A Global Path Planning Method for Constrained Four-Objective AUV Considering the Existence of Ocean Currents

Abstract

The present invention belongs to the field of AUV path planning, and discloses a constrained four-objective AUV global path planning method considering the presence of ocean currents. A three-dimensional ocean environment model is established considering ocean currents and seabed topography, and under the constraint conditions that the planned path is at a certain safe distance from obstacles and the path nodes of the planned path are inside the established environment model, an AUV navigation path with the shortest possible path length, the path nodes of the planned path as far away from obstacles as possible, the path as smooth as possible, and making full use of ocean currents to reduce energy consumption is searched for. And an improved C-TAEA algorithm with higher selection pressure and preventing from falling into local optimum is used to solve the AUV global path planning problem, and a set of optimal path solutions is obtained.

Description

Technical Field

[0001] The present invention belongs to the field of AUV path planning, and specifically relates to a global path planning method for AUV considering the existence of ocean currents based on a multi-objective evolutionary algorithm. Background Technique

[0002] Due to the extremely complex marine environment, it becomes very difficult for people to carry out some marine rescue activities or marine resource exploration. Autonomous underwater vehicles (AUVs) can effectively solve this problem. Therefore, AUVs currently play an important role in civilian, military, and scientific research. The autonomy of AUVs is mainly manifested in their accurate and efficient tracking and navigation capabilities. However, how to improve the accuracy, safety, etc. of AUVs during underwater navigation is worthy of in-depth study. Reasonable path planning for AUVs can address this problem.

[0003] The primary difficulty in path planning for AUVs is to model the marine environment. Whether the marine environment model is reasonable directly affects the performance of AUV path planning. However, current environmental modeling mostly remains on a two-dimensional plane and does not consider the existence of ocean currents (the path planning algorithm for underwater vehicles based on improved RRT by Yao Min). However, these two factors have a significant impact on AUV path planning because the actual environment where AUVs work is a three-dimensional marine environment, and ocean currents have an important impact on the energy consumption of AUVs. The ocean currents should be utilized to reduce unnecessary energy consumption caused by swimming against the current.

[0004] Currently, when establishing an optimization objective model for AUV path planning, the common method is to transform several objectives of AUV path planning into a single-objective optimization problem by weighting. However, the objectives may conflict with each other, and it is impossible to determine appropriate weight coefficients. Therefore, transforming it into a single-objective problem is inappropriate (the trajectory planning of an unmanned underwater vehicle with multi-objective functions under multiple constraints by Qiu Qianjun et al.). Therefore, in order to improve the tracking and navigation capabilities of AUVs, four objectives, namely path length, path safety, path smoothness, and energy consumption under the condition of the existence of ocean currents, should be considered under the constraints that the AUV is far from obstacles and the path nodes are within the modeled environment. Summary of the Invention

[0005] Ocean currents in the ocean, if utilized reasonably, can reduce the energy consumption during the navigation of an AUV. Conversely, they will have a negative effect. Moreover, there are conflict relationships among the four goals of shortening the path length, improving the safety of the planned path, keeping the path as smooth as possible, and reducing the energy consumption of the AUV in AUV path planning. Optimizing one goal may make the remaining goals worse. Therefore, in the case of known environment, in order to plan a collision-free path for the AUV from the starting point to the ending point, the present invention proposes a constrained four-goal AUV global path planning method considering the existence of ocean currents.

[0006] The technical solution of the present invention:

[0007] A constrained four-goal AUV global path planning method considering the existence of ocean currents, comprising:

[0008] (1) Under the condition of considering the existence of ocean currents and the seabed terrain formed by seamounts or seahills, establish a three-dimensional ocean environment model for constrained four-goal AUV global path planning, including:

[0009]

[0010] The above formula is the seabed terrain model, where n represents the number of seamounts or seahills, (x j , y j ) represents the central coordinate value of the j-th seamount or seahill, l j is the terrain parameter for controlling the height, (cx j , cy j ) is the attenuation amount of the j-th seamount or seahill along the x and y axes;

[0011]

