A multi-audonomous underwater vehicle path planning method and system

Abstract

The application provides a kind of multi-autonomous underwater vehicle path planning method and system, it is related to autonomous underwater vehicle path planning technical field, including according to the navigation environment where autonomous underwater vehicle is located, constructs three-dimensional underwater environment model;According to the optimization target and constraint condition of multi-autonomous underwater vehicle path planning are determined according to the three-dimensional underwater environment model;Based on weighted sum method and penalty function method, according to the optimization target and the constraint condition constructs multi-objective fitness function;The optimal path point sequence is obtained by solving the multi-objective fitness function through improved star jia optimization algorithm;After the optimal path point sequence is carried out cubic spline interpolation smoothing and is connected, the optimal navigation route of multi-autonomous underwater vehicle is obtained.The application solves the technical problems that multi-AUV cluster collaborative path planning faces in complex underwater unstructured environment, such as high-dimensional nonlinearity, multi-objective optimization, easy premature convergence, weak local search ability and cluster collaborative obstacle avoidance difficulty.

Description

Technical Field

[0001] This invention relates to the field of autonomous underwater robot path planning technology, and more specifically, to a path planning method and system for multiple autonomous underwater robots. Background Technology

[0002] Autonomous underwater vehicle (AUV) technology has been widely applied in civilian fields such as marine monitoring and offshore oil and gas pipeline monitoring in recent years. However, in complex application scenarios such as marine resource exploration and marine search and rescue operations, the limited sensing range, insufficient payload capacity, low mission efficiency, and low fault tolerance of a single AUV restrict its ability to perform complex tasks. Compared to a single AUV, AUV swarms have advantages in spatial coverage and mission payload capacity. Through mutual information sharing and collaboration, members of the swarm demonstrate higher work efficiency and fault tolerance. Path planning is one of the core tasks of AUV swarm operations, requiring all AUVs to reach the target location along a continuous trajectory from the starting point to the endpoint while meeting relevant constraints. However, the complex and ever-changing underwater environment poses severe challenges to collaborative path planning. The spatiotemporal variability of ocean currents and the unstructured nature of seabed topography transform collaborative path planning into a high-dimensional, nonlinear, and NP-hard problem with numerous local extrema. Therefore, how to rationally utilize ocean currents for energy conservation, safely avoid terrain obstacles, and achieve multi-objective collaborative optimization of energy consumption, safety, and distance is an important research problem in AUV swarm collaborative path planning.

[0003] Traditional planning algorithms (such as A*, fast exploratory random tree, and artificial potential field methods) suffer from drawbacks such as high computational cost, slow convergence, and lack of global search capability when dealing with complex 3D scenes. Deep reinforcement learning methods face challenges such as high training requirements and insufficient computing power for embedded devices. While swarm intelligence optimization algorithms offer an effective solution, mainstream algorithms generally suffer from low convergence performance and poor optimization results. The Nova Algorithm (NOA) exhibits outstanding global search capabilities, but it still has limitations when facing high-dimensional, non-convex, and multi-modal AUV swarm path planning problems, including weak local search, premature convergence, and insufficient adaptability to complex underwater environments. Summary of the Invention

[0004] The purpose of this invention is to provide a path planning method and system for multi-autonomous underwater robots to improve the aforementioned problems. To achieve this objective, the technical solution adopted by this invention is as follows:

[0005] Firstly, this application provides a path planning method for multiple autonomous underwater robots, including:

[0006] Based on the navigation environment of the autonomous underwater robot, a three-dimensional underwater environment model is constructed.

[0007] The optimization objectives and constraints for the multi-autonomous underwater robot path planning are determined based on the aforementioned three-dimensional underwater environment model.

[0008] Based on the weighted sum method and penalty function method, a multi-objective fitness function is constructed according to the optimization objective and the constraints.

[0009] The optimal path point sequence is obtained by solving the multi-objective fitness function using an improved star-raven optimization algorithm.

[0010] The optimal navigation route of the multi-autonomous underwater robot is obtained by smoothing the optimal path point sequence with cubic spline interpolation and then connecting them.

[0011] Secondly, this application also provides a multi-autonomous underwater robot path planning system, including:

[0012] The first construction module is used to build a three-dimensional underwater environment model based on the navigation environment of the autonomous underwater robot.

[0013] The determination module is used to determine the optimization objectives and constraints for the path planning of the multi-autonomous underwater robot based on the three-dimensional underwater environment model.

[0014] The second construction module is used to construct a multi-objective fitness function based on the weighted sum method and the penalty function method, according to the optimization objective and the constraints.

[0015] The solution module is used to solve the multi-objective fitness function using an improved star-raven optimization algorithm to obtain the optimal path point sequence;

[0016] The planning module is used to smooth the optimal path point sequence using cubic spline interpolation and then connect them to obtain the optimal navigation route for the multi-autonomous underwater robot.

[0017] The beneficial effects of this invention are as follows:

[0018] (1) This invention improves the traditional Star Raven optimization algorithm by using multi-strategy fusion, which significantly enhances the path planning performance of multi-AUV clusters in complex underwater environments. On the one hand, the initialization method based on multiple A* heuristic search and adaptive Perlin noise perturbation not only ensures the quality of the initial population through differentiated path guidance, but also effectively avoids the initial solution from falling into the obstacle area by using dynamic perturbation intensity adjustment and repulsion vector correction strategies, laying a high-quality foundation for the global exploration of the algorithm and greatly reducing the risk of premature convergence to inferior local optima. On the other hand, the sequential quadratic programming algorithm combined with the elite idea accurately strengthens the local search capability, which significantly improves the accuracy of the optimal solution. The adaptive dynamic hierarchical acceptance criterion based on the hierarchical temperature field realizes the intelligent balance between exploration and development behavior by dynamically allocating temperature to individuals at different levels, which enhances the robustness of the algorithm in complex environments such as unstructured terrain and spatiotemporally changing ocean currents.

[0019] (2) This invention also introduces a chaotic dynamic lens imaging reverse learning strategy, which uses the ergodicity and unpredictability of the Tent chaotic mapping to modulate the lens parameters, effectively solving the problem of insufficient perturbation intensity in the later stages of traditional algorithm iteration, enabling the optimization algorithm to efficiently escape deep local optima. The overall method comprehensively optimizes path length, collision threat, smoothness and ocean current energy consumption through a multi-objective fitness function, while satisfying the safety distance and environmental boundary constraints between multiple AUVs. The planned path is safe, efficient and energy-saving, and can be widely adapted to diverse scenarios such as marine resource exploration, underwater facility inspection, and emergency search and rescue, providing reliable technical support for multi-AUV cluster collaborative operations and significantly improving task execution efficiency and environmental adaptability.

