Anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm

Abstract

The invention discloses an anti-ship missile multi-base cross-domain route planning method based on a particle swarm optimization algorithm, and relates to the technical field of route planning, and the method comprises the steps: firstly obtaining description parameters of a combat environment, and carrying out the initialization of the description parameters; dividing a many-to-many route planning problem in a complex multi-base cross-domain combat scene into a plurality of single-side n-to-1 route planning sub-problems; a relative coordinate system is established for each sub-problem in a semi-rasterization modeling mode, and a particle swarm optimization algorithm is adopted to be combined with air route planning geometric knowledge for solving; and finally, the steps are repeatedly executed until the optimal planning result of all the sub-problems is obtained, the optimal planning result is converted back to the standard coordinate system, and a final many-to-many anti-ship missile collaborative route planning scheme is obtained. According to the method, the anti-ship missile route planning efficiency and precision in multi-base cross-domain combat can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of route planning, and in particular, to a multi-base cross-domain route planning method for anti-ship missiles based on a particle swarm optimization algorithm. Background Art

[0002] Collaborative Anti-ship Path Planning means that route planning is carried out for anti-ship missiles launched from multiple platforms on our side, and cooperative strikes are carried out on enemy ships in a very short time, with small resource consumption. The collaborative anti-ship path planning methods are mainly divided into two categories: classical path planning methods, including A* algorithm, Voronoi diagram method, rapidly exploring random tree, etc.; intelligent optimization algorithms, including particle swarm optimization algorithm, ant colony algorithm, genetic algorithm, simulated annealing algorithm, grey wolf algorithm, etc.

[0003] Compared with traditional algorithms, intelligent optimization algorithms are simpler, more efficient, and more adaptable, and are also a more mainstream method. Among them, the Particle Swarm Optimization (PSO) algorithm is a new type of heuristic intelligent optimization algorithm. This algorithm was initially inspired by the regularity of the activities of bird flocks, and then a simplified model was established using swarm intelligence. Based on the observation of the behavior of animal swarms, the particle swarm optimization algorithm uses the sharing of information among individuals in the swarm to make the movement of the entire swarm evolve from disorder to order in the problem-solving space, so as to obtain the optimal solution.

[0004] Due to the characteristic of anti-ship missiles flying at low altitude over the sea, most of the current collaborative anti-ship path planning methods simplify the model flat and establish it on a two-dimensional plane. However, in the complex combat scenario of multi-base cross-domain, the anti-ship missile launch platforms involve multiple spatial domains such as sea area, airspace, land area, and subsea area, and their spatial characteristic information is crucial. However, there is little research on three-dimensional collaborative anti-ship path planning at present. When using intelligent optimization algorithms to solve the problem of collaborative anti-ship path planning, generally, a planning area is delimited for each route first, and then single-route planning is carried out within their respective areas. Such a method ignores the geometric laws of anti-ship missiles themselves and the dynamic evolution laws of multi-missile cooperation. And these laws and knowledge of anti-ship missile routes can effectively guide the algorithm to accelerate convergence and obtain better solutions. In addition, when using intelligent optimization algorithms to solve the problem of collaborative path planning, since the adjustment of route point coordinates is achieved by random movement, problems such as uneven spacing between route points and poor smoothness often occur. Summary of the Invention

[0005] The objective of the present invention is to provide an anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm, aiming to improve the efficiency and accuracy of anti-ship missile route planning in complex combat environments.

[0006] The technical solution of the present invention is to provide an anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm, and this method includes:

[0007] S1. Obtain the environmental description parameters in the standard coordinate system and perform initialization definition on the parameters;

[0008] S2. Divide the many-to-many anti-ship missile route planning problem in the complex multi-base cross-domain combat scenario into several anti-ship missile multi-base cross-domain one-sided n-to-1 route planning sub-problems;

[0009] S3. For each anti-ship missile multi-base cross-domain one-sided n-to-1 route planning sub-problem, establish a relative coordinate system by using the semi-grid environmental modeling method, and convert the coordinate parameters in the standard coordinate system to the relative coordinate system;

[0010] S4. Combine the geometric knowledge and rules of anti-ship missile route planning, and solve the anti-ship missile multi-base cross-domain one-sided n-to-1 route planning sub-problem based on the particle swarm optimization algorithm;

[0011] S5. Repeat steps S3 - S4 for all the divided anti-ship missile multi-base cross-domain one-sided n-to-1 route planning sub-problems until the optimal planning results of all sub-problems are obtained;

[0012] S6. Re-convert the route planning results of all anti-ship missile multi-base cross-domain one-sided n-to-1 route planning sub-problems to the standard coordinate system to obtain the multi-to-many anti-ship missile cooperative route planning scheme in the complex multi-base cross-domain combat scenario.

[0013] In any of the above technical solutions, further, the environmental description parameters in step S1 include the position information of obstacles in the sea area, the coordinate information of each anti-ship missile launch platform and the target ship, and the basic combat parameters of each missile. The basic combat parameters include the range, the maximum turning angle, the minimum flight segment, the maximum number of route turning points, the ideal flight altitude range, the limit flight altitude, and the cooperative incident angle between each missile;

[0014] The obstacle is modeled as a cylinder model, and the modeling O w is described as:

[0015] O w =(x w ,y w ,z w ,R w ,H w );

[0016] Wherein, x w , y w , z w , R w respectively represent the x, y, z axis coordinates and radius of the center of the bottom circle of the cylinder in the standard coordinate system, H w represents the height of the cylinder, and w is the number of the obstacle.

[0017] In any of the above technical solutions, further, step S2 specifically includes:

[0018] Using the azimuth angle and the uniqueness of the target ship as the division basis, the azimuth relationship between the area where each anti-ship missile launch platform is located and the target ship determines the division of sub-problems;

[0019] All divided anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems are required to meet the following two conditions:

[0020] Same-side launch: In each unilateral n-to-1 route planning sub-problem, all launch platforms need to be located on the same side of the target ship;

[0021] Unique target ship: In each sub-problem, the target ships targeted by all launch platforms must be the same and unique.

