USV Path Planning in a Hybrid Map Using a Genetic Algorithm with a Feedback Mechanism

Abstract

Unmanned surface vehicles (USVs) often operate in real-world environments with long voyage distances and complex routes. The use of a single-grid map model presents challenges, such as the high computational costs for high-resolution maps and loss of environmental information for low-resolution maps. This article proposes an environmental modeling method using a hybrid map that combines topology units and grids. The approach involves calibrating key nodes based on the watershed skeleton line, constructing a topology map using these nodes, decomposing the original map into unit maps, converting each unit map into a grid map, and creating a hybrid map environment model that comprises topology maps, unit map sets, and grid map sets. Then, the article introduces an improved genetic algorithm, called Genetic Algorithm with Feedback (FGA), to address path planning in hybrid maps. Experimental results demonstrate that FGA has better computational efficiency than other algorithms in similar experimental environments. In hybrid maps, path planning with FGA reduces the path lengths and time consumption, and the paths are more logical, smooth, and continuous. These findings contribute to enhancing the quality of path planning and the practical value of USVs.

1. Introduction

Unmanned surface vehicles (USVs) have a wide range of applications, including resource exploration, ocean data acquisition, crisis search and rescue, anti-submarine operations, cruising, and water quality testing [1,2]. Path planning technology plays a crucial role in USV research to devise collision-free optimal or near-optimal paths from the initial point to the destination in a two-dimensional plane [3,4]. The algorithm optimization efficiency directly impacts the solution space for path planning problems, and the number of obstacles in the workspace is a key factor in the combinatorial optimization. Thus, enhancing the algorithm efficiency is essential for improving path planning solutions.

Currently, prevalent intelligent optimization methods to address path planning issues include the ant colony algorithm [5,6,7], particle swarm algorithm [8,9], brainstorming algorithm [10,11], bacterial foraging optimization algorithm [12], reinforcement learning [13,14], and various other optimization techniques. The Genetic Algorithm (GA) is commonly used to solve path planning problems for USVs. Ref. [15] combined the GA with a simulated annealing algorithm to address issues encountered in traditional genetic algorithms, such as limited search capabilities and high computational requirements. By introducing insertion and deletion operators, this method enhances the population evolution efficiency and optimizes the path generation process for USVs. Ref. [16] proposed a novel energy-saving path planning algorithm by combining the Voronoi roadmap algorithm, Dijkstra search algorithm, coastline extension algorithm, and GA. This new algorithm addresses the difficulties posed by spatially temporally variant sea currents and complex geographic map data. Ref. [17] introduced an enhanced GA to address the USV path planning problem. This algorithm increased the number of offspring by implementing the multi-domain inversion. In addition, a secondary fitness evaluation was performed to filter out undesirable offspring while retaining the most advantageous individuals. These improvements strengthened the effectiveness of the local search and the likelihood of producing high-quality individuals. Ref. [18] introduced an improved GA to create a higher quality initial population. Here, adaptive crossover and mutation probabilities were designed for enhanced performance. To enhance the capability of the robot to avoid dynamic obstacles and efficiently determine shorter and smoother paths, Ref. [19] introduced a fusion algorithm that combines an enhanced GA with the dynamic window approach. Ref. [20] introduced an enhanced genetic algorithm (IGA) that focused on finding the shortest path for USVs to reach the task nodes. Ref. [21] designed an adaptive genetic algorithm(AGA). In this algorithm, crossover and mutation formulas are designed, and path smoothness is introduced as a criterion for judging path quality in the fitness function.

