Risk awareness-based unmanned ship path planning method in anchored ground area

Abstract

The invention provides an anchoring ground area unmanned ship path planning method based on risk perception, and aims to improve the safety and efficiency of an unmanned ship sailing in an anchoring ground area. The method comprises the following steps: firstly, carrying out space division and rasterization on an anchored ground area through a Voronoi polygon, introducing a ship field and a Gaussian influence function to carry out risk assessment on each grid, and generating an initial path; sequentially carrying out two-time path smoothing on the initial path based on a Bresenham straight line algorithm and a cubic B spline algorithm, and carrying out autonomous navigation on the unmanned ship in the anchored ground area according to the two-time smoothed path; according to the method, the safety of the path is ensured, and the influence of a high-risk area is avoided; meanwhile, the path length is reduced on the premise of ensuring the safety, and the path execution efficiency is improved; in addition, the turning frequency is reduced through the smooth path, and the operability and stability of the path are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of ship path planning, and more specifically, to a risk-aware based unmanned ship path planning method for an anchorage area. Background Art

[0002] An unmanned surface vessel (USV) is a surface vehicle that can navigate autonomously and does not require crew operation. Unmanned ships can reduce the risk of collision in complex navigation environments and undertake tasks such as maritime monitoring and material transportation. Usually, unmanned ships are small in size and do not require manual operation, which significantly improves safety, improves operating efficiency, and reduces labor costs when crossing anchorage areas. Unmanned ships can monitor the marine environment and the status of anchored ships in real time, effectively improving safety management efficiency. In addition, unmanned ships can efficiently transport materials in various weather and sea conditions, and are particularly suitable for high-risk environments or areas that are not suitable for manual operation. In recent years, unmanned ships have been increasingly used in the fields of marine monitoring, environmental protection, channel cruising, port operations, etc.

[0003] As the core technology in USV autonomous navigation, path planning directly affects the safety, efficiency and energy consumption of navigation. In complex environments, path planning not only needs to consider the shortest length of the path, but also must effectively avoid obstacles, risk areas and dynamic environmental factors. At present, various path planning algorithms have been applied to different scenarios, including A* algorithm and Voronoi-based A* algorithm, Dijkstra algorithm, artificial potential field (APF), rapidly expanding random tree (RRT), genetic algorithm (GA) and particle swarm optimization (PSO).

[0004] In anchorage areas, the high density of ships moored makes traditional path planning complicated and difficult to ensure safety and efficiency at the same time. The close distance between ships increases the risk of collision of unmanned vessels (USVs). Although existing path planning algorithms have made important progress in many fields, they still have some problems when applied to path planning in complex environments. Although the traditional A algorithm and Voronoi-based A algorithm can generate the shortest path or avoid obstacles, they fail to effectively consider path safety, and the generated paths are often not smooth enough, with problems of operational complexity and high energy consumption. Although the RRT algorithm has strong exploration capabilities, it lacks path smoothness and global optimization capabilities, and is prone to falling into local optimal solutions. Although the PSO algorithm performs well in global optimization, it has shortcomings in path safety and efficiency.

[0005] In recent years, the application of deep learning technology in the field of path planning has gradually increased, especially in autonomous driving and drone navigation. Deep learning algorithms can predict potential risks in the path and optimize path selection by training a large amount of historical data. These methods are usually based on network structures such as convolutional neural networks (CNN) and recurrent neural networks (RNN), and can perform path planning in complex environments. However, deep learning path planning methods usually require a large amount of training data and computing resources, and the model training time is long and the real-time performance is poor. In addition, deep learning methods are also weak in considering path safety in dynamic environments, especially for unknown obstacles and risk areas.

[0006] Therefore, it is necessary to develop a path planning scheme that can ensure path safety while optimizing path smoothness and computational efficiency. Summary of the invention

[0007] In order to overcome the defects of the above-mentioned prior art that it is difficult to take into account path safety, path smoothness, computational efficiency and environmental adaptability when performing path planning in complex environments, the present invention provides an unmanned ship path planning method in an anchorage area based on risk perception. In combination with risk perception, a Gaussian influence function is used to model the risk field. After the path is optimized, a double-stage smoothing strategy (DPSS) is applied to smooth the path to ensure the smoothness and feasibility of the path, and to identify and avoid risk areas while maintaining the efficiency of path planning.

[0008] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0009] A method for unmanned ship path planning in an anchorage area based on risk perception comprises the following steps:

[0010] S1: obtaining an environmental map of an anchorage area, using the coordinates of each anchored ship in the anchorage area as seed points to generate Voronoi polygons, dividing the environmental map into a plurality of Voronoi polygons, and performing rasterization processing on the divided environmental map;

[0011] S2: Perform risk assessment on each grid inside each Voronoi polygon based on the Gaussian influence function, and perform initial path planning based on the risk assessment results to obtain the initial path;

[0012] S3: performing a first path smoothing on the initial path based on the Bresenham straight line algorithm to eliminate unnecessary turns and redundant nodes in the initial path, and obtaining a first smoothed path;

[0013] S4: performing a second path smoothing on the first smooth path based on a cubic B-spline algorithm to reduce the number of sharp turns in the first smooth path, and obtaining a second smooth path;

[0014] The unmanned ship performs autonomous navigation in the anchorage area according to the second smooth path.

[0015] Preferably, in step S1, each of the Voronoi polygons is independently subjected to risk assessment;

[0016] The distance between the coordinates of each anchored ship and the boundary of its corresponding Voronoi polygon is half of the ship spacing; each anchored ship only affects the navigable waters within its corresponding Voronoi polygon.

[0017] Preferably, in step S1, the coordinates of the anchored vessel are marked as (x 0 ,y 0 ), the ship heading angle is θ, then the safety area around the anchored ship is an elliptical no-navigation area, and the center point of the ellipse is (x 0 ,y 0 ), the semi-major axis is a, the semi-minor axis is b, and a and b are the first and second preset parameters respectively.

