E Mendes

L Cassayre

R Malmbeck

P Souček

R Jardin

J.-P Glatz

Recovery of Actinides from Actinide-Aluminium Alloys: Chlorination Route

A method for recovery of actinides (An) from An-Al alloys formed by electrochemical separation of metallic spent nuclear fuel on solid aluminium electrodes in molten chloride salts is described. The proposed route consists of three main steps: Vacuum distillation of salt adhered on the electrodes, chlorination of An-Al alloy by pure chlorine gas and sublimation of formed AlCl 3 . A thermochemical study of the route was performed to determine important chemical reactions and to find optimum experimental conditions for all process steps. Vacuum distillation of the electrode is efficient for complete removal of remaining salt and most fission products (FP), full chlorination of the An-Al alloys is possible at any working temperature and evaporation of AlCl 3 is achieved by heating under argon.. Experiments have been carried out using U-Al alloy in order to define parameters providing full alloy chlorination without formation of volatile UCl 5 and UCl 6 . It was shown that full chlorination of An-Al alloys without An losses should be possible at a temperature approx. 150°C.

INTRODUCTION

A promising pyrochemical reprocessing option regarding spent nuclear fuels is the groupedselective separation of all actinides (An's) by electrochemical methods in a LiCl-KCl molten salt. An's are electrochemically groupedselectively reduced from the mixture of fission products (FP) dissolved in the molten salt. In ITU a process based on electrorefining of metallic alloy fuel and the use of solid reactive aluminium cathodes is under development. In recent work, the efficiency of the process and selectivity over lanthanides has been demonstrated [START_REF] Serp | Electroseparation of Actinides on Solid Aluminium in LiCl-KCl Eutectic[END_REF][START_REF] Serp | Electroseparation of Actinides from Lanthanides on Solid Aluminum Electrode in LiCl-KCl Eutectic Melts[END_REF]. It has been shown that the use of solid aluminium cathodes leads to the formation of stable An-Al alloys [START_REF] Cassayre | On the formation of U-Al alloys in the molten LiCl-KCl eutectic[END_REF], highly loaded in An (up to about 70 wt. %) [START_REF] Soucek | Electrorefining of U-Pu-Zr-alloy fuel onto solid aluminium cathodes in molten LiCl-KCl Radiochimica[END_REF].

Efficient separation of An´s from Al-An is a key point for the feasibility of the process. The method to recover An´s proposed and studied in this work is a chlorination route based on a three step procedure as presented in Fig. 1. Initially, the salt, which is composed mainly of LiCl-KCl and some FP chlorides, adhered on the electrode after the electrorefining process is removed by vacuum distillation. The second step is a chlorination of the An-Al alloy in order to fully convert the alloy to chlorides. The last step consists of the sublimation of AlCl 3 . The final An chlorides can be further chemically processed to obtain the desired output product, e.g. An alloy. A method involving the chlorination of Al-U spent fuel has been proposed by Bohe et al. [START_REF] Bohe | Chlorination Reactions Applied to Reprocessing of Aluminium-Uranium Spent Nuclear Fuels[END_REF][START_REF] Bevilacqua | Radioactive Waste Reduction from LEU Al-U Spent Fuel Management by a Dry Chlorination Process[END_REF], but up to now is only based on thermochemical calculations without validation by experimental studies involving Uranium. In this work, a process using the chlorination of An-Al alloys by pure Cl 2 (g) is investigated.

Initially, a detailed thermochemical study of all process steps was carried out. Based on this study, experiments were focussed to optimise process conditions for a full recovery of uranium from U-Al alloys. The reason is that due to the high volatility of UCl 5 and UCl 6 , U is the most difficult element to convert to chloride form without any losses. For that purpose, chlorination experiments on a UAl 3 alloy were carried out in the temperature range 150-170°C.

THERMOCHEMICAL STUDY

The main idea of the chlorination route is to fully chlorinate the alloy and removal of AlCl 3 by sublimation. Thermochemical calculations using the Factsage software were performed, aiming to determine the most suitable conditions for the process. At first, a bibliographic study was carried out to collect available thermochemical data (∆ f H°, S m ° and C p(T) ) and phase diagrams. Most thermochemical data concerning the An's chlorides are tabulated, apart from AmCl n and CmCl n gaseous compounds [START_REF] Chase | NIST-JANAF Thermochemical Table[END_REF][START_REF] Guillaumont | Update on the Chemical Thermodynamics of Uranium, Neptunium, Plutonium, Americium and Technetium[END_REF][START_REF] Fuger | The Chemical Thermodynamics of Actinides Elements and Compounds, Part 8 -The Actinide Halides[END_REF][START_REF] Konings | The ITU Material: Property Data Base for f-elements and compounds, f-MPD[END_REF][START_REF] Konings | Thermodynamic properties of Actinides. 3rd ed. The Chemistry of Actinides and Transactinide Elements[END_REF]. Among An-Al alloys, the Gibbs energy of formation of UAl 3 , UAl 4 and PuAl 4 are available, together with phase diagrams for U-Al and Pu-Al systems [START_REF] Chiotti | The Chemical Thermodynamics of Actinide Elements Compounds Part 5: The Actinide Binary Alloys[END_REF]. In both systems, the melting point of the intermetallic compounds increases with the An content, UAl 2 and PuAl 2 having the highest melting temperature (1620°C and 1540°C, respectively). No phase diagram was found for Np-Al and Am-Al systems. However, three Np-Al intermetallic compounds are reported in the Inorganic Crystal Structure Database [START_REF]Inorganic Crystal Structure Database[END_REF]. No ternary or quaternary An-Al system was found.

First step: Distillation of remaining salt

To ensure a sufficient purity of both end products (An and Al), it is necessary to clean the cathode from the residual frozen salt adhering at the surface after the electrorefining step. This salt contains a mixture of LiCl-KCl with dissolved FP chlorides. The proposed technique is distillation of the salt from the An-Al alloys and recycling of the salt back in the electrorefiner. This requires sufficient difference in vapour pressures between the salt and the alloy. No thermochemical data exist to fully evaluate the vapour pressure of the salt mixture (LiCl-KCl + FP) and of the alloy (Al-U-Pu-Am-Np-Cm). However, as a first estimation, the vapour pressure, P M , of each individual compound (FP chlorides and An metals) can be calculated from available data according to:

RT 303 . 2 ) T ( G r M P log °∆ - = (1)
where ∆ r G° is the Gibbs energy of the equilibrium M(s,liq)=M(g).

Results for the most important An's and FP are plotted in Fig. 2. It can be seen that, except Am, all An metals exhibit a lower vapour pressure than all chloride compounds. As AnAl 3 -AnAl 2 intermetallic compounds have a much higher melting point than pure metals, their vapour pressures are most likely lower than the one of each individual metal. Therefore, the vapour pressure of alloyed Am will be lower than pure Am.

Pure LiCl-KCl salt is possible to remove by vacuum distillation at temperatures around 800°C, which was confirmed experimentally in the laboratory scale (2g of LiCl-KCl were completely distilled at 900°C and 5.10 -5 bar). However, other compounds, especially Ln chlorides, need stronger conditions to be removed. Available thermodynamical data indicate that a temperature of 1000°C is required to fully remove all lanthanide (Ln) chloride compounds, with a vacuum of 10 -5 bar, see horizontal dotted line in Fig 2 . However, distillation under these conditions is possibly still not sufficient for complete removal of some FP chlorides (e.g. MoCl 2 , SrCl 2 and BaCl 2 ).

Second step: Chlorination of An-Al alloy

The main target of the chlorination is to separate actinides from aluminium. All metal elements (U, Pu, Np, Am, Cm, Al) of the alloy have to be fully converted to chlorides and significantly more volatile aluminium chloride is consecutively evaporated in the following step. Each of presented metals forms a chloride compound in equilibrium with pure chlorine gas, even at relatively low temperatures (25°C). Therefore, the key point of the process is to control working conditions in order to provide formation of desired species only. Formation of gaseous actinide chlorides (e.g. UCl 5 and UCl 6 ) has to be suppressed to avoid actinide losses by volatilization

The thermochemical study of the chlorination of An-Al alloys is a complex problem, as many compounds can form, and the reactions are strongly dependent on the applied conditions. As a first approach, two main parameters of the process have been studied: -Temperature of the reaction, -Molar ratio Cl 2 /alloy.

For calculations, a constant volume of 1 dm 3 was used and the Cl 2 /alloy molar ratio was fixed by the considered amount of actinide alloy. The following calculations have been performed:

-Relative stability of An chlorides, -Chlorination of UAl 4 and PuAl 4 at 150°C, -Chlorination of UAl 3 in the 100°C-1000°C temperature range for a fixed Cl 2 /UAl 3 ratio.

Chlorination of pure An metals

The relative stability of An chlorides was calculated according to the Gibbs energy of the reaction:

) l , s ( AnCl x 2 ) g ( Cl ) l , s ( An x 2 x 2 = + (2)
In the 100-1000°C temperature range, all Gibbs energy values related to Eq. ( 2) are strongly negative (between -300 and -600 kJ/mol), indicating that the chloride form is thermodynamically promoted. The products of chlorination can be sorted according to their relative stability to the following sequence (ascending Gibbs energy): AmCl

2 > AmCl 3 > PuCl 3 > CmCl 3 > NpCl 3 > UCl 3 > UCl 4 > NpCl 4 .
Provided that the amount of chlorine gas is sufficient (i.e. at least a stoechiometric amount), the chlorination of considered metals will lead to the formation of the following solid chloride compounds at 150°C: PuCl 3 , AmCl 3 , UCl 4 , NpCl 4 and AlCl 3 . U forms gaseous species UCl 5 and UCl 6 in presence of an excess of chlorine gas as described later. At higher temperatures (up to 1000°C), the order of chlorination remains the same, but liquid and then gaseous compounds will form.