GA is a frequently utilized method to address path planning problems. Despite demonstrating effective search results, optimization strategies such as feedback are often overlooked in enhancing the search efficiency of an algorithm. Feedback involves leveraging optimization data from previous generations to influence the search behavior of the current generation to enhance the overall population quality. This article introduces a Genetic Algorithm with Feedback (FGA) to tackle the limitations of the conventional GA in solving the path planning problem, particularly for issues such as a slow convergence speed. In FGA, the population is stratified into two subpopulations according to the individual quality with a defined population quality metric. Then, feedback mechanisms are incorporated to assess the evolutionary traits of the population and dynamically adjust the crossover and mutation probabilities for each subpopulation to optimize the balance between the global and local search capabilities of the algorithm. This refinement enhances the solution quality of FGA. Subsequent comparative experiments demonstrate that FGA exhibits rapid convergence and high accuracy in addressing the USV path planning problem. Currently, common environmental modeling methods to solve path planning problems are the visual graph method [22], Voronoi graph method [23], grid map method [24], and the element decomposition method [25]. The grid map method is frequently used for environmental modeling due to its simplicity, intuitiveness, ease of use, and broad applicability. Ref. [26] introduced a weight heuristic A* algorithm to demonstrate the path planned on a 2D grid map with obstacles in a windless environment. Ref. [27] presented a Plant Grow Route (PGR) algorithm that incorporated a raster method as the spatial environment model for USVs. Ref. [28] proposed an A* with velocity variation and a global optimization algorithm to vary the velocity to avoid obstacles in path planning by including a temporal dimension in the map modeling process. The basic search map was a 2D grid map. Ref. [29] presented a novel path planning method based on a modified artificial fish swarm algorithm in combination with a path optimizer. To verify the effectiveness of the proposed methods, eight scenarios of binary maps were considered, including complex grid maps and open water cases. Ref. [30] presented a Predicted Trajectory Approach (PTA) for the global motion planning of an underactuated USV. In the present strategy, the predicted trajectories produced by the mathematical model of the USV are decomposed into a series of waypoints on the grid map.

The literature used the grid map method for environmental modeling and validated the algorithm for path planning on a single grid map. However, due to the operational conditions of USVs encompassing expansive areas with elongated rivers, conventional approaches that use high-resolution grid maps increase the computational complexity and time consumption. Low-resolution grid maps may result in a loss of environmental information, which impacts the accuracy of path planning. This article introduces an environment modeling method that uses a topology-unit-grid hybrid map to tackle path planning challenges in scenarios with long and narrow rivers in large-scale USV working environments. The approach calibrates key nodes in a high-resolution watershed map, creates a topology map from these nodes, decomposes the original map into a unit map set, processes this set to generate a grid map set, and ultimately constructs a hybrid map environment model. This method effectively balances the environmental modeling accuracy and path planning computational efficiency and offers a viable solution for USV path planning. Comparative experiments demonstrate that the hybrid map environment model reduces the path length and time and produces more reasonable and smooth continuous paths.

Due to the complexity and vastness of the USV working area, utilizing a GA algorithm for path planning alone results in high calculation costs. This study introduces a two-stage approach to path planning. The first stage presents a methodology for modeling a hybrid map environment combining topology and unit grids, specifically designed for large and complex single maps. This addresses both global path planning on topological graphs and local path planning on multiple smaller raster maps. The second stage introduces the FGA algorithm, aimed at enhancing the convergence speed of path planning on raster maps.

The paper presents a novel environment modeling approach using a hybrid topological cell grid map to address path planning challenges on a large and complex single map. This method transforms the path planning problem into global path planning on topological graphs and local path planning on smaller raster maps. Additionally, the paper introduces a feedback mechanism into the traditional genetic algorithm, enhancing information exchange among individuals and accelerating algorithm convergence. By integrating hybrid maps and feedback genetic algorithms, the proposed approach enables effective path planning for USVs in both local and global scenarios.

This paper is organized as follows: Section 2 details the implementation of the USV topology-unit-grid hybrid map environment modeling method, while Section 3 explains the implementation of the FGA algorithm. Section 4 presents simulation and comparison results to validate the efficacy of the proposed method. Finally, Section 5 provides a summary of the entire text.

2. Environmental Model

2.1. Grid Map

A USV typically consists of a stationary or dynamic surface, and the workspace is always confined to a 2D plane. Environmental modeling is crucial for solving path planning issues, and it converts the USV navigation plane into a digital format that algorithms can analyze. Commonly used methods for environmental modeling include the visual graph method, grid method, free space method, and the topology method. Among these methods, the grid method is favored for its simplicity, ease of implementation, and capability to effectively represent irregular obstacles. This paper focuses on utilizing the grid method to construct a foundational environmental model for USV operations, as depicted in Figure 1, where the black area signifies obstacles in the working environment of the USV, and the white area indicates feasible regions for the USV.

