A 3D path planning method for an underwater vehicle based on an improved particle swarm algorithm

Abstract

The present invention relates to the field of path planning, and particularly to a three-dimensional path planning method for an underwater vehicle based on an improved particle swarm optimization algorithm. The method includes the following steps: setting tasks and obtaining original data: setting the range of the task sea area and importing the terrain data of the task sea area; in three-dimensional space, establishing a path model from the starting point to the ending point using the three-dimensional coordinates of nodes; establishing an evaluation function considering the safety, executability, and economy of navigation; improving the traditional particle swarm optimization algorithm and using the algorithm to optimize the path; setting algorithm parameters, performing path planning, and obtaining the planning result. The present invention describes the path of the underwater vehicle in three-dimensional coordinates, improves the traditional particle swarm optimization algorithm to enhance the optimization effect, uses this method for path planning of the underwater vehicle, thereby obtaining the optimal planned path, which can significantly improve the optimization quality of the path of the underwater vehicle and enhance the applicability of the path.

Description

Technical Field

[0001] The present invention relates to the field of path planning, and in particular to a three-dimensional path planning method for an underwater vehicle based on an improved particle swarm optimization algorithm. Background Art

[0002] The path planning problem of an underwater vehicle is to construct a reasonable path under specific constraints to meet the navigation requirements of the underwater vehicle. Currently, the commonly used path planning methods mainly include: genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm, ant colony algorithm, and heuristic algorithm, etc. When the underwater vehicle performs tasks, it usually has a clear starting position and arrival position, and the navigation of the vehicle is restricted by its maneuverability. It is necessary to comprehensively consider factors such as the horizontal turning angle, climbing / descending angle, endurance of the underwater vehicle, and the safety and smoothness of the navigation path. However, the existing path planning methods mainly plan based on two-dimensional paths, considering fewer comprehensive factors, and the adopted environmental model does not fully conform to the actual situation, resulting in poor optimization effects of the algorithm and limited applications. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a three-dimensional path planning method for an underwater vehicle based on an improved particle swarm optimization algorithm in view of the deficiencies of the prior art, so that it can plan the path of the underwater vehicle according to the seabed terrain of the mission area, combined with the motion characteristics of the underwater vehicle, comprehensively considering the safety, executability, and economy of navigation, and accordingly perform the path planning of the underwater vehicle to improve the applicability of the planned path.

[0004] To achieve the above object, the present invention adopts the following technical solutions.

[0005] A three-dimensional path planning method for an underwater vehicle based on an improved particle swarm optimization algorithm includes the following steps:

[0006] S1. Set the task and obtain the original data: Set the range of the mission sea area, and import the terrain data of the mission sea area, where the terrain data includes the measurement information of the seabed elevation within the corresponding sea area range;

[0007] S2. Establish a path model: In a three-dimensional space, establish a path model from the starting point to the end point using the three-dimensional coordinates of the nodes;

[0008] S3. Establish a path evaluation model: Consider the safety, executability, and economy of navigation; establish a safety evaluation function based on the water depth of the area passed by the path; establish an executability evaluation function based on the turning angle sizes in the horizontal and vertical directions of the path; establish an economy evaluation function based on the path length of the path, and obtain a comprehensive evaluation function of the path through weighting;

[0009] S4. Improve the traditional particle swarm optimization algorithm and use the algorithm to optimize the path;

[0010] The subscript i is used to distinguish different paths, and the i-th particle represents the i-th path;

[0011] The i-th path is represented as

[0012] The jth node of the i-th path is represented by the three-dimensional coordinates p i,j =[x i,j ,y i,j ,z i,j ] T express;

[0013] The velocity vector of the i-th path is expressed as

[0014] The optimization direction of the middle node is calculated based on the position relationship of three consecutive nodes to improve the adjustment method of particle position; i,j-1 、p i,j and p i,j+1 Represents three consecutive nodes on the path, with the middle node as the starting point and the vector pointing to the previous and next nodes, that is, (p i,j-1 -p i,j ) and (p i,j+1 -p i,j ), set the weighting factors to be c 3 and c 4 , c 3 and c 4 is a random number between 0 and 1, the direction of the weighted sum of the two vectors is used as the position adjustment direction of the point, the direction of the adjustment vector is determined, the adjustment scale factor is h, and the size of the adjustment vector is determined;

[0015] Then node p i,j The speed change value is expressed as:

[0016]

[0017] Then the velocity adjustment matrix of all particles is expressed as u i =[u i,1 ,u i,2 ,...,u i,N ];

[0018] The position is adjusted based on the velocity adjustment matrix, and the particle position update method used is:

[0019] The superscript k represents the number of iterations of the optimization update.