Chlorination of UAl 4 and PuAl 4 at 150°C

As mentioned above, the only data available for An-Al alloys are related to UAl 3 , UAl 4 and PuAl 4 . These data were used to evaluate the behaviour of UAl 4 and PuAl 4 under pure chlorine atmosphere at 150°C (Fig. 3). These calculations show that Pu and U are chlorinated in preference to Al, leaving nonchlorinated Al metal. The behaviour of the alloys is thermodynamically very close to the behaviour of a mixture of pure compounds. However, this calculation shows only the equilibrium state towards which the system should tend. The considered heterogeneous reaction will be most probably limited by kinetic factors due to a surface passivation. Analogous to an oxide layer formation during some oxidation processes, a solid chloride layer is expected to be formed at the surface of the alloy, preventing from further chlorination. This problem can be solved if the electrode is crushed in order to obtain a powder and increase the surface of reaction.

Chlorination of UAl 3 in the 100°C-1000°C temperature range for fixed Cl 2 /UAl 3 ratios

It can be seen from previous calculations that, at 150°C, the chlorination of U yields solid UCl 4 (s), if the Cl 2 /U ratio is close to the stoechiometric amount (i.e. 6.5 mol, corresponding to the reaction UAl 3 + 6.5 Cl 2 = 3 AlCl 3 + UCl 4 ). This temperature is relatively low, and much more favourable reaction kinetics could be obtained, if higher temperatures are used. However, as shown in Fig. 4, an increase of temperature will lead to the formation of gaseous species: UCl 6 (g), UCl 5 (g) and finally UCl 4 (g) will predominantly form with increase of temperature from 150°C to 1000°C. The formation of compounds starting from UAl 3 alloy and Cl 2 (g) is plotted versus temperature in Fig. 4, using three different Cl 2 /UAl 3 initial ratio. It shows that the formation of gaseous uranium chloride compounds increases with temperature and also with the Cl 2 /UAl 3 ratio. These calculations indicate that, in order to prevent U losses in the gaseous phase, the reaction should be carried out with the smallest possible excess of Cl 2 . However, from the point of view of the reaction kinetics, the opposite is required, especially because of the reaction type (solid-gas). An experimental study is needed to determine the kinetics of the reaction and to optimise the Cl 2 /alloy molar ratio.

Third step: Sublimation of AlCl 3

A well managed chlorination step will lead to a mixture of solid chloride compounds composed of AlCl 3 , UCl 4 , PuCl 3 , NpCl 4 , AmCl 3 and CmCl 3 . The following step is to remove AlCl 3 by sublimation, keeping all An as solids in the reactor. A temperature increase under chlorine atmosphere causes volatilization of U together with Al, but the situation is different using inert Ar atmosphere. As shown in Fig. 5a, the sublimation of AlCl 3 starts at 180°C, while no other chloride compound volatilize before 450°C. At this point, NpCl 4 melts, and quickly volatilizes due to its high vapour pressure. The same behaviour was calculated for UCl 4 , but at a higher temperature (~ 550°C). As detailed in Fig. 5b, a temperature range of more than 200°C allows to remove AlCl 3 and thus to perform an effective separation of AlCl 3 from the An chlorides.

CHLORINATION EXPERIMENTS, RESULTS AND DISCUSSION

Although, from a thermodynamical point of view, all steps were proven possible, the applicability of the proposed method depends on the reactions kinetics under working conditions suitable for complete An recovery. The experimental study was carried out to determine realistic conditions for the process and to quantify the chlorination efficiency and actinides volatilization under these conditions.

The experiments were mainly focused on the chlorination step. UAl 3 alloy was selected as input material, since U represents the most difficult element to be completely chlorinated without formation of volatile chlorides. Accordingly, it is expected that the conditions suitable for recovery of U from U-Al alloy should be appropriate for a process including all An.

Experimental

The chlorination experiments were carried out in a glove box under nitrogen atmosphere, specially designed for work with Cl 2 (g). The box is equipped with a chlorine gas line ended by a system of gas wash bottles containing KOH solutions (4 and 8 M), where non reacted chlorine gas is absorbed. A quartz reactor placed in a vertical oven was used for the chlorination (see Fig. 6). Chlorine gas was introduced by a quartz tube guided through the lid of the reactor by a gastight connection. The lid was also equipped by sealed ports for a thermocouple and the gas outlet connected to the chlorine off gas treatment. Boron nitride crucibles were used as containers for the chlorinated material and positioned on the bottom of the reactor. The input material for chlorination experiments was selected to be UAl 3 alloy. Approx. 3.3g of U-Al alloy was prepared by melting in an arc furnace (>3000°C) in 1:3 molar ratio. The composition determined by X-Ray Diffraction (XRD) was 98 wt.% of UAl 3 , 1 wt.% of UAl 2 and 1 wt.% of Al (see Fig. 7). In order to increase the reacting surface, the alloy was crushed into a very fine powder. This was easily achieved manually using a mortar, as U-Al alloys are very brittle. The molar ratio Cl 2 /alloy was kept constant for all the chlorination experiments. The volume of Cl 2 (g) was fixed by the volume of the reactor (1dm 3 ) and the amount of powder to chlorinate was set to be 300 mg. The Cl 2 /alloy molar ration was then equal to 36 for all the experiments.

Three experiments were carried out in the temperature range 150 -170°C. Two experiments, at 150 and 160°C, consisted of two successive chlorinations during approx. 20 hours each. The last experiment at 170°C was a single 20 hours chlorination. In each chlorination experiment, the reactor was filled completely with chlorine gas and then isolated. After chlorination, samples of the chlorinated powder were taken for XRD analysis. In the two first experiments, the rest of the powder was refilled in crucible for further chlorination. Both the initial material and products from the complete chlorination were weighted to calculate a mass balance.

Observations

Experimental results are summarised in Tab. 1.

After the first chlorination, a grey/green powder was obtained for all experiments performed. It indicates the presence of UCl 3 and/or UCl 4 . An increase of powder mass was also observed. In two samples, i.e. ClUAl-150 and ClUAl-160, a part of the powder turned into agglomerate that remained stuck at the bottom of the crucible and could not be analysed. The formation of this agglomerate could be induced by the fine powder structure of the initial UAl material. It shows that the efficiency and the optimal conditions for the chlorination route are strongly dependent of the grains size of UAl alloy. After the second chlorination, a pure green powder was obtained for all experiments performed, indicating the presence of UCl 3 and/or UCl 4 as the major phases (see Fig. 8). The agglomerate part, when formed, was still observable but it became brittle which allowed its extraction and analysis.

Composition of the chlorinated product

XRD analysis of the powder, after the first chlorination, indicated a high efficiency of the chlorination, as less than 2% of the initial alloy remained non-chlorinated. After the second chlorination, the same kind of analysis (see Fig. 9) showed the conversion of original product UCl 3 to UCl 4 .

Fig. 9: X-Ray diffractogram of a sample after second chlorination at 150°C.

As expected, the analysis of the agglomerate revealed a lower efficiency of the chlorination, as roughly 15% of the UAl 3 remained in this part even after two chlorinations. This lower efficiency is caused by a limited diffusion of Cl 2 inside the agglomerate, which indicates a drawback in decreasing too much the grain size of the initial powder.

During the experiments, a part of the sublimated AlCl 3 , and eventually other volatile products, was deposited at the cold surface on the top of the reactor. This deposit was collected and analysed for presence of U compounds. No U was detected in the deposit after the chlorinations carried out at 150 and 160°C. Traces of UCl 5 were detected after chlorination at 170°C but quantification was not possible. However, it clearly shows that higher temperatures than 170°C can not be applied due to uranium losses by volatilisation.

It was impossible to make a quantitative evaluation of the AlCl 3 content by XRD due to its high solubility in the epoxy-resin used for the preparation of the sample. Accordingly, the concentration of AlCl 3 had to be calculated from the real mass of the chlorination product weighted after the experiment, which was deduced from the calculated theoretical mass of U chlorides and non-reacted residual alloy. The mass balance and an evaluated composition of the chlorination product from the three different experiments are shown in Tab. 1 (for the two first experiments, final mass was evaluated taking into account the mass of powder lost after the first chlorination for analysis). For each experiment, the final composition indicates that chlorination is almost fully efficient as less than 5 wt.% of the final product is composed of metallic U-Al, even at 150°C. The results indicate that a major part of AlCl 3 was evaporated already during the chlorination process. According to the calculations, a mass increase up to 686 -719 mg was expected after chlorination of the initial 300 mg of the alloy, if all AlCl 3 had remained in the product. The high percentage of AlCl 3 remaining in CLUAL170 is due to the shorter chlorination time, i.e. 20h (instead of 40h for the two other experiments). It also explains why only UCl 3 was formed during this experiment.

CONCLUSIONS

Pyrochemical processes for recovery of actinides from spent nuclear fuel using both solid and liquid aluminium are investigated at ITU, EC-JRC and CEA, France [START_REF] Conocar | Promising Pyrochemical Actinide/Lanthanide Separation Processes Using Aluminium[END_REF]. Final products for the studied techniques, i.e. electrorefining in molten LiCl-KCl eutectic and reductive extraction to liquid Al in molten LiF-AlF 3 , are actinide-aluminium alloys. As very high selectivity and efficiency has been demonstrated in laboratory scale for both methods, the key point for their further application is to identify a method for recovery of actinides from the formed alloys. According to the results described in this work, a chlorination process seems to be advantageous to fulfil this task.

