Cooperative coverage path planning method for heterogeneous unmanned surface vehicles based on barrier density

Abstract

The invention discloses a heterogeneous unmanned ship cooperative coverage path planning method based on obstacle density, and the method comprises the steps: introducing a spanning tree multi-constraint dynamic coupling weight function, comprehensively considering the maximum speed of each unmanned ship in a path planning process, and associating the maximum speed with the turning frequency and the density of surrounding obstacles. According to the method, the collaboration efficiency can be improved, the task completion time is shortened, and resource waste is avoided.

Description

Technical Field

[0001] The present invention relates to a method for planning a collaborative coverage path for heterogeneous unmanned boats based on obstacle density. Background Art

[0002] Currently, most algorithms for multi-robot area coverage are based on the STC algorithm, and these methods all use the grid method to model the environment.

[0003] (1) Grid method environment modeling: In the environment modeling of path planning, the grid method is one of the most commonly used methods. This method first divides the environment into cells of equal size and non-overlapping, each of which can store environmental information for path planning. In a grid map, each cell has an index mark, usually rectangular. In these maps, "0" and "1" are usually used to represent passable areas and impassable obstacle areas, respectively. If the size of the obstacle is less than or equal to the size of the cell, or it does not completely occupy a cell, the cell is considered an impassable area. Grid map information can directly correspond to the real environment and can be quickly updated to reflect changes in environmental information. Therefore, the grid method is the most widely used environment modeling method.

[0004] (2) STC algorithm: The STC algorithm is used to solve the area coverage path planning problem. The STC algorithm divides the working area into non-intersecting sub-areas based on the grid method, and then constructs a spanning tree to connect the sub-areas. The sub-area is divided into four cells, each of the same size as the robot. The robot completes the full coverage of the area by moving around the spanning tree once.

[0005] (3) Multi-robot area coverage based on STC: Since the STC algorithm can generate non-repeated coverage paths, its application in the field of multi-robots has attracted widespread attention from researchers. The following is a description of several multi-robot coverage algorithms based on the STC algorithm: 1. The MSTC algorithm is a multi-robot coverage algorithm that runs in polynomial time. Similar to the STC algorithm, the MSTC algorithm first converts the grid map into a node graph and selects the position of a robot as the starting point to build a spanning tree. This spanning tree can connect all feasible nodes. After the spanning tree is built, non-overlapping coverage paths are assigned to each robot according to the position of each robot in the spanning tree. 2. The MFC algorithm. The core idea of ​​the MFC algorithm is that each robot independently constructs its own spanning tree and only needs to cover its own spanning tree to achieve coverage of the entire area. The algorithm first converts the grid map into a node graph and sets the starting point of each robot as the root of the tree. Different spanning trees can share vertices and edges, ensuring that each node in the graph belongs to at least one spanning tree. Then, each robot moves along its own spanning tree to complete the full coverage of the map. 3. The DARP algorithm is an algorithm that first divides the area and then covers it. It first processes the grid map into a node graph and then divides the area into multiple sub-areas. Each robot performs single-robot coverage planning within its own sub-area. 4. The AWSTC algorithm is a distributed, artificially weighted spanning tree (STC) algorithm. In this algorithm, each robot is assigned a weight that enables it to independently construct a spanning tree while avoiding overlap with other robots' trees and expanding toward the center of uncovered areas.

[0006] Existing multi-robot area coverage algorithms (such as MSTC, MFC, DARP, and AWSTC) are all designed based on homogeneous robots (i.e., each robot has identical performance parameters). These methods perform well in theoretical simulations or on homogeneous platforms, but practical applications often require the coordinated operation of multiple unmanned vehicles with varying performance (heterogeneous). In response to this situation, existing technologies have the following shortcomings:

[0007] 1. Failure to consider the differences in the capabilities of heterogeneous unmanned vehicles leads to unreasonable task allocation

[0008] Because the aforementioned algorithm assumes all robots have the same speed and maneuverability, when deployed in a swarm of heterogeneous unmanned vehicles, it's impossible to assign appropriate operating areas and paths based on the performance characteristics of each vehicle. This results in high-performance unmanned vehicles failing to fully utilize their speed advantage, while low-performance unmanned vehicles may be assigned overly heavy tasks, resulting in a decrease in overall coverage efficiency.

