Gael Plantard
email: plantard@univ-perp.fr

Chloé Dezani

Enrique Ribeiro

Vincent Goetz

Modelling heterogeneous photocatalytic oxidation using suspended TiO 2 in a photoreactor working in continuous mode: application to dynamic irradiation conditions simulating typical days of July and February

2) , Brice REOYO-

adsorption capacity at equilibrium kg.kg -1 q m maximum monolayer adsorption capacity kg•kg -1 C e the equilibrium concentration kg.m -3 b the constant related to energy of adsorption m [START_REF] Ternes | [END_REF] .kg -1 m v the flow rate m [START_REF] Ternes | [END_REF] .s -1 C i the concentration at the inlet of the reactor kg.m -3 C 0 the concentration at the outlet of the reactor kg.m -3 V r the volume of the photoreactor m -3 V T the volume of the system including the loop and reactor m -3  r photoreaction rate kg.m -3 .s -1 α constant of the photoreaction m [START_REF]Water Framework Directive[END_REF] .J -1 β parameter modulating reaction rate with respect to concentration m [START_REF] Ternes | [END_REF] .kg -1 γ parameter modulating reaction rate with respect to irradiation m 2 .W -1 τ the residence time s τ irr the irradiation time s k the number of experimental data (-)

INTRODUCTION

It is now well established that organic compounds are a significant source of pollution and a very high risk to human health [1][START_REF]Water Framework Directive[END_REF][START_REF] Ternes | [END_REF] . To overcome the shortcomings of biodegradation-based processes, a number of innovative technologies [4][5][6][7][8][9][10][11][12][13][14] have been developed to eliminate biorecalcitrant organic pollutants, microorganisms, and more. In this context, compared to socalled tertiary treatment techniques, advanced oxidation processes (AOPs) hold huge promise and are particularly effective at removing persistent organic compounds in wastewater.

Membrane and adsorption processes can offer technical solutions to fix pollutants but not to degrade them, [START_REF] Stefan | Fundamentals and Applications IWA publishing[END_REF][START_REF] Wu | [END_REF] whereas photo-oxidation presents three significant advantages: lowtemperature operation, no chemical additives, and-crucially-the possibility to use solar energy to activate the photochemical process [17] . In heterogeneous photocatalysis based on the use of radiation, the highly oxidizing species are produced by a solid photocatalyst under UV irradiation. As a result, when combined with direct use of solar power, [9] this process is almost energy-self-sufficient and makes it possible to design a water treatment process that is simple, robust and inexpensive to install and operate [10][11][12][13] . In 2002, on the PSA site [10] researchers conducted pilot-scale experimental campaigns using solar energy. Using an experimental approach, they described pilot-scale wastewater treatment technologies and the allied parameters based on photochemical reactions. More recent research [18] shows that one of the major problems encountered in the field of AOPs is the use of sunlight. Indeed, if the objective is to use solar resources, we need to consider two specific features of solar radiation.

First, sunlight is particularly weak in the UV spectral region, unlike lamps that provide an intense and constant beam of light. The UV spectral region represents only 5% of total solar flux available at the Earth's surface, [START_REF] Galvez | Scientific and Cultural Organization[END_REF] which represents a maximum available irradiation of 50 W UV .m -2 . The second constraint to consider for efficient design and use of a photoreactor is the intermittency of sunlight. Radiation variations during day-night and seasonal cycles [20- 22] make it a complex task to select the right operating conditions and predict how the photochemical process will perform. Thus, to scale-up a solar oxidation process, it become essential to model the capacity of a photoreactor operating under dynamic conditions, both from the irradiation side and the supply conditions side. The vast amount of research carried out on pollutant degradation processes is almost entirely based on photoreactors operating in batch mode, [23][24] which makes it difficult to translate results into real-world-based processing operations which inevitably operate in a pseudo-continuous mode. Thus, in order to design solar-based photooxidation processes, it is necessary to conduct experimental campaigns in 'dynamic' conditions (typically irradiation and flow rate) and to develop modelling tools that describe photoreactor capacity in continuous-mode operation.

Here we developed a photochemical process capable of operating in continuous mode. This process consists of a photoreactor fed by single passage of pollutants. This photoreactor can operate under a flux density simulating solar irradiation conditions but also with variable This model, [25][26] which depends on flux density and pollutant concentration level, is primarily designed to account for the discontinuous nature of solar irradiation. We selected a target substance to perform the experiments under perfectly controlled conditions, and we used a database to propose, validate and test the model taking into account material balance in the photoreactor. Here we focus on aspects of process engineering with a photoreactor operating in dynamic mode, which have insufficiently addressed in the literature. The ultimate aim of this research was to assess the photocatalytic capacity of a photoreactor process using LEDs to apply irradiation simulating a day of sunshine.

MATERIALS AND METHODS

Catalyst, target substances and analytical tools

The photocatalyst was TiO 2 , the material most widely used for this purpose. In this study, P-25 was taken as the reference material on account of its photocatalytic behaviour. Its specific surface area (BET) was 54 m 2 .g -1 and the particles of TiO 2 [9-10, 25, 27] had an average diameter of about 20 nm. In a previous publication, [5] we correlated catalyst concentration with transmittance capacity to optimize catalyst design for different reactor geometries. In this study, a concentration of 0.2 g.L -1 was needed to absorb the total incident radiation at the surface of the photoreactor.

Methyl orange (MO) was chosen as an indicator to follow the effect of operating conditions. To determine the change in the methyl orange concentration after MO removal during UV irradiation, samples of the suspension were withdrawn regularly from the reactor, and suspended solid matter removed with a syringe filter (pore size 0.45 µm). The clean transparent solution was analyzed by UV-Vis spectroscopy (Thermo scientific Evolution 600 spectrophotometer) after filtration. The MO concentration was measured from the absorbance at 480 nm using a calibration curve. Repeat tests were done to ensure reproducibility. For kinetic analyzis, each sample taken from the reactor was divided into three different vials, and the final absorption was taken as the arithmetic average over the three measurements.

Experimental set-up

The photochemical process is in a flat-type configuration illustrated in Figure 1, [START_REF] Kacem | [END_REF] essentially consisting of a photoreactor irradiated by an LED panel. to the inlet of the loop (7). The photoreactor is fed with a solution consisting of a suspension of catalyst and MO at a given concentration. The photoreactor output ( 5) is also connected to the micropump to simultaneously empty the volume of solution corresponding to the one entering at the inlet of the photoreactor. In this configuration, range of flow can be made to vary between 0.016 and 0.16 (.10 -6 ) .m 3 .s -1 , thus maintaining a fixed volume of fluid in the system.

PRELIMINARY RESULTS

Isotherm capacity

Adsorption equilibrium experiments were performed under dark conditions. A stock solution of 1 kg.m -³ of pollutant was prepared by dissolving 0.001 kg of analytical reagent in 0.001 m³ of distilled water. The adsorption isotherms were derived from measurements carried out in magnetically-stirred beakers (0.00025 m³) each containing 0.0001 m³. The tests were carried out at several initial MO concentrations in the range 0.01-0.5 kg.m-³ while maintaining a constant catalyst concentration (1 kg.m-³). Once equilibrium is reached, the quantity of MO adsorbed (q e ) is deduced from the experimental data. The time required to reach the adsorption equilibrium was estimated based on a previous study [30] .

Figure 2 shows the MO adsorption isotherm on the catalyst slurry, where q e is plotted against C e , the concentration of MO remaining in the solution once equilibrium is reached. In agreement with the literature, [25] the catalyst has a low adsorption capacity, mainly due to its non-microporous texture. The adsorption equilibrium isotherms were modelled using the Langmuir isotherm. Langmuir's theory, [31] based on the hypothesis of monolayer adsorption occurring on a homogeneous surface, is represented by the following equation:

where q e is the adsorption capacity at equilibrium (kg.kg -1 ), q m is the maximum monolayer adsorption capacity (kg•kg -1 ), C e is the equilibrium concentration (kg.m -3 ), and b is a constant related to energy of adsorption (m 3 .kg -1 ). The Langmuir fittings were performed with q m = 0.25 kg.kg -1 and b = 25 m 3 .kg -1 . Experimental results and identification of q m showed that whatever the initial concentration of pollutant, a negligible quantity of MO was adsorbed. Due to the low adsorption capacities of MO/TiO 2 , the mass transfer could be neglected in degradation kinetic equations.

Continuous stirred tank photoreactor

To conduct the experiments, the photoreactor has to operate as a continuously-fed stirred-tank reactor. The characteristics of the processing loop, and in particular the residence time of the system, were therefore defined. Experimental residence time was determined taking into account photoreactor and circuit volume. The experimental data, i.e. the inlet and outlet concentrations of the photoreactor, were acquired under different operating conditions.

Different input concentrations were applied to assess the homogeneity of the system (Figure 3): the entire treatment loop was fed with MO solutions at concentrations of 0.2, 0.1, 0.02 and 0.01 kg.m -³, but at a fixed rate.

