Underwater unmanned underwater vehicle multi-target path planning method and system

Abstract

The invention belongs to the technical field of unmanned underwater vehicle path planning, and discloses an unmanned underwater vehicle multi-target path planning method and system. According to the multi-target path planning method for the unmanned underwater vehicle, the path length and the path safety serve as optimization targets, firstly, environment modeling is carried out by adopting a grid method combined with a topographic information gray value, and a path smoothness strategy is proposed according to a Bessel function; secondly, introducing an improved particle swarm optimization algorithm, and realizing the balance of diversity and convergence through crowding distance sorting and a Pareto frontier updating strategy; and finally, through non-dominated solution screening, outputting an optimal path solution set. According to the path planning method, the path searching capability and the path distribution diversity can be effectively improved during multi-target path planning, the method has high engineering applicability, and especially under the double consideration of the path length and the path safety index, the good solving and planning capability can be kept.

Description

Technical Field

[0001] This invention belongs to the field of underwater unmanned submersible path planning technology, specifically relating to a multi-objective path planning method and system for underwater unmanned submersibles. Background Technology

[0002] Unmanned underwater vehicles (UUVs) are intelligent devices that autonomously navigate underwater and perform tasks through remote or automatic control. They can be divided into four categories: towed TUVs, remotely operated remotely operated vehicles (ROVs), unmanned and untethered UUVs, and intelligent AUVs. Path planning is the core issue for UUVs to achieve autonomous navigation.

[0003] In actual underwater missions, unmanned underwater vehicles (UUVs) often operate in complex underwater terrain rather than open water. This underwater characteristic not only increases the complexity of path search but also makes obtaining the optimal navigation path a challenging task. To maximize path safety and minimize energy consumption, UUVs need to find relatively short paths to the target location while maintaining a sufficiently large safe distance from obstacles. Heuristic algorithms and swarm intelligence algorithms, with their good global search capabilities and strong robustness, have become research hotspots in recent years for solving multi-objective path planning problems in complex environments. Compared with traditional methods, these intelligent algorithms can simulate the cooperative behavior of natural groups, achieving information sharing of candidate solutions during the iteration process, thereby largely avoiding getting trapped in local optima.

[0004] Traditional path planning methods, such as Dijkstra's algorithm and A* algorithm, rely on systematic search and sampling of path nodes to plan collision-free paths. These methods perform well in static or simple environments, but their computational efficiency and path optimization effectiveness are often limited when facing dynamic and complex underwater environments. Specifically, while Dijkstra's algorithm is suitable for path planning, it suffers from high computational cost and low efficiency, especially when a complete search of every path node is required. While A* algorithm can effectively plan paths in complex environments, its search performance may not guarantee finding the optimal solution when multiple optimal paths exist. Furthermore, algorithms such as artificial potential fields and Rapid Expanding Random Trees (RRT) also exhibit limitations in terms of high computational complexity and insufficient path smoothness.

[0005] Swarm intelligence algorithms have become an indispensable technology in the field of path planning for underwater unmanned vehicles (UAVs). In multi-objective path planning research, many researchers have explored ways to improve ant colony algorithms. One approach directly incorporates environmental information to adjust the heuristic function and enhances global search capabilities by optimizing transition probabilities, ultimately achieving a significant improvement in path planning performance. Another approach first points out the limitations of traditional ant colony algorithms, namely their tendency to get trapped in local optima when dealing with complex environments, and their relatively low path smoothness and computational efficiency. Based on this problem, this method also employs a strategy of incorporating environmental information to adjust the heuristic function and optimize transition probabilities to enhance global search capabilities, thereby specifically addressing the shortcomings of traditional algorithms. While these algorithms can effectively handle complex environments and obstacle avoidance problems in path planning, there is still room for improvement in avoiding local optima, improving planning efficiency, and dynamically adjusting parameters. Summary of the Invention

[0006] The purpose of this invention is to propose a multi-objective path planning method for underwater unmanned vehicles. This method can improve the diversity and convergence of the solution set, has stronger path search capabilities, a wider path distribution range, and better robustness.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A multi-target path planning method for an underwater unmanned vehicle includes the following steps: Step 1. Establish a 3D geographic model of the underwater working environment of the unmanned underwater vehicle; Step 2. Based on the 3D geographic model of the underwater working environment of the unmanned underwater vehicle, design an objective function with terrain constraints for optimizing path length and path safety; Step 3. Generate and iterate paths based on the improved particle swarm optimization algorithm;

[0008] The improved particle swarm optimization algorithm fits the generated path using a smoothness strategy based on the Bessel function in each iteration, and calculates the objective function value based on the position of the discrete points generated by the Bessel function. Based on the calculated objective function value, the non-dominated solution of the generated path is screened through Pareto optimization. At the same time, a redundancy removal mechanism based on Euclidean distance is introduced to remove redundant solutions, thereby obtaining the Pareto front set. Step 4. After the improved particle swarm optimization algorithm completes its iterations, the final Pareto front set is obtained. The non-dominated solutions in the final Pareto front set are used as all paths for the planned underwater unmanned vehicle.

[0009] Furthermore, based on the multi-objective path planning method for underwater unmanned vehicles, this invention also proposes a multi-objective path planning system for underwater unmanned vehicles adapted to it, the technical solution of which is as follows: A multi-target path planning system for an underwater unmanned submersible includes: The environment modeling module is used to create a three-dimensional geographic model of the underwater working environment of the unmanned underwater vehicle. The objective function design module is used to design objective functions with terrain constraints based on the 3D geographic model of the underwater working environment of unmanned underwater vehicles, with the optimization objectives of path length and path safety. The path generation and iteration module is used for path generation and iteration based on the improved particle swarm optimization algorithm. The improved particle swarm optimization algorithm fits the generated path using a smoothness strategy based on the Bessel function in each iteration, and calculates the objective function value based on the position of the discrete points generated by the Bessel function. Based on the calculated objective function value, the non-dominated solution of the generated path is screened through Pareto optimization. At the same time, a redundancy removal mechanism based on Euclidean distance is introduced to remove redundant solutions, thereby obtaining the Pareto front set. And the final path planning module, after the improved particle swarm optimization algorithm has been iterated, obtains the final Pareto front set, and uses the non-dominated solutions in the final Pareto front set as all paths for the planned underwater unmanned vehicle.

