Fig. 1 Principle illustration of the problem. Raw point clouds of robots at different positions are collected, and their features are extracted to determine the room-level locations of the robots
connections between parts and the whole. The information obtained by combining the two methods is used as the basis for localization. The neural network algorithm may be a suitable method for classifying the above mentioned data. Considering that neural network algorithms require a large amount of raw data, data enhancement is employed to augment the amount of available data.
### 3.1 Point cloud registration
To acquire location information, it is necessary to establish a correlation between current point clouds and global point clouds.
The current point clouds are 3D point clouds of the current location collected by the robot. The global point clouds are the overall 3D point clouds within which the robot can move. Point cloud registration facilitates the determination of positional relationships between these two entities.
#### 3.1.1 Coarse registration
After the current point clouds are acquired from the LiDAR system, the first step is to extract feature points for registration. For a large number of point cloud data points, the correlation between current point clouds and global point clouds is established according to the features extracted, which improves efficiency and accuracy.
Intrinsic shape signature (ISS) A method called the intrinsic shape signature (ISS) describes the geometry of point clouds. The algorithm is a regional point cloud feature extraction method that measures the importance of points by calculating the curvature and normal change in point cloud data. This method enables the acquisition of various geometric features, which can be used for registration. The point cloud P contains i points $p_i$ ($x_i, y_i, z_i$). The coordinate system is established for each point $p_i$, and the search radius $r_{frame}$ is set. $p_i$ is considered the centre to select all the points with radius R, and the weight $w_{ij}$ is calculated.
$$ w_{ij}=1\bigg/\left\|p_{i}-p_{j}\right\|,\left|p_{i}-p_{j}\right|Fig. 2 Framework of the position recognition method
Fig. 3 Coordinate system parameters of feature points
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The element characteristics of $P_{i}$ and each of its domain points are calculated.
$$ \left\{\begin{aligned}\alpha&=\mathbf{v}\cdot\mathbf{n}_{k}\\ \phi&=\mathbf{u}\cdot\left(p_{k}-p_{i}\right)\big/d\\ \theta&=\arctan\left(\mathbf{w}\cdot\mathbf{n}_{k},\mathbf{u}\cdot\mathbf{n}_{k}\right)\end{aligned}\right. $$
The above feature element values of point $P_{i}$ and every point $P_{k}$ in its k neighbourhood are calculated and statistically obtained as a simplified point feature histogram (SPFH), which can be denoted SPFH( $P_{i}$).
Then, the SPFH of each point in the k neighbourhood of $P_{k}$ is calculated separately, and all the SPHHs are weighted statistically. The FPFH reduces the computational complexity of the algorithm but still retains most of the identification characteristics of the PFH. Therefore, the FPFH consists of two parts, and the formula is as follows.
$$ \mathrm{FPFH}(P_{i})=\mathrm{SPFH}(P_{i})+\frac{1}{k}\sum_{m=1}^{k}\frac{1}{d_{k}}\cdot\mathrm{SPFH}(P_{k}) $$
SPFH $(P_{k})$ is the feature of $P_{k}$ and each of its domain points. $d_{k}$ is the distance between $P_{i}$ and $P_{k}$. As shown in Fig. 4, the FPFH involves not only the relationships between feature points and points within radius r but also the relationships between points within radius r and additional point pairs outside it.
Three sets of features are statistically input into one histogram. All three features are angles and are related to normal vectors, which can be placed in the same interval. The value of each feature is divided into several subintervals according to the range. The number of points falling in each subinterval is counted, which is the histogram of the point feature.
Fig. 4 PPFH of the feature points
The feature points of the current point clouds are matched with the points of the global point clouds to find the closest point pair via the FPFH, which is the corresponding point.
Random sample consensus All the above methods are aimed at finding the corresponding point between two clouds. Next, random sample consensus (RANSAC) can achieve the coarse registration of point clouds. The algorithm is an iterative algorithm for robustly estimating model parameters from a dataset. In terms of point cloud processing, RANSAC can be used to find matching points for a pair of point clouds.
Three non-collinear points are randomly selected from the feature points of the current point cloud and denoted $(p_{1}, p_{2}, p_{3})$. The global point cloud is defined as Q, and the corresponding points of $(p_{1}, p_{2}, p_{3})$, called $(q_{1}, q_{2}, q_{3})$, are found. This set of point pairs is used to calculate the spatial transformation matrix R and T for the current points and global point clouds.
