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Non-invasive ventilation versus oxygen therapy after extubation in patients with obesity in intensive care units: the multicentre randomised EXTUB-OBESE study protocol

Audrey de Jong, Helena Huguet, Nicolas Molinari, Samir Jaber

To cite this version:

Audrey de Jong, Helena Huguet, Nicolas Molinari, Samir Jaber. Non-invasive ventilation versus oxygen therapy after extubation in patients with obesity in intensive care units: the multicentre randomised EXTUB-OBESE study protocol. BMJ Open, 2022, 12 (1), pp.e052712. 10.1136/bmjopen-2021-052712. hal-03539231


Georges Boulon
email: georges.boulon@univ-lyon1.fr

Y Guyot

G Alombert-Goget

M Guzik

T Epicier

Lin Chen

L Hu

W Chen

Localization of Yb3+, Er3+ and Co2+ Dopants in an Optical Glass Ceramics of MgAl2O4 Spinel Nano-crystals Embedded in SiO2 Glass

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Introduction

Evolution of Solid State Lasers from Nd 3C /Yb 3C -Doped Single Crystals to Nd 3C /Yb 3C -Doped Transparent Ceramics

Inorganic solid-state lasers based on light-pumped insulating host materials containing optically active dopants as metal transition ions (3d configuration) and rare earth ions (4f configuration) continue to occupy a prominent place among the different kinds of laser devices. Indeed, solid-state lasers are mainly used as oscillators or amplifiers in industrial, medical, military and scientific fields. The 1st laser has been demonstrated by Maiman at Hughes Lab with Cr 3C ions of 3d 3 configuration-doped Al 2 O 3 in 1960 [START_REF] Maiman | Stimulated optical radiation in ruby[END_REF], emitting the sharp line 2 E ! 4 A 2 at 694.3 nm. However, this ruby laser is an inefficient three-level scheme and it was necessary to look on more efficient four-level scheme. An important breakthrough was the discovery of Nd 3C -doped Y 3 Al 5 O 12 (YAG) garnet crystal by Geusic as fourlevel scheme with right parameters and its extension to Nd 3C -doped glasses [START_REF] Geusic | Yttrium gallium and gadolinium garnets[END_REF]. The improvement of laser efficiency of Nd 3C -doped YAG laser crystal is a slow process: it won a factor of only two, 20 years after the first growth in 1964 [START_REF] Boulon | 50 years of advances in solid-state laser materials[END_REF]. During this period of time, the focus of the respective fields, namely phosphors for lighting application and solid-state lasers, has converged toward common targets, in the sense that phosphor research and development has been heavily concerned with the luminescence properties of trivalent rare earth ions, while in the research for tunable, coherent sources, the interest in laser materials has veered toward the type of band emitters traditionally investigated in phosphor research. Then scientific know-how has somehow percolated between the two fields. The information exchange from the laser field to the phosphor field has not been restricted to theoretical models but has been important in the field of materials (apatites, garnets, sesquioxides) [START_REF] Pappalardo | Recent trends in laser material research[END_REF]. The most important driving forces and noteworthy developments of laser materials since 1960 were the following ones [START_REF] Boulon | 50 years of advances in solid-state laser materials[END_REF]:

-Understanding of optical spectroscopy of luminescent ions used as laser ions, -Laser fundamentals understandings, -Choice and improvement of crystal growth techniques, -Laser-diode-pumped solid state lasers as new sources, -Polycrystalline ceramic lasers as a new generation of laser materials

Nd 3C /Yb 3C -Doped Transparent Ceramics

The recent development of ceramic laser materials is probably the most important innovation in the field of laser material fabrication technology. The large-scale laser materials are necessary for high-power laser systems. Unfortunately, the size of single-crystal is limited and, the boule cross-section shows facets giving rise to difficulties during the growth. Single crystals are generally grown from the melt and they suffer from drawbacks such as segregation of the dopant from the host, optical inhomogeneity caused by stress during crystal growth, high cost and low productivity due to high temperature processing. Transparent polycristalline are advantageous over single crystals in many ways. The process is simple, cost effective and typically carried out at lower temperature. Most important, much higher doping concentrations in ceramics can be obtained without phase segregation as we often observe in single crystals. As a result, laser ceramics are quite attractive since 1995 and it has been possible to fabricate the large-scale laser materials by using ceramic technology applied on isotropic hosts like Y 3 Al 5 O 12 cubic garnets, (Y 2 O 3 ) sesquioxides, MgAl 2 O 4 spinels, CaF 2 fluorides [START_REF] Ikesue | Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method[END_REF][START_REF] Ikesue | Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers[END_REF][START_REF] Ikesue | Fabrication and laser performance of polycrystal and single crystal Nd:YAG by advanced ceramic processing[END_REF][START_REF] Lu | 110 W ceramic Nd 3C :Y 3 Al 5 O 12 laser[END_REF][START_REF] Yagi | Characterizations and laser performances of highly transparent Nd 3C :Y 3 Al 5 O 12 laser ceramics[END_REF][START_REF]Proceedings of the 1st international laser ceramic symposium -E-MRS fall meeting 2005, 1st international laser ceramic symposium[END_REF]. Producers are challenging to make various large size ceramics with high optical quality under rods, disks and slabs shapes and by playing with engineer profiles and structures and also composites like un-doped and doped ceramics [START_REF] Sanghera | Ceramic laser materials: Past and present[END_REF]. However, although high efficiencies have been demonstrated, one limitation can be associated with Nd 3C segregation at grain boundaries in transparent Nd 3C -doped YAG ceramics for lasers [START_REF] Ramirez | Three-dimensional grain boundary spectroscopy in transparent high power ceramic laser materials[END_REF], Ce 3C -doped (Y,Gd)Al 3 O1 2 [START_REF] Zhao | Evidence of the inhomogeneous Ce 3C distribution across grain boundaries in transparent polycrystalline Ce 3C -doped (Gd,Y) 3 Al 5 O 12 garnet optical ceramics[END_REF], Ce 3C -doped YAG [START_REF] Zhao | Ce 3C dopant segregation in Y 3 Al 5 O 12 optical ceramics[END_REF] for scintillators and also phosphors for white LED sources. Segregation was not observed in Yb 3C -doped YAG [START_REF] Esposito | Fabrication and laser performance of multilayered YAG-Yb 3C :YAG ceramics[END_REF][START_REF] Epicier | Spatial distribution of the Yb 3C rare earth ions in Y 3 Al 5 O 12 and Y 2 O 3 optical ceramics as analyzed by TEM[END_REF]o rY b 3C -doped Y 2 O 3 [START_REF] Epicier | Spatial distribution of the Yb 3C rare earth ions in Y 3 Al 5 O 12 and Y 2 O 3 optical ceramics as analyzed by TEM[END_REF]. We have interpreted such data by the variation of segregation coefficients of rare earth ions in oxide optical ceramics like in growth of crystals from the melt and/or flux. The lower is the segregation coefficient of the luminescent ions in the melt growth, the greater amount of luminescent ions will be collected on the grain boundaries of the ceramic material [START_REF] Chani | Correlation between segregation of rare earth dopants in melt crystal growth and ceramic processing for optical applications[END_REF]. It means that such segregation phenomenon can perturb kinetics of the fluorescence in transparent ceramics and then the best laser sources should be obtained with the best uniformity of Yb 3C and Nd 3C ions in optical ceramics.

Essays to Use Glass Ceramics

Another field of optical materials consists to develop rare earth/ transition metal ions-doped glass ceramics for laser sources or scintillators or phosphors. Until today, glass ceramics have been applied for thermal and mechanical properties. In spite of numerous experimental essays, optical properties of glass ceramics are not yet really exploited.

An original idea was proposed recently with transparent glass ceramics [START_REF] Duan | Absorption and photoluminescence characteristics of Co 2C :MgAl 2 O 4 nanocrystals embedded in sol-gel derived SiO 2 -based glass[END_REF][START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF] containing Yb 3C ,E r 3C ions in glass matrix and Co 2C -doped MgAl 2 O 4 nano-crystals of sizes of 10-20 nm, which can be used as compact self-Q-switched microchip laser. First of all, we have to show that the main conditions are fulfilled in glass ceramics for obtaining self-Q-switched microchip laser. Passively Q-switched, diode-pumped solid state lasers are currently being used as miniature or microlasers capable of delivering high peak output power at high repetition rates and short nanosecond (ns) temporal pulse width. These lasers are of great interest due to their potential applications in micro-machining, remote sensing, target, ranging, and microsurgery. Cr 4C and Co 2C dopants have been proposed as saturable absorbers for passive Q-switching of solid-state lasers operating in the near-infrared region. Most commonly, systems presently used are based on Nd 3C :Y AGorNd 3C :YVO 4 lasers, passively Q-switched by Cr 4C : YAG, where the unique well-known characteristics of Cr 4C garnets as saturable absorbers are applied [START_REF] Kalisky | Passively Q-switched diode-pumped Nd: YAG and Nd:YVO 4 using (Cr 4C ,Ca 2C ):YAG and (Cr 4C ,Mg 2C ):YAG saturable absorbers[END_REF][START_REF] Kalisky | Cr 4C doped garnets: Novel laser materials and non-linear saturable absorbers[END_REF][START_REF] Kalisky | Cr 4C doped garnets: Their properties as non-linear absorbers[END_REF][START_REF] Kalisky | Passively Q-switched diode-pumped Nd:YAG and Nd:YVO 4 using (Cr 4C ,Ca 2C ):YAG and (Cr 4C ,M g 2C ):YAG saturable absorbers[END_REF]. Another crystal like Cr 4C :Mg 2 SiO 4 was also proposed as saturable absorber [START_REF] Chen | Growth mechanism of Cr: Forsterite laser crystal with high Cr concentration[END_REF]. The most important application of the oxide crystals doped with tetrahedrally coordinated Co 2C ions is passive Q-switching of solid-state lasers operating in the near-infrared region. A number of crystals such as YAG, LaMgAl 11 O 19 (LMA), ZnSe was doped with Co 2C ions [START_REF] Stultz | Divalent uranium and cobalt saturable absorber Q-Switches at 1.5 m[END_REF][START_REF] Yumashev | Excited state absorption and passive Q-switch performance of Co 2C doped oxide crystals[END_REF]. As an example, passively Q-switched 1.34 mN d 3C :Y x Gd 1-x VO 4 laser with Co 2C : LaMgAl 11 O 19 saturable absorber was demonstrated [START_REF] Li | Passively Q-switched 1[END_REF].

