A Water Body Boundary Search Method Combining Chemotaxis Mechanism and High-Resolution Grid Based on Unmanned Surface Vehicles

Abstract

To address the issues of poor environmental adaptability and high costs associated with traditional methods of measuring water body boundaries, this paper proposes an innovative path planning approach for water body boundary measurement based on Unmanned Surface Vehicles (USVs)—the Chemotactic Search Traversal (CST) algorithm. This method incorporates the chemotaxis operation mechanism of the Bacterial Foraging Optimization algorithm, integrating it with high-resolution grid maps to enable efficient traversal and accurate measurement of water body boundaries within large-scale grid environments. Simulation experiments demonstrate that the CST algorithm outperforms the Brute Force Algorithm (BFA), Roberts operator, Canny operator, Log operator, Prewitt operator, and Sobel operator in terms of optimal pathfinding, stability, and path smoothness. The feasibility and reliability of this algorithm in real water environments are validated through experiments conducted with actual USVs. These findings suggest that the CST algorithm not only enhances the accuracy and efficiency of water body boundary measurement but also offers a cost-effective and practical solution for measuring water body areas.

1. Introduction

Lakes, rivers, and reservoir basins are typical inland water bodies that serve as vital freshwater resources and gene banks for species on Earth [1,2]. In recent decades, the quantity, form, and distribution of inland waters have been affected by climate change, environmental shifts, and human activities. The water body boundary directly reflects the coverage area of inland waters and is a key indicator for assessing changes in water volume [3]. Notably, variations in water levels and quantities over extended periods are particularly sensitive to regional climate change. Additionally, alterations in water body boundaries can influence the lives of both plants and animals. In the ecological environment, measuring the boundaries of water bodies is closely linked to species habitats [4]. In climate change research, these boundaries can indicate how water resource distribution responds to global warming, including the expansion of arid regions and alterations in flood risks [5]. In engineering, roads constructed alongside water bodies must consider the positioning of these boundaries. Similarly, urban expansion affects the spatial status of inland water bodies [6,7]. As a result, the measurement of water body boundaries has emerged as a critical and compelling area of research.

Numerous scholars have conducted extensive studies on the boundaries of inland water bodies, particularly lakes, utilizing Geographic Information System (GIS) technology and remote sensing satellite imagery [8,9,10]. Reference [11] introduced an innovative neural network designed for refined water body boundary measurement, aimed at accurately mapping surface water in complex environments. The study implements a surface water body boundary refinement module that enhances the delineation of surface water body boundaries and, consequently, improves overall accuracy. Reference [12], based on Landsat-8 remote sensing images, examines the effects of six machine learning algorithms and three threshold methods used for measuring the water body boundary. It evaluates the transfer performance of models applied to remote sensing images captured at different times and compares the differences among these models. Due to the complex distribution of ground objects and numerous influential factors in remote sensing image classification, accurately identifying small and dispersed water bodies presents a significant challenge in the research. Reference [13] proposed an automatic B-snake (AB-snake) method, which utilizes satellite images to automatically initialize and transform topologies. The method addresses the limitations of the traditional B-snake approach, which is hindered by non-automatic initialization and inflexible topology. The results indicate that the AB-snake method significantly enhances the performance of the B-snake method by improving the automatic initialization scheme, providing notable advantages in the boundary extraction of small tubular branches and deep concave branches. Reference [14] has developed an automatic method that integrates multiscale extraction with the Spectral Mixture Analysis technique to improve water body boundary measurement in urban areas from moderate-resolution satellite images. The experimental results show significant enhancements in water body boundary measurement within urban environments. Reference [15] proposed a water boundary measurement method utilizing the Dual-UNet deep learning architecture. The approach integrates LiDAR point cloud data with thermal infrared imaging to enhance the accuracy of water body boundary measurement in complex environments. Reference [16] introduces a novel method for mapping annual flood extents using multitemporal Sentinel-1 images. The approach leverages the temporal and orbital positions of the satellite, in conjunction with contextual information, to effectively identify false positives and delineate flood extents. The method demonstrates high accuracy when compared with observational data.

Despite significant advancements in the application of remote sensing technologies for monitoring lake water body boundaries, their practical implementation continues to face two critical constraints. Firstly, regarding data acquisition, adverse weather conditions such as cloud cover, fog, rain, and snow can diminish the signal-to-noise ratio of optical images, complicating the achievement of continuous all-weather monitoring. Secondly, the high operational costs present a major obstacle, as the utilization of high-resolution data combined with specialized processing software complicates the execution of real-time monitoring at high frequencies. These prominent temporal and spatial limitations, coupled with economic constraints, have prompted researchers to develop innovative monitoring solutions that enhance real-time responsiveness and cost-effectiveness.