R and T are used to transform the remaining points in P, and the distance error between the transformed points in P and the corresponding points in Q is calculated. If the error of the point pair is less than the threshold $\delta$, it is put into point set I. This process is repeated until the number of points in I reaches the threshold or the number of iterations reaches the maximum. The transformation matrix R and T with the largest number of points in I is selected as the optimal transformation to achieve coarse registration.
#### 3.1.2 Fine registration
The spatial transformation matrix derived from the RANSAC algorithm is computed via three pairs of feature points, which may contain errors within the overall point cloud. If the original point cloud is registered directly with coarse registration, the accuracy of the results is unsatisfactory. Consequently, further refinement is necessary to achieve precise registration.
The iterative closest point (ICP) algorithm [^45] [^46] is an accurate and efficient approach that is proposed to solve this problem, and it can solve the rigid registration problem. The ICP aims to find the optimal space transformation of two sets of data points. In essence, the algorithm is based on the least squares method to solve the optimal transformation matrix. In the current point cloud P, each point is defined as $\{P_m, m=1,2,...,N_p\}$, where $N_p$ is the number of current points. In the global point cloud Q, each point is defined as $\{Q_m, m=1,2,...,N_q\}$, where $N_q$ is the number of global points. The corresponding point set of point set Q and point set P in the k iteration calculation is $\{Q_{km}, m=1,2,...,N_p\}$. The objective of the alignment transformation is to minimize the objective function of the following Eq.
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$$ E(R,t)=\sum_{m=1}^{N_{p}}\left\|\boldsymbol{Q}_{m}-\left(R\boldsymbol{P}_{m}+t\right)\right\|^{2} $$
Each point in the current point set $P_m$ and the corresponding points in point set Q are taken, which minimizes $\|Q_m^k - P_m^k\|$. The rotation matrix $R_k$ and translation vector $t_k$ are calculated, which minimizes $E(R, t) = \sum_{m=1}^{N_p} \left\|Q_m^k - \left(R_m^k P_m^k + t_m^k\right)\right\|^2$. Then, the transformation coordinates $P_m^{k+1}$ are defined as $P_m^{k+1} = R_m^k P_m^k + t_m^k$. If $d^{k+1} = 1/N_p \sum_{m=1}^{N_p} \left\|P_m^{k+1} - Q_m^k\right\|^2$ is less than the defined dm, the next iteration is started.
The exact coordinate transformation matrix of the current point cloud and the global point cloud is obtained after the iteration is completed. The registration process is shown in Fig. 5. To further enhance the extraction of the proximity between the current point cloud and the global point cloud, the current point cloud and the global point cloud are compared. The overlap rate of the current point cloud is subsequently computed following fine registration.
The overlap rate is defined as c, which reflects the degree of overlap between the current point clouds and global point clouds. The distance between each point in the current point cloud and the nearest point of the global point cloud is calculated and denoted $d_{p}$. If $d_{p}$ is less than the set value $d_{min}$, it is marked as a coincidence point.
The overlap rate is as follows.
$$ c=\frac{N_{pc}}{N_{p}} $$
where $N_{p}$ is the number of current point clouds. $N_{pc}$ is the number of points that satisfy the distance requirement.
Fig. 5 Registration of the current and global point clouds
### 3.2 Point cloud object recognition
#### 3.2.1 Preprocessing for recognition
Preprocessing is indispensable for acquiring object information from a point cloud. Among the current point clouds, obtaining effective information from ground point clouds is difficult. Environmental features are usually focused on objects on the ground. Filtering the point cloud of the ground is a basic preprocessing operation in LiDAR and easily affects the clustering of objects.
Cloth simulation filtering To alleviate the influence of noise in the field environment, an initial filtration process is applied to the point cloud data. The ground filtering algorithm, known as cloth simulation filtering (CSF) [^47], is derived from the physical model simulation of "cloth". In computational graphics, a cloth can be conceptualized as a grid comprising interconnected particles with mass, forming what is known as a mass-spring model. The position and shape of the cloth are determined by the position of the particle in three-dimensional space. According to Hooke's law and Newton's second law, the relationship between position and force is as follows:
$$ m\frac{\partial X(t)}{\partial t^{2}}=F_{ext}(x,t)+F_{int}(x,t) $$
where x represents the position of the particle at time t. $F_{ext}(x,t)$ represents the external forces, which are composed of gravity and collision forces, and $F_{int}(x,t)$ represents the internal forces of the particles at position x and time t.
A flowchart of the CSF algorithm is depicted in Fig. 6, which can be comprehended as follows:
(1) The original point cloud is initially inverted.
