3.1. Transition zone phenomenon instead of switching point

Relying solely on a single threshold level while transitioning from one algorithm to another may lead to fluctuations or instability around the switching point due to the probabilistic nature of the pose estimation process and the presence of measurement and computation errors. Another challenge is posed by the physical limitations of AMRs, which require precise maneuvering to successfully dock at the desired location. Even when an AMR has entered the docking area, it may briefly exit this region during the maneuvering process. Therefore, choosing a fixed switching point may be inadequate for such scenarios.

To address this issue, a switching region can be employed instead of a single point, and the transition can be implemented with hysteresis behavior within this region. Suppose that the switching mechanism is based on the distance of the AMR to the target, whereby a large-scale localization approach is used until the distance to the target pose is greater than or equal to $r_1$ meters. Subsequently, the algorithm switches to a precise localization approach. However, to ensure stability, a hysteresis behavior is implemented, requiring the AMR to be more than $r_2$ meters from the target to switch back to the large-scale localization approach where $r_2 \gt r_1$ . However, heuristically using the distance between the AMR and the target as the sole parameter for the switching decision may not be sufficient since the difference in orientation between the target and current positions, as well as the initial pose accuracy parameters, are also crucial in achieving accurate pose estimation. These factors all contribute to the determination of the corresponding point for scan-matching-based precise localization approaches and ultimately affect the similarity between the model and data point sets. This similarity is a crucial factor in determining the accuracy of pose estimation, as it impacts the registration of point sets.

3.2. Similarity based on overlap ratio computation

When the similarity between the model and data point sets falls below a certain threshold level, the point sets may not be registered correctly, resulting in a reduction in pose estimation accuracy. Therefore, real-time computation of the similarity between the model and data sets enables the determination of the switching point for the transition from large-scale localization to precise localization or vice versa.

In the literature, the term overlap ratio is commonly used to express similarity between point sets. Performance evaluation of registration methods is carried out by adding disruptive components such as noises, outliers, and missing data to the point sets at known rates [Reference Wu, Chen, Du, Fu, Zhou and Zheng55, Reference Tian, Liu, Li and Wang56], and initial overlap ratios between the point sets are given to make performance comparisons between algorithms [Reference Yao, Du, Wan, Cui, Yang, Jing and Li57]. Therefore, the overlap ratio is easily quantifiable in such articles, given that the amount of disruptive components in the point sets is known or adjusted. However, estimating the degree of similarity between two given point sets becomes more challenging when there is no prior knowledge about the level of disruptive components.

In the trimmed ICP paper [Reference Chetverikov, Stepanov and Krsek58], which is one of the milestones in the point set registration field, a method for calculating the overlap ratio ( $\eta$ ) between a model and data point sets was proposed. Let two point sets denoted as $\mathcal{X}\triangleq \{\vec{x}_i\}_{i=1}^{\mathit{N_x}}$ and $\mathcal{Y}\triangleq \{\vec{y}_j\}_{j=1}^{\mathit{N_y}}$ represent the model and the data sets. Similarly, $\vec{y}_{j(i)}$ denotes the correspondence of $\vec{x}_i$ , the ith element of the data set, in the model set. The objective function to compute the optimal overlap ratio between point sets was defined as

(1) \begin{equation} \gamma (\eta ) = \dfrac{1}{N_\eta } \left (\dfrac{\sum _{k = 1}^{N_\eta } d_k^2}{\eta ^{1+\lambda }}\right ) \end{equation}

where $\lambda$ is a preset parameter to eliminate undesired cases such as the matching of symmetric parts of the point sets and $d_k$ represents the distance between the $k$ th corresponding point pair. The number of overlapping points can be calculated as $N_\eta = \lfloor \eta \cdot N_x \rceil$ for a certain overlap ratio $\eta$ . Here, the overlap ratio is a measure that ranges from 0 to 1 and indicates the degree of similarity between point sets. The least-squares criterion is the basis for finding the overlap ratio. However, least-squares approaches are not robust enough to process point sets containing noise and/or outlier components [Reference Chen, Zhang, Du, Wu and Zheng59]. Since disturbances such as noise, outliers, and missing parts are inevitable in real-world applications [Reference Yilmaz and Temeltas60], a new metric based on the correntropy criterion has been defined to be used in the decision mechanism developed to switch from large-scale localization to precise localization.