[0018] Preferably, in step S2, performing risk assessment on each grid inside each Voronoi polygon comprises the following steps:

[0019] The center point of the grid is marked as (x, y), and the coordinates of the unmanned ship at the grid position and the anchored ship (x) are calculated according to the following steps. 0 ,y 0 ) Risk value of collision:

[0020] Take the point (x, y) as the starting point, θ as the ship heading angle, and use the coordinates of the anchored ship (x 0 ,y 0 ) Rotate the ship heading coordinate system:

[0021] x rot =cos(θ)·(xx 0 )+sin(θ)·(yy 0 )

[0022] y rot = -sin(θ)·(xx 0 )+cos(θ)·(yy 0 )

[0023] Among them, (x rot ,y rot ) is the coordinate of the center point of the grid after rotation transformation;

[0024] Determine the center coordinates of the grid after rotation transformation (x rot ,y rot) is located in the elliptical no-fly zone: If the point (x rot ,y rot )satisfy Then the point (x rot ,y rot ) In the elliptical no-fly zone, the distance d from the center of the grid to the boundary of the no-fly zone is set to 0; otherwise, the point (x rot ,y rot ) is not within the elliptical no-fly zone, further calculate the point (x rot ,y rot ) to the boundary of the restricted area;

[0025] Based on the Gaussian influence function, the risk value D(n) of the grid is calculated according to the distance d:

[0026]

[0027] Where n is the identifier of the grid; σ is the parameter of the Gaussian influence function.

[0028] Preferably, when the point (x rot ,y rot ) is not within the elliptical no-fly zone, calculate the angle θ of the point relative to the center of the elliptical no-fly zone point :

[0029] θ point =arctan2(y rot ,x rot )

[0030] According to the angle θ point , calculate the corresponding boundary point (x edge ,y edge ):

[0031] x edge =acos(θ point )

[0032] y edge =bsin(θ point )

[0033] Calculate the center point coordinates (x rot ,y rot ) to the boundary of the restricted area:

[0034]

[0035] Preferably, in step S2, initial path planning is performed based on any one of an A* algorithm, a genetic algorithm and a reinforcement learning algorithm according to the risk assessment result to obtain the initial path.

[0036] Preferably, in step S2, initial path planning is performed based on the A* algorithm according to the risk assessment result, including the following steps:

[0037] The traditional A* algorithm is improved and expressed as:

[0038] f(n)=p(n)+h(n)

[0039]

[0040] Among them, f(n) is the total cost of the current node, p(n) represents the path cost from the starting point S to the current node n, h(n) represents the estimated minimum cost from the current node n to the target node G, (x G ,y G ) is the coordinate of the target node G; (x n ,y n ) is the coordinate of the current node n;

[0041] The improved A* algorithm is used to perform initial path planning in the rasterized environment map to obtain the initial path, which includes several discrete coordinate points P 0 ,P 1 ,..,P n .

[0042] Preferably, step S3 comprises the following steps:

[0043] S31: Using the starting point P of the original path 0 Initialize the first smooth path P smoothed , expressed as: P smoothed = {P 0};

[0044] S32: Set the starting point P 0 As the starting point, other points after the starting point in the original path are taken as the end points, and temporary connections are established using line segments, and the Bresenham straight line algorithm is used to obtain the discrete point set P between the two endpoints of each line segment. line ;

[0045] S33: Calculate each discrete point set P line The risk value of each point in the filter is used to select a discrete point set P whose risk value of all internal points does not exceed the preset risk threshold. l ′ ine , and obtain P l ′ ine The corresponding line segments;

[0046] S34: In P l′ ine In the corresponding line segments, add the endpoint of the longest line segment to the first smooth path P smoothed , update the first smooth path P smoothed ;

[0047] S35: The first smooth path P smoothed The newly added point in the image is used as the starting point of the new line segment, and steps S32 to S34 are repeated to continuously update the first smooth path P. smoothed , and the first smooth path P obtained by the last update smoothed Save and complete the first path smoothing.

[0048] Preferably, step S4 comprises the following steps:

[0049] In the first smooth path P smoothed In the example, new control points are inserted at fixed distances to obtain the path P after the control points are inserted. control , where P control = {P 0 , P 1 , ..., P m}, m is the number of path points after inserting the control point;

[0050] Using the path P after inserting the control point control Construct a third-order B-spline curve S(t):

[0051]

[0052] Among them, t∈[0,1] is the preset parameter; N i (t) is the basis function; P i P control The i-th point in ;

[0053] Generate a path P according to the third-order B-spline curve S(t) b-spline , the path P b-spline as the second smooth path.

[0054] Preferably, the step S4 further comprises:

[0055] Calculate the path P b-spline With the first smooth path P smoothed The absolute value of the total length difference is used to determine whether the absolute value of the difference is less than or equal to the preset change threshold. If so, the path P is b-spline as the second smooth path; otherwise, regenerate the path P b-spline , and make a new judgment.

[0056] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0057] The present invention provides a path planning method for an unmanned ship in an anchorage area based on risk perception. First, an environmental map of the anchorage area is obtained, the coordinates of each anchored ship in the anchorage area are respectively used as seed points to generate Voronoi polygons, the environmental map is divided into a plurality of Voronoi polygons, and the divided environmental map is rasterized; then, risk assessment is performed on each grid inside each Voronoi polygon based on a Gaussian influence function, and initial path planning is performed according to the risk assessment result to obtain an initial path; then, a first path smoothing is performed on the initial path based on a Bresenham straight line algorithm to eliminate unnecessary turns and redundant nodes in the initial path to obtain a first smoothed path; finally, a second path smoothing is performed on the first smoothed path based on a cubic B-spline algorithm to reduce the number of sharp turns in the first smoothed path to obtain a second smoothed path; the unmanned ship performs autonomous navigation in the anchorage area according to the second smoothed path;

[0058] The present invention proposes a risk-aware path optimization algorithm (denoted as RAPO algorithm), which has the following advantages over the prior art:

[0059] 1) Ensure path security:

[0060] The primary beneficial effect of the present invention is to ensure the safety of the path. Through the risk assessment mechanism, the present invention can effectively detect high-risk areas (such as obstacles, other ships, dangerous waters, etc.) in the path; in the process of path generation, the Gaussian influence function is combined with the Voronoi diagram to perform risk assessment on each point in the environment, thereby ensuring that the path avoids high-risk areas; in practical applications, each point of the path has undergone a safety check, and the path is only planned in the low-risk area, thereby effectively avoiding the possible safety defects of traditional algorithms;

[0061] 2) Reduce the path length while ensuring safety:

[0062] On the basis of ensuring the safety of the path, the present invention effectively reduces the total length of the path through the optimization algorithm. The reduction of the path length not only improves the efficiency of path planning, but also reduces the energy consumption required during the operation. Compared with the traditional algorithm, the present invention can avoid lengthy detours and generate a more direct and shorter path by comprehensively considering the safety of the path and the optimization goal.