[0012] The above formula is the mathematical expression of the Lamb vortex. The ocean current is modeled by superimposing multiple viscous Lamb vortices. Among them, u(s), v(s), and w(s) respectively represent the velocity magnitude components of the ocean current in the longitude, latitude, and depth directions, k is the vortex intensity magnitude, r is the vortex radius, s0 is the vortex center coordinate value, s represents the position coordinate of any point in the ocean current field, x0 is the x coordinate value of the vortex center, and y0 is the y coordinate value of the vortex center;

[0013] Establish the constraint conditions for AUV global path planning, specifically:

[0014]

[0015] Among them, each path is represented by path=(p1, p2,..., p n+1 ), x i , y i , z irespectively represent the path node p i The position at x, y, z; Z i is the seamount or seahill at node p i The height at; d safe is the safety distance, that is, the path node keeps a safe distance from the seamount or seahill; X upper , Y upper , Z upper is the upper bound of the three-dimensional ocean environment model in three dimensions, X lower , Y lower , Z lower is the lower bound in three dimensions;

[0016] (2) The path nodes in the planned path should leave a safety distance from the obstacles and the path nodes should be inside the established three-dimensional ocean environment model; construct a four-objective optimization model for AUV global path planning, including:

[0017] Construct the corresponding objective functions respectively with the objectives of minimizing the path length, maximizing the distance between the path nodes and the obstacles (i.e., improving safety), enhancing the smoothness of the planned path, and minimizing the AUV energy consumption under the condition of ocean currents;

[0018] Construct the objective function to minimize the path length, specifically:

[0019]

[0020] Among them, assume that each path path=(p1, p2,..., p n+1 ) has n + 1 path nodes, l(p i , p i+1 ) is the Euclidean distance between path nodes p i and p i+1 , p i is represented by (x i , y i , z i ), p i+1 is represented by (x i+1 , y i+1 , z i+1 );

[0021] Construct the objective function to maximize the distance between the path nodes and the obstacles (i.e., improving safety), specifically:

[0022]

[0023] Among them, z i is the z coordinate value (i.e., the height value) at path node p i , Z i is for p iThe height value of the seamount or seahill; d(z i ,Z i ) is the difference between z i subtracted by Z i . If d(z i ,Z i ) is negative, then set the value of d(z i ,Z i ) to 0;

[0024] Construct an objective function to improve the smoothness of the planned path, specifically:

[0025]

[0026] where l(p i ,p i+2 ) is the Euclidean distance between path nodes p i and p i+2 . The larger the angle formed by the nodes of a path, the smoother the path. The angle in a path is determined by three adjacent path nodes. If the angle is larger, the distance between the head and tail nodes of the three adjacent nodes is also larger. Therefore, the distance between the head and tail nodes of every three adjacent nodes in the path is used to evaluate the smoothness of the path;

[0027] Minimize the AUV energy consumption under the condition of ocean current existence, specifically:

[0028]

[0029] Since each path has n + 1 path nodes, each path consists of n sub-paths; where P auv is the thrust of the AUV, t i is the time taken to pass through the i-th sub-path, ken is a constant coefficient, v auv is the navigation speed of the AUV, l i is the i-th sub-path, is the combined speed of the AUV speed and the ocean current speed on the i-th sub-path;

[0030] (3) Use the improved C-TAEA algorithm to solve the AUV global path planning optimization model and obtain a set of AUV navigation path solutions from the starting point to the ending point, including:

[0031] First, set the starting and ending coordinates of the AUV's navigation, generate N paths from the starting point to the ending point as the initial population, and the nodes in each path are randomly generated; the improved C-TAEA algorithm, like the original algorithm, is still a dual-archive evolutionary algorithm, where the CA archive is used to maintain the convergence of the solutions, and the DA archive is used to maintain the diversity of the solutions; in the first iteration, both CA and DA are the initial population, and the choice of parents from CA or DA is determined according to the proportion information of the non-dominated solutions in the CA and DA archives; after selecting two parents, offspring are generated through simulated binary crossover and polynomial mutation operations, and after N iterations of such offspring generation operations, N offspring solutions can be generated;

[0032] From the second iteration to reaching the maximum number of iterations, both CA and DA select N relatively excellent solutions from the union of the parental population and the offspring population;