[0022] In any of the above technical solutions, further, step S3 specifically includes:

[0023] Select the projection position of the launch platform farther from the target ship on the horizontal plane as the origin, and establish a new three-dimensional coordinate system, and the axis direction of this coordinate system points to the target ship;

[0024] Next, according to the semi-grid modeling method, the environment is divided into multiple grid planes parallel to the y-axis. Each grid plane is parallel to the straight line where the target ship is located, and taking each launch platform as a reference, establish the planning areas of multiple routes. On these grid planes, plan the route turning points of the anti-ship missile, and distribute and adjust these route turning points according to the geographical positions of the target ship and the launch platform to ensure that the path planning can accurately cover all possible flight trajectories.

[0025] In any of the above technical solutions, further, step S3 converts the coordinate parameters in the standard coordinates in step S2 to the relative coordinate system, which is expressed as:

[0026]

[0027] Wherein, (xyz) T is the coordinate in the standard coordinate system, R 0 is the rotation matrix for converting the standard coordinate system to the relative coordinate system, (x g_far yg_far z g_far ) T is the coordinate of the launch platform farthest from the target ship.

[0028] In any of the above technical solutions, further, step S4 specifically includes:

[0029] S41. Obtain the environmental parameters in the relative coordinate system, including obstacle-related information, the coordinates of each launch platform, the coordinate information of the target ship, and the flight parameters of the anti-ship missile. The flight parameters include range, maximum turning angle, minimum flight segment, maximum number of waypoint turns, ideal flight altitude range, limit flight altitude, and cooperative incident angle between each missile;

[0030] S42. Take the maximum distance of the minimum flight segment among each anti-ship missile as the area distance L, divide the combat area according to this distance. After dividing the area, use the semi-grid environmental modeling method to determine the number of waypoint turns of all routes and their y-axis coordinates;

[0031] S43. Initialize all particles according to the geometric knowledge of anti-ship missile route planning and the law of spatial geometric gradual change. At this time, if the waypoint turns in a certain route do not conform to the law of spatial geometric gradual change, randomly generate new waypoint turns within the correction window formed by the intersection of the straight line between the previous waypoint and the launch platform and the grid plane until it conforms to the law of spatial geometric gradual change;

[0032] S44. Calculate the cooperative fitness function values of all initial particles, and calculate the current optimal and global optimal of the initial particles;

[0033] S45. During the particle swarm optimization process, initialize the particle velocity according to the predetermined update rule and select an appropriate initial velocity range;

[0034] S46. Update the particles according to the particle update formula. After each update of the particles, perform optimization processing using the avoidance operator, cooperative operator, and smoothing operator.

[0035] S47. After each optimization, recalculate the cooperative fitness function values of the updated particles, and update the current optimal solution and global optimal solution of each particle;

[0036] S48. As the iteration progresses, update the particle velocity according to the current iteration number and the preset particle update formula, and adjust the parameters therein;

[0037] S49. Repeat the operations of steps S45 to S48 until the maximum iteration number is reached. When the maximum iteration number is reached, output the global optimal particle as the final planning result of the anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problem.

[0038] In any of the above technical solutions, further, in step S43, a correction window is used to generate new route turning points, and the generation process includes:

[0039] Ship A launches an anti-ship missile to strike target ship B. When planning the reverse route, the route turning point P i deviates from the spatial geometric functional area. Taking the intersection point of the straight line connecting the previous turning point P i-1 and the launching ship A and the grid plane as the center, a circular area with a fixed radius r is generated on the grid plane, as shown by the black solid line area in the figure. This area is the correction window; a new route turning point P' is randomly generated in the correction window i , until it conforms to the spatial geometric gradual change law. Let P i-1 (x i-1 , y i-1 , z i-1 ), P i (x i , y i , z i ), A(x A , y A , z A ). The center coordinates W of the correction window can be expressed as:

[0040]

[0041] The correction window range can be expressed as:

[0042]

[0043] In any of the above technical solutions, further, the collaborative fitness function in step S44 is set as the difference between the objective function and the penalty function;

[0044] The objective function is expressed as:

[0045] f = a 1 α L + a 2 α d + a 3 α Num + a 4 α Z + a 5 α s ;

[0046] Among them, a 1 ~a 5 are the coefficient of each index, α L is the total route length, α d represents the sum of collaborative incident angle deviations, α Num is the total number of turning points, α s is the mean square deviation of the absolute value of the turning angle;

[0047] Sum of collaborative incident angle deviations α d The expression is:

[0048]

[0049] In the formula, α real is the route collaborative incident angle, α syn is the set collaborative incident angle, U is the number of collaborative incident angles, G is the number of routes, u is the subscript of the collaborative incident angle;

[0050] Each index of the objective function needs to be normalized so that the sum of a 1 ~a 5 is 1, and the normalized objective function f is expressed as F;

[0051] The penalty function is expressed as:

[0052] v = b 1 β 1 + b 2 β 2 + b 3 β 3 + b 4 β 4 ;

[0053] In the formula, v is the penalty function, b 1 ~b 4 are the index coefficients, and β 1 ~β 4 are respectively the penalty function index representing the degree of collision, the penalty function index representing the degree of route intersection, the penalty function index representing the degree of unreasonable flight altitude, and the penalty function index representing the degree of the turning angle exceeding the maximum turning angle limit;

[0054] Each index of the penalty function needs to be normalized so that the sum of the index coefficients b 1 ~b 4 is 1, and the normalized penalty function v is expressed as V;

[0055] The fitness function of the anti-ship missile multi-base cross-domain can be expressed as the difference between the normalized objective function F and the penalty function V, expressed as:

[0056] fit(X j ) = F - V;

[0057] In the formula, fit is the fitness function of the anti-ship missile multi-base cross-domain, X is the particle, and j is the particle number.

