Global Path Planning of Unmanned Surface Vehicle in Complex Sea Areas Based on Improved Streamline Method

Abstract

In this paper, an innovative method is proposed to improve the global path planning of Unmanned Surface Vehicles (USV) in complex sea areas, combining fluid mechanic calculations with an improved A* algorithm. This method not only generates smooth paths but also ensures feasible global solutions, significantly enhancing the efficiency and safety of path planning. Firstly, in response to the water depths limitation, this study set up safe water depths, providing strong guarantees for the safe navigation of USVs in complex waters. Secondly, based on the hydrological and geographical characteristics of the study sea area, an accurate ocean environment model was constructed using Ansys Fluent software and computational fluid dynamics (CFD) technology, thus providing USVs with a feasible path solution on a global scale. Then, the local sea area with complex obstacles was converted into a grid map to facilitate detailed planning. Meanwhile, the improved A* algorithm was utilized for meticulous route optimization. Furthermore, by combining the results of local and global planning, the approach generated a comprehensive route that accounts for the complexities of the maritime environment while avoiding local optima. Finally, simulation results demonstrated that the algorithm proposed in this study shows faster pathfinding speed, shorter route distances, and higher route safety compared to other algorithms. Moreover, it remains stable and effective in real-world scenarios.

1. Introduction

With the rapid development of communication, navigation, and artificial intelligence, the Unmanned Surface Vehicle (USV) has become an important research topic in the field of maritime studies. Due to its compact size, shallow draft, easy deployment, and high mobility, it is widely used in harbor patrols [1], sea rescues [2], marine resource exploration [3], and other tasks. Path planning is one of the core technologies for the autonomous navigation of USVs, directly affecting the navigation efficiency, safety, and mission completion quality of USVs. Therefore, generating a reliable and safe global path is essential for the realization of autonomous navigation of USVs.

The predominant path planning methods include search algorithms based on existing map information, random sampling algorithms, and intelligent optimization algorithms. The Dijkstra algorithm [4] is known for determining the shortest path between points. However, it can be slow due to irrelevant node expansion. In contrast, the A* algorithm enhances efficiency with a heuristic function and is widely used in ship path planning [5,6]. However, these algorithms have complex computations and high memory consumption, making them unsuitable for large environments. To address this issue, Gu [7] proposed using AIS data with the Rapidly exploring Random Tree(RRT) algorithm to enhance navigation safety and reliability. However, due to the random sampling properties, finding the optimal solution using the RRT algorithm is not guaranteed, and the searched paths often contain many sharp turns. During navigation, the path should be smooth to enhance USV efficiency and ensure safety. Therefore, Sang [8] proposed a multi-target artificial potential field algorithm based on an improved artificial potential field that complies with USV constraints and ensures smooth paths but struggles with local minima and jitter in complex environments. In addition, the algorithm needs to take into account the requirements of the ship’s characteristics.

To cope with the limitations of USVs, such as insufficient propulsion, large inertia, and time delays, and to ensure that they can accurately follow their intended routes, path planning must consider multiple objectives simultaneously, such as shortest path, safety, smoothness, and control constraints. In interdisciplinary applications, multi-objective optimization algorithms and strategies for Unmanned Aerial Vehicles can be borrowed to improve the efficiency and adaptability of the path-planning system [9,10,11,12]. Intelligent optimization algorithms solve the optimal path problem by constructing a cost function applicable to multiple constraints [13,14,15]. However, in practical applications, they may face challenges such as premature convergence, local optimality, difficult parameter tuning, large computational complexity, and slow convergence speeds.

In recent years, a streamline method incorporating the concept of ideal fluid from fluid mechanics has been integrated into path planning [16]. By constructing potential fields and generating smooth paths, Fluid dynamics methods effectively resolve issues of local minima and oscillations found in traditional algorithms and avoid the path distance issues associated with graph search algorithms. These methods have been applied to underwater gliders and USVs [17,18]. Suner [19] combined two-dimensional potential flow theory and computational fluid dynamics (CFD) to develop a traffic separation scheme for dynamic route planning in narrow channels. Zhang [20] proposed a flow-based VF-RRT* method that optimizes USV navigation in ocean currents. This approach used upstream coefficients, biased sampling, and tree pruning to generate smoother, quicker paths in dynamic oceanic environments. Zhou [21] proposed a customized fluid-guided incremental path planning method for USVs. This method thoroughly considers the dynamic factors of USVs, incorporating vortices and strictly adhering to international collision avoidance regulations. It effectively addresses the challenges posed by multiple dynamic obstacles in maritime traffic. However, while the streamline-based approach provides a smooth sailing path for USVs based on the principles of hydrodynamics, improvements are still needed in dealing with complex Marine environments.