[0009] 2. Path planning fails to adapt to the working conditions of the unmanned boat, resulting in insufficient efficiency and safety.

[0010] Existing allocation methods, such as MSTC and MFC, often divide routes based solely on initial positions or simple rules, lacking real-time adaptive adjustments to the UAV's current state (such as speed, remaining energy, and environmental complexity). This can cause high-speed UAVs to frequently turn in areas with dense obstacles, increasing energy consumption and collision risks.

[0011] 3. The coordination mechanism has limitations and is difficult to adapt to the efficient collaboration of heterogeneous unmanned boats in complex dynamic environments.

[0012] For example, the DARP algorithm focuses primarily on regional division and does not address real-time collaboration and information sharing between multiple unmanned vehicles. While the AWSTC algorithm introduces distributed collaboration and information sharing mechanisms, its primary design objective is to target homogeneous (isomorphic) robot swarms, and it lacks consideration for the task allocation and collaborative optimization issues arising from performance differences between heterogeneous unmanned vehicles. Consequently, existing methods still struggle to achieve efficient collaboration among heterogeneous unmanned vehicle swarms in complex and dynamic ocean environments. Summary of the Invention

[0013] In view of the shortcomings of the above-mentioned prior art, the purpose of the present invention is to:

[0014] A collaborative regional coverage path planning method for heterogeneous unmanned aerial vehicles (UAVs) is proposed. By introducing a multi-constraint dynamic coupling weight function that comprehensively considers multiple factors such as the maximum speed, number of turns, and obstacle density of each UAV, it achieves adaptive division of labor and efficient path generation based on the capabilities of the heterogeneous UAVs.

[0015] The key innovation of this invention lies in the proposed multi-constraint adaptive coupling mechanism: on the one hand, the maximum speed of the unmanned boat is dynamically coupled with the path turning penalty item, so that the higher the speed of the unmanned boat, the greater the turning penalty weight, thereby prompting high-speed boats to give priority to straight paths, improving energy efficiency and safety; on the other hand, the maximum speed of the unmanned boat is dynamically coupled with the obstacle density item, and the reward and penalty attributes of the obstacle density item are adaptively adjusted with the maximum speed of the unmanned boat, so that high-speed boats give priority to covering open areas and low-speed boats give priority to covering complex obstacle areas. This multi-constraint adaptive coupling mechanism breaks through the limitation of existing technologies that only consider multiple factors in parallel, and greatly improves the collaborative efficiency and intelligent division of labor capabilities of heterogeneous unmanned boat clusters.

[0016] ● Using a distributed autonomous spanning tree expansion and real-time information sharing mechanism, the coverage area and path of each unmanned boat can be dynamically adjusted to further improve overall collaboration efficiency;

[0017] ●Enable the unmanned boat swarm to collaboratively complete regional coverage tasks in large and complex environments with high efficiency and low risk.

[0018] Give full play to the overall performance advantages of heterogeneous platforms.

[0019] To achieve the above objectives, the present invention can be implemented through the following technical solutions:

[0020] A method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density includes the following steps:

[0021] 1) Initialization information: First, initialize each unmanned boat to obtain the node information of the sea area, the location information of all unmanned boats, and update the maximum speed information of each unmanned boat;

[0022] 2) Grid method environmental modeling;

[0023] 3) Taking the starting point of each unmanned vehicle as the root node, the spanning tree is independently expanded within the feasible region, and candidate nodes are optimized based on a multi-constraint dynamic coupling weight function, where the weight function dynamically couples the maximum speed of the unmanned vehicle with the steering penalty term and the obstacle density term to achieve adaptive division of labor and path adaptive optimization for heterogeneous unmanned vehicles.

[0024] 4) Generate a wrap-around path in the segmented network.

[0025] Furthermore, the step 2) specifically includes: modeling the environmental information through the grid method, representing the environmental information through the decomposed cells, combining the four cells into a 2*2 large cell, and dividing the feasible area and the infeasible area by defining the large cell. If there are any number of small cell obstacles in the large cell, this large cell is regarded as an infeasible area.