To describe the concentration variations in the photoreactor, we established the material balance including the inlet and outlet conditions and a term expressing photodegradation. In Equation ( 2), the variation of the pollutant concentration in the photoreactor is described assuming that sorption phenomena at the catalyst surface are negligible [START_REF] Kacem | [END_REF][24][25] .

o v v O r T () ( ) ( , , ) i dC t m C m C t V r C I t V dt     ( 2)
where v m is the flow rate (m 3 .s -1 ), C i is the inlet concentration (kg.m -3 ), C o is the outlet concentration (kg.m -3 ), V r is the irradiated volume (m -3 ), V T is the total volume of the loop (m -3 ),  r is the speed of the photoreaction (kg.m -3 .s -1 ) and o () dC t dt is the term for matter accumulation corresponding to the transient regime.

If the photoreactor is in the dark, the photo degradation term becomes zero. Thus the concentration in the reactor depends only on the input conditions, i.e. the concentration and the flow rate applied. The variation in the concentration is described by Equation (3).

o i i i0 ( ) ( ) ( ( ) ) t C t C t C t C e      (3)
where

T v V m  
is the average time a volume element of fluid stays in the system (called residence time) (s -1 ), C i0 is the initial input concentration applied to the photoreactor, and

C i (t)
is the stepped input concentration applied to the photoreactor. Theoretical concentrations from the resolution of Equation ( 3), taking into account the operating conditions (inlet and outlet concentration, volume of the system and flow rate) are also reported in Figure 3. The residence time τ was found with an optimization method using a trust-region-reflective algorithm [24] . The profiles of the calculated pollutant concentrations at the outlet of the processing loop were plotted against time. The curves of calculated and measured concentrations coincided, indicating that the processing loop operated as a CSTR. The calculated residence time was 0.67 h. The difference between the calculated and the experimental results gave a dead volume of less than 2% of the total volume, which was considered negligible in the rest of the study. This result validates the fact that the photoreactor can be assimilated to a perfectly agitated reactor.

EXPERIMENTAL RESULTS

To highlight the importance of the operating conditions, a series of experiments were conducted at different flux densities, flow rates and feed concentration. We aimed to quantify the effects of the key variables on the capacity of the photoreactor to degrade a target pollutant. The performance of the process is defined by the rate of photoreaction resulting from the matter balance in Equation (2).

4.1.Flux density effect

Given the inevitable variability in the levels of irradiation during solar experiments, reactor, the threshold corresponded to the steady state of the system for which the accumulation term was zero. Thus once this phase occurred, the rate of degradation was deduced directly from Equation (4).

knowing

4.2.Pollutant concentration effect

In the treatment by heterogeneous photocatalysis, the influence of concentration is widely described in the literature [27,[32][33] . However, most of these studies were conducted in batch systems. We therefore set out to assess the capacities of the photocatalytic treatment in the open reactor.

As regards the feed concentration of pollutant, it was decided to keep within the usual range of concentrations, namely 0.001-0.3 kg.m -3 . The experiments were built on the same mode, i.e. with fixed operating conditions: a flow rate of 0.08.10 -6 m 3 .s -1 which corresponded to a residence time of 1 h, and a flux density of 50 W.m -2 equivalent to that reached on a sunny day. Four feed concentrations spanning the range 0.02-0.003 kg.m -3 were applied. The time course of the concentrations at the outlet of the photoreactor is shown in Figure 5.

Whatever the feed concentration, the concentration curves decreased until it reached a threshold after about 3 h of treatment. We note that the equilibrium concentration decreased as the input concentration decreased. In agreement with the results obtained for other categories of substance, [24,32,34] the photodegradation rate increased as the feed concentration increased.

Flow rate effect

Experimental data were acquired for three flow rates, 0.016, 0.08 and 0.16 (.10 -6 ) m 3 .s -1 , while the other conditions were kept constant: feed concentration 0.020 kg.m -3 and an applied flux density of 50 W.m -2 . The successive experiments are depicted in Figure 6. Regarding the curves showing that the concentration at the output of the reactor decreased with the flow rate, we can confirm that the photodegradation rate was a function of the residence time

( T v V m   ).
The average irradiation time ( r irr v V m   ) was directly proportional to the residence time. Thus to control the pollution level at the outlet, we could act on the residence time.

Regardless of the concentration levels at the output, the variables such as flux density, residence time and feed concentration made it possible to optimize the degradation rates. On the other hand, high concentration and/or flow rate applied to the system were unfavorable to obtaining low concentrations at the reactor outlet. Operating conditions could be modulated to obtain the best performance according to the intended application.

MODELLING DEGRADADTION IN THE PHOTOREACTOR

A model taking into account variable setpoints

Our aim is to model the photodegradation rates according to operating conditions. This involves both writing the material balance on the photoreactor but above all defining a kinetic law representative of photodegradation processes taking place in the photoreactor. However, there is still no analytical law representative of the mechanisms occurring during heterogeneous photocatalysis. The generally empirical expressions are based on the double dependence of photodegradation rate on pollutant concentration and on radiation flux density [5] . They make it possible to describe situations with specific conditions such flow density or concentration ranges or restricted to the fields of application, or to a given chemical substance. For example, Emeline [32] showed that a power law with a ratio of 1 to 20 over a range of flux densities and concentrations can be used to represent the variation in degradation rate of a given molecule. However, dedicated studies seem to show that the heterogeneous degradation photoprocess proceeds in two distinct stages, i.e. one step corresponding to the transfer of matter to the solid phase (the pollutant migrates from the solution to the catalyst) and a photochemical step corresponding to compound degradation by radical attacks [33] . These two antagonistic mechanisms mean that pollutant concentration may be a limiting factor [21,[34][35] . It is possible to consider this limitation related to the transfer of compounds using Langmuir-Hinshelwood kinetics which account for effect of concentration on rate of degradation. In the literature, [5,24,[36][37] this formalism describing the effect of pollutant concentration has been successfully validated on a number of molecules, effluents and in-effluent active substances. Here we use the formalism described by Equation (5) expressing the dependency of degradation rate on flux density and concentration irrespective of the order of the reaction.

Ct It r C I t I t C t           o o () () ( , , ) 1 ( ) 1 ( )
where  r is the speed of the photoreaction (kg.m -3 .s -1 ), C o is the concentration in the photoreactor (kg.m -3 )the outlet concentration if we consider a CSTR -I(t) is the light flux density at the surface of the photoreactor (W.m -2 ), α (m 2 /J) is the kinetic constant of the photoreaction, and β (m 3 .kg -1 ) and γ (m 2 .W -1 ) are adjusting numerical parameters. These two constants respectively represent a parameter modulating reaction rate with respect to concentration and a parameter modulating reaction rate with respect to irradiation [START_REF] Kacem | [END_REF]25,38] . In this expression, I(t), the irradiation at the surface of the reactor, was intentionally adopted as the reference. Working with the mean volumetric irradiation conditions is easy using the ratio of the reactor surface area to the reactor volume. In the perspective of defining the degradation rates, the resolution of the differential equation expresses the variation in the concentration at the outlet of the photoreactor taking into account the operating conditions (flow rate, inlet concentration, flux density) and the reactor characteristics (volume, irradiated surface area). Hereafter, this equation will be used, based on only three parameters to be determined: α, β, and γ:

) ( 1 ) ( ) ( 1 ) ( . )) ( ) ( ( 1 ) ( t C t C t I t I V V t C t C dt t dC o o T r i o o                   (6)
Table 1 summarizes the various features of the processing loop, such as the total operating volume V T , the volume of the photo-reactor V r , the ratio of the irradiated volume to the total volume , the range of available radiation flux densities I, the range of available flow rates v m , the corresponding residence time τ and the residence time in the irradiated cell τ irr .

5.2.Parameter determination

One of the advantages of working in an open reactor and a steady state is having direct experimental access to degradation rates. These are calculated simply and accurately from Equation (4). These rates were set under different experimental conditions, ultimately resulting in terms for irradiation levels at the reactor surface and concentrations in the reactor.

As previously for estimating residence time, the parameters in the kinetic law (Equation ( 5)) were found by criterion minimization. However, the process was carried out in two stages. A first step working on the tests carried out at variable concentrations, but at an identical irradiation of 50 W.m -2 (Figure 5) gave    (m 3 .kg -1 ) and one value representative of the product of  and the term I/(1 + γIn a second step, the values of    m 2 .J -1 and γ = 1.91 10 -2 (m 2 .W -1 ) were determined for the experiments carried out at different levels of irradiation (Figure 4), keeping the previously determined value of γ.

In all cases, the selected kinetics associated with the values of the coefficients indicated above allowed an estimation in agreement with the experimental rates obtained for the various conditions of operation of the photoreactor. To validate the approach, the speed of degradation deduced from experimental data and Equation ( 5) are reported in Figure 7 as a function of the inlet concentration. In the range considered, the degradation rate increased significantly at low concentrations and tended to stabilize for larger values of feed concentrations.

These results, consistent with the literature, show that the model described by Equation ( 5) is closely representative of the capabilities of the photoreactor to degrade MO. We note that the parameters had been set beforehand (Tab. 1). For each applied flux density, the photodegradation rate also deduced from experimental and calculated data are reported in Figure 8 as a function of the flux density. This result, well established in the literature, shows that the more intense the irradiation, the faster the photodegradation. Although as expected the rate of degradation was increased with irradiation, saturation of the catalyst was not reached in the range of UV power from 1 to 3 suns. It can be seen that the variation of the speed as a function of the flux density can also be described with Equation ( 5) with determined parameters (Tab. 1).