Existing route planning algorithms often ignore the marine environment’s complex features and potential hazard factors, which are crucial considerations in route design to avoid risks such as ship grounding or collision. Safe water depths and minimum draft requirements are critical in shipping and waterborne construction, and ensuring adequate water depths for ships during navigation and berthing can significantly reduce the risk of grounding, thus protecting the ship’s safety [22,23,24]. Pan [25] proposed a modeling technique based on Delaunay triangulation to calculate safe water depths for ship navigation. This model also takes into account the size of the ship and tidal heights and uses Dijkstra’s algorithm to solve the adjusted network for adaptive path design. Yang [26] proposed a method that determines whether to activate surface or aerial navigation mode based on the current water depths. Setting a water depth reward function to control the timing of aerial flight and surface navigation ensures the safe operation of amphibious USVs in various environments, effectively avoiding risks. In addition to high-precision bathymetric data for enhanced accuracy and adaptability, it is crucial to consider USV characteristics and wave height factors to ensure vessels can safely navigate complex hydrographic conditions. The current study did not adequately consider the complex interaction of these factors.

In summary, the study of USV path planning in complex seas is still challenging and requires further research. In path planning studies, current methods often overlook marine environment characteristics and potential hazards, leading to planning outcomes that are less accurate and comprehensive. Many existing algorithms prioritize minimizing path length or energy consumption alone as evaluation criteria, neglecting navigation safety concerns. This oversight can cause planned routes to veer dangerously close to the boundaries of non-navigable areas, thereby heightening the risk of collisions. In this study, we propose a method that significantly enhances the navigation safety and efficiency of USVs in complex maritime environments. The main contributions are as follows.

• To enhance the navigation safety of USVs in complex maritime environments such as densely islanded areas and shallow waters minimum safe water depths have been established in this study.
• This study employs CFD technology to determine globally feasible paths for USVs, avoiding local optima. For complex maritime regions and areas with unknown hazards, we identified and marked potential dangers, using the improved A* algorithm for local path planning. This approach ensures a more comprehensive and practical global planning strategy.

2. Method

2.1. Process Framework

We employed a combined global and local path design approach to generate an overall decision-making planning path. The design process is illustrated in Figure 1. Firstly, environmental modeling preparation is conducted, including extracting ocean depth data and creating a three-dimensional depths map. Based on the characteristics and parameters of the USV, the minimum safest depth is determined, and the minimum safest depth contour lines are delineated to ensure navigation safety. Secondly, during the path planning stage, the streamline method simulates fluid motion within the flow field for path planning. Global path searching is performed in complex environments to avoid local optima. GeoNetworking-mode is introduced to alert against hazardous zones in locally complex sea areas and the improved A* algorithm is employed for detailed planning. This combined approach enhances the precision of path planning and ensures navigation safety and efficiency.

2.2. Global Streamline Method

The streamline method is a commonly used fluid mechanics analysis method, and its principle is inspired by the natural phenomenon of flowing water avoiding obstacles. When using the streamline method for trajectory planning, the environment is abstracted as a flow field and non-navigable areas are considered obstacles. By simulating fluid movement in the flow field, some streamlines that avoid obstacles can be generated, as shown in Figure 2. The advantage of this method is that the fluid can automatically find the desired outlet and flow out in a given scene due to its global path search capability. This approach avoids the issue of falling into local optimal solutions and is suitable for handling more complex environmental scenes. In addition, due to the flow characteristics of the fluid itself, the final planned route is relatively smooth and meets the restrictions of USV navigation. The article constructs an accurate and reliable chart environment model, calculates the fluid velocity field, and plots the streamlines using fluid dynamic theory, which can find the faster streamlines in the globally feasible solution and provides a reference for route selection.