As a highly integrated surface intelligent platform, the Unmanned Surface Vehicle (USV) operates across various aquatic environments, including oceans, rivers, lakes, and freshwater reservoirs [17]. Its high level of autonomy and versatility has facilitated successful applications in numerous civilian domains, such as lake patrol, maritime reconnaissance, surface search and rescue, marine environment monitoring, hydrographic surveys, and chart rendering [18,19,20]. Reference [21] proposed an enhanced genetic algorithm to tackle the path planning problem for USVs during lake patrols. However, the computational complexity escalates exponentially with increasing environmental complexity, leading to reduced time efficiency. Reference [22] developed a USV specifically for search and rescue operations in deep water environments. This autonomous surface vessel is equipped with a Global Positioning System (GPS) and underwater sensors capable of locating victims, black boxes, debris, and other evidence, both on the surface and underwater. However, in large-scale environments, the perception fusion of the search and rescue system is inadequate, resulting in issues of inaccurate detection. Reference [23] proposed a fault-tolerant multisensor data fusion technology, which was applied to the USV model named Springer. Although the Springer model successfully achieved environmental monitoring and pollutant tracking, it encountered challenges such as excessive response delays and deficiencies in the fault-tolerant mechanisms of the monitoring system. Reference [24] introduced an innovative path planning method for unmanned aerial vehicles (UAVs), offering an optimized solution for state monitoring of the electric scooter sharing system through the establishment of a mixed-integer programming model based on a spatiotemporal graph. Notably, the hybrid exact-heuristic algorithm framework proposed by the authors is not limited to UAV path planning; it can also be adapted, with appropriate modifications, for path optimization problems involving ground mobile vehicles, including USVs. Reference [25] innovatively integrated a chaotic optimization mechanism into the traditional particle swarm optimization algorithm, addressing the challenge of local optima traps in three-dimensional path planning for UAVs. Reference [26] proposed a multiobjective optimization framework that simultaneously considers three critical metrics: the dynamic characteristics of ocean current fields, energy consumption efficiency, and navigation safety. Through Pareto front analysis, this framework achieved an optimal trade-off between navigation efficiency and safety, providing new technical insights for USV path planning in complex hydrological conditions pertaining to water body boundary measurement.

USVs equipped with measurement functions have been successfully applied across various scenarios. Reference [27] explored the potential of simultaneously acquiring and integrating terrestrial laser scanner data and high-resolution shallow water multibeam echosounder data from USVs. The objective of this trial was to efficiently generate a seamless three-dimensional dataset that encompasses both above and below the waterline. However, the use of traditional rasterized measurement paths leads to low boundary coverage efficiency. Reference [28] demonstrated the use of USVs as carriers for coastline measurements. Utilizing the acquired measurement data, digital bottom models and bathymetric maps of reservoirs were created. Reference [29] provides a concise comparison between USV surveys and traditional vessel multibeam surveys. The resulting cartographic outputs from the hydrographic survey are presented, highlighting specific inaccuracies within the raw data and assessing the suitability of various hydrographic products for different user domains. Reference [30] introduces a methodology for directly processing 3D LiDAR data to accurately and consistently detect navigable regions. To validate the performance of the proposed detection scheme, field experiments were conducted in a narrow and complex river environment. These experiments aimed to demonstrate the effectiveness of the proposed scheme, alongside comparative experiments and ablation studies to assess the impacts of deep segmentation and Kalman Filter-based tracking methods. Utilizing a USV as the carrier, the studies yielded data on shoreline surveys, water temperature assessments, bottom model mapping, and water depth measurements. However, there exists a paucity of research focusing on water body boundary measurements. The identified deficiencies in boundary feature extraction, coupled with a lack of practical validation, present a novel perspective for this paper, which aims to optimize the measurement paths for water body boundaries.

The premise of this measurement task is to maintain the USV as close as possible to the boundary of the water body to enhance measurement accuracy. The irregular profile of the water body boundary presents challenges; however, the small USV can effectively address the traversal issues in shallow and boundary waters due to its minimal draft and flexible operation [31]. Although an analysis of equipment performance and application scenarios indicates that utilizing a small USV for water body boundary measurement is feasible, challenges remain in water body boundary perception and USV path planning [32].