Indeed, glasses containing nano-crystals embedded in a glass matrix can enhance existing or offer completely new properties compared to those of the precursor glass. These transparent glass ceramics possess the spectral requirements of both eye safe lasers by Er 3C 4 I 13/2 ! 4 I 15/2 emission in glass matrix between 1.5 and 1.6 m under Yb 3C pumping and saturable absorbers by 4 A 2 (F) ! 4 T 1 (F) transition of Co 2C -doped MgAl 2 O 4 nano-crystals so that, together, might be developed as self-Q-switched microchip laser. Obviously, the morphology of this new class of optical materials requires to solve the specific characterisations of the location of dopants in the two glassy and nano-spinel phases in order to check the feasibility of this system.

Consequently, the main goal of this lecture presented at the School is to conjugate TEM-EDX and optical spectroscopy tools to localize Yb 3C ,Er 3C and Co 2C dopants in a glass ceramics composed of MgAl 2 O 4 spinel nano-crystals of 10-20 nm size embedded in the SiO 2 glass [START_REF] Boulon | Conjugation of TEM-EDX and optical spectroscopy tools for the localization of Yb 3C ,Er 3C and Co 2C dopants in a laser glass ceramics composed of MgAl 2 O 4 spinel nano-crystals embedded in SiO 2 glass[END_REF].

Experimental Techniques

Sample Preparation

Glass with a composition (in wt. %) of 1.8Yb 2 O 3 -1.7Er 2 O 3 -11MgO-31.5Al 2 O 3 -47SiO 2 -4.5TiO 2 -2.5ZrO 2 -0.03CoO (CYE glass) was prepared, where TiO 2 and ZrO 2 were used as mixed nucleating agents [START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF]. Concentrations of Co 2C ,Y b 3C and Er 3C ions are 5.77 1018 cm 3 ,1 . 5 1020 cm 3 , and 1.46 1020 cm 3 , respectively. For comparison, CoO-un-doped glass (YE glass) with the same composition was also prepared. For two glasses, homogeneous mixtures (300 g) of analytical reagent grade raw materials, obtained by ball milling, were melted in a corundum crucible in a laboratory electric furnace at 1580 ı C for 4 h in air atmosphere with stirring. According to differential scanning calorimetry (DSC) analysis, CYE and YE glass samples were heat treated at 760 ı C for 12 h, and then at 930 ı C for 4 h. As a result, transparent CYE GC and YE GC were synthesized. The purity of Yb 2 O 3 and Er 2 O 3 is 4 N, while other reagents are analytical grade.

For comparative absorption analysis of samples containing different concentrations of Yb 3C and one Er 3C concentration we used the compositions (in wt.%) of 2Yb2Er, 4Yb2Er, and 6Yb2Er, it means

xYb 2 O 3 -1.1Er 2 O 3 -(3.3-x)La 2 O 3 -11MgO- 30.6Al 2 O 3 -47SiO 2 -4.5TiO 2 -2.5ZrO 2 -0.03CoO (x D 1.1, 2.2, 3.3), respectively.

Experimental Section

TEM-EDX Experiments

Experiments were conducted on the Cs-corrected TITAN Environmental Transmission Electron Microscope (ETEM) from FEI installed at CLYM (Centre Lyonnais de Microscopie, University of Lyon, www.clym.fr) and operated at 300 kV. Thin foils were prepared by ion bombardment (PIPS system from GATAN). According to this preparation method, some Ar C has been detected during EDX analysis with a SDD analyzer from Oxford Instruments (classical implantation of Ar C ions in glassy phases). Cu is also detected as spurious elements due to the sample environment in the microscope. During TEM work, irradiation effects were encountered due to the high electron flux at 300 kV. However, all reported observations were obtained in reasonably short times and prior to any significant degradation (e.g. drift, deformation or detectable structural chemical variation), unless otherwise specified. Especially, chemical analysis in EDX were limited to reduced doses and short acquisition times, thus limited the signal-to-noise ratio and the sensitivity of the measurements to detect the very small concentrations of Yb 3C ,Er 3C ,Co 2C dopants. Under these conditions, both the detection limit and the accuracy of the present results are estimated to be about 0.2 at.% for all species of special interest, i.e. the Yb 3C ,Er 3C and Co 2C doping ions. Nano-probe analysis and EDX elementary maps in the Scanning TEM (STEM) mode was performed using a probe of about 2-4 nm (Full-Width at Half-Maximum). Micrographs were acquired in both Cs-corrected High Resolution, and High Angle, Annular dark Field (HAADF) STEM modes.

Absorption Spectroscopy

Absorption spectra of glass and glass ceramic samples were measured both, at SIOM (Shanghai), at 293 K, using a Perkin Elmer UV/Visible/NIR Lambda 900 spectrophotometer in 300-2000 nm, and at the Faculty of Chemistry of the University of Wroclaw (Poland), at 293 K and 4 K, in the same spectral range with a Cary-Varian 5000 Scan spectrometer equipped with an Oxford CF 1204 helium flow cryostat. In addition, a special thin layer technique was used to detect the 4f ! 4f transitions of well-grounded nano-powder of Yb 3C -doped spinel samples. These homogenous samples were compressed in the form of pellets under 20 MPa pressure. Transparent samples prepared in this way were used for the absorption measurements only of the Yb 3C -doped spinel nano-powder.

Results and Discussion

Morphology of Samples Observed by TEM Measurements

A typical STEM-HAADF image is presented in Fig. 16.1a where spinel nanoparticles appear with a brighter contrast with respect to the vitreous matrix. Their size ranges typically between 4 to 20 nm with an average at around 10 nm. Lattice imaging clearly indicates the crystalline nature of the spinel phase as shown in Fig. 16.2. Cystallographic indexing was performed either in the conventional diffraction mode or by using Fourier transforms, or diffractograms, of the HREM images as reported as an insert in Fig. 16.2: all acquired data are fully consistent with the usual spinel, Fd-3 m structure of MgAl 2 O 4 with a D 0.808 nm. A confirmation of this finding is presented in Fig. 16.3 where a spinel crystallite is observed at High Resolution in the [001] viewing direction. This is important to evaluate the ratio between the MgAl 2 O 4 nano-spinel crystallites and the SiO 2 glassy phase. To do so, EDX results obtained on large areas of about 1 m 2 were fitted by a linear combination of the expected chemical formulae of both phases: x MgAl 2 O 4 (1-x) SiO 2 , where x represents the atomic fraction of the spinel phase. According to the usual consideration of absorption effects, linked to the sample thickness (estimated here to about 50 nm, with little incidence on the final spinel fraction in the interval 0-100 nm), the elemental contents for the major constituents O, Mg, Al, Si were deduced from the experimental and the spinel atomic fraction x was refined from a simple mean-least square fitting procedure (see Fig. 16.4): using this approach, an optimum value of x D 25 % was found.

Distribution of Yb 3C ,Er 3C ,Co 2C Dopants as Revealed by Nano-probe EDX

One main challenge of the present structural characterization is to know not only the distribution of Yb 3C ,E r 3C ,C o 2C dopants in both glassy and crystalline phases, but also at the interface between the nano-spinel crystals and the glass. The greatest difficulty when applying TEM-EDX technique is to find out adequate thin regions where no or very little overlap occurs between nano-cystals, due to high concentration of nano-crystals. EDX nanoprobe analysis was performed using the classical line scan procedure as employed previously to study the distribution of Yb 3C ions in grains and grain boundaries in Ce 3C -doped YAG ceramic bulky samples [START_REF] Zhao | Evidence of the inhomogeneous Ce 3C distribution across grain boundaries in transparent polycrystalline Ce 3C -doped (Gd,Y) 3 Al 5 O 12 garnet optical ceramics[END_REF][START_REF] Zhao | Ce 3C dopant segregation in Y 3 Al 5 O 12 optical ceramics[END_REF], Yb 3C -doped YAG and Yb 3C -doped Y 2 O 3 ceramic bulky samples [START_REF] Esposito | Fabrication and laser performance of multilayered YAG-Yb 3C :YAG ceramics[END_REF][START_REF] Epicier | Spatial distribution of the Yb 3C rare earth ions in Y 3 Al 5 O 12 and Y 2 O 3 optical ceramics as analyzed by TEM[END_REF] and Yb 3C -doped YAG nano-ceramics [START_REF] Boulon | Yb 3C ions distribution in YAG nano-ceramics analyzed by both optical and TEM-EDX techniques[END_REF].

TEM-EDX Well Adapted for Rare Earth Dopants But Not for Cobalt Dopant

A typical analysis is shown in Fig. 16.5. As can be seen from the HREM micrograph, we have chosen here a region where two spinel crystallites are surrounded by the glassy matrix, where no lattice fringes were resolved. 15 measurements were performed using a probe of about 3 nm, as indicated by the circle marks. The diagram in Fig. 16.5a, b shows the evolution of the Yb 3C ,Er 3C and Co 2C contents: enrichment in rare earth ions is clearly evidenced in the spinel phase whereas slight enrichment of the vitreous matrix is suggested by these data. We have to mention that the very low content measured for Co 2C and the strong overlapping between Co 2C and Er 3C high intensity lines as seen in Fig. 16.6, do not permit any definitive conclusion about any possible Co 2C distribution heterogeneity.

Interest of EDX Elementary Maps

To give a better global view of the dopant distribution, EDX elementary maps were recorded. Because of irradiation effects severely limiting the acceptable dose on the darker areas in STEM-HAADF images corresponds to the vitreous SiO 2 -based phase. These maps are treated in a quantitative way by the Aztec commercial software provided by the manufacturer of the EDX system, which means that overlap effects between X-ray lines is in principle correctly taken into account. According to this, the Yb 3C and Er 3C maps clearly confirm the greatest concentrations of Yb 3C , Er 3C dopants inside the nano-crystalline phase and much lower traces inside the SiO 2 glassy phase. Again, the Co 2C content appears too low in average and its strongest line overlaps too strongly with Er 3C line one, to rightly conclude about Co 2C ion distribution.