[0063] 3) Improve path smoothness:

[0064] The present invention effectively improves the smoothness of the path by introducing the Bresenham straight line algorithm and the B-spline smoothing algorithm; sharp turns and unnecessary deviations in the path are significantly reduced, and the generated path is smoother, which facilitates the unmanned ship (USV) to perform smooth navigation operations;

[0065] 4) Reduce computational complexity and improve computational efficiency:

[0066] In the process of path planning and optimization, the present invention adopts the Bresenham algorithm of integer operations, which greatly reduces the complexity of calculation and improves the calculation efficiency of path planning, especially in large-scale environments, and can quickly calculate the path and perform risk assessment and path optimization. Compared with traditional path planning algorithms, the present invention can achieve a better balance between efficiency and safety, and adapt to the needs of path adjustment in complex environments;

[0067] 5) Enhance the robustness and adaptability of path planning:

[0068] The path smoothing algorithm of the present invention has strong robustness and adaptability. In dynamic environments, especially in anchorage areas and complex marine environments, path optimization is crucial. By combining the Gaussian influence function with the B-spline smoothing algorithm, the path can be adjusted according to changes in the environment to ensure that the path always remains safe and exhibits high stability and accuracy during path execution. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of a method for unmanned ship path planning in an anchorage area based on risk perception provided in Example 1.

[0070] Figure 2 This is a schematic diagram of the elliptical ship field provided in Example 2.

[0071] Figure 3 This is a schematic diagram of the Gaussian influence function with σ=80 provided in Example 2.

[0072] Figure 4 This is a schematic diagram of risk distribution around a single anchored vessel provided in Example 2.

[0073] Figure 5 This is a schematic diagram of path smoothing based on the Bresenham algorithm provided in Example 2.

[0074] Figure 6 This is a schematic diagram of cubic B-spline path smoothing provided in Example 2.

[0075] Figure 7 This is a schematic diagram of the simulated ship position and Voronoi polygon division provided in Example 3.

[0076] Figure 8 This is a schematic diagram of the rasterization processing provided in Example 3.

[0077] Fig. 9 This is a risk distribution diagram of each anchored ship provided in Example 3.

[0078] Fig.10 This is a diagram of the path planning results using the RAPO algorithm provided in Example 3 when the risk tolerance is 1.5. DETAILED DESCRIPTION

[0079] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0080] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0081] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0082] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0083] Example 1

[0084] like Figure 1 As shown, this embodiment provides a method for unmanned ship path planning in an anchorage area based on risk perception, comprising the following steps:

[0085] S1: obtaining an environmental map of an anchorage area, using the coordinates of each anchored ship in the anchorage area as seed points to generate Voronoi polygons, dividing the environmental map into a plurality of Voronoi polygons, and performing rasterization processing on the divided environmental map;

[0086] S2: Perform risk assessment on each grid inside each Voronoi polygon based on the Gaussian influence function, and perform initial path planning based on the risk assessment results to obtain the initial path;

[0087] S3: performing a first path smoothing on the initial path based on the Bresenham straight line algorithm to eliminate unnecessary turns and redundant nodes in the initial path, and obtaining a first smoothed path;

[0088] S4: performing a second path smoothing on the first smooth path based on a cubic B-spline algorithm to reduce the number of sharp turns in the first smooth path, and obtaining a second smooth path;

[0089] The unmanned ship performs autonomous navigation in the anchorage area according to the second smooth path.

[0090] In the specific implementation process, firstly, the environmental map of the anchorage area is obtained, the coordinates of each anchored ship in the anchorage area are used as seed points to generate Voronoi polygons, the environmental map is divided into several Voronoi polygons, and the divided environmental map is rasterized;

[0091] Then, risk assessment is performed on each grid inside each Voronoi polygon based on the Gaussian influence function, and initial path planning is performed according to the risk assessment results to obtain the initial path;

[0092] Then, the initial path is smoothed for the first time based on the Bresenham straight line algorithm to eliminate unnecessary turns and redundant nodes in the initial path and obtain the first smooth path;

[0093] Finally, the first smooth path is smoothed for the second time based on the cubic B-spline algorithm to reduce the number of sharp turns in the first smooth path and obtain the second smooth path; the unmanned ship performs autonomous navigation in the anchorage area according to the second smooth path;

[0094] This method first ensures the safety of the path and avoids the impact of high-risk areas; secondly, under the premise of ensuring safety, the path length is reduced through a comprehensive optimization algorithm, thereby improving the efficiency of path execution; finally, the number of turns is reduced by smoothing the path, thereby improving the operability and stability of the path; compared with the existing technology, this method has significant improvements in the safety, optimization and computational efficiency of path planning, and is suitable for the practical application of autonomous navigation equipment such as USVs, and has important technical advantages.

[0095] Example 2

[0096] This embodiment provides a method for unmanned ship path planning in an anchorage area based on risk perception, comprising the following steps:

[0097] S1: obtaining an environmental map of an anchorage area, using the coordinates of each anchored ship in the anchorage area as seed points to generate Voronoi polygons, dividing the environmental map into a plurality of Voronoi polygons, and performing rasterization processing on the divided environmental map;

[0098] S2: Perform risk assessment on each grid inside each Voronoi polygon based on the Gaussian influence function, and perform initial path planning based on the risk assessment results to obtain the initial path;

[0099] S3: performing a first path smoothing on the initial path based on the Bresenham straight line algorithm to eliminate unnecessary turns and redundant nodes in the initial path, and obtaining a first smoothed path;

[0100] S4: performing a second path smoothing on the first smooth path based on a cubic B-spline algorithm to reduce the number of sharp turns in the first smooth path, and obtaining a second smooth path;

[0101] The unmanned vessel autonomously navigates in the anchorage area according to the second smooth path;