[0020] but The update is only related to the current particle position, as shown below:

[0021]

[0022] Particle velocity update method:

[0023] S5. Set the relevant parameters of the particle swarm algorithm, perform path planning, and obtain the planning result.

[0024] For further supplement or improvement of the above-mentioned three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm, the specific steps of step S1 include: determining the range of the mission sea area to be searched, including the X-direction range [X min , X max and the Y-direction range [Y min , Y max , where X min and X max respectively represent the minimum and maximum values of the mission sea area in the X direction, and Y min and Y max respectively represent the minimum and maximum values of the mission sea area in the Y direction; importing the seabed terrain data within this area, including the measurement information of the seabed elevation within the corresponding sea area range, for path evaluation.

[0025] For further supplement or improvement of the above-mentioned three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm, the X direction is the longitude direction of the sea area, and the Y direction is the latitude direction of the sea area.

[0026] For further supplement or improvement of the above-mentioned three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm, the specific steps of step S3 include:

[0027] S31. Establish an evaluation function model for the horizontal executability of the path

[0028] Determine the turning angles of each section of the navigation path in the horizontal and vertical directions through the nodes on the path. The entire path is divided into N - 1 sections. The path between the nth and (n + 1)th nodes is the nth section of the path, where 1 ≤ n ≤ N - 1. The azimuth angle and pitch angle of the nth section of the path are:

[0029]

[0030] Set the horizontal direction angle change threshold as Th α , and the horizontal turning angle between the nth and (n + 1)th sections in the horizontal direction is |α n+1 - α n |. The horizontal turning angle should be less than the corresponding threshold, |α n+1 - α n | < Th α ; then use the maximum value of the horizontal turning angle change to express the evaluation function of the horizontal executability of the path, that is: f α = max(|αn+1 -α n |) / 2π;

[0031] S32. Establish an executable evaluation function model for the vertical direction angle size and angle change size of the path

[0032] Let the threshold for climbing or descending in the vertical direction be Th β1 ; the threshold for the angle change amount be Th β2 ; the angle in the vertical direction of the nth path segment be β n , then the vertical direction angle change between the nth and the n+1th segments is β n+1 -β n , then the executable evaluation function for the vertical direction angle size and angle change size is:

[0033]

[0034] f β2 = max(|β n+1 -β n |) / 2π;

[0035] S33. Establish an executable evaluation function model for the vertical direction of the path

[0036] The vertical direction executability is through the evaluation function: f β = k 1 ·f β1 + k 2 ·f β2 ;

[0037] where, k 1 represents the horizontal direction execution weight, k 2 represents the weight of the vertical direction angle size and angle change size on the executability;

[0038] S34. Establish an economic evaluation function model for the path

[0039] Evaluate the economy of the path by the navigation distance of the whole path. The navigation distance of the whole path is calculated by the following formula:

[0040]

[0041] Use the ratio of the distance of the whole path to the straight-line distance between the starting point and the ending point as the economic evaluation function:

[0042]

[0043] The shorter the path distance, the closer f L is to 1;

[0044] S35. Establish a safety evaluation function model for the path

[0045] Let the elevation of the minimum seabed within the terrain of the waterway coverage area be denoted by Dpt, and Th DptL denote the depth margin from the seabed, Th DptL ≥0, Th DptH denote the depth margin from the water surface, Th DptH ≥0; PathL and PathH respectively denote the minimum elevation and the maximum elevation of this section of the path; Let c Dpt1 and c Dpt2 indicate whether the distance of this section of the path from the seabed and the sea surface is within the safe range, then:

[0046]

[0047] For a path with N nodes, the subscript n represents the path segment; then the safety evaluation function of the path is expressed as:

[0048] f γ = k 3 ·f Dpt1 + k 4 ·f Dpt2

[0049] k 3 and k 4 represent the weights of two indicators, which are determined according to the severity of the impact of the distance of this path from the seabed and the sea surface on safety. The greater the impact, the greater the weight, and the value range is 0 to 1;

[0050] S36. Establish a comprehensive evaluation function model for the path

[0051] The comprehensive evaluation function model of the underwater vehicle path is calculated by the following formula:

[0052] f = ω 1 f α + ω 2 f β + ω 3 f L + ω 4 f γ

[0053] Among them, ω 1 , ω 2 , ω 3 , ω 4 are respectively the weights of the horizontal angle limit, vertical angle limit, economy, and safety in the executability for the path evaluation.

[0054] Its beneficial effects are as follows:

[0055] The underwater vehicle path planning method based on the improved particle swarm algorithm of the present invention aims at the problems of poor optimization effect and limited application scope in the current underwater vehicle path planning. It directly combines the ocean water depth data, describes the path of the underwater vehicle in three-dimensional coordinates, and improves the traditional particle swarm optimization algorithm to enhance the optimization effect. By using this method for the path planning of the underwater vehicle, an optimal planned path can be obtained. This method can significantly improve the optimization quality of the underwater vehicle path and enhance the applicability of the path. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is the overall flowchart of the embodiment of the present invention;

[0057] Figure 2 are the results of the planned paths of this method and the traditional method;

[0058] Figure 3 are the statistical histograms of the fitness of the planning results of this method and the traditional method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The following describes the present invention in detail with reference to specific embodiments.

[0060] The underwater vehicle path planning method based on the improved particle swarm algorithm of the present invention is mainly used to improve the optimization effect of the underwater vehicle path planning and expand its application scope. It specifically includes the following steps:

[0061] Step 1), according to the task requirements, determine the range of the task sea area to be searched, including the range in the X direction [X min , X max and the range in the Y direction [Y min , Y max , where X min and X max respectively represent the minimum and maximum values in the X direction of the task sea area, and Y min and Y max respectively represent the minimum and maximum values in the Y direction of the task sea area. Generally, the X direction is the longitude direction of the sea area, and the Y direction is the latitude direction of the sea area.

[0062] Based on data content such as the "Digital Bathymetric DataBase", import the seabed terrain data in this area. This data at least includes the measurement information of the seabed elevation within the corresponding sea area range for path evaluation.

[0063] In step 2), establish a path model and set a path evaluation method;

[0064] (1) Path expression method: The path from the starting point to the ending point is represented by the three-dimensional coordinates of a series of nodes. For a path with N nodes, it can be expressed as follows:

[0065]

[0066] The nth column of the matrix represents the three-dimensional coordinates of the nth node on the path. x, y, and z are the coordinate values in three directions respectively.

[0067] (2) Path evaluation method: The evaluation indicators of the path include: mainly considering the safety, executability, economy, etc. of navigation. The safety is evaluated by the water depth of the area passed by the path, the executability is evaluated by the angle size and angle change size in the horizontal and vertical directions of the path, and the economy is evaluated by the path length of the path. The comprehensive evaluation result of the path is obtained by weighting.

[0068] Through the nodes on the path, the turning angles and their changes in the horizontal and vertical directions of each section of the navigation path can be determined. The whole path can be divided into N - 1 sections. The path between the nth and (n + 1)th nodes is the nth section of the path, where 1 ≤ n ≤ N - 1. The azimuth angle and pitch angle of the nth section of the path can be calculated from the node coordinates:

[0069]

[0070]

[0071] A) Executability

[0072] The executability is evaluated by the turning angles of the underwater vehicle in the horizontal and vertical directions on the path. Affected by its own motion performance, the turning angles of the vehicle in the horizontal and vertical directions cannot be too large.