Environment modeling serves as the foundation for agent environmental perception. As a model of the environment, grid maps are characterized by their simplicity and flexibility in editing [33,34,35]. Furthermore, they can effectively represent irregular obstacles, closely aligning with the actual features of water body boundaries. High-resolution grid maps can accurately depict water body boundaries; however, as the resolution increases, the scale of the map also expands. This increase in map scale results in a greater number of feasible solutions, thereby elevating computational complexity. The Bacterial Foraging Optimization (BFO) algorithm [36] exhibits excellent search characteristics and robust global search capabilities due to its intrinsic properties. As a result, the BFO algorithm has been widely applied to various path planning problems [37,38,39,40]. In summary, this paper presents an innovative path planning method based on USVs, referred to as the Chemotactic Search Traversal (CST) algorithm. This method addresses the challenge of water body boundary measurement. By integrating the chemotactic operation mechanism of the BFO algorithm and utilizing high-resolution grid maps for environmental modeling, the CST algorithm facilitates efficient traversal measurement of water body boundaries. It effectively resolves the inherent conflict between measurement accuracy and economic cost found in traditional measurement methods, achieving a harmonious balance of high precision and low cost. Experimental results demonstrate that, compared with traditional measurement algorithms, the CST algorithm exhibits superior performance in both measurement accuracy and smoothness, thereby providing a reliable solution for water environment monitoring.

The remainder of this paper is organized as follows: Section 2 introduces the fundamental methods of water environment modeling. Section 3 presents the definition of the chemotactic operation of the BFO algorithm within the environmental model. Building on this, a novel approach for solving the boundary path is proposed. Section 4 discusses experimental simulations and analyses. Finally, Section 5 concludes this paper and outlines anticipated future work.

2. Environmental Model

2.1. Grid Map

Grid maps are a common method for representing environmental data, characterized by their simple and flexible editing capabilities. They effectively depict irregular obstacles within the environment. In this paper, the environmental map utilized for measuring water body boundaries is a grid map derived from satellite imagery. Figure 1 illustrates the environmental information represented by the grid map, displaying a two-dimensional plane with a scale of $10\times 10$. In this representation, the yellow grid indicates infeasible areas, while the green grid denotes feasible areas, and the red path signifies the route planned by the USV. The grid coding method employed for these grid graphs is based on coordinates, specifically encoding the coordinates as (x, y), as demonstrated in Equation (1).

$$\begin{array}{c}\hfill \left\{\begin{array}{c}x=mod\left(i-1,n\right)+0.5,\hfill \\ y=n+0.5-ceil\left(i/n\right),\hfill \end{array}\right.\end{array}$$

(1)

In the formula, the operations mod and ceil serve as complementary functions, where mod represents the modulus operation and ceil denotes the ceiling function. Here, n signifies the grid scale, while (x, y) indicates the coordinates of a node.

2.2. Grid Map Resolution

The size of the grid is a critical index for evaluating the resolution of grid maps and serves as the primary factor influencing the quality of environmental models. During the measurement of water body boundaries, achieving the highest possible boundary accuracy is essential. A high-precision environmental model can effectively reconstruct the actual water body boundary information. In this paper, we use the satellite imagery of a reservoir’s water area as a case study, constructing environmental models at various grid scales, as illustrated in Figure 2.

As clearly illustrated in the figure, an increase in the resolution of the grid map results in a feasible path that is closer to the mountain. Consequently, high-precision grid maps, functioning as environmental models, play a crucial role in improving the accuracy of water body boundary measurements conducted by the USV.

3. Path Planning Method

Path planning methods are a fundamental component of autonomous control systems for intelligent robots. Common techniques for path planning include the Dijkstra algorithm, Best First Search algorithm, A* algorithm, artificial potential field method, and intelligent optimization algorithms. The primary optimization objective of these path planning methods is typically to minimize the distance from the starting point to the endpoint, achieving either an optimal or suboptimal solution. In light of the characteristics associated with water body boundary measurement, the path planning method proposed in this paper seeks to identify a route that maximizes the distance from the starting point to the endpoint, while adhering to the constraint of maintaining the shortest distance to the mountain.

3.1. Chemotactic Operation

The BFO algorithm is iteratively refined through three layers of nested loops, with the chemotactic operation representing the innermost layer. This operation is crucial as it updates the position of the agents, embodying the characteristics that enable the BFO algorithm to perform fine searches effectively. The chemotactic operation comprises two primary operators: flipping and swimming. The flipping operator simulates the clockwise rotation of bacterial flagella, facilitating movement, while the swimming operator mimics the counterclockwise rotation, propelling the organism forward. In the traditional BFO algorithm, a variable is utilized to represent the specific location of bacteria. This location information encompasses both the flipping and swimming behaviors of the bacteria, as illustrated in Equation (2).

$$\begin{array}{c}\hfill {\theta }^i\left(j+1,k,l\right)={\theta }^i\left(j,k,l\right)+c\left(i\right)·\phi \left(i\right),\end{array}$$

(2)

where $c\left(i\right)>0$ is the length of the swimming step, $\phi \left(i\right)$ is the turnover angle.

In this paper, the biological characteristics of chemotactic operation are applied to the grid map, as illustrated in Figure 3.