[0058] In any of the above technical solutions, further, the penalty function index representing the degree of collision is expressed as:

[0059]

[0060] In the formula, β 1 is the penalty function index for the degree of collision, representing the sum of the counts of the number of collisions; μ gs is the mark for collision. If a collision occurs, it is marked as 1, otherwise it is marked as 0; G is the number of air routes, g is the subscript of the air route, where S g is the number of flight segments of the g-th air route, and s is the subscript of the flight segment;

[0061] The penalty function index representing the degree of air route intersection is expressed as:

[0062]

[0063] In the formula, β 2 is the index representing the degree of air route intersection, and γ dt is the air route intersection mark. If an air route intersection occurs, the mark γ dt is 1, otherwise it is marked as 0; The detection of air route intersection involves permutations and combinations. D is the number of areas involved, d is the area number, and T d is the number of pairwise combinations of flight segments within the d-th area, and t is the number of the combination result within this area;

[0064] The penalty function index representing the degree of unreasonable flight altitude is expressed as:

[0065]

[0066] In the formula, β 3 is the index representing the degree of unreasonable flight altitude; G is the number of air routes, g is the subscript of the air route, and I g is the number of turning points of the g-th air route, and i is the subscript of the turning point of this air route; h gi is used to identify the degree to which the flight altitude of a single anti-ship missile is within the ideal altitude range, and h gi The calculation formula can be expressed as:

[0067]

[0068] Among them, (h min , h max ) is the ideal flight altitude range of the anti-ship missile, H is the maximum flight altitude of the missile, and z gi is the altitude of the i-th turning point of the g-th air route;

[0069] The index representing the degree to which the turning angle exceeds the maximum turning angle limit is expressed as:

[0070]

[0071] where β 4 is an index indicating the degree to which the steering angle exceeds the maximum steering angle limit, and is a flag for whether all steering angles are within the limit and the sum of the quantities; if the steering angle is within the limit, is 0, otherwise it is 1.

[0072] In any of the above technical solutions, further, the particle update formula in step S46 is expressed as:

[0073]

[0074] where X represents the particle position, k represents the current iteration number, V represents the particle velocity, and is calculated by the following velocity calculation formula:

[0075]

[0076] where ω is the inertia weight; c 1 , c 2 are learning factors; r 1 , r 2 are random factors, randomly generated in [0, 1).

[0077] The beneficial effects of the present invention are:

[0078] The technical solution in the present invention divides the many-to-many anti-ship missile route planning problem in the multi-base cross-domain combat scenario into multiple simple sub-problems, significantly reducing the computational complexity and improving the path planning efficiency.

[0079] Through the swarm intelligence mechanism of the particle swarm optimization algorithm, combined with rules such as collision avoidance, coordination, and path smoothing, it effectively avoids path crossing and interference between missiles, ensuring the coordination and safety of multi-missile cooperative combat.

[0080] In the preferred implementation mode of the present invention, by combining the flight characteristics of anti-ship missiles (such as maximum steering angle, ideal flight altitude, etc.), it is ensured that the generated route not only meets the mathematical optimization criteria but also adapts to the flight requirements in actual combat, improving the feasibility of the path and the combat effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The above and additional aspects of the present invention will become apparent and easy to understand when combined with the description of the embodiments with the following drawings, where:

[0082] Figure 1 is the algorithm flowchart of the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0083] Figure 2It is a schematic diagram of the multi-base cross-domain combat of an anti-ship missile for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0084] Figure 3 It is the anti-ship missile multi-base cross-domain route planning environment modeling for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0085] Figure 4 It is the flowchart of the particle swarm optimization algorithm for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0086] Figure 5 It is the schematic diagram of the correction window for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0087] Figure 6 It is the schematic diagram of the evasion operator optimized route for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0088] Figure 7 It is the simulation diagram of the effectiveness test result for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0089] Figure 8 It is the simulation result diagram of the superiority test for the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0090] Figure 9 It is the simulation diagram of the route planning for the four-to-one combat scenario of the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0091] Figure 10 It is the simulation diagram of the multi-base cross-domain collaborative route planning for the six-to-two combat scenario of the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention;

[0092] Figure 11 It is the simulation diagram of the multi-base cross-domain collaborative route planning for the seven-to-three combat scenario of the anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm according to an embodiment of the present invention. Detailed implementation manners

[0093] To better understand the above objects, features, and advantages of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0094] In the following description, many specific details are set forth to facilitate a thorough understanding of the present invention. However, the present invention may be practiced in other ways than those described herein. Therefore, the scope of the present invention is not limited by the specific embodiments disclosed below.

[0095] As Figure 1-2 shown, this embodiment provides an anti-ship missile multi-base cross-domain route planning method based on the particle swarm optimization algorithm, including:

[0096] S1. First, obtain the description parameters of the combat environment in the standard coordinate system and initialize and define each parameter. The description parameters include the position information of obstacles such as reefs and islands in the sea area, as well as the coordinate information of each anti-ship missile launch platform and the target ship. At the same time, obtain the basic combat parameters of each missile. The basic combat parameters include the range, maximum turning angle, minimum flight segment, maximum number of route turning points, ideal flight altitude range, limit flight altitude, and the cooperative incident angle between each missile, etc.

[0097] In the above process, the obstacles involved are modeled as cylinder models, and the modeling O w is described as:

[0098] O w =(x w ,y w ,z w ,R w ,H w );

[0099] In the formula, x w , y w , z w , R w respectively represent the x, y, z-axis coordinates and radius of the center of the bottom circle of the cylinder in the standard coordinate system, H w represents the height of the cylinder, and w is the number of the obstacle.

[0100] S2. After obtaining the above-mentioned environment and combat parameters in the standard coordinate system, next, divide the many-to-many anti-ship missile route planning problem in the complex multi-base cross-domain combat scenario into several anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems.

