R P Rini

F Nurosyid

Y Iriani

D Fasquelle

The addition of bismuth (Bi) to the barium titanate (BaTiO3) prepared by chemical solution deposition

The manufacture of BaTiO3 thin films and Ba1-xBixTiO3 have been conducted successfully on the quartz substrate using Chemical Solution Deposition method. The results of characterization using XRD showed that the crystals of BaTiO3 and Ba1-xBixTiO3 were perovskite. The diffraction angle shift between BaTiO3 and Ba1-xBixTiO3 shifts to the right as the mole concentration of Bi. The crystallinity of the Ba1-xBixTiO3 sample increases along with the increase of Bi mole concentration. The higher the sample annealing temperature, the crystallinity decreases. The addition of Bi mole concentrations and the increase of annealing temperature in Ba1-xBixTiO3 samples causes the crystal size of the thin film to increase. Lattice strain is greater with the addition of Bi concentration and the increase of annealing temperature. The result of UV-Vis showed that the transmittance of the thin film was relatively small. Therefore, the thin film made has a high ability to absorb light in the UV area. The greater the addition of Bi mole concentration, the greater the ability of light absorption. When the thin film was given an additional concentration of Bi mol, the refractive index value was greater. The addition of Bi mole concentrations in Ba1-xBixTiO3 thin films leads to an increase in dispersion values.

Introduction

Nowadays, research on the ferroelectric material attracts the physicists as the ferroelectric material is very promising towards the development of science and technology, especially in the material field. Ferroelectric material has fabricated characteristic based on the needs. Moreover, it is easily integrated. Ferroelectricity is a great potential material as new solar cells, light drivers, and optical sensors because of the anomaly photovoltaic (APV) effect [1]. Some methods have been successfully conducted in making epitaxial and polycrystalline films including metal-organic chemical vapor deposition (MOCVD), pulse laser deposition (PLD), metal-organic decomposition (MOD) and sol-gel technique or chemical solution deposition (CSD) [START_REF] Li | Proc. of SPIE[END_REF].

Barium Titanate (BaTiO3) is the most well-known ferroelectric compound studied largely because of the simplicity of the crystal structure. Thus, it can accommodate various types of dopants [START_REF] Fasasi | [END_REF]. BaTiO3 has a high dielectric constant, ferroelectric activity, spontaneous polarization, and nonlinear optical coefficients [4,5]. BaTiO3 is a ferroelectric material that has a perovskite crystalline structure of ABO3, where A is a cation with valence 1 and 2, B is a cation with valence 4 and 5, and O is oxygen [6]. Atom A is located in the corner of the cube. Atom B is located in the diagonal of the cube space and O atom is located in the diagonal plane of the cube [7]. Perovskite BaTiO3 has five types of crystal structures such as hexagonal, cubic, tetragonal, orthorhombic, and rhombohedral, each of which depends on the temperature of the phase [4].

This research used ferroelectric material namely BaTiO3 and Ba1-xBixTiO3. This material is formed from Barium Titanate added with bismuth. The addition of bismuth (Bi 3+ ) to Ba1-xBixTiO3 thin films can cause changes in the characteristics of the material. Thus, it can be useful to improve the quality and function. Bismuth is a donor doping that donates excess valence electrons to the Ba 2+ ion and the radius is almost the same as the radius of the Ba 2+ ion. The Bi 3+ doping ion radius is 1.03 Å [8], while the Ba 2+ ion radius is 1.35 Å and the Ti 4+ ion radius is 0.68 Å [9]. Doping is a common method for reducing the semiconductor band gap [1].

In this research, the growth of BaTiO3 and Ba1-xBixTiO3 thin film was conducted using Chemical Solution Deposition (CSD) method. Chemical Solution Deposition (CSD) is a way to make a thin film by deposition of chemical solutions on the substrate, then prepared by coating a spin coating at a certain rotational speed. This method is superior because stoichiometry is easily well-controlled [10]. BaTiO3 and Ba1-xBixTiO3 thin films are grown on quartz substrates with annealing temperature variations of 800C, 850 o C, and 900C. The thin film that has been formed was then tested for microstructure using X-Ray Diffraction (XRD) and optical properties testing using a UV-Vis spectrophotometer. X-Ray Diffraction (XRD) examination aims to determine the microstructure of the sample. The optical properties test aims to determine the absorption spectrum of BaTiO3 and Ba1-xBixTiO3 thin films.

Experiment

The materials used in this research were Barium Acetate [Ba(CH3COO)2] 99.00%, Bismuth Acetate [Bi(CH3COO)3] 99.9%, Acetic Acid [(CH3COOH)] 100%, Titanium Isopropoxide [Ti(OC3H7)4] 97%, and Ethylene Glycol [(HOCH2CH2OH)] 100%. The substrates used for the deposition of BaTiO3 and Ba1-xBixTiO3 films were quartz substrates. The manufacture of BaTiO3 and Ba1-xBixTiO3 thin films used the Chemical Solution Deposition method with three main stages: namely the making/manufacturing of a solution, the process of spin coating, and the annealing process. Ba1-xBixTiO3 thin films were prepared using a ratio of bismuth mole compositions of 0.10 and 0.15. The process of making the solution was mixed using a magnetic stirrer until all the ingredients were homogeneously mixed. The layer was deposited using a spin coater with a speed of 5000 rpm. After obtaining the desired number of films, it was then annealed using a furnace with annealing temperature variation of 800C, 850 o C, and 900C with a holding time of one hour. The sample was then characterized using X-Ray Diffraction (XRD) to determine the microstructure of the sample and using a UV-Vis spectrophotometer to determine the optical properties of the thin film.

Result and Discussion

The crystal structure of thin films of BaTiO3 and Ba1-xBixTiO3 was characterized using XRD. Samples of BaTiO3 and Ba1-xBixTiO3 varies with the concentration of mol Bi with an annealing temperature of 800 o C, 850 o C, and 900 o C. Figure 1 shows the diffraction patterns of BaTiO3 and Ba1-xBixTiO3 thin films with variations in the concentration of mol Bi annealed at temperatures of 800 o C, 850 o C, and 900 o C. Diffraction peaks resulted from XRD characterization had different plane orientations. The diffraction pattern was matched with the ICDD database to identify the angular shift that occurred between the theory and this research. Based on Figure 1, it shows that the sample still had other phases. The existence of other phases showed that Ba, Bi, Ti, and O atoms had not been able to diffuse completely. Other phases identified in the sample are phases of BaTi2O5. In the XRD diffraction pattern, the other phases are marked with . Figure 1 shows that the addition of Bi mole concentration causes a diffraction angle shift (2θ). The diffraction angle shift between BaTiO3 and Ba1-xBixTiO3 shifted to the right as the mole concentration of Bi was given. This result is under the research conducted by Alkathy and Raju [8]. The angular shift that occurred was not significant because the concentration of mol Bi added was very small. This angular shift was caused because the radius of the Bi atom was smaller than the radius of the Ba atom. The addition of Bi atoms to Ba1-xBixTiO3 samples acts as a substitute for Ba atoms in the perovskite structure of BaTiO3. Bi atoms can replace Ba atoms because they have nearly the same atomic radius.