[0010] Furthermore, based on the aforementioned multi-target path planning method for underwater unmanned vehicles, this invention also proposes a computer device, which includes a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements the steps of the multi-target path planning method for underwater unmanned vehicles described above.

[0011] Furthermore, based on the aforementioned multi-objective path planning method for underwater unmanned vehicles, this invention also proposes a computer-readable storage medium storing a program thereon; when executed by a processor, this program is used to implement the steps of the aforementioned multi-objective path planning method for underwater unmanned vehicles.

[0012] The present invention has the following advantages: As described above, this invention discloses a multi-objective path planning method for underwater unmanned vehicles (UUVs). This method first linearly normalizes and maps the terrain grayscale image of the UUV's underwater working environment into a three-dimensional grid, obtaining a three-dimensional geographic model that accurately depicts traversable areas and obstacles. Then, path length and path safety are used as optimization objectives. When considering path safety, the minimum and average safe distances are measured, and soft penalties for danger zones and hard penalties for lethal zones are introduced to suppress collision risks. Subsequently, an improved particle swarm optimization algorithm is used for path generation and iteration. During the solution process, a second-order annealing adaptive inertia weight and individual and global optimum maintenance are employed, combined with congestion distance and Pareto front updates, thus balancing solution set diversity and convergence. This invention also uses Bézier curves to fit the control points generated by the particle swarm optimization algorithm, achieving high-density sampling and precise calculation. Furthermore, a preset Euclidean distance threshold is used to remove redundant solutions at the front edge, thereby obtaining a uniformly distributed and highly representative non-dominated solution set. The path planning method proposed in this invention can output multiple smooth, executable, and robust alternative paths at once, making it suitable for rapid decision-making and engineering deployment in complex underwater missions. Attached Figure Description

[0013] Figure 1 This is a flowchart of a multi-target path planning method for an underwater unmanned submersible in an embodiment of the present invention.

[0014] Figure 2 This is a grayscale diagram illustrating the environmental modeling process in an embodiment of the present invention.

[0015] Figure 3 This is a schematic diagram of the grid matrix in the environmental modeling process of this invention.

[0016] Figure 4 This is a three-dimensional environment diagram illustrating the environment modeling process in an embodiment of the present invention.

[0017] Figure 5 This is a schematic diagram of Bessel function fitting in an embodiment of the present invention.

[0018] Figure 6 This is the first path planning simulation diagram obtained using the method of the present invention in an embodiment of the present invention.

[0019] Figure 7 This is a simulation diagram of the first path planning obtained based on the genetic algorithm in an embodiment of the present invention.

[0020] Figure 8 This is a comparison diagram of the Pareto front, also known as the Pareto front, from the first simulation in this embodiment of the invention.

[0021] Figure 9 This is a simulation diagram of the second path planning obtained using the method of the present invention in an embodiment of the present invention.

[0022] Figure 10 This is a simulation diagram of the second path planning based on the genetic algorithm in an embodiment of the present invention.

[0023] Figure 11 This is a comparison chart of the Pareto front from the second simulation in this embodiment of the invention. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This invention addresses complex underwater terrain by employing Pareto optimization to optimize both path length and safety. It employs a safety score and a safety penalty to comprehensively calculate path safety, and establishes a two-layer safety constraint mechanism in the penalty section to prevent collisions between the unmanned underwater vehicle and obstacles. Furthermore, this invention proposes an improved particle swarm optimization algorithm. By sorting solutions by crowding distance, the global optimal solution of particles is updated, significantly enhancing the algorithm's global search capability and preventing premature entrapment in local optima. Finally, simulation results demonstrate that even in complex underwater environments, the path planning method of this invention can still find a set of non-dominated path solutions that meet the conditions, exhibiting better global search and optimization capabilities compared to other algorithms.

[0025] The general idea of ​​the method of this invention is as follows: First, a multi-objective path planning mathematical model for an underwater unmanned vehicle is established, that is, two objective functions are designed, including objective functions for path length and navigation safety, and efficient path planning in complex geographical environments is achieved by balancing the objectives. Next, a raster method combining terrain information grayscale values ​​is used for environmental modeling. Based on the Bessel function path smoothing strategy, discrete control points generated by the particle swarm optimization algorithm are fitted, thereby further optimizing the smoothness of the path and ensuring the continuity and feasibility of the path. Finally, an improved multi-objective particle swarm optimization algorithm is used for iterative path optimization. Combining congestion distance sorting and Pareto front update strategies, the diversity and convergence of the solution set are effectively improved, and a non-dominated path that meets the conditions is found.

[0026] The following section provides a detailed description of the multi-objective path planning method for underwater unmanned vehicles based on an improved particle swarm optimization algorithm proposed in this invention. For example... Figure 1 As shown, the multi-target path planning method for underwater unmanned vehicles includes the following steps: Step 1. Use a raster method combining terrain information grayscale values ​​to model the environment and establish a three-dimensional geographic model of the underwater working environment of the unmanned underwater vehicle.

[0027] The method of this invention establishes a three-dimensional geographic model of the underwater working environment of an unmanned underwater vehicle, which can clearly distinguish between safe areas and obstacle areas in the underwater environment, thereby providing accurate environmental information for the path planning of the unmanned underwater vehicle.

[0028] In this embodiment, step 1 specifically includes: When performing environmental modeling, the grayscale image containing terrain information is first preprocessed. Each pixel value in the grayscale image is usually an integer, ranging from [0, 255]. The pixel values ​​of the grayscale image are linearly normalized to [0, 1], as shown in formula (1): (1)

[0029] in, This represents the value obtained after the pixel value has been normalized. The pixel value is a numerical value read from the grayscale image.

[0030] After normalizing the image, the relative height value corresponding to each pixel can be obtained. Using a two-dimensional grid system, each pixel in the grayscale image is mapped to a grid point in three-dimensional space, forming a graph containing three-dimensional spatial information. Coordinates. The original two-dimensional image data is transformed into three-dimensional raster data, resulting in a three-dimensional coordinate map, i.e., a three-dimensional image. Each raster point not only has horizontal and vertical coordinates, but also a corresponding height value, as shown in formula (2): (2) in, This represents a matrix containing pixel value information. Corresponding to the three-dimensional coordinate graph Coordinates, specifically the horizontal coordinates in a 3D image. Corresponding to the three-dimensional coordinate graph Coordinates, specifically the vertical coordinates in a 3D image.

