- Research Article
- Open Access

# Consistent map building in petrochemical complexes for firefighter robots using SLAM based on GPS and LIDAR

- Abu Ubaidah Shamsudin
^{1}Email authorView ORCID ID profile, - Kazunori Ohno
^{2}, - Ryunosuke Hamada
^{2}, - Shotaro Kojima
^{1}, - Thomas Westfechtel
^{1}, - Takahiro Suzuki
^{2}, - Yoshito Okada
^{1}, - Satoshi Tadokoro
^{1}, - Jun Fujita
^{3}and - Hisanori Amano
^{4}

**Received: **7 March 2017

**Accepted: **26 March 2018

**Published: **3 April 2018

The Correction to this article has been published in ROBOMECH Journal 2018 5:9

## Abstract

The objective of this study was to achieve simultaneous localization and mapping (SLAM) of firefighter robots for petrochemical complexes. Consistency of the SLAM map is important because human operators compare the map with aerial images and identify target positions on the map. The global positioning system (GPS) enables increased consistency. Therefore, this paper describes two Rao-Blackwellized particle filters (RBPFs) based on GPS and light detection and ranging (LIDAR) as SLAM solutions. Fast-SLAM 1.0 and Fast-SLAM 2.0 were used in grid maps for RBPFs in this study. We herein propose the use of Fast-SLAM to combine GPS and LIDAR. The difference between the original Fast-SLAM and the proposed method is the use of the log-likelihood function of GPS; the proposed combination method is implemented using a probabilistic mathematics formulation. The proposed methods were evaluated using sensor data measured in a real petrochemical complex in Japan ranging in size from 550–380 m. RTK-GPS data was used for the GPS measurement and had an availability of 56%. Our results showed that Fast-SLAM 2.0 based on GPS and LIDAR in a dense grid map produced the best results. There was significant improvement in alignment to aerial data, and the mean square root error was 0.65 m. To evaluate the mapping consistency, accurate 3D point cloud data measured by Faro Focus 3D (± 3 mm) was used as the ground truth. Building sizes were compared; the minimum mean errors were 0.17 and 0.08 m for the oil refinery and management building area and the area of a sparse building layout with large oil tanks, respectively. Consequently, a consistent map, which was also consistent with an aerial map (from Google Maps), was built by Fast-SLAM 1.0 and 2.0 based on GPS and LIDAR. Our method reproduced map consistency results for ten runs with a variance of ± 0.3 m. Our method reproduced map consistency results with a global accuracy of 0.52 m in a low RTK-Fix-GPS environment, which was a factory with a building layout similar to petrochemical complexes with 20.9% of RTK-Fix-GPS data availability.

## Keywords

## Introduction

The motivation of this study was to enable the autonomy of firefighter robots at petrochemical complexes. Petrochemical complexes in fire disasters pose a high environmental risk because large fires and explosions can cause injuries, fatalities, and devastation. The use of firefighter robots can reduce the risk to firefighters. Such a system is comprised of several vehicles, such as a water-shooting robot, a hose-extending robot, and an exploration robot. An autonomous capability facilitates their control and enables many robots to be controlled by only a few operators.

One key technology for autonomous firefighter robots is simultaneous localization and mapping (SLAM), which is required because petrochemical complexes are restricted areas and there are limited opportunities to update their maps. In addition, the maps are dynamically changed in real time with developments such as fires, explosions, moving firefighters and mobile trucks. Therefore, Fast-SLAM is used in such an environment.

In this work, two dimensional Fast-SLAM is used for a firefighter robot in petrochemical complexes. The road of a petrochemical complex has no difference in the ground level because the road is built to accommodate the large firefighter trucks and large water shooting nozzles. In this environment, we can develop a two-dimensional Fast-SLAM without considering ground level differences. Long-range light detection and ranging (LIDAR) sensors are used with Fast-SLAM to develop a map of petrochemical complexes.

Petrochemical complexes have a sparse layout of very large oil tanks, where distances between oil tanks are 40–80 m. LIDAR is suitable because it can measure distances of 0–100 m with high accuracy (e.g., Velodyne HDL-32E ± 0.02 m). Consequently, a map with a sparse oil tank layout can be built by SLAM.