The intensity of the diffraction pattern affected crystallinity values from BaTiO3 and Ba1-xBixTiO3 samples. The addition of mol Bi concentration in the sample caused the intensity of the diffraction pattern to increase. These results are under the research of Iriani et al., they state that with the addition of doping mole concentrations in the BaTiO3 thin film, the intensity value formed increases [9]. The higher the intensity, the greater the crystallinity of the sample. The crystallinity of the Ba1-xBixTiO3 sample increased with increasing mol Bi concentration. Besides, crystallinity samples were also affected by the sample annealing temperature. The higher the sample annealing temperature, the crystallinity decreased. This decrease in crystallinity was affected by the vibrations of the atoms scattered in each film. This is consistent with the results shown in Table 1. This crystallinity shows the level of regularity of a crystal. The crystallinity of BaTiO3 and Ba1-xBixTiO3 thin films can be calculated based on the ratio of the highest peak intensity in a specific field orientation with the highest number of intensities and the lowest intensity in a specific field orientation. The crystallinity of the thin film is determined by the equation as follow [11]: Based on the results of XRD characterization, it was obtained half the width of the diffraction peak or commonly known Full Width Half Maximum (FWHM). This FWHM value affected the size of the crystal. High diffraction peaks and sharp lines that resembled straight lines had a small FWHM value. It resulted in large crystal sizes, and vice versa, wide diffraction peaks that produced small crystal sizes. These results are in line with the research carried out by William et al., [12]. The crystal size of BaTiO3 and Ba1-xBixTiO3 thin films can be calculated using the following Scherrer equation:

% 𝐶𝑟𝑦𝑠𝑡𝑎𝑙𝑙𝑖𝑛𝑖𝑡𝑦 = 𝐼 𝑚𝑎𝑥 𝐼 𝑚𝑎𝑥 +𝐼 𝑚𝑖𝑛 × 100 (1
𝐷 = 𝑘 𝜆 𝛽 cos 𝜃 (2)
Where, β value is FWHM value, θ is the diffraction angle, 𝑘 is the Scherrer cosntant of 0.9, and  is the wavelength of the X-ray [1]. Table 2 shows the calculated crystal size values of the BaTiO3 and Ba1-xBixTiO3 samples toward the variation of the Bi mole concentration. It shows that the addition of mol Bi concentrations in Ba1-xBixTiO3 samples caused the crystal size of the thin film to increase. Following the addition of mol Bi concentration that with the annealing temperature increase, the crystal size from the sample was also getting bigger. These results are consistent with the results observed by Alkathy et al., as the mole concentration of doping increases, the crystal size value of the sample increases [13]. Based on the results of a research that has been done by Rini et al., when the annealing temperature increases, the crystal size of the thin film will get bigger [14]. The increase size of the crystal happened because the film could diffuse from one another. Thus, the reaction was more perfect. Table 3 shows that the addition of mol Bi concentrations in Ba1-xBixTiO3 samples caused the lattice strain from the thin film to increase. If the annealing temperature of the sample increased, the resulting lattice strain would be even greater. Based on the order of the ionic radius of Ti 4+ < Bi 3+ < Ba 2+ , it is possible that the lattice strain is getting bigger because bismuth undergoes substitution in barium [15]. Samples that had been manufactured over the quartz substrate were examined using a UV-Vis spectrophotometer. This test aimed to determine the optical properties of Ba1-xBixTiO3 samples in the wavelength range of 200 to 800 nm. The wavelength was the wavelength of UV light to be visible (visible light).

Based on the result of testing the optical properties, it was obtained the value of transmittance and absorbent of BaTiO3 and Ba1-xBixTiO3 thin films. Figure 2 shows the transmittance results of BaTiO3 and Ba1-xBixTiO3 thin films. The transmittance results showed that as the mole concentration of Bi increased, the transmittance value of the Ba1-xBixTiO3 thin film decreased. These results are consistent with the research conducted by Fu et al., they state that as the wavelength decreases, the transmittance value of the thin film also decreases [16]. This showed that the transmittance value of the thin film was relatively small. Thus, the thin film made had a high ability to absorb light in the UV region. The greater the addition of Bi mole concentration, the greater the ability of light absorption. The refractive index value of the thin film of BaTiO3 and Ba1-xBixTiO3 was calculated using the Swanepoel method. The following is an equation from the Swanepoel method [17]:

𝑛 = [𝑁 1 + (𝑁 1 2 -𝑠 2 ) 1 2 ] 1 2 (3)
In which, N and s are defined as: In which 𝑠 is the substrate transmission spectrum, 𝑁 1 is the area of transparent spectral, 𝑇 𝑆 is the transmittance of the quartz substrate, 𝑛 1 is the refractive index, and 𝑇 𝑚 is the transmittance of the sample.

𝑁 1 = 2𝑠 𝑇 𝑚 + 𝑠 2 + 1 2 𝑠 = 1 𝑇 𝑠 + √ 1 𝑇 𝑠 2 -1 (5)
Figure 3 shows the relationship between wavelength and refractive index of BaTiO3 and Ba1-xBixTiO3 thin films. The value of the refractive index produced by the Ba1-xBixTiO3 thin film was inversely proportional to the transmittance value. When the thin film was given the addition of mol Bi concentrations, the refractive index value was greater. This result is in line with Tian et al., in which the addition of doping mole concentration causes the refractive index value of the thin film to increase [18]. The addition of doping mole concentration caused the density of atoms in the film to increase. Thus, the refractive index value increased. The amount of light dispersion from BaTiO3 and Ba1-xBixTiO3 thin films is calculated using the following Equation [17]:

𝑛 2 = 1 + 𝐸 0 𝐸 𝑑 𝐸 0 2 -𝐸 2 (6)
In which, 𝐸 0 is single oscillator energy, 𝐸 𝑑 is dispersion energy, 𝐸 2 is photon energy,  = 1,9865x10 -25 kg m 3 /s 2 and 1 joule = 6,242x10 18 eV. The results of BaTiO3 and Ba1-xBixTiO3 thin-film dispersion calculations were displayed in the form of a relationship between 1/(n 2 -1) Vs E 2 . Based on the graph in Figure 4, it can be seen that the addition of mol Bi concentrations in the Ba1-xBixTiO3 thin film causes an increase in the dispersion value. It is supported by Mohamed et al., who state that light dispersion from thin films increases with the addition of doping mole concentrations [19]. Increasing the dispersion value in the film was caused by the density of atoms attached to the substrate.

Conclusions

Based on the results of the analysis, it was found that with the addition of Bi moles in the sample, there were still other phases. The existence of these other phases showed that the atoms of Ba, Bi, Ti, and O have not been able to diffuse completely. The diffraction angle shift between BaTiO3 and Ba1-xBixTiO3 shifts to the right as the mole concentration of Bi. The crystallinity of the Ba1-xBixTiO3 sample increases along with the increase of Bi mole concentration. The higher the sample annealing temperature, the crystallinity decreases. The addition of Bi mole concentrations and the increase of annealing temperature in Ba1-xBixTiO3 samples causes the crystal size of the thin film to increase. Lattice strain is greater with the addition of Bi concentration and the increase of annealing temperature. The result of UV-Vis showed that the transmittance of the thin film was relatively small. Therefore, the thin film made has a high ability to absorb light in the UV area. The greater the addition of Bi mole concentration, the greater the ability of light absorption. When the thin film was given an additional concentration of Bi mol, the refractive index value was greater. The addition of Bi mole concentrations in Ba1-xBixTiO3 thin films leads to an increase in dispersion values.

10th 3 Figure 1 .

 31 Figure 1. XRD patterns of BaTiO3 and Ba1-xBixTiO3 using annealing temperature variations (a) 800 o C, (b) 850 o C, and (c) 900 o C

10th

  International Conference on Physics and Its Applications (ICOPIA 2020) Journal of Physics: Conference Series 1825 (2021) 012065

Figure 2 .

 2 Figure 2. Transmittance of BaTiO3 and Ba1-xBixTiO3 using annealing temperature variations (a) 800 o C, (b) 850 o C, and (c) 900 o C

Figure 3 .

 3 Figure 3. Refractive index of BaTiO3 and Ba1-xBixTiO3 using annealing temperature variations (a) 800 o C, (b) 850 o C, and (c) 900 o C

( 4 )

 4 10th International Conference on Physics and Its Applications (ICOPIA 2020) Journal of Physics: Conference Series 1825 (2021) 012065 IOP Publishing doi:10.1088/1742-6596/1825/1/012065 7

Figure 4 .

 4 Figure 4. 1/(n 2 -1) Vs E 2 of BaTiO3 and Ba1-xBixTiO3 using annealing temperature variations (a) 800 o C, (b) 850 o C, and (c) 900 o C

Table 1 .