[0020] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the multi-autonomous underwater robot path planning method described in an embodiment of the present invention;

[0023] Figure 2This is a path planning diagram of the improved Star Raven optimization algorithm under a single AUV according to an embodiment of the present invention;

[0024] Figure 3 This is a comparison chart of the convergence curves of various algorithms for single AUV in this embodiment of the invention;

[0025] Figure 4 This is a path planning diagram of the improved Star Raven optimization algorithm under multiple AUVs in an embodiment of the present invention;

[0026] Figure 5 This is a path planning diagram of the improved Star Raven optimization algorithm based on real map information in an embodiment of the present invention;

[0027] Figure 6 This is a partial path planning diagram of the improved Star Raven optimization algorithm based on real map information in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0029] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0030] Example 1:

[0031] This embodiment provides a path planning method for multiple autonomous underwater robots.

[0032] It is understood that the path planning method provided in this embodiment can be widely applied to various practical scenarios such as marine resource exploration, underwater facility inspection, emergency search and rescue, and marine ecological monitoring, and is particularly suitable for the collaborative operation needs of multiple AUV clusters in complex underwater environments. For example, in scenarios such as deep-sea mineral resource exploration and offshore oil and gas pipeline inspection, AUV clusters need to face the problems of drastic seabed topography and irregular distribution of reefs and artificial obstacles; in marine ecological monitoring and underwater search and rescue scenarios, they need to cope with the challenges of significant temporal and spatial changes in ocean currents, a wide operating area, and the requirement for rapid response.

[0033] In these application scenarios, traditional path planning solutions generally face pain points: single AUV operations are inefficient and have limited coverage, while multiple AUVs working together are prone to problems such as path conflicts, excessive energy consumption, and untimely obstacle avoidance. At the same time, the unstructured nature of complex underwater environments makes it difficult for traditional algorithms to balance path length, safety, smoothness, and energy-saving requirements, often resulting in slow convergence and easy getting trapped in local optima.

[0034] See Figure 1 The figure shows that the method includes steps S1, S2, S3, S4 and S5.

[0035] Step S1: Construct a three-dimensional underwater environment model based on the navigation environment of the autonomous underwater robot;

[0036] Step S1 includes:

[0037] Step S11: The underwater environment topography is approximated by using a land-based mountain model. By superimposing trigonometric functions of different frequencies and amplitudes and adding Gaussian white noise, a baseline topography model is obtained.

[0038] In this step, a land-based mountain model is used to approximate the underwater basic topography. The terrain undulation is simulated by superimposing trigonometric functions with multiple frequencies and amplitudes, and Gaussian white noise is added to restore the natural randomness of the terrain.

[0039] Define horizontal plane projection coordinates As the plane reference of the benchmark terrain model, That is, the projected coordinates of any point in three-dimensional underwater space onto the horizontal plane, representing the vertical coordinates of that point, ignoring its vertical height (corresponding to the vertical coordinate). After that, Two-dimensional coordinates on a plane are used to locate the planar position of terrain. Represents the x-axis, Represents the vertical axis.

[0040] The baseline terrain model is:

[0041] ;

[0042] ;

[0043] In the formula, Indicates in The height function of the baseline terrain. Indicates about The Trigonometric functions, , This represents Gaussian white noise. This indicates that the expression follows a pattern with a mean of 0 and a variance of . The normal distribution Indicates the first The amplitude coefficients of each trigonometric function, , and Both represent spatial angular frequencies. This indicates the phase offset. , , and All represent surface shape coefficients. .

[0044] By adjusting , , , , , , , and To control the extent and degree of undulation of the terrain.

[0045] Step S12: Construct a model of seabed peaks in the navigation environment using an exponential function;

[0046] In this step, the total number of underwater peaks is set. For each mountain peak, key parameters are defined, including peak height and center coordinates. A height model of each mountain peak is constructed using these key parameters, and then the maximum height of all peaks is taken as the maximum value. The height of the mountain peaks was used to obtain the underwater mountain model:

[0047] ;

[0048] In the formula, Indicates in The height function of the underwater mountain peak, This indicates taking the maximum value. This indicates the total number of underwater peaks. Indicates the first The peak height of the underwater mountain and They represent the first The x-coordinate and y-coordinate of the center of each underwater mountain peak and They represent the first A seamount along shaft and The standard deviation of the axis is used to control the extent and steepness of mountain peaks. This represents an exponential function.

[0049] Step S13: Based on the characteristics of underwater terrain obstacles, construct spherical threat areas and cuboid threat areas;

[0050] In this step, based on the characteristics of underwater terrain obstacles (such as those resembling spheres or cuboids), such as lost containers from civilian cargo ships and naturally formed reefs, etc., , The coordinates in the three-dimensional underwater space are The points are used to construct the sphere's threat area. and cuboid threat area :

[0051] ;

[0052] ;

[0053] In the formula, Indicates the first The sphere threat area corresponding to each sphere obstacle. Indicates the first Each cuboid obstacle corresponds to a cuboid threat area. It refers to the three-dimensional coordinates of any point in the three-dimensional underwater space. Represents three-dimensional underwater Euclidean space. , and They represent the first The x-coordinate, y-coordinate, and y-coordinate of the center of each spherical obstacle. Indicates the first The radius of the spherical obstacle This indicates taking the absolute value. , and They represent the first The x-coordinate, y-coordinate, and y-coordinate of the center of the cuboid obstacle. , and They represent the first The length, width, and height of the rectangular obstacle.

[0054] Step S14: Simulate the underwater ocean current environment using a numerically superimposed viscous Lamb–Oseen eddy model and the seabed boundary layer effect;

[0055] In this step, a viscous Lamb–Oseen eddy model is used, superimposed with seafloor boundary layer effects, to simulate the underwater ocean current environment. Specifically, key ocean current parameters are set, including the number of eddies. , No. Intensity of each vortex , No. The radius of the vortex , No. The horizontal coordinate of the center of each vortex Vertical perturbation scaling factor and vertical attenuation coefficient .

[0056] Then based on the vertical attenuation coefficient Calculate the damping factor of the seabed boundary layer :

[0057] ;

[0058] In the formula, Indicates at point The seafloor boundary layer damping factor at that location, Represents an exponential function. This indicates taking the maximum value. Indicates in The terrain elevation at this location. for and Obtained by superposition.

[0059] Based on key ocean current parameters and ,calculate The three-dimensional ocean current velocity components at a point are used to simulate the underwater ocean current environment:

[0060] ;

[0061] ;

[0062] ;

[0063] In the formula, , and They represent points respectively. At axis, shaft and Ocean current velocity component along the axial direction, Point Horizontal projection coordinates to the first The distance of the horizontal coordinate of the center of each vortex This represents a constant used to prevent the addition of singularities; its value is much less than 1.