[0102] In the step S1, each of the Voronoi polygons is independently subjected to risk assessment;

[0103] The distance between the coordinates of each anchored ship and the boundary of its corresponding Voronoi polygon is half of the ship spacing; each anchored ship only affects the navigable waters within its corresponding Voronoi polygon;

[0104] In step S1, the coordinates of the anchored vessel are marked as (x 0 ,y 0 ), the ship heading angle is θ, then the safety area around the anchored ship is an elliptical no-navigation area, and the center point of the ellipse is (x 0 ,y 0 ), the semi-major axis is a, the semi-minor axis is b, a and b are the first and second preset parameters respectively;

[0105] In step S2, risk assessment of each grid inside each Voronoi polygon includes the following steps:

[0106] The center point of the grid is marked as (x, y), and the distance between the unmanned ship and the anchored ship (x) is calculated according to the following steps. 0 ,y 0 ) Risk value of collision:

[0107] Take the point (x, y) as the starting point, θ as the ship heading angle, and use the coordinates of the anchored ship (x 0 ,y 0 ) Rotate the ship heading coordinate system:

[0108] x rot =cos(θ)·(xx 0 )+sin(θ)·(yy 0 )

[0109] y rot = -sin(θ)·(xx 0 )+cos(θ)·(yy 0 )

[0110] Among them, (x rot ,y rot ) is the coordinate of the center point of the grid after rotation transformation;

[0111] Determine the center coordinates of the grid after rotation transformation (x rot ,y rot ) is located in the elliptical no-fly zone: If the point (x rot ,y rot )satisfy Then the point (x rot ,y rot ) In the elliptical no-fly zone, the distance d from the center of the grid to the boundary of the no-fly zone is set to 0; otherwise, the point (x rot ,y rot ) is not within the elliptical no-fly zone, further calculate the point (x rot ,y rot ) to the boundary of the restricted flight area;

[0112] Based on the Gaussian influence function, the risk value D(n) of the grid is calculated according to the distance d:

[0113]

[0114] Where n is the identifier of the grid; σ is the parameter of the Gaussian influence function;

[0115] When point (x rot ,y rot ) is not within the elliptical no-fly zone, calculate the angle θ of the point relative to the center of the elliptical no-fly zone point :

[0116] θ point =arctan2(y rot ,x rot )

[0117] According to the angle θ point , calculate the corresponding boundary point (x edge ,y edge ):

[0118] x edge =acos(θ point )

[0119] y edge =bsin(θ point )

[0120] Calculate the center point coordinates (x rot ,y rot ) to the boundary of the restricted area:

[0121]

[0122] In step S2, initial path planning is performed based on any one of the A* algorithm, the genetic algorithm and the reinforcement learning algorithm according to the risk assessment result to obtain the initial path; in this embodiment, the initial path planning based on the A* algorithm includes the following steps:

[0123] The traditional A* algorithm is improved and expressed as:

[0124] f(n)=p(n)+h(n)

[0125]

[0126] Among them, f(n) is the total cost of the current node, p(n) represents the path cost from the starting point S to the current node n, h(n) represents the estimated minimum cost from the current node n to the target node G, (x G ,y G ) is the coordinate of the target node G; (x n ,y n ) is the coordinate of the current node n;

[0127] The improved A* algorithm is used to perform initial path planning in the rasterized environment map to obtain the initial path, which includes several discrete coordinate points P 0 , P 1 , .., P n ;

[0128] The step S3 comprises the following steps:

[0129] S31: Using the starting point P of the original path 0 Initialize the first smooth path P smoothed , expressed as: P smoothed = {P 0};

[0130] S32: Set the starting point P 0 As the starting point, other points after the starting point in the original path are taken as the end points, and temporary connections are established using line segments, and the Bresenham straight line algorithm is used to obtain the discrete point set P between the two endpoints of each line segment. line ;

[0131] S33: Calculate each discrete point set P line The risk value of each point in the filter is used to select a discrete point set P′ whose risk value of all internal points does not exceed the preset risk threshold. line , and obtain P′ line The corresponding line segments;

[0132] S34: In P′ line In the corresponding line segments, add the endpoint of the longest line segment to the first smooth path Psmoothed , update the first smooth path P smoothed ;

[0133] S35: The first smooth path P smoothed The newly added point in the image is used as the starting point of the new line segment, and steps S32 to S34 are repeated to continuously update the first smooth path P. smoothed , and the first smooth path P obtained by the last update smoothed Save and complete the first path smoothing;

[0134] The step S4 comprises the following steps:

[0135] In the first smooth path P smoothed In the example, new control points are inserted at fixed distances to obtain the path P after the control points are inserted. control , where P control = {P 0 , P 1 , ..., P m}, m is the number of path points after inserting the control point;

[0136] Using the path P after inserting the control point control Construct a third-order B-spline curve S(t):

[0137]

[0138] Among them, t∈[0,1] is the preset parameter; N i (t) is the basis function; P i P control The i-th point in ;

[0139] Generate a path P according to the third-order B-spline curve S(t) b-spline , the path P b-spline as the second smooth path;

[0140] The step S4 further comprises:

[0141] Calculate the path P b-spline With the first smooth path P smoothed The absolute value of the total length difference is used to determine whether the absolute value of the difference is less than or equal to the preset change threshold. If so, the path P is b-spline as the second smooth path; otherwise, regenerate the path P b-spline , and make a new judgment.

[0142] In the specific implementation process, firstly, the environmental map of the anchorage area is obtained, the coordinates of each anchored ship in the anchorage area are used as seed points to generate Voronoi polygons, the environmental map is divided into several Voronoi polygons, and the divided environmental map is rasterized;

[0143] Then, risk assessment is performed on each grid inside each Voronoi polygon based on the Gaussian influence function. In this embodiment, risk assessment is performed independently on each Voronoi polygon.

[0144] The ship domain is a concept used to represent the safe area around a ship. Usually, it is defined as a two-dimensional area around a ship that other ships should avoid entering to prevent collision. The size and shape of the ship domain can vary depending on the size, speed and navigation environment of the ship; e.g. Figure 2 As shown in Figure 1, the ship domain is usually quantified by boundary radii in four directions: front (bow), rear (stern), left (port) and right (starboard). These boundary radii are usually expressed in multiples of the ship length (L). By establishing a no-sail zone around the ship, collision accidents can be effectively prevented.