[0101] Specifically, first, based on the combat requirements of anti-ship missiles, considering the geographical locations of each launch platform and the target ship, the azimuth angle and the uniqueness of the target ship are used as the division basis. The azimuth relationship between the area where each anti-ship missile launch platform is located and the target ship determines the division of sub-problems. For example, all launch platforms located on the same side of the target ship will be divided into one sub-problem, ensuring that the launch platforms in each sub-problem are planned for the same target ship, thus avoiding the problem of mutual interference between different platforms; this step ensures that each sub-problem can be centrally processed and solve the missile route planning problem related to it, improving the accuracy and efficiency of the planning process.

[0102] In addition, in this step, all divided anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems are required to meet the following two conditions: same-side launch and unique target ship.

[0103] Same-side launch: In each unilateral n-to-1 route planning sub-problem, all launch platforms need to be located on the same side of the target ship, so as to ensure that the planned routes in each sub-problem are consistent and avoid the complex cross paths that may be caused by launch platforms on both sides of the target ship.

[0104] Unique target ship: In each sub-problem, the target ships targeted by all launch platforms must be the same and unique. That is, all missiles in each sub-problem need to point to the same target ship, avoiding the problem of complex path planning among multiple targets.

[0105] S3. For each anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problem, a relative coordinate system is established using the semi-grid environment modeling method.

[0106] First, select the projection position of the launch platform far from the target ship on the horizontal plane as the origin, and establish a new three-dimensional coordinate system. The axis direction of this coordinate system points to the target ship. The establishment of this new coordinate system ensures that the planning of the entire combat area can better conform to the actual flight path and combat requirements of anti-ship missiles, converting the originally complex spatial problem into a simple geometric problem, which is convenient for subsequent path planning.

[0107] Next, according to the semi-grid modeling method, the environment is divided into multiple grid planes parallel to the y-axis. Each grid plane is parallel to the straight line where the target ship is located, and based on each launch platform, the planning areas of multiple routes are established. On these grid planes, the turning points of the anti-ship missile routes are planned, and the distribution and adjustment of these turning points are carried out according to the geographical locations of the target ship and the launch platforms to ensure that the path planning can accurately cover all possible flight trajectories.

[0108] Among them, the grid plane refers to an equidistant plane that divides the environmental space into several regions.

[0109] The purpose of this step is to reduce the computational complexity and simplify the environmental description through reasonable coordinate transformation and modeling methods. After this step is completed, all environmental information and the coordinates of the launch platform and the target ship will be in a unified relative coordinate system, thus providing a simplified and efficient environmental model for the subsequent particle swarm optimization algorithm.

[0110] For example, taking the sea level as the xoy plane, there are several launch platforms. Select the position of the projection of the launch platform that is farther from the target ship on the xoy plane as the origin, and establish a three-dimensional coordinate system with the y-axis pointing to the target ship. The cylinder is the obstacle area. Starting from the origin, a series of planes parallel to the xoz are placed equidistantly on the y-axis, and waypoint turning points are continuously arranged on the equidistant planes to form a complete route. Other routes are similar.

[0111] Such as Figure 3 shown, only the environmental information in the y-axis direction is divided into regions, and the continuously changing environmental information in the x-axis and z-axis directions is still retained. Figure 3 In it, B is the target ship, and A, C, D, etc. are anti-ship missile launch platforms, such as unmanned aerial vehicles, missile launch vehicles, ships, etc. I g is the number of waypoint turning points of the anti-ship missile route, and g is the route number, satisfying I g ≥1 and g≥1. The distance L between adjacent grid planes is max{L ming}, and L ming is the minimum flight segment distance of the anti-ship missiles of each launch platform.

[0112] Converting the coordinate parameters in the standard coordinates in step S2 to the relative coordinate system can be expressed as:

[0113]

[0114] In the formula, (xyz) T is the coordinate in the standard coordinate system, R 0 is the rotation matrix for converting the standard coordinate system to the relative coordinate system, and (x g_far y g_far z g_far ) T is the coordinate of the launch platform farthest from the target ship.

[0115] S4. In the above relative coordinate system, combining the geometric knowledge and rules of anti-ship missile route planning, use the particle swarm optimization algorithm to solve each one-sided n-to-1 route planning sub-problem. This step solves the optimal route of the anti-ship missile through an intelligent optimization algorithm, so that the path planning meets the requirements of flight safety, effectiveness and coordination.

[0116] Such as Figure 4 shown, the specific implementation steps include:

[0117] S41. Obtain the environmental parameters in the relative coordinate system, including obstacle-related information, the coordinates of each launch platform, the coordinate information of the target ship, and the flight parameters of the anti-ship missile. The flight parameters include the range, the maximum turning angle, the minimum flight segment, the maximum number of waypoint turns on the route, the ideal flight altitude range, the limit flight altitude, and the cooperative incident angle between each missile.

[0118] S42. Take the maximum minimum flight segment distance among all anti-ship missiles as the area distance L, and divide the combat area according to this distance. After dividing the area, the semi-grid environmental modeling method can determine the number of waypoint turns on all routes and their y-axis coordinates. The coding method of the particle swarm optimization algorithm can be described as:

[0119] Particle X j Contains the x-axis coordinate, y-axis coordinate, and z-axis coordinate information of the waypoint, and can be expressed as:

[0120]

[0121] In the formula, j represents the particle number, and total is the number of waypoint turns on all routes in the anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problem.

[0122] Since the waypoint turns move randomly on the grid plane, the speed in the y-axis direction is 0, and the particle speed V can be expressed as:

[0123]

[0124] Particle current optimal G j Can be expressed as:

[0125]

[0126] Global optimal G b Can be expressed as:

[0127]

[0128] S43. Initialize all particles according to the geometric knowledge of anti-ship missile route planning and the spatial geometric gradual change law. At this time, if the waypoint turns in a certain route do not conform to the spatial geometric gradual change law (that is, deviate from the reasonable flight trajectory), then randomly generate new waypoint turns within the correction window formed by the intersection of the straight line connecting the previous waypoint turn and the launch platform and the grid plane until it conforms to the spatial geometric gradual change law.