 1 ) Crystallinity with annealing temperature variations

			Crystallinity (%)
	Mole Concentration of	Annealing	Annealing	Annealing
	Bi (x)	Temperature of	Temperature of	Temperature of
		800 o C	850 o C	900 o C
	BaTiO3	66.73	83.33	69.57
	10%	67.8	71.56	71.098
	15%	69.61	72.72	71.76

Table 2 .

 2 crystal size with annealing temperature variations

			crystal size (nm)
	Mole Concentration of	Annealing	Annealing	Annealing
	Bi (x)	Temperature of	Temperature of	Temperature of
		800 o C	850 o C	900 o C
	BaTiO3	12	70	27
	10%	17	11	36
	15%	20	23	71

Table 3 .

 3 Lattice strain with annealing temperature variations

			Lattice Strain
	Mole Concentration of	Annealing	Annealing	Annealing
	Bi (x)	Temperature of	Temperature of	Temperature of
		800 o C	850 o C	900 o C
	BaTiO3	0.0295	0.3180	0.0080
	10%	0.0199	0.0324	0.0095
	15%	0.0423	0.0368	0.0030

10th International Conference on Physics and Its Applications(ICOPIA 2020)

10th International Conference on Physics and Its Applications (ICOPIA 2020) Journal of Physics: Conference Series

Acknowledgments

The authors wish to thank Kementrian Riset, Teknologi & Pendidikan Tinggi for financial support through Penelitian Dasar 2019 No 719/UN27.21/PP/2019.


Issam Khedher
email: issam.khedher@univ-lyon2.fr

Jean-Marie Favreau

Serge Miguet

Gilles Gesquière

A Multimodal Deep Learning Approach for High-Resolution Land Surface Temperature Estimation

Keywords: conditional Generative Adversarial Networks (cGANs), Multimodal Approach, Land Surface Temperature (LST) Estimation, Urban Heat Islands (UHI)

Urban Heat Islands (UHI), characterized by elevated temperatures, present important challenges to sustainability. This study introduces a novel multimodal approach for high-resolution Land Surface Temperature (LST) estimation, a critical component in addressing UHI. The methodology initially employs RGB orthophotography for LST estimation and progressively integrates additional relevant variables correlated with LST, including elevation and land cover. Leveraging conditional Generative Adversarial Networks (cGANs), LST maps are generated, enabling informed urban planning. Experimental results highlight the potential of this multimodal approach, emphasizing that the combination of all data variables yields the most favorable outcomes. These findings advance UHI research and support data-driven urban climate management.

Introduction

UHI persist as a prominent concern in the realms of urban planning and environmental science. These localized zones, characterized by elevated temperatures within urban environments compared to their surroundings, exert a profound influence on energy consumption, air quality, and public health [START_REF]European Environment Agency: Healthy environment, healthy lives: how the environment influences health and well-being in Europe[END_REF] [10] [START_REF]World Bank: Analysis of heat waves and urban heat island effects in central european cities and implications for urban planning[END_REF]. In light of these challenges, the accurate estimation of LST assumes paramount importance, given its central role in UHI characterization and urban climate studies [START_REF] Kumar | Effect of lst on urban heat island in varanasi city, india[END_REF] [16] [START_REF] Mas'uddin | Erizal: Urban heat island index change detection based on land surface temperature, normalized difference vegetation index, normalized difference built-up index: A case study[END_REF].

LST estimation relies on various key parameters that influence its spatial distribution. Among these, RGB imagery offers valuable insights into urban characteristics, such as buildings, roads, and green spaces. This visual data aids in understanding how these features influence LST patterns. For example, densely built-up areas with extensive impervious surfaces tend to absorb and re-emit heat, contributing to elevated LST values, while water bodies and vegetation act as cooling agents by reducing surface temperatures through evaporation and shading [START_REF] Rahman | Impact of urbanization on urban heat island intensity in major districts of bangladesh using remote sensing and geo-spatial tools[END_REF]. Furthermore, RGB channels, combined with other satellite channels, are pivotal for deriving and quantifying specific biophysical indices closely linked to LST, providing deeper insights into the relationships between urban characteristics and temperature variations [START_REF] Kim | Examining the relationship between land use/land cover (lulc) and land surface temperature (lst) using explainable artificial intelligence (xai) models: A case study of seoul, south korea[END_REF]. These biophysical indices like the Normalized Difference Vegetation Index (NDVI) and the Normalized Difference Built-up Index (NDBI) are instrumental in assessing the impact of vegetation density and urbanization on LST. Higher NDVI values indicate denser vegetation, associated with cooler temperatures due to shading and transpiration, whereas elevated NDBI values signify intensified urban heat effects [START_REF] Guechi | Correlation analysis between biophysical indices and lst using remote sensing and gis in guelma city (algeria)[END_REF] [START_REF] Kim | Examining the relationship between land use/land cover (lulc) and land surface temperature (lst) using explainable artificial intelligence (xai) models: A case study of seoul, south korea[END_REF]. Furthermore, authors in [START_REF] Khandelwal | Assessment of land surface temperature variation due to change in elevation of area surrounding jaipur, india[END_REF] [START_REF] Peng | Correlation analysis of land surface temperature and topographic elements in hangzhou, china[END_REF] confirm that Digital Elevation Models (referred to as (D) in this paper) provide topographic information, as elevation significantly impacts temperature patterns; higher altitudes generally exhibit cooler temperatures, while slope steepness affects heat dispersion and accumulation. Among the key parameters that influence the spatial distribution of LST estimation, land cover types are critical determinants, encompassing a range of surface materials, such as impervious urban areas, vegetation, water bodies, and barren [START_REF] Igun | Impact of urban land cover change on lst[END_REF] [11] [START_REF] Yin | Relationship between urban morphology and land surface temperature-a case study of nanjing city[END_REF]. These land cover categories exhibit distinct thermal properties, resulting in significant LST variations [START_REF] Safariah | The contribution of housing area to lst in bandung[END_REF] [24] [START_REF] Xian | The effects of urban land cover dynamics on urban heat island intensity and temporal trends[END_REF]. These interrelated parameters emphasize the importance of integrating multi-source data, including RGB, D, and land cover, to enhance the accuracy of LST estimation models, a crucial aspect addressed in this study.

Various methods have been developed to estimate LST using satellite data. [START_REF] Sekertekin | Validation of physical radiative transfer equation-based land surface temperature using landsat 8 satellite imagery and surfrad in-situ measurements[END_REF] involves the use of radiative transfer models, such as the Planck-Blackbody equation, which leverages thermal infrared (TIR) bands from multispectral sensors to calculate LST. Additionally, in [START_REF] Liu | Simultaneous retrieval of land surface temperature and emissivity from the fengyun-4a advanced geosynchronous radiation imager[END_REF], temperature-emissivity separation (TES) methods are employed to separate surface temperature from emissivity, offering more accurate results. Furthermore, mono-window algorithm (MWA), split window algorithm (SWA), and single-channel (SC) make use of different TIR bands to correct for atmospheric effects [START_REF] Käfer | Comparative analysis of split-window and single-channel algorithms for land surface temperature retrieval of a pseudo-invariant target[END_REF] [START_REF] Wang | Comparison of three algorithms for the retrieval of lst from landsat 8 images[END_REF]. Advanced methods incorporate ancillary data like (D) to correct for topographic influences, and machine learning algorithms are increasingly applied for their ability to capture complex spatial and spectral relationships in multispectral imagery [START_REF] Wang | Estimation of 30m lsts over the entire tibetan plateau based on landsat-7 etm+ data and machine learning methods[END_REF] [START_REF] Xu | Spatial downscaling of land surface temperature based on a multi-factor geographically weighted machine learning model[END_REF]. While these methods provide valuable insights into surface temperature dynamics, they are not without limitations. These LST estimation methods often face challenges. They may struggle to account for fine-scale surface heterogeneity, leading to inaccuracies in areas with complex land cover patterns. They also rely on detailed knowledge of sensor calibration and atmospheric parameters, which can be a source of uncertainty. Furthermore, different satellite platforms exhibit trade-offs between data frequency and spatial resolution. Some satellites provide frequent data but at a moderate spatial resolution, while others offer higher spatial resolution with less frequent data. Moreover, these satellites often encounter challenges such as missing data. In such cases, a robust model bases its imputation of missing LST data on available information, thereby addressing the limitations associated with satellite data characteristics.