[0033] In the update process of CA, first calculate the objective values and constraint violation values of the solutions in the union, and then, according to the relationship between the number of feasible solutions in the union and N, use different selection strategies to select N solutions from the union; if the number of feasible solutions is equal to N, the new CA is these feasible solutions; if the number of feasible solutions is greater than N, use a ratio-based binary index and grid difference to select N solutions among the feasible solutions; if the number of feasible solutions is less than N, use a method based on the feasible rate to adaptively balance convergence and feasibility to select N solutions in the union;

[0034] The method based on the feasible rate to adaptively balance convergence and feasibility can prevent the solutions from falling into local optima, specifically:

[0035] f r = Num / N

[0036]

[0037] f = ((1 - f r ) × f′1) + (f r * f′2)

[0038] where, f r is the feasible rate, Num is the number of feasible solutions, N is the size of CA, f1 is the constraint violation, f2 is the fitness value of the solution obtained by the Chebyshev aggregation function, f′1 and f′2 are the normalization functions of f1 and f2, f is the single-objective function transformed by the feasible rate, and in order to maintain the diversity of the solutions at the same time, 1.3 × N solutions are selected from the union according to the function f, and individuals with poor convergence are sequentially deleted from the most crowded area until the size of the solutions in the population is N;

[0039] During the update process of DA, the solutions in the union are divided into different sub-regions. An attempt is made to select one solution in each sub-region to ensure the diversity of solutions. If there is more than one solution in the sub-region, the solution with the best fitness value in the sub-region is selected. If the sub-region is empty, a solution is randomly selected from the union.

[0040] Then, the selection, crossover, and mutation operations are repeated until the maximum number of iterations is reached. The improved C-TAEA algorithm generates an optimal path set for solving the AUV global path planning.

[0041] Advantages of the present invention: Under the conditions of considering ocean currents and seabed topography, the present invention establishes a three-dimensional ocean environment model. And under the constraint conditions that the planned path is at a certain safe distance from obstacles and the path nodes are inside the established environment model, an AUV navigation path with the shortest possible path length, the path nodes of the planned path being as far away from obstacles as possible, the path being as smooth as possible, and making full use of ocean currents to reduce energy consumption is searched for. And the improved C-TAEA algorithm with higher selection pressure and the characteristic of preventing getting stuck in local optimum is used to solve the AUV global path planning problem, and a set of optimal path solutions is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow schematic diagram of the method of the present invention.

[0043] Figure 2 It is a three-dimensional ocean environment model diagram. DETAILED DESCRIPTION OF THE INVENTION

[0044] The following further describes the specific embodiments of the present invention in conjunction with the drawings and technical solutions.

[0045] The present invention is a method for solving the AUV global path planning in a complex ocean environment. In order to improve the accuracy of path planning, a three-dimensional ocean environment including ocean currents and seabed topography is established, and a constrained four-objective AUV global path optimization model is established. However, there are conflicts among the four established objectives.

[0046] Since the evolutionary algorithm can generate several solutions in one solution search, the evolutionary algorithm is very suitable for solving multi-objective optimization problems. However, how to balance the convergence, diversity, and feasibility of the solutions obtained by the evolutionary algorithm is a problem worthy of in-depth study. The present invention improves the C-TAEA algorithm, enhances the selection pressure of the algorithm and prevents getting stuck in local optimum when solving constraint problems, and uses the improved algorithm to solve the constrained AUV global path planning problem to obtain a set of optimal path solutions.

[0047] A constrained four-objective AUV global path planning method considering the existence of ocean currents includes the following steps:

[0048] S1 Complex three-dimensional ocean environment modeling

[0049] S1.1 Ocean current modeling

[0050] The ocean current model established in the present invention does not change with time and is only related to its position. The magnitudes and directions of ocean currents at different positions are different. The ocean current is modeled by superimposing multiple viscous Lamb vortices. The specific model expression is as follows:

[0051]

[0052]

[0053]

[0054] Where u(s), v(s), and w(s) represent the velocity magnitude components of the ocean current in the longitude, latitude, and depth directions respectively, k is the vortex intensity magnitude, r is the vortex radius, s0 is the vortex center coordinate value, s represents the position coordinate of any point in the ocean current field, x0 is the x coordinate value of the vortex center, and y0 is the y coordinate value of the vortex center.