[0129] As Figure 5 shown, ship A launches an anti-ship missile to strike target ship B. During reverse route planning, waypoint turn Pi Deviate from the spatial geometric functional area, with the previous turning point P i-1 and the intersection point of the straight line where the launching ship A is located and the grid plane as the center, generate a circular area with a fixed radius r on the grid plane, as shown by the black solid line area in the figure. This area is the correction window; randomly generate a new route turning point P' in the correction window i , until it conforms to the spatial geometric gradual change law. Let P i-1 (x i-1 ,y i-1 ,z i-1 ), P i (x i ,y i ,z i ), A(x A ,y A ,z A ). The center coordinate W of the correction window can be expressed as:

[0130]

[0131] The correction window range can be expressed as:

[0132]

[0133] S44. Calculate the co - fitness function values of all primary particles, and calculate the current optimal and global optimal of the primary particles.

[0134] The co - fitness function is the standard for evaluating the path quality. The co - fitness function is set as the difference between the objective function and the penalty function. The optimization factors considered in the objective function include the total route length, the sum of co - incident angle deviations, the total number of turning points, the sum of the absolute values of the turning angles, and the mean square deviation of the absolute values of the turning angles. The objective function is expressed as:

[0135] f = a 1 α L + a 2 α d + a 3 α Num + a 4 α Z + a 5 α s ;

[0136] Among them, a 1 ~a 5 are the coefficient of each index, α L is the total route length, α d represents the sum of co - incident angle deviations, α Num is the total number of turning points, α s is the mean square deviation of the absolute values of the turning angles.

[0137] Sum of collaborative incident angle deviations α d The expression is as follows:

[0138]

[0139] In the formula, α real is the route collaborative incident angle, α syn is the set collaborative incident angle, U is the number of collaborative incident angles, G is the number of routes, and u is the subscript of the collaborative incident angle.

[0140] Each index of the objective function needs to be normalized so that the sum of a 1 to a 5 is 1, and the normalized objective function f is expressed as F.

[0141] The penalty function index considers four situations: collision with an obstacle, route intersection, unreasonable flight altitude, and the steering angle exceeding the maximum steering angle limit:

[0142] The penalty function index representing the degree of collision is expressed as:

[0143]

[0144] In the formula, β 1 is the penalty function index representing the degree of collision, which represents the sum of the counts of the number of collisions; μ gs is the mark of collision. If a collision occurs, it is marked as 1, otherwise it is marked as 0; G is the number of routes, g is the route subscript, where S g is the number of route segments of the g-th route, and s is the subscript of the route segment.

[0145] The penalty function index representing the degree of route intersection is expressed as:

[0146]

[0147] In the formula, β 2 is the index representing the degree of route intersection, γ dt is the route intersection mark. If a route intersection occurs, the mark γ dt is 1, otherwise it is marked as 0; The detection of route intersection involves permutations and combinations. D is the number of areas involved, d is the area number, T d is the number of pairwise combinations of route segments within the d-th area, and t is the number of the combination result within this area.

[0148] The penalty function index representing the degree of unreasonable flight altitude is expressed as:

[0149]

[0150] In the formula, β 3An index indicating the unreasonableness of the flight altitude; G is the number of air routes, g is the subscript of the air route, and I g is the number of turning points of the g-th air route, and i is the subscript of the turning point of this air route; h gi is used to identify the degree to which the flight altitude of a single anti-ship missile is within the ideal altitude range, h gi The calculation formula can be expressed as:

[0151]

[0152] where (h min , h max ) is the ideal flight altitude range of the anti-ship missile, H is the maximum flight altitude of the missile, and z gi is the altitude of the i-th turning point of the g-th air route.

[0153] The index indicating the degree to which the turning angle exceeds the maximum turning angle limit is expressed as:

[0154]

[0155] In the formula, β 4 is the index indicating the degree to which the turning angle exceeds the maximum turning angle limit, and is the sum of the number of all turning angles within the limit range ; if the turning angle is within the limit range, is 0, otherwise it is 1.

[0156] Therefore, the penalty function is expressed as:

[0157] v = b 1 β 1 + b 2 β 2 + b 3 β 3 + b 4 β 4 ;

[0158] In the formula, v is the penalty function, and b 1 ~b 4 are index coefficients.

[0159] Each index of the penalty function needs to be normalized so that the sum of the index coefficients b 1 ~b 4 is 1, and the normalized penalty function v is expressed as V.

[0160] The fitness function of the multi-base cross-domain anti-ship missile can be expressed as the difference between the normalized objective function F and the penalty function V, which is expressed as:

[0161] fit(X j ) = F - V;

[0162] In the formula, fit is the fitness function of the multi-base cross-domain of the anti-ship missile, X is the particle, and j is the particle number.

[0163] S45. During the particle swarm optimization process, select an appropriate initial velocity range according to the predetermined update rule to initialize the particle velocity.

[0164] S46. Update the particle according to the particle update formula. After each update of the particle, use the avoidance operator, cooperation operator, and smoothing operator for optimization processing.

[0165] The particle update formula is expressed as:

[0166]

[0167] Among them, X represents the particle position, k represents the current iteration number, V represents the particle velocity, and is calculated through the following velocity calculation formula:

[0168]

[0169] Among them, ω is the inertia weight; c 1 、c 2 are learning factors; r 1 、r 2 are random factors, randomly generated in [0, 1).

[0170] The inertia weight ω linearly decreases from 0.9 to 0.4 according to the number of iterations: ω = 0.9 - 0.5k / Gen; Gen is the number of iterations; the learning factor c 1 linearly decreases from 1.5 to 0 according to the number of iterations: c 1 = 1.5 - 1.5k / Gen; c 2 linearly increases from 2 to 0 according to the number of iterations: c 2 = 2k / Gen.