[0031] Let the maximum height be In a three-dimensional coordinate graph The value is the pixel value after grayscale image normalization. With maximum height The product of: (3) Formula (3) maps each pixel in the grayscale image to a three-dimensional space, forming a three-dimensional image. Coordinates. The original two-dimensional image data is transformed into three-dimensional raster data. Each raster point not only has horizontal and vertical coordinates, but also a corresponding height value. The method of this invention can accurately represent the underwater terrain undulations through modeling, and reflect different obstacle areas through changes in grayscale values.

[0032] Step 2. Based on the 3D geographic model of the underwater working environment of the unmanned underwater vehicle, design an objective function with terrain constraints for optimizing path length and path safety, and achieve efficient path planning in complex geographic environments by balancing the objectives.

[0033] The method of this invention addresses two optimization objectives: path length and path safety. It designs two objective functions to represent path length and path safety (i.e., navigation safety), respectively. By calculating the objective functions, the path length and safety values ​​can be obtained.

[0034] In this embodiment, step 2 specifically includes: Design two objective functions: path length and path security.

[0035] The path was generated by the particle swarm optimization algorithm. After the initial control points are established, the curve is then smoothed using a Bézier curve. discrete points, In this embodiment, the total number of discrete points in the Bessel-fitted path, i.e., the smoothed path, is... , When calculating the objective function, all fitted points are used.

[0036] Objective function of path length This is used to calculate the sum of Euclidean distances between discrete adjacent points along a Bézier curve in a path, thus obtaining the path length. The objective function for determining the path length is then designed. As shown in formula (4): (4) in, , Indicates the first path A discrete control point containing three-dimensional coordinates is called a discrete point. , Representing discrete control points 3D coordinates; Indicates the first path A discrete control point containing three-dimensional coordinates. , Representing discrete control points The three-dimensional coordinates.

[0037] To ensure path security, the method of this invention uses a combination of security scoring and security penalty to calculate the objective function for path security. This allows for the simultaneous optimization of both overall and local path security.

[0038] Safety scoring is achieved by calculating the minimum safe distance between each point on the path and surrounding obstacles. The minimum safe distance represents the shortest distance between a path point and an obstacle. A larger distance indicates that the path point is farthest from the obstacle, and the path's safety is improved. To comprehensively assess path safety, this invention also introduces the concept of average safe distance, which is the average of the minimum safe distances of all points on the path. This indicator measures the overall safety level of the path; a larger average safe distance indicates that the path is generally far from dangerous areas.

[0039] Specifically, define the safe distance for each waypoint. The distance between a pathpoint and the nearest obstacle in the environment. Its safe distance As shown in formula (5): (5)

[0040] in, path point The minimum Euclidean distance between the device and all obstacles, i.e., the [missing term] The safe distance between each path point. The first one used to represent the underwater working environment of an unmanned underwater vehicle The location of the obstacle.

[0041] Calculate the path points using formula (5) With all obstacle points The minimum value among the distances between the two paths is selected as the safe distance for that path point. Then, from the safe distance of all path points The minimum value is selected as the minimum safe distance for the path. The process is shown in formula (5): (6)

[0042] Average safe distance of the path Safe distance for all waypoints The average value is expressed as shown in formula (7): (7)

[0043] Security rating It is calculated by the minimum safe distance of the path. and average safe distance It is obtained by multiplying the products, and its expression is shown in formula (8): (8) The safety score balances the overall safety of the path with its local safety, ensuring that the path stays as far away from obstacles as possible while avoiding potential local safety hazards. The higher the safety score, the safer the entire path.

[0044] This invention introduces a two-layer safety constraint mechanism in safety penalties, including soft penalties for dangerous areas and hard penalties for fatal areas.

[0045] The hazard zone soft penalty is a penalty imposed when a path point approaches an obstacle, aiming to prevent the path from entering or getting too close to an obstacle. The path will be subject to the hazard zone soft penalty when the safe distance of a path point is less than a preset safety boundary. The fatal zone hard penalty is a strong constraint used to prevent the path from entering a highly dangerous area. The path will be subject to the fatal zone hard penalty when the safe distance of a path point is not greater than a preset fatal zone threshold.

[0046] set up and To achieve two safety thresholds, the distance range must meet... The area is defined as a safe zone, and the distance range meets the following conditions. The area is defined as a danger zone, and the distance range meets the following conditions. The area is defined as the fatal zone. The specific settings for the two-layer security zone are shown in Table 1.

[0047] Table 1 Design of the Double-Layer Safety Zone For satisfying The path accumulation hazard zone soft penalty is applied when the distance between the waypoint and the obstacle is increased. Distance less than the preset safety boundary At that time, an exponentially increasing soft penalty for danger zones is imposed on the path.

[0048] Soft punishment items in danger zones The expression is shown in formula (9): (9) in, For indicator functions. When the condition When it was established =1, otherwise It is 0.

[0049] For satisfying The path accumulation fatal zone hard penalty, i.e., when the distance between the waypoint and the obstacle... Not greater than the preset fatal area threshold At that time, a critical penalty of 1000 is added to the path for fatal zones, which is a severe penalty. The safety of the path is ensured by significantly reducing the safety score.

[0050] The penalty items for the fatal zone hard penalty The expression is shown in formula (10): (10) Among them, when the condition When it is established, the indicator function =1, otherwise It is 0. It should be noted that for... The critical zone will not only inflict the critical zone hard penalty, but also the danger zone soft penalty, and the total penalty is the penalty item. and The accumulation of.

[0051] The method of this invention processes path security by setting two layers of security zones. Through the design of security scoring and security penalty, the objective function for measuring path security is finally determined. Represented as: (11) in, This represents the parameter used to balance security scores and security penalties.

[0052] Objective function for measuring path safety This invention not only evaluates path safety but also removes all paths that may encounter obstacles during the iteration process using the Pareto front's non-dominated solution filtering mechanism, thus achieving better obstacle avoidance capability.

[0053] Objective function of multi-objective path planning As shown in formula (12): (12) The objective function of the two objectives in this invention The design can simultaneously optimize both path length and path safety, thereby shortening the underwater vehicle's travel distance while ensuring path safety.