Fig. 6 Flowchart of the CSF algorithm
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(2) Subsequently, the cloth model is superimposed onto the inverted point cloud.
(3) Then, the position constraints for the fabric nodes are analyzed to simulate and determine the ground shape and position.
Density-based spatial clustering of applications with nodes The ground point cloud is removed, and the remaining point cloud is clustered. Density-based spatial clustering of applications with nodes (DBSCAN) is a type of density-based clustering algorithm. The algorithm assumes that the clustering structure can be determined by the tightness of the sample distribution. According to the perspective of sample density, the continuity between samples is investigated, and the clustering is continuously expanded to obtain the final result.
The radius (EPS) and density threshold (MinPts) of the DBSCAN algorithm are defined. A circle with each point $P_m$ as the centre and EPS as the radius is drawn. This circle is called the $P_m$ neighbourhood. If the number of points in a circle exceeds the density threshold MinPts, the centre of the circle is denoted the core point. All the points in the neighbourhood of the core point $P_M$ are called the density direct of $P_M$. If both $P_i$ and $P_j$ are direct points of $P_m$ density, $P_i$ is connected to $P_j$ density. A cluster is formed by connecting these points of connected density. In this process, the current point cloud is clustered into several distinct parts.
#### 3.2.2 Object recognition via PointNet
Before PointNet [^23] was proposed, point clouds could not be dealt with directly because of the characteristics of 3D point clouds. If the order of the points in the set is disturbed, the same point cloud is still represented. After the rigid transformation (rotation and translation) of the point cloud, the classification result of the output remains unchanged. Features are extracted from the point cloud dataset by solving the classification task for point clouds. The structure of PointNet is shown in Fig. 7.
For each $N \times 3$ input dataset of point clouds, T-Net is used to learn the rotation transformation of the point clouds for calibration and align it in this dimension. Next, a multilayer perceptron (MLP) is used to map the image to 64 dimensions. Each $1 \times 3$ vector point is raised into a $1 \times 64$ vector through two MLP layers. $N \times 3$ input data becomes $N \times 64$ data and is aligned a second time in this dimension by T-net. Then, the MLP is used to map the data to 1024 dimensions in the same way. Each point is currently represented by a vector of 1024 dimensions, which is redundant for the 3-dimensional point cloud data. The maximum pooling operation is introduced to retain the maximum value of all channels in 1024 dimensions. The $1 \times 1024$ vector obtained is the global feature of N point clouds.
Using global features as input, the probability of each object is obtained through a trained multilayer MLP. The point cloud is labelled with the object corresponding to the maximum probability value. The number of objects corresponding to each subpoint cloud after clustering is counted and defined as $\{o_{kn}, n=1,2,...,N_{o}\}$.
### 3.3 Positioning based on the SAE and BPNN
In this section, we propose a method to recognize the current position on the basis of the data obtained. First, the registration and object recognition data are combined. The process of using a stacked autoencoder (SAE) to enhance data is described below. Finally, the structure of the back propagation neural network (BPNN) and the whole classification process are given.
The BPNN is a machine learning model based on neural networks that can automatically extract features from patterns and address nonlinear problems. The advantages of the BPNN model are that the process is relatively simple and that the number of computations is small. Neural network algorithms always need large amounts of data for training. Nevertheless, a finite amount of point cloud data are obtained from metallurgical workshops. In this study, an SAE is used to increase the one-dimensional original training data. The decoding and encoding of the SAE extract the original data features in the process of lossy
Fig. 7 Structure of PointNet
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Fig. 8 Structure of the AE
data compression and generate a new dataset on the basis of the retained data features. The SAE can directly train raw data to generate similar data, which is more efficient than the GAN.
#### 3.3.1 Data enhancement via the SAE
Autoencoders (AEs), which are unsupervised learning algorithms, constitute the basic unit of the SAE. For an AE, there is no need to label the data. It is a feedforward neural network consisting of an input layer, an output layer, and a hidden layer. The AE consists of two components, namely, the encoder and decoder, as shown in Fig. 8. The encoder maps the input data to the hidden layer to extract the data features. The decoder restores the data in the hidden layer to the original data and reconstructs the data.
The AE is essentially the same as that of normal neural networks. Since the output data are a reconstruction based on the input data, ideally, the output should be equal to the input. Therefore, the output of the AE is not the labelled data but the input data itself.