SIMULATION OF A SOLAR EXPERIMENT

Although there are already a wide range of research studies related to the photocatalytic degradation of pollutants using sunlight, [22,[39][40] almost all are designed for degradation assessment in batch operations. The scant experimentation reported on the effect of illumination cycles was conducted on gas-phase photodegradation [23] . To open up the possibility of real applications in this field, we needed to simulate the capacity of a photoreactor to treat water in dynamic mode. A dynamic mode involves operating with an open reactor under variable setpoints. Knowing that solar irradiation is an intermittent resource that depends on the local irradiation of the daily and seasonal cycles, [24,41] the photoreactor was employed in experiments conducted under artificial illumination simulating daily variation of sunlight.

Secondly, experiments conducted in a dynamic mode are essential for testing the robustness and reliability of the kinetic model. To this end, once steps of parameter identification and validation had been completed by means of the results obtained for different operating conditions, a simulated solar irradiation experiment was carried out. These experiments were conducted under irradiation conditions corresponding to typical days in February and July at Perpignan, generated using METEONORM software. To be consistent with the conditions of the experiments, the UV irradiation conditions were determined for a surface oriented north-south and tilted at 45°. The variation in the flux density during the day is reported in Figure 9 and 10. The experiment began early in the morning and ended late in the evening.

The level of the outlet concentration of the photoreactor was observed between 6:30 and 17:30 up to the level of the feeding concentration (Figure 9). As expected, the degradation of the pollutant increased as the solar irradiation increased during the morning from 0 to 27 W.m -2 . When the maximal conditions were reached in the middle of the day, the concentration in the reactor was 6.62 kg.m -3 , which corresponds to a rate of degradation of 2.1 .10 -6 kg.m -3 .s -1 . During the second phase of the day, irradiations declined to zero flux density after 10 h of experiment. Conversely, under low irradiation conditions, degradation was reduced.

At the end of the day, the concentration tended towards the concentration of feed (C = 0.0105 kg.m -3 ). The system perfectly mirrored, with opposite sign, the time course of the flux density. We clearly see the dependence of the speed of degradation on the level of the flux density, and the process was able to adapt to external conditions. In Figure 10, the second campaign conducted on a typical July day shows similar behaviour.

To simulate the variation of the pollutant concentration, Equation ( 6) was solved taking into account the inlet conditions applied to the system, but especially the irradiation conditions: the irradiation setpoint of a typical February day represented by the function I(t) is integrated in Equation (6). We emphasize that no supplementary adjustment of α, β and γ was done. Values previously determined for the three parameters involved in the kinetic law    m 2 .J -1 ,     m 3 .kg -1 and γ = 1.91 10 -2 m 2 .W -1 , were used directly in the simulation. Experimental and simulated data are reported in Figure 9 and 10. The fact that the concentration profiles from the experiments and the modelling coincided throughout the entire course of the reaction helps validate the model proposed for simulating the photoreactor. It is interesting to observe the changes in the simulated concentration with the level of irradiation.

The two daily periods displayed a significant increase and decrease in the degradation kinetics corresponding to the variation in the daily irradiation.

It is noteworthy that the model, whose parameters had been identified when the photoreactor operated in a steady state, perfectly described the situation of degradation during a sunny day. This involves dynamic operation due to both the continuous feed of pollutant at the reactor input and the irradiation conditions, so the flow density is variable over time. The formalization used with Equation ( 5) thus seems to accurately describe the time course of the photoreactor in both steady and transient states.

CONCLUSION

In this work, we developed a flat-plate open reactor irradiated with a LED panel to study photocatalytic MO degradation in a permanent working mode. The utility of this operating mode was that we could apply varied setpoints to assess the degradation capacity of the photoreactor under conditions close to those of a real processing system. The initial conditions applied mimicked sunny conditions (flux density corresponding to the range of solar irradiation) and the residence time that of biological treatment ponds. The photoreactor subjected to different feed conditions (flow rate and concentration) and irradiation (fixed or variable flow density) showed a strong dependence of the responses on the operating conditions. The numerous experimental results yielded a representative model of the different conditions tested. With three adjustment parameters (   m 2 .J -1 ,    m 3 .kg -1 and γ = 1.91 10 -2 m 2 .W -1 ) characteristic of concentration and irradiation dependences that were set (and not adjusted) for all the tests performed, this model was robust over conditions close to those envisaged for treatment applications: irradiation range 1-170 Wm -2 , concentration range 0.001-0.002 kg.m -3 and flow rate range 0.016-0.16 (.10 -6 ) m 3 .s -1 (corresponding to residence times of 0.06-0.6 h). The experimental results obtained in permanent and transient conditions were accurately described by the proposed formalization.

The purpose of this work was to acquire experimental data under simulated solar irradiation representative of typical days during the year (February and July were selected as an example). The model established under these dynamic conditions, with the objective of providing a dimensioning tool for the design and scale-up of solar reactors working in dynamic mode, was validated. In took good account of the influence of UV flux density, pollutant concentration, and the discontinuous nature of sunlight irradiation.

  pollutant concentrations and flowrates. The experimental set-up equipped with an LED panel makes it possible to apply firmly-controlled irradiation setpoints. Thus, unlike UV incandescent lamps whose flux density cannot be precisely fixed or modulated at small timesteps, LEDs can produce variable flux densities as well as daylighting setpoint of a typical day. Experimental tests were performed in different operating conditions-flow rate, flux density, and concentration-to study the influence of these variables. Modelling the capacities of the photoreactor made it possible to simulate the pilot's responses, as well as providing sizing tools for the design and scaling of solar reactors operating in dynamic mode.

  photoreactor. It essentially consists of a multi-channel peristaltic pump (1) (Watson-Marlow 205CA) to maintain the continuous flow regime. The pump is connected to a storage tank and

  the influence of the UV flux density on the kinetics is necessary to simulate the concentration profile as a function of time. In the laboratory set-up, photodegradation was investigated under different UV radiation fluxes, in the range 1-170 W m -2 , corresponding to flux from 0 to 3 suns (incident on the earth's surface). This set of experiments was carried out with fixed operating conditions, namely a concentration of MO of 0.02 kg.m -3 and a flow rate of 0.08.10 -6 m 3 .s -1 applied at the input of the reactor. The photoreactor window was irradiated at a flux density of 170 W m -2 , thereby engaging the photoreaction. The concentration in the system decreased until an equilibrium concentration was reached. Operating in an open

  photodegradation.

AKNOWLEDGEMENTS

This work received European sponsorship via the FEDER funds under the " Interreg SUDOE" program (Innovec'eau SOE1/P1/F0173) and government sponsorship via the National Research Agency under the "Avenir investissements" program (ANR-10-LABX-22-01).


Yiran Zhang
email: yiran.zhang@limsi.fr

Nicolas Ladevèze
email: nicolas.ladeveze@limsi.fr

Huyen Nguyen
email: huyen.nguyen@limsi.fr

Cédric Fleury
email: cedric.fleury@lri.fr

Patrick Bourdot
email: patrick.bourdot@limsi.fr

Virtual Navigation considering User Workspace: Automatic and Manual Positioning before Teleportation

Keywords: Human-centered computing → Virtual reality, Interaction techniques, User studies Locomotion, teleportation, real workspace, virtual workspace, virtual object access, spatial awareness

Teleportation is a navigation technique widely used in virtual reality applications using head-mounted displays. Basic teleportation usually moves a user's viewpoint to a new destination of the virtual environment without taking into account the physical space surrounding them. However, considering the user's real workspace is crucial for preventing them from reaching its limits and thus managing direct access to multiple virtual objects. In this paper, we propose to display a virtual representation of the user's real workspace before the teleportation, and compare manual and automatic techniques for positioning such a virtual workspace. For manual positioning, the user adjusts the position and orientation of their future virtual workspace. A first controlled experiment compared exocentric and egocentric manipulation techniques with different virtual workspace representations, including or not an avatar at the user's future destination. Although exocentric and egocentric techniques result in a similar level of performance, representations with an avatar help the user to understand better how they will land after teleportation. For automatic positioning, the user selects their future virtual workspace among relevant options generated at runtime. A second controlled experiment shows that the manual technique selected from the first experiment and the automatic technique are more efficient than the basic teleportation. Besides, the manual technique seems to be more suitable for crowded scenes than the automatic one.

INTRODUCTION

Teleportation is a popular locomotion technique that allows a user to move beyond the limits of their available physical space while minimizing simulator sickness [START_REF] Mp | Rapid, continuous movement between nodes as an accessible virtual reality locomotion technique[END_REF][START_REF] Wei𝛽ker | Spatial updating and simulator sickness during steering and jumping in immersive virtual environments[END_REF]. Using such technique, the user can select a destination point and instantaneously appear at this new location in the virtual environment (VE). However, this technique usually does not consider the physical space surrounding the user and their position inside this space. Due to a lack of awareness of the real workspace boundaries, the user may quickly reach the limits of their workspace while performing a virtual task.