[0026] Furthermore, the step 3 specifically includes: taking the robot starting point as the root node, expanding the spanning tree from the starting point, using the obtained relevant information, adding all expandable neighbors to the priority queue with corresponding weights, and the weights are calculated by the weight function, that is, formula (1):

[0027]

[0028] in,

[0029] E a =m1d1, d1 is the Euclidean distance between the selected node and the centroid of the uncovered area of ​​the mission sea area, and m1 is the control parameter;

[0030] d2 is the Euclidean distance between the selected node and other unmanned boat nodes, and m2 is the control parameter;

[0031] E t =m3s1α1 is the speed-steering constraint coupling term, m3 is the control parameter, α1 is the steering indicator variable (1 for turning, otherwise 0), s1 is the maximum speed of the unmanned boat, realizing the speed-steering constraint coupling;

[0032] E c =m4s2α2 is the correlation term between speed and obstacle density, α2 is the obstacle density indicator variable (the obstacle density near the node is 1 if it is greater than 0.2, otherwise it is 0), m4 is the control parameter, s2 is adaptively adjusted according to the ratio of the maximum speed of the unmanned boat to the maximum speed of the cluster, and s2 is negative (reward) when the maximum speed is less than 50% of the maximum speed of the cluster, thus realizing speed-obstacle density coupling.

[0033] Furthermore, when expanding a node, only adjacent cells that are not covered and are not obstacles are considered. Each time, the cell with the smallest (optimal) weight is taken out from the queue for expansion, and the neighboring node with the smallest weight is selected as the next node to connect to the current node. The node is marked as covered, and its own position is broadcast to other robots. The weight of each expandable cell in the neighborhood of the node is calculated, and then the cycle continues until the queue is empty or all cells are covered; each unmanned boat performs this step in parallel.

[0034] Furthermore, the maximum speed parameters, steering capability and obstacle density of the unmanned boat are adjusted in real time according to the heterogeneous performance of the actual unmanned boat platform. The coupling relationship in the weight function is flexibly set through parameter learning, adaptive adjustment or preset empirical rules to adapt to different sea environments and cluster configurations.

[0035] Furthermore, the speed-steering constraint coupling mechanism of the dynamic coupling weight function enables unmanned boats with higher maximum speeds to give priority to straight paths with fewer turns when generating paths, thereby reducing energy consumption and control difficulty, improving the operating efficiency of high-performance unmanned boats, and optimizing cluster division of labor and collaboration.

[0036] Furthermore, the speed-obstacle density coupling mechanism of the dynamic coupling weight function enables the influence of the obstacle density term on the path weight to be adaptively switched to reward or penalty according to the ratio of the maximum speed of the unmanned boat to the maximum speed of the cluster, thereby achieving high-speed unmanned boats giving priority to open areas and low-speed unmanned boats giving priority to covering obstacle-dense areas, thereby improving the rationality of task division and overall operational efficiency of heterogeneous clusters.

[0037] Furthermore, in the process of generating the surrounding path, a subdivided grid and a depth-first traversal algorithm are used, and the path movement order is set to clockwise or counterclockwise. For each step of movement, it is determined whether the target cell is an obstacle. It is prohibited to cross the spanning tree boundary within the same original cell. When moving across the original cell, there must be a spanning tree edge connection. If it is movable, it is pushed into the stack, otherwise it is backtracked until all boundaries are traversed, and finally a closed surrounding path with no omissions, no duplications, and no conflicts is generated, thereby realizing efficient full coverage of the target sea area by the unmanned boat.

[0038] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0039] Because the weight function dynamically associates the maximum speed of the unmanned boat with the path turning penalty, high-speed boats are more inclined to follow straight paths, reducing energy consumption and operational difficulty, and leveraging their speed advantage, while low-speed boats can flexibly cope with complex areas, avoiding requiring low-performance boats to undertake high-load tasks; through adaptive adjustment of obstacle density and speed, high-speed boats prioritize open areas, while low-speed boats cover obstacle-dense areas, improving overall operational efficiency and reducing conflicts and duplications; distributed information sharing and local decision-making mechanisms make multi-boat collaboration more flexible and improve system robustness. When a single boat fails, other boats can quickly take over the mission area to ensure the smooth completion of the mission; subdivided grids and DFS backtracking surround path generation ensure efficient coverage of the target area without omissions, duplications, or conflicts.