[0064] Step S15: Based on the baseline terrain model, seabed mountain model, spherical threat area, cuboid threat area, and underwater ocean current environment, a three-dimensional underwater environment model is constructed;

[0065] In this step, the baseline terrain model and the seabed mountain model are superimposed to obtain the height distribution of the global terrain. Then, the sphere threat area and cuboid threat area corresponding to all spheres and cuboid obstacles are superimposed with the global terrain and underwater ocean current environment to identify the forbidden areas in the environment. At the same time, the three-dimensional ocean current velocity component is dynamically adjusted with the terrain height to realize the damping effect of the terrain on the ocean current.

[0066] Step S16: Determine the starting position and target position of the multiple autonomous underwater robots in the three-dimensional underwater environment model.

[0067] In this step, the number of autonomous underwater vehicles (AUVs) is determined, and a unique identifier is assigned to each AUV, and the starting position and target position of each AUV are set.

[0068] Step S2: Determine the optimization objective and constraints for the multi-autonomous underwater robot path planning based on the three-dimensional underwater environment model;

[0069] Step S3: Based on the weighted sum method and penalty function method, construct a multi-objective fitness function according to the optimization objective and the constraints;

[0070] Step S3 includes:

[0071] Step S31: Based on the weighted sum method, construct an objective function according to the optimization objective and constraints. The optimization objective includes path length, collision threat, smoothness and ocean current energy consumption. The constraints include boundary constraints and inter-cluster spatial distance constraints.

[0072] In this step, the objective function for:

[0073] ;

[0074] In the formula, Indicates the number of AUV clusters. Indicates the first The weighting coefficients of each optimization objective. Indicates the first The optimization objective is... The fitness function under the following conditions Indicates in The boundary constraint cost function is as follows. This represents the cost function constrained by spatial distance between multiple AUV clusters. Indicates the first A complete set of waypoints for each AUV This represents the complete set of waypoints that include all AUVs.

[0075] in, It is actually a path that includes multiple waypoints.

[0076] Step S32: Construct the fitness function for each optimization objective based on the three-dimensional underwater environment model;

[0077] This step presents the process of constructing fitness functions for different optimization objectives.

[0078] Step S321: Construct the fitness function for path length;

[0079] The path segment length is measured using the Euclidean distance between two adjacent points. Therefore, the total path length is defined as the sum of the lengths of all adjacent path segments, resulting in the fitness function for the path length. :

[0080] ;

[0081] In the formula, This indicates that the first optimization objective is in The fitness function under the following conditions This indicates the number of waypoints for the AUV. and They represent the first The first AUV The and the first The coordinate vectors of each waypoint This represents the Euclidean norm.

[0082] Step S322: Construct a fitness function for the AUV collision threat cost;

[0083] The functional expression for the AUV collision threat cost is:

[0084] ;

[0085] In the formula, This indicates that the second optimization objective is in The fitness function under the following conditions Indicates in The cost of the spherical obstacle threat. Indicates in The rectangular obstacle below threatens costs. Indicates in The cost of underwater mountain obstacles.

[0086] in, , and for:

[0087] ;

[0088] ;

[0089] ;

[0090] In the formula, Indicates the number of evaluation points. Indicates the number of obstacles on the sphere. This represents the penalty coefficient for sphere collisions. Indicates the first The radius of the spherical obstacle Indicates the first The geometric center of the spherical obstacle Indicates the first The first AUV Coordinates of each evaluation point Denotes the Euclidean norm. This indicates the number of rectangular obstacles. This represents the collision penalty coefficient for a cuboid. Indicates the first The first AUV The assessment point is located at the [number]th [location]. When the area is within a rectangular prism-like threat region, the minimum remaining margin to the nearest box face is... Indicates the first after safe expansion Each cuboid obstacle corresponds to a cuboid threat area. This represents the collision penalty coefficient for mountain peaks. Indicates the first The first AUV The safe height threshold at each assessment point Indicates the first The first AUV The vertical coordinates of each evaluation point.

[0091] in, , express transpose, , Indicates in At the height of the underwater mountain peak, Indicates the minimum safe distance. and They represent the first The first AUV The x-coordinate and y-coordinate of each evaluation point.

[0092] It should be noted that the evaluation points are a large number of intermediate points generated through dense resampling on the path segment consisting of two adjacent waypoints.

[0093] Step S323: Construct the fitness function for smoothness;

[0094] The navigation path of the AUV swarm needs to meet practical motion constraints, avoiding sharp turns on the horizontal plane and violent pitch movements on the vertical plane. (Horizontal turning angles...) Defined as the angle between adjacent path segments, vertical pitch angle Defined as the angle between the path segment and the horizontal plane, the fitness function for smoothness is:

[0095] ;

[0096] ;

[0097] ;

[0098] In the formula, Indicates the first The first AUV Horizontal turns of each path segment Indicates the first The first AUV Vertical pitch angle of each path segment and They represent the first The first AUV The and the first The projection vectors of path segments onto the horizontal plane, where, , , and The first The first AUV Each path segment is in axis, shaft and Increment of axis, and These are the weighting coefficients for controlling the costs of horizontal and vertical smoothness, respectively. This indicates that the third optimization objective is in The fitness function is as follows.

[0099] Step S324: Construct the stress function for ocean current energy consumption:

[0100] Ocean currents are an unavoidable factor affecting AUV clusters during underwater navigation; therefore, it is assumed that the AUVs travel at a constant speed.

[0101] For the first The path after dense resampling of each AUV Segmentation ( (For paths that include multiple evaluation points), passing through adjacent evaluation points and Form minimal path segments and calculate the coordinates of the midpoint of each minimal path segment. ,in, and They represent the first The first AUV The and the first Coordinates of each evaluation point express and The coordinates of the midpoint of the corresponding minimal path segment.

[0102] For the midpoint of each minimal path segment, the ocean current velocity vector at that point is synthesized by calculating the three-dimensional ocean current velocity components in the Cartesian coordinate system and multiplying them with the seafloor boundary layer damping factor. , express The ocean current velocity vector.

[0103] The ocean current velocity vector is decomposed into parallel and lateral components along the direction of travel. Let the first... AUV and The heading unit vector corresponding to the minimum path segment is Then parallel components and lateral component amplitude The definition is as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] In the formula, express Parallel components, express The lateral component, express The transpose of .

[0108] pass and Construct the stress function for ocean current energy consumption:

[0109] ;

[0110] ;

[0111] In the formula This indicates that the fourth optimization objective is in The fitness function under the following conditions Indicates the number of evaluation points. Indicates the first AUV and The energy cost corresponding to the minimum path segment, Indicates the first AUV and The length of the corresponding minimum path segment , and These represent the reverse flow penalty coefficient, the downstream flow reward coefficient, and the lateral flow penalty coefficient, respectively.