Common solutions, such as alerting the user when they approach the boundaries, increase the user's mistrust in virtual reality (VR) systems, and often break their immersion and sense of presence. These solutions also induce the user to stay still and perform many small teleportations, instead of using their real movements to reach objects of the VE, especially when they get stuck in a corner or against a boundary of their real workspace. On the other hand, real walking could be highly beneficial for improving immersion. Solutions like redirected walking [START_REF] Razzaque | Redirected Walking[END_REF] provide a compelling approach for the user to explore large VEs while overcoming the constraints of the real workspace. However, the redirected walking algorithms usually require physical spaces larger than 6m × 6m [START_REF] Mahdi Azmandian | Physical Space Requirements for Redirected Walking: How Size and Shape Affect Performance[END_REF]. It may not be possible for common users with head-mounted displays (HMD) because their real workspace is also limited by the room size.

This work aims to help the user to gain a prior knowledge of the accessible area of the VE, which allows them to access multiple virtual objects with real walking and avoid reaching the real workspace limits. To achieve this goal, we propose to display and manipulate a virtual representation of the real workspace when using the teleportation technique. This virtual representation of the real workspace, also called virtual workspace in this paper, is similar to the concepts of vehicle [START_REF] Bourdot | Polyvalent Display Framework to Control Virtual Navigations by 6DOF Tracking[END_REF] or stage [START_REF] Fleury | A generic model for embedding users' physical workspaces into multi-scale collaborative virtual environments[END_REF].

Optimizing future access of the user to multiple objects within their physically accessible area could be useful in many scenarios. For example, in VR escape room games [START_REF]Tales of escape[END_REF]2], if the user can position their virtual workspace close to some area of interest where the clues are possibly hidden, they can fully explore this area by walking and thus avoid a lot of unnecessary teleportations. With first-person shooter games [START_REF]HalfLife Alyx[END_REF], by choosing an appropriate virtual workspace position, they can physically move to hide and attack enemies. Another example is some complex VR training system [START_REF]Self Guided VR Training[END_REF] that consists of several assembly tasks at different locations in the VE. Positioning the virtual workspace around an assembly area of each sub-task might help the user to focus better on knowledge acquisition and assembly procedure learning as they do not need to manage virtual objects' accessibility while completing this sub-task.

In order to help the user to define the position and orientation of this virtual workspace, we explore two strategies, named manual positioning and automatic positioning. The former allows the user to manually adjust the position and orientation of their future virtual workspace. The latter, using clustering techniques, automatically generates a series of possible virtual workspaces considering the interactive object layout in the VE. The user can select their future virtual workspace among the relevant options proposed by the system. We investigated these different positioning techniques in two controlled experiments. In the first one (pre-study), we assessed three manual positioning techniques and selected the most appropriate one. In the second one, we compared the selected manual positioning and the automatic positioning techniques to the basic teleportation technique. We evaluated the user performance in terms of efficiency, number of teleportations, and cognitive load, considering various virtual object layouts. From the results, we derived some usability guidelines for such techniques.

The paper is organized as follows. Section 2 reviews related work about teleportation and navigation techniques that take the user's real workspace into account. Section 3 details the two positioning strategies. Section 4 describes the two experiments and analyze the results. Finally, section 5 concludes by proposing some guidelines and discussing open problems of this contribution.

RELATED WORK

The mapping between the real and virtual world is a fundamental issue of every VR applications, and various previous works explore solutions to manage this relationship. To avoid the user's collisions with the real world and grant direct access to virtual objects, some applications choose to have a fixed one-to-one mapping between the real and virtual environments. For example, Cheng et al. [START_REF] Cheng | VRoamer: Generating On-The-Fly VR Experiences While Walking inside Large, Unknown Real-World Building Environments[END_REF] and Sra et al. [START_REF] Sra | Procedurally generated virtual reality from 3D reconstructed physical space[END_REF] propose to procedurally generate the virtual environment based on a 3D scan of the real world with a depth camera. Consequently, the size and shape of the virtual environment are constrained. Redirected walking [START_REF] Razzaque | Redirected Walking[END_REF] or other view distortion techniques [START_REF] Sun | Mapping virtual and physical reality[END_REF] can be used to map a large virtual environment to a small real workspace while allowing the user to walk freely. Impossible Space [START_REF] Suma | Impossible spaces: Maximizing natural walking in virtual environments with self-overlapping architecture[END_REF] also uses a self-overlapping architectural layout to allow the user to walk through multiple virtual rooms while staying in the same real room. However, these solutions are not suitable for all applications since they require a reasonably large real workspace, and physical walking could also be tiresome when the user has to travel long distances.

Virtual navigation is a generic solution which allows the user to go beyond the real workspace limits [START_REF] Bowman | Travel in immersive virtual environments: An evaluation of viewpoint motion control techniques[END_REF]. However, it breaks the one-to-one mapping between the real and virtual environment. Such mismatch may result in safety issues as the user could collide with physical obstacles that are invisible in the virtual world. The user may feel afraid of encountering real-world obstacles [START_REF] Koilias | Real and Virtual Environment Mismatching Induces Arousal and Alters[END_REF] and thus alter their movement behaviors [START_REF] Koilias | Real and Virtual Environment Mismatching Induces Arousal and Alters[END_REF][START_REF] Simeone | Altering user movement behaviour in virtual environments[END_REF]. In such cases, it is crucial to provide the user with a way to visualize and understand the limits of their real workspace. For example, 3DM [START_REF] Butterworth | 3DM: a three-dimensional modeler using a head-mounted display[END_REF] not only allows the user to walk naturally on a magic carpet representing the tracking space, but also to move this magic carpet over a long-distance using a steering technique. Magic Barrier Tape [START_REF] Cirio | The magic barrier tape: a novel metaphor for infinite navigation in virtual worlds with a restricted walking workspace[END_REF] employs a virtual barrier tape to indicate the available walking area to the user. The user can go beyond the boundaries by "pushing" the tape. More recently, Chen et al. [START_REF] Chen | Refined experiment of the altered human joystick for user cohabitation in multistereocopic immersive CVEs[END_REF] present a human-joystick technique that takes the real workspace boundaries into account to prevent collisions during navigation.

Teleportation is another virtual-navigation technique widely used in VR applications. Basic teleportation allows the user to instantly appear at a remote target position using a pointing technique [START_REF] Bowman | Travel in immersive virtual environments: An evaluation of viewpoint motion control techniques[END_REF]. The instantaneous transition of viewpoint avoids the sensory conflict between the visual feedback and the user's vestibular systems, which reduces simulator sickness compared to other locomotion techniques [START_REF] Mp | Rapid, continuous movement between nodes as an accessible virtual reality locomotion technique[END_REF][START_REF] Wei𝛽ker | Spatial updating and simulator sickness during steering and jumping in immersive virtual environments[END_REF]. However, teleportation lacks optical flow, which limits the user's ability to perform path finding and leads to disorientation [START_REF] Bakker | Effects of head-slaved navigation and the use of teleports on spatial orientation in virtual environments[END_REF][START_REF] Bhandari | Teleportation without spatial disorientation using optical flow cues[END_REF]. Several existing approaches aim to improve teleportation. Point and Teleport technique [START_REF] Bozgeyikli | Point & teleport locomotion technique for virtual reality[END_REF][START_REF] Funk | Assessing the Accuracy of Point & Teleport Locomotion with Orientation Indication for Virtual Reality using Curved Trajectories[END_REF] allows the user to specify their orientation before the teleportation. Jumper [START_REF] Bolte | The jumper metaphor: an effective navigation technique for immersive display setups[END_REF] employs the user's eye gaze to specify the target destination and thus enables hand-free teleportation. Dash [START_REF] Bhandari | Teleportation without spatial disorientation using optical flow cues[END_REF] quickly but continuously displaces the user's viewpoint to retain optical flow cues. The out-of-body locomotion technique [START_REF] Navarro | Out-of-body locomotion: Vectionless navigation with a continuous avatar representation[END_REF] allows the user to seamlessly switch between a first-person and a third-person view to reduce the confusion caused by discontinuous avatar movements for multiple-user teleportation.

Some approaches combine teleportation with real walking to better use the available real workspace and facilitate real walking. For example, Redirected Teleportation [START_REF] Liu | Increasing walking in VR using redirected teleportation[END_REF] requires the user to step into a portal to activate teleportation, which unobtrusively reorients and re-positions the user away from the tracking space boundary. Interactive Portals [START_REF] Freitag | Reorientation in virtual environments using interactive portals[END_REF] reorient the user to a safe position via portals sliding up from the ground in the center of the CAVE. Switch techniques [START_REF] Zhang | Switch Techniques to Recover Spatial Consistency Between Virtual and Real World for Navigation with Teleportation[END_REF] help the user to recover a one-to-one mapping between real and virtual workspace inside some areas in the VE. The user can access the virtual objects of the areas by walking. However, these areas need to be predefined according to the layout of VE and the shape of the real workspace, which makes it hard to apply in a generic context. Apart from that, the SteamVR plugin for Unity [START_REF]Essential introduction to Steam VR and Unity part 2: Teleporting and navigating around your scene[END_REF] can provide a virtual representation of the real workspace boundaries before the teleportation. However, the user cannot manipulate the orientation of this virtual representation.

In this paper, we overcome the limits of the existing approaches by designing two types of positioning techniques (manual vs. automatic) that allow the user to manage their virtual workspace before each teleportation, and to develop strategies to access multiple objects by real walking. These techniques do not rely on specific virtual object layouts or prior knowledge of the user's real workspace.

POSITIONING TECHNIQUES

In this section, we will present our considerations and design for the virtual workspace positioning techniques.