[0040] Therefore, compared with the existing technology, the present invention can enable heterogeneous unmanned boats to adaptively collaborate and complete efficient coverage of large and complex mission areas based on their own parameters, significantly improving the rationality of path planning, the system's operating efficiency and adaptability, and expanding the application scope of unmanned boat clusters in actual complex scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of the obstacle density-based collaborative coverage path planning method for heterogeneous unmanned boats proposed in the present invention;

[0042] Figure 2 This is a schematic diagram of the environment model after rasterization;

[0043] Figure 3 A tree structure is generated for the coverage path generated by the method of the present invention;

[0044] Figure 4 The following is an effect diagram of the coverage paths of each unmanned boat obtained by using the method of the present invention. DETAILED DESCRIPTION

[0045] The following describes the embodiments of the present invention through specific embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification.

[0046] The flow chart of the present invention is as follows Figure 1 As shown, the first step is to initialize the environmental information and the unmanned boat information, and then use the grid method to model the environmental information. The modeling effect is as follows Figure 2 As shown in the figure, the gray part represents the obstacle area, and the white area is the unexplored area. Then each robot constructs a spanning tree based on the weight function until the spanning tree covers the entire area. The generation effect of the spanning tree is shown in Figure 3As shown, the green solid line represents the spanning tree of the unmanned boat with a larger maximum speed, and the blue solid line represents the spanning tree of the unmanned boat with a smaller maximum speed. Then, a depth-first traversal is used in the subdivided cells to generate a surrounding path. This is the final coverage path of the unmanned boat. The effect diagram is as follows Figure 4 As shown in the figure, it can be clearly seen that the complex environment areas are covered by robots with lower maximum speeds, while robots with higher maximum speeds explore open areas. This enables heterogeneous unmanned boats to adaptively collaborate based on their own parameters to complete efficient coverage of large-area complex task areas, significantly improving the rationality of path planning, the system's operating efficiency and adaptability, and expanding the application scope of unmanned boat clusters in actual complex scenarios.

[0047] The detailed steps are as follows:

[0048] (1) Initialization information: First, initialize each unmanned boat to obtain the node information of the sea area, the position information of all unmanned boats, and update the maximum speed information of each unmanned boat.

[0049] (2) Grid method environmental modeling: The environmental information is modeled using the grid method. The environmental information is represented by the decomposed cells. Four cells are combined into a 2*2 large cell. The feasible area and the infeasible area are divided by the definition of the large cell. If there are any number of small cell obstacles in the large cell, this large cell is regarded as an infeasible area.

[0050] (3) Generation of spanning tree: Taking the robot starting point as the root node, the spanning tree is expanded from the starting point. Using the relevant information obtained, all expandable neighbors are added to the priority queue with corresponding weights. The weights are calculated by the weight function, i.e., formula (1).

[0051]

[0052] E a =m1d1 (2)

[0053]

[0054] E t =m3s1α1 (4)

[0055] E c =m4s2α2 (5)