Our procedure using Fast-SLAM for the autonomy of a firefighter robot is explained here. The purpose of Fast-SLAM is to build a map for facilitating autonomy. First, Fast-SLAM is used to construct a map in a normal environment by human firefighters manually controlling the robot. Next, using the Fast-SLAM constructed map, human firefighters set a target point for the robot and the robot autonomously moves to the target by localizing its position using the map. Therefore, the autonomy of firefighter robots can be realized by using the Fast-SLAM map.

The main purpose of this research is map consistency because a map can be used not only by firefighter robots, but also by human firefighters who operate these robots. The use of GPS helps increase the consistency. In this study, we used GPS and LIDAR data to build the map. GPS and LIDAR provided the heterogeneous data; their combination therefore required consideration for the map consistency.

This paper describes a method that employs two Rao-Blackwellized particle filters (RBPFs). The method is based on GPS and LIDAR for map consistency in petrochemical complexes. Fast-SLAM 1.0 (FS 1.0) and Fast-SLAM 2.0 (FS 2.0) by Grisetti et al. both in a grid map, were used for the RBPFs [1]. Their weight functions were revised for the RBPFs based on the GPS and LIDAR sensor for map consistency in petrochemical complexes. GPS and LIDAR data have heterogeneous characteristics. These sensor data are complementary and can be used to improve the accuracy and consistency of the resulting map. Therefore, we propose the use of Fast-SLAM to combine GPS and LIDAR. The difference between the original Fast-SLAM and the proposed method is the use of the log-likelihood function of GPS; the proposed combination method is implemented using probabilistic mathematics formulation.

The remainder of this paper is organized as follows. In “Related works” section, review on related works are described. In “Simultaneous localization and mapping to maintain consistency in large areas” section, the proposed method is formulated. In “Evaluation” section, we describe the experiments conducted for evaluating the map consistency estimated by our method. In “Discussion” section, the experimental results are presented. In “Conclusion” section, our conclusions are provided.

## Related works

There are two types of SLAM. The first includes filter SLAM, such as RBPFs [3], extended Kalman filter (EKF) [4], sparse information filter [5], and topological/hierarchical filter [6, 7]. The other type includes batched SLAM, such as respective graph-based [8], square-root-based [9], sparse-pose-adjustment (SPA) [10], and incremental-smoothing-and-mapping (iSAM) methods [11]. This research used filter SLAM, which is an RBPFs because of limited processing power. The filter SLAM showed better results in the case of limited processing power [12].

RBPFs were first introduced by Doucet et al. [13]. Montemerlo et al. extended RBPFs into Fast-SLAM 1.0 by using EKF for landmark feature representation [14]. Later, Montemerlo et al. extended it into a faster RBPFs, specifically, Fast-SLAM 2.0 (FS 2.0) [14]. Their research determined that the use of scan-matching results for proposal distribution could increase Fast-SLAM 1.0 speed and accuracy. Furthermore, Grisetti et al. formulated Fast-SLAM 2.0 in a dense grid map environment [1]. Therefore, FS 1.0 and FS 2.0 were selected for the RBPFs SLAM. To increase the SLAM consistency, sensors with high consistency, such as GPS, could be used.

Several researchers used GPS to increase map consistency. For example, Gamma-SLAM uses GPS to improve the camera-based RBPF results [15]. In the first step, the map and trajectory are estimated by RBPFs. The map and trajectory are then aligned using GPS data to minimize the error between the GPS and RBPF trajectories. Singular value decomposition (SVD) and a batch algorithm are used. In addition, Schleicher proposed hierarchical SLAM [16]. For low-level sub-maps, a wide-angle-camera-based EKF SLAM was fused with GPS for consistency. Each sub-map was then combined by using batch-algorithm multi-level relaxation (MLR) based on GPS to increase the global consistency of the combined map. Our work fuses GPS data with LIDAR inside RBPFs by the proposed weight function for RBPFs, which fuses LIDAR and GPS. This method does not require an additional batch SLAM. GPS and LIDAR are heterogeneous sensors; therefore, the correct sensor fusion is required to achieve a complementary result.