Direct Observation of Heavy Yb 3C and Er 3C Rare Earth Individual Ions

Another original worthwhile observation should be mentioned here concerning the HRTEM imaging of individual dopants. According to (i) the resolution permitted by the spherical aberration corrector, (ii) the large 'weight' (atomic number) difference between rare earth ions (Er 3C ,Y b 3C ) compared to the spinel and glassy phase elements (O 2 ,Al 3C ,Mg 2C ,Si 4C ), it can be postulated that in the thinnest regions, an 'absorption-type' contrast could allow the direct visualization of heavier rare earth individual ions. In convenient so-called 'Scherzer images', atoms are expected to appear as dark dots on a brighter background. Figures 16.8a and 16.8b can be examples of such an experimental evidence in which this is even possible to distinguish rare earth pairs. We note that rare earth ions are mainly detected in the spinel nano-crystal phase. An interesting data is the possibility to observe Yb 3C -Yb 3C pairs also detected by cooperative luminescence in many Yb 3C -doped crystal or ceramic materials or here in glass ceramics which should be only doped by Yb 3C . As a general conclusion of this TEM-EDX analysis, elemental maps of Fig. 16.7 (and, to some extent, HREM imaging in Fig. 16.8) confirm the results obtained from simple line scans in Figs. [START_REF] Epicier | Spatial distribution of the Yb 3C rare earth ions in Y 3 Al 5 O 12 and Y 2 O 3 optical ceramics as analyzed by TEM[END_REF].5 and 16.6, less representative from the point of view of spatial distribution but more representative from a quantitative point of view: Er 3C and Yb 3C ions are preferentially located in the spinel nano-crystallites. This is "a priori" the same conclusion for Co 2C ions but again the low concentration of this ion and the overlapping with Er 3C line cannot permit any unambiguous location so that we need some useful help from the spectroscopic data as related in the next section.

In parallel, we did not measure any significant gradient or segregation phenomenon, especially for Yb 3C and Er 3C ions, in the area of the interface between the spinel nano-crystals and the vitreous phase, although the induced damages from irradiation did not make possible to perform long acquisitions which would have been needed to gain the desirable sensitivity. This segregation was never seen for Yb 3C heavy ions in garnets and sesquioxides, but was encountered for example in the grain boundaries of the YAG ceramics doped with the first Nd 3C and Ce 3C rare earth ions [START_REF] Zhao | Ce 3C dopant segregation in Y 3 Al 5 O 12 optical ceramics[END_REF][START_REF] Esposito | Fabrication and laser performance of multilayered YAG-Yb 3C :YAG ceramics[END_REF][START_REF] Epicier | Spatial distribution of the Yb 3C rare earth ions in Y 3 Al 5 O 12 and Y 2 O 3 optical ceramics as analyzed by TEM[END_REF][START_REF] Chani | Correlation between segregation of rare earth dopants in melt crystal growth and ceramic processing for optical applications[END_REF]. As we will discuss it later, Yb 3C spectroscopic characterizations give some information on Yb 3C location on the disturbed surface of the nanocrystals. In order to better understand the assignments of the electronic transitions we remind the energy level diagram of Er 3C and Yb 3C ions in Fig. 16.10.

Spectroscopic Properties of the Glass and the Glass Ceramic Samples

As for Co 2C ions, we detect the presence within two spectral ranges by the transition of both 4 T 1g ! 4 T 1g ( 4 P) (expected approximatively O h symmetry of glass) and 2

A 1 I 2 T 2 ( 2 G) C 4 T 1 ( 4 P) C 2 E 2 T 1 ( 2 G) (T d Co 2C
) (expected T d symmetry of Mg 2C site in MgAl 2 O 4 spinel nano-crystals) between 500 and 680 nm and, in the near IR, between 1100 and 1700 nm, mainly by the 4 A 2 ! 4 T 1 ( 4 F) (T d Co 2C )of the T d symmetry in nano-spinels. This superposition of the two types of transitions justify the potentiality of this glass ceramic composition as saturable absorbers since the Co 2C broad absorption overlaps widely the expected laser emission from the Er 3C emission near 1550 nm. It has been already shown that this sample possesses excellent transparency up to nearly 87 % at the near-infrared band [START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF].

Discussion on the Location of Co 2C Ions in Glass Ceramics

In the previous paper [START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF], the question on the location of Yb 3C and Er 3C rare earth ions as dopants in the glass ceramics from spectroscopic data has not been unambiguously solved, the assignment of Co 2C ions was only clearly established between glass and MgAl 2 O 4 spinel nano-crystals of the glass ceramics. Let's remind that Co 2C ions optical transitions belong to transition metal ions with high oscillator strength (f 10 2 ) and high absorption cross-section in crystals much easier to detect than rare earth ions which are characterized by much smaller f 10 6 one. Consequently, Co 2C ions can be seen at low concentration on absorption spectra as it has been described here and can allow to give complementary results which were not obtained by TEM-EDX due to the overlapping of Co 2C and Er 3C X-Ray lines.

We show in Fig. 16.9a the weak Co 2C near infrared absorption in glass as mentioned by the spectrum 3, intensity difference of the spectrum 1 of Co 2C ions in the glassy phase of Co 2C -Yb 3C -Er 3C -doped silicate glass (CYE glass) and the spectrum 2 of Yb 3C -Er 3C -doped silicate glass (YE glass). The strongest absorption of Co 2C ions in glass ceramics as observed in Fig. 16.9b by the spectrum 6, intensity difference between 4 and 5 spectra, is assigned to Co 2C into Mg 2C sites of T d symmetry in Co 2C -doped MgAl 2 O 4 nano-crystals of the (CYE glass ceramics). As a result the absorption results are in favor of the strongest population of Co 2C ions rather in glass ceramics than in glass.

Discussion on the Location of Yb 3C Ions in Glass Ceramics

The previous analysis of TEM-EDX experiments indicates we should expect the optical transitions of the three Co 2C ,Y b 3C and Er 3C dopants in both the SiO 2 glassy phase and the MgAl 2 O 4 nano-crystallite phase. We will report now that spectroscopic data brings new results for these glass ceramic samples. It was found out in the absorption spectra the appearance of a new absorption line between 4 K and room temperature near 970 nm, so that it was necessary to compare the absorption of different samples containing different concentrations of Yb 3C and Er 3C ions in the two hosts of glasses and glass ceramics. First, we have pointed out the double structure of the Yb 3C ions between 965 and 985 nm by two broad lines of practically similar intensity, so-called 0-phonon lines, with maximum at 970 and 975 nm respectively as seen in Fig. 16.11b. Previously only one peak at 977 nm was observed [START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF]. These two broad lines characterize the 2 F 7/2 ! 2 F 5/2 transitions of Yb 3C ions between the lowest Stark energy level of each 2 F 7/2 and 2 F 5/2 manifolds rather than those of Er 3C ions, due to the much larger absorption coefficient of Yb 3C ions.

Concentration dependences of the Yb 3C absorption spectra of both glasses and glass ceramic samples containing the same amounts of Yb 3C and Er 3C rare earth ions are shown in Fig. 16.11a, b. Absorption spectra intensities presented for both glasses and glass ceramics are dependent on the Yb 3C concentration increasing. One can see the 2 F 7/2 (1) ! 2 F 5/2 (5) double broad lines of Yb 3C 0-phonon lines with maxima at 970-975 nm. Absorption spectra of Yb 3C -doped glass ceramics exhibit a higher degree of structuration than that glass spectra. By comparing these absorption spectra one might assume that the line at 975 nm in glass ceramics has the same glassy origin as that in glass samples with maximum at 975.5 nm. It might be due to the presence of a double phase, like for example, both the glassy one and the nano-spinel crystalline phase with different line intensities, but this hypothesis has to be discussed as the following. This is interesting to compare the spectra of Yb 3C -doped silica glass with those we obtained recently for Yb 3C -doped calcium alumino-silicate glasses (CAS and LSCAS) for excitation and emission spectra [START_REF] Guyot | Spectroscopic properties, concentration quenching and laser investigations of Yb 3C -doped calcium aluminosilicate glasses[END_REF]. The spectra in these glasses are much more resolved than that of Yb 3C -doped silica glass, showing distinctive three 2 F 7/2 ! 2 F 5/2 components of the absorption spectra and four 2 F 5/2 ! 2 F 7/2 components of the emission spectra, as expected. The main reason of this difference between the two types of glasses is the presence of Ca and Al cations in the glass network of CAS and LSCAS which contribute to increase of the site symmetry inside the glassy phase. The Yb 3C 0-phonon line in CAS and LSCAS glasses is located at 977 nm, very close to the 975.5 nm in the silica glass of the glass ceramics, and consequently this comparison might be another proof of the assignment of the 975.5 nm peak to the silica glass phase in the glass ceramic sample.

Since the glass ceramic sample is composed of both the silicate phase and the nano-spinel crystalline phase, we also need some comparison with spectra of rare earth-doped spinel nano-crystalline phase. We have recently published the concentration dependences of the absorption spectra of Yb 3C -doped MgAl 2 O 4 spinel nano-crystals in the range of 10-30 nm size, prepared by the sol-gel method and characterized by both structural and spectroscopic properties [START_REF] Wiglusz | Structural and spectroscopic properties of Yb 3C -doped MgAl 2 O 4 nano-crystalline spinel[END_REF]. The first striking feature is the overlapping between the Yb 3C 0-phonon absorption line in the silica glass at 975.5 nm and the 0-phonon line of Yb 3C -doped MgAl 2 O 4 spinel nano-crystals at 976 nm (Fig. 16.12).