[0145] Reasonable establishment of a no-fly zone can significantly reduce the risk of collision, improve navigation efficiency, and enhance overall safety. In this embodiment, an ellipse is directly used as a restricted area. Using an ellipse as a no-fly zone around a moored ship has significant advantages. The major axis of the elliptical no-fly zone is aligned with the longitudinal axis of the ship, providing a larger front and rear safety distance, and the minor axis provides a lateral safety distance to prevent other ships from approaching the side of the moored ship, thereby reducing the risk of collision. In this embodiment, the elliptical no-fly zone is set based on the captain's navigation experience. For example, if the length of the ship is L, the semi-major axis of the major axis is 1.2L; if the width of the ship is W, the semi-minor axis of the minor axis is 2W, and the grid risk value in the no-fly zone is set to infinity. In this embodiment, the coordinates of the anchored ship are marked as (x 0 ,y 0 ), the ship heading angle is θ, then the safety area around the anchored ship is an elliptical no-navigation area, and the center point of the ellipse is (x 0 ,y 0 ), the semi-major axis is a, and the semi-minor axis is b;

[0146] When an unmanned ship (USV) is sailing in an anchorage area, the anchored ship poses a certain risk to the USV, which can be characterized by a Gaussian function. The Gaussian influence function is a variant of the Gaussian function, which is mainly used to describe the exponential influence of a certain quantity with distance or time. Its form is shown in the following formula:

[0147]

[0148] In the Gaussian influence function, the value of f(x) ranges from (0,1), which is consistent with the typical risk value range; the Gaussian influence function is used to describe the ship domain and evaluate the risk with high reliability and effectiveness. In risk assessment, the Gaussian influence function represents the attenuation of risk with distance, providing an intuitive and computationally simple model for path planning and obstacle avoidance; its smoothness and symmetry ensure the continuity and uniformity of risk distribution, making it particularly suitable for representing high-risk areas near moored ships, where the risk gradually decreases with increasing distance; in this embodiment, the map is divided into Voronoi polygons, and the distance from each ship to the boundary of the Voronoi polygon is half of the ship spacing, and the risk brought by each moored ship is limited to its assigned Voronoi polygon; for example, a Gaussian influence function with a parameter of σ=80 can be used to depict the risk value, such as Figure 3 As shown;

[0149] The Gaussian influence function ensures that the risk gradually decreases with the increase of distance, and naturally simulates the risk brought by the moored ship to the surrounding environment. By calculating the distance d from a point to the boundary of the no-fly zone and applying the Gaussian influence function, an accurate risk assessment can be provided for path planning, thereby enhancing navigation safety and the effectiveness of path selection. In this embodiment, the map is converted into a grid, where d is the distance from the center of the grid to the boundary of the no-fly zone, and its calculation method is as follows:

[0150] The center point of the grid is marked as (x, y), and the distance between the unmanned ship and the anchored ship (x) is calculated according to the following steps. 0 ,y 0 ) Risk value of collision:

[0151] Take the point (x, y) as the starting point, θ as the ship heading angle, and use the coordinates of the anchored ship (x 0 ,y 0 ) Rotate the ship heading coordinate system:

[0152] x rot =cos(θ)·(xx 0 )+sin(θ)·(yy 0 )

[0153] y rot = -sin(θ)·(xx 0 )+cos(θ)·(yy 0 )

[0154] Among them, (x rot ,y rot ) is the coordinate of the center point of the grid after rotation transformation;

[0155] Determine the center coordinates of the grid after rotation transformation (xrot ,y rot ) is located in the elliptical no-fly zone: If the point (x rot ,y rot )satisfy Then the point (x rot ,y rot ) In the elliptical no-fly zone, the distance d from the center of the grid to the boundary of the no-fly zone is set to 0; otherwise, the point (x rot ,y rot ) is not in the elliptical no-fly zone, calculate the angle θ of this point relative to the center of the elliptical no-fly zone point :

[0156] θ point =arctan2(y rot ,x rot )

[0157] According to the angle θ point , calculate the corresponding boundary point (x edge ,y edge ):

[0158] x edge =acos(θ point )

[0159] y edge =bsin(θ point )

[0160] Calculate the center point coordinates (x rot ,y rot ) to the boundary of the restricted area:

[0161]

[0162] Then, based on the Gaussian influence function, the risk value D(n) of the grid is calculated according to the distance d:

[0163]

[0164] Where n is the identifier of the grid; σ is the parameter of the Gaussian influence function;

[0165] Each grid outside the restricted navigation area has a risk value, which is set in the range of [1,2). When d>0, the point is outside the restricted navigation area, and the risk gradually decreases with the increase of distance; when d=0, the point is on the boundary, and the risk value is set to infinity (∞); when d<0, the point is in the restricted navigation area, and the risk value is also set to infinity (∞). The risk caused by a single ship to its surrounding environment is displayed on the grid map, such as Figure 4 As shown, the risk decreases gradually from inside to outside;

[0166] Then, the initial path planning is carried out according to the risk assessment results to obtain the initial path. The traditional A* algorithm only uses the path length as the heuristic function, which causes the planned path to be close to obstacles and cannot effectively guide the unmanned ship (USV) to sail safely and smoothly. To solve this problem, the RAPO algorithm combines the ship domain and the Gaussian influence function to determine the risk area formed by the moored ship for other ships. The risk function is included as part of the RAPO path planning evaluation function.