The complexity and variability of maritime navigation conditions result in highly complex wave flows. In order to simplify the model, the following assumptions must be made by selecting the appropriate fluid calculation equations: consider the fluid as inviscid and ignore heat exchange due to viscous forces. The fluid is also assumed to be incompressible and its density is constant, not varying with time or position. Therefore, the fluid satisfies the law of conservation of mass, momentum, and energy. This paper satisfies the following two basic equations:

Conservation of mass (continuity) equation:

$$\nabla ·\left(\rho v\right)=0$$

(1)

Conservation of momentum equation:

$$\rho (dv/dt)=-\nabla p$$

(2)

where $\rho$ is the fluid density, v is the fluid velocity vector, ∇ is the gradient operator, · is the divergence operator, and $(dv/dt)$ is the time derivative of the fluid velocity vector (i.e., the acceleration of the fluid) and its pressure.

With the development of high-performance computers, computer simulation is widely used in various fields. CFD uses numerical analysis to simulate fluid flow and calculate fluid forces quickly, accurately, and reliably. Its primary advantage is its ability to find the optimal numerical solutions to nonlinear control equations under complex geometries and boundary conditions. Considering complex hydrodynamic factors, CFD can accurately predict USV motion and response in the ocean, enabling precise route planning. CFD technology is flexible and applicable to different environments and mission requirements, saving the time and resources required to find the optimal navigation strategy for the current situation. In this paper, CFD software is used to simulate the motion state of USVs in a natural marine environment, quickly predict the flow state, and visualize and analyze it in detail, which helps to evaluate the advantages and disadvantages of different routes and guide smarter decisions. Although the streamline method can provide a global solution, its limitation is that the water flow only turns when it encounters an obstacle. It is impossible to predict and avoid obstacles in advance. To overcome this issue, local complex sea areas are divided and planned to ensure the USV can navigate safely and efficiently in regional areas. USVs typically have longer reaction times for collision avoidance and require less precision in their movements in open ocean environments, where obstacles are sparse. On the other hand, more precise route planning is required to account for the size and obstacle avoidance requirements of the USV in regions with dense obstacles. Therefore, the precision of route planning should be adjusted according to the environment’s obstacle density and the USV’s size. In this paper, an improved A* algorithm is used, and the risk level of each grid is considered when planning for the safe navigation of a segmental local complex maritime area using a USV.

2.3. Locally Improved A* Algorithm

The A* algorithm is a standard path search algorithm, usually used to find the shortest path in a graph. It combines the advantages of the Dijkstra algorithm and the greedy best–first search and uses a heuristic function to guide the search process. The basic idea is to evaluate the cost of each node to determine the optimal path. During the search, nodes are selected through the two-state tables of $Openlist$ and $Closelist$. The search is based on the grid map and each node is examined. The path nodes to be examined are placed in the $Openlist$ table, and the nodes that have been examined are placed in the $Closelist$ table. The cost value evaluation function examines the nodes to find the optimal path. The path evaluation function is:

$$F\left(n\right)=g\left(n\right)+h\left(n\right)$$

(3)

where $F\left(n\right)$ is the total cost from the starting point to point n, $g\left(n\right)$ is the actual cost from the starting point to point n in the running environment, and $h\left(n\right)$ is the estimated cost of the best path from point n to the target point.

There are four-directional search and eight-directional search patterns. Considering the movement characteristics of the USV in the ocean, this paper used the eight-directional search pattern to search the navigable waters, as shown in Figure 3, where $g\left(n\right)$ is the distance from the starting point to the current node and $h\left(n\right)$ is the estimated distance from the current node to the target node, calculated using the Euclidean distance:

$$h\left(n\right)=\sqrt{{\left(x_g-x_c\right)}^2+{\left(y_g-y_c\right)}^2}$$

(4)

where $(x_g,y_g)$ is the coordinate of the target point and $(x_c,y_c)$ is the coordinate of the current node.

Generally speaking, the traditional A* algorithm evaluates many nodes with low overall efficiency. When planning a path, many redundant points are generated. In a complex search space, especially when the number of nodes and edges is large, the A* algorithm may require many computing resources, affecting performance and efficiency. This paper improves the algorithm from the following three aspects.

• Add safety distance

The traditional A* algorithm usually only considers path length as an evaluation function when finding a path, which may cause the planned path to be too close to the edge of an unnavigable area, such as a shoal, coral reef, or artificial obstacle, thereby increasing the risk of collision or of being affected by environmental factors, posing a potential threat to the safe navigation of the USV. To solve this problem, we introduced a “safe distance” constraint as part of the algorithm when finding the path, ensuring that the planned route is away from the edge of the dangerous area, significantly improving the safety of the route. In the improved A* algorithm, whenever the algorithm tries to expand from the current node to an adjacent node, it not only calculates the cost from the starting point to the node and the estimated cost from the node to the target point but also adds a judgment condition to ensure that the node maintains a specified safe distance from any known unnavigable area. This safe distance can be dynamically adjusted according to the size of the USV, its operational flexibility, and the environmental risk level.