The training datasets are defined as $\{x=x_1, x_2, \ldots, x_n\}$. where $x_n\in\mathbb{R}^{m*1}$. The process of encoding is as follows.
$$ \mathbf{h}_{n}=\sigma(\mathbf{W}_{1}\mathbf{x}_{n}+\mathbf{b}_{1}) $$
The process of decoding is as follows.
$$ \hat{\mathbf{x}_{n}}=\sigma(\mathbf{W}_{2}\mathbf{h}_{n}+\mathbf{b}_{2}) $$
Fig. 9 Structure of the SAE
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Fig. 10 Framework of position recognition. Combining raw and generated data as a dataset for neural network algorithms
$h_n$ is the hidden layer vector corresponding to $x_n$, and $\hat{x}_n$ is the output layer vector corresponding to $h_n$. $\sigma$ is the activation function, and W and b are the weight and bias, respectively.
The error function is as follows and is usually expressed in terms of the second-order norm.
$$ L\big(\mathbf{x}_{n},\widehat{\mathbf{x}_{n}}\big)=\left\|\mathbf{x}_{n}-\widehat{\mathbf{x}_{n}}\right\|^{2} $$
The mean square error function is used to calculate the reconstruction error of the SAE.
$$ \mathrm{MSE}=\frac{1}{N}\sum_{n=1}^{N}L\big(\mathbf{x}_{n},\widehat{\mathbf{x}_{n}}\big) $$
To minimize the mean square error function, stochastic gradient descent (SGD) is used to find the optimal parameter configuration.
As shown in Fig. 9, the SAE is a stack of two or more AEs. It learns abstract vectors of different dimensions from complex input data by increasing the number of hidden layers. With the increase in the number of neural network layers, deeper features are obtained, but the training time increases rapidly. The three-layer SAE can extract more representative features while ensuring the calculation efficiency.
Fig. 11 Robot platform with LiDAR
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(A)
(B)
(C)
(D)
Fig. 12 Several different areas in the steel plant
Fig. 13 Global point cloud. It is divided into the steel plant, the waste area, continuous casting workshop A, and continuous casting workshop B.
Fig. 14 Current point clouds
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Fig. 15 Registration of the current and global point clouds
Table 1 Overlap rates of the current point cloud
| No. | Area 1 | Area 2 | Area 3 | Area 4 |
| $c^{(1)}$ | 86.29% | 7.34% | 14.60% | 17.45% |
| $c^{(2)}$ | 79.51% | 16.46% | 14.02% | 19.45% |
| $c^{(3)}$ | 85.55% | 13.07% | 10.98% | 9.92% |
| $c^{(4)}$ | 92.37% | 8.08% | 11.00% | 4.53% |
| $c^{(5)}$ | 80.53% | 18.39% | 19.23% | 13.61% |
| ... | ... | ... | ... | ... |
By training stacked autoencoders, the input original data pass through multiple layers of encoders to extract features and decoders to generate new data. The generated data are different from the original data when the features are retained. It can be used to compensate for an insufficient sample set.
#### 3.3.2 Position recognition by the BPNN
The framework of position recognition based on the BPNN is shown in Fig. 10.
The overlap rate c is obtained via point cloud registration. Considering the error in the registration process and the unification of the dimensions of the neural network input data, the results of registration are defined as $\{c_{km}, m=1,2,\ldots,N_{w}\}$. This array evaluates the level of the point cloud registration results for the current point cloud and each workshop's point cloud. $N_{w}$ is defined as the number of workshops, and k is the number of current point clouds. We obtain the list of the objects in the current points, which is defined as $\{o_{kn}, n=1,2,\ldots,N_{o}\}$. $N_{o}$ is defined as the number of types of objects.
The input of a BPNN is usually in the form of a one-dimensional array. To retain the registration and object recognition features, we combine two arrays and define them as $\{c_1, ..., c_{km}, o_1, ..., o_{kn}\}$, which can be replaced by $\{F_k = f_1, f_2, ..., f_{kM}, M = N_w + N_o\}$.
Fig. 16 Labelling of the point cloud. Most of the point cloud data involve the construction of structures and massive equipment
The trained encoder and decoder generate new data using $F_k$ as the original input data. The generated data are defined as $\{y_k = y_{k1}, y_{k2}, \ldots, y_{kM}, M = N_w + N_o\}$. $F_k$ and $y_k$ are merged as the training dataset for the BPNN.
According to the training data, the position recognition problem can be transformed into a place classification problem. The different workshops are defined as numbers 1 to $N_{w}$, and the training data are labeled with the number of workshops. Since the present study is a classification problem, it is imperative to employ cross-entropy loss as the designated loss function. The formula for this purpose can be expressed as follows.
$$ E=-\sum_{i=1}^{M}\hat{y}_{i}\ln y_{i} $$
In each iteration, to minimize L, the backpropagation algorithm is used to update the network parameters $(w, b)$. The formula is as follows.