[0054] Step 3. Generate and iterate paths based on the improved particle swarm optimization algorithm; The improved particle swarm optimization algorithm fits the generated path with a smoothness strategy based on the Bessel function in each iteration to increase the smoothness of the path; it calculates the objective function value based on the position of the discrete points generated by the Bessel function; based on the calculated objective function value, it filters the non-dominated solutions of the generated path through Pareto optimization; at the same time, it introduces a redundancy removal mechanism based on Euclidean distance to remove redundant solutions, thereby maintaining the uniformity and distribution of the Pareto front and obtaining the Pareto front set.

[0055] In this embodiment, step 3 includes particle swarm initialization, particle position and velocity update, path generation and optimization, Pareto front optimization, result display and visualization, etc.

[0056] The particle swarm initialization process is as follows: each particle represents a control point in the path, and the initial position of the particle swarm is randomly generated within a preset 3D spatial boundary. For each particle, its velocity is initialized to zero, and its fitness value is calculated. The fitness value is used to measure the quality of the path, and the initial path and optimal solution (Best) for each particle are stored.

[0057] The particle position and velocity update process is as follows: Particle velocity updates are based on dynamic adjustments of inertia weights and learning factors. The inertia weights are gradually reduced through a double annealing mechanism, ensuring the particle focuses on global search initially and local search later. Particle position updates are controlled by position boundaries to ensure the particle remains within a pre-defined three-dimensional space. After updating, the particle calculates a new fitness value based on its current position and updates its individual and global optimal solutions.

[0058] The path generation and optimization process specifically involves fitting and optimizing the path using Bézier curves. By performing Bézier fitting on the control points of the particle path, corners in the path are eliminated, increasing the smoothness of the path. The path length and safety are calculated based on the discrete point positions generated by the Bézier curves, forming the objective function value of the path, which is used to optimize the quality of the path.

[0059] The Pareto front optimization process is as follows: A non-dominated solution selection mechanism is used to calculate the objective function value for each path, and the Euclidean distance is used to determine whether a new solution is too close to existing Pareto front solutions. If the Euclidean distance between a new solution and an existing solution is less than a preset threshold, the new solution is considered redundant and removed from the solution set, thus ensuring that the final output path solution set has good uniformity and distribution.

[0060] The process of displaying and visualizing the results is as follows: the final optimized path solution set is displayed in the graphical interface, the path is visualized using 3D graphics, graphs of indicators such as path length and safety are provided, and the optimization process and performance of path planning are displayed through the output results.

[0061] In step 3 of this embodiment, the improved particle swarm optimization algorithm generates a sequence containing... The unfitted path of each control point is represented by a position vector.

[0062] The velocity update in the improved particle swarm optimization algorithm is shown below: (13) in, This is the current iteration number. Indicates the first The particle in the first The speed of generation Indicates the first The particle in the first The speed of generation; Indicates inertia weight, , Represents the learning factor. , Represents a random number; Indicates the individual's historical best position; Indicates the first The position vector of the substitute; This represents the optimal position experienced by all particles in the swarm.

[0063] The position update is shown in formula (14): (14) in, Indicates the first The position vector after iteration.

[0064] The present invention designs an adaptive inertia weight update strategy in the form of secondary annealing, as shown in formula (15), to achieve dynamic adjustment of the search capabilities of the improved particle swarm optimization algorithm in the early and late stages, so that the algorithm focuses on global search in the early stage and local search in the later stage: (15) in, Indicates inertia weight, This is the current iteration number. This represents the maximum number of iterations. and These are the preset upper and lower bounds of inertia, respectively. The squared update form of the weights allows the weights to decrease, thus enabling particles to focus on global searches in the early stages and local searches in the later stages.

[0065] An improved particle swarm optimization algorithm is used for path generation and iteration, and the particle search is guided by updating individual optimal solutions and the global optimal solution.

[0066] Specifically, after the particle swarm completes one iteration, the non-dominated solutions from the previous generation are retained as the basis for the next generation's computation. These non-dominated solutions provide the individual optimal solutions for the next generation's particle update. and the global optimal solution The improved particle swarm optimization algorithm uses individual optimal solutions as a reference to further guide the particle search. A key step in the iterative process is to use these individual optimal solutions. and the global optimal solution The update guides the search for particles.

[0067] In each iteration, the particle updates its individual optimal solution, i.e., its individual optimal position, according to the dominance relationship. .

[0068] Individual optimal position The update follows the dominance criterion shown in formula (16). The objective function values ​​of the path length and path safety corresponding to the current solution and the original solution are calculated respectively. If the objective function value of the path length satisfies that the current solution is not greater than the original solution, and the objective function value of the path safety satisfies that the current solution is greater than the original solution, then the current solution is determined to dominate the original solution, and the current solution replaces the original solution; otherwise, the current solution is determined not to dominate the original solution, and the original solution is retained. (16) in, Indicates the current solution. This represents the original solution. This indicates that the current solution dominates the original solution. This indicates that the current solution does not dominate the original solution.

[0069] Global optimal solution The selection is based on the distribution characteristics of the Pareto front.

[0070] When the Pareto front set is not empty, the solutions in the Pareto front set are first sorted based on the objective function value, resulting in the sorted solution set. ,in Let be the number of solutions in the Pareto front set. to This represents each solution in the solution space. By calculating the normalized difference between each solution and the solutions on the left and right sides in the solution space, we can reflect the sparsity of the solutions in the target space.

[0071] make The crowding distance for each solution is defined as shown in formula (17): (17) in, For the sorted solution set, the first... The crowded distance of each solution; , Indicates the number of objective functions. The first objective function is the objective function for path length. The second objective function is the objective function for path safety. ; will the first The values ​​of the objective functions are denoted as follows: ,when hour Objective function for path length The value when hour The objective function for path security The value; and They represent the first and second solutions in the sorted solution set, respectively. and the The solution is at the th solution. The values ​​of each objective function; Indicates the first The maximum value of each objective function. Indicates the first The minimum value of an objective function. Denominator Used for normalization.

[0072] To prevent boundary solutions from being prematurely eliminated, their crowding degree is defined as infinite. That is, when calculating the crowding distance for solutions in the Pareto front set, the crowding distance of the boundary solutions of each objective function is assigned to infinity to protect boundary diversity. The boundary solutions are specifically the individuals corresponding to the minimum and maximum values.