Initially, the theoretical study showed thermodynamical possibility of all steps proposed for the process.

The conclusions from the study were:

-Vacuum distillation is efficient to remove the remaining salt including most fission products, except MoCl 2 , SrCl 2 and BaCl 2 (proposed conditions: T=1000°C, P=10 -5 bar).

-Full chlorination of the alloy is possible at any considered temperature (studied temperature range: 25 -1000°C). In this case, as it is a solidgas reaction, the reaction kinetic is the most important factor.

-Best conditions for the chlorination step are to chlorinate the finely crushed alloy at 150°C, using minimum acceptable Cl 2 / alloy mass ratio in order to avoid the formation of gaseous U compounds.

-Heating of the chlorination products under inert argon atmosphere at 350-400°C allows to evaporate AlCl 3 and consequently to recover pure solid An chlorides.

The experimental study was focused mainly on the kinetic aspects of the chlorination step. Three experiments showed that chlorination of UAl 3 can be efficiently performed in the 150-170°C temperature range. Approx. 20 hours of chlorination yielded products mainly composed of solid UCl 3 and UCl 4 even at a temperature of 150°C, which is in good agreement with the conclusions of the thermodynamic study. Further chlorination led to the conversion of UCl 3 into UCl 4 . Traces of volatile UCl 5 were identified in the condensate after the chlorination at 170°C. Also in previous experiments it was demonstrated that important amounts of volatile UCl 5 and UCl 6 are formed during chlorinations at temperatures higher than 180°C. As a consequence, for optimum efficiency of the chlorination, temperatures higher than 170°C should not be applied. In addition, a single chlorination step running for 20 hrs at 150°C is enough to sublimate the major part of produced AlCl 3 .

On the other hand, the experiments showed that too finely crushed input material can decrease the total efficiency of the reaction, as non-fully chlorinated agglomerates were formed inside the crucible.

The influence of working temperature on the efficiency of the chlorination process was evaluated during the experiments and future investigations will be focused on the optimisation of the molar ratio between Cl 2 (g) and the alloy.

Fig. 1 :

 1 Fig. 1: Principle of the chlorination route (An=actinides, FP=fission products)

Fig. 2 :

 2 Fig. 2: Vapour pressure vs. reverse of temperature for various metals and chlorides.

Fig. 3 :

 3 Fig. 3: Chlorination of UAl 4 (1.0 mol) and PuAl 4 (0.5 mol) at 150°C -Influence of the amount of Cl 2 (g).

Fig. 4 :

 4 Fig. 4: Chlorination of UAl 3 alloys -Calculation of the evolution of the amount of chloride compounds with temperature and Cl 2 /UAl 3 molar ratio. Initial conditions: 1 dm 3 reactor containing 2000 -300 -10 mg of solid UAl 3 alloy and 4.843 10 -2 mol of Cl 2 (g) (P=1.2 bars at 25°C).

Fig. 5 :

 5 Fig. 5: Sublimation of AlCl 3 from the chloride mixture. a) Evolution of the composition with T. b) Evolution of the volatilization with T. Initial conditions: mixture of 1 mole of An chlorides, 2 moles of AlCl 3 and Ar (1 atm).

Fig. 6 :

 6 Fig. 6: Experimental set-up for chlorination -Quartz reactor

Fig. 7 :

 7 Fig. 7: X-Ray diffractogram of the U-Al alloy prepared with arc furnace and used as input material.

Fig. 8 :

 8 Fig. 8: Pictures of the powder before chlorination and after second chlorination at 150°C.

TABLE 1

 1

	Composition of the input material and
	the solid chlorination product
			Concentration [wt.%]
		Specie	Input material	Product
		UCl 3	0.0	18
	CLUAL150	UCl 4	0.0	72.9
	Temp. 150°C	UAl 3	98.0	2.2
	Two	UAl 2	1.0	0.5
	chlorinations	AlCl 3	0.0	6.4
	20h	Al	1.0	0.0
		mass [mg]	300.5	371.1
		UCl 3	0.0	19.0
	CLUAL160	UCl 4	0.0	64.0
	Temp. 160°C	UAl 3	98.0	4.7
	Two	UAl 2	1.0	0.0
	chlorinations	AlCl 3	0.0	12.2
	20h	Al	1.0	0.0
		mass [mg]	300.2	396.4
		UCl 3	0.0	84.5
	CLUAL170 Temp. 170°C one chlorination 20h	UCl 4 UCl 5 UAl 3 UAl 2 AlCl 3 Al	0.0 0.0 98.0 1.0 0.0 1.0	0.0 traces 0.6 0.0 14.9 0.0
		mass [mg]	301.04	375.5


Vincent G Chapin

Romaric Neyhousser

G Dulliand

Patrick Chassaing

J & Teeters

Al

DESIGN OPTIMIZATION OF INTERACTING SAILS THROUGH VISCOUS CFD

In this paper, we present ADONF, a new numerical simulation platform for viscous flows. This platform is developed and validated to compute analysis, design and optimization of real flows around complex sails configurations through a large number of automated Reynolds Averaged Navier-Stokes (RANS) simulations. We illustrate the ability of ADONF to search for robust, high performance, optimized fluid flows, in the field of the aerodynamic of sailing boats. Results presented focus on the optimization of the design and trimming of interacting sails because it is a question of major interest for many competitive sailors. Because ADONF is based on Navier-Stokes equations in RANS or URANS formulations, sail shape and trimming optimization in upwind and downwind sailing conditions may be addressed as will be shown. For future applications, it will be possible to extend and apply ADONF to hydrodynamic of sailing boats or any other fields in fluid mechanics governed by Navier-Stokes Equations. ¶ NOMENCLATURE β -Apparent wind angle c -Sail chord C d , C l -Drag and lift force coefficients C r -Driving force coefficient C h -Heeling force coefficient C p -Pressure coefficient δ -Sail trim angle δ GV1 -Windward mainsail trim angle δ GV2 -Leeward mainsail trim angle δ f , δ jib -Jib trim angle f -Sail camber f GV1 -Windward mainsail camber f GV2 -Leeward mainsail camber F h -Aerodynamic heeling force F r -Aerodynamic driving force i -Aerodynamic angle of attack M c -Aerodynamic heeling moment S -Sail surface x f -Location of the sail maximum camber 1.

INTRODUCTION

The work presented in this paper is a tentative of response to the following question: how to better design and better trim interacting sails to maximize sailing boats performance? Sail designers and competitive sailors know that this is a complex question. Existing tools are frequently based on crude modelization of the real flow. Moreover, VPP are necessary to predict sailing boat speed for a given measured or predicted aerodynamic force. Today, VPP are based on simplified aerodynamic and hydrodynamic models to predict aero-hydrodynamic forces and there dependences to design parameters. These models are crude representation of the real forces acting on sailing yachts [START_REF] Claughton | Development in the IMS VPP Formulations[END_REF][START_REF] Fossati | Wind Tunnel Techniques for Investigation and Optimization of Sailing Yachts Aerodynamics[END_REF][START_REF] Jackson | An improved upwind sail model for VPPs[END_REF][START_REF] Oossanen | Predicting the Speed of Sailing Yachts[END_REF]22]. Some of their drawbacks are known to result in some misleading predictions but increase their performance is not an easy task [START_REF] Claughton | Development in the IMS VPP Formulations[END_REF][START_REF] Fossati | Wind Tunnel Techniques for Investigation and Optimization of Sailing Yachts Aerodynamics[END_REF][START_REF] Jackson | An improved upwind sail model for VPPs[END_REF][START_REF] Oossanen | Predicting the Speed of Sailing Yachts[END_REF]22]. As said before by Korpus [START_REF] Korpus | Performance Prediction without Empiricism: A RANS-Based VPP and Design Optimization Capability[END_REF], experiments are probably the best method to predict theses forces by taking into account real world effects like viscous separation, unsteadiness, etc… But it is difficult to discard scaling effects during the transposition to real yachts. It is always difficult to take into account aero-structural coupling which may be important in sail design. Another difficulty specific to experiment is the ability to access all physical variables needed to better understand flow around bodies which may be helpful to guide future design.

The best validated modelization we have today is viscous Computational Fluid Dynamics (CFD) through RANS simulations [START_REF] Chapin | Analysis, Design and Optimization of Navier-Stokes Flows around Interacting Sails[END_REF][START_REF] Chapin | Sailing Yacht Rig Improvements through Viscous CFD[END_REF][START_REF] Chapin | Viscous CFD as a relevant decisionmaking tool for mast-sail aerodynamics[END_REF][START_REF] Korpus | Reynolds Averaged Navier-Stokes in an Integrated Design Environment[END_REF][START_REF] Korpus | Performance Prediction without Empiricism: A RANS-Based VPP and Design Optimization Capability[END_REF]. The question of the usefulness of these advanced numerical tools for sail design is open. RANS codes have a critical drawback when used to predict forces acting on a yacht. They are time-consuming. But, the highest time consuming task in the process is the engineer time needed to generate meshes with a high quality standard. Moreover, design and optimization are complex multi parameters processes which need a large number of configuration variations.

These facts drive three questions to make RANS methods useful for yacht and sail designer:

• Is it possible to automate mesh generation and integrate RANS simulations into a user-friendly environment? • Is it possible to qualify RANS predictions with experiments representative to real separated, unsteady flow conditions? • Is it possible to decrease the time needed to compute hundred or more RANS simulations to search for optimums and robust designs?