[0055] S1.2 Seabed terrain modeling

[0056] The present invention uses the modeling method of mountains in the UAV flight environment to simulate seamounts or seahills in the ocean environment. The mathematical model of the seabed terrain can be expressed by the following function:

[0057]

[0058] Where n represents the number of seamounts or seahills, (x j ,y j ) represents the center coordinate value of the j-th seamount or seahill, l j is the terrain parameter controlling the height, and (cx j ,cy j ) is the attenuation amount of the j-th seamount or seahill along the x and y axes.

[0059] S2 AUV global path planning optimization model establishment

[0060] S2.1 Constraint condition establishment

[0061] The present invention considers two constraint conditions. One is that the planned path cannot collide with obstacles, and the other is that the planned path should be within the established ocean environment model. Each path is represented by path=(p1,p2,…,p n+1 ), and the path node p i is represented by (x i ,y i ,z i ). The constraint expressions are as follows:

[0062]

[0063] Where x i , y i , z i represent the positions of the path node p i at x, y, and z respectively, and Z i is the height of the seamount or seahill at the node p i , and d safe is the safety distance, that is, the path node should maintain a certain safety distance from the seamount or seahill. X upper , Y upper , Z upper are the upper bounds of the three-dimensional ocean environment model in the three dimensions, and X lower , Y lower , Z lower are the lower bounds in the three dimensions.

[0064] S2.2 Establishment of the objective function

[0065] Under the constraints of ensuring that the planned path nodes do not collide with obstacles and are within the established three-dimensional environment, the corresponding objective functions are constructed with the optimization objectives of minimizing the path length, maximizing the distance between the path nodes and obstacles (i.e., improving safety), enhancing the smoothness of the planned path, and minimizing the AUV energy consumption under the condition of the existence of ocean currents.

[0066] (1) With the optimization objective of minimizing the path length:

[0067] When performing path planning for the AUV, the path should be made as short as possible to avoid ineffective driving that is repetitive, time-consuming, and energy-consuming. The path length is the sum of the Euclidean distances of each path node. It is expressed by the following mathematical formula:

[0068]

[0069] Where l(p i , p i+1 ) is the Euclidean distance between the path nodes p i and p i+1 . Since the generated path is in a three-dimensional environment, p i can be represented by (x i , y i , z i ), and p i+1 can be represented by (x i+1 , y i+1 , z i+1 ).

[0070] (2) Taking the maximization of the distance between path nodes and obstacles, that is, improving safety, as the optimization goal:

[0071] The path safety is calculated by computing the distance between each path node in the path and the seabed terrain height. The expression is as follows:

[0072]

[0073] Where z i is the z - coordinate value (height value) at path node p i , and Z i is the height value of the seamount or seahill at p i . d(z i , Z i ) is the difference between z i subtracted by Z i . If d(z i , Z i ) is negative, then d(z i , Z i ) is taken as 0.

[0074] (3) Taking the improvement of the smoothness of the planned path as the optimization goal:

[0075] If the angles formed by the nodes of a path are larger, then the path is smoother, and a smoother path is more beneficial for the navigation of the AUV. The angle in a path is determined by three adjacent path nodes. If the angle is larger, then the distance between the first and the last nodes among the three adjacent nodes is also larger. Therefore, the present invention uses the distance between the first and the last nodes among every three adjacent nodes in the path to evaluate the smoothness of the path. The expression is as follows:

[0076]

[0077] Where l(p i , p i+2 ) is the Euclidean distance between path nodes p i and p i+2 .

[0078] (4) Taking the minimization of the AUV energy consumption under the condition of the existence of ocean currents as the optimization goal:

[0079] There is a close relationship between the energy consumption during the AUV navigation and the ocean currents. It should sail as much as possible along the current to reduce energy consumption. The mathematical expression of the energy consumption is as follows:

[0080]

[0081] Since each path has n + 1 path nodes, each path consists of n sub - paths. Where P auv is the thrust of the AUV, ti is the time taken for the i-th sub-path, ken is a constant coefficient, v auv is the navigation speed of the AUV, l i is the i-th sub-path, is the combined speed of the AUV speed and the ocean current speed on the i-th sub-path.