3.3. Using correntropy criterion for similarity rate computation

The correntropy criterion, which is a combination of the terms correlation and entropy, addresses a generalized measure of similarity between two random variables [Reference Du, Xu, Zhang, Zhang, Gao and Chen61]. The least-squares criterion may be used to get information about the difference between point sets, whereas the similarity between point sets can be inferred with the correntropy criterion [Reference Zhu, Hu, Lu, Chen, Li and Li62]. Let $\rho$ be the similarity rate between the point sets to be calculated using the correntropy criterion, in this case, the objective function to be optimized to get the similarity rate can be constructed as

(2) \begin{equation} \phi (\rho ) = \dfrac{\partial e_{corr}(\rho )}{\partial \rho } \end{equation}

where $e_{corr}$ represents

(3) \begin{equation} e_{corr}(\rho ) = \dfrac{1}{N_\rho }\sum _{k = 1}^{N_\rho } \exp \left ( -\dfrac{d_k^2}{2\sigma ^2}\right ) \end{equation}

summation where $\sigma$ is the kernel width for the correntropy criterion. As a result, the value at which the change of the $e_{corr}$ with respect to $\rho$ is minimum gives the similarity rate between the point sets. For a particular similarity rate $\rho$ , the number of similar points between the model and data sets can be executed via $N_\rho = \lfloor \rho \cdot N_x \rceil$ relation. The optimal value of the similarity rate can be computed by following the procedure below:

1. 1. Find corresponding points between the model and data sets using the initial transformation $(\textbf{R},\vec{t})$ kd-trees nearest neighbor searching method [Reference Greenspan and Yurick63] is employed to determine corresponding point pairs.

2. 2. Sort the point pairs in ascending order considering the distance between the corresponding point pairs $d_k = \lVert (\textbf{R}\vec{x}_k+\vec{t})-\vec{y}_{j(k)}\rVert$ relation is used to calculate this distance for $(\vec{x}_k,\vec{y}_{j(k)})$ point pair.

3. 3. Determine $\sigma$ parameter for existing model and data sets according to the distribution of distance values between the corresponding point pairs. In this work, the standard deviation calculated by ignoring the distance values greater than twice the median value of the distribution has been selected as the $\sigma$ value.

4. 4. Apply Golden Section Search [Reference Press, Teukolsky, Vetterling and Flannery64] or similar algorithm to find the optimal $\rho$ that makes the $\phi (\rho )$ in (2) minimum.

It is common to use the correntropy criterion to obtain the transformation that maximizes the similarity between point sets. However, the use of the correntropy criterion in evaluating how similar two point sets are may have been put forward in this study. For this reason, it would be appropriate to examine the performance of the derived similarity rate definition in finding the similarity rate between point sets.

3.4. Verification of similarity rate definition

First, synthetic point sets have been generated to investigate and demonstrate the feasibility of similarity rate definition in expressing similarity between point sets. Imitated laser scan measurement sets are utilized for this purpose.Footnote 1 The model and data sets, point sets to be employed for similarity rate and overlap ratio analysis, are generated as in Fig. 2. A laser scanner with 30 m range and 0.25 $^\circ$ resolution is placed on the blue point on the occupancy grid map, and the original point set is obtained. Then uniformly distributed noise is inserted into each point in the set, and noisy points with Gaussian distribution are added to the point set to construct the data set. The original occupancy grid map is slightly modified for the model set production by adding a simple obstacle to the environment, and a fake laser scanner with the same specifications is located at the red point to get the modified point set. Then, since it is aimed to calculate the similarity rate in different cases, the modified point set is cropped at different rates.

Figure 2. Synthetic laser scan data generation for similarity rate definition performance tests.

The real similarity of two point clouds can not be computed since this is a probabilistic definition. That is why the similarity rate computed according to the aforementioned definition is compared with the real (ground truth reference) overlap ratio between the point sets in terms of whether they have similar increase/decrease profiles.

Figure 3. Performance of overlap ratio and similarity rate approaches in estimating two laser scan sets’ relation through ten separate cases for different initial transformation states: initial transformation between two laser scan sets is (a) Zero, (b) 1% for translation and $\pm 7^\circ$ for orientation, (c) 2% for translation and $\pm 14^\circ$ for orientation, and (d) 3% for translation and $\pm 21^\circ$ for orientation. The graphs show the characteristic of similarity estimation results for each initial transformation pair.