[0073] By comparing the crowding distances of the non-dominated solutions, the sparsest solution, i.e., the one with the largest crowding distance, is selected as the global optimal solution for the particle swarm. This method guides the particle swarm to search for sparse regions in the target space, preventing premature convergence. The method selects the non-dominated solution with the largest crowding distance as the global optimum. This drives particles to evolve towards low-density regions of the target space, thereby maintaining a uniform distribution of the Pareto front. The existence of crowding distance effectively prevents populations from concentrating in a single sub-region, thus allowing for more efficient exploration of sparse regions and increasing solution diversity.

[0074] When the Pareto front set is empty, randomly select the optimal position of an individual particle. As the global optimal solution .

[0075] Through the synergistic effect of Pareto front set updates, individual optimal maintenance, and global optimal solution selection mechanisms, the improved particle swarm optimization algorithm can achieve an effective trade-off between path length and safety, continuously generating high-quality, diverse non-dominated solution sets during the iterative process.

[0076] After generating the control points of the initial path, the algorithm introduces Bessel functions to optimize the path because the path is represented by points generated by the particle swarm algorithm. Since the path is mostly a polyline with poor smoothness and few control points, it is not conducive to the accurate calculation of the objective function.

[0077] The control points for the initial path are generated by the particle swarm optimization (PSO) algorithm; that is, the PSO algorithm selects the control points from the start point to the end point. Let each point be a control point of the path. .

[0078] A path is fitted using a smoothing strategy based on Bézier functions, and a Bézier curve algorithm is used to generate... The Bézier curve of the path is approximated by discrete points, and the polygonal path formed by these control points is transformed into a smooth path.

[0079] Generate using the Bézier curve algorithm The path is approximated by a Bézier curve using discrete control points.

[0080] Bézier curve of the path As shown in formula (18): (18)

[0081] in, , Indicates the first unfitted path The coordinates of the control points; This represents the parameters used to control the generation of Bézier curves. During the process of fitting the path using a smoothing strategy based on the Bessel function, Discretized into At each time point, from the 1st to the 2nd... The time points are respectively It is used as input to formula (18) to calculate the path. At discrete points, as T changes from 0 to 1, the Bézier curve will move from the control point... Reaching the last control point via intermediate control points .

[0082] This invention uses a Bessel function path smoothness strategy to fit control points for particle swarm generation, further optimizing path smoothness and ensuring path continuity and feasibility. After Bessel function fitting, the higher-order continuity of the path effectively eliminates abrupt corner changes in the polygonal path, and further improvements can be made through… The objective function values ​​for path length and path safety are calculated at each point. The fitting of the Bessel function can lay the foundation for the efficient application of unmanned underwater vehicles in underwater exploration and mission execution scenarios.

[0083] In step 3, the process of filtering non-dominated solutions from the generated paths using Pareto optimization is as follows: The objective function value is calculated based on the position of the discrete points generated by the Bessel function. For two objective vectors as shown in formula (19) and : (19) in, , These are two sets of calculated objective function values; and They represent Objective function values ​​for path length and security score; and They represent The objective function value of the path length and security score; if and ,but Dominate Shorter path length and higher safety are the dual objectives of path planning: minimizing path length and maximizing path safety.

[0084] Pareto sort is used to filter non-dominated solutions for the path.

[0085] For each iteration of the improved particle swarm optimization algorithm, the Pareto front set is traversed to determine the current solution. If the current solution is not dominated by any solution in the Pareto front set, add the current solution to the Pareto front set; then determine whether there exists a solution in the Pareto front set dominated by the current solution. If a dominant solution exists, remove the solution dominated by the current solution from the Pareto front set.

[0086] The final Pareto front set is the set of optimal solutions that cannot be dominated by other solutions in both the path length and path safety objective spaces.

[0087] The use of Pareto optimization solves the challenge of handling multiple conflicting objectives, enabling simultaneous optimization for two conflicting objectives. Compared to weighted methods, it is more suitable for solving multi-objective problems and better preserves the diversity and integrity of the solutions. This invention's method provides multiple feasible paths for underwater vehicle path planning through non-dominated solution sets, offering more path choices for practical applications and better meeting the actual needs of multi-objective path planning.

[0088] This invention utilizes an improved multi-objective particle swarm optimization algorithm for path iterative optimization, combining crowding distance sorting and Pareto front update strategy to effectively improve the diversity and convergence of the solution set, and to find non-dominated paths that meet the conditions.

[0089] In step 3, the redundancy removal mechanism for the leading edge solution based on Euclidean distance is as follows: As the optimization process progresses, the particle swarm optimization may generate a large number of non-dominated redundant solutions. These solutions are too close to each other and have little difference, which affects the search efficiency of the algorithm and the diversity of the final solution set. To avoid this situation, the method of this invention introduces a redundancy removal mechanism based on Euclidean distance to remove redundant solutions in the front, thereby maintaining the diversity and dispersion of the Pareto front.

[0090] To determine whether a new solution is redundant, based on the objective function of multi-objective path planning, the Euclidean distance between the new solution and each solution in the current Pareto front set is calculated. This involves calculating the Euclidean distance between the objective function vector of the newly generated solution and the objective function vector of each solution in the current Pareto front set. If the new solution has the minimum distance to any existing solution in the current Pareto front set... Less than the preset value If the new solution is already fully covered in the solution space and cannot provide further diversity, it will not be added to the frontier; that is, the new solution is considered redundant and will not be added to the current Pareto front set. If the new solution is too close to an existing solution in the current Pareto front set, it is considered a redundant solution and will not be added to the Pareto front set.

[0091] distance The calculation process is shown in formula (20): (20) in, The objective function vector of the new solution. The current Pareto frontier focuses on the first The objective function vector of each solution, the objective function vector and Both include two objective function values: path length and path security. For Euclidean distance.

[0092] Step 4. After the improved particle swarm optimization algorithm completes its iterations, the final Pareto front set is obtained. The non-dominated solutions in the final Pareto front set are used as all paths for the planned underwater unmanned vehicle.

[0093] In this embodiment, step 4 specifically includes: After the improved particle swarm optimization algorithm completes its update iterations, the final Pareto front set, i.e. the optimal path solution set, is obtained, which contains non-dominated solutions, i.e., non-dominated path solutions.

[0094] The non-dominated path solutions in the optimal path solution set are taken as the final paths searched by the multi-objective path planning of the underwater unmanned vehicle, that is, all paths of the underwater unmanned vehicle that are finally planned.