[0112] Step S33: Apply penalties to the paths subject to boundary constraints and inter-cluster spatial distance constraints to obtain the corresponding cost function;

[0113] In this step, the cost function includes the spatial distance constraint cost function between multiple AUV clusters and the boundary constraint cost function.

[0114] When calculating the spatial distance constraint cost function among multiple AUV clusters, we first assume that the AUVs depart at the same time and travel at the same speed. Let... To minimize the safety margin, calculate the distance between all pairs of points in the path space for any two distinct paths. If there exists any pair of evaluation points with a distance less than 1 / 3... If a collision occurs, it is considered that there is a conflict between AUVs. Therefore, the cost function for the cooperative safety distance constraint of the AUV cluster is defined as:

[0115] ;

[0116] In the formula, This represents the cost function constrained by spatial distance between multiple AUV clusters. This represents the cooperative collision avoidance penalty coefficient. This indicates the number of AUVs in the cluster. Indicates the first The first AUV Coordinates of each evaluation point Indicates the number of samples after dense resampling. The first AUV There are several assessment points. Among them, A positive number is used to amplify the penalty for close-range collisions.

[0117] Constructing the boundary constraint cost function To ensure the safety of AUV navigation and the success of mission completion, the planned waypoints must meet the environmental constraints defined in the formula. For waypoints that exceed altitude limits and boundaries, penalties will be imposed respectively. and The mathematical expression is as follows:

[0118] ;

[0119] ;

[0120] ;

[0121] In the formula, and All represent positive penalty coefficients. and These represent the first penalty item and the second penalty item, respectively. This indicates the number of waypoints for the AUV. , and They represent the first The first AUV The x, y, and y coordinates of each waypoint and These represent the minimum and maximum values ​​of the x-axis, respectively. and These represent the minimum and maximum values ​​of the ordinate, respectively. and These represent the minimum and maximum values ​​of the vertical coordinates, respectively. This indicates an indicator function that takes the value 1 if the condition is true, and 0 otherwise.

[0122] Step S34: Substitute the fitness function and the cost function into the objective function to obtain the multi-objective fitness function.

[0123] In this embodiment, the cooperative path scheme of each AUV is optimized with the goal of minimizing the multi-objective fitness function.

[0124] Step S4: Solve the multi-objective fitness function using the improved Star Raven optimization algorithm to obtain the optimal path point sequence;

[0125] Step S4 includes:

[0126] Step S41: Generate differentiated guidance paths based on the A* algorithm, and initialize multiple populations according to the guidance paths;

[0127] In this step, three guidance paths are generated using the A* algorithm: distance priority, safety priority, and smoothness priority. Each guidance path is a single complete waypoint sequence for an AUV.

[0128] The total population is divided into three populations based on the guidance path, with each population corresponding to one guidance path. For each population, adaptive Perlin noise (dynamically adjusting the disturbance intensity according to the distance to obstacles and superimposing a three-dimensional offset vector) is superimposed on each waypoint node on the guidance path, based on the corresponding guidance path, to generate multiple differentiated single paths, each of which corresponds to the path of an AUV.

[0129] These multiple differentiated single paths are combined to form a single individual, i.e., a cooperative path scheme for multiple AUVs. This process is repeated to generate a predetermined number of individuals for each population.

[0130] Furthermore, for each individual's multiple AUV paths, a repulsion vector correction strategy is adopted. If the noise disturbance direction points to the obstacle, it is projected and corrected, the normal collision component is removed, and the tangential component along the obstacle surface is retained, so that the disturbance path naturally avoids the obstacle, ensuring that each path is feasible for obstacle avoidance, and the initial distance between AUVs satisfies the safety constraint, thus obtaining an initial population including multiple feasible individuals.

[0131] Understandably, this step, based on a hybrid initialization method of multiple A* heuristic search and adaptive Perlin noise perturbation, can more effectively improve the quality and diversity of the initial population in dense obstacle environments, avoid generating a large number of infeasible solutions that fall into obstacles, provide better initial anchor points for the global exploration of the subsequently improved Star Raven Optimization Algorithm, and greatly avoid the algorithm from prematurely converging to poor local optima due to low quality of initial solutions.

[0132] Step S42: Based on the nonlinear convergence parameter, switch the foraging strategy of the star jays and perform a preliminary update for each population;

[0133] Step S42 includes:

[0134] Step S421: For each population, obtain the temperature of each individual within the current population;

[0135] Step S422: Calculate the average temperature of the population using the temperature of each individual;

[0136] Step S423: Calculate the nonlinear convergence parameters of each population using the average temperature and boundary control constant of the population. The nonlinear convergence parameters include the global switching probability and the local switching probability.

[0137] In this step, the formula for calculating the nonlinear convergence parameter is:

[0138] ;

[0139] ;

[0140] In the formula, and They represent the first Global switching probability and local switching probability at the next iteration Indicates the number of individuals in a population. Indicates the first During the nth iteration The temperature of each individual and These represent the minimum boundary control constant and the maximum boundary control constant, respectively.

[0141] Step S424: Generate three random numbers for each population, and select a foraging strategy for each population based on the random numbers and the nonlinear convergence parameter;

[0142] In this step, three random numbers are generated. , and ,and , , .

[0143] when When, then according to the nonlinear convergence parameter Make a judgment when Choose the global exploration strategy for the spring / summer phase; otherwise, choose the development strategy for the spring / summer phase.

[0144] when When, then according to the nonlinear convergence parameter Make a judgment when Choose the global exploration strategy for the autumn / winter phase; otherwise, choose the development strategy for the autumn / winter phase.

[0145] Step S425: Update the individual positions of the corresponding population according to the selected foraging strategy, which includes spring / summer strategy and autumn / winter strategy.

[0146] Step S43: When the number of generations of stagnation of an individual exceeds the preset stagnation threshold, the elite individuals in the updated population are locally optimized using a sequential quadratic programming algorithm;

[0147] In this step, the preset stagnation threshold is a dynamic threshold that decreases adaptively with the number of iterations. Local optimization of elite individuals is only performed when the number of stagnation generations of an individual exceeds the preset stagnation threshold.

[0148] Understandably, in the population evolution stage, this step combines the sequential quadratic programming algorithm to enhance the local search capability of the improved Star Raven optimization algorithm, thereby improving the accuracy of the final converged solution. Introducing the elite concept can better balance search accuracy and search efficiency.

[0149] Step S43 includes:

[0150] Step S431: Calculate the fitness of each individual in the updated population, and sort the individuals in ascending order according to their fitness to obtain an ordered set;

[0151] Step S432: Obtain elite individuals from the ordered set;

[0152] In this step, considering the computational cost of the sequential quadratic programming algorithm, only the top-ranked items in the ordered set are selected. For each individual, local optimization is performed on the elite individuals, while the unselected individuals retain their original state.