The similarity rate computation results for the model and data sets described in Fig. 2 are given in Fig. 3 over four experiments. In the first experiment seen in Fig. 3(a), there is no initial transformation between the model and data sets. For this scenario, the ground truth (GT) reference and the results computed by the trimmed ICP method almost completely overlap as expected. The similarity rate calculations developed within the scope of this study based on the correntropy criterion are parallel with the results of GT.

In other experiments in Fig. 3(b-d), the data set is transformed with a certain initial transformation involving a rotation and a translation. Although the overlap ratio definition in trimmed ICP seems to be sufficient in calculating the similarity between point sets in low-rate transformations, its performance rapidly decreases when the amount of rotation and translation between point sets increases. However, when the similarity rate definition is utilized to calculate the similarity between the point sets, it is seen that similar results are produced for different initial transformations. The results reveal that consistent outputs are obtained when the similarity between point sets is calculated with the similarity rate definition based on the correntropy criterion.

3.5. Probabilistic switching mechanism using similarity rate

As explained by the transition zone phenomenon in Section 3.1, designing a transition technique using a single threshold level may cause instability at the time of transition due to calculation and measurement errors. In the developed probabilistic approach, the similarity rate between the point sets will determine the boundaries of this transition region, as shown in Fig. 4(b). However, when the transition is made according to the similarity rate, these boundaries become floating rather than a fixed distance, as demonstrated in Fig. 4(a). In this case, the switching region will take shape depending on which side the AMR reaches the target and how the obstacles are located around the docking region. This arrangement will support the provision of docking at industrial standards.

Figure 4. Probabilistic switching decision mechanism between coarse and fine localization approaches based on similarity rate parameter.

An example describing that the similarity rate may differ for the same distance to the target is given in Fig. 5. It can be deduced that the similarity rate may be lower for a point closer to the target, depending on the environmental conditions. This result supports the necessity of the presented probabilistic switching idea.

Figure 5. Demonstration of floating boundaries over a scenario: (a) Map of the environment, (b) Four different paths followed to reach target pose, and (c) Similarity profiles of the reference and measured point sets for entire paths.

Figure 6. Flowchart for probabilistic switching algorithm between large-scale coarse localization and precise localization.

The preceding section elaborated on the proposed switching mechanism and its operation principle. Fig. 6 illustrates the algorithmic flowchart for implementing the probabilistic switching approach. The flowchart highlights that coarse localization involves the global localization phase as well. Upon completion of the global localization stage, a decision is made regarding whether the AMR is in the delivery or docking stage to execute the corresponding localization approach. The operational logic of the multi-stage localization approach is highlighted in Algorithm 1.

Algorithm 1 Multi-stage localization framework pseudocode

4.1. Experimental setup

Within the scope of the experimental setup sub-section, the vehicle employed in the field tests and the test environment are introduced.

4.1.1. Test unit: ITU-AGV

The field tests employed the ITU-AGV, as depicted in Fig. 7, which is a laboratory-type AMR equipped with state-of-the-art sensors, including front and rear 2D laser scanners (SICK LMS200) and an inertial measurement unit (IMU, Xsens MTi-300). The dimensions of the differential-drive ITU-AGV unit are 49 cm in width, 82 cm in length, and 22 cm in height (sensorless). The sensorless ITU-AGV weighs approximately 70 kg and can carry loads of up to 100 kg. It is essential to note that the ITU-AGV can benefit from all the facilities of the ROS.

Figure 7. ITU-AGV: a ROS-enabled and differential-drive laboratory-type AMR unit.

Figure 8. ITU robotics laboratory, the field test environment: (a) The occupancy grid map of the environment, the real scene from (b) the delivery, and (c) Docking zones of the lab.

4.2. Test scenarios

The prepared scenarios to validate the developed approach with field tests are demonstrated in Fig. 9. In the first two scenarios, the AMR started to move from an initial point and reached the target pose by following the waypoints. In the third and last scenario, the AMR moved from a starting point to a region close to the target and docked to the target by moving backward direction. The point that distinguishes the first scenario from the others is that, in the first scenario, the AMR started to move from a region relatively close to the target in terms of distance. However, it is desired to be shown that the similarity rate between the point sets will remain low since the field of view of the AMR is different for initial and target poses, even though the distance to the target is relatively short.

Figure 9. The scenarios performed for performance evaluations: (a) case 1, (b) case 2, and (c) case 3.