[0095] The method of this invention has strong path diversity. When faced with complex underwater environments, the path planning method proposed in this invention can find a set of non-dominated path solutions that meet the conditions. Compared with other algorithms, it has better global search ability and better optimization ability.

[0096] To verify the effectiveness of the method proposed in this invention, the following specific experiments are also provided in this embodiment: Path planning simulations were conducted in two different terrain environments. The initial path point of the first group of unmanned underwater vehicles was set to (170, 16, 10), and the path termination point was set to (127, 286, 80). The initial path point of the second group was set to (50, 50, 100), and the path termination point was set to (280, 160, 245).

[0097] Under the same initial environment, the underwater unmanned vehicle multi-objective path planning method proposed in this invention and the path planning method based on genetic algorithm are used to perform multi-objective path planning for the unmanned underwater vehicle.

[0098] Figure 6 and Figure 7 The three-dimensional path planning diagrams are obtained when the improved particle swarm optimization algorithm and genetic algorithm proposed in this invention are used to simulate the path planning of an underwater unmanned vehicle in the first terrain environment. Figure 6 and Figure 7 The current solutions are 65 and 43, respectively.

[0099] Figure 8 The image shows a comparison of the Pareto fronts obtained from the first path planning simulation for two different path planning methods. The Pareto front obtained by the particle swarm optimization algorithm is the Pareto front obtained using the method of this invention, while the Pareto front obtained by the genetic algorithm is the Pareto front obtained using the path planning method based on the genetic algorithm.

[0100] Figure 9 and Figure 10 The three-dimensional path planning diagrams are obtained when the improved particle swarm optimization algorithm and genetic algorithm proposed in this invention are used to simulate the path planning of an underwater unmanned vehicle in a second terrain environment. Figure 9 and Figure 10 The current solutions are 54 and 69, respectively.

[0101] Figure 11 The image shows a comparison of the Pareto front obtained from the second path planning simulation for the two path planning methods.

[0102] Comparative analysis of simulation experiments on multi-objective path planning using the method proposed in this invention and the genetic algorithm reveals that both the improved particle swarm optimization algorithm and the genetic algorithm can find a large number of mutually non-dominant paths that meet the application conditions in the created environment, but there are significant differences in their optimization capabilities. The improved particle swarm optimization algorithm proposed in this invention can find better paths for both path length and safety objectives, and it also performs better than the genetic algorithm in maintaining path diversity. Furthermore, the method of this invention exhibits higher robustness in different geographical environments. Regarding overall algorithm safety, the average safety score of the paths found by the method of this invention is generally higher than that of the comparative algorithms, and it also has a faster computation speed, enabling it to quickly obtain the required path. In summary, the improved particle swarm optimization algorithm proposed in this invention can effectively plan more diverse and ideal paths while ensuring the safety of unmanned underwater vehicles, allowing for the selection of suitable paths for practical application based on actual conditions.

[0103] This invention presents a multi-objective path planning method for underwater unmanned vehicles (UUVs). It optimizes path length and navigation safety, transforming the underwater path planning problem into a multi-objective optimization problem. Environmental modeling is performed using a raster method based on terrain information grayscale values, and the path is smoothed using a Bessel function. An improved multi-objective particle swarm optimization algorithm is combined to filter non-dominated solutions. Furthermore, crowding distance sorting and Pareto front update strategies enhance the diversity and convergence of the solution set, resulting in a more powerful path search capability, a wider path distribution range, and better robustness.

[0104] Specifically, this invention proposes a novel multi-objective particle swarm optimization algorithm, namely an improved particle swarm optimization algorithm, which can effectively solve path planning problems in complex geographical environments. The method first takes path length and navigation safety as two optimization objectives, employs a raster method combining terrain information grayscale values ​​for environmental modeling, and proposes a path smoothness strategy based on the Bessel function. The method also introduces an improved particle swarm optimization algorithm, achieving a balance between diversity and convergence through congestion distance sorting and Pareto front update strategies. Finally, the method outputs the optimal path solution set through non-dominated solution filtering. The proposed method can effectively improve the path search capability and path distribution diversity in multi-objective path planning, has strong engineering applicability, and maintains good solution and planning capabilities, especially when considering both path length and path safety indicators.

[0105] Example 2 This embodiment 2 describes a multi-objective path planning system for underwater unmanned vehicles, which is based on the same inventive concept as the multi-objective path planning method for underwater unmanned vehicles in embodiment 1.

[0106] Specifically, the multi-target path planning system for this underwater unmanned vehicle includes the following modules: The environment modeling module is used to create a three-dimensional geographic model of the underwater working environment of unmanned underwater vehicles.

[0107] In this embodiment, the environment modeling module is used to construct a three-dimensional geographic model of the underwater environment. By preprocessing the grayscale image containing terrain information, the image pixel values ​​are normalized to the range [0,1] and mapped to the three-dimensional space to generate raster data suitable for path planning.

[0108] The objective function design module is used to design objective functions with terrain constraints based on the 3D geographic model of the underwater working environment of unmanned underwater vehicles, with the optimization objectives of path length and path safety.

[0109] In this embodiment, the objective function design module includes a security evaluation module.

[0110] The safety assessment module is used to optimize the safety of the path by calculating the minimum safe distance between each point in the path and obstacles, combining the average safe distance of the path and the safety score, and introducing a two-layer safety zone mechanism, including soft penalties for danger zones and hard penalties for fatal zones, to ensure that the path avoids danger zones and avoids collisions with obstacles.

[0111] The path generation and iteration module is used for path generation and iteration based on an improved particle swarm optimization algorithm.

[0112] The improved particle swarm optimization algorithm fits the generated path using a smoothness strategy based on the Bessel function in each iteration, and calculates the objective function value based on the position of the discrete points generated by the Bessel function. Based on the calculated objective function value, the non-dominated solutions of the generated path are filtered through Pareto optimization. At the same time, a redundancy removal mechanism based on Euclidean distance is introduced to remove redundant solutions, thereby obtaining the Pareto front set.

[0113] In this embodiment, the path generation and iteration module includes a path optimization module and a result filtering module.

[0114] The path optimization module is used to optimize paths using an improved particle swarm optimization algorithm. It utilizes a particle swarm search strategy, a Pareto front non-dominated solution filtering mechanism, and a redundant solution removal strategy to optimize the length and safety of paths and generate a path solution set that meets the requirements of multi-objective optimization.