[0167] The improved A* algorithm is expressed as:

[0168] f(n)=p(n)+h(n)

[0169]

[0170] Among them, f(n) is the total cost of the current node, p(n) represents the path cost from the starting point S to the current node n, h(n) represents the estimated minimum cost from the current node n to the target node G, (x G ,y G ) is the coordinate of the target node G; (x n ,y n ) is the coordinate of the current node n;

[0171] The improved A* algorithm is used to perform initial path planning in the rasterized environment map to obtain the initial path, which includes several discrete coordinate points P 0 , P 1 , .., P n ;

[0172] The initial path generated by the improved A* algorithm, although combined with risk assessment, may contain many redundant nodes and turns. In order to optimize this path, this method uses the Bresenham straight line algorithm to check the connection between each pair of adjacent nodes. The schematic diagram of the Bresenham straight line path smoothing is shown in Figure 5 As shown; if the risk values ​​of all intermediate nodes between the current node and the remote node are within an acceptable range (not exceeding the set threshold), these nodes can be directly connected, thereby skipping the redundant nodes in the middle;

[0173] The overall idea of ​​the first smoothing is to fix the starting point, continuously traverse new end points, find the farthest end point that meets the risk value requirements, and then use this farthest end point as the new starting point, repeat the traversal, and finally skip the redundant nodes in the middle to generate the first smooth path. Specifically:

[0174] S31: Using the starting point P of the original path 0 Initialize the first smooth path Psmoothed , expressed as: P smoothed = {P 0};

[0175] S32: Set the starting point P 0 As the starting point, other points after the starting point in the original path are taken as the end points, and temporary connections are established using line segments, and the Bresenham straight line algorithm is used to obtain the discrete point set P between the two endpoints of each line segment. line ;

[0176] S33: Calculate each discrete point set P line The risk value of each point in the filter is used to select a discrete point set P′ whose risk value of all internal points does not exceed the preset risk threshold. line , and obtain P′ line The corresponding line segments;

[0177] S34: In P′ line In the corresponding line segments, add the endpoint of the longest line segment to the first smooth path P smoothed , update the first smooth path P smoothed ;

[0178] S35: The first smooth path P smoothed The newly added point in the image is used as the starting point of the new line segment, and steps S32 to S34 are repeated to continuously update the first smooth path P. smoothed , and the first smooth path P obtained by the last update smoothed Save and complete the first path smoothing;

[0179] After the initial smoothing of the Bresenham algorithm, although redundant nodes and sharp turns have been partially reduced, there may still be significant angle changes; these changes will lead to larger turning angles, thereby increasing the energy consumption and operating difficulty of the USV in actual operation; in order to further optimize the smoothness and continuity of the path, this embodiment introduces a path smoothing method based on cubic B-splines in the second stage of DPSS; the mathematical definition of the B-spline curve is shown in the following formula:

[0180]

[0181] In the above formula, C(u) represents the point on the curve, P i is the i-th control point, N i，k (u) is the B-spline basis function, where k=3 represents cubic B-spline;

[0182] The recursive definition of the cubic B-spline basis function is as follows:

[0183] For the zero-order B-spline basis function, the formula is as follows:

[0184]

[0185] For higher order B-spline basis functions, as shown in the following formula:

[0186]

[0187] In order to generate a smooth B-spline curve, this embodiment uses uniformly distributed node vectors. If there are n+1 control points, the node vector is usually defined as:

[0188] u={u 0 , v 1 , ..., u k -1,u k , ..., u n ,u n+1 , ..., u n+k}

[0189] These evenly distributed knot vectors ensure smooth transitions between control points in the B-spline curve;

[0190] Specifically, in this embodiment, on the first smooth path P smoothed In the example, new control points are inserted at fixed distances to obtain the path P after the control points are inserted. control , where P control = {P 0 , P 1 , ..., P m}, m is the number of path points after inserting the control point;

[0191] Using the path P after inserting the control point control Construct a third-order B-spline curve S(t):

[0192]

[0193] Among them, t∈[0,1] is the preset parameter; N i (t) is the basis function; P i P control The i-th point in ;

[0194] Generate a path P according to the third-order B-spline curve S(t) b-spline ;

[0195] In order to verify the path smoothing effect, it is necessary to compare the path length, number of turns and curvature before and after smoothing; the number of turns of the path should be significantly reduced, and the curvature should be kept within a reasonable range; the change in path length should be small, so as to ensure the smoothness of the optimized path; this embodiment calculates the path P b-spline With the first smooth path Psmoothed The absolute value of the total length difference is used to determine whether the calculated value is less than or equal to the preset change threshold. If so, the path P is b-spline as the second smooth path; otherwise, regenerate the path P b-spline , re-judge;

[0196] Path P b-spline The total length is calculated according to the following formula:

[0197]

[0198] Finally, the path P that meets the conditions b-spline As the second smooth path, Figure 6 As shown; the unmanned ship performs autonomous navigation in the anchorage area according to the second smooth path;

[0199] First, this method ensures the safety of the path and avoids the impact of high-risk areas; second, under the premise of ensuring safety, the path length is reduced through a comprehensive optimization algorithm, thereby improving the efficiency of path execution; finally, the number of turns is reduced through a smooth path, thereby improving the operability and stability of the path; compared with the existing technology, this method has significant improvements in the safety, optimization, and computational efficiency of path planning, and is suitable for the practical application of autonomous navigation equipment such as USVs, and has important technical advantages;

[0200] It is worth mentioning that the path smoothing and optimization algorithm used in this embodiment can also be combined with other types of path planning and optimization algorithms to replace or enhance them to meet different application requirements; the following are several possible alternatives:

[0201] 1) Path optimization based on genetic algorithms: In the process of path planning, if a more global path search and optimization is required, a genetic algorithm (GA) can be used to replace the traditional A* algorithm; genetic algorithms can effectively find the optimal path in a complex environment by simulating natural selection and genetic operations, and are particularly suitable for multi-objective optimization and nonlinear problems; although the computational complexity of genetic algorithms is relatively high, they are still highly applicable in some applications that require more precision;

[0202] 2) Path planning based on reinforcement learning: In a dynamic environment, if the path needs to be adjusted in real time, reinforcement learning (RL) can be considered as an alternative to path planning. Reinforcement learning can continuously optimize path selection based on environmental feedback, and is particularly suitable for path planning in unmanned driving, drones, and dynamic environments with complex obstacles. In this case, the optimization of path safety and efficiency will be automatically adjusted by the learning algorithm to adapt to complex and dynamically changing environments.