The scenarios are operated as follows:

1. 1. AMR follows the pre-determined waypoints using ground truth reference pose data and reaches the target.

2. 2. During the motion, the switching mechanism determines which localization method will be active.

3. 3. With the active localization approach, the current pose of the AMR is estimated in real time.

4. 4. The localization results are compared with the ground truth to evaluate the performance.

Before providing the implementation procedure of the localization framework, it would be appropriate to clarify how the ground truth reference data were derived for field tests.

4.3. Ground truth reference system

Ground truth reference data are required for comparison to analyze or assess the performance of any novel method or strategy. Producing ground truth data is challenging because it requires a reference source that yields more accurate results than the proposed approach. Since the architecture proposed in this study is aimed at docking to a target with sub-centimeter accuracy, ground truth reference data should include fewer error rates in the docking region.

As shown in Fig. 8(a) and Fig. 8(c), the Optitrack motion capture (MoCap) system is utilized to generate ground truth reference data. According to the datasheet, this optical system is able to produce 3D position and 3D orientation information with error levels less than 0.3 mm and 0.05 $^\circ$ , respectively. In the calibration stage, the average error is achieved as 0.551 mm before the experiments.

In the delivery stage, however, the pose estimation accuracy is lower. Therefore, the accuracy and precision of the fluorescent reflectors-based ground truth data are sufficient and these data are employed in the delivery zone of the field test environment. The layout of the fluorescent reflectors for Case 2 is shown in Fig. 8(b).

4.4. Implementation procedure of the multi-stage localization algorithm

The working principle of the switching decision mechanism is explained with the flowcharts in Fig. 6. As demonstrated there, for the probabilistic approach, the switching parameter is similarity rate definition $(\rho )$ . The upper and lower bounds for the switching parameter can be chosen differently according to the application. The literature suggests that scan-matching-based approaches yield satisfactory results when the overlap ratio between point sets is above 50% [Reference Chetverikov, Stepanov and Krsek58]. When examining the relationship between overlap ratio and similarity rate definitions over synthetic laser scan sets, as shown in Fig. 3, it was found that the similarity rate value is generally higher than the overlap ratio. Therefore, the center of the transition region from large-scale to precise localization is determined as 0.7 for the probabilistic switching decision mechanism. By adding a $\mp 5\%$ deviation, $\rho _1 = 0.75$ and $\rho _2 = 0.65$ can be assigned as the upper and lower threshold values, respectively, for the probabilistic switching mechanism.

Since the ITU-AGV mobile platform, depicted in Fig. 7, operates in the ROS environment, the developed switching decision approach was adapted to this platform. To achieve this, the switching mechanism was initially implemented in MATLAB-SIMULINK and subsequently transferred to the ROS environment. Further details of this process are provided in the Appendix section.

The authors utilized the scan-matching-based method from their previous publication [Reference Yilmaz, Sumer and Temeltas42] as a precise localization method in the docking zone of the experiments conducted in this study. Details on transferring the method to the ROS environment can be found in the relevant publication. In the delivery zone of field tests, an MCL variant called SA-MCL, which was introduced in ref. [Reference Yilmaz and Temeltas19], was implemented as a large-scale coarse localization approach since it has demonstrated similar localization performance throughout the entire operating field.

4.5. Results and comparisons

Within the scope of this study, it is stated that the autonomous logistics operation can be divided into two parts, delivery and docking, and the regions of these operations may vary according to the environmental conditions. While the important thing in the delivery region is to carry out the logistics operation without interruption, it is to reach the target, which gains more importance in the docking region, with high accuracy. As a result, a multi-stage localization strategy that can be suitable for the delivery and docking zones and a decision mechanism that can be used to move from the delivery zone to the docking zone or vice versa is presented. The validation results of the proposed mechanism by field tests are discussed in this section in terms of showing why the similarity rate concept is used in the decision mechanism, assessing the performance of the multi-stage localization framework, and comparing it with the state-of-the-art methods.

4.5.1. Insufficiency of overlap ratio for switching

This study employs the similarity rate as a correntropy criterion-based metric, which serves as the decision variable in the switching mechanism for transitioning between large-scale coarse and precise localization. While the overlap ratio is another measure of similarity between point sets that could also be used as a decision variable, field tests have shown that it only produces reliable results when the transformation between point sets is precisely known. For instance, in Fig. 10(a), the overlap ratio outputs are reasonable when the transformation between the point sets is known exactly, which corresponds to the precisely known pose in field tests. However, when using the pose estimation calculated by SA-MCL, which contains some error, for the transformation, the overlap ratio outputs become distorted, as shown in Fig. 10(b). On the other hand, the similarity rate can still predict the similarity between point sets with significant distinctiveness and effectiveness, as demonstrated in Fig. 10(c). Therefore, the similarity rate is utilized as the decision variable in the switching mechanism.