[0171] As Figure 6 shown, traverse the navigation section, and use the avoidance operator to process the navigation section where a collision occurs:

[0172] If the navigation section P i P i+1 collides with the cylindrical obstacle O w , then move the navigation section parallel to the grid plane direction until it is tangent to the side of the cylinder, but do not change its y and z axis coordinates, and adjust it to P i ′P′ i+1 , P i ′P′ i+1 The x-axis coordinates x′ i 、x′ i+1 can be expressed as:

[0173] x′ i = x′ i+1 = x w + R w ·sign;

[0174] Wherein, x w is the x-axis coordinate of the center of the bottom surface of the obstacle O w R is the radius of the obstacle, w is the number of the obstacle. When the flight path segment is located above the center O w , sign takes 1, otherwise -1. w

[0175] Traverse the detection pairs on the grid plane, and use the cooperation operator to process the flight path segments where flight path intersections occur:

[0176] Use the dynamic interaction mechanism to sequentially determine whether any two flight path segments in the area are likely to intersect. First, calculate the overlapping area of the spatial functional areas where these two flight path segments are located. This area is called the flight path intersection monitoring area. If the monitoring points on the flight path segments do not fall within the flight path intersection monitoring area, it is determined that there is no intersection, and the next pair of flight path segments in this area is continued to be checked; if there are monitoring points falling within the flight path intersection monitoring area, the cooperation operator further determines whether these two flight paths are coplanar, that is, checks whether these two flight paths are in the same plane; in three-dimensional space, if two flight paths are coplanar, it means they may intersect, if not coplanar, the possibility of intersection can be excluded; for coplanar flight path segments, the cooperation operator further determines whether the flight paths intersect through a straddle test. The straddle test determines whether two flight paths intersect in space by detecting the spatial relationship between the two end points of the flight path segment. If an intersection occurs, the cooperation operator will further adjust the flight path.

[0177] When it is determined that there is an intersection between two flight path segments, the cooperation operator will adjust the position of the flight path turning point. The adjustment method is usually to move the flight path turning point along the normal direction of the flight path to ensure that the two flight paths no longer intersect. In this way, the missile flight path is corrected to a path that will not conflict, thus ensuring the cooperative combat effect of multiple missiles.

[0178] Traverse the flight path segments and use the smoothing operator to optimize the particles:

[0179] The smoothing operator is mainly used to optimize the flight path of the anti-ship missile, ensure that the flight path is smoother, and remove unnecessary turning points to avoid sharp turns in the path.

[0180] The smoothing operator identifies redundant turning points that have no actual impact on the overall path shape of the flight path and deletes them; the smoothing operator will select some adjacent turning points, connect them into new flight path segments, and form a smoother path segment.

[0181] In some cases, the smoothing operator also adjusts the turning points to be deleted, that is, equivalently translates them onto the straight line where the new flight path segment is located.

[0182] S47. After each optimization, recalculate the co - adaptation fitness function value of the updated particles, and update the current optimal solution and the global optimal solution of each particle.

[0183] S48. As the iteration progresses, update the velocity of the particles according to the current iteration number and the preset particle update formula, and adjust the parameters ω, c 1 , c 2 , r 1 , r 2 .

[0184] S49. Repeat the operations in steps S45 to S48 until the maximum number of iterations is reached. When the maximum number of iterations is reached, output the global optimal particle as the final planning result of the anti - ship missile multi - base cross - domain unilateral n - to - 1 route planning sub - problem.

[0185] S5. Repeat steps S3 - S4 for all the anti - ship missile multi - base cross - domain unilateral n - to - 1 route planning sub - problems until the optimal planning results of all sub - problems are obtained.

[0186] S6. Re - transform the route planning results of all the anti - ship missile multi - base cross - domain unilateral n - to - 1 route planning sub - problems into the standard coordinate system to obtain the multi - to - multi anti - ship missile cooperative route planning scheme in the complex multi - base cross - domain combat scenario.

[0187] Through the above - mentioned implementation manners, the present invention can, in a complex multi - base cross - domain combat environment, make full use of the flight laws and spatial geometric characteristics of the missile itself, and use the particle swarm optimization algorithm to efficiently solve the flight path of the anti - ship missile. It not only ensures the safety of the path (avoiding collisions with obstacles and route intersections), but also improves the accuracy and overall coordination of route planning, thus significantly enhancing the cooperative combat effectiveness of the anti - ship missile.

[0188] To test and verify the performance of the anti - ship missile multi - base cross - domain route planning method based on the particle swarm optimization algorithm proposed by the present invention, three experiments of effectiveness test, superiority test, and generality test are designed:

[0189] The effectiveness test mainly verifies the effectiveness of the three operators: the avoidance operator, the cooperation operator, and the smoothing operator. The implementation test design is shown in Table 1 below:

[0190] Table 1 Effectiveness Test Design

[0191]

[0192] The validity test designed four groups of comparative experiments. Among them, the anti-ship missile multi-base cross-domain route planning algorithm based on the particle swarm optimization algorithm with all operators was the control group, and the remaining anti-ship missile multi-base cross-domain route planning algorithms based on the particle swarm optimization algorithm without the avoidance operator, without the smoothing operator, and without the cooperation operator were the experimental groups. These four algorithms were respectively experimented in the same simulation environment. The experimental scenario selected a relatively typical multi-base cross-domain route planning unilateral n-1 sub-problem. In this scenario, the anti-ship missile launch platforms included multiple spatial domains such as airspace, sea area, and land area. The environmental parameters under the standard coordinate system were set as shown in Table 2 below:

[0193] Table 2 Environmental Parameter Settings for Validity Test

[0194]

[0195] Other parameter settings were as follows: The cooperation incident angle was set as: for the shore-based missile launch vehicle - launch ship, it was π / 3; for the shore-based missile launch vehicle - unmanned aerial vehicle, it was π / 3; for the launch ship - unmanned aerial vehicle, it was 2π / 3. The maximum turning angle was π / 4, the distance L between grid planes was 15.0, the safety distance D between routes save was 0.5, the correction window radius r was set to 0.5, the ideal flight height range (h min , h max ) was (0.2, 2.0), the limit flight height H of the missile was 50.0, with the unit of km. The objective function index coefficients a 1 ~a 5 were respectively set as 0.3, 0.3, 0.2, 0.1, 0.1, and the penalty function index coefficients b 1 ~b 4 were all set as 0.25, the population size popsize was set as 25, and the maximum number of iterations Gen was set as 50.