Both of these two lines are very broad. In glasses this is due to the un-equivalent Yb 3C sites as usually expected in disordered amorphous materials and in MgAl 2 O 4 spinel nano-crystals this is due to the following anti-site phenomenon:

MgAl 2 O 4 ! .Mg 1 2x Al 2x /OEMg 2x Al 2 2x O 4 :
Indeed, some Al 3C and Mg 2C cations are exchanged between the cation sublattices forming pairs of anti-site defects and thus a degree of inversion is created. This degree of inversion x ranges from almost 0 for the normal spinel up to 0.5 for the inverse spinel structure. Apparently, in the spinel nano-crystal phase in [START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF] the unresolved Yb 3C components indicate at large inverse spinel as a (50 pm) [START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF]. This substitution was also proposed for the Yb 3C -Er 3C -co-doped MgAl 2 O 4 phosphor powders prepared by the combustion method [START_REF] Singh | Synthesis, Characterization, Optical absorption, luminescence and defect centres in Er and Yb co-doped MgAl 2 O 4 phosphor[END_REF]. In addition, other perturbed Yb 3C ions exist due to the morphology of the surface of the grains in contrary with the regular structure of the internal grain. It means there are several reasons to increase disorder in spinel lattice and to observe large broadening of both absorption and emission spectra. As a result, in the glass ceramic samples the line located at 975 nm can be assigned to the 2 F 7/2 (1) ! 2 F 5/2 (5) transition either with Yb 3C ions in the glassy phase or with Yb 3C ions in the MgAl 2 O 4 inverse spinel nano-crystalline phase. There is a surprising situation, adding difficulties for the final interpretation, never reported, with two Yb 3C -doped phases, one with SiO 2 glass, another one with inverse MgAl 2 O 4 nano-crystalline phase, which show Yb 3C lines in coincidence.

Consequently we can assign the line at 975 nm of the glass ceramics to both the glass and the nano-crystalline phases but the higher population detected with TEM-EDX plays in favor of the detection first of the nano-crystalline phase and like a noisy signal for the glass phase.

At last we need to find new data to interpret the absorption line at 970 nm. The different excitations of the Ti-Sapphire laser pump are mentioned. The absorption spectrum of the sample at 4 K, almost the same as at RT, is indicated in blue as a reference. The first obvious feature is the absence of luminescence emission from Yb 3C ions characterized by the 0-phonon line at 970 nm. Only the Yb 3C 0-phonon lines around 977 nm associated to both SiO 2 glass and MgAl 2 O 4 nano-crystal phases are the emitting centres shifted as expected from multi-sites in the glass ceramics. In addition we have not detected any energy transfer between the two centers responsible for these two broad absorption lines at 970 and 975 nm, respectively.

In Fig. 16.13, the site selective laser excitation at 77 K has been applied especially into the two broad 2 F 7/2 (1) ! 2 F 5/2 (5) 0-phonon lines of Yb 3C ions which were detected in absorption with maxima at around 970 nm and 975 nm. Then, the different excitations are now in the range 966-980 nm. In red and black lines are reported the 2 F 5/2 (5) ! 2 F 7/2 (1, 2, 3, 4) emission spectra under excitation at 966 nm and 969 nm, respectively into the new absorption peak present in the GC. In green, dark blue and brown colors are reported the 2 F 5/2 (5) ! 2 F 7/2 ( 1 ,2 ,3 ,4 )e m i s s i o n spectra under excitation at 974.8 nm, 975.8 nm and 977.8 nm, respectively, into the absorption peak already observed with glassy phase. We confirm only the Yb 3C lowest energy peak at 976 nm is giving radiative transitions and we see clearly the resolved Yb 3C emission spectra into excitation at 976 nm. A very weak emission is recorded under excitation at around 970 nm, due indeed to the excitation of the foot of the 976 nm absorption line since the overlapping of the two absorption peaks can't be avoided.

Consequently, the Yb 3C center associated with the line at 970 nm is only absorbing and not emitting. It means that the Yb 3C resolved emission spectra observed in Fig. 16.13 can be associated only to pumping of the broad line at around 976 nm and reflect mainly the intensity of Yb 3C -doped nano-spinel crystalline due to higher population of Yb 3C ions than in the glass.

At this point of the discussion, we interpret Yb 3C ions (and then associated neighbor Er 3C ions of similar ionic radii) in the two phases. Only Yb 3C -doped nano-crystalline phase is observed due to the highest population leading to higher fluorescence intensity. In the previous discussion on the emission properties we pointed out a radiation-less Yb 3C center associated to the 0-phonon absorption line at 970 nm only within the glass ceramic sample. Then, we think this is the result of strong perturbation acting on these centers due to the location of Yb 3C ions in vicinity of the surface of the nano-crystals. Such localization of this type of Yb 3C quencher ions on the surface close to the edges leads to stronger distortion by the crystal field than those of the regular ions inside the nano-crystal.

Another hypothesis is the presence of Yb 3C aggregates at the surface of nanocrystals so that migration of the energy by resonance between the 0-phonon lines at 970 nm might explain the quenching. However, TEM-EDX results did not detect any segregation of dopants at the interface of the nano-crystals and the glass and this is why we think the probability of the formation of aggregates is very weak.

Conclusion

The main goal of this work was to show how it is possible to characterize the location of Yb 3C and Er 3C rare earth ions and Co 2C transition metal ions by conjugating, what is rather rare, TEM-EDX and optical spectroscopy tools in a glass ceramics composed of MgAl 2 O 4 spinel nano-crystals of 10-20 nm size embedded in SiO 2 glass. The application targeted is a compact self-Q-switched microchip laser for which spectroscopic properties are fulfilled. Here we have chosen this example at this School for pedagogical reasons to show the special way of assignment by applying the two independent tools of TEM-EDX and spectroscopy techniques.

The previous analysis had shown that Yb 3C and Er 3C rare earth ions seem to remain in SiO 2 glass matrix in the glass ceramics, while Co 2C occupy the tetrahedral sites in MgAl 2 O 4 nano-crystals. The use of TEM-EDX technique led to the result that Yb 3C ,E r 3C and Co 2C dopants are located into the two phases but preferentially located in the spinel nano-crystals. This important result has been clearly confirmed by the elemental mapping of Yb 3C and Er 3C rare earth ions and also by the spectroscopic results of Co 2C ions. TEM-EDX measurements was not be accurately applied to the very low Co 2C concentration whereas the assignment of Yb 3C ion spectroscopic properties was more difficult due to the overlapping of broad 2 F 7/2 (1) ! 2 F 5/2 (5) 0-phonon lines belonging to both glassy and spinel nanocrystalline phases. Yb 3C ions localized either in the SiO 2 glass or in the MgAl 2 O 4 spinel nano-crystalline are surprisingly absorbing at almost the same wavelength, around 975 nm with the characteristic of the greatest intensity line coming from the greatest population of the spinel nano-crystalline phase. The glassy phase was not really resolved at this wavelength in the glass ceramics due to the lower intensity of the 0-phonon line. A new radiationless Yb 3C centre most probably localized on the strongly perturbed area of the edge of the nano-crystal surface has been pointed out by the presence of an absorption line at 970 nm of comparable intensity with that of the regular Yb 3C ions inside the spinel nano-crystal structure.

Triply-doped glass ceramics composed of the spinel nano-crystals imbedded in a silicate glassy phase is a good example of material for which two complementary techniques like TEM-EDX and optical spectroscopy are necessary to assign the distribution of dopants. This is the reason why it has been exposed for the School. Undoubtedly, optimization of Yb 3C ,E r 3C and Co 2C concentrations is expected in this glass ceramics before any development.

Fig. 16 . 1 Fig. 16 . 2 Fig. 16 . 3

 161162163 Fig. 16.1 (a) Typical STEM-HAADF image showing the distribution of spinel nanocrystallites embedded in the silicate glassy phase (spinel nanoparticles appear with a brighter contrast with respect to the vitreous matrix). (b) Size histogram of micrograph shown in a); a mean equivalent (Ferret's) diameter of 10 ˙0.3 nm can be deduced from a Gaussian fit (dotted curve)

Fig. 16 .Fig. 16 .Fig. 16 . 6

 1616166 Fig. 16.5a Typical HRTEM: Energy-Dispersive X-ray spectroscopy line scan applied to the same Yb-Er-Co-doped glass ceramic sample analyzed in Fig. 16.2b (probe size is about 3 nm). The two yellow zones are analyzed as spinel 1 and spinel 2 in Fig. 16.5b

Fig. 16 . 7

 167 Fig. 16.7 Typical semi-quantitative elemental mapping of the Yb 3C ,E r 3C ,C o 2C dopants and the Al 3C component of the nano-crystalline phase and Si 4C component of the vitreous phase. The scale of 500 nm for all diagrams is shown in the left side of the first image showing the position of the analyzed nano-crystal

Fig. 16 .Fig. 16 .

 1616 Fig. 16.8a Typical Yb 3C and Er 3C ions as observed by black points in spinel nanoparticle as seen with a set of lattice planes resolved andalsoinglass.

Fig. 16 . 9

 169 Fig. 16.9 (a) Comparison of the absorption of Co-Yb-Er-doped silicate glass (CYE glass) sample with respect of Yb-Er-doped silicate glass (YE glass) at RT. Co 2C ion absorption in glass has been deduced [19]. (b) Comparison of the absorption of Co-Yb-Er-doped glass ceramic (CYE-GC) sample with respect of Yb-Er-doped silicate glass (YE glass) at RT. Co 2C ion absorption mainly into Mg 2C sites of MgAl 2 O 4 nano-crystals glass ceramics has been deduced[START_REF] Chen | Preparation and spectroscopic properties of nanostructured glass-ceramics containing Yb 3C ,Er 3C ions and Co 2C -doped spinel nanocrystals[END_REF]

2 FFig. 16 .

 216 Fig. 16.10 Energy level diagram of Yb 3C and Er 3C ions in materials. The main down and up transitions are mentioned

Fig. 16 . 11 6 900

 16116 Fig. 16.11 Concentration dependence of x% Yb 3C ion absorption in both glass (a) and glass ceramics (b) samples at RT. X D 2, 4, 6

Fig. 16 .