In this paper we propose ADONF, a new numerical simulation platform which may be a response to these questions. The first novelty of ADONF is that it proposes a solution to the first question with an automated mesh generation process. The second one is we use a solver based on RANS equations and not inviscid ones. And the necessity of a viscous modelization for flow around mast and sails has been shown previously [START_REF] Chapin | Viscous CFD as a relevant decisionmaking tool for mast-sail aerodynamics[END_REF][START_REF] Chapin | Aérodynamique grand voile -mât[END_REF][START_REF] Jones | International America's Cup class yacht design using viscous flow CFD[END_REF]. Also, with ADONF it is now easy to simulate hundred or thousand two-dimensional sails configurations to compute optimal design of multi parametric problems on a laptop [START_REF] Chapin | Analysis, Design and Optimization of Navier-Stokes Flows around Interacting Sails[END_REF][START_REF] Chapin | Sailing Yacht Rig Improvements through Viscous CFD[END_REF]. Extension to three-dimensional configurations is in progress and should not pose new specific problems. One difference should be true for few years: simulation time should not be compatible with laptop but should require a multiprocessor workstation or a supercomputer for computing hundred or more threedimensional configurations. In this paper, we will first present the computational model used by going through the solver, mesh issues, transition and turbulence modelling issues. Then, we will briefly describe the integrated, user friendly environment developed in ADONF. Then, in the next part, ADONF potential in sail design and optimization will be illustrated though examples. Typical and original configurations with one, two or three sails in upwind or downwind sailing conditions have been chosen.

COMPUTATIONAL MODEL

In this section, main elements of the computational model are described. First the fluid dynamics equations used to simulate the flow around interacting sails are presented then the solver and physical models and limitations are described. We are using viscous Navier-Stokes equations on hybrid meshes with structured and unstructured mesh part in the computational domain with conformal or non-conformal interfaces between domains. This is a powerful technology with high flexibility for mesh generation of interacting sails for two and three-dimensional flows.

GOVERNING EQUATIONS

The flow simulations around interacting sails presented in this paper are based on the numerical resolution of the following Reynolds Averaged Navier-Stokes equations:

] [ ) ( ) ( 0 ) ( ij ij j i j i i i i R x x p u u x u t u t t + ∂ ∂ + ∂ ∂ - = ∂ ∂ + ∂ ∂ = ∂ ∂ + ∂ ∂ τ ρ ρ ρ ρ With the viscous stress tensor ] 3 1 [ 2 ij k k ij ij x u S δ µ τ ∂ ∂ - = the deformation tensor ) ( 2
1 i j j i ij x u x u S ∂ ∂ + ∂ ∂ =
and the turbulent Reynolds stress tensor R ij which should be modelled (see turbulence modelling part). Following Boussinesq hypothesis this tensor may be approximated by:

ij ij k k ij T ij k x u S R δ ρ δ µ ) ( 3 2 ] 3 2 [ - ∂ ∂ - ≅

SOLVER

The software package used to resolve the Navier-Stokes equations is Fluent 6. It is a steady or unsteady, compressible or incompressible, threedimensional solver which resolve the previously given Reynolds Averaged Navier-Stokes (RANS) equations. In the simulations presented, we have used the segregated solver and the Spalart-Allmaras turbulence model in its vorticity-based or strain-vorticity-based production term. When not explicitly specified, second-order spatial and temporal schemes were used in the steady version.

To solve the Navier-Stokes equations proper boundary conditions are required on all calculation domain frontiers. At wall boundary, the no-slip condition is applied. A pressure outlet boundary condition is applied at the outlet. A velocity inlet boundary condition is applied on other frontiers (inlet, up and down).

MESH ISSUES

The mesh generation is a crucial step in the process of RANS simulation. First of all, it is a time consuming activity which need engineer experience and long practice to rigorously clean the CAD geometry and do the best choice for the mesh topology. Secondly, the mesh influence on results on typical sails configurations is may be important and should be carefully evaluated and bounded by relevant choices in mesh size distribution over main flow regions. Boundary layers have to be well resolved on all bodies (mast and sails) and this impose some critical criteria on mesh size in the normal and tangential direction to walls. But these criteria are not enough to obtain a good flow description and results independent to mesh. Other flow gradients may have to be well resolved. This is not a simple task on typical sails because of the zero thickness and the subsequent leading-edge pressure gradient when angle of attack is not ideal as frequently supposed in inviscid methods. From that point of view, hybrid mesh technology may be a critical issue for high-fidelity RANS simulations [START_REF] Chapin | Viscous CFD as a relevant decisionmaking tool for mast-sail aerodynamics[END_REF].

In fact, it is good to know that results are never totally independent to the chosen mesh as opposed to what is frequently argued. The relevant question when interpreting RANS results on sails is: how bounded is the mesh influence on physical quantities of interest.

To illustrate the mesh convergence, figure 1, the lift-to-drag ratio convergence with mesh number of points on a typical sail (f/c = 12.5%, Re = 1.4 x 10 6 ) calculated on four meshes have been shown. A good convergence of this critical performance parameter with the mesh number of points may be seen. Another important feature of mesh is their adaptability or flexibility to be used with different kind of sail geometries and trim angles. A critical point for yacht rig aerodynamic studies is the necessity to generate meshes on multiple bodies (mast, mainsail, jib, etc…) which interact and may be displaced relative to others. The challenge is to generate good quality meshes in the boundary layers regions of each body without using too high aspect ratio cells. To respect these topologic constraints and obtain good mesh control, a good candidate is hybrid meshes (as may be seen on figure 2) with eventually non conformal interface between the inner structured region around masts and sails and the outer unstructured region around all interacting structured domains (figure 2) as was done with Gambit 2.2 [START_REF]Gambit 2.3 & Fluent 6.2 users guide and tutorials[END_REF]. The mast trailing-edge with link to the zerothickness sail is a region of difficulty for the structured mesh part and need much more attention and some tricks.

TRANSITION & TURBULENCE MODELING

A reliable prediction of the boundary layer transition through computer simulation is always a challenge today. The transition of a boundary layer is a highly complex physical phenomenon. It is a problem of stability of the Navier-Stokes equations which are highly sensitive to background turbulence level, pressure gradient, surface roughness, etc… The range of existing transition prediction methods extends from simplified empirical relationships through those based on linear stability to direct numerical simulations. All of these methods have critical limitations. No transition models are implemented in RANS simulations. Eventually transition may be tripped when transition location is known.

In the same time, mast and sail aerodynamic is highly concerned with separation bubble, turbulent transition and turbulent reattachment process and it is well known that these phenomenon and their associated pressure losses may have critical influence on pressure and friction distribution on sails. Also an accurate representation of laminar and turbulent separated flow regions is critical when we are concerned with drag prediction.

Despite this, we will see in this paper that a simple low cost turbulence model like the Spalart-Allmaras model may have coherent qualitative behaviour on mast-sail geometries and may reveal to be better than more sophisticated ones.

The Spalart-Allmaras turbulence model used is a one equation model with standard coefficients values. The equation is a transport equation for the turbulent viscosity as follow:

4187 . 0 , 0 . 2 , 3 . 0 , 1 1 . 7 , 3 / 2 , 622 . 0 , 1355 . 0 ~, ) ( , ] 1 [ 2 , 2 , 2 ) , 0 min( ) ( 2 1 , 2 , , ~) ( )] ) ( ) [( [ 1 1 1 , , ~) ( ) (

INTEGRATED & AUTOMATED COMPUTATIONAL ENVIRONMENT

Fluid motion around interacting sails in their real environment is complex with separated flow regions and unsteady phenomena. Because there are a lot of parameters that define a sail design or a complete rig design, there is a crucial need to integrated and automate the entire simulation process. Turnaround time of the simulation process is another constraint. ADONF is a response which gives us the ability to analyse a large number of configurations and design. It opens a new way to design and optimize fluid motion around interacting sails through viscous methods.

Because, we think that this is a central question for the usefulness of RANS simulations in yacht design, we have developed this new numerical tool which integrate and automate the entire computational environment of RANS flow simulation from CAD definition, to mesh generation, flow simulation, flow analysis and design modifications through optimization following the diagram of figure 3. The main difficulty is the mesh generation process automation. When the problem has been resolved, we have obtained a tool which generates meshes of high reliability. This particular property of automated meshes increases our ability to compare and rank different design or sail trim. It also increases ease to study the mesh density influence on results.

As it will be shown through examples, with ADONF, it becomes possible to investigate and resolve new questions about fluid motion around designed bodies and their related performances.

The first level of new questions that can be investigated is the "what-if" questions. What will be the performance of this rig design if I change the mast section? What will be the performance of this rig if I change the sail recovery factor preserving a constant sail surface? Etc… It is only the imagination of the sail designer which limits the process. We don't need many engineers to generate all the meshes needed to respond to these questions.

In a second phase, we have implemented optimization algorithms in ADONF. With optimization algorithms, a second, higher level, set of questions becomes open to the designer. How to change the rig design or the deck plan to increase the performance of that particular sailing boat in given wind conditions? How to change rig trimming to increase boat speed in given wind conditions? What is the best camber and trim of these two interacting sails to maximize driving force or driving to heeling force ratio? Etc… Let us illustrate this through examples now.

OPTIMUM CAMBER OF A SINGLE SAIL

From the excellent work of F. Bethwaite [START_REF] Bethwaite | High performance sailing[END_REF], we know that in real viscous flow, there exists an optimum sail camber. This observed fact has been chosen as an interesting question to test the ability of ADONF and implemented optimization algorithms to resolve sail design questions.