Manual Techniques

The manual positioning techniques use a 3D volume representing the user's real workspace, and the user can directly control its position and orientation in the VE to customize the teleportation.

Interacting with a predefined volume has been used for multipleobject selection (MOS) [START_REF] Finley | Design and evaluation of 3D multiple object selection techniques[END_REF][START_REF] Stenholt | Efficient selection of multiple objects on a large scale[END_REF] to select the enclosed objects at once. The user can use manipulation techniques, such as the go-go technique [START_REF] Finley | Design and evaluation of 3D multiple object selection techniques[END_REF], to manipulate this volume remotely to select distant objects. In our approach, we extended the ray casting technique [START_REF] Mark R Mine | Virtual environment interaction techniques[END_REF] to enable the virtual workspace manipulation.

In our first manual technique, the 3D volume of the virtual workspace appears when the user presses the touch pad of the controller. The intersection point between the virtual ray and the virtual ground determines the future position of this volume. The user can rotate the volume around its vertical axis (see Figure 1(a)) by sliding the finger in a circle on the touch pad with a one-to-one mapping. The objects fully or partially enclosed by the volume are selected and highlighted with a more intense colour. The user can release the touch pad to end the manipulation, and then they will be teleported into the newly specified virtual workspace with a correct matching to their real workspace.

To enhance the spatial awareness [START_REF] Bowman | Travel in immersive virtual environments: An evaluation of viewpoint motion control techniques[END_REF], we propose two other techniques, which add additional visual information to the virtual workspace representation: an avatar showing directly how the user will land after the teleportation. This avatar is a ghost representation of the user at their future location, which helps them to get selfrelated information.

These techniques differ in their rotation axis position. One technique uses an exocentric manipulation by rotating the 3D volume and the avatar around the volume's central vertical axis (see Figure 1(b)). The exocentric information can help people to see global trends [START_REF] Barfield | Situation awareness as a function of frame of reference, computer-graphics eyepoint elevation, and geometric field of view[END_REF] and enhances the size judgment [START_REF] Suzanne | 14 Size and speed constancy[END_REF]. The other technique uses an egocentric manipulation by rotating the 3D volume around the avatar's vertical axis (see Figure 1(c)). The egocentric cues can help people to gather the self-related information and result in more accurate distance estimation [START_REF] Jack M Loomis | Visual space perception and visually directed action[END_REF].

Automatic Technique

In many VR applications, the virtual objects that the user can directly interact with are usually predefined in the scenarios. Based on the layout of these objects and considering the user's actual real workspace, the system can compute possible virtual workspaces and propose them to the user. The user can then select their future virtual workspace among relevant options depending on the task requirements. Our approach to compute a set of suitable virtual workspaces is to: (i) organize objects into clusters by grouping or splitting them; (ii) compute bounding volumes for each cluster; and (iii) repeats the above steps until the size of the bounding volume and the size of user's real workspace become equivalent.

In the first step of the approach, bottom-up or top-down algorithms can be used to cluster virtual objects. The bottom-up algorithms treat each virtual object as a singleton cluster at the beginning, and then successively merge pairs of clusters until the user's real workspace can no longer enclose the bounding volume of a cluster. The top-down algorithms start with a cluster that includes all virtual objects and split the cluster recursively until each sub-cluster is smaller than the user's real workspace. Different criteria can be applied to organize objects into a cluster. For example, K-means is a fast and straightforward heuristic to group pairs of clusters based on their nearest mean [START_REF] Krishna | Genetic K-means algorithm[END_REF]. Beyond those geometrical approaches, one can also use semantic knowledge about the scene to align objects of the same kind [START_REF] Stuerzlinger | Efficient manipulation of object groups in virtual environments[END_REF], or use collisions to define clusters when simulating the real-world behaviors [START_REF] Oh | Group selection techniques for efficient 3D modeling[END_REF].

Algorithm 1 Virtual workspaces positioning algorithm

Input: ObjList, UsrRWS Output: PosList 𝑁 ← ObjList.length

3: if 𝑁 = 1 then 4:
PosList.Add(𝐴𝐴𝐵𝐵(𝑂𝑏 𝑗𝐿𝑖𝑠𝑡).𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛)

5:
return PosList

𝑏𝑏𝑜𝑥 ← AABB(𝑂𝑏 𝑗𝐿𝑖𝑠𝑡)

8: if !𝐸𝑛𝑐𝑎𝑝𝑇 𝑒𝑠𝑡 (𝑏𝑏𝑜𝑥, 𝑈 𝑠𝑒𝑟𝑅𝑒𝑎𝑙𝑊 𝑆) then 9:
𝑙𝑁 , 𝑟 𝑁 ← Kmeans(𝑂𝑏 𝑗𝐿𝑖𝑠𝑡, 2)

𝑃𝑜𝑠𝐿𝑖𝑠𝑡 .append(TopDown(𝑙𝑁 , 𝑈 𝑠𝑟𝑅𝑊 𝑆))

11:

𝑃𝑜𝑠𝐿𝑖𝑠𝑡 .append(topDown(𝑟 𝑁 , 𝑈 𝑠𝑟𝑅𝑊 𝑆))

12:

else 13:
return PosList

As a first prototype, we implemented a simple top-down algorithm (see Algorithm 1) to compute the possible virtual workspace positions in sublinear time. It uses K-means (with k=2) to split the inputting objects (ObjList) into disjoint subsets based on their 2D positions (x, z), and generates a bounding volume around each subset using axis-aligned bounding box (AABB) approach [START_REF] Goldsmith | Automatic creation of object hierarchies for ray tracing[END_REF]. The recursive splitting creates a binary tree, and processes until a subset either contains only one virtual object, or its bounding volumes can be encapsulated in the user's real workspace (UsrRWS). By traversing the binary tree, the algorithm creates and returns a list of bounding volume positions from the leaf nodes. Based on this list, the system can subsequently instantiate 3D volumes at each bounding volume position to represent the possible virtual workspaces. In the example of Figure 2, our algorithm provides five virtual workspaces for a given configuration of the VE and a 3m × 3m user's real workspace. This algorithm is a first implementation to test the related interaction technique and user acceptability of an automatic technique. It can be improved later by considering arbitrary-oriented bounding boxes (OBB) or other clustering methods.

The proposed virtual workspaces are normally invisible to the user. As soon as the user's virtual ray collides with a virtual workspace, it is displayed along with an avatar indicating the user's future destination (see Figure 3(a)). When the user walks into an overlapping area between multiple virtual workspaces, the system allows the user to switch directly from their current virtual workspace to one of the connected workspaces by showing their related avatars (see Figure 3 (b)). The user can then select a new workspace by pointing the virtual ray to its associated avatar (see Figure 3 (c)). The virtual objects enclosed inside the selected workspace are highlighted with a more intense color.

EXPERIMENT 1

As a first step, we conducted a controlled experiment to evaluate the three manual techniques proposed in section 3.1. We aimed to assess the benefits of including an avatar at the user's future destination in the virtual workspace. We also wanted to compare egocentric and exocentric manipulation techniques in terms of user spatial awareness and performance. The experiment thus compared the following techniqes (see Figure 4):

• Exo-without-avatar is an exocentric technique allowing the user to move the virtual workspace representation and to rotate it around its central axis. No preview of the user's future position is offered. • Exo-with-avatar is an exocentric technique for which the rotation axis is still at the center of the virtual workspace representation. An avatar is included to show the user's future position. This avatar is a simplified human body wearing a head-mounted display. • Ego-with-avatar is an egocentric technique that uses the future position of the user (i.e. the avatar position) as the rotation axis of the virtual workspace representation. The same simplified avatar is used in this condition.

We did not include an egocentric technique without the avatar because the rotation axis is invisible, making it difficult for the user to understand the manipulation. The experiment was a within-subject design with techniqe as a factor. The order of the techniqes was counterbalanced across participants using a balanced Latin square.

Hypothesis

We expected the conditions with the avatar would help the user to anticipate their next position in the virtual scene. We also assumed that Exo-with-avatar would highlight the entire virtual workspace and would make it easier to enclose the targeted virtual objects, while Ego-with-avatar focuses on the user's future destination and causes less disorientation. Therefore we formulated the following hypotheses:

H1 Exo-with-avatar and Ego-with-avatar will reduce disorientation and the time required to find a target after the teleportation, compared to Exo-without-avatar. H2 Less time will be required for positioning the virtual workspace representation with Exo-with-avatar than with Ego-withavatar. H3 Less time will be required to find a target after the teleportation with Ego-with-avatar than with Exo-with-avatar.

Participants

We recruited 12 participants, aged between 25 and 31 (6 men and 6 women). Only one person was left-handed. Three participants had VR experience. 11 out of 12 rated their everyday usage of headmounted displays as very low.

Experiment setup

The VR setup consisted of an HTC Vive Pro Eye with both position and orientation tracking, as well as integrated eye-tracking technology. The virtual environment was rendered using Unity with a resolution of 1440 × 1600 pixels per eye at 90 Hz. The experiment room supported a 3m × 3m tracking area. User input was detected using a Vive handheld controller.