GANs [START_REF] Goodfellow | Generative adversarial networks[END_REF] empower the acquisition of profound insights by implicitly modeling complex, high-dimensional data distributions using two competitive submodels: the generator and the discriminator. This capability extends to conditional Generative Adversarial Networks (cGANs), wherein the generator and discriminator are conditioned on external information, enabling precise image generation. The emergence of cGANs, specially pix2pix [START_REF] Isola | Image-to-image translation with conditional adversarial networks[END_REF], has seen them excel in numerous image-to-image translation tasks, including RGB/(NDVI and NDRE) translation [START_REF] Davidson | Ndvi/ndre prediction from standard rgb aerial imagery using deep learning[END_REF], RGB/NIR translation [START_REF] Akagic | Mapping rgb-to-nir with pix2pix image-to-image translation for fire detection applications[END_REF], and Areal/Map transformations [START_REF] Henry | Pix2pix gan for image-to-image translation[END_REF]. This impressive track record naturally prompts the question: given a sufficiently extensive training dataset, can cGANs proficiently translate multimodal data into LST maps?

The paper is structured into four sections that (at least partially) answers the question. Section 2 will delve into the intricacies of the methodology, providing a breakdown of the data pipeline and system architecture. In section 3, the findings will be presented, offering both qualitative and quantitative insights. Section 4 will be dedicated to the in-depth discussion of the results. Finally, in section 5, we will draw this paper to a close, summarizing the conclusions and outlining potential avenues for future research.

Methodology

In this section, we provide a detailed description of the methodology followed to estimate LST from diverse data modalities and sources, including raster RGB imagery, raster Digital Elevation Model (D) data, vector Corine Land Cover (C) data, and additional vector Land Cover (L) data. The approach is based on a four-step pipeline designed to maximize the utilization of both vector and raster information from these heterogeneous data sources while ensuring spatial consistency. An overview of this pipeline is presented below (see Fig. 1).

Data collection

LST Imagery. Incorporated within the dataset is the LST surface imagery sourced from [START_REF]Data grand lyon[END_REF], depicted through a gradient of colors that represent varying degrees of warmth and coolness. This raster dataset is monochannel, with each pixel representing a 30-meter section of terrain, corresponding to the spatial resolution of the source data from Landsat 8. The snapshot was captured on July 4, 2015, at 10:20 UTC (12:20 local time). The dataset was subjected to correction procedures to mitigate atmospheric, topographic, and emissivity effects, ensuring the accuracy of the temperature readings. This LST dataset provides insights into the warmest surface areas as observed from the sky during daylight hours. In densely populated areas, the LST primarily reflects the temperature of rooftops, while in wider thoroughfares, it encompasses temperature information from roadways and other surfaces. The LST imagery can be visualized in Fig. 2. Digital Elevation Model (D). The (D) dataset employed is provided in the Raster TIFF format in [START_REF]Data grand lyon[END_REF] and is generated from raw data sources, including slope break lines and ground-level reference points. The pixel size of this dataset is 10 meters, offering a detailed representation of the terrain's elevation characteristics. The accessibility and the availability of elevation information provides a robust foundation for the integration of such data into our analysis.

Corine Land Cover dataset (C). Corine Land Cover (C) data, available as vector data in [START_REF]Data grand lyon[END_REF], provides comprehensive land cover information for the C data is also integrated with selected vector data, such as Grand-Lyon cadastre (buildings and parcels), to enhance urban context understanding. Notably, C data achieves a spatial precision of 1 hectare (locally lower for continuity preservation), compared to the 25hectare granularity of the standard Corine Land Cover dataset. It is noteworthy that the widespread availability of Corine Land Cover data, as exemplified by its presence beyond specific regional datasets such as the one for Lyon Metropolis in this study, underscores its importance. It is noteworthy that this ubiquity makes Corine Land Cover data a valuable asset for integration into diverse analytical contexts.

Land Cover data (L). The Land Cover Data (L), available as vector data in [START_REF]Data grand lyon[END_REF], offers a comprehensive perspective on the land use, classifying it into 45 distinct classes. This fine-grained data serve as a complementary source of information to enhance the understanding of land use patterns in urban and peri-urban environments. It's worth noting that the Land Cover Data achieves a spatial precision level, with a Minimum Mapping Unit (MMU) of 100 m² and a Minimum Mapping Width (MMW) of 5 meters, maintaining continuity of at least 1 meter.

Data preprocessing

The dataset employed in this study comprises a diverse array of geospatial information, encompassing both vector and raster data with distinct characteristics. These datasets exhibit variations in coordinate systems, projection methods, and spatial resolutions. To harness their full potential for analysis and modeling, a comprehensive data preprocessing stage is imperative. This section elucidates the preprocessing procedures undertaken to harmonize, reproject, and optimize the disparate datasets, rendering them compatible and ready for subsequent analysis and model training.

Warping. The first step in this preprocessing involves transforming the data into a uniform Coordinate Reference System (CRS). The chosen CRS for this purpose is the EPSG:3946 -RGF93 / CC46, characterized by its utilization of the Lambert Conformal Conic projection method. This transformation harmonizes the spatial references across all datasets.

Scaling for Resolution Uniformity. In order to ensure consistent data handling, a preprocessing step involves both downscaling and upscaling of the various datasets to achieve a uniform spatial resolution of 1 meter. 1 meter is considered appropriate as it aligns with the resolution interval present in our dataset. The resolution of LST data is enhanced. Simultaneously, the spatial resolution of the RGB imagery is reduced to the same 1-meter resolution, while the (D) underwent an upscaling process. These scaling operations were performed using the GDAL library, specifically the gdal translate tool, with cubic spline interpolation to maintain spatial fidelity Rasterization. To enhance their utilization within the cGANs model, rasterization of vector datasets: (C) and (L) are conducted. Both datasets were transformed into raster format with a uniform resolution of 1 meter. During this process, each class from (C) (25 categories) and (L) (45 distinct classes) is mapped to pixel values within the [0, 255] range. The rasterization procedure is executed using the gdal rasterize tool. This conversion ensures that the vector data can be employed for further processing and training.

Data preparation

Data is standardized to share common characteristics, encompassing a raster data type, uniform spatial projection, and an identical spatial resolution. These measures have set the stage for the subsequent Data Preparation phase, where we focus on preparing the datasets specifically for the cGANs-based training of the model.

Step 1: Regular Grid Generation. This step involves the application of a consistent grid to all data layers. This process results in the creation of monochannel tiles, each with dimensions of (1, 256, 256). These monochannel tiles collectively cover the entire study area without overlap, forming a systematic grid. The retiling phase are executed using gdal retile tool.

Step 2: Data Combination. The monochromatic tiles are joined to obtain multichannel tiles of size (H, 256, 256) using Python. H varies from 3 to 6, depending on which data layers being integrated. Data combinations explored in this study encompass RGB, DCL, RGBD, RGBC, RGBL, RGBDC, RGBDL, RGBCL, RGBDCL. These diverse data combinations enable to investigate how the integration of different information sources impacts the accuracy of the pix2pix cGANs model for LST estimation.

cGANs Training

Architecture overview. The pix2pix model employs a conditional Generative Adversarial Network (cGANs) architecture. The generator is based on the U-Net architecture, which takes combined tiles as input and generates LST output images. The discriminator, composed of conventional layers, assesses pairs of combined tiles and LST images to distinguish plausible transformations. Through adversarial training, the generator aims to produce LST images that are indistinguishable from real ones, enhancing the overall image generation quality.

Areas of experiments: Urban zone and extended zone. These studies are conducted in two zones: an urban zone and an extended zone encompassing the urban environment and its surroundings. Beginning in the urban zone allows a progressive complexity assessment, ensuring model reliability before extending it. It also aids in addressing urban-specific challenges and implementing data augmentation for urban environments, enhancing overall performance.