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Fig. 17 Accuracy and loss of PointNet
Table 2 Quantification of object recognition
| No. | Steel furnace | Crane bracket | Wall | Steel frame | Rail car | Digger | Rigging | Semi-finished product | ... |
| $o^{(1)}$ | 3 | 15 | 6 | 0 | 0 | 0 | 0 | 0 | ... |
| $o^{(2)}$ | 3 | 13 | 4 | 2 | 0 | 0 | 0 | 0 | ... |
| $o^{(3)}$ | 3 | 6 | 1 | 0 | 0 | 0 | 0 | 0 | ... |
| $o^{(4)}$ | 3 | 8 | 1 | 1 | 0 | 0 | 0 | 0 | ... |
| $o^{(5)}$ | 5 | 6 | 1 | 1 | 0 | 0 | 0 | 0 | ... |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
Table 3 Dataset after fusion
| No. | Overlap rate | Object recognition quantity statistics |
| $y^{(1)}$ | $\mathsf{c}^{(1)}$ | $o^{(1)}$ |
| $y^{(2)}$ | $\mathsf{c}^{(2)}$ | $o^{(2)}$ |
| $y^{(3)}$ | $\mathsf{c}^{(3)}$ | $o^{(3)}$ |
| $y^{(4)}$ | $\mathsf{c}^{(4)}$ | $o^{(4)}$ |
| $y^{(5)}$ | $\mathsf{c}^{(5)}$ | $o^{(5)}$ |
| ...... | ... | ... |
Table 4 Loss rates with the structure
| Test No. | Number of neurons in each layer of the SAE | Loss rate |
| Layer 1 | Layer 2 | Layer 3 |
| 1 | 14 | 30 | 60 | 0.5993 |
| 2 | 14 | 50 | 80 | 0.5883 |
| 3 | 14 | 20 | 26 | 0.2511 |
| 4 | 14 | 13 | 12 | 0.0874 |
| 5 | 14 | 12 | 10 | 0.0744 |
$$ \Delta w=-\eta*\frac{\partial E}{\partial w},\Delta b=-\eta*\frac{\partial E}{\partial b} $$
### 3.4 Summary of the methods
The global point cloud is defined as $P_g$ and is divided into several room point clouds $P_m$ according to the enclosed space. The current point cloud at different locations collected in each room is represented as $P_i$, and the room number is labeled. The coincidence rate $c_n$ between the current point clouds $P_i$ and $P_m$ is calculated after coarse and fine registration, respectively. Moreover, the current point cloud $P_i$ is preprocessed for object recognition through PointNet. The number of objects in the current point cloud is denoted $o_m$. The dataset $y_{m+n}$ was obtained via data enhancement after combining $o_m$ and $c_n$. All the datasets are taken as input datasets of the BPNN, which are divided into training sets and test sets. The accuracy of the model parameters obtained by training is verified on the test set.
## 4 Case study
In this section, a series of experiments are conducted to verify the performance of the model via the point cloud dataset obtained via LsLiDAR -C32. The robot platform equipped
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Fig. 18 Grey images of the original and reconstructed data. The resemblance between the original data and the reconstructed data can be visually demonstrated more intuitively.
Fig. 19 Results of the object recognition data
Fig. 20 Results of the overlap rate data
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Fig. 21 Results of the combined data
with LiDAR in this experiment is shown in Fig. 11. The model is implemented in Python 3.8 and executed on Windows 10 with a GTX 3060ti GPU.
The effectiveness of the proposed localization method is evaluated on the basis of the dataset. In this section, how to process the original point cloud dataset is introduced first. Subsequently, the details of the neural network and evaluation criterion are described. Finally, the method is evaluated experimentally.
### 4.1 Point cloud dataset preprocessing
We collected samples from several different functional areas of the Masteel Special Steel Plant. These areas also vary in volume and device, as shown in Fig. 12. First, to obtain global point cloud data, it is necessary to merge scanned point clouds due to physical constraints. The LiDAR device is mounted on a mobile robot platform that systematically traverses the factory in a predetermined sequence. A global point cloud of the metallurgical plant was subsequently constructed. The different workshops in the metallurgical plant can be regarded as larger rooms within a broader scope, each with its function. Therefore, the global point cloud of a metallurgical plant is divided into rooms 1 to 4, which are the converter steel plant, the waste area, continuous casting workshop A, and continuous casting workshop B, respectively. (Fig. 13).