In the grid map, the flip angle $\alpha$ of the bacteria is represented by Equation (3). The swimming distance L of bacteria is represented by Equation (4).

$$\begin{array}{c}\hfill \alpha ={\displaystyle \frac{k\pi }{4}},k\in \left[0,8\right],\end{array}$$

(3)

$$\begin{array}{c}\hfill L=\left\{\begin{array}{c}1,k=0,2,4,6,8,in\alpha ,\hfill \\ \sqrt{2},k=1,3,5,7,9,in\alpha ,\hfill \end{array}\right.\end{array}$$

(4)

3.2. Chemotactic Search Traversal Algorithm

The algorithm identifies the nearest obstacle node from the current position using displacement operations. It calculates the distance, denoted as $f\left(n\right)$, between the nearest obstacle node and the feasible nodes adjacent to the current position. The calculation formula for $f\left(n\right)$ is presented in Equation (5). By comparing the values of $f\left(n\right)$, the algorithm selects the node with the smallest $f\left(n\right)$ as the next node for traversal. This process continues until the initial node is reached again, thereby completing the cycle and the water body boundary measurement plan. When evaluating the performance of the CST algorithm, both the total length of the water body boundary measurement path and the smoothness of the path are crucial metrics. The total length of the water body boundary measurement path, denoted as $L_{total}$, can be calculated by Equation (6). Meanwhile, the path smoothness is assessed based on Equations (7) and (8). These two metrics reflect the performance of the CST algorithm in water body boundary measurement path planning from different perspectives, thereby playing a key role in the comprehensive assessment of the algorithm’s performance. Here, $P_{u-1},P_u,P_{u+1}$ represent the coordinates of three consecutive path nodes; $R_u$ denotes the curvature radius; and $S_u$ represents the smoothness.

$$\begin{array}{c}\hfill f\left(n\right)=\sqrt{{\left(x-x_n\right)}^2+{\left(y-y_n\right)}^2},\end{array}$$

(5)

$$\begin{array}{c}\hfill L_{total}=\sum _{u=1}^{n-1}\sqrt{{\left(x_{u+1}-x_u\right)}^2+{\left(y_{u+1}-y_u\right)}^2},\end{array}$$

(6)

$$\begin{array}{c}\hfill R_u={\displaystyle \frac{\Vert P_u-P_{u-1}\Vert ·\Vert P_{u+1}-P_u\Vert ·\Vert P_{u+1}-P_{u-1}\Vert }{2·\mid \left(P_u-P_{u-1}\right)·\left(P_{u+1}-P_u\right)\mid }},\end{array}$$

(7)

$$\begin{array}{c}\hfill S_u={\displaystyle \frac{1}{R_u}},\end{array}$$

(8)

Figure 4 illustrates four scenarios in which bacteria utilize $f\left(n\right)$ to navigate towards the nearest water body boundary during the chemotaxis process. In the figure, the gray grid represents obstacles, while the white grid denotes feasible pathways. Solid blue nodes indicate the position of the bacteria, black nodes represent the nearest obstacles to the bacteria, and hollow blue nodes indicate potential positions to which the bacteria can move. It is important to note that the red hollow node in the figure marks the bacteria’s previous location; thus, the current chemotactic movement cannot redirect the bacteria back to the position of the red hollow node. To ensure that the node traversed by the bacteria is closest to the obstacle, it is essential to minimize $f\left(n\right)$. The position of the yellow node, as depicted in the figure, represents the optimal solution obtained through the comparison and calculation outlined in Equation (5). In Figure 4a–c, bacteria can directly calculate $f\left(n\right)$ to identify the node closest to the boundary of the obstacle. However, in the scenarios illustrated in Figure 4d,e, bacteria must evaluate $f\left(n\right)$ in both cases and ultimately compare the results to determine the optimal solution.

3.3. Algorithm Description

In this paper, a CST algorithm is proposed to address the path planning problem of USVs for water body boundary measurement. The algorithm utilizes the chemotactic operation of the BFO algorithm to identify the nearest obstacle relative to the current node. Subsequently, it calculates the shortest distance between the nearest obstacle and the feasible node to establish the search criterion for the next node. The pseudocode of the CST algorithm is shown in Algorithm 1.