[0153] Step S433: Using the current position of each elite individual as the initial point, construct a local optimization subproblem;

[0154] In this step, elite individuals The current position is the current collaborative path scheme for multiple AUVs. Indicates the first The first iteration Each individual is an elite. Furthermore, the local optimization subproblem aligns with the global objective, namely, minimizing the multi-objective fitness function.

[0155] Step S434: Solve each local optimization subproblem using the SQP algorithm to obtain candidate solutions for elite individuals;

[0156] In this step, the local optimization subproblem is transformed into a quadratic programming subproblem, which is solved using the SQP algorithm to obtain variable increments. Based on these increments, the initial point is iteratively updated multiple times to obtain candidate solutions for elite individuals. , Indicates the first The first iteration Candidate solutions corresponding to each elite individual.

[0157] Step S435: Determine whether to accept the update based on the fitness of the elite individual and the corresponding candidate solution. If yes, update the elite individual to the corresponding candidate solution; otherwise, retain the elite individual.

[0158] In this step, the fitness of elite individuals and the fitness of corresponding candidate solutions are calculated (obtained through a multi-objective fitness function), and then updated using a greedy algorithm:

[0159] when When that time comes, accept the update and... As the corresponding individual position in the next iteration, i.e. , Indicates the first The first iteration An elite individual, otherwise .in, express Adaptability, express The degree of adaptability.

[0160] Step S436: Combine the updated elite individuals with other non-elite individuals in the updated population to obtain a locally optimized population.

[0161] Step S44: Based on the adaptive dynamic hierarchical acceptance criterion of the hierarchical temperature field, calculate and evaluate the individual states in all current populations to obtain the solution set;

[0162] In this step, during the population individual position update stage, an adaptive dynamic hierarchical acceptance criterion based on the hierarchical temperature field is designed to dynamically assign different temperatures to each individual in the population, enabling them to adaptively balance exploration and development behaviors according to their own historical evolutionary trends, thereby enhancing the robustness of the algorithm in complex environments.

[0163] Step S44 includes:

[0164] Step S441: For each individual, calculate the fitness memory value using an adaptive exponential moving average strategy;

[0165] In this step, the fitness memory value is:

[0166] ;

[0167] ;

[0168] In the formula, and They represent the first Second and third During the nth iteration The fitness memory value of an individual. Indicates the first During the nth iteration The fitness memory value of an individual. Indicates the first During the nth iteration Smoothing factor for each individual and They represent the first The and the first The individual in the first The optimal fitness value after the nth iteration. and These are the base smoothing factor and the adjustment coefficient, set to 0.7 and 0.4, respectively. To avoid extremely small numbers with a denominator of zero, This indicates taking the absolute value.

[0169] Step S442: Sort all individuals in the current population in global ascending order according to their fitness memory value, and record the sort number of each individual;

[0170] In this step, individuals from the three populations are sorted together to obtain their sort numbers.

[0171] Step S443: Convert the sequence number of each individual into a normalized ratio;

[0172] In this step, the individual ranking is transformed into a scale-independent ranking ratio within the interval [0,1], whose normalized ratio is:

[0173] ;

[0174] In the formula, Indicates the first During the nth iteration The normalization ratio of each individual, Indicates the first During the nth iteration The sequence number of each individual. This represents the total number of individuals in the entire population. Among them, This represents the globally optimal individual. This represents the worst individual globally.

[0175] Step S444: Calculate the global base temperature based on the number of iterations;

[0176] In this step, the global base temperature is:

[0177] ;

[0178] In the formula, and They represent the first Second and third The global base temperature at the next iteration This indicates the cooling rate, with a set value of 0.99.

[0179] Step S445: Calculate the temperature of each individual using the global base temperature and the normalization ratio;

[0180] In this step, a nonlinear power function is used to map the normalization ratio, differentiating the exploration and development behaviors of individuals in the upper, middle and lower layers. A power exponent parameter greater than 1 is set to suppress the temperature increase of individuals in the top-ranked region, thus constructing a low-temperature development zone. Individuals in the tail region with a normalization ratio close to 1 are kept at a high temperature, thus constructing a high-temperature exploration zone.

[0181] Specifically, the individual's temperature is:

[0182] ;

[0183] In the formula, Indicates the first During the nth iteration The temperature of each individual and These are both range control constants for temperature mapping, with values ​​of 0.5 and 1.5 respectively. This represents the power exponent parameter.

[0184] Step S446: For each individual, calculate the fitness difference based on the current fitness and the fitness at the time of the previous iteration;

[0185] Step S447: Based on the fitness difference and the individual's temperature, perform the Metropolis criterion to select the position of each individual in the current iteration round and obtain the result.

[0186] In this step, if If the new solution is better, then accept it directly, and mark the accepted position as the new position to be retained.

[0187] like Then calculate the acceptance probability:

[0188] ;

[0189] In the formula, Indicates the first During the nth iteration The fitness difference between individuals Indicates the first During the nth iteration The probability of acceptance for each individual.

[0190] Then generate a random number. ,when If the new position is accepted (i.e., the suboptimal solution is accepted), then the new position is accepted; otherwise, the position is rejected and the accepted position is marked as retaining the original position.

[0191] Step S448: Based on the position, accept the result and retain the new or original position of each individual in the solution set.

[0192] Step S45: For stagnant individuals in the solution set, update them using a chaotic back-learning strategy;

[0193] In this step, the ergodicity and unpredictability of the chaotic Tent map are used to modulate the lens scaling factor, which can still generate strong intermittent perturbations in the later stages of iteration. This effectively improves the algorithm's ability to escape deep local optima and avoids the problem of insufficient perturbation strength in the later stages due to scale contraction in traditional linear decay.

[0194] Step S45 includes:

[0195] Step S451: Calculate the chaos value of each stagnant individual, where the stagnant individual is the individual in the solution set of the current iteration round that has not found a better solution and has not accepted a suboptimal solution through the Metropolis criterion;

[0196] In this step, a chaotic sequence is generated using Tent mapping:

[0197] ;

[0198] In the formula, and Representing the chaotic sequence's first... The and the first One chaotic element, the initial chaotic element Random selection and , , is the Tent mapping threshold parameter, which is set to 0.7.

[0199] It should be noted that the process is regenerated in each iteration. A new chaotic sequence is obtained, and the chaotic elements are assigned to each stagnant individual as the corresponding chaotic value.

[0200] Step S452: Calculate the unconstrained lens parameters for each stagnant individual using the chaos value and the current iteration round;

[0201] In this step, the parameters of the unrestricted lens are:

[0202] ;

[0203] In the formula, Indicates the first The unconstrained lens parameters at the next iteration and These represent the upper and lower bounds of the lens parameters, respectively. Indicates the current iteration round. Indicates the maximum number of iterations. This represents the chaotic perturbation coefficient. Indicates the first The chaos value of a stagnant individual.