When the robot arrives at an area or starts up, it acquires the current location point cloud. The robot rotates once in place, and the point cloud obtained is the current point cloud. The experimenters collected samples at 15 random locations in each room, once every hour, 3–4 times. If the robots are located in certain rooms, we label their sensor data with the corresponding room number. The current point cloud collected at several locations in the plant is shown in Fig. 14.
To establish the correlation between the current and global point clouds, a progressive coarse-to-fine registration approach is employed, which is shown in Fig. 15. The current point cloud can be considered a submap of the global point cloud. Given the potential similarity among different regions and the inherent registration error, submaps are aligned with each corresponding area on the global map. The overlap rate of the current point cloud is presented in Table 1 as depicted below.
Before point cloud recognition, a preprocessing step is conducted to eliminate outliers and downsample the data to reduce their density. The current point cloud is clustered by removing the ground points, considering each segment of the classified point cloud as an individual object. The point cloud data were labeled manually and are depicted in Fig. 16.
The labeled point cloud obtained after processing the collected current point cloud serves as both the training and test sets for PointNet in deep learning. The accuracy and loss are shown in Fig. 17.
After the completion of PointNet training, each segmented point cloud is evaluated via PointNet calculations. The quantity of partial objects in each group of point clouds is presented in Table 2 below.
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Table 5 Results of several datasets
| Datasets | No. 1 | No. 2 | No. 3 | No. 4 |
| Accuracy | Loss | Accuracy | Loss | Accuracy | Loss | Accuracy | Loss |
| $c^{(n)}$ | 0.9781 | 0.7535 | 0.9635 | 0.7573 | 0.9745 | 0.7522 | 0.9671 | 0.7522 |
| $o^{(n)}$ | 0.887 | 0.8596 | 0.8953 | 0.8645 | 0.8733 | 0.8661 | 0.8833 | 0.8495 |
| $y^{(n)}$ | 0.9917 | 0.753 | 0.9908 | 0.7466 | 0.9981 | 0.7466 | 0.9963 | 0.7456 |
| Datasets | No. 5 | No. 6 | No. 7 | No. 8 | No. 8 | No. 8 | No. 8 | No. 8 |
| Accuracy | Loss | Accuracy | Loss | Accuracy | Loss | Accuracy | Loss |
| $c^{(n)}$ | 0.9652 | 0.7421 | 0.9525 | 0.7453 | 0.9865 | 0.7328 | 0.9655 | 0.7472 |
| $o^{(n)}$ | 0.876 | 0.8656 | 0.8825 | 0.8325 | 0.8733 | 0.8551 | 0.8644 | 0.8475 |
| $y^{(n)}$ | 0.9912 | 0.753 | 0.991 | 0.7376 | 0.9901 | 0.7467 | 0.9893 | 0.7427 |
Next, the data combined with the overlap rate, the overlap rate, and the object recognition data are used as the training set for localization. Table 3 shows the dataset after fusion, which is expressed as $\mathbf{y}^{(n)} = [\mathbf{c}^{(n)}, \mathbf{o}^{(n)}]$.
### 4.2 Hyperparameter optimization
To enhance the performance of the SAE and BPNN models and optimize the experimental results, each parameter of the model is meticulously optimized in this study. The testing accuracy and loss rate are usually taken as standards to measure the performance of the model. In this study, the optimal parameter is selected by adjusting the influence of a parameter on the precision. The final results fluctuate slightly in many experiments because the training of the neural network is affected by its random initial value. Therefore, the average results of ten simulation experiments under the same conditions are used for all the listed final data to reduce the influence of experimental error and the uncertainty of the results.
The above datasets of each point cloud group are fused as the training set. Each dataset can be represented as $\{F_k = f_{kl}, f_2, \ldots, f_M, M = N_w + N_o\}$. To exert a more pronounced influence on subsequent training using the augmented dataset, a varied combination of neuron numbers is employed, as illustrated in Table 4. By manipulating the various configurations of neurons to increase the diversity of the generated data, the robustness and precision of the neural network model can be improved.
Figure 18 compares the original and the reconstructed data, which are presented in pixel format. By showcasing grayscale images, the resemblance between the original data and the reconstructed data can be visually demonstrated more intuitively.