[0082] Through the above analysis, the constrained AUV global path planning model is as follows:

[0083]

[0084] Each objective is expressed in a minimized form. If an objective needs to be maximized, its reciprocal or other transformation methods are taken as the new objective function.

[0085] S3 Solving the AUV Global Path Planning Optimization Problem

[0086] The improved C-TAEA algorithm is used to solve the established constrained four-objective AUV global path planning optimization model. After multiple iterations, a set of optimal solutions for the AUV navigation path from the starting point to the ending point is obtained. The improved C-TAEA algorithm introduces a ratio-based binary indicator and a grid-difference-based selection mechanism to ensure the convergence and diversity of the solutions. And in order to better balance the convergence and feasibility of the solutions and prevent the solutions from falling into local optima, an adaptive balance mechanism based on the feasibility rate is proposed. The improved C-TAEA algorithm is compared with the original C-TAEA algorithm and several advanced algorithms AGE-MOEA, PPS, TiGE-2, DCNSGA-III for solving constrained multi-objective optimization problems.

[0087] The improved C-TAEA algorithm is still a double-archive evolutionary algorithm. The CA archive maintains the feasibility and convergence of the solutions, and the DA archive maintains the diversity of the solutions.

[0088] S3.1 Population Initialization

[0089] Set the starting and ending coordinates of the AUV navigation, generate N paths from the starting point to the ending point as the initial population, and the nodes in each path are randomly generated.

[0090] S3.2 Offspring Generation Mechanism

[0091] The present invention follows the offspring generation mechanism in C-TAEA, combines CA and DA into Hm, calculates the proportion of non-dominated solutions in CA and DA in the solutions in Hm. The archive with a larger proportion of non-dominated solutions means better convergence. Then select the first parent P1 from this archive, and the other parent P2 is selected according to the proportion P of non-dominated solutions in CA C for selection. If the generated random number p between 0 and 1 f<P C If so, parent P2 is selected from CA; otherwise, P2 is selected from DA. After the selection operation, simulated binary crossover and polynomial mutation are used to generate offspring.

[0092] S3.3 CA Update Mechanism

[0093] First, CA and the offspring population Q are merged and denoted as Hc. Calculate the number of feasible solutions Sc in Hc. Different mechanisms are selected to update CA according to the relationship between the number of feasible solutions and the population size N, which are divided into the following three categories:

[0094] (1) If the number of feasible solutions is equal to N, the new CA is the feasible solution Sc in the current merged population Hc.

[0095] (2) If the number of feasible solutions is greater than N, a ratio-based binary index and grid difference are used as the solution selection mechanism.

[0096] (3) If the number of feasible solutions is less than N, a method based on the feasible rate to adaptively balance convergence and feasibility is used to select solutions in the merged population Hc.

[0097] The main idea of the method based on the feasible rate to adaptively balance convergence and feasibility is to transform the two objectives of minimizing the constraint violation value and minimizing the fitness value of the solution calculated by the Chebyshev aggregation function into a single-objective problem through the feasible rate of the solutions in the population. The formed single-objective optimization problem has different emphases on the two objectives according to the feasible rate. The feasible rate f r is calculated as follows:

[0098] f r = Num / N

[0099] where Num is the number of feasible solutions. Since the size of CA is N, the ratio of Num to N is used as the feasible rate.

[0100] Let the constraint violation be the first objective f1, and the fitness value of the solution obtained by the Chebyshev aggregation function be the second objective f2. First, f1 and f2 are normalized, and then f1 and f2 are transformed into a single objective through the feasible rate.

[0101]

[0102] f = ((1 - f r ) × f'1) + (f r * f'2)

[0103] It can be seen from f that when the feasible rate is low, more attention is paid to the feasibility of the solution; when the feasible rate is high, more emphasis is placed on the convergence of the solution. Such an adaptive balance mechanism can prevent the solution from falling into a local optimum.