The method for fusion of GPS with LIDAR was proposed by several researchers. Wei et al. used a normalized innovation squared (NIS) method to evaluate each camera/laser/GPS sensor validity before fusing the sensors with an unscented information filter for localization [17]. Soloviev used a Kalman filter with GPS, inertial measurements, and LIDAR [18]. Hentsche et al. used a Kalman filter to integrate GPS and the inertia measurement. For position estimation, the Kalman filter result was added to Monte Carlo localization by replacing 10% of the overall particles with the lowest weight [19]. Our present research aims to achieve sensor fusion of GPS and LIDAR with a complementary effect. To this end, the proposed method employs RBPFs with an importance weight function for the fusion.

Fusion of GPS with an RBPF importance function was previously proposed. Fusion of GPS and IMU by the Kalman filter for RBPF particle reweighting was used in [20, 21]. These RBPFs are similar to FS 1.0 in that sensors are fused by EKF. Ren et al. used the Kalman filter to separately estimate GPS and IMU [20]. Depending on the sensor availability, only the sensor will be updated to the particle filter. Fusion of sensors is successful because the particle filter follows a Bayesian rule. Both approaches employ fusion data using a method similar to FS 1.0 for a landmark-based environment. Our approach focuses on fusion of GPS and LIDAR for FS 1.0 and FS 2.0 for grid-map environments.

## Simultaneous localization and mapping to maintain consistency in large areas

We herein propose RBPFs based on GPS and LIDAR to maintain map consistency. GPS and LIDAR sensor data are complementary. SLAM based on LIDAR uses scan matching to localize the robot positions. A characteristic of LIDAR scan matching is local accuracy in management and oil refinery building areas in which several buildings are located near a road. However, scan matching increases errors in areas with large oil tanks, where tanks and building layouts are sparse (more than 80 m between structures). On the other hand, a characteristic of GPS data is that they are globally absolute and accurate in areas including large-oil-tank areas, especially where there is high satellite availability. The errors in GPS measurements increase in management buildings and oil refinery areas because of satellite signal diffraction. For effective fusion, complementary sensors, which are GPS and LIDAR, are used for map consistency. We propose two extension methods of RBPF based on GPS and LIDAR using a dense grid map. FS 1.0 and FS 2.0, both renowned methods for RBPFs, were used, as formulated by Grisetti et al. [1]. To achieve a complementary effect on sensor fusion of RBPF based on GPS and LIDAR, probabilistic mathematics was used to combine GPS and LIDAR data in RBPFs importance weight \(w_{t}^{(i)}.\) For implementation, the RBPFs importance weight was formulated using the log-likelihood.

### RBPFs based on GPS and LIDAR

Douce et al. showed that RBPFs are an effective solution for SLAM by factorizing the states of maps and paths [13]. RBPFs use importance resampling to prevent correct particles from being resampled away. To obtain sensor fusion, a probabilistic mathematical formulation is used; in particular, the formulation of importance weight \(w^{(i)}_{t},\) mentioned above, is proposed to handle the GPS and LIDAR data. Figure 2 shows the graphical model of our proposed RBPFs, which contains two observations \(z_{\mathrm {GPS}~t}\) and \(z_{\mathrm {LIDAR}~t}\) as parts of observation \(z_{t}.\)

### Formulation of RBPFs

*m*from the sensor data, including motion \(u_{1:t}\) and observation \(z_{1:t}.\) Equation (1) shows the factorization of RBPFs [22]:

*i*). The importance weight can be calculated by using a recursive formula [24]. This involves recursive multiplication of the previous weight, \(w^{(i)}_{t-1},\) with the current observation, \(p(z_{t})\). It thus becomes:

### Formulation of RBPFs based on GPS and LIDAR

*z*is

*j*is the potential pose of the robot and

*K*is the number of potential robot poses. Therefore, the new \(w^{(i)}_{t}\) becomes

### Implementation of balance weight fusion

For implementation, the log-likelihood function is used to calculate the weights for both (a) FS 1.0 based on GPS and LIDAR and (b) FS 2.0 based on GPS and LIDAR. This is because the log-likelihood calculation is more efficient owing to its use of summation rather than multiplication.