For a single sail the optimization problem may be formulated as follow: for a given apparent wind angle, what is the optimal camber and related trim angle which maximize the driving force Fr? The same question is also posed for maximizing the lift-to-drag ratio Fr/Fh. The apparent wind angle chosen was β = 30°. Other sail parameters are listed in the following table:

β x f C f 0 δ 0 30° 30% 6500 7% 13°
The optimization algorithm first used was a gradient based algorithm known as the Simplex method. After about twenty RANS simulations, a good convergence is obtained (figure 4,5,6) and ADONF found the following optimal solutions for maximum driving force and maximum lift-to-drag ratio:

Objective f GV i GV Max(Fr) 18% 7° Max(Fr/Fh) 8% 3°
The number of needed RANS simulations to determine the optimal solution was dependent to the initial condition but the optimal solution was independent to the initial condition. An example of algorithm It is interesting to note that the optimal solution, maximizing the driving force, present a separation near the trailing-edge on the suction surface (figure 7). This point clearly illustrates the ability of viscous CFD to make a trade-off, between high camber and massive separation, through RANS simulations.

TWO INTERACTING SAILS

A more challenging optimization problem is the two interacting sails problem which is typical of mainsail-jib interaction on a sailing boat and is well known as a problem of long debates and controversies [START_REF] Arvel | The Aerodynamics of Sail Interaction[END_REF][START_REF] Marchaj | Sail Performance[END_REF]. The question is to know if ADONF may be used to clarify this problem without passion.

The optimization problem may be formulated as follow: for a given apparent wind angle, what are the optimal cambers and related trim angles which maximize the driving force Fr? The same question is also posed for maximizing the lift-to-drag ratio Fr/Fh. The apparent wind angle chosen was β = 30°.

As in the previous case, we have used the Simplex algorithm for optimization process. The results found are listed in the following table: The solution that maximizes the driving force is visualized on figure 8. As in the previous case, small separation regions are found near the trailing-edge on the suction surfaces. For further investigation on this problem, it will be possible to take into account a constraint on the heeling moment to obtain more realists designs for a given boat. This constraint may be easily added through a penalty method or another efficient constraint handling method [START_REF] Deb | An efficient constraint handling method for genetic algorithms[END_REF][START_REF] Müller | Bio-Inspired Optimization Algorithms for Engineering Applications[END_REF].

THREE INTERACTING SAILS

Another interesting and complex problem of interacting sails on which we have had the chance to work is the double rig of the Hydraplaneur of Yves PARLIER, an ocean racing multihull design by the Aquitaine Design Team [START_REF] Chapin | Gréement Gerris[END_REF]. This new rig, as shown in figure 9 opens new questions about sail design. One question is related to the differential trimming and differential loading between the windward and the leeward rig. Is there an optimum? How this optimum change with apparent wind direction?

Here, the question of the optimum driving force of this double rig with three interacting sails in downwind sailing conditions is open.

A design of experiment on a three sails configuration with five variables has been done with ADONF (figure 10). A set of points have been obtained in the driving force, heeling moment plane (figure 11). The mesh influence on results has been qualified to choose the mesh number of points. From the three sails design of experiment, a complementary set has been defined and another one with 4 sails and nine variables (figure 11). It is shown that the 3 sails complementary set and the 4 sails set increase the aerodynamic performance of the initial set. It may be interesting to evaluate multi-objective optimization methods to determine the Pareto frontier of this rig with more precision.

Another recurrent question is to know if the addressed optimization problem presents a complex response surface with local optimums and a global optimum. If the response to this question is positive, optimum solutions found by gradient based algorithm like the Simplex method may be dependent to the initial condition of the optimization process. It may be useful, in this case, to use evolutionary algorithms. This argument is frequently used to justify the usefulness of genetic algorithms but problems with this property are difficult to find [START_REF] Pulliam | Comparison of Evolutionary (Genetic) Algorithm and Adjoint Methods for Multi-Objective Viscous Airfoil Optimizations[END_REF]! Also we have tried to visualize a sub-problem response surface of the three sails optimization problem by taking into account only the two major variables of the five variables problem. These variables are trim angles of the two mainsails (δ GV1 , δ GV2 ). The response surface based on these two variables is shown on figure 12. It is interesting to note that this response surface exhibits three local optimum of the driving coefficient and a global optimum. This fact clearly illustrates the usefulness of evolutionary algorithms for aerodynamic optimization of viscous flows based on RANS or URANS simulations.

5.

CONCLUSIONS

Results obtained with ADONF software package and presented in this paper demonstrate that today, it is possible to do analysis, design and optimization of complex interacting sails configurations with viscous CFD through automated RANS simulations.

Needed conditions to do a good job with this kind of viscous CFD are the following:

• To have a user-friendly environment to run hundred or more RANS simulations with ease on a laptop. • To use a high-fidelity RANS solver with appropriate hybrid meshes for separated flows on mast and sail configurations [START_REF] Chapin | Viscous CFD as a relevant decisionmaking tool for mast-sail aerodynamics[END_REF]. • To implement optimization algorithms and probably evolutionary methods for complex rig configurations with multi-modal optimal solutions. • To have a background in sail design and an expertise in viscous CFD to resolve conceptual design questions through optimization.

Today, we are working on the extension of ADONF to three dimensional flows with a parameterization of sail shape relevant for sail designers. For future applications, it will be interesting to couple ADONF with a hydrodynamic solver. Then design optimization might be done directly on boat speed.

6.

Figure 1 :

 1 Figure 1: lift-to-drag ratio convergence with mesh refinement (number of points divided by 1000

Figure 2 :

 2 Figure 2: hybrid mesh example

Figure 3 :

 3 Figure 3: ADONF software package diagram

  on figures 2 & 3 for camber, trim angle and driving force.

Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 4567 Figure 4: configurations of the optimization problem

Figure 8 :

 8 Figure 8: stream function around two interacting sails for maximum driving force at β β β β = 30°

Figure 9 :Figure 10 :Figure 11 :Figure 12 :

 9101112 Figure 9: Hydraplaneur double rig

Table 4 : optimum design & trimming results

 4

	Objective	f GV	i GV	f JIB	i JIB
	Max(Fr)	27%	27°	30%	-2°
	Max(Fr/Fh)	4%	20°	19%	-1°


Vincent Brebion
email: vincent.brebion@hds.utc.fr

Julien Moreau
email: julien.moreau@hds.utc.fr

Franck Davoine
email: franck.davoine@hds.utc.fr

Learning to Estimate Two Dense Depths from LiDAR and Event Data

Keywords: Sensor fusion, Machine learning, Dense depth estimation

Event cameras do not produce images, but rather a continuous flow of events, which encode changes of illumination for each pixel independently and asynchronously. While they output temporally rich information, they lack any depth information which could facilitate their use with other sensors. LiDARs can provide this depth information, but are by nature very sparse, which makes the depth-to-event association more complex. Furthermore, as events represent changes of illumination, they might also represent changes of depth; associating them with a single depth is therefore inadequate. In this work, we propose to address these issues by fusing information from an event camera and a LiDAR using a learning-based approach to estimate accurate dense depth maps. To solve the "potential change of depth" problem, we propose here to estimate two depth maps at each step: one "before" the events happen, and one "after" the events happen. We further propose to use this pair of depths to compute a depth difference for each event, to give them more context. We train and evaluate our network, ALED, on both synthetic and real driving sequences, and show that it is able to predict dense depths with an error reduction of up to 61% compared to the current state of the art. We also demonstrate the quality of our 2-depths-toevent association, and the usefulness of the depth difference information. Finally, we release SLED, a novel synthetic dataset comprising events, LiDAR point clouds, RGB images, and dense depth maps.

Introduction

Rather than accumulating light to create images, event cameras perceive changes of illumination for each pixel independently and asynchronously. Thanks to their high temporal resolution (in the order of the µs) and high dynamic range, event cameras are a sensor of choice for dynamic applications in complex environments (fast motions, extreme illumination conditions), where traditional cameras reach their limits.

LiDAR sensors offer accurate but sparse 3D information of their surrounding environment. They are a key component for autonomous navigation, helping to solve multiple problems, e.g., obstacle detection and tracking, SLAM, etc. Yet, their sparsity often constitutes a limiting factor. While 64-or 128-channel LiDARs are starting to be commercialized, they come at a significantly high cost, and are still not as dense as cameras.

In this work, we focus on the fusion of LiDAR and event data, which we consider as a dual problem: (1) LiDAR depths densification and (2) eventsdepths association. Regarding problem [START_REF] Baldwin | Time-ordered recent event (TORE) volumes for event cameras[END_REF], we are interested in densifying the LiDAR data using the events as a guide. As a result, dense depth maps are obtained, which allow for a dense 3D perception of the observed scene. As for problem (2), we are interested in associating a depth to each event. By doing so, each event can be projected in 3D, and then even be backprojected in 2D in another vision sensor. For a fully calibrated and synced setup, this process would allow for the superimposition of events and RGB images, a task which is only possible at the moment through the use of specific low-resolution frame+events cameras like the DAVIS240C [2].

Estimating dense depth maps from sparse LiDAR data is a well-regarded problem as it solves the sparsity drawback of the LiDAR while keeping its metric scale. However, using events to densify depth maps (i.e., problem [START_REF] Baldwin | Time-ordered recent event (TORE) volumes for event cameras[END_REF]) might be inaccurately seen as a task that inherently includes problem (2), as corresponding depths for the events could be taken from the dense depth map. We argue in this work that, as each event represents a change in illumination, it might also represent a change in depth. As such, two depths should be associated to each event, and we will therefore compute two depth maps: one before the events happen, and one after they happen.