The safety distance is defined as the distance from the node to the nearest obstacle and it must be greater than or equal to the specified safety distance, which can be determined according to specific needs. During the path planning process, for the current coordinate point $Current(x_c,y_c)$, the obstacle coordinate point $Obstacle(x_i,y_i)$, and the neighbor node $Neighbo{r}_i(x_n,y_n)$ to be expanded, the shortest distance from the $Neighbo{r}_i$ to the nearest $Obstacle$ is calculated first, as shown in Equation (5). If this distance is less than the preset safety distance $d_{min}$, the neighbor node is abandoned and is not added to the pending $Openlist$ for subsequent processing. Only when the distance of the $Neighbo{r}_i$ node meets the safety requirements will it be considered to be added to the $Openlist$ for subsequent path search, as shown in Equation (6). The diagram illustrating safe distances is shown in Figure 4. This method ensures that nodes in dangerous areas are not selected as path points during the path planning process, thereby effectively ensuring the generated path’s safety and feasibility.

$$d({\mathit{Neighbor}}_i,\mathit{Obstacle})=min\left(\sqrt{{(x_n-x_i)}^2+{(y_n-y_i)}^2}\right)$$

(5)

$$d({\mathit{Neighbor}}_i,\mathit{Obstacle})\ge d_{\min }$$

(6)

where $d({\mathit{Neighbor}}_i,\mathit{Obstacle})$ is the distance from the $Neighbo{r}_i$ node to be expanded to the nearest $Obstacle$ and $d_{\min }$ is the minimum safety distance.

• Remove redundant nodes

When searching for paths using the A* algorithm, staircase or jagged paths often appear, especially in a grid environment. In order to optimize these paths and reduce the redundant nodes, this paper traverses the nodes on the path. This method can eliminate redundant nodes without increasing the path cost to achieve smooth optimization of the path, turn multiple broken lines into straight lines, improve the smoothness of the path, and meet the kinematic characteristics of the USV.

Specifically, this method traverses all nodes in the path, first checking if three consecutive nodes $A(x_a,y_a)$, $B(x_b,y_b)$ and $C(x_c,y_c)$ are collinear and defining vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ as shown in Equations (7) and (8). If Equation (9) is satisfied, it indicates that $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear, meaning nodes A, B, and C lie on the same straight line. Next, it checks if it is possible to directly connect from node A to node C without encountering any obstacles. If a direct connection is feasible without obstruction, the intermediate redundant node B is removed, transforming the path from $A\to B\to C$ to $A\to C$, as shown in Figure 5a. Repeat this process until a direct connection is no longer possible or the path ends. Retain the starting point, endpoint, and all necessary turning points, removing redundant nodes to optimize the path.

$$\overrightarrow{a}=(x_b-x_a,y_b-y_a)$$

(7)

$$\overrightarrow{b}=(x_c-x_b,y_c-y_b)$$

(8)

$${\displaystyle \frac{(x_b-x_a)}{(y_b-y_a)}}={\displaystyle \frac{(x_c-x_b)}{(y_c-y_b)}}$$

(9)

If Equation (10) is satisfied, indicating that the path consists of line segments with directional changes, node B serves as the turning point. Connecting nodes A and C, where $P(x_p,y_p)$ is any point on the straight line $A\to C$, conduct a safety distance check for the nodes traversed by the segment $A\to C$ and compare the path lengths. If there are impassable nodes, this indicates that the segment $A\to C$ is not feasible and the path remains $A\to B\to C$. If Equations (11) and (12) are met, where the length of path $A\to C$ is shorter than $A\to B\to C$ and meets the safety distance requirements, the redundant turning point B is removed, transforming the path from $A\to B\to C$ to $A\to C$, as shown in Figure 5b.

$${\displaystyle \frac{(x_b-x_a)}{(y_b-y_a)}}\ne {\displaystyle \frac{(x_c-x_b)}{(y_c-y_b)}}$$

(10)

$$d\left(P,Obstacle\right)=\underset{i}{min}\left(\sqrt{{\left(x_p-x_i\right)}^2+{\left(y_p-y_i\right)}^2}\right)\ge d_{min}$$

(11)

$$\sqrt{{\left(x_c-x_a\right)}^2+{\left(y_c-y_a\right)}^2}\ge \sqrt{{\left(x_b-x_a\right)}^2+{\left(y_b-y_a\right)}^2+{\left(x_c-x_b\right)}^2+{\left(y_c-y_b\right)}^2}$$

(12)

In this way, check whether a straight line can directly connect the starting point and end point of the turning and oscillating path. If feasible, only these points are retained. After this processing, the path only contains the starting point, end point, and necessary turning points, significantly reducing the redundant nodes in the path and making the path more concise and efficient.