The motion space of the USV is visualized on a 2D plane, where X is the horizontal axis, and Y is the vertical axis. The values for the horizontal and vertical axes range from the minimum scale of half of the grid unit to the maximum side length of the grid map. Each coordinate (x, y) in the plane corresponds to a sequential number: grid (1,1) in the upper left corner is numbered 1, the next grid counted horizontally (2,1) is numbered 2, and so forth. The mathematical relationship between coordinates and sequential numbers in a grid-based working environment is represented by Formula (1):

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

(1)

where mod() is the remainder operation and Ceil() is the rounding-up operation.

2.2. Hybrid Map

This section introduces the construction method of a hybrid map environment model based on binarized satellite watershed maps. In this map, white pixels represent watershed areas, and black pixels represent obstacles. Key nodes are extracted from the map to create a topology node map for the preliminary global path planning. Then, the original watershed map is decomposed into unit maps using key nodes with the unit decomposition method. Each unit diagram has two key nodes, and adjacent unit diagrams share the same key node. These unit images are converted into a grid to create a grid map set, where the USV occupies a pixel for local fine path planning. This method establishes a topology-unit-grid hybrid map environment model, as shown in Figure 2.

2.2.1. Topology Map Construction

This section uses a refinement algorithm to generate the skeleton lines of the watershed and uses these lines to select topological features for constructing the topology map. The Zhang Suen fast parallel algorithm [31], which is used to generate the skeleton lines of the watershed, is known for its fast speed, ability to maintain the connectivity of the refined curve, and absence of burrs. The steps of the algorithm are as follows:

• Traverse the points with values of 1 in the binary image and their eight neighboring points to form a 3 × 3 window image, as shown in Figure 3. Based on deletion condition 1, determine whether to delete the point: deletion implies assigning a value of 0, and retention implies keeping it as 1.
• Traverse the points with values of 1 in the binary image. Generate a 3 × 3 binary image as in step 1 and determine whether to delete the point based on deletion condition 2. The deletion process is identical to that in step 1.
• Iterate step 1 and step 2 repeatedly until there are no points to delete.

Delete condition 1:

$$\begin{array}{c}\left(a\right)2\le \mathrm{B}\left(\mathrm{P}1\right)\le 6\hfill \\ \left(b\right)A\left(P1\right)=1\hfill \\ \left(c\right)P2\ast P4\ast P6=0\hfill \\ \left(d\right)P4\ast P6\ast P8=0\hfill \end{array}$$

Delete condition 2:

$$\begin{array}{c}\left(a\right)2\le \mathrm{B}\left(P1\right)\le 6\hfill \\ \left(b\right)A\left(P1\right)=1\hfill \\ \left(c\right)P2\ast P4\ast P8=0\hfill \\ \left(d\right)P2\ast P6\ast P8=0\hfill \end{array}$$

where A(P1) is the number of transitions from 0 to 1 in the P2 → P3 → P4 → P5 → P6 → P7 → P8 → P9 → P2 sequence, and B(P1) is the number of pixels in domain P1 that have values of 1.

In this paper, the topological features of the watershed are analyzed by extracting the key nodes from the skeleton lines. These features are categorized into three main types and must be extracted in a specific order. The first type is the endpoint of the skeleton line, which is the terminal point along the line. The second type is the intersection point of skeleton lines, where two or more lines meet. Finally, the interval point involves selecting two connected points, such as ➀ and ➁, from all endpoints and intersections. Starting from point ➀ (or point ➁), an interval point ➀ is selected along the skeleton line to ensure that the maximum distance between this point and point ➀ in the horizontal or vertical direction is equal to ${\mathrm{Cut}}_{\mathrm{L}}$. Subsequently, interval point ➁ is selected to ensure that the maximum distance between this point and the previous interval point ➀ is also equal to ${\mathrm{Cut}}_{\mathrm{L}}$. This process continues until the maximum distance between the selected point and point ➁ is less than or equal to ${\mathrm{Cut}}_{\mathrm{L}}$. The unit map length ${\mathrm{Cut}}_{\mathrm{L}}$ is determined following Formula (2):