Training configuration. In the urban zone, the data is composed of 400 tiles, with 80% (320 tiles) allocation for training and the remaining 20% (80 tiles) for testing. In the extended zone, we follow a similar 80% (6,500 tiles) training and 20% (1,623 tiles) testing split, totaling 8,123 tiles. A consistency is maintained in hyperparameters. The Adam optimizer, known for handling complex neural networks, is employed. The learning rate is set at 0.0002 and a batch size of 1 is used. The training loss function combines mean absolute error and cross-entropy loss, capturing both generation and classification aspects, following the same approach as the original pix2pix paper. Over 50 epochs, our model iteratively learns and refines from the data.

Evaluation Metrics. Root Mean Square Error (RMSE) is the evaluation metric employed to assess the performance of the model.

RMSE quantifies the average difference between the predicted LST images and their corresponding ground truth LST images. Specifically, the RMSE is calculated between every pair of predicted and ground truth images and then compute the mean RMSE across all pairs. RMSE is calculated using the following formula:

RM SE = 1 N N i=1 (P i -G i ) 2 (1)
where N represents the total number of pixels in the image, (P i ) denotes the pixel value of the predicted LST image, (G i ) denotes the pixel value of the corresponding ground truth LST image.

Results

Fig. 3 Fig. 4 depict the evolution of mean RMSE over epochs. During the training phase, the model is saved after each epoch, employing these saved models for test image inference in test set. RMSE is calculated between the generated and ground truth images and the mean RMSE is computed for each model. Fig. 5 and Fig. 6 display the multimodal data to LST translation results for six example sites using nine different data combinations for both the urban and extended zones, respectively.

Fig. 3: mean RMSE in the urban zone

Urban zone

The initial input modality to the model is RGB alone, given its wide availability and applicability to various regions. The mean RMSE hovers around 1.5°C. Visual comparison with ground-truth LST imagery reveals low performance when Fig. 4: mean RMSE in the extended zone using only RGB data, as the generated LST imagery does not align well with the ground truth. Subsequently, (D) modality is introduced due to its common availability. Unfortunately, (D) has an adverse effect when merged with RGB.

The RGBD combination yields the poorest performance. Notably, the inclusion of (D) in the majority of combinations has a negative impact on performance. This can be explained by the urban zone's somewhat constrained terrain elevation variability. This will be further discussed in section 4. As a next step, land cover data is incorporated, which provides additional information relevant to LST. Here, performance improvements are observed, and the model exhibits proficiency in generating LST imagery. Both qualitative and quantitative analyses reveal that RGBCL and RGBDCL produce equivalent results, demonstrating the best performance, with a slight advantage leaning toward RGBCL.

Extended zone

In the extended zone analysis, the objective is to augment the dataset and introduce increased complexity by incorporating additional vegetation, slopes, and terrain variations. This expansion aims to provide more challenging conditions for the system, thus further assessing its performance. Following a similar approach as in the urban zone, the model is initially trained exclusively on RGB data, resulting in unsatisfactory performance characterized by the highest RMSE and numerous errors in the generated tiles, as evidenced by the visual examples in the figure. To enhance the model's performance, the (D) modality is introduced to provide additional information. This inclusion yields significant improvements in results, as clearly observed in the third example, where a substantial disparity is evident between the LST generated solely from RGB data and that generated from RGBD. Subsequently, land cover data, (C) and (L), is integrated leading to a notable enhancement in system performance. This improvement is exemplified in the fifth example in Fig. 6, where the model accurately identified urban areas in the lower-left and upper-right corners among other vegetated regions along the diagonal, a capability not achieved with RGBD and RGB alone. Among all combinations, RGBDL and RGBDC consistently yield the best results where all three types of information are included (orthophotography, elevation and land cover).

Discussion

The model demonstrates robust performance in both geographic zones we have delineated. However, it is noteworthy that its performance in the urban zone surpasses that in the extended zone. This discrepancy can be attributed to several factors that warrant further elucidation. Firstly, the urban zone inherently includes less complex and varied data compared to the extended zone. Within the extended zone, we encounter instances such as non-cultivated fields, which exhibit higher temperatures, yet the model tends to estimate them as cooler. Similarly, forested areas and mountainous terrain, typically characterized by lower temperatures, may not be accurately captured by the model due to a relative scarcity of training data for such high-elevation forested regions. The models based only on RGB data do not exhibit substantial performance, which can be attributed to the limitation of utilizing orthophotography data alone for estimating surface temperatures. An illustrative case encountered in our study is the similarity in RGB color between natural and synthetic football fields, despite a notable difference in surface temperatures.

In the urban observations, a negative impact of the elevation (D) is noticed. This can be attributed to the urban zone's relatively limited variability in terrain elevation. Incorporating (D) to the input data, for this area, does not bring any useful information for temperature estimation, makes learning only more challenging, and contributes to diminishing the model's ability to discern relevant patterns.

The transition to the extended zone allows to leverage the positive effect of D more effectively. In this scenario, the dataset featured a broader spectrum of elevation variations, enabling the model to better utilize the D information and understand its significance in the context of LST estimation.

The inclusion of land cover data proves to be beneficial to the model, regardless of whether it is combined with RGBD or RGB. This further underscores the importance of land cover information in the model. Consequently, when estimating surface temperature, integrating such land cover data can significantly enhance the accuracy of LST estimations. Notably, this integration allows for the differentiation between synthetic sports fields and other natural terrains, as well as distinguishing various types of vegetation and other land cover types.

Collectively, these observations underscore that the system relies on the synergy of all types of data (RGB, elevation and land cover data) to achieve accurate LST estimations.

Amongst related works employing pix2pix in various image-to-image translation tasks [START_REF] Mustafa | Generating synthetic x-rays using generative adversarial networks[END_REF] [21] [START_REF] Zhou | Automatic responsive-generation of 3d urban morphology coupled with local climate zones using generative adversarial network[END_REF] and using RMSE as an evaluation metric, our study demonstrates a comparable level of performance, as evidenced by the achieved low RMSE, despite the complexity of the task.

While the study produces promising results, it is crucial to acknowledge certain limitations that may influence outcomes. The impact of data quality and resolution on results cannot be overlooked, and adaptations may be necessary when applying the model to diverse datasets. It is noteworthy that the training set consistently demonstrates superior performance compared to the test set, although occasional artifacts were observed between adjacent generated tiles. In future iterations of this work, addressing these challenges will involve implementing data augmentation methods, such as overlapping tiles, to mitigate artifacts and enhance the model's performance across both training and test sets. Despite the correlation between RGB and other modalities with LST, it's crucial to note that these inputs don't provide the exact LST value. This underscores the need for a thorough understanding of the model's capabilities and limitations, aligning with our roadmap for LST estimation. Despite these challenges, the study presents significant potential for innovative applications in LST remote sensing and temperature monitoring. Emphasizing the importance of context-awareness and the utilization of high-quality data is paramount for achieving optimal results in such endeavors.

Conclusion

This study investigates the utilization of conditional Generative Adversarial Networks (cGANs) to transform RGB data into LST imagery. The results firmly establish the feasibility of this data conversion task, showcasing significant improvements when integrating elevation and land cover data, thereby aligning the generated imagery more closely with ground-truth values. The uniqueness of this work lies in its reliance on RGB (and the other modalities) to generate LST images, a novel approach not explored in previous research based on our findings. Additionally, our work highlights the capability of the pix2pix network to manipulate and produce this type of imagery, a facet that has not been thoroughly tested before. Demonstrating its proficiency in this task, despite its complexity and dependency on various factors, showcases the adaptability of the pix2pix model. This contributes to the originality of our research, offering a valuable perspective on the broader applicability and versatility of pix2pix network. The implications of this research extend far beyond the confines of the study itself. They hold the potential to revolutionize various aspects of LST remote sensing applications, offering precise LST estimations and creating opportunities for applications spanning UHI analysis, climate change monitoring, and thermal anomaly detection.