Algorithm 1 CST algorithm

1: while not terminal converged do do  2:     Chemotaxis;  3:     $A=\left(x,y\right)$ //Current position coordinate.  4:     for i = 1:n do //Eight fields of the current node.  5:         if $t=0$ then //$t=0$ indicates that the node cannot pass, and $t=1$ indicates that the node can pass.  6:            $tem=notcross$  7:         else  8:            $t=1$,$tem=cross$  9:            if $tem=notcross$ then 10:                $L=\sqrt{2}\Vert 1$ 11:                $B=\left(x_{L\left(min\right)},y_{L\left(min\right)}\right)$//Location of the nearest obstacle to the current node. 12:            else 13:                $tem=cross$ 14:                $L_1=\sqrt{{\left(x_{L\left(min\right)-}{x}_{tem}\right)}^2+{\left(y_{L\left(min\right)}-y_{tem}\right)}^2}$ 15:                $A=\left(x_{L1\left(min\right)},y_{L1\left(min\right)}\right)$//Update the location of A. 16:                if $L_1=L_1^{*}$ then//There are two viable nodes with equal and minimum distances from the nearest obstacle. 17:                    $L_2=\sqrt{{\left(x^{\prime }-x_1\right)}^2+{\left(y^{\prime }-y_1\right)}^2}$ 18:                    if $L_{2\left(1\right)}>L_{2\left(1\right)}$ then// Determine the distance between two nodes and the previous node. 19:                        $A=\left(x_{L2\left(1\right)},y_{L2\left(1\right)}\right)$ 20:                    else 21:                        $A=\left(x_{L2\left(2\right)},y_{L2\left(2\right)}\right)$ 22:                    end if 23:                end if 24:            end if 25:         end if 26:     end for 27: end while

4. Unmanned Surface Vehicle Structure

As shown in Figure 5, the USV utilized in this study features an advanced double-shell and double-propeller structural design. The hull is constructed from a combination of high-strength carbon fiber composite materials and stainless steel, ensuring both structural integrity and a lightweight design. Regarding the sensing system configuration, the USV is equipped with a multimode sensor fusion system, which includes a Livox Horizon LiDAR (Livox, Shenzhen, China) for 360° environmental perception and a Hikvision DS-2CD7 series high-speed camera (Hikvision, Hangzhou, China) that supports 4 K resolution video capture, along with night vision and wide dynamic range capabilities. The navigation system employs the CTI P3DU high-precision inertial navigation GPS system (CTI Systems S.A., China), achieving positioning accuracy at the centimeter level. Concurrently, it is equipped with high-sensitivity water leakage and temperature and humidity sensors, which facilitate real-time monitoring of the hull’s condition.

In terms of energy power systems, the USV is equipped with two high-performance 20AH lithium battery packs and employs an intelligent battery management system to ensure continuous and stable power output. The propulsion system utilizes dual 1000 W rated brushless motor thrusters, combined with advanced vector control algorithms, enabling the USV to achieve precise speed regulation and flexible maneuverability within the range of 0 to 12 knots. The actual image is presented in Figure 6.

5. Results and Discussion

The experiments presented in this paper were conducted on a 64-bit operating system equipped with an Intel(R) Core(TM) i5-7200 CPU (HP, China) running at 2.50 GHz and 8.00 GB of memory. In the practical USV experiment, a specific safe natural water body boundary was chosen as the test subject.

5.1. A Comparative Analysis of Brute Force Algorithm, Five Kinds of Image Edge Detection Operators, and CST Algorithm

In this section, we conduct simulation experiments on the Brute Force Algorithm (BFA) and the CST algorithm under identical conditions, utilizing both horizontal and vertical resolutions of 500 pixels. From the perspective of algorithmic principles, both methods employ ergodic scanning technology, systematically searching all potential solutions through their respective scanning strategies to identify the optimal solution. Figure 7 illustrates the optimal path determined by the BFA in water body boundary measurement, highlighting its local details. In this figure, the yellow path denotes the optimal water body boundary path identified by the algorithm. Conversely, Figure 8 presents the detection results of the optimal path determined by the CST algorithm, with the red path indicating the optimal boundary path established by this method.

To further evaluate the performance of the two algorithms, experiments were conducted 20 times in the same experimental environment, utilizing both horizontal and vertical resolutions of 500 pixels. Subsequently, a consistent area was selected for a comparative analysis of local details, as illustrated in Figure 9. By comparing the path planned by the algorithm with the original edge of the image, it is evident that the BFA algorithm produces several redundant path points (highlighted with red solid rectangular boxes in the figure) during the path planning process. These unnecessary path points significantly increase the length of the final planned path. In contrast, as depicted in Figure 10, the detection results of the CST algorithm closely align with the original boundary contour, demonstrating superior edge detection accuracy. The comparative results unequivocally highlight the superiority of the CST algorithm in the water body boundary measurement task.

The Roberts operator is one of the simplest edge detection operators. It is a local difference operator that identifies edges by calculating the approximate gradient amplitude based on the diagonal differences between two adjacent pixels. The Sobel operator is primarily employed for edge detection; it is a discrete difference operator that approximates the gradient of the image brightness function. The Prewitt operator is a first-order differential operator used for edge detection, utilizing the gray differences between adjacent pixels to identify extreme values at the edges. The Log operator combines Gaussian blur and smoothing processes for effective edge detection. Finally, the Canny operator is a multistage optimization operator that incorporates filtering, enhancement, and edge detection.