$${\mathrm{Cut}}_{\mathrm{L}}=US{V}_{size}\ast r_{size}$$

(2)

where $US{V}_{size}$ is the number of pixels occupied by the width of the USV in this map, and $r_{size}$ is the size of the grid map during path planning. If $US{V}_{size}$ is taken as 4 and $r_{size}$ is taken as 25 in this article, then ${\mathrm{Cut}}_{\mathrm{L}}$ is equal to 100.

After successfully identifying three types of key nodes, one must designate a fourth type of key node in the watershed based on the specific circumstances, that is, the parking location of the USV. In Figure 4, the images show the extracted representations of these four types of key nodes. Black pixels in the images represent obstacles, white pixels indicate areas where the USV can navigate, and blue pixels outline the skeleton of the watershed. Red dots mark the endpoints of the skeleton, green dots mark the intersections of the skeleton, yellow dots are the interval points, and teal dots are the parking points.

After the key nodes have been extracted, the next step is to draw the node topology diagram, as shown in Figure 5.

2.2.2. Construction of the Unit Mapping Set

Upon construction of the node topology map, the watershed map should be decomposed into unit maps based on the node configuration to establish a set of unit maps. Each unit map is constructed using two adjacent nodes as the fundamental unit, where one point is designated as the starting point, and the other is the ending point. Before this process, the segmentation point must be identified based on the positional alignment of the two nodes. If the longitudinal distance between two points exceeds the transverse distance, the segmentation point can be determined according to Formula (3):

$$\begin{array}{c}Cu{t}_x=min(Star{t}_x,En{d}_x)+abs(Star{t}_x-En{d}_x)/2+Cu{t}_L/2\hfill \\ \left\{\begin{array}{c}Cu{t}_y=Star{t}_{y}Star{t}_y\le En{d}_y\hfill \\ Cu{t}_y=Star{t}_y-{\mathrm{Cut}}_{\mathrm{L}}+1Star{t}_y>En{d}_y\hfill \end{array}\right.\hfill \end{array}$$

(3)

If the longitudinal distance between two points is less than the transverse distance, the segmentation point can be calculated according to Formula (4):

$$\begin{array}{c}Cu{t}_y=min(Star{t}_y,En{d}_y)+abs(Star{t}_y-En{d}_y)/2+Cu{t}_L/2\hfill \\ \left\{\begin{array}{c}Cu{t}_x=Star{t}_{x}Star{t}_x\le En{d}_x\hfill \\ Cu{t}_x=Star{t}_x-{\mathrm{Cut}}_{\mathrm{L}}+1Star{t}_x>En{d}_x\hfill \end{array}\right.\hfill \end{array}$$

(4)

where $Cu{t}_x$ is the horizontal coordinate of the segmentation point in the watershed map, $Cu{t}_y$ is the vertical coordinate of the segmentation point in the watershed map, $Star{t}_x$ is the horizontal coordinate of the starting point in the watershed map, $Star{t}_y$ is the vertical coordinate of the starting point in the watershed map, $En{d}_x$ is the horizontal coordinate of the endpoint in the watershed map, $En{d}_y$ is the vertical coordinate of the endpoint in the watershed map, $Cu{t}_L$ is the pixel length of the unit map, min() is the minimum value function, and abs() is the absolute value function.

After the segmentation point has been determined, the watershed map is segmented using a square window with a side length of $Cu{t}_L$. The segmentation point will be aligned with the top left vertex of this window. Figure 6 shows three different unit maps: (a) a unit map with node 1 as the starting point and node 15 as the ending point, (b) a unit map with node 15 as the starting point and node 41 as the ending point, and (c) a unit map with node 41 as the starting point and node 16 as the ending point.

2.2.3. Construction of the Grid Map Set

Upon successfully obtaining the unit map, all unit maps can be converted into a grid map of size n. Figure 7 shows the grid map rendering process, where subparts (a), (b), and (c) correspond to the conversions of subparts (a), (b), and (c) in Figure 6, respectively.