[0204] Step S453: Perform boundary constraint processing on the unconstrained lens parameters to obtain the dynamic lens parameters for each stationary individual;

[0205] In this step, the dynamic lens parameters are:

[0206] ;

[0207] In the formula, Indicates the first Dynamic lens parameters at the next iteration This indicates taking the minimum value.

[0208] Step S454: For each dimension of the individual's location, calculate the corresponding midpoint of the search space;

[0209] Step S455: Based on the midpoint of the search space and the dynamic lens parameters, perform reverse imaging mapping on the current position of each stagnant individual to obtain the updated position of the stagnant individual.

[0210] In this step, the stationary individual undergoes a reverse imaging perturbation, mapping its position to a symmetrical region of the search space to obtain the reverse solution for the corresponding stationary individual, which serves as the updated position of the stationary individual:

[0211] ;

[0212] In the formula, Indicates the first During the next iteration The reverse solution, Indicates the first The midpoint of the search space of dimension, Indicates the first During the nth iteration The first stagnant individual 3D coordinates. Where the dimension is actually 1. , and The coordinate dimensions of the axis.

[0213] Through each dimension You can get the first During the nth iteration The reverse solution of a stagnant individual .

[0214] Step S46: Calculate the fitness of each individual using the multi-objective fitness function and determine whether the iteration stopping condition has been met. If so, stop the iteration and obtain the individual with the lowest fitness in the current iteration. Otherwise, switch the star raven's foraging strategy again and proceed to the next iteration.

[0215] In this step, the iteration stops after the preset maximum number of iterations is reached; otherwise, the updated individuals are used as the initial population for the next iteration, and the star raven's foraging strategy is switched for the next iteration.

[0216] Step S47: Select the set of waypoints corresponding to the individual with the lowest fitness as the optimal path point sequence.

[0217] In this step, the individual includes the paths of all AUVs, that is, it includes multi-AUV cooperative path schemes. The waypoint set corresponding to the individual with the lowest fitness is taken as the optimal cooperative path scheme, that is, the optimal waypoint sequence is obtained.

[0218] Step S5: After smoothing the optimal path point sequence by cubic spline interpolation, connect the points to obtain the optimal navigation route for the multi-autonomous underwater robot.

[0219] Example 2:

[0220] To verify the effectiveness of the improved Star Raven Optimization Algorithm (INOA-SQP algorithm) designed in this invention for path planning in complex underwater environments, a comparative experiment was designed. The INOA-SQP algorithm was compared with the traditional NOA algorithm, and also with several representative swarm optimization algorithms, including the Grey Wolf Optimization (GWO) algorithm, the Levy-Particle Swarm Optimization (L-PSO) algorithm, the Whale Optimization (WOA) algorithm, the Snake Optimization (SO) algorithm, and the Slime Mushroom (SMA) algorithm. The experiment mainly compared five aspects: path length, collision threat, energy consumption, smoothness, and fitness value.

[0221] like Figure 2 and Figure 3 As shown, in a single AUV scenario, compared to other metaheuristic algorithms, the INOA-SQP algorithm proposed in this invention has a smoother path, without sharp turns, a shorter path length, no detours, and higher path quality.

[0222] Combination Figure 3 Analysis of the fitness convergence curve shows that the INOA-SQP algorithm has a more ideal iterative convergence curve. It can find path regions with low fitness in the early stage, achieve stable convergence in the early and middle stages, and the final fitness value is significantly better than other comparison algorithms.

[0223] Analysis of the data in Table 1 shows that the proposed algorithm has significant advantages in terms of travel distance, energy consumption, and collision risk. It converges to a better fitness value on the fitness function, and the quality of the solution is significantly improved. This fully demonstrates that the algorithm of this invention has stronger search capabilities and faster convergence speed, effectively searching for the optimal path and obtaining a better fitness function value.

[0224] Table 1 Performance Comparison of Different Optimization Algorithms

[0225] algorithm sailing distance Deflection angle Collision risk Energy consumption Minimum fitness value L-PSO 204.73 24.45 740.01 712.12 39759.13 WOA 274.81 23.34 822.38 636.56 73739.25 GWO 284.56 9.56 685.54 530.22 77332.22 SO 154.82 8.81 8.04 329.05 12997.55 SMA 234.79 14.53 417.43 587.32 37984.11 NOA 195.75 8.58 14.49 695.61 43094.88 INOA-SQP 110.07 5.61 7.05 277.75 9295.98

[0226] To verify the performance of multiple AUVs in collaborative path planning under complex marine environments, particularly focusing on two key indicators—safe distance control among AUV crew members throughout the entire path and safe arrival rate at the target point—an experiment was designed to simulate the path planning of three AUVs under a defined environment. Unlike some multi-AUV path planning studies that set multiple AUVs at the same start and end point, this invention considers the physical collision avoidance requirements of multiple AUVs during actual deployment and recovery phases. It sets the start and target points of each AUV within adjacent areas to simulate collaborative navigation scenarios of multiple AUVs in a densely deployed environment. Figure 4 As shown, AUV1, AUV2 and AUV3 represent different AUVs.

[0227] In addition, to verify the practicality of the INOA-SQP algorithm, this embodiment also extracted seabed topographic elevation data for the Xisha Islands region from the GEBCO global ocean topography dataset, covering latitudes of 17.5° to 15.5° N and longitudes of 111.0° to 113.0° E and latitudes of 16.65° to 16.45° N and longitudes of 111.55° to 111.85° E. A realistic seabed topographic environment was constructed to verify the path planning performance of multiple AUVs under real-world environmental information. The simulation results are as follows: Figure 5 and Figure 6 Place.

[0228] In summary, even in complex marine environments with multiple obstacles and eddy currents, the method of this invention can maintain efficient cooperative path planning when applied to multiple AUVs. The safe distance between AUV members can be dynamically adjusted according to a preset minimum safety threshold. A smaller safe distance helps the AUV swarm form a more compact formation, allowing the AUV swarm to avoid obstacles from the same side while maintaining close proximity, thus shortening the travel distance. While a larger safe distance increases the travel distance, it also significantly reduces the risk of collisions between swarms, providing necessary safety redundancy for navigation missions in dense environments.

[0229] Example 3:

[0230] This embodiment provides a multi-autonomous underwater robot path planning system, the system comprising:

[0231] The first construction module is used to build a three-dimensional underwater environment model based on the navigation environment of the autonomous underwater robot.

[0232] The determination module is used to determine the optimization objectives and constraints for the path planning of the multi-autonomous underwater robot based on the three-dimensional underwater environment model.

[0233] The second construction module is used to construct a multi-objective fitness function based on the weighted sum method and the penalty function method, according to the optimization objective and the constraints.