 16 Fig. 16.12 Temperature dependence of absorption spectra of Yb 3C -doped MgAl 2 O 4 spinel nanocrystals prepared by sol-gel method[START_REF] Wiglusz | Structural and spectroscopic properties of Yb 3C -doped MgAl 2 O 4 nano-crystalline spinel[END_REF]

16.3.3.1 Absorption Spectra of Co 2C ,Yb 3C and Er 3C Ions in the Visible and the IR Spectral Ranges

  ! 4 F 7/2 (488 nm),4 I 15/2 ! 2 H 11/2 (521 nm), 4 I 15/2 ! 4 S 3/2 (543 nm), 4 I 15/2 ! 4 F 9/2 (653 nm), 4 I 15/2 ! 4 I 9/2 (797 nm) (not presented here), 4 I 15/2 ! 4 I 11/2 is hidden by 2 F 7/2 ! 2 F 5/2 of Yb 3C ions which have much higher absorption strength (965-985 nm) and 4 I 15/2 ! 4 I 13/2 (1510-1540 nm), respectively.

	The absorption spectra of a glass ceramic sample shown in Fig. 16.9a, b are
	composed of both sharp lines from Er 3C and Yb 3C rare earth ions and broader bands
	from Co 2C transition metal ions.
	We can easily see the usual Er 3C ion transitions from the 4 I 15/2 ground state:
	4 I 15/2 ! 2 H 9/2 (407 nm), 4 I 15/2 ! 4 F 3/2 (442 nm), 4 I 15/2 ! 4 F5/2 (451 nm),
	4 I 15/2

nm 969.6 nm glass ceramic 975.5 nm Fig. 16.13 Site

  selective laser excitation within the two broad 2 F 7/2 ! 2 F 5/2 0-phonon lines of Yb 3C ions which were detected in absorption at RT and 4 K

				Yb	3+ :	2 F 5/2	2 F 7/2
	Relative Intensity (a.u.)				absorption at 4 K emission at 77K λ ex = 966 nm 969.5 nm 974.8 nm 975.8 nm 977.8
	Yb	3+ :	2 F 7/2	2 F 2/2
	940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160
				Wavelength (nm)

16.3.3.4 Site Selective Spectroscopy as a Contribution to the Assignment of the Yb 3C Centres Site

  selective laser excitation within the range 880-950 nm of Yb 3C ion into the two highest excited levels of the 2 F 7/2 ! 2 F 5/2 transitions of GC can be observed in Fig.16.13 at 77 K.

Acknowledgements

We are grateful to the CLYM (Centre Lyonnais de Microscopie, www.clym.fr) for its guidance in the Ly-EtTEM (Lyon Environmental tomographic TEM) project, which was financially supported by the CNRS, The Région Rhône-Alpes, The 'Greater Lyon' and the French Ministry of Research and Higher Education. We wish to warmly thank the Faculty of Chemistry of the University of Wroclaw for the access of low temperature absorption measurements.


Daniel Alshamaa

Andrea Cherubini

Robin Passama

Simon Pla

Loïc Damm

Sofiane Ramdani

RobCap: A Mobile Motion Capture System Mounted on a Robotic Arm

Keywords: motion capture, robotic arm, error, rigid transformation, system calibration

Fixed Motion Capture systems (Mocap) are well-established nowadays and are available in indoor and outdoor environments. Here, we introduce RobCap, a Moving Motion Capture System designed for acquiring accurate three-dimensional kinematics of human motion with large displacements. RobCap consists of an optoelectronic Mocap (Codamotion © ) mounted on a robotic arm, to track the human motion in the local moving frame. This paper presents this device and expresses the local kinematics of the markers in a global coordinate system. We have acquired a set of 560 measurements, by controlling the Robotic arm to follow the subject's movement and to track the markers attached to his wrist. The performance of the RobCap is evaluated through comparison with state-of-the-art technologies. The 3D error is found to be 9.7±4.1 mm and 3.9 ± 0.8 mm, respectively without and with calibration. RobCap increases the nominal capture volume of the fixed Mocap from 75 m 3 to 523 m 3 and the operational volume from 105 m 3 to 1436 m 3 . Our findings show that the RobCap is accurate and precise enough to be used as a mobile Mocap system for large displacements.

I. INTRODUCTION

M OTION capture systems (Mocap) have received a huge interest in recent years. A wide range of applications in the robotics [START_REF] Mazhar | Towards real-time physical human-robot interaction using skeleton information and hand gestures[END_REF], health [START_REF] Zheng | Human motion capture system based 3D reconstruction on rehabilitation assistance stability of lower limb exoskeleton robot climbing upstairs posture[END_REF], [START_REF] Antonio | Validation of a 3D markerless system for gait analysis based on OpenPose and two RGB webcams[END_REF] and sports [START_REF] Wang | Tracking a golf ball with high-speed stereo vision system[END_REF]- [START_REF] Wilk | Multimodal sensor fusion for low-power wearable human motion tracking systems in sports applications[END_REF] fields have motivated researchers and engineers to develop systems which accurately track human motion. Optoelectronic Mocap systems such as Vicon © , OptiTrack © , Qualisys © , Codamotion © , among others, are well-established nowadays and achieve millimetric accuracy [START_REF] Van Der Kruk | Accuracy of human motion capture systems for sport applications; state-of-the-art review[END_REF], [START_REF] Topley | A comparison of currently available optoelectronic motion capture systems[END_REF]. These systems differ by the type of markers, the number of cameras, the field of view and the reconstruction algorithm. One common feature is that they are all fixed, a characteristic which limits the work envelope to the field of view of the Mocap system. This technology uses passive or active markers. In the former case, it uses multiple fixed high speed cameras around the measurement area to triangulate a precise marker position. Infrared lighting allows the capture of high contrast images of the reflective markers up to 2kHz. At least two cameras at a time must capture a marker otherwise there are occlusion errors. Post-processing is required to differentiate the markers and restore the correct path [START_REF] Alshamaa | A radar sensor for automatic gait speed analysis in walking tests[END_REF]. In the latter case, active optical markers act as a light source instead of a reflector and are deployed as infrared emitting diodes. Here, the measurement frequency is reduced but less This manuscript was submitted on June 2021. This work is part of the 'MOVCAP' project, funded by the European Regional Development Fund, region Occitanie in France. D. Alshamaa, A. Cherubini, R. Passama and S. Ramdani are with LIRMM, Univ. Montpellier, CNRS, Montpellier, France (e-mail of corresponding author: alshamaa@opta-lp.com).

S. Pla and L. Damm are with EuroMov, Univ. Montpellier, Montpellier, France post-processing is required since since individual diodes can be identified.

A more flexible and less expensive solution is based on computer vision using an RGB-D camera and deep learning algorithms, e.g., OpenPose and DeepPose. As compared to optical technology, this is a more challenging and severely underconstrained problem. RGB-based pose estimation in 2D has been widely researched, but estimates only the 2D pose [START_REF] Chen | Articulated pose estimation by a graphical model with image dependent pairwise relations[END_REF], [START_REF] Cao | Openpose: realtime multi-person 2d pose estimation using part affinity fields[END_REF]. Learning-based discriminative methods in general and deep learning methods in particular, represent the current state of the art in 2D pose estimation [START_REF] Newell | Stacked hourglass networks for human pose estimation[END_REF], [START_REF] Toshev | Deeppose: Human pose estimation via deep neural networks[END_REF]. Estimating the 3D pose using this technology is even a much harder challenge tackled by relatively fewer methods [START_REF] Yu | Robust robot pose estimation for challenging scenes with an RGB-D camera[END_REF]- [START_REF] Mehta | Vnect: Real-time 3d human pose estimation with a single rgb camera[END_REF]. While this solution is promising and improves quickly with advancements in deep learning architectures, computation capacities and training databases, its current accuracy is still far behind that of optoelectronic technology. The average errors of such systems range from 5 to 15 centimeters, according to the complexity of the application and to the position of the joint being tracked, as compared to the millimetric accuracy of optoelectronic solutions.

Kinect is a low-cost sensor developed by Microsoft and uses an RGB camera and an infrared projector and sensor to track human joints in the three dimensional space [START_REF] Li | Three-dimensional pose estimation of infants lying supine using data from a kinect sensor with low training cost[END_REF]- [START_REF] Clark | Threedimensional cameras and skeleton pose tracking for physical function assessment: A review of uses, validity, current developments and Kinect alternatives[END_REF]. However, the skeleton data obtained from this system exhibit a high level of jitter due to noise and estimation error. This jitter worsens when there is occlusion or a subject moves slightly out of the field of view of the sensor [START_REF] Shu | Application of extended Kalman filter for improving the accuracy and smoothness of Kinect skeletonjoint estimates[END_REF].

Other systems worth mentioning rely on inertial technology [START_REF]Neuron[END_REF], [START_REF]Xsens[END_REF]. Such systems use a set of inertial measurement units, containing a combination of gyroscopes, magnetometers and accelerometers to reconstruct the motion of the subject [START_REF] Baldi | Upper body pose estimation using wearable inertial sensors and multiplicative kalman filter[END_REF], [START_REF] Zihajehzadeh | UWB-Aided Inertial Motion Capture for lower body 3-D dynamic activity and trajectory tracking[END_REF]. For deducing joint kinematics, usually one sensor is positioned on each body segment to be captured. A calibration procedure is typically performed in order to obtain the relations between the IMUs and the segment coordinate systems. As compared to the optical technology, the placement procedure is less time-consuming and can possibly be performed by a non-expert. However, a major limitation of this technology is that positions are not measured directly. Rather, the trajectory of a person is approximated through the motion of a pre-defined biomechanical model that is driven by the IMU measurements [START_REF] Anwary | Validity and consistency of concurrent extraction of gait features using inertial measurement units and motion capture system[END_REF]. These latter are not accurate as they suffer from noisiness and bias in the measured angular velocities, accelerations, and magnetic fields. As a result, although being a relatively cheaper technology, it is still far from millimetric accuracy achieved by the optical technology for instance.