In this study, we conducted 20 repeated simulation experiments using five classical edge detection operators: Roberts, Sobel, Prewitt, Log, and Canny. By focusing on the same region, we compared and analyzed the detection results of each operator against the original edge contour, yielding the following experimental results.

Figure 11 illustrates the edge detection results obtained using the Log operator, where the purple path denotes the locally optimal path determined by the operator. A comparison with the original edge contour reveals a significant occurrence of edge omission (indicated by the blue dashed circle in the figure), resulting in the extracted edge path being considerably shorter than the actual edge path. Figure 12 presents the detection results from the Sobel operator, with the green path representing the locally optimal path determined by this operator. The experimental findings indicate that the Sobel operator exhibits limitations in edge positioning accuracy (highlighted by the blue dashed circles in the figure), leading to a noticeable deviation between the measured water body boundary and the true boundary, thereby failing to accurately represent the actual edge characteristics. Figure 13 presents the detection results produced by the Prewitt operator, with the pink path indicating the locally optimal path determined by this operator. Similar to the Sobel operator, the Prewitt operator also encounters the issue of inaccurate edge localization (marked by the blue dashed circle in the figure), which adversely affects the reliability of edge detection to a certain extent. Figure 14 illustrates the detection effect of the Roberts operator. Compared with the original edge contour, it is evident that the algorithm generates several redundant path points (highlighted within the red solid rectangular boxes in the figure), resulting in an extracted edge path length that exceeds the actual edge path length. Figure 15 presents the detection results of the Canny operator. The analysis indicates that this algorithm not only suffers from the issue of redundant path points (also marked with red solid rectangular boxes in the figure), but also, based on the spatial distribution of these redundant points in the original contour image, it can be inferred that the extraction accuracy of the edge contour by the Canny operator requires enhancement. The presence of these redundant path points further contributes to the extracted edge path length being greater than the actual edge path length.

The experimental results indicate that various algorithms exhibit significant differences in their performance regarding water body boundary measurement. Notably, both the BFA and Roberts operator introduce path redundancy during the boundary measurement process, leading to a planned path length that noticeably exceeds the actual contour. Conversely, the Sobel, Prewitt, and Log operators suffer from insufficient edge location accuracy, making it challenging to accurately represent the true edge characteristics, resulting in extracted edge path lengths that are considerably shorter than the actual edge paths. Additionally, the Canny operator faces the dual challenges of path redundancy and inaccurate edge localization, indicating that its detection performance still has substantial room for enhancement. In contrast, the CST algorithm demonstrates significant advantages in boundary measurement. Its planned path closely aligns with the original boundary contour, surpassing traditional algorithms in both path length control and edge positioning accuracy. Therefore, regarding the accuracy of boundary measurement, the overall performance of the CST algorithm is markedly superior to that of the BFA and five classical image edge detection operators, offering a more reliable solution for water body boundary measurement.

Through the local path analysis of various algorithms, the accuracy of the CST algorithm in measuring water body boundaries has been intuitively demonstrated. To further validate this conclusion, we conducted a quantitative data analysis under consistent environmental conditions.

In terms of path accuracy, as illustrated in Figure 16, the optimal path lengths for the BFA, Roberts operator, and Canny operator exceed that of the CST algorithm by 6.3, 9.3, and 21.3 units, respectively. This finding indicates that these algorithms exhibit issues with redundant path points during water body boundary measurement. Conversely, the optimal path lengths for the Log operator, Prewitt operator, and Sobel operator are shorter than that of the CST algorithm by 289.7, 267.7, and 269.7 units, respectively. This suggests that these algorithms possess significant deficiencies in path planning accuracy, which adversely affects the precision of local water body boundary measurements. The measurement value of the water body boundary measurement path is shown in

Table 1. Seven algorithms with 20 running times and measurement values.