2.4. Warning of Dangerous Area of USV Based on GeoNetworking Mode

In the marine environment, USVs encounter challenges such as incomplete nautical charts and unforeseen incidents, complicating the process of marking all the danger zones. Effective communication is crucial, but traditional Internet Protocols (IP) struggle in high humidity and fog conditions, impacting the transmission of critical warning information [27,28,29,30].

Additionally, when multiple USVs operate simultaneously, traditional networks struggle to identify warning needs, leading to redundant data transmission and network congestion [31,32]. To address these issues, USV communication networks can adopt the GeoNetworking model. By sending obstacle avoidance warnings to USVs in target areas, the GeoNetworking model avoids large-scale broadcasting, reducing information redundancy and network congestion [33,34,35,36]. Compared to the traditional IP model, the GeoNetworking model has significant advantages in the maritime field, effectively addressing the challenges of incomplete nautical charts and unexpected events, avoiding irrelevant communications, and improving information exchange efficiency and safety.

Considering the potential maritime obstacles and dangers that USVs might encounter, a maritime obstacle-avoidance scenario is designed, as shown in Figure 6. In this scenario, the red area represents the stop zone and the yellow area represents the warning zone, explicitly indicating the geographic area where the GeoNetworking modal sends warning information. The USV needs to be aware of these areas in advance to avoid obstacles effectively. Therefore, the obstacle avoidance warning zone is configured as a circular area. This design is described using three pieces of information: the center coordinates, radius, and identifier of the zone. This simplifies the warning information design and improves information transmission efficiency.

The GeoNetworking routing base station receives and broadcasts obstacle avoidance alert information in this scenario. The USV updates its location information in the cooperative awareness message format to the onboard GeoNetworking protocol stack, which packages the cooperative awareness message information into Beacon packets and periodically sends them to the GeoNetworking routing base station. Upon receiving the Beacon packets, the base station checks whether the USV is within the alert area. If the USV is in the alert area, the base station sends an alert message to the USV; if it is not, no alert is sent.

In obstacle avoidance scenarios, GeoNetworking’s broadcast function is used to transmit information to USVs within the obstacle warning range. This method improves information exchange efficiency, reduces communication pressure, and enhances the flexibility of obstacle avoidance information transmission. Applying this multimodal communication network effectively enhances the operational capabilities of USVs in complex maritime environments.

3. Safety Analysis and Environmental Modeling

3.1. Research Area

The region defined in this article spans a latitude range of 67°∼76° N and a longitude range of 88°∼105° W. The starting point for the path planning is the Port of Houston $({29}^{\circ }{45}^{\prime }{46}^{″}$ N, ${95}^{\circ }{22}^{\prime }{59}^{″}$ W) and the endpoint is the Port of Cartagena $({37}^{\circ }{36}^{\prime }{46}^{″}$ N, $0^{\circ }{59}^{\prime }$ W), as shown in Figure 7.

Sailing in densely islanded waters poses numerous challenges for USVs, primarily due to the widespread presence of shallow areas, the complex terrain, and the unpredictability of some of the obstacles. Firstly, islands are often surrounded by rocks or coral reefs that cause shallow depths. Combined with the effects of tides and currents, sedimentation can further reduce water depths. Such terrain conditions necessitate vessels to reduce speed or adjust course during navigation to avoid running aground. Additionally, the presence of islands and obstacles increases collision risks. It can influence surrounding sea currents, leading to the formation of local turbulence, increased flow velocity, or sudden changes in flow direction. These changes may generate underwater eddies and backflows, thereby increasing the complexity and risks of navigation. Therefore, when the USV navigates densely islanded waters, it is crucial to consider the specificity of the water area and potential risks. This involves implementing appropriate navigation measures, such as setting minimum safe depths and increasing buffer zones around obstacles, before proceeding with path planning to complete missions successfully. Figure 8 depicts the USV information, while

Table 1. Ship parameters.