*N*is the total number of LIDAR laser beams and

*n*is the identification number for a laser beam. The log-likelihood importance weight becomes

*N*is the total number of LIDAR laser beams and

*n*is the identification number for a laser beam. The log-likelihood importance weight thus becomes:

## Evaluation

Our method was evaluated in a closed petrochemical complex in Japan (shown in Fig. 3), which was characterized by typical attributes of Japanese petrochemical complexes. The size of the environment was 550 m in width and 380 m in length. There were two areas: (1) management and oil refinery buildings located near a road (Area 1), and (2) large oil tanks sparsely distributed for safety reasons (Area 2). An electric vehicle (EV) was used to collect sensor data because firefighter robots have a car-like mechanism and the EV has the same mechanism and size. During data collection, the EV was manually driven at a speed of 5 km/h for safety concerns. The EV was equipped with an RTK-Fix-GPS receiver with an error of 0.02 m, a long-range 3D LIDAR with an error of 0.02 m, an inertial measurement unit (IMU) with an error of 0.1 deg/s, and an odometer equipped with a rotary encoder having an error of 0.1 m/s.

The sensor data were recorded during data collection. The vehicle was stopped at each cross-junction until the GPS measurement acquired an RTK-Fix-GPS for additional RTK-Fix-GPS data. The junctions had wide satellite visibility and were thus suitable for acquiring RTK-Fix-GPS measurements. During the whole experiment, the RTK-Fix-GPS availability was 56% as shown in Fig. 4.

For validation, we compared (a) FS 2.0 based on GPS and LIDAR, which is proposed in this paper, (b) FS 2.0 based on LIDAR [1], (c) FS 1.0 in a grid map (FS 1.0) based on GPS and LIDAR, also proposed in this paper, (d) FS 1.0 based on LIDAR, (e) FS 1.0 based on GPS, and (f) Karto SLAM based on LIDAR, which is a kind of open-source graph-based SLAM in a grid map [25]. We evaluated (1) global accuracy of the maps based on aerial map data and (2) local accuracy of the maps based on FARO Focus 3D data for different SLAMs. Map consistency was also evaluated by comparing the maps with aerial images.

These SLAM methods used open source libraries provided by OpenSLAM and Robot Operating System (ROS).

For Fast-SLAM, we modified the SLAM Gmapping library. The authors of Gmapping are Giorgio Grisetti, Cyrill Stachniss, and Wolfram Burgard. It is distributed by OpenSLAM, and the ROS wrapper is provided by the ROS community. We modified the weight of importance based on Eqs. 13 and 18 for FS 1.0 and FS 2.0 based on GPS and LIDAR, respectively. In addition, for FS 1.0 based on GPS and LIDAR, we disabled scan matching for the motion model based on scan matching [26].

The parameters used for Fast-SLAM are explained here. A grid map resolution of 0.2 m and 50 particles were used because they comprise the maximum values allowed by our computer for this environment size. The adaptive resampling threshold was set to a value of 0.01 because we desired a higher resampling rate when GPS value was available. We strived to use GPS as a closed loop; that is, when we received sufficient GPS data, we desired to have a closed loop by resampling. The beam end-point model two-dimensional scan matcher was used because it produced better results than ICP in unstructured outdoor environments [23]. The computation time for our implementation was the same as that of Grisetti et al. [1] because the additional weight calculation was very short.

We have chosen 2 m as the \(\sigma _{\mathrm {gps}}\) value to compensate for the RTK-Fix-GPS multipath error when moving near the building area. Lee et. al. have evaluated the RTK-Fix-GPS horizontal multipath error, which is 1.069 m [27]. To prevent overconfidence on the RTK-Fix-GPS data, we carefully fused GPS data setting a value of 2 m for \(\sigma _{\mathrm {gps}}.\)

For Graph SLAM, we used Karto SLAM [28]. We used a default parameter because it produced the best results when compared with several parameters.

### Result

#### Global map consistency

Aerial map building position data were used as the global positioning reference. For the evaluation, a robot 2D map and the aerial map were overlapped based on their respective GPS coordinates. Figure 6 shows the visual result. Figure 7 shows the numerical result. FS 2.0 and FS 1.0 based on GPS and LIDAR showed small position errors of 0.65 and 0.81 m, respectively.

#### Local map consistency

Figures 9 and 10 show the local accuracy of the map by evaluating the local building size. Faro Focus 3D data with high accuracy was used as the building size reference, as shown in Fig. 8, while a Fig. 3 shows the locations of Area 1 and Area 2.