	BFA	Roberts	Canny	Prewitt	Sobel	Log	CST
No. 1	0.0855	0.0433	0.0890	0.0164	0.0215	0.1070	0.0329
No. 2	0.0834	0.0199	0.0723	0.0065	0.0052	0.0654	0.0320
No. 3	0.0709	0.0231	0.0325	0.0133	0.0039	0.0558	0.0338
No. 4	0.0835	0.0382	0.0246	0.0046	0.0044	0.0554	0.0349
No. 5	0.0835	0.0092	0.0650	0.0104	0.0175	0.1070	0.0317
No. 6	0.0796	0.0477	0.0124	0.0115	0.0046	0.0498	0.0327
No. 7	0.0866	0.0035	0.0166	0.0041	0.0033	0.0472	0.0304
No. 8	0.0931	0.0394	0.0397	0.0050	0.0047	0.0702	0.0306
No. 9	0.0763	0.0070	0.0355	0.0029	0.0035	0.0728	0.0328
No. 10	0.0755	0.0042	0.0504	0.0040	0.0126	0.0425	0.0307
No. 11	0.0715	0.0070	0.0124	0.0132	0.0130	0.0527	0.0342
No. 12	0.0834	0.0199	0.0723	0.0065	0.0052	0.0654	0.0320
No. 13	0.0784	0.0035	0.0109	0.0069	0.0028	0.0509	0.0302
No. 14	0.0800	0.0069	0.0446	0.0036	0.0115	0.0585	0.0316
No. 15	0.0753	0.0050	0.0393	0.0172	0.0124	0.0439	0.0335
No. 16	0.0789	0.0066	0.0138	0.0196	0.0038	0.0721	0.0311
No. 17	0.0804	0.0141	0.0095	0.0150	0.0049	0.0535	0.0333
No. 18	0.0819	0.0029	0.0340	0.0047	0.0071	0.0408	0.0316
No. 19	0.0752	0.0031	0.0130	0.0074	0.0062	0.0511	0.0347
No. 20	0.0848	0.0035	0.0160	0.0040	0.0032	0.0514	0.0304
Average time	0.0799	0.0146	0.0340	0.0091	0.0075	0.0595	0.0323
Variance	$3.1\times {10}^{-5}$	$2.33\times {10}^{-4}$	$5.13\times {10}^{-4}$	$2.8\times {10}^{-5}$	$2.9\times {10}^{-5}$	$3.56\times {10}^{-4}$	$0.2\times {10}^{-5}$
Measurement value	1236	1239	1251	962	960	940	1229.7

. In summary, the CST algorithm demonstrates a marked superiority over the other six algorithms regarding water body boundary measurement accuracy.

In terms of time efficiency, as illustrated in Figure 16b, the average running time of the CST algorithm outperforms that of the BFA, Log operator, and Canny operator. Although it is slower than the Prewitt, Sobel, and Roberts operators, this is attributable to the inaccurate measurement of water body boundaries by the Prewitt and Sobel operators, while the Roberts operator suffers from redundancy points. Each point in the graph represents a single runtime, and the bar chart depicts the average runtime of each algorithm. As presented in Table 1, the average running time of the CST algorithm is superior to that of the BFA by 0.7665 seconds, the Log operator by 0.5624 seconds, and the Canny operator by 0.0017 seconds. Furthermore, the variance of the CST algorithm is more favorable than that of the BFA ($2.9\times {10}^{-5}$), Roberts ($2.31\times {10}^{-4}$), Canny ($5.11\times {10}^{-4}$), Prewitt ($2.6\times {10}^{-5}$), Sobel ($2.7\times {10}^{-5}$), and Log ($3.54\times {10}^{-4}$). This finding indicates that the CST algorithm exhibits superior stability.

In terms of path smoothness, as illustrated in Figure 16c, the average curvature value of the CST algorithm is 0.00003 superior to that of the BFA, 0.18186 greater than that of the Roberts operator, 0.17501 better than the Canny operator, 0.16031 superior to the Prewitt operator, 0.15732 better than the Sobel operator, and 0.14956 greater than the Log operator. These results indicate that the paths extracted by the CST algorithm exhibit the most favorable smoothness characteristics.

In summary, this study systematically verifies the superior performance of the CST algorithm in water boundary measurement tasks through comparative experiments. The experimental results demonstrate that, compared with the brute-force traversal algorithm and five traditional boundary measurement operators, the CST algorithm exhibits significant advantages in both boundary measurement accuracy and path smoothness. Although it may not be the most time-efficient, its robustness and comprehensive performance in complex environments are notably superior to those of the algorithms compared. These advantages render the CST algorithm particularly suitable for engineering applications with stringent measurement accuracy requirements, such as waterway mapping and flood monitoring, thereby providing reliable technical support for intelligent water monitoring.

5.2. Unmanned Surface Vehicle Experiment

To enhance the credibility of the research, this chapter presents a real USV experiment aimed at verifying the feasibility of the CST algorithm. In this experiment, the grid method proposed in [41] was employed to preprocess the satellite map, thereby discretizing the continuous geographic space into regular grids. To comprehensively evaluate the performance of the algorithm, three types of grid maps with varying resolutions, $20\times 20$, $40\times 40$, and $80\times 80$, were established in the experiment, and the CST algorithm was utilized to measure the water body boundary for each. Figure 17a–c illustrate the water body boundary measurement paths planned by the CST algorithm across three resolution grid maps, with yellow dots indicating the measurement path nodes of the algorithm. Based on the path planning results generated by the CST algorithm, the latitude and longitude coordinates of the paths obtained under three grid sizes are input into the USV control system to enable the USV to cruise at a fixed point at a constant speed. The experimental results presented in Figure 18a–c were obtained by recording the actual operating trajectory of the USV in real time, where the red line segment represents the actual sailing trajectory of the USV, and the yellow triangle denotes the sailing direction.