Fig. 1 :

 1 Fig. 1: Overall pipeline. LST: Land surface temperature; R: Red; G: Green; B: Blue; D: Digital Elevation Model; C: Corine Land Cover; L: Land Cover Data. *Vector data

Fig. 2 :

 2 Fig. 2: False-Color LST Visualization of the Lyon Metropolitan Area in July 2015

Fig. 5 :Fig. 6 :

 56 Fig. 5: Translation results in the urban zone

Acknowledgments

This work was supported by the IATOAURA project of the Auvergne Rhône-Alpes Region, laureate of the Défis pour l'IA call. It was also supported by the LabEx IMU (ANR-10-LABX-0088) of Université de Lyon, within the Plan France 2030 operated by the French National Research Agency (ANR)


Johannes Mersch
email: johannes.mersch@tu-dresden.de

Danny Friese

Hung Le

-Ing J Mersch

H Le Xuan

Automating the 3D robotic filament winding process for high-performance composite materials

Keywords: robotic filament winding, path planning, automated robot programming, high-performance composite materials, coreless robotic winding

Robotic filament winding of high-performance materials in 3D geometries presents a promising avenue for advancing lightweight and civil engineering. However, the unique challenges posed by filament winding necessitate the development of novel path planning algorithms. Traditional slicing techniques, commonly used in regular 3D printing, are inadequate due to the complexities of filament winding processes and the utilization of materials with exceptional mechanical properties. In this article, we propose an innovative approach to automate 3D coreless robotic filament winding. The key focus of our work lies in overcoming the limitations of conventional algorithms and addressing the specific boundary conditions associated with diverse applications. Our method builds upon Hierholzer's algorithm that is then expanded to accommodate the intricate constraints of filament winding. We achieve a comprehensive path planning framework capable of navigating complex 3D geometries while optimizing the utilization of high-performance materials. This approach allows efficient and precise filament winding, preserving the ultra-strong mechanical properties of the materials. Furthermore, we demonstrate the conversion of the generated path into a robot program. The outcomes of our research offer promising prospects for various industrial sectors, including aerospace, automotive, and construction industry. This facilitates the utilization of cutting-edge materials in engineering applications in the future.

Introduction

Several mega-trends are addressed by the emerging technology of robotic filament winding. On the one hand, it is the need to decrease carbon dioxide emissions. The construction industry currently produces about 37 % of these emissions. [START_REF] Crippa | Fossil CO2 and GHG emissions of all world countries: 2019[END_REF] Carbon fiber-reinforced concrete, which avoids the corrosion-vulnerability of steel, can drastically decrease the amount of required concrete. [START_REF] Ilki | Building for the Future: Durable, Sustainable, Resilient[END_REF]3] On the other hand, with the increasing lack of skilled workers and demographic change, automation, and enhanced productivity become vital, particularly for established economies. [START_REF] Von Zuben | 19th World Textile Conference on Textiles at the Crossroads[END_REF] Robot-guided winding of high-performance fibers allows to create a highly automated process and simultaneously takes advantage of their extremely anisotropic but excellent mechanical properties. With usual layer-by-layer additive manufacturing processes, for which a plethora of slicing algorithms have been established and commercialized in the last few years, this is not possible. In the last ten years, the use and research of coreless robotic winding (CRW) technologies has been growing both for classic composite applications as well as civil engineering. [START_REF] Minsch | [END_REF][START_REF] Bodea | 3D printing and additive manufacturing[END_REF] The winding of reinforcement fibers around core structures is a widely established technology to produce highperformance composites. [START_REF] Koustas | [END_REF]8] Using a core is beneficial for some applications, especially for tanks. Because the fibers' superior mechanical properties are only present if they are loaded with tensile stress in fiber direction, the core-wound composites are ideal for pressure vessels or torsionally loaded components such as drive shafts. [9] However, this technology restricts the possibilities of the shape and the fiber orientations on said shape. [10,11] A different option to leverage the properties of reinforcement fibers is to disperse short fibers in either concrete or thermoplastic materials, which can then be extruded in layers in an additive process. [12] The options to include reinforcement yarns in layer-by-layer additive manufacturing processes are described by Safari et al.. [13] Disadvantages of short fibers and a layer-by-layer process are the lack of adhesion and especially the lack of reinforcement fibers between layers. [14] In addition, the short fiber-reinforced materials have much lower moduli and strength than long fiber-reinforced materials. [15] Therefore in recent years, coreless robotic winding has been proposed both with polymeric and mineral matrix systems. [16,[START_REF] Oval | Proceedings of IASS Annual Symposia[END_REF] With the CRW-technology the reinforcement fibers are wound around small winding elements on tubes positioned arbitrarily in space. The winding elements are pin-shaped or have pins [16] , (c) coreless with crossings and intersections attached to them that hold the fibers in place. The difference to the classic winding approach is illustrated in Figure 1c. Further developments of this approach with complex fiber orientations or fabrics instead of single fibers have been proposed but are still limited to circumferential reinforcements. [START_REF] Gantner | Third RILEM International Conference on Concrete and Digital Fabrication[END_REF][START_REF] Ou | 3D printing and additive manufacturing[END_REF] As demonstrated by Daimler, CRW allows to produce mechanically highly-optimised truss-based composite structures. [START_REF] Minsch | [END_REF]21] The growing availability of computational power and efficient algorithms makes the topology optimization for complex load cases feasible within appropriate time frames. [22] The design and topology of such composite truss structures may be derived from a wide variety of approaches. [START_REF] Beckmann | Building for the Future: Durable, Sustainable, Resilient[END_REF] They can range from biologically inspired fiber distributions [24,25] , force-flow approaches [START_REF] Gantner | Third RILEM International Conference on Concrete and Digital Fabrication[END_REF] to established methods like the solid isotropic material with the penalization (SIMP) interpolation model. [START_REF] Hu | Integrated Computer Technologies in Mechanical Engineering[END_REF] Although this is one research area of enormous importance for the further development of composite technology, it is not the focus of this work. How the geometry and truss dimensions are derived from the boundary conditions is not discussed within this work but is taken as a given input to the algorithm. Another essential point that is currently missing on the path to fully automated high-performance composite manufacturing are algorithms for converting the topology optimized truss structure to robotic paths. [START_REF] Oval | ISARC 2020: The 37th International Symposium on Automation and Robotics in Construction[END_REF] This poses a challenge, particularly for structures that consist of intersecting and branching fibers in three-dimensional (3D), i.e. out-of-plane reinforcements. [START_REF] Minsch | [END_REF] In the last three years two major contributions have been made to the automated path planning for CRW. One is the work of Bodea et al. who focused on hyperboloid structures (see Figure 1b), particularly for the construction of pre-assembled building blocks. They used the Grasshopper plug-in for Rhino to create the motion commands for their kinematic system. This leads to large-scale coreless composite structures. Nevertheless, the path planning itself is relatively simple because the component is rotated during the manufacturing process. Therefore, the end-effector is only moving above the surface of the component on quasi-linear curves, which eliminates the risk of collision with the already positioned yarns. At the same time, this approach is limited to hyperboloid shapes. Oval et al. pursued a more general approach for shell structures, in which the winding elements are positioned on curved shells and connected by different amounts of reinforcement fibers. [START_REF] Oval | Proceedings of IASS Annual Symposia[END_REF] Each winding element can be connected to one or multiple other winding elements. When abstracting the winding elements to nodes and the fibers in between connections, the structure can be represented as a graph. The problem of inserting a certain number of yarns between the nodes represents a version of the chinese postman problem (CSP). [START_REF] Dreifus | 3D printing and additive manufacturing[END_REF] One algorithm to solve the CSP is Hierholzer's algorithm and finding Eulerian paths connecting the nodes until all connections have been traveled. [START_REF] Crippa | Fossil CO2 and GHG emissions of all world countries: 2019[END_REF] After finding a suitable path, Oval et al. derived the robot program by moving around each winding element in circles and between circles by straight lines. This approach is sufficient for winding elements distributed on curved surfaces but it cannot deal with connections that are at a larger angle to the x-y-plane or fibers that cross in z-direction as illustrated in Figure 1c. To extend the capabilities of CRW to 3D structures, we propose a new path planning algorithm, which can deal with winding elements, i.e. winding elements, on multiple levels and intersections. The approach is divided into two steps. First, the abstract graph level is considered to leverage the capabilities of established algorithms like the Hierholzer algorithm. Nevertheless, the restrictions of the 3D-CRW technology, where already deposited yarns are obstacles, and other manufacturing-related particularities are considered in our approach. Based on this graph representation, the actual path of the robot's end-effector is derived. Finally, the path for an exemplary structure will be automatically planned and implemented on a small-scale 6-axis robot.