[0073] Let the horizontal direction angle change threshold be Th α , and the horizontal turning angle between the nth and (n + 1)th sections in the horizontal direction can be represented by |α n+1 -α n |. If the horizontal turning angle is less than the corresponding threshold, |α n+1 -α n | < Th α . The executability of a path in the horizontal direction is measured by the maximum value of the horizontal turning angle change:

[0074] f α =max(|α n+1 -α n |) / 2π

[0075] At the same time, there are also certain restrictions on the angle and its change amount of the vehicle in the vertical direction. First of all, the climb or descent in the vertical direction cannot exceed a certain threshold, which is represented by Th β1Secondly, the angle change amount cannot exceed a certain limit, denoted by Th β2 denoted by β n If β n+1 denotes the angle in the vertical direction of the n-th path segment, then the change in the vertical direction angle between the n-th and the (n + 1)-th path segments can be denoted by β n+1 -β n The evaluation method of the vertical direction angle magnitude and the angle change magnitude on the executability is described by the following formula.

[0076]

[0077] f β2 = max(|β n+1 -β n |) / 2π

[0078] Then, the executability in the vertical direction can be comprehensively evaluated from two aspects:

[0079] f β = k 1 ·f β1 + k 2 ·f β2

[0080] where k 1 and k 2 represent the weights of the two indicators. According to the influence degrees of the vertical direction angle magnitude and the angle change magnitude on the navigation, the values of k 1 and k 2 are determined.

[0081] B) Economy

[0082] The economy of the path is evaluated by the navigation distance of the whole path, and the navigation distance of the whole path can be calculated as follows:

[0083]

[0084] Using the ratio of the distance of the whole path to the straight-line distance between the starting point and the ending point as the evaluation criterion:

[0085]

[0086] The shorter the path distance, the closer f L is to 1.

[0087] C) Safety

[0088] The safety of the path mainly considers three aspects: ① the distance of the path from the seabed; ② the distance of the path from the water surface; ③ the lateral distance of the path from obstacles. Being too close to the seabed may lead to grounding accidents, while being closer to the water surface may expose one's own position. At the same time, set the safety distance of the shipping lane, otherwise it may also cause the ship to hit the wall when bypassing obstacles. By comparing the path elevation and the water depth in the corresponding area of the shipping lane, it is determined whether the navigation safety requirements are met.

[0089] For a certain section of the path, let Dpt represent the minimum seabed elevation of the terrain in the shipping lane coverage area, which may be negative, and use Th DptL to represent the depth margin from the seabed (Th DptL ≥0), and Th DptH to represent the depth margin from the water surface (Th DptH ≥0). PathL and PathH respectively represent the minimum elevation and the maximum elevation of this section of the path. Use c Dpt1 and c Dpt2 to represent whether the distance of this section of the path from the seabed and the sea surface is within the safe range:

[0090]

[0091] For a path with N nodes, the subscript n represents the path segment. The evaluation index of path safety can be expressed as:

[0092] f γ = k 3 ·f Dpt1 + k 4 ·f Dpt2

[0093] k 3 and k 4 represent the weights of the two indexes, which are determined according to the severity of the impact of the distance of this path from the seabed and the sea surface on safety. The greater the impact, the greater the weight, and the value range is 0 to 1.

[0094] Through the above analysis, a comprehensive evaluation of the path of the underwater vehicle can be achieved, and it can be calculated by the following formula:

[0095] f = ω 1 f α + ω 2 f β + ω 3 f L + ω 4 f γ

[0096] Among them, ω 1 , ω 2 , ω 3 , ω 4They are the weights of horizontal angle limit, vertical angle limit, economy, and safety on path evaluation in executability, respectively. The weights are set according to the importance of each factor and the actual impact requirements.

[0097] In step 3), the traditional particle swarm velocity update method is improved and used in path planning.

[0098] Use the subscript i to distinguish different paths, then the i-th path can be expressed as p i :

[0099]

[0100] The j-th node of the i-th path can be represented by the three-dimensional coordinate p i,j = [x i,j , y i,j , z i,j T Correspondingly, the velocity vector also has the same dimension. The velocity of the i-th path (i.e., the i-th particle) can be expressed as:

[0101]

[0102] Specifically, the optimization direction of the middle node is calculated based on the positional relationship of three consecutive nodes, and the adjustment method of the particle position is improved. Use p i,j-1 , p i,j and p i,j+1 to represent three consecutive nodes on the path. Taking the middle node as the starting point, vectors pointing to the front and rear nodes are made, namely (p i,j-1 - p i,j ) and (p i,j+1 - p i,j ). Set the weighting factors as c 3 and c 4 , c 3 and c 4 are random numbers between 0 and 1. The direction of the weighted sum of the two vectors is used as the position adjustment direction of this point to determine the direction of the adjustment vector, and the adjustment scale factor is h to determine the magnitude of the adjustment vector. The velocity change value of node p i,j can be expressed as:

[0103]

[0104] Then the velocity adjustment matrix of all particles is expressed as u i = [u i,1 , u i,2 ,..., u i,N . Based on the new position adjustment method of the above velocity, a new particle position update method is adopted: the superscript k represents the iteration number of the optimization update.