The experimental results demonstrate that the USV can effectively perform water body boundary measurements according to specified instructions across three test scenarios with varying resolutions ($20\times 20$, $40\times 40$, and $80\times 80$). This fully validates the practical operability of the paths generated by the CST algorithm. Significantly, even in complex aquatic environments, the USV maintains stable navigation performance, thereby confirming the algorithm’s robust environmental adaptability and significant engineering value.

To verify the robustness of the CST algorithm in various environments, the research team conducted supplementary experiments. As illustrated in Figure 19, under the new experimental conditions, the measurement paths planned by the CST algorithm in grid maps with three resolutions—20 × 20 (a), 40 × 40 (b), and 80 × 80 (c)—completely covered the target area. The yellow markers in the figure clearly depict the distribution of path nodes generated by the algorithm, with their spatial density significantly increasing as the map resolution improves, which aligns with theoretical expectations. After importing the coordinates of these paths into the USV navigation system, the actual navigation trajectory is displayed in Figure 20. In low-resolution scenarios (a), the red trajectory of the USV, although not closely aligned with the boundary, successfully conducted water body boundary measurements. At medium resolution (b), the trajectory accuracy significantly improved. Under high-resolution conditions (c), the trajectory closely matched the water body boundary, achieving precise detection at complex bends. Notably, in the test area characterized by multiple headlands and coves, the USV did not experience any trajectory loss or collision warnings throughout the process. This result not only verifies the environmental adaptability of the CST algorithm but also reveals the quantitative relationship between map resolution and measurement accuracy: the higher the grid resolution, the more precise the water body boundary measurement.

In conclusion, this study validates the superior performance of the CST algorithm in water body boundary measurement through multiple sets of actual ship experiments. The experimental results demonstrate that the algorithm not only generates precise measurement paths but also exhibits excellent environmental adaptability and robustness in practical applications. These findings confirm the engineering utility of the CST algorithm and provide reliable technical support for the application of USVs in hydrographic surveys.

6. Conclusions

Compared with existing methods reported in the literature, precise measurement of water body boundaries, which is a crucial technology for hydrological monitoring and environmental assessment, currently relies primarily on Geographic Information Systems (GIS) and remote sensing satellite imagery. However, these traditional methods encounter two significant technical bottlenecks in practical applications: First, their measurement accuracy is severely affected by meteorological and lighting conditions, leading to considerable uncertainty in the results; second, the high acquisition costs of high-resolution satellite data and the need for specialized processing software create economic barriers that limit their widespread application in long-term monitoring projects. In response to these challenges, this study innovatively proposes the Chemotactic Search Traversal (CST) algorithm, which optimizes water body boundary measurement through three key technological breakthroughs: first, it integrates the chemotaxis operation mechanism of the Bacterial Foraging Optimization (BFO) algorithm to establish a dynamic distance evaluation model, enabling real-time calculations of the optimal distance between the current node and the nearest obstacle node; second, it develops a node optimization selection strategy based on spatial distribution characteristics, achieving adaptive path planning adjustments by analyzing the topological relationships of surrounding feasible nodes; finally, it constructs a multiobjective optimization function to simultaneously enhance measurement accuracy, minimize path length, and improve energy consumption efficiency.

The experimental results demonstrate that the algorithm significantly enhances the accuracy of water body boundary measurement while also improving the smoothness of boundary extraction. In the full-scale ship experiments, the research team conducted water body boundary measurements by establishing maps with various grid sizes and found a significant positive correlation between map resolution and measurement accuracy. Specifically, higher resolution maps yield measurement results that more accurately reflect the characteristics of the real environment. Future research directions will unfold along three dimensions: First, to address the issue of algorithm time complexity, we plan to adopt parallel computing architectures, such as GPU acceleration, and heuristic rule optimization strategies, aiming to enhance computational efficiency by over 40 while maintaining current measurement accuracy. Second, we will consider introducing a multiagent collaboration mechanism to expand the scope of monitoring through the cluster operations of three–five Unmanned Surface Vehicles (USVs) while researching dynamic task allocation algorithms to resolve collaborative path planning issues. Finally, we will explore adaptive parameter tuning methods based on deep reinforcement learning to enhance the robustness of the algorithm across various hydrological environments, including rivers, lakes, and offshore areas. These improvement directions arise from the limitations of current research in areas such as adaptability to complex environments and efficiency in large-scale water monitoring. The proposed solutions are expected to propel intelligent water monitoring technology towards real-time operation, swarm intelligence, and self-adaptation.