3. Path Planning Based on the Genetic Algorithm with Feedback

3.1. Encoding

The path of the USV is represented by grid numbering to ensure no obstacles or duplicates in each path. This method converts continuous paths into discrete sequence number combinations, makes all individuals in the initial population effective paths, and improves the overall quality of the population.

3.2. Population Initialization

To ensure diversity in the initial population P, a random path of size M is generated. The process begins with the USV starting from point S and marking it as an obstacle. Then, the USV randomly selects a free grid adjacent to the current point and repeats this process until reaching the endpoint G.

3.3. Fitness and Population Quality Calculation

The fitness value of an individual in this study is calculated as the reciprocal of the path length, where its magnitude is a direct measure of the individual’s quality. The fitness function is given by Formula (5)

$$Fi{t}_i=\frac{1}{{\displaystyle \sum _{i=S}^G}nod{e}_{i,i+1}}$$

(5)

where S and G are the starting point and endpoint of the USV, respectively.

We calculate the fitness size of individuals based on the fitness function, divide individuals with fitness values below the average into subpopulations, and divide other solutions into subpopulations. The quality definition of the t-th generation population P is according to Formula (6):

$${\mathfrak{M}}_{t,su{b}_m}=Fi{t}_{su{b}_m,best,i}+\eta ·\frac{{\displaystyle \sum _{j=1}^{\left|su{b}_m\right|}}Fi{t}_j}{N-1}(j\ne i,m=1,2)$$

(6)

where $Fi{t}_{su{b}_m,best,i}$ is the fitness value of the optimal solution in the t-th generation subpopulation $su{b}_1$ with parameter $\eta$ = 0.2. From Equation (6), a larger ${\mathfrak{M}}_{t,su{b}_m}$ corresponds to a better quality subpopulation.

3.4. Genetic Operators

The genetic operator comprises selection, crossover, and mutation operations, as inspired by the evolutionary principle of “survival of the fittest” in species evolution. Evolution is driven by the individual fitness, where higher fitness individuals are more likely selected for evolution. This article uses the roulette wheel selection method to construct the next generation population in the following selection process:

• Calculate the selection probability of each solution $x_i$ in $su{b}_1$ following Formula (7):

  $$p_i=\frac{Fi{t}_i}{{\displaystyle \sum _{j=1}^{\left|su{b}_1\right|}}Fi{t}_j}$$

  (7)

  where $p_i⩾0$; $p_1+p_2+\cdots +p_{\left|su{b}_1\right|}=1$; $i=1,2$.
• Use Formula (8) to calculate the cumulative probability of each solution $x_i$.

  $$q_i={\sum }_{j=1}^i{p}_j,i=1,2,\cdots ,\left|su{b}_1\right|$$

  (8)
• Repeat the following steps $\left|su{b}_1\right|$ times.

  (a)

  Generate a uniformly distributed random number $rand$ between [0,1];

  (b)

  If $rand⩽q_1$, select solution $x_1$ as the genetic individual of the next generation; otherwise, if $q_{i-1}<rand<q_i$ and $i>1$, select solution $x_i$ as the genetic individual of the next generation.

Ref. [21] shows the specific steps for the crossover and mutation operations. Let the crossover probabilities be $p_{c,su{b}_1}={\gamma }_1$ and $p_{c,su{b}_2}={\gamma }_2$ and the mutation probabilities be $p_{m,su{b}_1}={\beta }_1$ and $p_{m,su{b}_2}={\beta }_2$. Set ${\gamma }_1<{\gamma }_2$ and ${\beta }_1>{\beta }_2$. This method enables each of the two subpopulations to evolve with different focuses; the higher quality subpopulation focuses on the local search, and the lower quality subpopulation focuses on the global search. After the crossover and mutation operations have been completed, calculate ${\mathfrak{M}}_{t+1,su{b}_m}(m=1,2)$ of the population. If ${\mathfrak{M}}_{t+1,su{b}_m}<{\mathfrak{M}}_{t,su{b}_m}$, maintain the crossover and mutation probabilities of subpopulation $su{b}_m$ unchanged; otherwise, if $p_i=p_1$, then $p_{c,su{b}_1}={\gamma }_2$, $p_{m,su{b}_1}={\beta }_2$; if $p_i=p_2$, then $p_{c,su{b}_2}={\gamma }_1$, $p_{m,su{b}_2}={\beta }_1$. After the crossover and mutation operations, assess the quality of the subpopulation to dynamically adjust the feedback mechanism of the crossover and mutation probabilities in the next-generation evolution process, which effectively enhances the optimization efficiency of the GA.