Route planning based on graph representation

The input to the algorithm is the positions of the winding elements, which are then considered as nodes in the representation as a graph. These are stored as a list with each node having a number and their position in x, y, and z. Each node is connected to at least one other node by a connection. The connections are usually represented by an adjacency matrix Adj orig where connections or missing connections are ones or zeros, respectively. Here we additionally modify the adjacency matrix, so it contains the numbers of yarns that need to be deposited between two nodes, which is stored as Adj ext . The number of yarns is derived from the desired cross-section area according to the topology optimization and the reinforcement yarn to be used. The Adj orig is still saved to navigate through the graph if the yarns of some connections have already been deposited sufficiently, similar to the rural postman problem. [START_REF] Eiselt | [END_REF] The output of this part of the path planning routine is the ordered sequence of nodes to be connected.

Restrictions due to collisions

In contrast to the geometry considered by Oval et al., where every winding element can be connected to any other winding element at all times, with multi-level structures and intersections in z-direction, already deposited yarns may block other connections between nodes. [START_REF] Oval | Proceedings of IASS Annual Symposia[END_REF] This is also a major difference from classic slicing algorithms for other additive manufacturing methods. Consequently, there are three kinds of collisions with the yarn guide, which have to be avoided. First, the yarn guide should not crash into winding elements. Second, the yarn guide should not collide with already deposited yarns while traveling around a winding element. Both of these are dealt with in the spatial path planning. However, the third type of possible collision cannot be avoided in the spatial path planning but has to be addressed during the first step, because if the nodes are not in a feasible order, the winding becomes practically impossible. This is illustrated in Figure 2. After winding the connections from nodes 1 -2 -3 -8 -7, the connection between 2 and 4 (dotted green line) is covered. Therefore, guiding the yarn around node 4 would result in a collision with the already deposited yarn between nodes 7 and 8. Such restrictions have to be considered when deriving the node sequence based on the Hierholzer algorithm.

Hierholzer-based Algorithm

The basic algorithm of Hierholzer is shown in 3 and illustrated in Figure 3. The starting node is selected by user input because in practice a dummy node is introduced where the reinforcement yarn is fixed.

Algorithm 1 Basic Hierholzer Algorithm.

while node with open connections exists do find node with open connections find subcircle K Sub insert K Sub in overall circle K end while return K

As described in the previous subsection, the basic Hierholzer algorithm needs to be expanded to cope with the mentioned restrictions. Therefore, before initializing the algorithm, a check is conducted, which connections cover which connections. The connections covering other connections are then set to zero in the adjacency matrix Adj current until the desired yarn count is reached for the covered connection. In addition, before the subcircle K Sub is inserted, a check is performed, whether K Sub is covered by any connections before the insertion position or covers any connections after the insertion position. If no feasible insertion position is found, K Sub is added to the end of the sequence. The path from the last node of the existing K and the first node of K Sub is calculated using Dijkstra's algorithm based on the Euclidean distances between nodes. [START_REF] Wang | second international conference on mechanic automation and control engineering[END_REF] 2.3 Process-related improvements of the path planning procedure

In addition, other process-or application-related particularities can be considered and implemented in the algorithm. These mainly concern the specific requirements of fiber-reinforced plastics versus fiber-P r e p r i n t Not peer-reviewed 2.3 Process-related improvements of the path planning procedure reinforced concrete. For example, in many plastic composite applications the matrix material is applied during the winding process or pre-impregnated yarns are used. The structure is then used -as is -after curing. The winding elements can or often should remain in the structure. They either serve as stabilization or are used to join the composite with other parts. It is also possible to use other functional parts such as bearings or sensors as winding elements. Because these winding elements should remain as part of the structure, the adhesion between reinforcement yarn and winding elements is important. Therefore, fully or partially wrapping the yarn around their circumference may be beneficial. In addition, crosses of yarns without a winding element (e.g. the connections 1-5 and 2-4 in Figure 3) should be wound alternately to improve the adhesion and thereby increase shear stability. For concrete composites, however, the winding elements should be removed, so the concrete can fill their space, to fix the reinforcement structure and to avoid porous areas which are potential crack initiation points. In such applications, long sections of yarns without deviations of large angles are preferred to maximise the load-bearing capacity of the reinforcement yarns. Moreover, we found that disfavoring connections that go from lower to higher positioned nodes helps to avoid the blocking of yarns, and thus, makes the algorithm faster for the configurations we tested. Without this feature, dead ends occur regularly. Because other than in a normal Eulerian path:

• Connections can require multiple visits by the postman (i.e. yarn depositions),

• number of visits can vary drastically between connections based on the topology optimization and

• nodes can have an uneven number of connections.

Therefore, nodes without feasible connections can be encountered during the construction of K Sub . In that case, the current K Sub is stored and a new subcircle is initiated at another node. If no successful subcircle can be constructed starting from one of the nodes with remaining connections, a sub-routine is initiated. This is a classic genetic algorithm with the order of nodes to be connected as the genome. The result is a close-to-optimal path between nodes of the missing yarns that don't cover other connections, which are connected via feasible connections according to Adj current . That is necessary because not all or realistically very few application-relevant structures can be wound as perfect Eulerian circles or paths. Thereby, the amount of excess deposited material and consequently weight is minimized. Apart from the savings in the amount of material, any winding of excess yarns increases the overall process length. Therefore, procedures that keep the yarn number and distribution as close as possible to the result of the topology optimization are advantageous. All of these practically relevant criteria are evaluated to determine which node to move to based on the current and last node. The importance of each criterion is set by the user based on the requirements of his or her application. An overview of the algorithm is given in Algorithms 2 and 3. During the path planning the yarn guide is always routed around the winding elements on this perimeter to guarantee zero collisions between the yarn guide and the winding elements. Therefore, the path between winding elements is always checked for intersections with the perimeters of the elements to be connected as well as every other winding element. However, not only the path around the winding elements is essential but also the direction, in which the yarn guide moves around them. This is illustrated in Figure 5. If the next element (no. 3) is on the left of the two previous ones, the path around the current winding element (no. 2) needs to be conducted counterclockwise. Equivalently, if it is positioned on the right, the path needs to be conducted clockwise. Otherwise, either the winding element will not be incorporated in the structure or an unnecessary length of yarn will be deposited on the winding element. In case, the current element (no. 4) is on a straight line between the previous and next elements, the direction has to be identical to the one on the previous pin. These rules are implemented in Matlab to form the basis of our spatial path planning algorithm. This abstraction and planning step is purely done in 2D, i.e. the x-y-plane.

Deposition of yarn on the winding elements

However, to successfully deposit yarns on the winding elements not only the path around and in between the winding elements is important but also the lay-in mechanism where the yarn is positioned between the pins. Therefore, a part of the path around the winding elements is identified as the lay-in section. During the lay-in section, the yarn guide needs to be at the correct height at the right position on the x-y-plane in order to successfully deposit the yarn. This is illustrated by the top-view schematic in Figure 6. To determine the section of the perimeter that is critical for the lay-in process the base of the last pin is used. From this point, lines are drawn with the secondary points being located at the end of the next pin but shifted out and in (labeled l lay-in ) according to the yarn diameter plus a safety margin. We used double the yarn diameter, which worked well in the tested cases. Now the intersections of these lines with the perimeter define the lay-in section. Once the second of these points is reached (labeled "Point of deposition"), the yarn has been deposited successfully between the pins. During the lay-in section, the height of the yarn guide is critical as the side-view schematic in Figure 7 shows.