[0234] The solution module is used to solve the multi-objective fitness function using an improved star-raven optimization algorithm to obtain the optimal path point sequence;

[0235] The planning module is used to smooth the optimal path point sequence using cubic spline interpolation and then connect them to obtain the optimal navigation route for the multi-autonomous underwater robot.

[0236] The first building module includes:

[0237] The first building unit is used to approximate the underwater environment topography using a land-based mountain model. By superimposing trigonometric functions of different frequencies and amplitudes and adding Gaussian white noise, a baseline topography model is obtained.

[0238] The second building unit is used to construct a model of seabed peaks in the navigation environment using an exponential function.

[0239] The third building unit is used to construct spherical threat areas and cuboid threat areas based on the characteristics of underwater terrain obstacles.

[0240] The simulation unit is used to simulate underwater ocean current environments using a numerically superimposed viscous Lamb–Oseen eddy model and seafloor boundary layer effects.

[0241] The fourth building unit is used to construct a three-dimensional underwater environment model based on the benchmark terrain model, the seabed mountain model, the spherical threat area, the cuboid threat area, and the underwater ocean current environment.

[0242] The determining unit is used to determine the starting position and target position of the multiple autonomous underwater robots in the three-dimensional underwater environment model.

[0243] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0244] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0245] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A path planning method for multi-autonomous underwater robots, characterized in that, include: Based on the navigation environment of the autonomous underwater robot, a three-dimensional underwater environment model is constructed. The optimization objectives and constraints for the multi-autonomous underwater robot path planning are determined based on the aforementioned three-dimensional underwater environment model. Based on the weighted sum method and penalty function method, a multi-objective fitness function is constructed according to the optimization objective and the constraints, including: Based on the weighted sum method, an objective function is constructed according to the optimization objectives and constraints. The optimization objectives include path length, collision threat, smoothness, and ocean current energy consumption. The constraints include boundary constraints and inter-cluster spatial distance constraints. The objective function for: ； In the formula, Indicates the number of AUV clusters. Indicates the first The weighting coefficients of each optimization objective. Indicates the first The optimization objective is... The fitness function under the following conditions Indicates in The boundary constraint cost function is as follows. This represents the cost function constrained by spatial distance between multiple AUV clusters. Indicates the first A complete set of waypoints for each AUV This represents the complete set of waypoints including all AUVs; A fitness function for each optimization objective is constructed based on the aforementioned three-dimensional underwater environment model; The fitness function for the path length is: ； In the formula, This indicates that the first optimization objective is in The fitness function under the following conditions This indicates the number of waypoints for the AUV. and They represent the first The first AUV The and the first The coordinate vectors of each waypoint Denotes the Euclidean norm; The fitness function for the collision threat is: ； In the formula, This indicates that the second optimization objective is in The fitness function under the following conditions Indicates in The cost of the spherical obstacle threat. Indicates in The rectangular obstacle below threatens costs. Indicates in The cost of underwater mountain obstacles; The fitness function for the smoothness is: ； ； ； In the formula, Indicates the first The first AUV Horizontal turns of each path segment Indicates the first The first AUV Vertical pitch angle of each path segment Indicates the first The first AUV Vertical pitch angle of each path segment and They represent the first The first AUV The and the first The projection vectors of path segments onto the horizontal plane, where, , express transpose, , and The first The first AUV Each path segment is in axis, shaft and Increment of axis, and These are the weighting coefficients for controlling the costs of horizontal and vertical smoothness, respectively. This indicates that the third optimization objective is in The fitness function under the following conditions Indicates the total number of underwater peaks; The fitness function for the ocean current energy consumption is: ； ； In the formula This indicates that the fourth optimization objective is in The fitness function under the following conditions Indicates the number of evaluation points. Indicates the first AUV and The energy cost corresponding to the minimum path segment, Indicates the first AUV and The length of the corresponding minimum path segment , and These represent the reverse flow penalty coefficient, the downstream flow reward coefficient, and the lateral flow penalty coefficient, respectively. and They represent the first The first AUV The and the first Coordinates of each evaluation point express Parallel components, express The lateral component, express The ocean current velocity vector, express and The coordinates of the midpoint of the corresponding minimal path segment. This indicates taking the maximum value; Penalties are applied to the paths subject to boundary constraints and inter-cluster spatial distance constraints to obtain the corresponding cost functions, which include the inter-cluster spatial distance constraint cost function and the boundary constraint cost function. The cost function for the collaborative safety distance constraint of multiple AUV clusters is: ； In the formula, This represents the cooperative collision avoidance penalty coefficient. Indicates the number of AUV clusters. Indicates the first The first AUV Coordinates of each evaluation point Indicates the number of samples after dense resampling. The first AUV One assessment point, Minimum safe distance; The boundary constraint cost function is: ； ； ； In the formula, and All represent positive penalty coefficients. and These represent the first penalty item and the second penalty item, respectively. , and They represent the first The first AUV The x, y, and y coordinates of each waypoint and These represent the minimum and maximum values ​​of the x-axis, respectively. and These represent the minimum and maximum values ​​of the ordinate, respectively. and These represent the minimum and maximum values ​​of the vertical coordinates, respectively. This indicates an indicator function that takes the value 1 if the condition is true, and 0 otherwise. Indicates environmental constraints; Substituting the fitness function and the cost function into the objective function yields a multi-objective fitness function; The optimal path point sequence is obtained by solving the multi-objective fitness function using an improved star-raven optimization algorithm. After smoothing the optimal path point sequence with cubic spline interpolation, the optimal navigation route of the multi-autonomous underwater robot is obtained by connecting the points. The step of solving the multi-objective fitness function using the improved Star Raven optimization algorithm to obtain the optimal path point sequence includes: Differentiated guidance paths are generated based on the A* algorithm, and multiple populations are initialized according to the guidance paths; Based on the foraging strategy of the Star Crow with nonlinear convergence parameter switching, each population is initially updated. When the number of generations of stagnation of an individual exceeds a preset stagnation threshold, the elite individuals in the updated population are locally optimized using a sequential quadratic programming algorithm. Based on the adaptive dynamic hierarchical acceptance criterion of the hierarchical temperature field, the individual states in all current populations are calculated and evaluated to obtain the solution set; For stagnant individuals in the solution set, updates are performed using a chaotic reverse learning strategy; The fitness of each individual is calculated using a multi-objective fitness function, and it is determined whether the iteration stopping condition has been met. If so, the iteration is stopped, and the individual with the lowest fitness in the current iteration is obtained. Otherwise, the star raven's foraging strategy is switched again, and the next iteration is carried out. The set of waypoints corresponding to the individual with the lowest fitness is taken as the optimal path point sequence.