4. Calculation Experiments and Analysis

4.1. Path Planning Experiment Based on the Genetic Algorithm with Feedback

This experiment was conducted on a 64-bit operating system with an Intel^® Core^TM i5-8300H CPU @ 2.30 GHz and 8.00 GB of memory. MATLAB software was used to run simulation experiments on three algorithms: FGA, GA, and AGA. The environment had a grid size of 20 × 20, where three randomly distributed environmental conditions featured obstacle proportions of 30%, 40%, and 50%, as illustrated in Figure 8.

The main parameters of FGA were $N,{\gamma }_1,{\gamma }_2,{\beta }_1,{\beta }_2$ and the maximum number of iterations T. Three levels for each parameter were selected: N: 80, 100, and 120; ${\gamma }_1$: 0.4, 0.5, and 0.6; ${\gamma }_2$: 0.7, 0.8, and 0.9; ${\beta }_1$: 0.2, 0.3, and 0.4; ${\beta }_2$: 0.1, 0.2, and 0.3. Orthogonal experiment is an important design method to study multiple factors and levels, through which the relative optimal parameter combination of the experiment can be determined. For a grid size of 20 × 20, the optimal parameter combination for FGA search quality was determined through orthogonal experiments as $N=120, {\gamma }_1=0.5, {\gamma }_2=0.8, {\beta }_1=0.3, {\beta }_2=0.1$. The parameters of GA were $N=120$, $p_c=0.5$, and $p_m=0.1$. The parameter settings of AGA are consistent with those in reference [21]. The termination condition for all three algorithms was set to the maximum number of iterations, i.e., T = 100.

In Figure 9, the iterative curves of the three algorithms converged to the optimal solution in the maps with obstacle proportions of 30%, 40%, and 50%. In Figure 9a, FGA successfully identified the global optimum of 29.799 in the 15th generation, i.e., it outperformed GA and AGA. In Figure 9b, FGA reached the global optimum of 29.213 in the 30th generation. In Figure 9c, FGA reached the global optimum of 30.385 in the 28th generation. These results suggest that FGA has a notably better convergence speed than the comparison algorithm.

Considering the impact of various random factors, 20 independent experiments were conducted with FGA, GA, and AGA in the specified environments.

Table 1. Data table of path planning results in three experimental environments.

The Proportion of Environmental Obstacles	Algorithm	Average Number of Iterations	Optimal Path	Worst Path	Average Path	Standard Deviation (Std.) of Path Length
	FGA	79.95	29.80	33.56	32.15	0.972
30%	AGA	80.25	30.39	36.97	32.24	1.38
	GA	84.10	29.80	33.80	31.74	1.09
	FGA	70.90	29.21	32.39	30.31	0.75
40%	AGA	73.95	29.21	32.39	30.87	0.95
	GA	74.15	29.21	32.39	30.55	0.85
	FGA	64.20	30.39	34.14	31.85	1.21
50%	AGA	64.40	30.39	34.73	32.36	1.22
	GA	65.10	30.97	34.97	32.30	1.24

presents the statistical results of the path length and iteration times from each simulation, including the average number of iterations, optimal solution path length, worst solution path length, average solution path length, and the standard deviation of the path length across environments. The quantity and arrangement of obstacles in a grid map directly affect the feasible solutions for combinatorial optimization problems. In this study, obstacles were randomly distributed with a linear increase in number. The data in Table 1 reveal that FGA outperforms GA and AGA in terms of the average iterations, optimal path length solution, worst path length solution, average path length, and standard deviation of the path length under varying obstacle distributions. Thus, FGA performs better than GA and AGA.