[0056] Where, E a is the distance term between the selected node and the centroid of the uncovered area of ​​the mission sea area, m1 is the control parameter, m1<0, d1 is the Euclidean distance between the selected node and the centroid of the uncovered area of ​​the mission sea area. The purpose of this design is to encourage the robot to cover the uncovered area from the outside to the inside and improve the global planning efficiency; is the distance penalty term between the node selected by the current unmanned boat j and other unmanned boats k participating in the area coverage, where n is the total number of unmanned boats, m2 is the control parameter, and m2>0, and d2 is the Euclidean distance between the selected node and the nodes of other unmanned boats k participating in the coverage task. The purpose of this design is to make robots tend to stay away from other robots, reduce overlap between each other, and improve the efficiency of multi-robot collaboration; E t is the turning penalty term of the selected node, which is related to the speed of the unmanned boat, m3 is the control parameter, m3>0, s1 is the maximum speed of the unmanned boat, and α1 is a binary function: when the node is selected to turn, the value is 1, otherwise it is 0. The purpose of this design is to punish frequent turns and encourage the robot's path to be as straight as possible, especially for unmanned boats with a large maximum speed, which helps to reduce energy consumption and execution difficulty; E c is the speed-obstacle density correlation term, m4 is the control parameter, m4>0, s2 is used to control whether the obstacle density is a penalty term or a reward term for the node selection of the unmanned boat. When the maximum speed of the unmanned boat j is less than 50% of the maximum speed of the unmanned boats in the cluster, the obstacle density term is set as a reward term; when the maximum speed of the unmanned boat j is not less than 50% of the maximum speed of the cluster, the term is a penalty term, s2∈(-1,1], α2 is a binary function: when the obstacle density near the selected node is >0.2, the value is 1, otherwise it is 0. The role of this term is to make the robot speed in the area with high obstacle density greatly increase the weight and reduce the high Prioritize dense areas, so high-speed robots prefer open areas, while slow-speed robots can operate in complex areas. This allows for dynamic adaptation of robot capabilities, improving collaborative efficiency and reducing conflicts. When expanding a node, only adjacent cells that are uncovered and not obstacles are considered. Each time, the cell with the smallest (optimal) weight is selected from the queue for expansion. The neighboring node with the smallest weight is selected as the next node to connect to the current node, marking it as covered and broadcasting its location to other robots. The weight of each expandable cell in the node's 3-way neighborhood is calculated, and the process continues until the queue is empty or all cells are covered. Each unmanned boat performs this step in parallel.

[0057] (4) Generation of the circling path: Based on the spanning tree generated by each robot, a complete circling path is generated on the boundary of the area covered by the spanning tree using depth-first traversal (DFS). The circling path is generated in the subdivided cells. Finally, the unmanned boat can achieve coverage of the sea area by circling counterclockwise or clockwise. The specific steps are as follows: 1. Initialization: Starting from the subdivided coordinates (2r, 2c) of the cell where the robot is initially located. 2. DFS traversal: Starting from the subdivided coordinates (2r, 2c) of the cell where the robot is last located, each attempt is made to explore the next subcell in the clockwise direction (right, down, left, up). 3. Movement legitimacy judgment: For each step of movement within the subdivided grid, it is determined that the target cell is not an obstacle. When moving within the same original cell, it cannot cross the boundary of the spanning tree (that is, it cannot be blocked by the edge of the tree). When moving across original cells, there must be an edge connected to the spanning tree and the target cell must belong to the spanning tree. 4. Circling traversal: If it is possible to move, it is pushed into the stack, otherwise it is backtracked until all boundaries are traversed.

[0058] In the present invention, the maximum speed parameters, steering capability and obstacle density items of the unmanned boat are adjusted in real time according to the heterogeneous performance of the actual unmanned boat platform. The coupling relationship in the weight function is flexibly set through parameter learning, adaptive adjustment or preset empirical rules to adapt to different sea environments and cluster configurations; the speed-steering constraint coupling mechanism of the dynamic coupling weight function enables the unmanned boat with a larger maximum speed to give priority to a straight path with fewer turns when generating a path, thereby reducing energy consumption and control difficulty, improving the operating efficiency of high-performance unmanned boats, and optimizing the division of labor and cooperation of the cluster; the speed-obstacle density coupling mechanism of the dynamic coupling weight function enables the influence of the obstacle density item on the path weight to be adaptively switched to reward or penalty according to the ratio of the maximum speed of the unmanned boat to the maximum speed of the cluster, thereby achieving high-speed unmanned boats giving priority to open areas and low-speed unmanned boats giving priority to covering obstacle-dense areas, thereby improving the rationality of task division and overall operating efficiency of heterogeneous clusters.

[0059] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density, characterized in that: The following steps are involved: 1) Initialization information: First, initialize each unmanned boat to obtain the node information of the sea area, the location information of all unmanned boats, and update the maximum speed information of each unmanned boat; 2) Grid method environmental modeling; 3) Taking the starting point of each unmanned vehicle as the root node, the spanning tree is independently expanded within the feasible region, and candidate nodes are optimized based on a multi-constraint dynamic coupling weight function, where the weight function dynamically couples the maximum speed of the unmanned vehicle with the steering penalty term and the obstacle density term to achieve adaptive division of labor and path adaptive optimization for heterogeneous unmanned vehicles. 4) Generate a wrap-around path in the segmented network.