[0203] The path planning and optimization algorithm of this embodiment is not only applicable to unmanned ships (USVs), but can also be flexibly applied to other types of automated navigation platforms, such as:

[0204] Autonomous vehicles: This algorithm can be used for path planning of autonomous vehicles to ensure that obstacles are avoided on the road and the path is smooth; by optimizing the vehicle path, sharp turns and invalid paths are reduced, thereby improving driving efficiency and riding comfort;

[0205] Unmanned aerial vehicle (UAV): For UAVs, especially in complex urban or post-disaster environments, the path planning method of this embodiment can effectively avoid obstacles in flight (such as buildings, wires, bird flocks, etc.), optimize the flight path under the premise of safety, and improve flight stability and endurance;

[0206] The path planning method of this embodiment can also be used in other fields, such as:

[0207] Disaster rescue and emergency response: In disaster rescue or emergency response scenarios, the path optimization algorithm of this embodiment can help emergency vehicles, robots or drones quickly plan the optimal path;

[0208] Maritime logistics and shipping management: The path planning solution of this embodiment can also be applied to maritime logistics and shipping management to provide ships with efficient and safe navigation paths, avoid high-risk waters, and improve shipping efficiency and safety;

[0209] In some applications, path planning should not only focus on safety and path length, but also may need to consider other optimization objectives, such as:

[0210] Minimizing energy consumption: In unmanned ships or unmanned vehicles, the path planning goal can be extended to minimize energy consumption by optimizing the curves and smoothness of the path, reducing sudden acceleration and braking, and extending the energy life;

[0211] Obstacle avoidance optimization: In complex environments, the goal of path planning may be obstacle avoidance optimization. In other words, in addition to ensuring path safety, it is also necessary to consider how to efficiently avoid sudden obstacles (such as other ships, pedestrians, animals, etc.) in a dynamic environment to ensure obstacle avoidance effectiveness.

[0212] Example 3

[0213] This embodiment provides a simulation experiment for verifying the effectiveness of the unmanned ship path planning method in the anchorage area based on risk perception described in Embodiment 2;

[0214] The simulation experiment was carried out on a computer equipped with a Microsoft Windows 11 operating system, an Intel i5 3.10GHz twelve-core CPU and 16GB of memory; in order to verify the rationality and efficiency of the RAPO algorithm proposed in Example 2, the simulation was carried out on a 2D static grid map, and the development environment used was PyCharm.

[0215] In the specific implementation process, referring to the anchorage and anchored ships in a certain water area, the size of the simulated anchorage is set to 5.5km×4.8km, including 60 anchored ships, each of which is between 90 and 150 meters long; the distance between ships is set to 500 to 750 meters; the heading of each ship is evenly distributed between 135° and 165°; the specific positions of the anchored ships are determined by setting their position coordinates; the length of 13 ships is between 90 and 110 meters; the length of 24 ships is between 110 and 130 meters; the length of 23 ships is between 130 and 150 meters; using the coordinates of these anchored ships, the anchorage area is divided by Voronoi polygons to prepare for the risk of introducing anchored ships; through Voronoi polygon division, the distribution of ships in the defined anchorage area is simulated as follows Figure 7 As shown;

[0216] When dealing with environmental maps, grid-based maps are the most commonly used representation and processing form because they can effectively convey spatial information and support the application of various algorithms; considering that the normal length of an unmanned vehicle (USV) is about 10 meters, the grid size is set to 30 meters × 30 meters; Figure 8 The raster maps used in risk assessment are shown;

[0217] Before the simulation experiment, a risk value was assigned to each grid according to the Gaussian influence function; each anchored ship formed a risk area, and the anchored ship was used as a seed point of the Voronoi polygon; each polygon was a risk assessment unit; it was assumed that each anchored ship only affected the navigable waters within its corresponding Voronoi polygon; the distance between anchored ships ranged from 500 to 750 meters, and the shortest distance from an anchored ship to the boundary of its Voronoi polygon was about 250 meters; considering that the main influence range of the Gaussian distribution is concentrated in [-3σ, +3σ], the corresponding actual risk range is 250 meters, so 3σ = 250 is set, and σ≈80 is obtained; therefore, the parameter σ in the Gaussian influence function is set to 80;

[0218] After converting the map to a raster, each grid is assigned a risk value. For the no-fly zone, the risk value is set to infinity; the grid in this area is displayed in white; the risk value of the risk area ranges from 1 to 2; Fig. 9The risk distribution diagram of anchored ships is shown, where “Start” is the starting point and “Goal” is the end point;

[0219] The RAPO algorithm combines risk assessment and DPSS. To verify that the RAPO algorithm can be applied to path planning in the anchoring area, simulation experiments were conducted; Fig.10 The path planning results of the RAPO algorithm when the path risk value is 1.5 are shown, where the three solid lines represent the initial path generated by the risk-modified A* algorithm in RAPO, the path smoothed by the Bresenham algorithm in the first stage, and the final path smoothed by cubic B-spline in the second stage;

[0220] The path planning results show that the RAPO algorithm significantly improves the path length and number of turns by combining DPSS, and performs well under different path risk tolerances. Table 1 shows the path length, number of turns, and maximum turning angle results of the RAPO algorithm when the path risk tolerance is 1.2, 1.5, and 1.8.

[0221] Table 1 Comparison of path length, number of turns and maximum turning angle before and after smoothing under different risk tolerances

[0222]

[0223] Compared with the original path generated by risk assessment in the RAPO algorithm, the length of the smoothed path was reduced by 7.13%, 7.60% and 7.70% respectively; the number of turns was reduced by 81.13%, 90.57% and 94.34% respectively, while the maximum turning angle was reduced by 17.78%, 13.33% and 11.11% respectively; in the comparison of smoothed paths under different risk tolerances, the path length when the risk tolerance was 1.5 was reduced by 4.9% compared with the risk tolerance of 1.2, and the number of turns was reduced by 57.14%; the path length when the risk tolerance was 1.8 was reduced by 0.51% compared with 1.5, and the number of turns was reduced by 50%; the path length when the risk tolerance was 1.8 was reduced by 0.61% compared with 1.2, and the number of turns was reduced by 70%; with the increase of risk tolerance, the generated path length continued to shorten and the number of turns decreased, thereby reducing the operating difficulty and energy consumption of the USV and ensuring the economy of the path.