### 4.3 Results of different datasets
Several comparative experiments were conducted to validate the model's performance by comparing it with that of other datasets. The training process begins by solely utilizing object recognition data. The overlap rates are subsequently exclusively employed for further training. Finally, the fused data are incorporated into a comprehensive training set. The figure below illustrates the accuracy and loss rate of this meticulous training procedure. (Figs. 19,20 and 21)
Owing to the sensitivity of neural network algorithms to random initial values, a total of 8 experiments were conducted under identical conditions. Eight sets of experiments were repeated to select the data with low fluctuations and averages to reduce the error. The refined findings are presented in Table 5.
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Table 6 Results of several datasets
| Datasets | No. 1 | No. 2 | No. 3 | No. 4 |
| Accuracy | Loss | Accuracy | Loss | Accuracy | Loss | Accuracy | Loss |
| $y_{{0}}$ | 0.8756 | 0.8325 | 0.8953 | 0.8741 | 0.8622 | 0.8774 | 0.8996 | 0.8335 |
| $y_{{1l}}$ | 0.9781 | 0.7911 | 0.9755 | 0.7878 | 0.9645 | 0.7822 | 0.9782 | 0.7822 |
| $y_{{12}}$ | 0.9852 | 0.7724 | 0.9855 | 0.7573 | 0.9723 | 0.7713 | 0.9871 | 0.7723 |
| $y_{{13}}$ | 0.9891 | 0.7635 | 0.9843 | 0.7611 | 0.9864 | 0.7656 | 0.9833 | 0.7695 |
| $y_{{14}}$ | 0.9982 | 0.7624 | 0.9855 | 0.7973 | 0.9865 | 0.7622 | 0.9872 | 0.7638 |
| $y_{{15}}$ | 0.9881 | 0.7535 | 0.9855 | 0.7673 | 0.9965 | 0.7677 | 0.9982 | 0.7645 |
| $y_{{1c}}$ | 0.9921 | 0.7513 | 0.9914 | 0.7356 | 0.9967 | 0.7652 | 0.9963 | 0.7531 |
The above data indicate that the accuracy of the fused dataset is significantly higher than that of all the datasets before fusion. Moreover, the convergence speed is higher, and the loss rate is lower. Finally, the model achieved an impressive test accuracy of 99% while concurrently maintaining a loss value of 0.75.
Different datasets are obtained according to different combinations of neuron numbers in the previous SAE, which are denoted $y_{t}$ to $y_{t5}$. The raw datasets that were not enhanced are denoted $y_{0}$. In addition, the same amount of data is extracted from 5 groups of data and combined, the combination of which is denoted $y_{tc}$. The accuracy and loss rate are obtained by applying different combinations to the BPNN calculation, as shown in the table.(Table 6)
According to the accuracy and loss rates in the table, data enhancement improves the calculation accuracy. Different combinations of neurons have different computational accuracies. The dataset after the fusion of various combinations further improves the accuracy of the algorithm. In other words, in the case of insufficient sample data, the method presented in this paper provides a model for accurate positioning in industrial workshops.
The authors of another paper aimed to achieve robust and cost-effective room-level localization for an indoor mobile robot [^3]. A robotic room-level localization method is proposed, and the performance of the different coding strategies is evaluated on the collected sonar measurement dataset. Several samples were collected from ten different functional areas in a university building.
Different difficulty levels are set, and the performance for the different cases is evaluated independently. The accuracies for the three cases are 0.92, 0.81, and 0.78. However, the introduction of disturbances can have a significant effect on recognition. In this paper, the location accuracy of the proposed method is calculated by using the data collected by LiDAR in different workshops of the metallurgical plant.
Table 7 shows a comparison of the two robot localization methods. CSP, CSWA, CSWB, and WA represent the converter steel plant, continuous casting workshop A, continuous casting workshop B, and the waste area, respectively. HSF, KIT, CAF, INF, STO, HFF, and GYM represent the hall on the second floor, the kitchen, the café, the information desk, the storage room, the hall on the first floor, and the gymnasium, respectively.
Compared with the methods mentioned above, our method involves the collection of several samples in several functional areas in an industry workshop. Industrial workshops are much larger than office buildings. In addition, the devices and objects inside frequently move and change, and many interference factors exist within them. On this basis, the accuracy of the method proposed in this paper is still superior.