2. The method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density according to claim 1 is characterized in that: The step 2) specifically includes: modeling the environmental information through the grid method, representing the environmental information through the decomposed cells, combining the four cells into a 2*2 large cell, and dividing the feasible area and the infeasible area by defining the large cell. If there are any number of small cell obstacles in the large cell, this large cell is regarded as an infeasible area.

3. The method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density according to claim 1 is characterized in that: The step 3 specifically includes: taking the robot starting point as the root node, expanding the spanning tree from the starting point, using the obtained relevant information, adding all expandable neighbors to the priority queue with corresponding weights, and the weights are calculated by the weight function, that is, formula (1): in, E a =m1d1, d1 is the Euclidean distance between the selected node and the centroid of the uncovered area of ​​the mission sea area, and m1 is the control parameter; d2 is the Euclidean distance between the selected node and other unmanned boat nodes, and m2 is the control parameter; E t =m3s1α1 is the speed-steering constraint coupling term, m3 is the control parameter, α1 is the steering indicator variable (1 for turning, otherwise 0), s1 is the maximum speed of the unmanned boat, realizing the speed-steering constraint coupling; E c =m4s2α2 is the correlation term between speed and obstacle density, α2 is the obstacle density indicator variable (the obstacle density near the node is 1 if it is greater than 0.2, otherwise it is 0), m4 is the control parameter, s2 is adaptively adjusted according to the ratio of the maximum speed of the unmanned boat to the maximum speed of the cluster, and s2 is negative (reward) when the maximum speed is less than 50% of the maximum speed of the cluster, thus realizing speed-obstacle density coupling.

4. The method for planning a collaborative coverage path for heterogeneous unmanned vehicles based on obstacle density according to claim 3 is characterized in that: When expanding a node, only adjacent cells that are not covered and are not obstacles are considered. Each time, the cell with the smallest (optimal) weight is taken out of the queue for expansion. The neighboring node with the smallest weight is selected as the next node to connect to the current node. The node is marked as covered and its position is broadcast to other robots. The weight of each expandable cell in the neighborhood of the node is calculated, and then the cycle continues until the queue is empty or all cells are covered. Each unmanned boat performs this step in parallel.

5. The method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density according to claim 3 is characterized in that: The maximum speed parameters, steering capability and obstacle density of the unmanned boat are adjusted in real time according to the heterogeneous performance of the actual unmanned boat platform. The coupling relationship in the weight function is flexibly set through parameter learning, adaptive adjustment or preset empirical rules to adapt to different sea environments and cluster configurations.

6. The method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density according to claim 3 is characterized in that: The speed-steering constraint coupling mechanism of the dynamic coupling weight function enables unmanned boats with higher maximum speeds to give priority to straight paths with fewer turns when generating paths, thereby reducing energy consumption and control difficulty, improving the operating efficiency of high-performance unmanned boats, and optimizing cluster division of labor and collaboration.

7. The method for planning a collaborative coverage path for heterogeneous unmanned vehicles based on obstacle density according to claim 3 is characterized in that: The speed-obstacle density coupling mechanism of the dynamic coupling weight function enables the influence of the obstacle density term on the path weight to be adaptively switched to reward or penalty based on the ratio of the maximum speed of the unmanned boat to the maximum speed of the cluster. This enables high-speed unmanned boats to prioritize open areas and low-speed unmanned boats to prioritize covering areas with dense obstacles, thereby improving the rationality of task division and overall operational efficiency of heterogeneous clusters.

8. The method for collaborative coverage path planning of heterogeneous unmanned vehicles based on obstacle density according to claim 1 is characterized in that: In the process of generating the described surrounding path, a subdivided grid and a depth-first traversal algorithm are used, and the path movement order is set to clockwise or counterclockwise. For each step of movement, it is determined whether the target cell is an obstacle. Crossing the spanning tree boundary within the same original cell is prohibited. When moving across the original cell, there must be a spanning tree edge connection. If it is movable, it is pushed into the stack, otherwise it is backtracked until all boundaries are traversed. Finally, a closed surrounding path without omissions, duplications, or conflicts is generated, thereby achieving efficient full coverage of the target sea area by the unmanned boat.

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