Leagth Overall	Beam	Speed	Draft
69.83 m	10.9 m	17.5 knots	3.5 m

details the ship parameters.

3.2. Data Source

Before conducting experiments and analysis, the experimental data need to be preprocessed, including extracting the required elements from real geographic data and converting them into spatially defined layers. This paper uses the Bedrock elevation Network Common Data Form (NetCDF) dataset in the 15 Arc-Second Resolution of the latest version of ETOPO2022, which integrates regional and global topography, bathymetry, and coastline data and describes the surface geophysical characteristics comprehensively and with high resolution. The land elevation and coastline data are from the American Geophysical Data Center, and the water depths data are from S57. Due to the differences in resolution and attribute information in the data mentioned above, there are options other than direct analysis. Therefore, the data need to be converted using the WGS-84 geographic coordinate system and the resolution needs to be unified. The bathymetric data used in this study are in a NetCDF format. The NetCDF data must be converted to a Shapefile format for subsequent spatial analysis. Shapefile is a vector format capable of storing geometric types such as points, lines, and polygons, making it ideal for storing and analyzing geographic information. Converting the data format facilitates spatial analysis and environmental modeling.

3.3. Setting Safe Water Depths

When planning the route, it is necessary to avoid crossing particular areas, such as military exercise areas, anchoring areas, and no-go areas, and to determine safe water depths to prevent grounding. When setting safety contours, the USV’s draft and Under-Keel Clearance must be considered, and reasonable values must be determined based on the ship’s conditions, water characteristics, and voyage requirements. Determining the minimum safe water depths for USV navigation is a complex process that comprehensively considers factors such as USV parameters, underwater equipment location, maneuverability, and sea conditions. Figure 9 shows a schematic diagram of the minimum safe water depths, and the final safe water depth is given by Equation (6).

$$H_{min}=D+{\displaystyle \frac{1}{2}}{H}_w+C$$

(13)

where D is the draft depth of the USV, $H_w$ is the wave height, and C is the draft safety margin of the USV.

This study utilizes the “Xin Hong Zhuan” from Dalian Maritime University as an example, which has a design draft of 3.5 m. Determining adequate clearance depth is influenced by various factors, such as navigational environment uncertainties and the reliability of ship equipment. To ensure safe navigation, it is essential to have a sufficient safety margin to cope with uncertainties and avoid being overly conservative in fully utilizing water resources. Generally, the surplus depth is determined through empirical values, analytical formulas, semi-empirical formulas, and ship squat tests [37]. This study’s surplus depth is set at 1 m based on empirical values. The average wave height along the coast within the study area ranges from 0.2 m to 0.7 m, with a design wave height of 0.7 m for this experiment. Incorporating these values into Equation (6) establishes a safety contour depth of 5.2 m for this experiment. This paper further extracts and reclassifies bathymetric data based on minimum safety depth requirements and constructs depth contours. Areas with depths greater than 5.2 m are designated as navigable zones, while regions shallower than 5.2 m are marked as shallow water navigation hazards. Depth processing is illustrated in Figure 10. Doing so creates a grid map of navigable and hazardous areas for the research maritime area, effectively preventing the designed navigation route from crossing shallow points and ensuring navigational safety.

3.4. Environmental Modeling

The Electronic Nautical Chart has been widely used in maritime navigation. However, applying traditional path search algorithms is complicated due to the complex geometric figures that characterize the marine environment’s geographical information data. Therefore, solving the environmental modeling problem and simplifying the complex chart data into an environmental model with transparent geometric relationships is necessary. Implementing path planning with the center of all grids as a node allows path search algorithms to search and plan more efficiently across these grids. This helps improve the efficiency of the path search algorithm during analysis and processing. Use the grid method to design the appropriate grid size, coding method, and representation method according to the navigation area and ship characteristics. Divide the marine environment into navigable and non-navigable areas by setting a state for each grid that reflects its navigability in the actual environment. Doing so helps optimize the navigation routes of the USV and ensures its safe navigation in the marine environment. Environment modeling is an essential foundation for route planning using the A* algorithm and the quality of a route is closely related to the size of the grid. Using a too-small grid may shorten the path distance but significantly increase the search time. Conversely, a too-large grid may decrease the accuracy of path planning and increase navigation risks. Therefore, the selection of grid size has a crucial impact on the quality of route planning.