[0105] ​

[0106] The update is only related to the current particle position, as shown in the following equation

[0107]

[0108] The particle velocity is updated in the same way:

[0109]

[0110] In step 4), the planning result is obtained.

[0111] Set the relevant parameters of the particle swarm algorithm, perform path planning, and obtain the planning result.

[0112] To verify the effectiveness of the present invention, taking the path planning of a certain sea area as an example, a simulation experiment was carried out. The present invention is designed based on the particle swarm algorithm. In the experiment, the range of the mission sea area is [0, 100] km in the X direction and [0, 120] km in the Y direction; the starting point of the path is set at (37.42, 91.58, -0.12) km. The number of path nodes is set to 16, the number of particles is 40, the number of iterations is 200, the inertia factor w = 0.4, and the learning factors c 1 = 1, c 2 = 0.2. Figure 2 The path planning results using the present method and the traditional particle swarm algorithm are given. It can be clearly seen that the paths planned by both methods can accurately avoid obstacles, and the path planned by the present method to reach the target position is shorter, with smaller fluctuations and smoother. At the same time, 500 simulations were carried out to obtain the fitness values of the planning results under different initial paths, and the distribution histogram is as Figure 3 shown. The mean and standard deviation of the fitness values of the two methods were statistically analyzed. The mean of the traditional method is 0.586, and the standard deviation is 0.134. The mean of the present method is 0.193, and the standard deviation is 0.036. It can be seen that the fitness of the present method is significantly better than that of the traditional method and is more robust.

[0113] The above description shows and describes the embodiments of the invention application. However, as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be changed within the scope of the inventive concept described herein through the above teachings or the techniques in related fields. And the changes and variations made by those skilled in the art without departing from the spirit and scope of the invention shall all be within the protection scope of the appended claims of the invention.

Claims

1. A three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm, characterized in that, it includes the following steps: S1. Set the task and obtain the original data: Set the range of the task sea area, and import the terrain data of the task sea area, where the terrain data contains the measurement information of the seabed elevation within the corresponding sea area range; S2. Establish a path model: In three-dimensional space, establish a path model from the starting point to the ending point using the three-dimensional coordinates of the nodes; S3. Establish a path evaluation model: Consider the safety, executability, and economy of navigation; Based on the water depth of the area passed by the path, establish a safety evaluation function; Based on the turning angles in the horizontal and vertical directions of the path, establish an executability evaluation function; Based on the path length of the path, establish an economy evaluation function, and obtain the comprehensive evaluation function of the path through weighting; S4. Improve the traditional particle swarm algorithm and use this algorithm to optimize the path; Use the subscript i to distinguish different paths, and the i-th particle represents the i-th path; The i-th path is represented as The j-th node of the i-th path is represented by the three-dimensional coordinate p i,j =[x i,j , y i,j , z i,j T denote;​ The velocity vector of the i-th path is expressed as Calculate the optimization direction of the middle node based on the positional relationship of three consecutive nodes, and improve the adjustment method of particle positions; use p i,j-1 , p i,j , and p i,j+1 to represent three consecutive nodes on the path. Taking the middle node as the starting point, vectors pointing to the front and rear nodes are made, namely (p i,j-1 - p i,j ) and (p i,j+1 - p i,j ). Set the weighting factors as c 3 and c 4 . c 3 and c 4 are random numbers between 0 and 1. Take the direction of the weighted sum of the two vectors as the position adjustment direction of this point, determine the direction of the adjustment vector, the adjustment scale factor is h, and determine the magnitude of the adjustment vector; Then the node p i,j The change value of the speed is expressed as: Then the velocity adjustment matrix of all particles is represented as u i = [u i,1 , u i,2 ,..., u i,N ; Based on the velocity adjustment matrix, perform position adjustment, and the adopted particle position update method is: The superscript k represents the iteration number of the optimization update Then The update is only related to the current particle position, as follows: Particle velocity update method: S5. Set the relevant parameters of the particle swarm algorithm, perform path planning, and obtain the planning result.