Electromagnetic systems (EMSs) find the unknown positions of the measurement transponders by means of timeof-flight of the electromagnetic waves-radio waves-travelling from the transponder to the base stations. EMS provides large capture volumes, but are less accurate than optical systems. The advantage here is that such systems require to determine the positions of the transponders; moreover the human body is transparent for the field applied [START_REF] Schepers | Stochastic magnetic measurement model for relative position and orientation estimation[END_REF]. However, this technology suffers from several issues. One of the drawbacks of the system, at the level of the experimental setup, is the sensitivity for ferromagnetic material in the environment, leading to a decrease in the accuracy [START_REF] Schuler | Evaluation of an electromagnetic position tracking device for measuring in vivo, dynamic joint kinematics[END_REF]. Moreover, such systems generally have low sampling frequencies, which are even lowered more when using multiple markers. For all the aforementioned reasons, we will focus in the rest of the paper on optoelectronic Mocap, since our approach relies on this technology, to obtain a high accuracy mobile motion capture system.

One major drawback of optoelectronic Mocap systems is that they are based on fixed cameras. This limits their work envelope to the sensor field of view. Yet, many applications (e.g. tracking the movement of runners, footballers, ski racers, among other sports, or monitoring patients in mobile environments) require a Mocap that can move with the subject to be tracked [START_REF] Alshamaa | Decentralized kernel-based localization in wireless sensor networks using belief functions[END_REF], [START_REF] Alshamaa | Fusion of multiple mobility and observation models for indoor zoning-based sensor tracking[END_REF]. As a consequence, the human motion can be studied only over a few number of cycles [START_REF] Pietraszewski | Three-dimensional human gait pattern-reference data for normal men[END_REF], [START_REF] Mirek | Assessment of gait therapy effectiveness in patients with Parkinson's disease on the basis of three-dimensional movement analysis[END_REF]. The range of available Mocap systems is currently a couple of cubic meters. For instance, a simulation on the Vicon visualization website [33] shows that 8 infrared cameras achieve an excellent tracking quality only within 76% of a 5 × 5 × 3 m 3 volume. A larger working envelope or capture volume requires a higher number of cameras.

To solve the problem, the intuitive solution was to try to use stationary equipment such as treadmills and ergometers [START_REF] Bini | Kinetics and kinematics analysis of incremental cycling to exhaustion[END_REF], [START_REF] Riley | A kinematic and kinetic comparison of overground and treadmill walking in healthy subjects[END_REF]. In walking, for example, it is shown that treadmill and overground movements are similar, but can present significant differences in the extracted kinematic parameters, although reports argue that the order of these differences is relatively small [START_REF] Riley | A kinematic and kinetic comparison of overground and treadmill walking in healthy subjects[END_REF]. Nonetheless, because of restrictions to the allowed movement excursion, such tools only partially reproduce the real motion and the treadmill walking and running mechanics cannot be generalized to the overground condition [START_REF] Sinclair | Three-dimensional kinematic comparison of treadmill and overground running[END_REF]. An-other solution to address the problem of wider capture volumes has been proposed by Kanade et al. [START_REF] Kanade | Virtualized reality: Constructing virtual worlds from real scenes[END_REF] who installed more than 50 cameras on a dome to cover larger displacements. In addition to the cost aspects, this solution introduces many technical difficulties, e.g, in defining a common volume for calibrating all cameras. Due to these limitations, participants are asked to perform only partial movements, limited to the capture volume of the Mocap system. This introduces a bias when evaluating the motion-related parameters of participants because the dynamics of partial and unconstrained movements can differ, and affect the performances.

To overcome these limits, researchers have proposed moving Mocap systems. These consist in fixing the cameras to a rigid rolling framework [START_REF] Colloud | An innovative solution for 3d kinematics measurment for large volumes[END_REF] or to a boat [START_REF] Kersting | Threedimensional assessment of on water rowing technique: a methodological study[END_REF]. The Mocap can move according to the motion of the participant, to ensure a larger working envelope. A challenge for these systems is the error induced in the reconstructed 3D joint positions as the Mocap moves. Along with the noise and vibrations caused by the device carrying the Mocap, other issues (e.g., delays, variable angles of sight) can affect the reconstruction algorithm. Nonetheless, the implementation of these systems has shown encouraging results in [START_REF] Colloud | An innovative solution for 3d kinematics measurment for large volumes[END_REF] and [START_REF] Kersting | Threedimensional assessment of on water rowing technique: a methodological study[END_REF]. Yet, their application was restricted to 2D motion capture in TV sports events and in the movie production industry and they were not considered for accurate 3D kinematics acquisition. The authors of [START_REF] Begon | Computation of the 3d kinematics in a global frame over a 40 mlong pathway using a rolling motion analysis system[END_REF] and [START_REF] Bernardina | Moving system with action sport cameras: 3D kinematics of the walking and running in a large volume[END_REF] show that accurate 3D kinematic acquisition with a moving Mocap is possible. To this end, they install a set of Vicon cameras, capturing 3D motion, on a rolling framework. Yet, their device is complex, since it requires installing a heavy rolling framework in addition to a large number of cameras all around the participant's area to ensure proper 3D motion capture.

In this paper, we present a new device, called RobCap, featuring a compact optoelectronic Mocap system mounted on a robotic arm. The objective is to develop a high accuracy mobile Mocap for 3D kinematics acquisition in large areas. We mount Codamotion © , a Mocap made up of a compact bar with three 3 infrared cameras, on a robotic arm with six degrees of freedom. By controlling the robot arm, we can move the Mocap, so that it can follow the motion of an individual, equipped with infrared markers. As the Mocap moves, the participant's kinematics are acquired in the local frame of the cameras. Since the participant is moving with respect to the Mocap, which is itself moving with respect to the fixed global frame, it is not straightforward to estimate the global 3D kinematics of the individual. Hence, it also becomes very difficult to assess the RobCap estimation performance. To overcome this issue, we design a coordinate frame of 3 infrared markers rigidly attached to the mobile Mocap system, to form a local frame. These markers, i.e. the local frame, is visible in the global frame throughout the acquisition. This allows us to represent the motion of the local frame in the global frame and therefore transform the kinematics of the individual from the local to the global frame.

The rest of the paper is organized as follows. Section II describes the materials and methods used to develop the proposed system. Sections III and IV present and discuss the obtained results, respectively. Section V concludes the paper and lists some perspectives.

II. MATERIALS AND METHODS

In this section, we present the materials and methods used to develop and evaluate RobCap. We first describe the RobCap setup, and then the experimental protocol. Finally, we detail the method used to acquire the global kinematics from the local motion, to calibrate RobCap and to evaluate its performance.

A. Experimental setup and protocol

The experimental setup is composed of 3 parts, shown in Fig. 1. The first part is dedicated to the RobCap. The second -for evaluating the RobCap performance -consists of a fixed Mocap system, with the corresponding global frame. The last part is the area where the participants' motion takes place.

The RobCap itself is composed of 3 elements: a robotic arm, a Codamotion Mocap system and a rigid structure. The robot used in our work is KUKA KR500-3 available at the EuroMov laboratory, Montpellier, France. It is a 6-axis robot arm that offers a 500 kg payload, 2825 mm reach and a repeatability of 0.08 mm. The role of the robotic arm is to displace the Mocap system according to the motion of the individual. The Codamotion is a classic Mocap device, which relies on active infrared optoelectronic technology. It is characterized by its compact size (a bar of 3 cameras of dimensions 800 × 112 × 80 mm and 5 Kg weight). Its resolution is 0.3 mm along the depth axis and 0.05 mm along the two other axes, and it has a nominal capture volume (where maximum accuracy is maintained) of 5×3×5 = 75m 3 and an operational working volume of 105 m 3 . This Mocap device is the main element of the setup, as it must reconstruct the 3D trajectories of the markers being tracked. The third element is a rigid metallic chassis. It is rigidly attached to the Codamotion. The 2D dimensions of the plane of the chassis are 200 × 100 mm. At the far end of this structure lies a plate of dimensions 100 × 100 mm, where a set of three active infrared markers, designated O, A, and B are placed, to form a 2D Cartesian coordinate system. The objective of this structure will be made clear in the next paragraph.

To acquire the global kinematics of the individual and evaluate the performance of the RobCap, a second Codamotion CXS is fixed in the experimental area. The sampling frequency of both Mocap systems is set to 100Hz. The two systems are synchronized using a Sync cable. Data are sent to a hub then saved on a PC for offline processing. Data are processed using Matlab 2017 on an i7 Windows PC.

The movement of the participants must take place in the area visible to both the RobCap and this fixed Mocap. Three male participants (age = 30 ± 5 years, height = 1.80 ± 0.1 m, weight = 80 ± 5 Kg) are equipped with a set of 4 markers on their wrist. They are requested each at a time to move in the motion area and move their hand at their convenience, resulting in random patterns. We use a remote control, to make the robot follow the participants' motion. A total of 186 random movement patterns is acquired. These include random movement of RobCap, of the participants and their hands with the associated markers. During data acquisition, all 7 markers (4 on the participant and 3 on RobCap) are tracked by both Codamotion. Since processing markers gaps is out of the scope of this paper, we only keep the acquisitions where all the markers are detected for at least 95% of the total number of frames. This leaves only a set of 140 of the 186 original signals. We obtain the samples missing in these 140 signals, by linear interpolation. A short video for the system in action is attached to this paper as supplementary material.

B. Data processing

Suppose both the fixed and mobile Mocap are tracking a marker in the motion area. The coordinates of this marker as viewed by the RobCap, i.e. in the local frame, are denoted as

p M = [x M , y M , z M ] ⊤ .
The same marker has coordinates

p F = [x F , y F , z F ] ⊤
in the global fixed frame. We also suppose that an acquisition j ∈ {1, . . . , N t } (N t being the total number of acquisitions) is composed of N j points. This means that the n marker's coordinates (n ∈ {1, . . . , N j }) at acquisition j are

p M (n) = [x M (n), y M (n), z M (n)] ⊤ and p F (n) = [x F (n), y F (n), z F (n)] ⊤ ,
in the local and global frames respectively. In this work, a total of N t = 560 measurements is acquired, so j ∈ {1, . . . , 560}.