P r e p r i n t

Not peer-reviewed In particular, if the nodes are not at the same height. Due to the safety distance between the yarn guide and winding elements, the yarn to be deposited is not at the same height as the pins. This difference ∆z leads to missed lay-in processes. Therefore, the z-coordinate of the path during the lay-in section will be chosen based on a tilted plane constructed from three points: the base points of the last and current pin on the winding elements and the tip of the pins of the current winding element. When the tip of the yarn guide travels on that plane, the yarn will be at the correct height during the lay-in procedure.

Transition around and in between the winding element

To determine the z-coordinate of the path around and in between winding elements that are not part of the lay-in section the same plane is used but superimposed by the positions of already deposited yarns that need to be avoided. This height map is generated by Matlab's "scatteredInterpolant" function and outputs the z-coordinates to the x-and y-values calculated in the previous steps.

4 Path planning and winding of a demonstrator structure Initially, both the graph-based algorithm and the spatial path planning were tested on two-dimensional structures with increasing complexity. Starting from the simplest possible structure of two connected nodes, going over to four connected nodes with a cross and six unevenly spaced nodes. The basic configurations are displayed in Figure 8 along with the winding path visualized in Matlab. These are similar to the structures shown by Oval et al.. [START_REF] Oval | ISARC 2020: The 37th International Symposium on Automation and Robotics in Construction[END_REF] These are evaluated for different distances between nodes and layers of reinforcement yarn. Due to the limited reach of the available KUKA KR6 robot, the calculated winding is validated by winding polyester yarns around 3D-printed winding element. After successfully winding these three structures a three-dimensional case was chosen to demonstrate P r e p r i n t Not peer-reviewed that the approach also works for more complex winding geometries than those demonstrated in literature before. The structure is based on a topology optimized truss with four fixed points and four points where loads in different directions are applied, so the structure in total is torsionally distorted. With regard to this loading scenario the topology optimization leads to a truss structure with crossing reinforcement yarns between the winding elements as illustrated in Figure 9. From these, the winding path is derived as shown and finally, the winding process is demonstrated on lab-scale. Videos of the winding process are available as supplementary material.

Conclusion

In summary, we have designed and validated a two-step algorithm to automatically plan the trajectories for coreless robotic winding. The approach allows for arbitrary numbers of yarns to be used and nodes on different heights even if they are positioned one above the other. After implementing the algorithms in Matlab, they were validated on four different structures. However, this needs to be extended to more geometries in the future. Other avenues of research to pursue are:

• In our set-up the angle of the end-effector is kept constant. At times this leads to small bending radii of the fiber around the edge of the yarn guide, which is particularly disadvantageous for brittle yarns such as carbon fibers. An improvement might be achieved by inclining the yarn guide at an angle closer to the fiber trajectory.

• Not all truss structures can be manufactured with this type of coreless robotic winding. There may be combinations of three or more trusses, which cover each other, making them impossible to deposit. Possible improvements in that regard are either to develop new approaches to topology optimization or introduce more degrees of freedom in the process. The second option includes the use of more than one manipulator or additional actuators on the end-effector to guide yarns around already deposited ones. But because this drives cost and complexity, the development of novel topology optimization strategies is also promising. If the process constraints could already be coped with during the optimization step, resulting in a truss structure that is definitely processable, the presented approach could quickly and automatically yield tailored high-performance composites.

• Further improvements can be made with regard to the winding elements, the end-effector, and the impregnation process of the reinforcement yarns. Both are critical for a strong composite structure and reliable winding process but have only received marginal research efforts from the scientific community.

• Finally, the presented algorithm is designed to avoid collisions between the yarn guide, winding elements, and reinforcement yarns. Still, it is currently not possible to test the output digitally. Therefore, a simulation environment could be beneficial to test and adjust the path before employing it on the actual system.

P r e p r i n t

Not peer-reviewed P r e p r i n t

Not peer-reviewed

Figure 1 :

 1 Figure1: Different types of robotic winding (a) on core (b) coreless hyperboloid according to[16] , (c) coreless with crossings and intersections

Figure 2 :

 2 Figure 2: Illustration of a potential collision between the yarn guide and deposited yarns.

3 P

 3 r e p r i n t Not peer-reviewed 2.2 Hierholzer-based Algorithm

1 Figure 3 :

 13 Figure 3: Illustration of the Hierholzer algorithm.

P

  r e p r i n t Not peer-reviewed P r e p r i n t Not peer-reviewed 3.1 Deposition of yarn on the winding elements

Figure 5 :

 5 Figure 5: Path of the yarn guide between winding elements and the correct and incorrect traveling directions.

Figure 6 :

 6 Figure 6: Schematic of the path of lay-in process as a top-view.

3. 2 Figure 7 :

 27 Figure 7: Schematic of the path of lay-in process as a side-view.

Figure 8 :

 8 Figure 8: Schematics and winding path for the two-dimensional demonstrator structures.

Figure 9 :

 9 Figure 9: Design, path planning, and real-world winding of the three-dimensional demonstrator structure.

P r e p r i n t

Acknowledgements

The authors are grateful for the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -SFB/TRR280, Project-ID 417002380.

The resulting sequence of nodes K then serves as the input for the spatial path planning described in the following section.

Path planning in three-dimensional space

To successfully convert the node sequence to a sequence of motions for the robot end-effector several steps have to be taken. In our approach we first plan the motions on the x-y-plane with the limitation that the tubes and their winding elements are oriented in or only at small angles (< 5 • ) to the z-axis. Usually, the winding elements' projections onto the x-y-plane are round but arbitrary shapes can be coped with by discretization of their convex hull. For clarity, only circular elements are considered in the following description. The first thing to consider is the distance between yarn guide and winding elements to ensure collisionfree motions. Therefore, the yarn guide is programmed to move around the winding elements on a circle. The radius of this circle is the sum of the winding element's radius r W E , its pin length l P in , the yarn guide's radius r Y G , and a safety distance d S , as illustrated in Fig 4.

P r e p r i n t Not peer-reviewed

In conclusion, the described algorithm presents a major step forward to automatic path planning of the winding process for topology optimized truss structures. However, many challenges remain. Therefore, the coreless robotic winding technology is a field with continuing relevance and many research opportunities to be approached.

6 Experimental Section

Coreless filament winding setup

To test the developed 3D winding procedure a KUKA KR 6 robot was used (KUKA AG, Augsburg, Germany) with an aluminum tube as the end-effector. The tool center point was taught using KUKA's teaching procedure. A thin polyester thread was used for the minituarized set-up and wound around 3D-printed (Fused Filament Deposition) winding elements with 2 mm thick aluminum pins. The yarn was tensioned by a yarn guide with a 100 g weight, which were positioned over the robot together with the let-off spool. Corresponding geometry files are available from the authors upon request.

Conversion to a robot program for a 6-axis system

After the three-dimensional coordinates have been calculated for the node sequence of K, an additional Matlab script converted the coordinates to the KUKA Robot Language (KRL). Based on templates according to the individual robot, which in our case is a KUKA KR6 with a reach of 910 mm, the sequence and points are written to the .dat-and .src-files. If the winding of one structure exceeds the limited number of points within one program, they are divided into subprograms, which are called from a main program. The motions of the robot can be programmed to be either linear (SLIN, slow but accurate) or point-to-point (SPTP, faster but less accurate). For our cases, the SPTP-option was sufficiently accurate and used in the winding of the exemplary structure described in section 4. We wrote the algorithms in Matlab due to its ease-of-use for debugging and integrated functions to quickly develop such algorithms. However, this is hardly suitable for real-world production environments and should be addressed in the future.

Supporting Information

As the supplementary materials two videos of the winding process can be found using the following DOI: 10.5281/zenodo.8279498 . The first video displays a part of the winding process of the three-dimensional configuration. The second part shows a section of the winding of the six-node configuration, where a yarn is wound around one of the winding elements. This article presents a novel two-step approach for automating the 3D coreless winding of high performance composites for lightweight or civil engineering applications. Inspiration for such highly load-adapted structures can be drawn from nature or topology optimization. With the presented approach unnecessary surplus material is minimized and the ultra high strength of carbon or basalt fibers is maximally exploited.

P r e p r i n t