[0196] Both the experimental groups and the control group were tested 20 times repeatedly. The optimal experimental results obtained are shown in Figure 7 , and the detailed test results are shown in Table 3 below:

[0197] Table 3 Detailed Validity Test Results

[0198]

[0199] From the results, it can be obtained that: when comparing the algorithm without the avoidance operator with the algorithm with all operators, its penalty function index β 1 is higher, indicating that the avoidance operator can effectively avoid obstacles and ensure the validity of the route; when comparing the algorithm without the smoothing operator with the algorithm with all operators, the total number of turning points α Num is higher, indicating that the smoothing operator can effectively optimize the route and reduce unnecessary turning points of the route; when comparing the algorithm without the cooperation operator with the algorithm with all operators, its penalty function index β 2It is relatively high, indicating that the collaborative operator can solve the route intersection problem encountered in collaborative route planning. The avoidance operator, smoothing operator, and collaborative operator all meet their expected performance. The experimental results of the full-operator algorithm have the highest collaborative fitness function, indicating that the algorithm can not only meet the requirements of avoiding obstacles and smoothing the route for a single route, but also well meet the requirements of multi-base cross-domain route planning.

[0200] In the superiority test, three classic algorithms applicable to three-dimensional route planning were selected, namely: A* algorithm, genetic algorithm, particle swarm optimization algorithm, and the anti-ship missile multi-base cross-domain route planning algorithm based on particle swarm optimization algorithm proposed in this paper were used for route planning in the same simulation environment. The relevant parameters of the launch platform and the target platform are kept consistent with those in the effectiveness test. The relevant parameter settings of the obstacles in the base coordinate system are shown in Table 4 below:

[0201] Table 4 Superiority test environment parameter settings

[0202]

[0203] The distance L between the grid planes is 20.0, with the unit of km. The settings of the remaining other parameters are kept consistent with those in the effectiveness verification experiment part.

[0204] Since the traditional algorithm can only plan the route of one missile in each operation, while the anti-ship missile multi-base cross-domain route planning algorithm based on particle swarm optimization algorithm proposed in the present invention can plan the routes of multiple missiles in one operation. The processing here is: use the traditional algorithm multiple times to plan all the routes, and then use the collaborative fitness function proposed in this paper to evaluate all the routes. The step size of the A* algorithm is set to 40, and the number of route turning points of a single route in the GA and PSO algorithms is randomly generated between 2 and 9. The experiment is repeated 50 times, and the optimal test results obtained by different algorithms are shown in Figure 8 , details are shown in Table 5 below:

[0205] Table 5 Superiority test result details

[0206]

[0207]

[0208] Table 5 has two types of details: comprehensive index details and optimal route result details. Among them, the former is mainly used to evaluate the overall effect of the 50 repeated experiment results, and the latter is mainly used to analyze the optimal route results. Generally speaking, the average collaborative fitness function value of the anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm is at least 40% higher than that of other algorithms in comparison, and the variance of the collaborative fitness function value is small, indicating relatively high stability. The average penalty function index β 1 of the A*, GA, and PSO algorithms, and the average penalty function index β 2A non-zero value indicates that in repeated trials, collisions with obstacles and route intersections still occur for these three types of algorithms. However, the multi-base cross-domain route planning method for anti-ship missiles based on the particle swarm optimization algorithm effectively avoids these situations.

[0209] From the optimal route results, by comparing the collaborative fitness function values, it shows that the multi-base cross-domain route planning method for anti-ship missiles based on the particle swarm optimization algorithm has significant superiority in solving the multi-base cross-domain route planning problem for anti-ship missiles. Then, by comparing each index of the collaborative fitness function, including the total route length α L 、the deviation of the collaborative incident angle and α d 、the total number of turning points α Num 、the penalty function index β 1 、the penalty function index β 2 、the penalty function index β 3 , they are all smaller in the optimal experimental results of the multi-base cross-domain route planning method for anti-ship missiles based on the particle swarm optimization algorithm. It can be shown that the multi-base cross-domain route planning method for anti-ship missiles based on the particle swarm optimization algorithm has significant superiority mainly in preventing route intersections and controlling the collaborative incident angle, and also has certain superiority in reducing the voyage, smoothing the route, and avoiding obstacles.

[0210] From the experimental results, it can be concluded that the multi-base cross-domain route planning method for anti-ship missiles based on the particle swarm optimization algorithm is more suitable for multi-base cross-domain combat scenarios.

[0211] In the generality test, simulation combat scenarios of four-to-one, six-to-two, and seven-to-three were designed, and the proposed method was used for multi-base cross-domain route planning of anti-ship missiles. As mentioned before, complex multi-base cross-domain combat scenarios can be divided into multiple multi-base cross-domain route planning sub-problems according to the actual situation, and then route planning is carried out for each sub-problem respectively. Therefore, the four-to-one, six-to-two, and seven-to-three combat scenarios can all be split into multiple multi-base cross-domain route planning sub-problems for solution.