### 4.4 Discussion
The accuracy of the algorithm is evaluated by the experiments above, but many works are worthy of further investigation. Laser radar needs to collect a certain amount of data when the current position point cloud is acquired before it can be identified and located. Therefore, it takes time to obtain accurate positioning information, and the calculation result has a certain lag. The process of data enhancement requires encoding and decoding of input data, which consumes certain computing resources. When the amount of point cloud data exceeds a certain level, the hardware equipment installed by the robot may not be able to complete the calculation in time, affecting the real-time performance of the algorithm. If the number of samples is too small, overfitting problems may be introduced even with the blessing of data enhancement. Then, in unstructured factory environments where these areas lack clearly defined routes and typical building structures, the application of this method may pose significant challenges. Second, we use only a single LiDAR device to collect point cloud data without considering factors that may affect the results, such as gradient, distance, and density, which may lead to incomplete or incorrect point clouds. In addition, the point cloud data of only 4 metallurgical workshops were collected in this paper, and the identification of more rooms and more variable environments needs further research.
On the basis of the above shortcomings, we will conduct further research on the following aspects in the future. First,
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Table 7 Comparison of the two robot localization methods
| Rooms | CSP | CSWA | CSWB | WA | HSF | KIT | CAF | INF | STO | HFF | GYM |
| Accuracy | 0.99 | 0.98 | 0.99 | 0.98 | 0.83 | 0.85 | 0.83 | 0.83 | 0.92 | 0.80 | 0.88 |
| Size (m) | 100 $\times$ 250 | | | | 4.8 $\times$ 21 | | | | | | |
we reduce the scanning time for LiDAR to acquire the current location point cloud. We will study how to address the point cloud in the case of insufficient data to ensure accurate positioning under the premise of improving real-time performance. We will study the potential limitations of the algorithm. We will investigate how data enhancement specifically affects the cost of computing and determine an upper limit to the amount of data that can be guaranteed for the algorithm. We will examine how to mitigate or avoid overfitting problems in the case of insufficient data, as well as the minimum amount of data required to ensure the implementation of the algorithm. We will further determine what size and level of chaos in the environment will affect the implementation of the method. Second, we will increase the type and number of sensors used to obtain a variety of environmental information to address the problem of insufficient raw data. Then, we will further improve the existing model and adjust the necessary parameters to improve the operation efficiency so that the method can achieve better real-time positioning. In addition, we will collect data from larger industrial plants in the future that have more workshops and more variable working environments. The proposed method was further improved by increasing the difficulty of the experiment.
## 5 Conclusion
A room-level location method for mobile robots based on point cloud registration and target recognition is proposed. The proposed method is based on two directions of 3D LiDAR positioning methods, namely, retrieval-based and registration-based methods. The feature data of the two methods are extracted as the basis of positioning, and the original data amount is increased by data enhancement to solve the problem of insufficient raw data. The localization problem is converted into a classification problem, and the backpropagation neural network algorithm is used to identify the problem. On this basis, we collected original point cloud data from a metallurgical plant and carried out experiments to verify the accuracy of the proposed method.
The method proposed in this paper provides a feasible method for robot localization in complex environments. The positioning of mobile robots in complex industrial environments is especially important. Because of the shortcomings of the method, we further study the efficiency and accuracy of the algorithm from the aspects of the timeliness of the algorithm, multisensor information fusion, and the effect of the algorithm in more complex environments.
Data Availability The datasets for this study have been uploaded to GitHub and can be accessed via the following link: .
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## Declarations
Competing interests The authors declare that they have no competing interests.
Ethical and informed consent for the data used This study was performed by the authors, and no human participants other than the authors were involved. Informed consent was obtained from all the authors.
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Yunzhi Li is a doctoral student at Anhui University of Technology and has participated in multiple national-level research projects. His main research direction is the development of intelligent equipment and industrial applications of artificial intelligence.
Libin Tan is a master's supervisor at Anhui University of Technology. His main research areas are intelligent equipment development, digital design and manufacturing, and industrial applications of artificial intelligence. He has led and participated in multiple national-level scientific research projects, including the National Key Research and Development Program and the National Natural Science Foundation.
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Xiangrong Xu is a doctoral supervisor at Anhui University of Technology, a member of the Institute of Electrical and Electronics Engineers (IEEE) and the ASME Society, and serves as a reviewer for multiple international academic journals and conferences. His research interests include bionics, aerial robots, robot trajectory planning and control, biomechanics, and more. He has led and participated in multiple national-level scientific research projects, including the National Key Research and Development Program and the National Natural Science Foundation.
Zequn Zhang is a postdoctoral fellow and master's supervisor at Nanjing University of Aeronautics and Astronautics. His main research areas are Intelligent Manufacturing Systems and Artificial Intelligence. He has led and participated in multiple national-level scientific research projects, including the National Key Research and Development Program, National Natural Science Foundation, and National Defense Basic Research Projects.