Experimental task

To assess spatial awareness, existing studies [START_REF] Bowman | Travel in immersive virtual environments: An evaluation of viewpoint motion control techniques[END_REF][START_REF] Froehlich | Multi-Ray Jumping: Comprehensible Group Navigation for Collocated Users in Immersive Virtual Reality[END_REF] measure the time needed for participants to reorient themselves and find objects previously seen in the virtual scene. We used a similar task to evaluate the three techniqes in terms of spatial awareness and manipulation efficiency. Before each trial, the participant was asked to walk to a starting point presented by a green dotted circle the floor. Then, a set of pillars were displayed, and the trial started. The pillar set consists of one red and seven blue pillars located on four sides of a 3m × 3m square. The participant had to adjust the virtual workspace position to enclose all the pillars as if they wanted to be able to access all of them without having to perform additional teleportations. Once all the pillars were enclosed, the participant could release the Vive controller touch pad to travel to the selected destination. Subsequently, the participant needed to touch the red pillar with the Vive controller to end the trial.

Procedure

Each participant was welcomed, received instructions on the task, and signed an informed consent form. After setting up the headmounted display, we calibrated the eye tracker. For each techniqe, the participant first experienced training trials. Next, the participant completed 24 trials in randomized order resulting from a particular subset of the full combination of 6 starting points in the real space, 8 relative directions between the starting point and the pillar set (-135°, -90°, -45°, 0°, 45°, 90°, 135°, 180°), 3 distances between the starting point and the pillar set (4m, 6m, 8m) and 3 orientations of the pillar set (0°, 22.5°, 45°), as illustrated in Figure 5.

After each techniqe, the participant filled out a questionnaire. At the end of the experiment, the participant also ranked the three techniqes according to their preference. The whole experiment lasted approximately 45 minutes.

Data collection

We registered 864 trials: 3 techniqes × 24 repetitions × 12 participants. For each trial, we logged the following measures:

• Task Completion Time (TCT): the total duration of a trial. The measurement started when the participant arrived at the starting point and ended when the red pillar was touched. • Manipulation time: the time used to enclose all the pillars. The measurement started when the virtual workspace representation collided with one of the pillars and ended when the participant triggered the teleportation. • Target identification time: the time that the participant needed to reorient themself to find the red pillar. The measurement started just after the teleportation, and ended when the eye gaze of the participant collided with the red pillar (measured by the eye-tracking system of the HTC Vive).

We used the NASA-TLX questionnaire [START_REF] Hart | Development of NASA-TLX (Task Load Index): Results of Empirical and Theoretical Research[END_REF] and also added two more questions about anticipation (Were you able to anticipate where you would be after teleportation?) and disorientation (Did you feel disoriented after teleportation?). Criteria were graded on a 21-point scale and later converted to a 100-point score.

Statistical results

For each measure, we used normal QQ-plots and Shapiro-Wilk Tests to analyze data normality. TCT, manipulation time and target identification time were not normally distributed, so we applied a log-transformation to analyze them, as recommended by Robertson & Kaptein [START_REF] Robertson | Modern Statistical Methods for HCI[END_REF] (p. 316). To minimize the noise in our data, we averaged the 24 repetitions of each techniqe. We then ran a one-way ANOVA test and conducted post-hoc analysis with paired sample T-tests with Bonferroni corrections 1 . Means (M) are reported with standard deviations.

For TCT (see Figure 6, left), we did not find a significant effect of techniqe (𝐹 2,22 = 1.291, 𝑝 = 0.295), and all conditions had close mean values: Exo-without-avatar (M = 10.18±4.21s), Exo-withavatar (M = 11.09±3.43s) and Ego-with-avatar (M = 12.56±3.85s).

For manipulation time (see Figure 6, right), we observed a significant effect of techniqe (𝐹 2,22 = 4.683, 𝑝 = 0.0202). Pairwise comparisons showed that participants spent less time with Exo-withoutavatar (M = 6.54±3.32s) than with Ego-with-avatar (M = 10.66±4.07s, 𝑝 = 0.0042). No significant differences were found between Exowithout-avatar and Exo-with-avatar (M = 10.66±4.07s, 𝑝 = 0.132), and between Exo-with-avatar and Ego-with-avatar (𝑝 = 0.64).

For target identification time (see Figure 7, left), we detected a significant effect of techniqe (𝐹 2,22 = 17.40, 𝑝 < 0.0001). Pairwise comparisons showed that target identification time was significantly shorter with Exo-with-avatar (M = 0.81±0.20s, 𝑝 = 0.0021) and Ego-with-avatar (M = 0.77±0.38s, 𝑝 = 0.0015) than with Exowithout-avatar (M = 1.79±1.06s). No significant differences were found between Exo-with-avatar and Ego-with-avatar (𝑝 = 0.57). For the subjective questionnaire, we used Friedman's tests and Wilcoxon signed-rank tests for post-hoc analysis in conformity with such non-parametric data. For cognitive load, we did not find a significant effect of techniqe (𝜒 2 (2) = 1.721, 𝑝 = 0.423) on the NASA-TLX score (see Figure 7, right). However, we detected a significant effect of techniqe on anticipation (𝜒 2 (2) = 19.19, 𝑝 < 0.0001) and disorientation (𝜒 2 (2) = 21.80, 𝑝 < 0.0001). Post-hoc analysis shows that Exo-with-avatar (M = 16.67±12.67, 𝑝 = 0.0057) and Ego-with-avatar (M = 15.00±12.06, 𝑝 = 0.0061) resulted in a significantly better anticipation (see Figure 8, left) compared to Exowithout-avatar (M = 85.83±9.00). It shows that significantly less disorientation (see Figure 8, right) was perceived by the participants with Exo-with-avatar (M = 20.00±19.19, 𝑝 = 0.015) and Ego-withavatar (M = 16.08±19.08, 𝑝 = 0.0099) than with Exo-without-avatar (M = 63.33±30.70). In addition, 11 out of 12 participants preferred Exo-with-avatar and Ego-with-avatar over Exo-without-avatar, and 8 out of 12 participants ranked Ego-with-avatar as their favorite condition.

Discussion

Despite the non-significant difference in task completion time, we found that the use of an avatar has a significant impact on manipulation time and target identification time. On the one hand, participants performed faster the manipulation task of the virtual workspace with Exo-without-avatar than with Ego-with-avatar. Manipulation with Exo-without-avatar seems also slightly faster than with Exo-with-avatar, but the difference is not significant. On the other hand, the two conditions with avatar resulted in significantly less disorientation and thus a shorter target identification time, which supports H1. Even if the results could be predictable since the visual feedback directly shows how the user will "land" in the VE, it is interesting to measure its actual impact. While the user spends slightly more time positioning the avatar, they can plan and better understand the upcoming teleportation, decreasing disorientation and the time needed to complete the task after the teleportation. In the conditions with avatar, positioning the avatar can increase the cognitive load, but finding the target requires less cognitive effort. This can explain why the overall difference in cognitive load is not significant.

Contrary to our expectations, we were not able to find significant differences between exocentric and egocentric techniques in term of user performance. For manipulation time, the difference is not significant, which does not support H2. For target identification time, no significant difference was found between Exo-with-avatar and Ego-with-avatar, which rejects H3. We also did not detect significant differences between Exo-with-avatar and Ego-with-avatar for cognitive load, anticipation and disorientation. However, participants preferred Ego-with-avatar to Exo-with-avatar according to the questionnaires. In particular, participants reported that Ego-withavatar allowed them to "focus more on themselves" (P6) during the manipulation step, was "easier for positioning themselves" (P9), and was "easier for finding" (P3) the target objects after teleportation.

The two conditions with avatar seem to reach close performance levels. However, we wanted to select one of them to compare it with the automatic positioning technique in the second experiment. Consequently, we decided to choose the Ego-with-avatar based on the user preference.

EXPERIMENT 2

The goal of this experiment is to compare the manual technique selected from the first experiment (i.e., Ego-with-avatar) and the automatic technique to a basic teleportation. In this experiment, we set up a more realistic task similar to an escape room game. The VE consisted of a series of virtual rooms. Participants needed to select multiple objects to escape each room and continue the exploration. The experiment followed a [3×2] within-subject design with the following factors:

• techniqe: Basic, Manual and Automatic,

• layout: Overlap and No-overlap.

For techniqe (see Figure 9), the three variations are:

• Basic is the basic teleportation technique used as a baseline. A virtual ray appeared when participants pressed the controller's touchpad. The teleportation position was determined by the collision point between the ray and the virtual floor. It was represented by a green dotted circle. Participants activated teleportation by releasing the touch pad. • Manual is the manual Ego-with-avatar technique described in section 4. Participants used the virtual ray to manipulate the virtual workspace representation instead of the dotted circle used in the Basic technique. • Automatic is the automatic technique described in Section 3.

Participants used the virtual ray to select a virtual workspace among the relevant options proposed by Algorithm 1.

For layout, two different object layouts were used:

• No-overlap: objects were laid out in two separate areas, which could be included in the participant's real workspace. The Automatic technique thus proposed one virtual workspace for each area. • Overlap: objects were spread in an area larger than the participant's real workspace. The Automatic technique proposed a set of virtual workspaces which enclosed only a subset of the objects.

The order of the techniqes was counter-balanced across participants using a balanced Latin square, and the order of the layout was also counter-balanced for each techniqe.