Figure 10. The overlap ratio/similarity rate estimations of trimmed ICP and correntropy for the followed trajectory of case 1: overlap ratio estimates of the trimmed ICP (a) Under the assumption that the initial pose is exactly known, (b) Using initial pose information calculated by SA-MCL, and (c) Similarity rate estimates of the correntropy with the aid of initial pose data computed by SA-MCL.

4.5.2. Performance evaluations of the developed switching strategy

The results of the experiments conducted to highlight the importance and advantages of using a coarse localization approach in the delivery zone and a precise positioning technique in the docking zone are presented in Fig. 11. The results are analyzed over three different cases, demonstrating the issues that may arise when using large-scale coarse localization throughout the entire path or relying solely on precise localization to reach the target. Fig. 11(b) shows that if coarse localization is employed continuously from the initial pose to the target pose, the mean error will remain at a certain level throughout the entire route, but it may not meet industrial standards to reach the target. Conversely, using precise localization from start to end may result in accurate and precise docking to the target, but the AMR may get lost in areas far from the target due to the decrease in pose estimation performance, as shown in Fig. 11(c).

Figure 11. The localization performance of two-stage approach demonstrated through three cases: (a) Waypoints followed, localization by (b) SA-MCL, (c) SM, and (d) SA-MCL + SM vs GT data.

The distance to the target at the switching point in Fig. 11(d) is different for each case. This is because the switching point is determined based on the similarity rate parameter, which is affected by the environmental conditions and the specific path followed by the AMR. In Case 1, the switching point is closer to the target since the path is shorter and more straightforward, while in Case 3, the switching point is farther away since the path is longer and has more turns. However, in all three cases, the multi-stage localization approach leads to a more accurate and reliable docking operation. This demonstrates the necessity and benefit of using a combination of coarse and precise localization techniques in autonomous logistics operations, depending on the specific environmental conditions and operational requirements.

If the switching steps are examined through Case 2, it can be deduced that the switching point determined by similarity rate is quite efficient. As seen in Fig. 12, the pose estimation performance of the SM is low in the region where coarse localization, that is, SA-MCL, is active. As of the switching point, coarse localization is deactivated, and fine localization becomes active. It is seen that the pose estimation performance of SM is satisfactory in the docking zone where the SM is active. This allows for reaching the target with the desired accuracy.

Figure 12. Two-stage localization approach application for case 2 - the SA-MCL is active during the delivery stage, and the SM becomes active (docking stage) when the switching point is reached, according to the similarity rate computed employing the measurements: (a) Similarity rate profile, (b) and (c) Pose estimation performance of the algorithms for x and y axes, respectively, and (d) the trajectory followed in case 2 and estimated poses by the algorithms.

At the switching point, there can be a significant difference between the last calculated pose of coarse localization and the first pose computed by fine localization, depending on the pose estimation accuracy rate of coarse localization. In such cases, jumps may occur in the position estimation, as shown in Fig. 12(b). These jumps may cause fluctuations in the controller output used for path following. To avoid such unwelcome situations, one of the following two remedies can be implemented: (1) When a transition from coarse to precise localization or vice versa is decided, the AMR should first stop and resume movement after the transition is completed. (2) In the transition zone, a weighted average of the estimated poses can be used to ensure a smooth switching.

Figure 13. The pose estimation error rates of the approaches (SA-MCL (dashed-blue), SM (solid-orange), SA-MCL + SM(dotted-yellow)): average, minimum, and maximum (a) Position and (b) Orientation estimation error rates for entire trajectories, overall (c) Position and (d) Orientation estimation error rates of reaching target pose for 100 separate offline trials.