[0224] The same or similar reference numerals correspond to the same or similar components;

[0225] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0226] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for unmanned ship path planning in an anchorage area based on risk perception, characterized in that: The following steps are involved: S1: obtaining an environmental map of an anchorage area, using the coordinates of each anchored ship in the anchorage area as seed points to generate Voronoi polygons, dividing the environmental map into a plurality of Voronoi polygons, and performing rasterization processing on the divided environmental map; S2: Perform risk assessment on each grid inside each Voronoi polygon based on the Gaussian influence function, and perform initial path planning based on the risk assessment results to obtain the initial path; S3: performing a first path smoothing on the initial path based on the Bresenham straight line algorithm to eliminate unnecessary turns and redundant nodes in the initial path, and obtaining a first smoothed path; S4: performing a second path smoothing on the first smooth path based on a cubic B-spline algorithm to reduce the number of sharp turns in the first smooth path, and obtaining a second smooth path; The unmanned ship performs autonomous navigation in the anchorage area according to the second smooth path.

2. The method for unmanned ship path planning in an anchorage area based on risk perception according to claim 1 is characterized in that: In the step S1, each of the Voronoi polygons is independently subjected to risk assessment; The distance between the coordinates of each anchored ship and the boundary of its corresponding Voronoi polygon is half of the ship spacing; each anchored ship only affects the navigable waters within its corresponding Voronoi polygon.

3. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 1 is characterized in that: In step S1, the coordinates of the anchored ship are marked as (x0, y0), and the ship's heading angle is recorded as θ. Then the safety area around the anchored ship is an elliptical no-navigation area, the center point of the ellipse is (x0, y0), the semi-major axis is a, and the semi-minor axis is b, where a and b are the first and second preset parameters respectively.

4. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 3 is characterized in that: In step S2, risk assessment of each grid inside each Voronoi polygon includes the following steps: The center point coordinates of the grid are marked as (x, y), and the risk value of the unmanned ship colliding with the anchored ship (x0, y0) at the grid position is calculated according to the following steps: Take the point (x, y) as the starting point, θ as the ship heading angle, and use the coordinates (x0, y0) of the anchored ship to rotate the ship heading coordinate system: x rot =cos(θ)·(x-x0)+sin(θ)·(y-y0) y rot =-sin(θ)·(x-x0)+cos(θ)·(y-y0) Among them, (x rot ,y rot ) is the coordinate of the center point of the grid after rotation transformation; Determine the center coordinates of the grid after rotation transformation (x rot ,y rot ) is located in the elliptical no-fly zone: If the point (x rot ,y rot )satisfy Then the point (x rot ,y rot ) In the elliptical no-fly zone, the distance d from the center of the grid to the boundary of the no-fly zone is set to 0; otherwise, the point (x rot ,y rot ) is not within the elliptical no-fly zone, further calculate the point (x rot ,y rot ) to the boundary of the restricted area; Based on the Gaussian influence function, the risk value D(n) of the grid is calculated according to the distance d: Where n is the identifier of the grid; σ is the parameter of the Gaussian influence function.

5. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 4 is characterized in that: When point (x rot ,y rot ) is not within the elliptical no-fly zone, calculate the angle θ of the point relative to the center of the elliptical no-fly zone point : θ point =arctan2(y rot ,x rot ) According to the angle θ point , calculate the corresponding boundary point (x edge ,y edge ): x edge =acos(θ point ) and edge =bsin(θ point ) Calculate the center point coordinates (x rot ,y rot ) to the boundary of the restricted area:

6. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 5 is characterized in that: In the step S2, based on any one of the A* algorithm, the genetic algorithm and the reinforcement learning algorithm, initial path planning is performed according to the risk assessment result to obtain the initial path.

7. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 6 is characterized in that: In step S2, initial path planning is performed based on the A* algorithm and the risk assessment result, including the following steps: The traditional A* algorithm is improved and expressed as: f(n)=p(n)+h(n) Among them, f(n) is the total cost of the current node, p(n) represents the path cost from the starting point S to the current node n, h(n) represents the estimated minimum cost from the current node n to the target node G, (x G ,y G ) is the coordinate of the target node G; (x n ,y n ) is the coordinate of the current node n; The improved A* algorithm is used to perform initial path planning in the rasterized environment map to obtain the initial path, which includes several discrete coordinate points P0, P1, .., P n .

8. The method for unmanned ship path planning in an anchorage area based on risk perception according to claim 1 or 7, characterized in that: The step S3 comprises the following steps: S31: Initialize the first smooth path P using the starting point P0 of the original path smoothed , expressed as: P smoothed ={P0}; S32: Taking the starting point P0 as the starting point and other points after the starting point in the original path as the end points, respectively use line segments to establish temporary connections, and respectively use the Bresenham straight line algorithm to obtain the discrete point set P between the two end points of each line segment line ; S33: Calculate each discrete point set P line The risk value of each point in the filter is used to select a discrete point set P whose risk value of all internal points does not exceed the preset risk threshold. l ′ ine , and obtain P l ′ ine The corresponding line segments; S34: In P l ′ ine In the corresponding line segments, add the endpoint of the longest line segment to the first smooth path P smoothed , update the first smooth path P smoothed ; S35: The first smooth path P smoothed The newly added point in the image is used as the starting point of the new line segment, and steps S32 to S34 are repeated to continuously update the first smooth path P. smoothed , and the first smooth path P obtained by the last update smoothed Save and complete the first path smoothing.

9. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 8 is characterized in that: The step S4 comprises the following steps: In the first smooth path P smoothed In the example, new control points are inserted at fixed distances to obtain the path P after the control points are inserted. control , where P control = {P0,P1,…,P m }, m is the number of path points after inserting the control point; Using the path P after inserting the control point control Construct a third-order B-spline curve S(t): Among them, t∈[0,1] is the preset parameter; N i (t) is the basis function; P i P control The i-th point in ; Generate a path P according to the third-order B-spline curve S(t) b-spline , the path P b-spline as the second smooth path.

10. The method for unmanned ship path planning in anchorage area based on risk perception according to claim 9 is characterized in that: The step S4 further comprises: Calculate the path P b-spline With the first smooth path P smoothed The absolute value of the total length difference is used to determine whether the absolute value of the difference is less than or equal to a preset change threshold. If so, the path P is b-spline as the second smooth path; otherwise, regenerate the path P b-spline , and make a new judgment.

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