[0104] To simultaneously maintain the diversity of solutions, 1.3×N solutions will be selected from Hc, and individuals with poor convergence will be sequentially deleted from the most crowded regions until the size of the solutions in the population is N.

[0105] S3.4 DA Update Mechanism

[0106] The update mechanism of DA is to select N solutions from the union Hd of DA and the offspring population Q. Therefore, DA is used to maintain the diversity of solutions, so constraints are not considered in the update of DA. The solutions in Hd are associated with weight vectors and divided into N sub-regions. DA will select one solution from each sub-region. If the sub-region is empty, a solution will be randomly selected from Hd. If the number of solutions associated with the sub-region is greater than one, the Chebyshev aggregation function will be used to calculate their fitness values, and the solution with the minimum fitness value in the sub-region will be selected.

[0107] Example:

[0108] First, model the ocean current and seabed topography to simulate the three-dimensional environment of AUV navigation. Then, set the starting point and ending point of AUV navigation, and randomly generate N paths as the initial population. Calculate the constraint violation values of each path solution in the population according to the constraint conditions established in S2.1, and calculate the objective function values of each solution according to the objective function established in S2.2. Next, use the improved C-TAEA algorithm to solve the AUV global path planning optimization problem. Use the offspring generation mechanism in S3.2 to iterate N times to generate an offspring solution population Q with a population size of N. Then, execute the CA update mechanism in S3.3 and the DA update mechanism in S3.4 in the union of the parent population and the offspring population. The CA update mechanism in S3.3 performs different selection operation mechanisms according to the number of feasible solutions in the union of the parent population and the offspring population, and retains N optimal solutions. The DA update mechanism in S3.4 maintains the diversity of solutions and aims to select one solution from each sub-region. Iterate the offspring generation in S3.2, the CA update mechanism in S3.3, and the DA update mechanism in S3.4 until the maximum number of iterations is reached. Finally, the N path optimal solutions are in the CA archive.