As an answer to these issues, we propose in this work a learning-based fusion method for estimating pairs of dense depth maps from events and sparse LiDAR data. Our main contributions are as follows:

-We propose to revise the principle of associating a single depth to each event to rather estimate two depths: one "before" the event happens, and one "after". Following this, we introduce the notion of "depth change map", to give more context to each event.

-We propose a novel convolutional network, the ALED (Asynchronous LiDAR and Events Depths densification) network, able to fuse asynchronous events and LiDAR data, and to estimate the two dense depth maps from them, while surpassing state-of-the-art accuracy. -We finally build and share a high-definition simulated dataset, the SLED (Synthetic LiDAR Events Depths) dataset, used as part of the training of the network and its evaluation.

If the reader is interested, supplementary material, the SLED dataset, source codes, as well as videos showcasing results on both simulated and real data are all available at https://vbrebion.github.io/ALED.

Related Work

LiDAR Densification

LiDAR sensors only produce sparse point clouds, which is challenging for numerous applications (3D reconstruction, object detection, SLAM, etc). As a consequence, LiDAR depth completion is a subject that has been widely studied in the literature.

Some authors try to obtain dense depth maps while only relying on the sparse data from the LiDAR. These methods either use machine learning [START_REF] Chodosh | Deep convolutional compressed sensing for Li-DAR depth completion[END_REF][START_REF] Huang | HMS-Net: Hierarchical multi-scale sparsity-invariant network for sparse depth completion[END_REF][START_REF] Uhrig | Sparsity invariant CNNs[END_REF] or traditional image processing operations [START_REF] Ku | In defense of classical image processing: Fast depth completion on the CPU[END_REF].

The most successful approaches use a secondary modality as a guide for the densification process. While most of these approaches employ a RGB camera as the secondary sensor [START_REF] Gansbeke | Sparse and noisy Li-DAR completion with RGB guidance and uncertainty[END_REF][START_REF] Huang | HMS-Net: Hierarchical multi-scale sparsity-invariant network for sparse depth completion[END_REF][START_REF] Jaritz | Sparse and dense data with CNNs: Depth completion and semantic segmentation[END_REF][START_REF] Xu | Depth completion from sparse LiDAR data with depth-normal constraints[END_REF], other authors have proposed using alternative modalities, such as stereo cameras [START_REF] Maddern | Real-time probabilistic fusion of sparse 3D LIDAR and dense stereo[END_REF] or more recently event cameras [START_REF] Cui | Dense depth-map estimation based on fusion of event camera and sparse LiDAR[END_REF].

Fusion of Events and Other Modalities

Due to their relative youth, the literature on the fusion of data from event cameras with other sensors is quite sparse.

Most of the investigations focused on the fusion of events and frames, thanks to sensors offering both modalities like the DAVIS camera [2]. These works include frame interpolation and deblurring [START_REF] Paikin | EFI-Net: Video frame interpolation from fusion of events and frames[END_REF][START_REF] Pan | Bringing a blurry frame alive at high frame-rate with an event camera[END_REF][START_REF] Scheerlinck | Continuous-time intensity estimation using event cameras[END_REF], feature tracking [START_REF] Gehrig | EKLT: Asynchronous photometric feature tracking using events and frames[END_REF][START_REF] Kueng | Low-latency visual odometry using event-based feature tracks[END_REF], object detection [START_REF] Cao | Fusion-based feature attention gate component for vehicle detection based on event camera[END_REF][START_REF] Jiang | Mixed frame-/event-driven fast pedestrian detection[END_REF][START_REF] Tomy | Fusing event-based and RGB camera for robust object detection in adverse conditions[END_REF], or even steering prediction [START_REF] Hu | DDD20 end-to-end event camera driving dataset: Fusing frames and events with deep learning for improved steering prediction[END_REF].

In the past few years, a few authors have started investigating the fusion of events and LiDAR data. Explored issues include calibration [START_REF] Song | Calibration of event-based camera and 3D LiDAR[END_REF][START_REF] Ta | L2E: Lasers to events for 6-DoF extrinsic calibration of lidars and event cameras[END_REF], and very recently, point clouds enhancement with events [START_REF] Li | Enhancing 3-D LiDAR point clouds with event-based camera[END_REF] and LiDAR densification [START_REF] Cui | Dense depth-map estimation based on fusion of event camera and sparse LiDAR[END_REF].

Depth Estimations with Events

Several approaches have been proposed in order to estimate sparse or dense depth maps by using a single event camera. Kim et al. [START_REF] Kim | Real-time 3D reconstruction and 6-DoF tracking with an event camera[END_REF] used probabilistic filters to simultaneously estimate the motion of the camera, reconstruct a log intensity image of the observed scene, and construct a sparse inverse depth map. Zhu et al. [START_REF] Zhu | Unsupervised event-based learning of optical flow, depth, and egomotion[END_REF] used a convolutional network to jointly predict depth and egomotion, by trying to minimize the amount of motion blur in the accumulated events. Hidalgo-Carrió et al. [START_REF] Hidalgo-Carrió | Learning monocular dense depth from events[END_REF] were the first to estimate dense depth maps from a monocular event camera, through the use of a recurrent convolutional network.

In parallel, other authors have advocated for the use of a secondary sensor to help the depth estimation. Schraml et al. [START_REF] Schraml | An event-driven stereo system for realtime 3-D 360°panoramic vision[END_REF][START_REF] Schraml | Dynamic stereo vision system for real-time tracking[END_REF] and Nam et al. [START_REF] Nam | Stereo depth from events cameras: Concentrate and focus on the future[END_REF] used two event cameras, and estimated depths by creating images of accumulated events for each camera and applying stereo matching. While [START_REF] Schraml | An event-driven stereo system for realtime 3-D 360°panoramic vision[END_REF][START_REF] Schraml | Dynamic stereo vision system for real-time tracking[END_REF] used traditional model-based approaches, [START_REF] Nam | Stereo depth from events cameras: Concentrate and focus on the future[END_REF] entirely relied on learning-based networks: an attention-based network to construct detailed events representations, then a convolutional network for depth map inference. Other authors have also combined the event camera with a RGB sensor; Gehrig et al. [START_REF] Gehrig | Combining events and frames using recurrent asynchronous multimodal networks for monocular depth prediction[END_REF] for instance designed a recurrent network to fuse asynchronous data and estimate dense depths from them. Finally, some authors have also used depth sensors in direct combination with event cameras. Weikersdorfer et al. [START_REF] Weikersdorfer | Event-based 3D SLAM with a depth-augmented dynamic vision sensor[END_REF] used an RGB-D camera to obtain dense depths, and used the depth-augmented events to perform SLAM. Li et al. [START_REF] Li | Enhancing 3-D LiDAR point clouds with event-based camera[END_REF] used a LiDAR sensor to associate a depth to each event through the use of a Voronoi diagram and a set of heuritic rules. Cui et al. [START_REF] Cui | Dense depth-map estimation based on fusion of event camera and sparse LiDAR[END_REF] also employed a LiDAR, to derive dense depth maps by using 3D geometric information.

Depth Change Map: Two Depths per Event

The fusion of depths and events is a problem that can have two different goals:

(1) obtaining dense depth maps from events and sparse LiDAR data, or (2) determining a depth for each event. While problem (1) can be interpreted as a LiDAR densification method guided by the events, we argue here for problem (2) that associating a single depth to an event is inadequate.

By definition, an event represents a significant change in illumination observed by a given pixel. Under motion, observed events can either originate from (a) texture changes inside an object; or from (b) the contour of an object. In case (a), associating a single depth to these events can be coherent, as depth inside an object should be subject to little variation. However, doing so in case (b) is erroneous, as the events are likely to denote also a depth change.

Instead, we propose to estimate two dense depth maps: one before the events happen, which we will denote D bf in the rest of this article, and one after the events happen, which we will denote D af . We can then formulate the depth change map as D af -D bf and compare the two depths d bf and d af for each pixel. Three meaningful cases can be distinguished:

1. d af -d bf ≈ 0: the pixel is located in an area where depths do not vary much, i.e., inside an object; 2. d af -d bf 0: the pixel was at the edge of an object, and is now on an object further away; 3. d af -d bf 0: the pixel was located on a far object, and is now at the edge of a closer object.

The depth difference information given by the depth change map can especially help events processing to differentiate real objects from artifacts such as shadows and even noise. An illustration of some possibilities offered by the depth change map on events is given in Fig. 1. Other applications could also take advantage of the pair of depth maps D bf and D af : ego-motion and speed estimation, objects clustering, scene flow, etc.

Method

The ALED Network

Inspired by the Recurrent Asynchronous Multimodal Network (RAMNet) architecture of Gehrig et al. [START_REF] Gehrig | Combining events and frames using recurrent asynchronous multimodal networks for monocular depth prediction[END_REF] for RGB and events fusion, we propose here a fully Thresholds:

d af -d bf < -1m d af -d bf ∈ [-1m, +1m] d af -d bf > +1m
(c) Thresholded depth change map, using the events as a mask Fig. 1: Example of the importance of the depth change map for each event on the "Town01_00" sequence from our SLED dataset. Notice how simple thresholds on this depth difference help distinguishing the events linked to the contour of real objects from the events corresponding to the texture of the road, the halo from the street lamp, or even the noisy events in the sky.

convolutional recurrent network to estimate dense depths from asynchronous Li-DAR and events data. We call it the ALED Net, for Asynchronous LiDAR and Events Depths densification network. Our network can be decomposed in two main parts: an encoder, tasked with fusing asynchronous events and LiDAR features at different scales, and a decoder, tasked with interpreting the fused features for estimating dense depths.