When modeling the chart environment, obstacles in the water are treated as follows: first, obstacles smaller than the grid size are inflated to fill the entire grid to ensure accuracy. Second, suppose the distance between adjacent obstacles is smaller than the safe radius of the USV. In that case, the obstacles will be classified as the same obstacle to avoid local deadlock and collision risk, ensuring the connectivity and feasibility of the obstacles. Through these processes, the chart environment can be established more accurately, improving the integrity and reliability of the environmental model. The grid environment model is shown in Figure 11.

4. Simulation Result

All simulations in this paper were performed on a PC equipped with an Intel i9 2.70 GHz quad-core CPU (Intel Corporation, Santa Clara, CA, USA) and a GeForce RTX 4070 (NVIDIA Corporation, Santa Clara, CA, USA) graphics card running on the Microsoft Windows 10 operating system. The simulation of the global streamline method was completed using Ansys Fluent 2021R1 software (Ansys, Inc., Canonsburg, PA, USA), while the locally improved A* algorithm was simulated using Matlab 2022a software (MathWorks, Inc., Natick, MA, USA).

4.1. Streamline Global Route Planning

According to the selected nautical chart, part of the coastline outline of the sea area chosen was simplified for the convenience of calculation. Using the numerical simulation software Space Claim from ANSYS FLUENT, a physical model of the surrounding environment of the sea area was constructed, as shown in Figure 12.

This paper used the Fluent Meshing geometry processing function to mesh the established model. Unstructured grids are used for discretization during division, the minimum grid size is set to mm, and the grid elements mainly use tetrahedral grids. Meshing is a critical requirement for fluid simulation and its quality directly affects the accuracy of simulation results. An excessive mesh size will reduce simulation accuracy and lead to erroneous results. However, a larger mesh size increases the computation time and leads to easier-to-converge results. Therefore, it is crucial to choose the right mesh size. The flow field mesh division in this study is shown in Figure 13. The number of grids is 102,694, the number of nodes is 129,267, and the grid quality is above 0.3. No negative volume will affect the simulation, which meets the Fluent calculation requirements.

The boundary conditions and initial physical quantities are set after creating the fluid analysis model. The final flow field solution is obtained using the iterative solution of the equations during the simulation. The fluid boundary conditions are set as velocity–inlet, velocity–outlet, and wall. The governing equation adopts the inviscid Euler equation and dimensions are in three dimensional double precision mode. The solver uses steady, pressure-based, and absolute velocity formulation. Set the operating pressure of the operating conditions to a standard atmospheric pressure and the operating density to the default value $1.225$ kg/m³. Check the gravity effect, since the y-axis is vertically upward and set the y-direction acceleration to $-9.81$ m/s², opposite to the gravity acceleration’s direction. The simulation calculation model is shown in Figure 14.

When generating the global route of the USV, it is necessary to post-process the data and analyze the simulation results. In this study, the results show convergence when the iteration is 200 steps. The simulation results of this paper are shown in Figure 15, including the velocity cloud diagram, velocity vector diagram, and streamline diagram.

The velocity cloud diagram displays the velocity of the fluid flow using different colors, and the color scale demonstrates the spatial distribution of the fluid velocity, which is used to understand the overall velocity distribution of the fluid flow and the trend of velocity change; the velocity vector map shows the flow velocity and direction of the fluid in the form of arrows, which is suitable for detailed study of the velocity and direction of the fluid as well as local characteristics; and the streamline map presents the flow route of the fluid in the form of curves, in which the direction of each streamline tangent is consistent with the direction of the velocity vector, which helps us understand the path and overall trend of the fluid in the system.

Velocity cloud and vector diagrams provide detailed flow velocity and directional information. In contrast, streamline diagrams are suitable for understanding the fluid’s trajectory and overall flow pattern. All three are combined to provide a comprehensive visualization of fluid flow. By generating and displaying an appropriate number of streamlines from CFD simulation results, features such as fluid trajectories and flow patterns in the entire flow field can be demonstrated for design tuning and optimization. We used the streamline technique to obtain the visualized vector field from the three-dimensional CFD simulation results, and the generated global optimal paths are shown in Figure 16.

