le montre la figure 1).…”

“…Plusieurs protocoles expérimentaux ont été proposées pour déterminer ce seuil de détection. Le plus utilisé est probablement le protocole de choix à deux alternatives forcées (2AFC) [3,12,16,23,26,32] : à chaque essai le participant est exposé à l'illusion avec une valeur différente du paramètre étudié. À la fin de l'essai, le participant indique dans quelle direction il pense que la main virtuelle a été déplacée par rapport à la main réelle (et cela, même si aucune illusion a été exposée).…”