[0115] The result filtering module is used to filter the optimal path solution set through the Pareto front non-dominated solution filtering and redundant solution removal mechanism, ensuring the diversity and uniformity of the path solution set, and providing multiple feasible paths for practical applications.

[0116] And the final path planning module, after the improved particle swarm optimization algorithm has been iterated, obtains the final Pareto front set, and uses the non-dominated solutions in the final Pareto front set as all paths for the planned underwater unmanned vehicle.

[0117] It should be noted that the implementation process of the functions and roles of each functional module in the underwater unmanned vehicle multi-target path planning system is detailed in the implementation process of the corresponding steps in the method of Example 1, and will not be repeated here.

[0118] Example 3 This embodiment 3 describes a computer device that includes a memory and one or more processors.

[0119] The memory stores executable code, which, when executed by the processor, is used to implement the steps of the multi-target path planning method for underwater unmanned submersibles in Embodiment 1 above.

[0120] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0121] Example 4 This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of a multi-target path planning method for an underwater unmanned submersible.

[0122] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0123] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A multi-objective path planning method for an underwater unmanned submersible, characterized in that, Includes the following steps: Step 1. Establish a three-dimensional geographic model of the underwater working environment of the unmanned underwater vehicle; Step 2. Based on the 3D geographic model of the underwater working environment of the unmanned underwater vehicle, design an objective function with terrain constraints for optimizing path length and path safety; Step 3. Generate and iterate paths based on the improved particle swarm optimization algorithm; The improved particle swarm optimization algorithm fits the generated path using a smoothness strategy based on the Bessel function in each iteration, and calculates the objective function value based on the position of the discrete points generated by the Bessel function. Based on the calculated objective function value, the non-dominated solution of the generated path is screened through Pareto optimization. At the same time, a redundancy removal mechanism based on Euclidean distance is introduced to remove redundant solutions, thereby obtaining the Pareto front set. Step 4. After the improved particle swarm optimization algorithm completes its iterations, the final Pareto front set is obtained. The non-dominated solutions in the final Pareto front set are used as all paths for the planned underwater unmanned vehicle.

2. The multi-objective path planning method for underwater unmanned submersibles according to claim 1, characterized in that, Step 1 specifically involves: When performing environmental modeling, grayscale images containing terrain information are preprocessed by linearly normalizing the pixel values ​​of the grayscale images to the range [0,1]. The process is shown in formula (1): (1) in, This represents the value obtained after the pixel value has been normalized. This represents the pixel value read from the grayscale image; Using a two-dimensional grid system, each pixel in a grayscale image is mapped to a grid point in three-dimensional space, forming a grid containing three-dimensional spatial information. The coordinates are transformed from the original two-dimensional image data into three-dimensional raster data, resulting in a three-dimensional coordinate map, i.e., a three-dimensional image, as shown in formula (2): (2) in, This represents a matrix containing pixel value information; Corresponding to the three-dimensional coordinate graph Coordinates, specifically the horizontal coordinates in a 3D image; Corresponding to the three-dimensional coordinate graph Coordinates, specifically the vertical coordinates in a 3D image; Let the maximum height be In a three-dimensional coordinate graph The value is the pixel value after grayscale image normalization. With maximum height The product of: (3)。 3. The multi-objective path planning method for underwater unmanned submersibles according to claim 2, characterized in that, Step 2 specifically involves: The path was generated by the particle swarm optimization algorithm. After the initial control points are formed, they are smoothed using the Bézier curve algorithm. discrete points, This represents the total number of discrete points obtained after fitting the generated path using a smoothing strategy based on Bessel functions. Objective function of path length This is used to calculate the sum of Euclidean distances between discrete adjacent points in a path, thus obtaining the path length; an objective function for the path length is designed. As shown in formula (4): (4) in, , Indicates the first path A discrete control point containing three-dimensional coordinates is called a discrete point. , Representing discrete control points 3D coordinates; Indicates the first path A discrete control point containing three-dimensional coordinates. , Representing discrete control points 3D coordinates; Objective function of path security It is calculated using two parts: security score and security penalty. The discrete points that make up the path are called path points, and the safe distance for each path point is defined. The distance between a pathpoint and the nearest obstacle in the environment. Its safe distance As shown in formula (5): (5) in, path point The minimum Euclidean distance between the device and all obstacles, i.e., the [missing term] Safe distance between each path point; The first [unmanned underwater vehicle] in the underwater working environment One obstacle; Calculate the path points using formula (5) With all obstacle points The distances between them are calculated, and the minimum value is selected as the safe distance for that path point. Then, from the safe distance of all path points The minimum value is selected as the minimum safe distance for the path. The process is shown in formula (5): (6) in, This represents the operation of selecting the minimum safe distance from all path points; Average safe distance of the path Safe distance for all waypoints The average value is expressed as shown in formula (7): (7) Safety rating It is calculated by the minimum safe distance of the path. and average safe distance It is obtained by multiplying the products, and its expression is shown in formula (8): (8) Introduce a two-layer safety constraint mechanism in the safety penalty system, including soft penalties for dangerous areas and hard penalties for fatal areas; set up and To achieve two safety thresholds, the distance range must meet... The area is defined as a safe zone, and the distance range meets the following conditions. The area is defined as a danger zone, and the distance range meets the following conditions. The area is defined as a fatal zone; For satisfying The path accumulation hazard zone soft penalty is applied when the safe distance between the waypoint and the obstacle is reached. Distance less than the preset safety boundary At that time, an exponential soft penalty is imposed on the path for danger zones; Soft punishment items in danger zones The expression is shown in formula (9): (9) in, For indicator functions; when the condition When it was established =1, otherwise =0; For satisfying The path accumulation fatal zone hard penalty, i.e., when the safe distance between the waypoint and the obstacle... Not greater than the preset critical area threshold At that time, a hard penalty for fatal zones is applied to the path. The penalty items for the fatal zone hard penalty The expression is shown in formula (10): (10) Among them, when the condition When it is established, the indicator function =1, otherwise =0; Objective function for measuring path safety Represented as: (11) in, This represents the parameter used to balance security scores and security penalties; Design an objective function vector with terrain constraints. As shown in formula (12): (12)。 4. The multi-objective path planning method for underwater unmanned submersibles according to claim 3, characterized in that, In step 3, the improved particle swarm optimization algorithm generates a sequence containing... The unfitted paths of each control point are represented by position vectors; The velocity update in the improved particle swarm optimization algorithm is shown below: (13) in, This is the current iteration number. Indicates the first The particle in the first The speed of generation Indicates the first The particle in the first The speed of generation; Indicates inertia weight, , Represents the learning factor. , Represents a random number; Indicates the individual's historical best position; Indicates the first The position vector of the substitute; This represents the optimal position experienced by all particles in the swarm; The position update in the improved particle swarm optimization algorithm is shown in Equation (14): (14) in, Indicates the first The position vector after iteration; The adaptive inertia weight update strategy in the form of secondary annealing is designed as shown in Equation (15): (15) in, Indicates the first The inertial weight of the generation; and These are the preset upper and lower limits of inertia, respectively; Indicates the maximum number of iterations; The search for particles is guided by updating the individual optimal solution and the global optimal solution; In each iteration, the particle updates its individual optimal solution, i.e., its individual optimal position, according to the dominance relationship. ; Individual optimal position The update follows the dominance criterion shown in formula (16). The objective function values ​​of the path length and path safety corresponding to the current solution and the original solution are calculated respectively. If the objective function value of the path length satisfies that the current solution is not greater than the original solution, and the objective function value of the path safety satisfies that the current solution is greater than the original solution, then the current solution is determined to dominate the original solution, and the current solution replaces the original solution; otherwise, the current solution is determined not to dominate the original solution, and the original solution is retained. (16) in, This indicates that the current solution is the new solution generated after the iteration. This indicates that the original solution is the solution already present in the Pareto front set. This indicates that the current solution dominates the original solution. This indicates that the current solution does not dominate the original solution; Global optimal solution The selection is based on the distribution characteristics of the Pareto front; When the Pareto front set is not empty, the solutions in the Pareto front set are sorted, and the sorted solution set is represented as follows: ,in Let be the number of solutions in the Pareto front set. to These represent the solutions in the solution space. By calculating the normalized difference between each solution and the solutions on the left and right in the solution space, the sparsity of the solutions in the target space is reflected. make Define the first solution in the sorted solution set. The crowding distance of individual solutions As shown in formula (17): (17) in, , Indicates the number of objective functions. ; will the first The values ​​of the objective functions are denoted as follows: , hour That is, the objective function for path length. The value, hour That is, the objective function of path security. The value; and They represent the first and second solutions in the sorted solution set, respectively. and the The solution is at the th solution. The values ​​of each objective function; Indicates the first The maximum value of each objective function. Indicates the first The minimum value of an objective function; When calculating the crowding distance for solutions in the Pareto front set, the crowding distance of the boundary solutions of each objective function is assigned to infinity, and the non-dominated solution with the largest crowding distance is selected as the global optimum. ; When the Pareto front set is empty, randomly select the optimal position of an individual particle. As the globally optimal solution .