Hypothesis

In comparison to the basic teleportation, we expected that the manual and the automatic positioning techniques would allow the user to access more easily multiple objects using physical walking. With the automatic technique, the user could select their future virtual workspace among the proposed ones and thus would be able to avoid the manipulation step required for positioning it. However, in a crowded virtual environment, the large number of proposed virtual workspaces could be confusing for the user. We, therefore, formulated the following hypotheses: H1 Automatic and Manual will result in better user performance, compared to the Basic teleportation. H2 Automatic and Manual will result in better sense of presence, compared to the Basic teleportation. H3 In No-overlap, Automatic performs better than Manual. H4 In Overlap, Manual performs better than Automatic.

Participants

We recruited 12 participants, aged between 25 and 32 (7 men, 5 women). 6 participants had VR experience. 8 out of 12 rated their everyday usage of head-mounted displays as very low.

Experiment setup

The VR setup was the same as in Experiment 1.

Experimental task

Participants traveled in a large virtual environment composed of nine rooms. In each room, they had to select multiple objects. When participants reached their real workspace limits, a warning sign appeared in their field of view with an alarm sound to ensure participants' safety. The first room was used for the training task, and the other eight were set up for the evaluation: half with the No-overlap layout and half with the Overlap layout. Both types of layouts required participants to access ten target objects, grab them with the controller, and bring them back to one of two treasure boxes one by one (see Figure 10). With the No-overlap layout, the objects and the treasure boxes were located within two disjointed 3m × 3m areas. Each area contained five targets and one treasure box located randomly on 6 of 9 positions. With the Overlap layout, the objects and the treasure boxes were placed randomly on 12 of 25 positions located in a single 5m × 5m area. In Automatic condition of this layout, the algorithm computed four overlapping virtual workspace positions to cover the full area.

Procedure

Each participant was welcomed, received instructions on the task, and signed an informed consent form. For each techniqe, the participant first completed the training task with eight targets and two treasure boxes located inside four 3m × 3m areas (three overlapped and one not-overlapped). During this step, the experimenter was allowed to answer their questions, if any. Next, the participant completed eight trials (4 with No-overlap and 4 with Overlap, or vice versa). After each techniqe, they filled out an Igroup Presence Questionnaire (IPQ) [START_REF] Regenbrecht | Real and illusory interactions enhance presence in virtual environments[END_REF][START_REF] Schubert | The sense of presence in virtual environments: A three-component scale measuring spatial presence, involvement, and realness[END_REF] to measure the sense of presence and two NASA-TLX questionnaires [START_REF] Hart | Development of NASA-TLX (Task Load Index): Results of Empirical and Theoretical Research[END_REF] to assess the cognitive load of each layout. We used the color of the rooms to help the participant to differentiate the two layouts. At the end of the experiment, the participant also ranked the three techniques according to their preference. The whole experiment lasted around 60 min.

Data collection

We registered 288 trials: 3 techniqes × 2 layouts × 4 repetitions × 12 participants. For each trial, we collected the following measures: Each question of the NASA-TLX was graded on a 21-point scale and converted to a 100-point score. Each question of the IPQ was graded on a 7-point Likert scale (from 0 to 6).

Statistical results

To minimize the noise in our data, we averaged the 4 repetitions of each techniqe × layout. Means (M) are reported with standard deviations.

For TCT, we used normal QQ-plots and Shapiro-Wilk Tests to analyze data normality. The data was not normally distributed, so we applied a log-transformation to analyze it following statistical recommendations [START_REF] Robertson | Modern Statistical Methods for HCI[END_REF]. A two-way repeated measures ANOVA with the model techniqe × layout revealed a effect of techniqe (𝐹 2,22 = 11.08, 𝑝 = 0.0005) and interaction effect (𝐹 2,22 = 4.79, 𝑝 = 0.019), but no significant effect of layout (𝐹 1,11 = 2.13, 𝑝 = 0.17) was found. For techniqe, post-hoc Tukey HSD tests indicated that performing the task with Manual (M = 45.70± 9.65s, 𝑝 = 0.0019) and Automatic (M = 45.40±9.46s, 𝑝 = 0.0011) was significant faster than with Basic (M = 61.70 ± 20.19s). For techniqe × layout (see Figure 11, left), post-hoc Tukey HSD tests shown the task with the No-overlap layout was significant faster to achieve with Manual (M = 43.75±10.63s, 𝑝 = 0.0005) and Automatic (M = 39.80±8.75s, 𝑝 < 0.0001) than with Basic (M = 64.02±20.60s). For the task with the Overlap layout, Basic (M = 58.99±19.23s) was significantly different from Manual (M = 46.97±10.86s, 𝑝 = 0.044), but not from Automatic (M = 49.87±13.75s, 𝑝 = 0.17). In all cases, no significant differences were found between Manual and Automatic.

For Warnings, we used non-parametric tests in conformity with the nature of count data. We first aggregated the data by techniqe and a Friedman test revealed a significant effect of techniqe (𝜒2 (2) = 11.51, 𝑝 = 0.0032). Wilcoxon Signed Rank tests 2 shown that participants triggered significantly more Warnings with Basic (M = 3.38±3.32) than with Manual (M = 1.50±1.11, 𝑝 = 0.041) and Automatic (M = 0.90±0.67, 𝑝 = 0.034). No significant differences were found between Manual and Automatic. We then split the data by layout and ran a Friedman test for each layout (see Figure 11,right). For No-overlap, it indicated a significant effect of techniqe For Teleportations, we also used non-parametric tests. We first aggregated the data by techniqe and a Friedman test revealed a significant effect of techniqe (𝜒 2 (2) = 19.50, 𝑝 < 0.0001). Wilcoxon Signed Rank tests shown that participants teleported significantly more with Basic (M = 19.00±17.49) than with Manual (M = 3.00 ± 0.85, 𝑝 = 0.0050) and Automatic (M = 3.53 ± 0.90, 𝑝 = 0.0015). No significant difference was found between Manual and Automatic. We then split the data by layout and ran a Friedman test for each layout (see Figure 12). For both layouts, we had similar results to that of the aggregated data, pointing out that there was probably no interaction effect of techniqe×layout.

For the NASA-TLX questionnaires, we aggregated the data by techniqe and did not detect a significant effect of techniqe (𝜒 2 (2) = 2.426, 𝑝 = 0.2974). We also aggregated the data by layout and observed that the Overlap layout (M = 42.22±21.72) induced a significantly higher cognitive load than the No-overlap layout (M = 38.75±19.76, 𝑝 = 0.0050). Further analysis on the data split by layout revealed that a significant higher cognitive load was required with Automatic (M = 32.98 ± 18.76) than with Manual (M = 28.96±17.95, 𝑝 = 0.031) for the Overlap layout.

For the IPQ questionnaire (see Figure 13), a Friedman test revealed a significant effect of techniqe (𝜒 2 (2) = 19.63, 𝑝 < 0.0001). Wilcoxon Signed Rank tests reported a significantly better presence with Manual (M = 3.89 ± 0.47, 𝑝 = 0.0025) and Automatic (M = 4.80±0.53, 𝑝 = 0.0025) than with Basic (M = 4.75±0.69).

Finally, 11 out of 12 participants preferred Manual and Automatic for both tasks over the Basic condition. For the No-overlap layout, 6 out of 12 participants ranked Automatic as their favorite, and 5 participants preferred Manual. For the Overlap layout, 6 out of 12 participants preferred Manual, and 5 participants preferred Automatic.

Discussion

The results provide evidence that the Manual and Automatic techniques outperformed the Basic teleportation. In particular, participants completed the task significantly faster when they were able to choose the position of the future virtual workspace, compared to the Basic teleportation. This supports H1. It can be explained by the fact that the participants could reach multiple virtual objects easily with physical walking, avoiding unnecessary teleportations. It is In addition to the better performance, the Manual and Automatic techniques also resulted in higher sense of presence compared to the Basic teleportation, according to the IPQ questionnaire. This supports H2. With Basic teleportation, since the user "cannot imagine the accessible area" (P3) and "cannot determine if an object is accessible" (P7), a larger number of warnings were triggered while performing the task, compared to Manual and Automatic. Excessive warnings often lead the user to distrust the VR system and break the immersion. For example, participants "feel fear" (P4) and were "afraid to move" (P5) with Basic teleportation. The fact that the user performs a more significant number of teleportations and walks less with the Basic teleportation is also detrimental to their immersion.

For the task with the No-overlap layout, no significant differences in TCT were found between Manual and Automatic, which does not support H3. However, significantly more warnings were detected with Manual condition than with Automatic. The Manual technique requires the user to position the virtual workspace manually, and they may sometimes make mistakes, e.g., not including all the target objects or putting the objects too close to the real workspace's limits. As a result, they trigger warnings when they try to access these objects. But the user seems to be able to quickly reposition the virtual workspace when facing issues with the Manual technique, which explains the non-significant differences for TCT. Consequently, both techniques are suitable in a virtual environment with no-overlapping interaction areas. However, the Automatic technique seems more appropriate in such a context since fewer warnings are triggered, thus avoiding immersion breaks.