Since RobCap moves to follow the motion of the participant, its local frame is not known anymore as it moves also with it. This prevents us from determining the global kinematics to interpret the human motion, and from evaluating the RobCap's performance in terms of 3D reconstruction accuracy. This is why we attach the rigid structure with the three markers O, A and B to RobCap. At initialization, we use these markers to define both the local frame of the RobCap and the global frame of the fixed Mocap. As the RobCap moves, these markers, visible by the fixed Mocap, allow us to know the exact position of the local frame in the global frame. The coordinates of the markers in the global frame are denoted as O F (n), A F (n) and B F (n), respectively. Throughout the acquisition, the coordinates of these markers in the local frame are constant and given by:

       O M (n) = [0, 0, 0] ⊤ A M (n) = [1, 0, 0] ⊤ B M (n) = [0, 1, 0] ⊤ ∀n ∈ {1, . . . , N j } .
We are interested in transforming the coordinates p M (n) of the marker in the motion area from the local coordinate frame to the global coordinate frame, so that they can be compared with p F (n). Suppose the transformed coordinates of p M (n) are denoted p tr (n) = [x tr (n), y tr (n), z tr (n)] ⊤ . The relation between p tr (n) and p M (n) is governed by the following equation [START_REF] Chi | A novel multi-camera global calibration method for gaze tracking system[END_REF]:

p tr (n) = F T M (n) • p M (n), (1)
where F T M (n) is the transformation matrix between the local mobile frame M and the global fixed frame F for each point n ∈ {1, . . . , N j } for any acquisition j ∈ {1, . . . , N t }.

Suppose that the bases of frames M and F at any point n are -→ m(n) and -→ f (n), respectively. The transformation matrix

F T M (n) is a change of basis from -→ m(n) to -→ f (n), as shown in the following equation, -→ f (n) = F T M (n) • -→ m(n), (2)
where the coordinates of

-→ f (n) are expressed in -→ m(n). The transformation matrix F T M (n) can be thus deduced, F T M (n) = -→ f (n) • -→ m -1 (n). (3)
To determine the components of the two bases -→ m(n) and -→ f (n), we use the coordinates of the three markers O, A and B in both bases at each point n. As we can notice from the coordinates of these markers in the local frame M , the basis -→ m(n) is the identity matrix and hence

-→ m -1 (n) = -→ m(n) = I 3 =     1 0 0 0 1 0 0 0 1     . (4)
To determine the basis -→ f (n), we have to express the coordinates of the fixed frame in the mobile frame. At first, we create a normalized vector

V F (n) = u(n) |u(n)| , v(n) |v(n)| , w(n) |w(n)| T , such that u(n) = ----→ O F A F (n), v(n) = ----→ O F B F (n) and w(n) = u(n) × v(n).
As a reminder, the coordinates O F , A F and B F of the three markers O, A and B respectively can be easily acquired by the fixed Mocap. The vectors u(n) and v(n) form the 2D basis of the coordinate system in the plane of (AOB) and w(n) is the cross product of vectors u(n) and v(n) forming the third axis of the coordinate system. Once the vector V F (n) is defined, the basis -→ f (n) can be easily determined as follows,

-→ f (n) = V T F (n) O F (n) 0 T 1 . (5)
Replacing ( 4) and ( 5) in (3) and then injecting the latter in equation ( 1), allows us to transform the coordinates of any marker in the motion area at any point of the acquisition from the local frame to the global frame at any point P M ,

P tr (n) = V T F (n) O F (n) 0 T 1 • P M (n). (6)
Algorithm 1 gives the pseudocode for transforming the 3D motion acquired by the RobCap in its local frame, to the global frame.

C. System calibration

In the previous paragraph, we have transformed the coordinates of any marker in the motion area from the local mobile frame of the RobCap to the global fixed frame to obtain p tr (n), n ∈ {1, . . . , N j }, j ∈ {1, . . . , N t }. However, Fig. 2: A photo of the actual setup. a source of error that has the potential to negatively affect the expression of the 3D kinematics of the motion acquired by the RobCap in the global frame is the initial definition of both frames. When a set of markers is used to define the origin and the 2D axes of motion, both Mocap systems compute internal transformations so that the current coordinates of these markers form a Cartesian coordinate system. In addition, the error of the Mocap systems varies as a function of the angle of view of the cameras with respect to the position of the marker. Moreover, the number of cameras that detect each marker affects the reconstruction accuracy. Begon and Lacouture [START_REF] Begon | Accuracy of 3-d reconstruction with occlusions[END_REF] have shown that changes in couples of cameras to reconstruct the 3D marker positions causes systematic error in position estimation. All these sources of error, although in the order of millimeters each, add up and may yield a relevant difference between the transformed coordinates and those measured directly in the global frame. To account for these errors, we propose to go through a calibration phase. Before going into the details of the calibration, it is important to note the following. At first, the objective of this phase is to suppress the sources of errors indicated above. However, it requires the presence of a fixed Mocap system as it will be explained in the next paragraph. This means that the absence of Mocap system other than the one used in RobCap hinders the application of this phase. In all cases, this phase is not mandatory for the functioning of the system.

We recall that p F (n) and p tr (n), n ∈ {1, . . . , N j }, j ∈ {1, . . . , N t } designate the coordinates of the marker as measured in the global fixed frame and those transformed from the mobile local frame of the RobCap into the global frame respectively. We suppose that all sources of error resulting in a difference between these coordinates can be accounted through a calibration matrix C, such that,

p F (•) = C • p tr (•), (7)
where the calibration matrix C is defined as, Algorithm 1: Acquiring global 3D kinematics from the local motion of the RobCap device.

Input : P M (n), O F (n), A F (n), B F (n) Output: P T r (n) 1 for j ∈ {1, . . . , N t } do 2 for n ∈ {1, . . . , N j } do 3 u(n) = ----→ O F A F (n); 4 v(n) = ----→ O F B F (n); 5 w(n) = u(n) × v(n); 6 V F (n) = u(n) |u(n)| , v(n) |v(n)| , w(n) |w(n)| T ; 7 P tr (n) = V T F (n) O F (n) 0 T 1 • P M (n);
To calibrate our system, we need to determine the 12 unknown elements of C. To this end, we do or use a single acquisition of N C points. Since the calibration matrix has to be same for all the points of the acquisition, ( 7) can be written:

      x F (n) y F (n) z F (n) 1       =      
      •      
x tr (n)

y tr (n) z tr (n) 1       , (9)
∀n ∈ {1, . . . , N C }. The elements of the calibration matrix C are computed so as to minimize the mean square error between the observed coordinates p

F (n) = [x F (n), y F (n), z F (n)]
p C (n) = C • p tr (n), (10)
n ∈ {1, . . . , N j }, j ∈ {1, . . . , N t }. Algorithm 2 describes the pseudocode for calibrating the proposed system.

                   x tr (
x tr (N C ) y tr (N C ) z tr (N C ) 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x tr (N C ) y tr (N C ) z tr (N C ) 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x tr (N C ) y tr (N C ) z tr (N C ) 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x tr (N C ) y tr (N C ) z tr (N C ) 1                    (4N C ×16) •                                      
                                      (16×1) =                                x F (1) y F (1) z F (1) 1 x F (2) y F (2) z F (2) 1 . . . x F (N C ) y F (N C ) z F (N C ) 1                                (4N C ×1) (11)
Algorithm 2: Calibration of the RobCap device.

Input : P tr (n), N C Output: P C (n) 1 j = 3; 2 for n ∈ {1, . . . , N C } do

III. RESULTS

As explained in Section II, we evaluate the proposed system by tracking 140 times the positions of 4 markers, attached to the participants' wrists, resulting in a total of N t = 560 measurements. At first, we transform the coordinates of the markers acquired by RobCap to the global frame, via Algorithm 1. Then, the system is calibrated using one acquisition of N C points following Algorithm 2.

To assess RobCap's performance, we calculate its 3D error as the Euclidean distance between the transformed coordinates and the ones measured by the fixed Codamotion (ground truth). Prior to calibration, we calculate this error at each point n as

(x F (n) -x tr (n)) 2 + (y F (n) -y tr (n)) 2 + (z F (n) -z tr (n)) 2 .
After calibration, we calculate the error as

(x F (n) -x C (n)) 2 + (y F (n) -y C (n)) 2 + (z F (n) -z C (n)) 2 .
Figure 3 compares the trajectory of one of the markers attached to the participant's wrist acquired by the RobCap and transformed into the global frame, to that measured by the fixed Codamotion. Figures 3(a) and 3(c) show the x, y and z coordinates along with the 3D motion without system calibration, while Figures 3(b) and 3(d) show the same coordinates and motion after system calibration. The average, standard deviation and maximum error of x, y, z and the 3D coordinates of the system with and without system calibration over all points of all 560 acquisitions are shown in Table I.

Here, one single acquisition of N C = 100 points is considered to calibrate the system. To study the influence of the length of the calibration acquisition, we vary N C and evaluate the overall performance of RobCap transformed into the global frame. Figure 4 plots the errorbar of the system upon varying N C from 0 to 250 with a step of 50. Finally, the proposed system is compared to stateof-the-art technologies. Table II compares the different approaches according to several criteria, such as accuracy, volume of capture, complexity and cost.

IV. DISCUSSION

As Table I shows, the maximum error in reconstructing the 3D motion of RobCap transformed into the global frame without calibration is 22.8mm with an average of 9.7mm over all 560 measurements. The maximum error of reconstructing motion in the xand y-directions does not exceed 10.8mm with an average not exceeding 5.4mm but could reach 16.1mm with an average of 9.7mm in the z-direction. The higher error along z is probably due to the fact that motion along this axis is computed when transforming it into the global frame through the vectorial product and not directly measured. Any errors in both x or y directions will add contribute to the z-direction error. On the other hand, the relatively small variation of error with a standard deviation of 4.1mm also shows that the system is quite precise. These results show that the RobCap has a high accuracy and precision in reconstructing the motion even in a situation when the whole environment is mobile, where the RobCap, the participant and the markers to be tracked are all moving.