To test the algorithms in terms of docking accuracy, 100 offline trials were performed on the paths of case 1, case 2, and case 3. Fig. 13(a) and Fig. 13(b) indicate minimum, maximum, and average error rates for entire trajectories. As seen from them, multi-stage localization has lower average errors in both position and orientation. On the other hand, Fig. 13(c) and Fig. 13(d) show the mean, minimum, and maximum values of docking errors in terms of position and orientation, respectively. Although overall performance is sufficient, it is seen that docking with high accuracy to a target may not be possible if a large-scale coarse localization approach is used along the entire route. However, with the aid of the switching mechanism, the use of large-scale localization in the delivery zone and precise positioning in the docking zone makes both having a sufficient localization performance overall and reaching a target at industrial standards possible.

4.5.3. Performance comparisons with the state-of-the-art

The results of field tests conducted to demonstrate the superiority of the developed two-stage localization approach over the single-level approach have been provided up to this point. In this section, on the other hand, the developed multi-stage localization method will be compared with some of the state-of-the-art methods in the literature. The proposed approach in this study has been compared with multi-stage localization approaches that combine MCL and entropy-based TrimICP proposed by Sun et al. [Reference Sun, Wang, Meng, Liu and Xie45] and the scan-matching-based refinement performed after particle filter proposed by Garrote et al. [Reference Garrote, Barros, Pereira and Nunes54].

The results evaluating the overall localization performance of the methods are presented in Fig. 14, utilizing three cases previously used in the tests. The results in Fig. 14(b-d) clearly indicate that state-of-the-art multi-stage methods outperform in terms of localization when the coarse localization is active. However, as highlighted throughout the article, for the delivery stage, what matters significantly is the rough estimation of the pose and the secure transportation of the AMR to the docking area. In our approach developed, although the localization performance in the delivery region is relatively lower, it is sufficient to reach the docking region. Moreover, considering the computational costs shown in Table I, it can be observed that the localization process is three times faster in our developed method for the delivery stage.

Figure 14. The localization performance comparisons through three cases: (a) Cases (b) Case 1, (c) Case 2, (d) Case 3 results, and (e) Close-up view of Case 3 results around target pose.

Table I. Performance comparison with state-of-the-art methods in terms of fastness and computational load (PF: particle filter, SM: Scan matching, SW: Switching).

When specifically discussing the docking area, although the superior performance of our developed method in terms of localization might not be distinctly discernible from Fig. 14(e), it is clearly evident in Table II that our approach can estimate the position of the AMR with sub-centimeter accuracy and precision level. Furthermore, in the docking region, pose estimation frequency is higher in our method (see Table I). The primary reason for this lies in the fact that other methods require sequential computations of both particle filters and scan-matching approaches for pose estimation in the docking region. This brings additional computational load and allows our algorithm to achieve higher frequency in localization around the vicinity of the target pose since the computational burden of the switching decision process is negligible, whose operating frequency is around 300 Hz.

Table II. Performance comparison with state-of-the-art methods in terms of localization accuracy (PF: particle filter, SM: scan matching, SW: switching).

In summary, the proposed multi-stage localization framework in this study dynamically switches between particle filter-based localization and scan-matching-based localization approaches based on the prevailing conditions. A continuously operating switching mechanism in the background determines which localization system will be active. The computational load of the decision mechanism is relatively low, enabling faster localization predictions compared to other state-of-the-art methods. When considering all these results together, it can be inferred that the multi-stage localization method developed, which includes the correntropy-based switching mechanism, can be confidently utilized for the localization problem of AMRs used for logistics purposes in factory-like environments.

4.6. Brief discussion on achievements

In the preceding sections, we have presented a comprehensive multi-stage localization framework, addressing the challenges of large-scale navigation and precise docking for AMRs in smart factory environments. Our focus has been on achieving sub-centimeter precision during the docking phase, a critical requirement for the seamless integration of AMRs into dynamic production landscapes.

Now, turning our attention to potential avenues for further enhancement and exploration, we consider opportunities for refining the precise localization component. For the precise localization component, the implementation of the ICP algorithm with improved speed and the use of the SLAMICP library [Reference Clotet and Palacín66] for updating the map in response to changing environmental obstacles could be explored. This approach may enable an increase in the current localization frequency, which is approximately 6 Hz, to around 20 Hz.

Moreover, while this study concentrated on achieving accurate position data for the docking process, it is imperative to delve into the realm of precise path tracking within the docking zone. Particularly in dynamic environments, where docking maneuvers may vary, numerous studies have addressed the high-accuracy tracking of dynamically changing routes [Reference Gong, Wu, Gao, Sun, Le and Liu67]. Considering these factors during the implementation of the methods derived from this study is crucial for optimizing overall performance.