2. The multi-autonomous underwater robot path planning method according to claim 1, characterized in that, The construction of a three-dimensional underwater environment model based on the navigation environment of the autonomous underwater robot includes: A land-based mountain model is used to approximate the underwater environment topography. By superimposing trigonometric functions of different frequencies and amplitudes and adding Gaussian white noise, a baseline topography model is obtained. Models of underwater mountains in the navigation environment are constructed using exponential functions; Based on the characteristics of underwater terrain obstacles, spherical and cuboid threat areas are constructed. The underwater ocean current environment was simulated using a numerically superimposed viscous Lamb–Oseen eddy model and the seafloor boundary layer effect; A three-dimensional underwater environment model was constructed based on the baseline terrain model, the submarine mountain model, the spherical threat area, the cuboid threat area, and the underwater ocean current environment. Determine the starting and target positions of the multiple autonomous underwater robots in the three-dimensional underwater environment model.

3. The multi-autonomous underwater robot path planning method according to claim 1, characterized in that, The foraging strategy for star ravens based on switching nonlinear convergence parameters involves an initial update for each population, including: For each population, obtain the temperature of each individual within the current population; The average temperature of the population is calculated by measuring the temperature of each individual. The nonlinear convergence parameters of each population are calculated using the average temperature and boundary control constant of the population. These nonlinear convergence parameters include the global switching probability and the local switching probability. Three random numbers are generated for each population, and the foraging strategy for each population is selected based on the random numbers and the nonlinear convergence parameter. The individual locations of the corresponding population are updated according to the selected foraging strategy, which includes spring / summer strategy and autumn / winter strategy.

4. The multi-autonomous underwater robot path planning method according to claim 1, characterized in that, The step of using a sequential quadratic programming algorithm to locally optimize the elite individuals in the updated population includes: Calculate the fitness of each individual in the updated population, and sort the individuals in ascending order according to their fitness to obtain an ordered set; Identify elite individuals from ordered sets; Starting from the current position of each elite individual, construct a local optimization subproblem; The SQP algorithm is used to solve each local optimization subproblem to obtain candidate solutions for elite individuals; Determine whether to accept the update based on the fitness of the elite individual and the corresponding candidate solution. If yes, update the elite individual to the corresponding candidate solution; otherwise, retain the elite individual. The updated elite individuals are combined with other non-elite individuals in the updated population to obtain a locally optimized population.

5. The multi-autonomous underwater robot path planning method according to claim 1, characterized in that, The adaptive dynamic stratified acceptance criterion based on the hierarchical temperature field calculates and evaluates the individual states in all current populations to obtain a solution set, including: For each individual, an adaptive exponential moving average strategy is used to calculate the fitness memory value; Sort all individuals in the current population in global ascending order according to their fitness memory value, and record the sort number of each individual; Convert the sequence number of each individual into a normalized ratio; Calculate the global base temperature based on the number of iterations; The temperature of each individual is calculated using the global baseline temperature and the normalization ratio; For each individual, calculate the fitness difference based on the current fitness and the fitness at the time of the previous iteration; Based on the fitness difference and the individual's temperature, the Metropolis criterion is used to select the individual and determine the position of each individual in the current iteration round. Based on the location, the new or original location of each individual is retained in the solution set.

6. The multi-autonomous underwater robot path planning method according to claim 1, characterized in that, The update of stagnant individuals in the solution set through a chaotic back-learning strategy includes: Calculate the chaos value for each stagnant individual, which is an individual in the solution set of the current iteration round that has not found a better solution and has not accepted a suboptimal solution through the Metropolis criterion; The unconstrained lens parameters for each stagnant individual are calculated using the chaos value and the current iteration round; Boundary constraints are applied to the unconstrained lens parameters to obtain the dynamic lens parameters for each stationary individual. For each dimension of an individual's location, calculate the corresponding midpoint of the search space; Based on the midpoint of the search space and the dynamic lens parameters, the current position of each stagnant individual is reverse-image mapped to obtain the updated position of the stagnant individual.

7. A multi-autonomous underwater robot path planning system, implemented based on the multi-autonomous underwater robot path planning method according to any one of claims 1-6, characterized in that, include: The first construction module is used to build a three-dimensional underwater environment model based on the navigation environment of the autonomous underwater robot. The determination module is used to determine the optimization objectives and constraints for the path planning of the multi-autonomous underwater robot based on the three-dimensional underwater environment model. The second construction module is used to construct a multi-objective fitness function based on the weighted sum method and the penalty function method, according to the optimization objective and the constraints. The solution module is used to solve the multi-objective fitness function using an improved star-raven optimization algorithm to obtain the optimal path point sequence; The planning module is used to smooth the optimal path point sequence using cubic spline interpolation and then connect them to obtain the optimal navigation route for the multi-autonomous underwater robot. The step of solving the multi-objective fitness function using the improved Star Raven optimization algorithm to obtain the optimal path point sequence includes: Differentiated guidance paths are generated based on the A* algorithm, and multiple populations are initialized according to the guidance paths; Based on the foraging strategy of the Star Crow with nonlinear convergence parameter switching, each population is initially updated. When the number of generations of stagnation of an individual exceeds a preset stagnation threshold, the elite individuals in the updated population are locally optimized using a sequential quadratic programming algorithm. Based on the adaptive dynamic hierarchical acceptance criterion of the hierarchical temperature field, the individual states in all current populations are calculated and evaluated to obtain the solution set; For stagnant individuals in the solution set, updates are performed using a chaotic reverse learning strategy; The fitness of each individual is calculated using a multi-objective fitness function, and it is determined whether the iteration stopping condition has been met. If so, the iteration is stopped, and the individual with the lowest fitness in the current iteration is obtained. Otherwise, the star raven's foraging strategy is switched again, and the next iteration is carried out. The set of waypoints corresponding to the individual with the lowest fitness is taken as the optimal path point sequence.

8. The multi-autonomous underwater robot path planning system according to claim 7, characterized in that, The first building module includes: The first building unit is used to approximate the underwater environment topography using a land-based mountain model. By superimposing trigonometric functions of different frequencies and amplitudes and adding Gaussian white noise, a baseline topography model is obtained. The second building unit is used to construct a model of seabed peaks in the navigation environment using an exponential function. The third building unit is used to construct spherical threat areas and cuboid threat areas based on the characteristics of underwater terrain obstacles. The simulation unit is used to simulate underwater ocean current environments using a numerically superimposed viscous Lamb–Oseen eddy model and seafloor boundary layer effects. The fourth building unit is used to construct a three-dimensional underwater environment model based on the benchmark terrain model, the seabed mountain model, the spherical threat area, the cuboid threat area, and the underwater ocean current environment. The determining unit is used to determine the starting position and target position of the multiple autonomous underwater robots in the three-dimensional underwater environment model.

Images