In its encoder part, illustrated in Fig. 2, the LiDAR and events inputs are fed independently. Both of them go through an encoding head, computing a first feature map of 32 channels while keeping their original height and width. Convolutional encoders (in the form of ResNet Basic Blocks [START_REF] He | Deep residual learning for image recognition[END_REF]) are then used to compute feature maps at scales 1/2, 1/4, and 1/8, doubling the number of channels every time. Each of these feature maps is then used as the input of convolutional gated recurrent unit (convGRU) blocks [START_REF] Siam | Convolutional gated recurrent networks for video segmentation[END_REF], updating its corresponding state. Since these states are shared between the LiDAR and events encoders, both parts of the network can update them asynchronously.

In its decoder part, illustrated in Fig. 3, the convGRU state at the lowest scale first goes through two residual blocks. Then, for each following scale, the decoded feature map from the previous scale is upscaled by using convex upsampling [START_REF] Teed | RAFT: Recurrent all-pairs field transforms for optical flow[END_REF]. While a simple bilinear upsampling was used in RAMNet [START_REF] Gehrig | Combining events and frames using recurrent asynchronous multimodal networks for monocular depth prediction[END_REF], convex upsampling allows our network to learn how to upscale features from a lower scale, using information from a higher scale. We propose to design the convGRU such that the first half of its state (in purple in Fig. 2 and3) guides the convex upsampling. Fusion of the upsampled decoded features and the state from the current scale is then performed by concatenating the output of the convex upsampling block with the remaining half of the convGRU state (in green in Fig. 2 and3), and by applying a convolution to reduce the number of channels. After the last scale, a prediction head is used to obtain the two final depth maps, D bf and D af , in the form of a two-channel tensor, at the same full resolution as the events input.

Regarding the implementation, both encoding heads use a kernel size of 5. LiDAR and events encoders use a kernel size of 5, with stride 2. Both the con-vGRU and residual blocks use a kernel size of 3. The convolutions in the convex upsampling blocks use a kernel size of 5, while the convolutions following the concatenations use a kernel size of 1. Finally, the prediction layer also uses a kernel size of 1. Convolutions are followed by a PReLU activation function [START_REF] He | Delving deep into rectifiers: Surpassing humanlevel performance on imagenet classification[END_REF], and instance normalization is used in the ResNet encoders as proposed by Pan et al. [START_REF] Pan | Two at once: Enhancing learning and generalization capacities via IBN-Net[END_REF]. In total, the network contains 26 millions of trainable parameters.

Data Representation

Events We use Discretized Event Volumes [START_REF] Zhu | Unsupervised event-based learning of optical flow, depth, and egomotion[END_REF] as the input representation for the events. We follow the formulation of Perot et al. [START_REF] Perot | Learning to detect objects with a 1 megapixel event camera[END_REF], where the Discretized Event Volume V for input events {e i = (x i , y i , p i , t i )} N i=1 is described as:

V t,p,y,x = ei,xi=x,yi=y,pi=p max(0, 1 -|t -t * i |) (1)
t * i = (B -1) t i -t 0 t N -t 0 (2)
where (x, y) is the position of the event, t its timestamp, and p its polarity.

In our experiments, we set B = 5 bins, and concatenate the negative and positive polarity bins along the first dimension, resulting in a tensor of shape (10, H, W ).

LiDAR and Depths LiDAR data is fed to the network as a 1-channel depth image. To do so, each LiDAR point cloud is projected onto the image plane of the event camera. Pixels where one or more LiDAR points fall into are given as value the lowest depth. Pixels without any LiDAR point are given a value of 0. For an easier learning, the LiDAR projection and ground truth images are normalized between 0 and 1 based on the maximum LiDAR range (200m in the case of our synthetic SLED dataset, 100m in the case of the MVSEC dataset [START_REF] Zhu | The multivehicle stereo event camera dataset: An event camera dataset for 3D perception[END_REF]).

Loss functions

To train our network, we combine the use of two losses: a pixel-wise 1 loss L pw , and a multiscale gradient matching loss L msg .

The pixel-wise 1 loss operates as the main supervision loss, applied on both the "before" and the "after" depth maps, and is defined as follows:

L pw = x,y D(x, y) -D(x, y) 1 (3)
where D and D are the respectively the estimated and ground truth depth maps.

However, when supervised by the 1 loss alone, the network tends to produce blurry and non-smooth depth images. To solve this issue, we use here a multiscale gradient matching loss inspired by [START_REF] Ummenhofer | DeMoN: Depth and motion network for learning monocular stereo[END_REF], also applied on both the "before" and the "after" depth maps, and defined as

L msg = h∈{1,2,4,8,16} x,y g[D](x, y, h) -g[ D](x, y, h) 2 (4)
with the discrete gradient function g of an image f defined as

g[f ](x, y, h) = (f (x + h, y) -f (x, y); f (x, y + h) -f (x, y)) T (5)
This loss helps regulating the depth results, by making depth discontinuities more prominent, and by smoothing homogeneous regions.

Our total loss L for a sequence of length T is finally defined as

L = T t=0 bf,af (L t pw + αL t msg ) (6)
where α is a weight parameter for the multiscale gradient matching loss.

In our experiments, we observed that giving too much importance to the multiscale gradient matching loss early in the training makes the network unable to derive correct depth estimates. Therefore, we always set α = 0.1 during the first epoch of training, to force the network to use mainly the 1 loss and converge towards good initial depth estimates. For the remaining epochs, we set α = 1.

The SLED Dataset

In order to train and evaluate the proposed network, we require a dataset containing both events, LiDAR point clouds, as well as a dense ground truth on depths. While we can use the MVSEC dataset [START_REF] Zhu | The multivehicle stereo event camera dataset: An event camera dataset for 3D perception[END_REF] for low-resolution cameras, its ground truth is constructed by accumulating point clouds from a LiDAR sensor, a solution which introduces errors in case of moving objects. A similar dataset does not exist for sensors of higher resolution.

For these reasons, we use the CARLA simulator [START_REF] Dosovitskiy | CARLA: An open urban driving simulator[END_REF] (version 0.9.14) to generate a dataset with perfect synchronization and calibration of the sensors, and perfect ground truth depth. We call it SLED, for Synthetic LiDAR Events Depths dataset. It is composed of 160 sequences of 10 seconds each, for a total of more than 20 minutes of data. These sequences are recorded on the Town01 to Town07 and Town10HD maps (20 sequences for each map), each sequence starting from a different geographic location. By doing so, a wide range of environments is represented within the dataset, as detailed in Table 1.

Each sequence contains a 1280×720 event camera, a 40-channel LiDAR, and a 1280×720 depth camera which is perfectly aligned with the event camera. Both the event data and the depth images are recorded at 200Hz, while the LiDAR is configured to run at 10Hz. RGB images (1280×720) are also provided at a 30Hz rate, aligned with the event-based sensor. The LiDAR sensor is configured with a maximum range of 200 meters. For realism and diversity purposes, AI-controlled vehicles and pedestrians are added to the simulation. Sun altitude also varies, resulting for each map in 4 night recordings, and the other 16 recordings ranging from early morning (where the sun can be directly in front of the camera) to midday (where the sun is at its apogee). Varying cloudiness conditions are also used, adding more or less texture to the sky, and making shadows more diverse.

We also configure the event camera in CARLA to use a linear intensity scale rather than the default logarithmic one, making the events produced by the simulator more realistic. More details on that topic, as well as an overview of the data contained in the dataset, are given in the Supplementary Material.

Evaluation

Dense Depths

On the SLED Dataset For training on the SLED dataset, we use the Adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] with a learning rate of 10 -4 and a batch size of 4, and train for a total of 50 epochs. To augment input data, we randomly crop it to 608 × 608, and apply random horizontal flipping.

Numerical results on the testing set are presented in the "Dense depths errors" column of Table 2. Evaluations are conducted on Town01 and Town03 maps, which contain challenging environments with many unique features (bridges, tunnels, . . . ) that are not present in the training maps. For the max range of 200 meters, ALED estimates depth maps with an average absolute error slightly over 4.5 meters for Town01, and around 5 meters for Town03. The respective average relative error is around 18% for Town01, and around 22% for Town03. A first element that can explain these errors is that the LiDAR has a small Table 2: Errors on the testing set of the SLED dataset for various cutoff depth distances. From left to right: average absolute and relative depth errors on both the "before" D bf and "after" D af depth maps; average absolute depth errors when associating a depth to each event; average absolute depth difference errors and percentage of correctly classified events based on this depth difference. Fig. 4: Two qualitative results on our synthetic SLED dataset, on Town01 (left) and Town02 (right). From top to bottom: events, LiDAR, predicted depth map, ground truth, color scale.

vertical coverage of the image: close ground objects or the top of close buildings are not reached by the LiDAR, meaning that accurate depth estimations for these objects are complex to achieve. In opposition, sky pixels (for which ALED produces good results) are only accounted for at the full 200m cutoff. These observations can be correlated to the larger relative errors observed for close cutoff distances than for the full 200m cutoff. It can also be observed that errors on the "after" depth maps are slightly higher. This is to be expected, as the network has to make use of the events to estimate the movement and propagate the depths accordingly. If the reader is interested, results for each sequence of the testing set are given in the Supplementary Material.