5. The multi-objective path planning method for underwater unmanned submersibles according to claim 4, characterized in that, In step 3, the process of fitting the path using a smoothing strategy based on the Bessel function is as follows: Generate using the Bézier curve algorithm The path is approximated by a discrete control point using a Bézier curve. make The Bézier curve of the path is obtained. As shown in formula (18): (18) in, For the unfitted path, the th The coordinates of the control points; These are the parameters used to control the generation of Bézier curves.

6. The multi-objective path planning method for underwater unmanned submersibles according to claim 5, characterized in that, In step 3, the process of filtering non-dominated solutions from the generated paths using Pareto optimization is as follows: The objective function value is calculated based on the position of the discrete points generated by the Bessel function. For two objective vectors as shown in formula (19) and : (19) in, , These are two sets of calculated objective function values; and They represent The objective function values ​​for path length and path security in the middle path; and They represent The objective function values ​​for path length and path security; if and ,but Dominate ; The Pareto sort is used to filter non-dominated solutions for the path; For each iteration of the improved particle swarm optimization algorithm, the Pareto front set is traversed to determine the current solution. If the current solution is not dominated by any solution in the Pareto front set, add the current solution to the Pareto front set; then determine whether there exists a solution in the Pareto front set dominated by the current solution. If a dominant solution exists, remove the solution dominated by the current solution from the Pareto front set. The final Pareto front set is the set of optimal solutions that cannot be dominated by other solutions in both the path length and path safety objective spaces.

7. The multi-objective path planning method for underwater unmanned submersibles according to claim 6, characterized in that, In step 3, the redundancy removal mechanism for the leading edge solution based on Euclidean distance is specifically as follows: Based on the objective function with terrain constraints, calculate the Euclidean distance between the objective function vector of the new solution generated by the improved particle swarm optimization algorithm and the objective function vector of each solution in the current Pareto front set. If the minimum distance between the new solution and the existing solutions in the current Pareto front set is... Less than the preset value If the new solution is found to be redundant, it will not be added to the current Pareto front set. distance The calculation process is shown in formula (20): (20) in, The objective function vector of the new solution. The current Pareto frontier focuses on the first The objective function vector of each solution, the objective function vector and Both include two objective function values: path length and path security. For Euclidean distance.

8. A multi-target path planning system for an underwater unmanned submersible, characterized in that, include: The environment modeling module is used to create a three-dimensional geographic model of the underwater working environment of the unmanned underwater vehicle. The objective function design module is used to design objective functions with terrain constraints based on the 3D geographic model of the underwater working environment of unmanned underwater vehicles, with the optimization objectives of path length and path safety. The path generation and iteration module is used for path generation and iteration based on the improved particle swarm optimization algorithm. The improved particle swarm optimization algorithm fits the generated path using a smoothness strategy based on the Bessel function in each iteration, and calculates the objective function value based on the position of the discrete points generated by the Bessel function. Based on the calculated objective function value, the non-dominated solution of the generated path is screened through Pareto optimization. At the same time, a redundancy removal mechanism based on Euclidean distance is introduced to remove redundant solutions, thereby obtaining the Pareto front set. And the final path planning module, after the improved particle swarm optimization algorithm has been iterated, obtains the final Pareto front set, and uses the non-dominated solutions in the final Pareto front set as all paths for the planned underwater unmanned vehicle.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the multi-objective path planning method for underwater unmanned submersibles as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the multi-objective path planning method for underwater unmanned submersibles as described in any one of claims 1 to 7.

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