FS 1.0 and FS 2.0 based on GPS and LIDAR had a high local accuracy in both Areas 1 and 2. For FS 2.0 based on GPS and LIDAR, the error in Area 1 was 0.17 m (Fig. 9), and the error in Area 2 was 0.08 m (Fig. 10). For FS 1.0 based on GPS and LIDAR, the error showed a small increase compared to that of FS 2.0: in Area 1 it was 0.25 m (Fig. 9); in Area 2 it was 0.26 m (Fig. 10). For both methods, no building shape duplication is visually evident in Figs. 9 and 10.

In addition, FS 2.0 based on LIDAR showed a high accuracy in Area 1 and a low accuracy in Area 2. On the other hand, FS 1.0 based on LIDAR had a high accuracy in Area 2 and a low accuracy in Area 1. FS 2.0 based on LIDAR showed a high accuracy of 0.39 m in Area 1 (Fig. 9) and very low local accuracy in Area 2 of 3.04 m (Fig. 10). FS 1.0 based on LIDAR had a very low accuracy of 2.85 m occurring in Area 1 because of a failed close-loop (Fig. 9) and a high local accuracy of 0.61 m in Area 2 (Fig. 10). The local error is visually apparent from obviously duplicated buildings for FS 2.0 based on LIDAR in Fig. 10 and for FS 1.0 based on LIDAR in Fig. 9.

Furthermore, FS 1.0 based on GPS had a low local accuracy in Areas 1 and 2. The error in Area 1 was 0.31 m (Fig. 9) and that in Area 2 was 0.57 m (Fig. 10). Duplicates of building shapes are observed in Figs. 9 and 10. The graph SLAM based on LIDAR in a grid map (Karto SLAM) [25] had a high accuracy in Area 2, but a low accuracy in Area 1, which was caused by a failed closed loop. The low accuracy in Area 1 was 1.18 m (Fig. 9) and the high accuracy in Area 2 was 0.18 m (Fig. 10). Duplicates of building shapes are evident in (Fig. 10).

#### Visual map consistency with an aerial image

#### Reproducibility by multiple runs

We validated our method reproducibility based on the results of global position variance between ten runs in runs in the petrochemical complexes. To evaluate the reproducibility, we selected four points to cover the entire area on the map because three is the minimum number of points required to evaluate plane geometrical differences, which include rotation, location, and scale. The result shows the global position variance between all runs is ± 0.3 m.

#### Reproducibility for different environments.

In addition, we intended to confirm SLAM reproducibility in petrochemical complexes with low-RTK-Fix-GPS availability. Because GPS data availability is one of the main factors for map consistency, we selected two additional environments for this purpose. The first environment was Factory A with 20.9% RTK-Fix-GPS availability, as shown in Fig. 14a. The second environment was Factory B, which was similar to a petrochemical complex management area with 29.9% RTK-Fix-GPS availability, as shown in Fig. 15a.

Global accuracy

SLAM | Global accuracy (m) | |
---|---|---|

Factory A | Factory B | |

FS 2.0 GPS and LIDAR | 0.52 | 0.72 |

FS 1.0 GPS and LIDAR | 0.70 | 0.77 |

FS 2.0 LIDAR | 23.91 | 32.91 |

FS 1.0 LIDAR | 16.23 | 29.20 |

Karto LIDAR | 61.20 | 91.28 |

Reproducibility of global accuracy for FS 2.0 based on GPS and LIDAR in Factories A and B were 0.52 and 0.72 m, respectively. For FS 1.0 based on GPS and LIDAR, the reproducibility in Factories A and B were 0.70 and 0.77 m, respectively. On other hand, for other me thods of FS 2.0 based on LIDAR, FS 1.0 based on LIDAR, and Karto SLAM the global errors were larger than 16.23 m.

## Discussion

The proposed approach employs two SLAMs based on GPS and LIDAR and the RBPF weight of importance for sensor fusion. Our results showed that the robot-obtained map corresponded well with a geo-referenced map. This is very important for firefighters because they send target positions to robots using robot obtained maps, and they can understand the robot obtained maps by referencing real maps.

In our study, both Fast-SLAM successfully aligned positions with GPS geo-referenced data and produced locally consistent maps. FS 2.0 based on GPS and LIDAR showed the best consistency with real maps, as evidenced by comparing results with those of FS 1.0 based on GPS and LIDAR, FS 2.0 and FS 1.0 based on LIDAR, FS 1.0 based on GPS, and Karto SLAM based on LIDAR. FS 2.0 based on GPS and LIDAR had accurate alignment with the geo-referenced positions: the trajectory error was 0.65 m based on the aerial map data, as shown in Fig. 7. The map distortion was 0.17 m near buildings and 0.08 m near the area with oil tanks (Figs. 9 and 10).