Qualitative results are given in Fig. 4. They showcase the ability of the network to estimate accurate depths for the whole image, by using events as a guide for the areas the LiDAR sensor can not reach. This is particularly visible for the trees and the light pole for the left column, or the ceiling of the tunnel for the right column. If the reader is interested, more visual results are given in the Supplementary Material and in the videos linked in the introduction.

On the MVSEC Dataset In order to be able to compare our results with the other approaches in the literature, we also train and evaluate ALED on the MVSEC dataset [START_REF] Zhu | The multivehicle stereo event camera dataset: An event camera dataset for 3D perception[END_REF]. We conduct our evaluation under three different sets of weights from different training setups described below:

-ALED S : the network is only trained in simulation, on proposed SLED dataset; -ALED R : the network is only trained on real data, on the MVSEC dataset; -ALED S→R : the network is first trained on the SLED dataset, then finedtuned on the MVSEC dataset.

We use a batch size of 4 and a learning rate of 10 -4 (10 -5 when fine-tuning). 50 epochs are used when training the network from zero, 5 when fine-tuning it. We also augment input data, by randomly cropping it to 256 × 256, and by applying random horizontal flipping. Numerical results are given in Table 3.

Comparing our three sets of trained weights, it appears clearly that training on synthetic data before fine-tuning the network on the MVSEC dataset (S → R) produces the best results. Training from zero on the MVSEC dataset (R) is not as good as the S → R variant due to the limited data available for training. Finally, training solely on the SLED dataset (S) produces the worst results, due to the large differences in terms of resolution and LiDAR models between the two datasets, and as simulation is not a perfect reproduction of real data.

Proposed ALED S→R network greatly outperforms all the other approaches of the state of the art. Most impressive results are obtained with distant cutoff depths, where fewer LiDAR points are available: our network is still able to infer accurate depths, while reference methods show large errors. Compared to the frames+events EvT + method of Sabater et al. [START_REF] Sabater | Event transformer+. A multi-purpose solution for efficient event data processing[END_REF], we improve the error by {-2.7%, 13.4%, 31.3%} at minimum and by {60.6%, 58.8%, 57.0%} at maximum for each of the {10m, 20m, 30m} cutoff distances respectively. Compared to the LiDAR+events method of Cui et al. [START_REF] Cui | Dense depth-map estimation based on fusion of event camera and sparse LiDAR[END_REF], this improvement is of {32.7%, 17.4%, 56.7%} at minimum and of {59.7%, 39.9%, 79.1%} at maximum. Table 3: Average absolute depth errors (in meters) on the MVSEC dataset for various cutoff depth distances. This evaluation is performed on the "before" depth map D bf , to be consistent with the methods we compare ourselves to.

Recording

Cutoff Event-based Event-and frame-based LiDAR-and event-based Zhu et al. [START_REF] Zhu | Unsupervised event-based learning of optical flow, depth, and egomotion[END_REF] E2Depth [START_REF] Hidalgo-Carrió | Learning monocular dense depth from events[END_REF] RAMNet [START_REF] Gehrig | Combining events and frames using recurrent asynchronous multimodal networks for monocular depth prediction[END_REF] EvT Qualitative results are presented in Fig. 5. All three ALED variants produce results which are visually close to the ground truth for ground objects. Since the MVSEC dataset lacks ground truth depth for the sky, and since the rare elements to have a ground truth for this part of the image are close buildings, close trees, or power lines, the network cannot learn to derive correct depth estimations for the corresponding pixels, leading to the purple blobs in the upper parts of Fig. 5e and5f. Only the S variant is able to predict accurate values for sky areas (as our SLED dataset contains valid ground truth depths for all pixels), but has more difficulties for ground objects due to the lack of fine-tuning. Between the R and S → R variants, improvement can still be seen, for instance for the edges of the objects of Fig. 5e and5f, which are less uneven in the S → R variant. Finally, when comparing our results to RAMNet, we can clearly observe that our method provides in all cases more accurate depth maps, where object boundaries are more prominent, and where estimated depths are closer to the ground truth. This observation further demonstrates that the use of a LiDAR input -even if very sparse -is of great help for obtaining accurate dense depth maps.

Associating a Depth to Each Event

As stated in Sections 1 and 3, our goal is not only to estimate dense depth maps, but also to associate two depths to each event, allowing for their 3D reprojection and depth difference analysis. Evaluation of the depth association to each event on proposed SLED dataset is given in the "Sparse depths errors" column of Table 2.

The sparse event-LiDAR fusion literature is limited to the method of Li et al. [START_REF] Li | Enhancing 3-D LiDAR point clouds with event-based camera[END_REF]. However, their approach only considers one depth per event, and is intended for a Road Side Unit (RSU) application (i.e., their event camera is fixed and evaluation is conducted on a specific dataset). Therefore, we decided to compare ourselves to a more naive (and faster) baseline: the Nearest Neighbor (NN) approach, where each event is given the depth of its closest LiDAR point. As the Nearest Neighbor approach can not infer correct depths for events which are too far from a LiDAR scan, and so as to provide a fair comparison, we only consider the events between the bottom and top LiDAR scans.

As displayed in Table 2, in the "before" D bf case, depending on the map and the cutoff distance, best results are shared between the NN approach and our ALED S network. These results can be explained by the fact that our network is more likely to commit large errors for events at the boundary of close objects, as it might estimate that they should be given the depth of the more distant background. On the contrary, the NN approach will always attribute the depth of the closest LiDAR point, and will therefore commit more frequent but smaller errors. In the "after" D af case, despite this potential source of error, our network ALED S nearly always obtains the best results, as it has correctly learned the temporal propagation of the depths, a task which cannot be completed natively with the NN approach. We also remind here that these results are given for the parts of the image where LiDAR data is available: the NN method would not be able to derive correct estimations for the other parts of the image. Numerical results on each sequence of the dataset are given in Supplementary Material.

Depth Difference

We finally estimate the quality of our "two depths per event" approach through the depth change map, as presented in Section 3. We perform two evaluations on our SLED dataset: (1) the average error on the depth change map D af -D bf compared to the true depth changes, and (2) the percentage of correctly classified events when using a difference threshold of 1m on the depth change map. Results of these evaluations are given in the "Depth change map errors" column of Table 2. Numerical results on each sequence of the dataset, as well as some visual results, are given in Supplementary Material.

We can observe here that, despite a significant absolute error on the depth change maps, events can still be classified correctly, with a rate of success over 75% on Town01, and over 77% on Town03. We remind here that the ALED network is not trained on these depth change map and classification tasks. As such, we believe that, while even more accurate individual depth maps could improve both the depth change map and classification errors, further improvements could be brought by designing a network specifically dedicated to these tasks.

Conclusion

In this article, a novel learning-based approach for estimating dense depth maps from asynchronous LiDAR and event-based data has been proposed. A novel "two depths per event" notion has also been proposed, to solve the issue of events representing a change of depth. A synthetic multimodal dataset has also been recorded, to train and evaluate our method. Multiple evaluations on our synthetic and a real driving datasets have been performed to show the relevance of our contributions. In particular, on the MVSEC dataset, an improvement of up to 79.1% compared to the current LiDAR-and-events state of the art has been achieved, on complex daytime and nighttime recordings.

In hindsight, further improvements could be brought to the method. Attentionbased networks provide state-of-the-art results in numerous vision-based applications, and could improve the fusion of the event and LiDAR modalities. Making the network predict directly sparse depths for each event could also potentially provide better results for the depth to event inference. This could be achieved by using sparse convolutional networks [START_REF] Messikommer | Event-based asynchronous sparse convolutional networks[END_REF] for instance, and could be subject to future work. The use of the Event Volume with a fixed time window as the input representation for the events in our network could also be revised, as it can become ill-suited under large motions. A solution could be to use an alternative representation, such as TORE Volumes [START_REF] Baldwin | Time-ordered recent event (TORE) volumes for event cameras[END_REF], or to use adaptive accumulation times using methods such as the one proposed by Liu and Delbrück [START_REF] Liu | Adaptive time-slice block-matching optical flow algorithm for dynamic vision sensors[END_REF]. Finally, the recording of a real dataset with a high resolution event camera could also be considered, to complete the possibilities offered by the low-resolution MVSEC dataset.

  (a) D bf (b) D af

Fig. 2 :

 2 Fig. 2: The encoder part of the network.

Fig. 3 :

 3 Fig. 3: The decoder part of the network.

Fig. 5 :

 5 Fig. 5: Qualitative results on "Outdoor day 1" from the MVSEC dataset with real data.

Table 1 :

 1 Detailed content of our SLED dataset containing 160 sequences of 10 seconds each.

	Map	Set	Environment	Features	Night seq. Day seq.
	Town01	Test	Town	Small buildings, bridges, distant forests and mountains, palm trees	4	16
	Town02	Train	Town	Small buildings, plazas, forest road	4	16
	Town03	Test	City	Tall and small buildings, roundabouts, tunnel, aerial railway	4	16
	Town04	Val.	Town	Small buildings, highway, parking, lake, forests and mountains	4	16
	Town05	Train	City	Tall buildings, parking, aerial beltway and railway	4	16
	Town06	Train	Suburban	Small buildings, U-turns, distant hills	4	16
	Town07	Train	Countryside	Barns, grain silos, fields, mountain road	4	16
	Town10HD Train	City	Buildings, monuments and sculptures, playgrounds, seaside	4	16

Supported in part by the Hauts-de-France Region and in part by the SIVALab Joint Laboratory (Renault Group-Université de technologie de Compiègne (UTC)-Centre National de