For the task with the Overlap layout, no significant differences in TCT were found between Manual and Automatic, which does not support H4. However, while the task was significantly faster to achieve with Manual compared to Basic, similar results were not reported for Automatic, suggesting that a small difference could exist between Manual and Automatic. In addition, the score from the NASA-TLX shown that Manual significantly reduced the cognitive load, compared to Automatic. As the virtual workspaces proposed by the system can be numerous and overlapped each other, the user sometimes has to pass through an intermediate virtual workspace to reach the one behind, which can be time consuming and increase the cognitive load. Users also felt "constrained" (P2, P7) as they needed "to adapt to a previously defined position" (P5). Consequently, the Manual technique seems more appropriate than the Automatic one when the VE is crowded with many objects in the same area.

CONCLUSION

In this paper, we proposed and evaluated several techniques helping a user to be aware of their future virtual workspace and manage its position and orientation before the teleportation. Such techniques are interesting to facilitate access to multiple virtual objects through the user's physical movements in their real workspace without reaching its limits. To this aim, we investigated manual and automatic techniques for positioning this virtual workspace.

A first experiment focused on manual positioning techniques. It demonstrates that using an avatar to represent the user's future position in the virtual workspace reduces disorientation and thus the time needed to locate targeted objects after teleportation. It also shows that exocentric and egocentric techniques with an avatar result in a close performance levels, but the egocentric technique seems to be preferred by users. A second experiment compared the egocentric manual technique with an avatar and an automatic technique to a basic teleportation. The manual and automatic positioning techniques outperform the basic teleportation in terms of efficiency and immersion. Although these two positioning techniques reach equivalent performances, each one seems to have its advantages depending on the layout of the virtual environment. Compared to the manual technique, the automatic one causes fewer collisions with the real workspace limits in sparse virtual object layouts, but it induces a higher cognitive load for crowded scenes. In conclusion, this study demonstrates the benefits of the virtual workspace positioning approaches over the basic teleportation.

The future work consists of enhancing the automatic technique by adapting the clustering algorithm to obtain a good balance between the number of proposed virtual workspaces according to the virtual scenario and the real workspace configuration. Moreover, further investigations are required to evaluate these techniques considering different shapes and sizes of real workspaces, the density of the interactive objects in the virtual environment, and the needs of the VR applications. In addition, it remains unclear how the techniques would perform in other VR scenarios or more cognitively challenging situations, for example, in an exploration task where the main goal is not purely to interact with objects. Depending on user expectations, skills and experiences, the virtual workspace's visual feedback could be automatically adjusted based on the amount of the information contained in the scene [START_REF] Freitag | Comparison and Evaluation of Viewpoint Quality Estimation Algorithms for Immersive Virtual Environments[END_REF] to avoid overloading the user's field of view and to fit virtual scenario needs. Finally, the suitability of automatic techniques could be studied for specific scenarios that require a perfect match between the real and virtual environments, for example, to provide tangibility to virtual objects [START_REF] Cheng | iTurk: Turning Passive Haptics into Active Haptics by Making Users Reconfigure Props in Virtual Reality[END_REF][START_REF] Simeone | Substitutional reality: Using the physical environment to design virtual reality experiences[END_REF][START_REF] Suzuki | Substitutional reality system: a novel experimental platform for experiencing alternative reality[END_REF] or in collaborative co-located applications.

Figure 1 :

 1 Figure 1: Three manual positioning techniques: the user (a) rotates the volume around its central vertical axis; (b) rotates the 3D volume and an avatar around the central axis; and (c) rotates the 3D volume around the avatar's vertical axis.

1 :

 1 procedure TopDown(𝑂𝑏 𝑗𝐿𝑖𝑠𝑡, 𝑈 𝑠𝑟𝑅𝑊 𝑆) 2:

Figure 2 :

 2 Figure 2: Results of the positioning algorithm: five virtual workspaces (green) are proposed to the user for 12 interactive objects (light blue) located in three virtual rooms (white). Three workspaces are disjointed (no overlap rooms), and two overlap each other (overlap room).

Figure 3 :

 3 Figure 3: Top view of the user (a) selects a virtual workspace among relevant options; (b) enters an overlapping area and the system displays avatars to represent the connected virtual workspaces; and (c) selects a subsequent workspace by pointing the virtual ray to its corresponding avatar.

Figure 4 :

 4 Figure 4: Conditions of the first experiment: (a) Exo-withoutavatar, (b) Exo-with-avatar and (c) Ego-with-avatar.

Figure 5 :

 5 Figure 5: Each starting position in the virtual scene positioned the participant at one of the 6 positions in the real space (left). The pillar set was located with 3 different orientations, in one of the 8 directions around the participant, and at one of the 3 distances from the participant (right).

Figure 6 :

 6 Figure 6: Mean TCT (left) and manipulation time (right) by techniqe. Error bars show 95% confidence intervals (CI).

Figure 7 :

 7 Figure 7: Mean target identification time (left) and NASA-TLX score (right) by techniqe. Error bars show 95% CI.

Figure 8 :

 8 Figure 8: Mean anticipation (left) and disorientation (right) score by techniqe. Error bars show 95% CI.

Figure 9 :

 9 Figure 9: Three conditions for techniqe: (a) Basic teleportation; (b) Manual technique selected from Experiment 1; (c) Automatic technique: the user selects their future virtual workspace among relevant options (left), or selecting avatars in overlapping conditions (right).• Overlap: objects were spread in an area larger than the participant's real workspace. The Automatic technique proposed a set of virtual workspaces which enclosed only a subset of the objects.

Figure 10 :

 10 Figure 10: Two object layouts were used: (left) No-overlap in which objects (red) and treasure boxes (gray) were randomly located in two disjointed 3m × 3m areas; and (right) Overlap in which objects (red) and treasure boxes (gray) were randomly placed in a single 5m × 5m area. The light gray rectangles represent the virtual workspaces computed in the Automatic condition.

Figure 11 :

 11 Figure 11: Mean TCT (left) and warnings (right) by techniqe × layout. Error bars show 95% CI. • Task Completion Time (TCT): the total duration of a trial. The measurement started when the participant entered a room and ended when all objects were put in the treasure boxes. • Warnings: the number of times the participant triggered the warning sign. • Teleportations: the number of teleportations performed.

Figure 12 :

 12 Figure 12: Mean Teleportations by techniqe × layout. Error bars show 95% CI. (𝜒 2 (2) = 14.28, 𝑝 = 0.0008). Wilcoxon Signed Rank tests shown that participants triggered significant more Warnings for the No-overlap layout with Basic (M = 3.29±2.91) than with Manual (M = 1.35±1.41, 𝑝 = 0.029) and Automatic (M = 0.33 ± 0.44, 𝑝 = 0.011). Manual was also significantly different than Automatic (𝑝 = 0.032) for Nooverlap. For Overlap, no significant effect of techniqe was found (𝜒 2 (2) = 4.95, 𝑝 = 0.084).For Teleportations, we also used non-parametric tests. We first aggregated the data by techniqe and a Friedman test revealed a significant effect of techniqe (𝜒 2 (2) = 19.50, 𝑝 < 0.0001). Wilcoxon Signed Rank tests shown that participants teleported significantly more with Basic (M = 19.00±17.49) than with Manual (M = 3.00 ± 0.85, 𝑝 = 0.0050) and Automatic (M = 3.53 ± 0.90, 𝑝 = 0.0015). No significant difference was found between Manual and Automatic. We then split the data by layout and ran a Friedman test for each layout (see Figure12). For both layouts, we had similar results to that of the aggregated data, pointing out that there was probably no interaction effect of techniqe×layout.For the NASA-TLX questionnaires, we aggregated the data by techniqe and did not detect a significant effect of techniqe (𝜒 2 (2) = 2.426, 𝑝 = 0.2974). We also aggregated the data by layout and observed that the Overlap layout (M = 42.22±21.72) induced a significantly higher cognitive load than the No-overlap layout (M = 38.75±19.76, 𝑝 = 0.0050). Further analysis on the data split by layout revealed that a significant higher cognitive load was required with Automatic (M = 32.98 ± 18.76) than with Manual (M = 28.96±17.95, 𝑝 = 0.031) for the Overlap layout.For the IPQ questionnaire (see Figure13), a Friedman test revealed a significant effect of techniqe (𝜒 2 (2) = 19.63, 𝑝 < 0.0001). Wilcoxon Signed Rank tests reported a significantly better presence with Manual (M = 3.89 ± 0.47, 𝑝 = 0.0025) and Automatic (M = 4.80±0.53, 𝑝 = 0.0025) than with Basic (M = 4.75±0.69).Finally, 11 out of 12 participants preferred Manual and Automatic for both tasks over the Basic condition. For the No-overlap layout, 6 out of 12 participants ranked Automatic as their favorite, and 5 participants preferred Manual. For the Overlap layout, 6 out of 12 participants preferred Manual, and 5 participants preferred Automatic.

Figure 13 :

 13 Figure 13: Results from the IPQ questionnaire by techniqe × layout. Error bars show 95% CI.

All statistical analyses were performed with R and we used a significance level of 𝛼 = 0.05 for all tests.

In this experiment, all Wilcoxon Signed Rank tests were performed with Holm-Bonferroni corrections.

ACKNOWLEDGMENTS

This work was partially supported by European Research Council (ERC) grant n°695464 "ONE: Unified Principles of Interaction"; and by Agence Nationale de la Recherche (ANR) grants ANR-10-EQPX-26-01 "EquipEx DIGISCOPE" as part of the program "Investissement d'Avenir" ANR-11-IDEX-0003-02 "Idex Paris-Saclay".