Figure 12 shows that FS 2.0 based on GPS and LIDAR is consistent with an aerial map. FS 1.0 based on GPS and LIDAR had a small increase of alignment error to GPS compared to FS 2.0. The trajectory error was 0.81 m based on the aerial map data (Fig. 7). The map distortion was 0.25 m near buildings and 0.026 m near the area with oil tanks (Figs. 9 and 10). Figure 13 shows that FS 1.0 based on GPS and LIDAR is also consistent with the aerial map.

Our method could reproduce the map variance of 0.3 m for 10 runs. Furthermore, we could reproduce map consistency for our method in two low-RTK-Fix-GPS environments by using both RTK-Fix-GPS and RTK-Float-GPS. The visual cue and global accuracy were used to show map consistency.

FS 2.0 based on GPS and LIDAR are visually consistent, as shown in Fig. 19a in Factory A and Fig. 20a in Factory B. The global accuracy is 0.52 and 0.72 m in Factory A and B, respectively. FS 1.0 based on GPS and LIDAR are also visually consistent, as shown in Fig. 19b for Factory A, and Fig. 20b for Factory B. The global accuracy error, specifically, 0.18 m in Factory A and 0.05 m in Factory B, increased compared to that of FS 2.0 based on GPS and LIDAR.

The limitation of this method pertains to roads with no ground level differences. This method does not work well in environments with large ground level differences. However, this method satisfies the firefighter robot requirement in petrochemical complexes where the roads have no ground differences.

In this work, we selected RTK-Fix-GPS and RTK-Float-GPS. In addition to filter good measurements, we filtered GPS data with the horizontal dilution of precision (HDOP) \(>1.2\) to use only accurate data. However, we still observed incorrect RTK-Fix-GPS and RTK-Float-GPS when moving near building. These errors caused GPS multipath signal errors. To prevent over overconfidence on RTK-GPS data, we carefully fused GPS data by using large GPS sigma \(\sigma _{\mathrm {gps}}.\)

## Conclusion

In this study, we extended two RBPFs based on GPS and LIDAR for consistent map construction in petrochemical complexes. FS 2.0 and FS 1.0, both in a grid map, were used for SLAM. We herein proposed a weight function that fuses GPS and LIDAR data inside the RBPFs. An importance weight function is derived to achieve sensor fusion. The weight function enables maintenance of the respective advantages of both GPS and LIDAR sensors. Therefore, these RBPFs based on GPS and LIDAR not only have local consistency, but also global consistency. An experiment was conducted in a closed petrochemical complex in Japan (550 m × 380 m). RTK-GPS availability was 56% in the petrochemical complex. Our results showed FS 2.0 had the best result with a significant improvement of alignment to geo-referenced positions. The mean global error was 0.65 m. A significant result for mapping consistency was 0.17 m near buildings and 0.08 m near sparsely placed oil tanks. Results also showed that both maps had consistency with an aerial map [2]. Our method could reproduce map consistency results for ten runs with a variance of ± 0.3 m. Our method reproduced map consistency results in low RTK-Fix-GPS environment, which was a factory with a building layout similar to petrochemical complexes with 20.9% of RTK-Fix-GPS data availability. The best global accuracy achieved was 0.52 m (Additional file 1).

## Notes

## Declarations

### Authors’ contributions

AUS and KO developed the methodology idea, performed the implementation and experimentation, gathered and analyzed data, and wrote the manuscript. KS and TH provided invaluable technical advice. TS, HR and YO provided the methodology idea and helped revise the manuscript. ST, HA and JF helped initiate the concept, provided facility and technical support, and helped revise the manuscript. All authors read and approved the final manuscript.

### Acknowledgements

This research was supported by the Project of Development of Fire Fighting Robots Responding to Disaster in Energy and Industrial Infrastructures, and the CREST Recognition, Summarization and Retrieval of Large-scale Multimedia Data.

### Competing interests

The authors declare that they have no competing interests.

### Ethics approval and consent to participate

Not applicable.

### Publisher’s Note

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## Authors’ Affiliations

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