4.2. Improved A* Algorithm Local Path Planning

The global streamline method is a path planning method that uses fluid mechanic principles to generate a smooth path by calculating streamlines. However, this method is slow to respond when encountering obstacles and usually only turns when close to the obstacle, making the USV prone to path failure or at risk of collision when navigating in complex sea areas. In order to solve this problem, this study proposes a strategy to segment and plan complex sea areas. The operation process is shown in Figure 17. Specifically, global planning uses the streamline method to determine the overall path direction. When it is detected that the path passes through a complex obstacle area, it enters the local segmentation and planning stage. The improved A* algorithm is used for precise path planning for local planning. By setting a safe distance and making appropriate adjustments and optimizations at crucial turning points or nodes, the generated path can avoid obstacles while maintaining a relatively smooth path. This method significantly improves the effectiveness and safety of path planning by predicting and avoiding obstacles in advance.

The path planning for local complex sea areas is shown in Figure 18. As can be seen from the figure, the search path without setting a safety distance will be close to the obstacle, while the search path with a safety distance will be far away from the obstacle. When the safety distance is not set, the path of the USV will be very close to the obstacle, and there is an excellent risk of collision. Although this path that closely follows the obstacle may sometimes shorten the distance, it also increases the uncertainty and danger during navigation, especially when the sea conditions are complex or the obstacle is in motion. It is more likely to cause path failure or collision accidents. On the contrary, the path planning method with a safety distance setting shows significant improvements, ensuring that a specified safety distance is maintained around the obstacle. This dramatically reduces the risk of collision and provides the USV with more ample navigation space, making it easier to adjust and avoid obstacles when encountering emergencies.

In this paper, to ensure the safety and efficiency of the USV during navigation, we conduct a comprehensive analysis and set the safety distance to 10 grid units. The paths planned by the traditional A* algorithm are close to the obstacles as shown in Figure 19a, while the RRT algorithm shown in Figure 19b has many turning points. In this paper, we improve the A* algorithm by introducing a safe distance to avoid obstacles and smoothing the critical turning points with Bessel curves, as shown in Figure 19c. These improvements not only ensure that the path is far away from obstacles but it is also more consistent with the kinematics of the USV. These improvements significantly increase the safety and efficiency of the path planning, the feasibility of the path, and the smoothness of the navigation. The comparison between the time and the path length of several of these algorithms is shown in detail in

Table 2. Comparison of the algorithms.

Comparison of Different Algorithms	Search Time	Path Length
The traditional A* algorithm	4.83 s	246.22
The introduction of the safe distance A* algorithm	4.71 s	246.63
The RRT algorithm	7.86 s	295.59
The improved A* algorithm	4.66 s	242.09

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Figure 20 shows the effect of adding warnings for dangerous sea areas in the GeoNetworking mode, and this paper sets the safety distance to 5 grid units. Through the broadcast mechanism and warning information of the GeoNetworking network mode, the USV can obtain information and avoid unknown dangerous areas more quickly. This system not only improves the safety of USVs but also ensures that they can complete tasks efficiently and avoid mission interruptions or failures caused by collisions or other accidents, thus providing a solid guarantee for the safe and efficient navigation of USVs in complex sea environments.

4.3. Validation of the USV

This paper demonstrated the effectiveness of the proposed method through a real-world validation test using the USV in a school lake, as shown in Figure 21. Initially, we set the starting and ending points and calculated a globally feasible path using the global streamline method. Then, we subdivided the areas with local obstacles and applied an improved A* algorithm for detailed local path planning. Maintaining a safe distance was emphasized throughout this process, and Bézier curves were used to smooth key turning points, optimizing the path. The final test results confirmed the practical applicability of the method proposed in this chapter, as shown in Figure 22.

5. Conclusions

This paper proposed a USV global path planning approach based on a streamline method and an improved A* algorithm. During the implementation of this method, the USV navigated smoothly under global flow guidance and employed an improved A* algorithm for local planning when approaching complex obstacles to avoid them effectively. Additionally, this article introduced a maritime hazard warning system using the GeoNetworking mode, which significantly enhanced the dynamic response capabilities of path planning through real-time information transmission. Simulations confirmed that combining global streamline and improved A* algorithms enabled USVs to navigate complex waters effectively and safely. However, this paper did not consider the effects of hydrographic conditions, such as ocean currents, sea breezes, and waves, which significantly impacted path planning. Future work will focus on these dynamic factors. We will consider introducing dynamic information about other USVs and follow the international rules of collision avoidance at sea for dynamic collision avoidance to realize a more practical and comprehensive path planning.