To enhance the credibility of the proposed algorithm, the satellite map of a specific region was used as the real-world navigation environment for the USV. Then, this map was converted into the grid map outlined in this study. The ultimate experiment used the FGA to determine the most optimal path in the grid map, as depicted in Figure 10.

4.2. Experimental Path Planning Based on Hybrid Maps

Path planning algorithms were applied to grid map environment models with varying grid resolutions on the same map and the hybrid map environment model developed in this study. Simulation experiments were performed to statistically compare and analyze the path length and planning time of path planning across different environment models. Figure 11b–f illustrate the environmental models with different grid resolutions (from 20 × 20 to 150 × 150). Figure 11g shows a hybrid map environmental model developed according to the methodology in this paper. The experiment involved conducting path planning from parking location 15 to parking location 17 in various environmental models.

Figure 12 illustrates the optimal path generated using the FGA across various environmental models. To account for the impact of random factors on the algorithm performance, FGA conducted 20 independent experiments in different environmental settings. In Figure 12a, the limitations of a 20 × 20 grid map, such as the inability to accurately represent obstacles and other features, hindered the path planning algorithm from finding the optimal path. Figure 12b–e show that increasing the resolution of the grid map can lead to an unreasonable optimal path due to potential overfitting issues. The algorithm may focus too much on minor map details, neglect the overall path planning objectives, and potentially get trapped in the local optima. Conversely, Figure 12f reveals that the optimal path in the hybrid map environment model is more sensible than that in the other models, since it exhibits smoother and more continuous connections between path points.

The study utilized the FGA, AGA, and GA to conduct 20 experiments in various environmental models. Figure 13 and Figure 14 show the path length and time consumption from each simulation as boxplots, respectively. Figure 13 reveals that in the grid map environment, smaller grid map scales correlate with less time consumption and a higher data concentration. For a 60 × 60 grid map environment, the average time consumption of the FGA, AGA, and GA was 41.58412, 16.3603, and 15.55993, respectively. In the hybrid map environment model discussed in this study, the average time consumption of the FGA, AGA, and GA was 23.95037, 11.78067, and 13.36005, respectively, which demonstrates a significant improvement over the 60 × 60 grid map environment. Figure 14 shows that in the grid map environment, smaller grid map scales result in shorter path lengths and higher data concentrations. For a 60 × 60 grid map environment, the average path length of the FGA, AGA, and GA was 383.5316, 387.3097, and 385.9917, respectively. In the hybrid map environment model, the path planning length was more concentrated; the average path length of the FGA, AGA, and GA was 370.2344, 374.5113, and 370.4912, respectively, which also shows significant improvement over the 60 × 60 grid map environment. These experimental findings highlight the superior path planning performance of the hybrid map environment model in terms of length, planning time, and path smoothness compared to a single grid map environment.

5. Conclusions

The path planning of USVs in a single-scale scenario is challenged by the high computational costs of high-resolution maps and the loss of environmental information with low-resolution maps. This article introduced an environmental modeling approach using a hybrid map, which consisted of topology maps, unit map sets, and grid map sets, and enhanced the algorithmic solution quality through FGA.

The construction of a topological map was achieved through the extraction of river skeleton lines and key nodes as topological features using the Zhang Suen fast parallel algorithm. This paper introduces a method of unit decomposition based on key nodes for constructing a unit atlas, which is then rasterized to create a raster atlas. By constructing a composite map that combines genetic algorithm path planning with raster maps, it ensures a quick convergence of the path planning process while retaining sufficient environmental information. The FGA algorithm utilizes optimization data from previous generations to enhance the search behavior of the current generation, thereby improving the overall population quality. Compared to traditional genetic algorithms, the FGA algorithm demonstrates faster convergence speed. The effectiveness of these methods is validated through two sets of experiments in this study.

Future research will investigate adaptive scale adjustments of the hybrid map to adapt to varying environmental conditions and more intricate working scenarios. This includes incorporating USVs and drones in dynamic environments for path planning. Additionally, we plan to validate and optimize in real water environments, while also taking into account path planning considering USV energy loss.