2. The three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm according to claim 1, characterized in that, The specific steps of step S1 include: determining the range of the mission sea area to be searched, including the X-direction range [X min , X max and the Y-direction range [Y min , Y max , where X min and X max respectively represent the minimum and maximum values of the X direction of the mission sea area, and Y min and Y max respectively represent the minimum and maximum values of the Y direction of the mission sea area; importing the seabed terrain data within this area, including the measurement information of the seabed elevation within the corresponding sea area range, for path evaluation.

3. The three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm according to claim 2, characterized in that, The X direction is the longitude direction of the sea area, and the Y direction is the latitude direction of the sea area.

4. The three-dimensional path planning method for an underwater vehicle based on an improved particle swarm algorithm according to claim 1, characterized in that, The specific steps of step S3 include: S31. Establish an executability evaluation function model for the horizontal direction of the path Determine the turning angles in the horizontal and vertical directions of each section of the navigation path through the nodes on the path. The whole path is divided into N - 1 sections. The path between the n-th and n + 1-th nodes is the n-th section of the path, 1 ≤ n ≤ N - 1. The azimuth angle and pitch angle of the n-th section of the path are: Set the horizontal direction angle change threshold as Th α , the horizontal rotation angle between the nth and (n + 1)th segments in the horizontal direction is |α n+1 - α n |, the horizontal rotation angle is less than the corresponding threshold, |α n+1 - α n | < Th α ; then use the maximum value of the horizontal rotation angle change to express the path horizontal direction executability evaluation function, that is: f α = max(|α n+1 - α n |) / 2π; S32. Establish an executability evaluation function model for the angle size and angle change size in the vertical direction of the path Set the threshold value for vertical climb or descent as Th β1 ; the threshold value for the amount of angle change is Th β2 ; the vertical angle of the nth path segment is β n , then the vertical angle change between the nth and the (n + 1)th segments is β n+1 -β n , then the executable evaluation function for the vertical angle magnitude and the angle change magnitude is as follows: f β2 = max(|β n+1 - β n |) / 2π; S33. Establish an executability evaluation function model for the vertical direction of the particle size The vertical direction execution is through the evaluation function: f β = k 1 · f β1 + k 2 · f β2 ; Among them, k 1 represents the weight for horizontal direction execution, and k 2 represents the weights of the vertical direction angle magnitude and the angle change magnitude on the executability; S34. Establish an economy evaluation function model for the path Evaluate the economy of the path by the navigation distance of the whole path. The navigation distance of the whole path is calculated by the following formula: Use the ratio of the distance of the whole path to the straight-line distance between the starting point and the ending point as the economy evaluation function: The shorter the path distance, the closer f L is to 1; S35. Establish a safety evaluation function model for the path Let Dpt represent the elevation of the lowest seabed within the terrain of the waterway coverage area, and use Th DptL to represent the depth margin Th from the seabed DptL ≥0, Th DptH to represent the depth margin Th from the water surface DptH ≥0; PathL and PathH respectively represent the minimum elevation and the maximum elevation of this section of the path; use c Dpt1 and c Dpt2 to represent whether the distance of this section of the path from the seabed and the sea surface is within the safe range, then: For the path of N nodes, The subscript n represents the path segment; then the safety evaluation function of the path is expressed as: f γ = k 3 · f Dpt1 + k 4 · f Dpt2 k 3 and k 4 represent the weights of two indicators, which are determined according to the severity of the impact of the path on the safety levels of the seabed and the sea surface. The greater the impact, the greater the weight, and the value range is 0 to 1; S36. Establish a comprehensive evaluation function model for the path The comprehensive evaluation function model of the underwater vehicle path is calculated by the following formula: f = ω 1 f α + ω 2 f β + ω 3 f L + ω 4 f γ Among them, ω 1 , ω 2 , ω 3 , ω 4 are the weights of the horizontal angle limit, vertical angle limit, economy, and safety in the executability for path evaluation, respectively.

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