Claims

1. A global path planning method for a constrained four-objective AUV considering the existence of ocean currents, characterized in that, Including: (1) Establish a three-dimensional ocean environment model for the global path planning of an AUV with constrained four objectives under the conditions considering ocean currents and the existing seabed topography formed by seamounts or seaknolls, including: The above formula is the seabed terrain model, where n represents the number of seamounts or seaknolls, and (x j , y j ) represents the central coordinate value of the j-th seamount or seaknoll. l j is the terrain parameter for controlling the height, and (cx j , cy j ) is the attenuation amount of the j-th seamount or seaknoll along the x and y axes; The above formula is the mathematical expression of Lamb vortices. The ocean current is modeled by superimposing multiple viscous Lamb vortices. Among them, u(s), v(s), and w(s) respectively represent the velocity magnitude components of the ocean current in the longitude, latitude, and depth directions, k is the vortex intensity magnitude, r is the vortex radius, s0 is the coordinate value of the vortex center, s represents the position coordinate of any point in the ocean current field, x0 is the x coordinate value of the vortex center, and y0 is the y coordinate value of the vortex center; Establish the constraint conditions for the global path planning of the AUV, specifically: Among them, each path is represented by path=(p1, p2, …, p n+1 ), where x i , y i , z i respectively represent the positions of the path node p i at x, y, and z; Z i is the height of the seamount or seahill at the node p i ; d safe is the safety distance, that is, the path node maintains a safe distance from the seamount or seahill; X upper , Y upper , Z upper are the upper bounds of the three-dimensional ocean environment model in three dimensions, and X lower , Y lower , Z lower are the lower bounds in three dimensions; (2) The path nodes in the planned path should leave a safety distance from the obstacles and the path nodes should be inside the established three-dimensional ocean environment model; construct a four-objective optimization model for the global path planning of the AUV, including: Construct corresponding objective functions respectively with the objectives of minimizing the path length, maximizing the distance between the path nodes and the obstacles (i.e., improving safety), enhancing the smoothness of the planned path, and minimizing the energy consumption of the AUV under the condition of the existence of ocean currents; Construct an objective function for minimizing the path length, specifically: Among them, assume that each path path = (p1, p2, …, p n+1 ) has n + 1 path nodes, and l(p i , p i+1 ) is the Euclidean distance between path nodes p i and p i+1 . p i is represented by (x i , y i , z i ), and p i+1 is represented by (x i+1 , y i+1 , z i+1 ); Construct an objective function for maximizing the distance between the path nodes and the obstacles (i.e., improving safety), specifically: where z i is the z - coordinate value (i.e., the height value) at path node p i , and Z i is the height value of the seamount or seahill at p i ; d(z i , Z i ) is the difference between z i and Z i . If d(z i , Z i ) is negative, then d(z i , Z i ) is taken as 0; Construct an objective function for enhancing the smoothness of the planned path, specifically: where l(p i , p i+2 ) is the Euclidean distance between path nodes p i and p i+2 . The larger the angle formed by the nodes of a path, the smoother the path. The angle in a path is determined by three adjacent path nodes. If the angle is larger, the distance between the head and tail nodes among the three adjacent nodes is also greater. Therefore, the distance between the head and tail nodes of every three adjacent nodes in the path is used to evaluate the smoothness of the path; Minimize the energy consumption of the AUV under the condition of the existence of ocean currents, specifically: Since each path has n + 1 path nodes, each path consists of n sub-paths; among them P auv is the thrust of the AUV, t i is the time taken to pass through the i-th sub-path, ken is a constant coefficient, v auv is the navigation speed of the AUV, l i is the i-th sub-path, is the combined speed of the AUV speed and the ocean current speed on the i-th sub-path; (3) Use the improved C-TAEA algorithm to solve the AUV global path planning optimization model to obtain a set of AUV navigation path solutions from the starting point to the ending point, including: First, set the starting and ending point coordinates of the AUV navigation, generate N paths from the starting point to the ending point as the initial population, and the nodes in each path are randomly generated; the improved C-TAEA algorithm is still a double-archive evolutionary algorithm like the original algorithm. Among them, the CA archive is used to maintain the convergence of the solutions, and the DA archive is used to maintain the diversity of the solutions; in the first iteration, both CA and DA are the initial population, and it is decided whether to select parents from CA or from DA according to the proportion information of the non-dominated solutions in the CA and DA archives; after selecting two parents, offspring are generated through simulated binary crossover and polynomial mutation operations. After the offspring generation operation is iterated N times, N offspring solutions can be generated; From the second iteration to reaching the maximum number of iterations, both CA and DA select N relatively excellent solutions from the union of the parent population and the offspring population; During the update process of the CA, first calculate the objective values and constraint violation values of the solutions in the union, and then, according to the relationship between the number of feasible solutions in the union and the size of N, use different selection strategies to select N solutions from the union; if the number of feasible solutions is equal to N, the new CA is these feasible solutions; if the number of feasible solutions is greater than N, use a ratio-based binary index and grid difference to select N solutions from the feasible solutions; if the number of feasible solutions is less than N, use a method based on the feasible rate to adaptively balance convergence and feasibility to select N solutions from the union; The method based on the feasible rate to adaptively balance convergence and feasibility can prevent the solutions from falling into local optima, specifically as follows: f r = Num / N f = ((1 - f r ) × f1 ′ ) + (f r * f2 ′ ) where f r is the feasibility rate, Num is the number of feasible solutions, N is the size of the CA, f1 is the constraint violation, f2 is the fitness value of the solution obtained by the Chebyshev aggregation function, f1 ′ and f2 ′ are the normalization functions of f1 and f2, f is the single-objective function transformed by the feasibility rate. To maintain the diversity of solutions simultaneously, 1.3×N solutions will be selected from the union according to the function f, and the individuals with poor convergence will be deleted from the most crowded area in turn until the size of the solutions in the population is N; During the update process of the DA, divide the solutions in the union into different sub-regions, and strive to select one solution in each sub-region to ensure the diversity of the solutions. If there is more than one solution in the sub-region, select the solution with the best fitness value in the sub-region. If the sub-region is empty, randomly select one solution from the union; Then repeat the selection, crossover, and mutation operations until the maximum number of iterations is met, and the improved C-TAEA algorithm generates an optimal path set for solving the global path planning of the AUV.

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