System calibration using one acquisition of N C = 100 points reduces the average 3D error to 3.9mm with a maximum of 7.2mm. This number of points is determined by varying N C and noting the error. Fig. 4 shows that the error of the system reaches its minimum with N C = 100 points. Longer calibration acquisitions do not result in better reconstruction accuracy. The achieved accuracy demonstrates the efficiency of the proposed calibration technique and equally the high accuracy of the RobCap after proper calibration. The calibration also has a significant positive impact on the precision of the system, enhancing the standard deviation of the error to around 0.8mm. Nonetheless, one downside of the proposed calibration is the need for a fixed Mocap system in the experimental area, which is not always the case. Another downside is that the system has to be calibrated at each new definition of the initial and global frames. This means that each time new frames are defined, the previous calibration is not valid anymore and a new acquisition has to be considered. It is noteworthy recalling here that the calibration of the RobCap with the global frame serves only to express the motion acquired by the RobCap in the global frame. This might not be needed all the time, especially when the relative motion is sufficient.

In Table II, we compare the proposed system to other existing technologies and approaches. The criteria chosen here in our comparison are the error, the volume of capture, the complexity comprising the number of cameras and the difficulty to mount the system and the overall cost. Although other criteria could have also been chosen, we suppose that these four are the most relevant to evaluate a mobile Mocap system, especially that exact information regarding other criteria might not be available for all systems. We compare the proposed system RobCap to two fixed and three mobile Mocap systems. The first fixed Mocap system is of the same type as the one used to build our RobCap device, 'Codamotion'. We use this system as a reference to show the utility of making our proposed system mobile. The second fixed Mocap system is proposed by Kanade et al. [START_REF] Kanade | Virtualized reality: Constructing virtual worlds from real scenes[END_REF]. Here, the authors build a system of 50 cameras on a hemispherical dome of radius 5m to enlarge the capture volume. We consider that the error of these fixed Mocap systems is equal to 0, as they form the global coordinate system and thus the reference that other systems compare with. The first mobile Mocap system is an RGB Camera-based solution using deep learning models for pose estimation [START_REF] Zhou | Human motion capture using a drone[END_REF]. Although this technology can be used for fixed and mobile Mocap systems, we consider here the broader range of applications for a fair comparison with our proposed system. The second mobile Mocap system is proposed by Kersting et al. [START_REF] Kersting | Threedimensional assessment of on water rowing technique: a methodological study[END_REF]. It is composed of three Basler cameras sampled at 30Hz mounted on a large catamaran-type motor boat with cameras set at various heights and the most distant cameras about 14m apart. The third system is proposed by Begon et al. [START_REF] Begon | Computation of the 3d kinematics in a global frame over a 40 mlong pathway using a rolling motion analysis system[END_REF] where a rolling motion analysis system is built using eight cameras of type 'Vicon' placed at a 2.35m height and sampled at 100Hz. The system expresses the local kinematics of the participant walking on a pathway in a global system of coordinates. Table II provides approximate ranges of the performance of the system with respect to the four chosen criteria. This is because the performance of each system varies according to the experimental conditions. We thus consider an average value representing the performance of each system with respect to each As the table shows, the proposed system outperforms the other mobile Mocap systems in terms of the overall accuracy, as shown by the lowest error. As mentioned earlier in this section, the fixed Mocap systems are the reference that we compare the performance of the mobile systems with and for that reason their error is said to be 0. The advantage of the mobile Mocap systems lies in enlarging the capture volume. As we can see, the proposed system along with the pose estimation method achieve the largest capture volume. The values shown here correspond to the nominal capture volume of all systems. In practice, operational working volumes are much higher than that. As compared to the fixed Mocap system of the same type, the device increases the nominal capture volume from 75m 3 to 523m 3 and the operational volume from 105m 3 to 1436m 3 . We would argue that mounting the proposed system is relatively of low complexity, especially that the Mocap system is compact and ready to use and can be easily attached to a robotic arm. However, building the whole system in order to acquire the global kinematics, adds a non-negligible complexity. Another major challenge of such system is occlusion. In order to obtain measurements with a high detection (> 95% of the total frames), we had to realize the experiments in a very controlled environment in a way that all markers stay visible and detected by the Mocap systems. In practical environments, when the whole body of the person is equipped with markers, it would be difficult to guarantee such high visibility and detection rate. In such cases, methods to deal with occlusion and thus missing data have to be proposed. Another challenge that face the proposed system is the automatic control of the robotic arm. Here, it was displaced via a remote control, but a tracking system to follow the motion of the person and control the robotic arm is highly recommended. This might influence the quality of acquired signals and thus the high 2D reconstruction accuracy. Moreover, the proposed system comes at a relatively higher cost than the existing systems, with the cost of the robotic arm, the Codamotion Mocap system and miscellaneous costs of implementation. However, the major advantages of the proposed system as compared to the cheaper and less complex ones, is that it has at the same time a higher error and a larger capture volume, yet at the expense of higher cost and complexity.

V. CONCLUSION AND PERSPECTIVES

In this paper, we presented a new mobile Mocap system, called RobCap. The device is composed of a robotic arm and a compact Mocap system of type Codamotion. As compared to its fixed counterpart, the device increases the nominal capture volume from 75m 3 to 523m 3 and the operational volume from 105m 3 to 1436m 3 . At first, the motion acquired by the RobCap was transformed to the global frames. After that, a calibration approach was proposed to account for the sources of error that affect the quality of the reconstruction when defining the local and the global frame. The system was evaluated on 560 measurements and the performance of the system was then compared to a fixed Mocap system of the same type, Codamotion. We noted an error of 9.7 ± 4.1mm without calibration and 3.9 ± 0.8mm with calibration using a single acquisition. The influence of the length of the calibration acquisition was studied and results showed that best performance was recorded for 100 points. System calibration using acquisitions beyond this number of points showed no additional improvement in the overall performance. Although of relatively higher cost and a bit more complex, the proposed system outperforms existing technologies in terms of accuracy and volume of capture. As a summary, the obtained results show that RobCap can act as a mobile Mocap device for large displacements.

Future work will investigate the usage of the real time processing function of the markers coordinates of Codamotion. This allows for real time motion tracking of the participant and thus automating the control of the robotic arm. Moreover, we aim to propose strategies to handle occlusion. As opposed to other optoelectronic Mocap systems where cameras generally surround the participant's motion, the compact Mocap system used here allows for only one side of view of motion, which implies having more markers occluded. At the experimental level, we aim to use and evaluate the proposed system in real applications with complex activities and 3D full-body reconstruction.

Fig. 1 :

 1 Fig. 1: An illustration of the experimental setup. RobCap is a mobile Mocap mounted on a robotic arm. Three markers are attached to the structure of the RobCap to form a plane, rigidly linked to the Mocap. All markers are detected by RobCap and by the fixed Mocap.

c

  11 c 12 c 13 c 14 c 21 c 22 c 23 c 24 c 31 c 32 c 33 c 34

c 11 c 12 c 13 c 14 c 21 c 22 c 23 c 24 c 31 c 32 c 33 c 34

 142434

1 K

 1 ⊤ and the transformed coordinates p tr (n) = [x tr (n), y tr (n), z tr (n)] ⊤ over all the points of the acquisition n ∈ {1, . . . , N C }. To determine these 12 unknown elements c ij , i ∈ {1, 2, 3}, j ∈ {1, 2, 3, 4}, we transform equation (9) into another solvable form shown in equation (11) using all N c points. Let us denote K the (4N C × 16) matrix, C R the newly formatted (16 × 1) C matrix and L the (4N C × 1) matrix in equation[START_REF] Cao | Openpose: realtime multi-person 2d pose estimation using part affinity fields[END_REF]. As we can notice, equation (11) is in the form of KC R = L. The least square solution of this equation is ĈR = K T K -T L, which allows to determine all the elements c ij , i ∈ {1, 2, 3}, j ∈ {1, 2, 3, 4}. Having computed the calibration matrix C using the N C points, we use it to determine the final transformed and calibrated coordinates p C (n) = [x C , y C , z C ] T of any marker in the motion area from the local mobile frame of the RobCap to the global frame,

3 for 4 KC do 7 L 1 K

 3471 i ∈ {0, . . . , 3} do [n + i, [:, n : n + j] = [P F (n) 1] T L %deduce elements c ij thus C; 12 for j ∈ {1, . . . , N t } do 13 for n ∈ {1, . . . , N j } do 14 P C (n) = C • P tr (n);

Fig. 3 :

 3 Fig. 3: Comparison between 3D motion coordinates of one marker acquired directly by a fixed Mocap system (blue) and those acquired by the RobCap and transformed to the global frame (red) without (left) and with (right) system calibration.

Fig. 4 :

 4 Fig. 4: Influence of the length of calibration acquisition N C on the overall performance of the RobCap transformed into the global frame.

TABLE I :

 I The 3D reconstruction accuracy of the RobCap after transformation to the global frame as compared to a fixed Mocap system, with and without system calibration.

	Error (mm)		without calibration		with calibration N C = 100
		x	y	z	3D	x	y	z	3D
	mean	5.2	5.4	8.8	9.7	1.8	1.7	2.9	3.9
	std	2.6	2.8	3.1	4.1	0.3	0.4	0.7	0.8
	max	10.6	10.8	16.1	22.8	4.2	3.3	4.9	7.2

TABLE II :

 II Comparison between the proposed system and state-of-the-art technologies in terms of accuracy, volume of capture, complexity and cost.

	Criterion	error (mm) volume (m 3 ) complexity	cost
	System
	Fixed Mocap [45]	0	≈ 75	low	average
	Kanade et al. [37]	0	≈ 60	high	high
	Pose estimation [44] 100 -150	> 500	low	low
	Kersting et al. [39]	≈ 30	≈ 35	average	low
	Begon et al. [40]	20 -24	≈ 90	average	average
	RobCap	4 -12	> 500	average	high
	criterion.

ACKNOWLEDGMENTS

The authors thank Hugo Rodriguez for his help in the implementation of the experimental setup and the participants for their willingness to realize the experiments.

CONFLICTS OF INTEREST

The authors declare no conflicts of interest.

APPENDIX

A video for the system in action is attached to the paper as supplementary material.