[0212] The environmental parameter settings under the base coordinates of each scenario are as shown in Table 6 below:

[0213] Table 6 Environmental parameter settings under the base coordinates of each scenario in the generality test

[0214]

[0215] In the four-to-one combat scenario, it can be divided into two multi-base cross-domain route planning sub-problems: the sub-problem with the shore-based missile launch vehicle 1 and the shore-based missile launch vehicle 2 as the launch platforms, and the sub-problem with the unmanned aerial vehicle 1 and the unmanned aerial vehicle 2 as the launch platforms. Therefore, the collaborative incident angle is set as: π / 2 for shore-based missile launch vehicle 1 - shore-based missile launch vehicle 2, and π / 2 for unmanned aerial vehicle 1 - unmanned aerial vehicle 2. The distance L between the grid planes is 15.0, and the safety distance D between the routessave is 0.5, the correction window radius r is set to 0.5, and the ideal flight height range (h min , h max ) is (0.2, 2.0), the maximum flight height H of the missile is 50.0, with the unit of km. The objective function index coefficients a 1 ~a 5 are respectively set to 0.3, 0.3, 0.2, 0.1, 0.1, and the penalty function index coefficients b 1 ~b 4 are all set to 0.25, the population size popsize is set to 25, and the maximum number of iterations Gen is set to 50. The planning results are as Figure 9 shown.

[0216] In the six - against - two combat scenario, it can be divided into two multi - base cross - domain unilateral n - against - 1 route planning sub - problems: the sub - problem with the shore - based missile launch vehicle 3, shore - based missile launch vehicle 4, and UAV 3 as the launch platforms, and the sub - problem with UAV 4, UAV 5, and launch ship 1 as the launch platforms. Therefore, the cooperative incident angles are set as: shore - based missile launch vehicle 3 - shore - based missile launch vehicle 4, shore - based missile launch vehicle 3 - UAV 3, UAV 4 - UAV 5, UAV 4 - launch ship 1 are all π / 3. Shore - based missile launch vehicle 4 - UAV 3, UAV 5 - launch ship 1 are both 2π / 3. The settings of the remaining other parameters are the same as those in the four - against - one scenario. The planning results are as Figure 10 shown.

[0217] In the seven - against - three combat scenario, it can be divided into three multi - base cross - domain unilateral n - against - 1 route planning sub - problems: the sub - problem with the shore - based missile launch vehicle 5, UAV 6, and shore - based missile launch vehicle 6 as the launch platforms, the sub - problem with launch ship 2 and UAV 7 as the launch platforms, and the sub - problem with launch ship 3 and UAV 8 as the launch platforms. Therefore, the cooperative incident angles are set as: shore - based missile launch vehicle 5 - shore - based missile launch vehicle 6, shore - based missile launch vehicle 5 - UAV 6, launch ship 2 - UAV 7, launch ship 3 - UAV 8 are all π / 3, and UAV 6 - shore - based missile launch vehicle 6 is 2π / 3. The settings of other parameters are the same as those in the four - against - one scenario. The planning results are as Figure 11 shown.

[0218] The anti - ship missile multi - base cross - domain route planning method based on the particle swarm optimization algorithm can better solve the anti - ship missile multi - base cross - domain route planning problems of four - against - one, six - against - two, and seven - against - three, and has good generality.

[0219] In summary, the present invention proposes an anti - ship missile multi - base cross - domain route planning method based on the particle swarm optimization algorithm, including:

[0220] S1. Obtain the environmental description parameters in the standard coordinate system and initialize and define the parameters.

[0221] S2. Divide the many-to-many anti-ship missile route planning problem in the complex multi-base cross-domain combat scenario into several anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems.

[0222] S3. For each anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problem, adopt a semi-grid environmental modeling method to establish a relative coordinate system, and convert the coordinate parameters in the standard coordinate system to the relative coordinate system.

[0223] S4. Combine the geometric knowledge and rules of anti-ship missile route planning, and solve the anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problem based on the particle swarm optimization algorithm.

[0224] S5. Repeat steps S3 - S4 for all the divided anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems until the optimal planning results of all sub-problems are obtained.

[0225] S6. Re-convert the route planning results of all the anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems to the standard coordinate system to obtain the multi-to-many anti-ship missile cooperative route planning scheme in the complex multi-base cross-domain combat scenario.

[0226] In the present invention, terms such as "installation", "connection", "linkage", "fixation" should be understood in a broad sense. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; "linkage" can be a direct linkage or an indirect linkage through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0227] The shapes of the various components in the drawings are schematic, and there is no exclusion of a certain difference from their actual shapes. The drawings are only used to illustrate the principle of the present invention and are not intended to limit the present invention.

[0228] Although the present invention has been disclosed in detail with reference to the drawings, it should be understood that these descriptions are merely exemplary and are not used to limit the application of the present invention. The protection scope of the present invention is defined by the appended claims and may include various modifications, adaptations, and equivalent solutions made to the invention without departing from the protection scope and spirit of the present invention.

Claims

1. A multi-base cross-domain route planning method for anti-ship missiles based on particle swarm optimization algorithm, characterized in that: The method includes: S1. Obtain the environment description parameters in the standard coordinate system and initialize and define the parameters; S2. Divide the multi-to-multi anti-ship missile route planning problem in a complex multi-base cross-domain combat scenario into several anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems; S3. For each anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problem, a relative coordinate system is established by using a semi-grid environment modeling method, and the coordinate parameters in the standard coordinate system are converted to the relative coordinate system; S4. Combining the geometric knowledge and rules of anti-ship missile route planning, the particle swarm optimization algorithm is used to solve the multi-base cross-domain unilateral n-to-1 route planning sub-problem of anti-ship missile; S5, repeating steps S3-S4 for all the divided anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems until the optimal planning results of all sub-problems are obtained; S6. Reconvert the routing results of all anti-ship missile multi-base cross-domain unilateral n-to-1 routing sub-problems into the standard coordinate system to obtain a multi-to-multi anti-ship missile coordinated routing plan in a complex multi-base cross-domain combat scenario.

2. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm according to claim 1 is characterized in that: The environmental description parameters in step S1 include the location information of obstacles in the sea area, the coordinate information of each anti-ship missile launch platform and the target ship, and the basic combat parameters of each missile, and the basic combat parameters include the range, the maximum turning angle, the minimum route segment, the maximum number of route turning points, the ideal flight altitude range, the extreme flight altitude and the coordinated incidence angle between each missile; The obstacle is modeled as a cylindrical model, modeling O w Described as: O w =(x w ,y w ,z w ,R w ,H w ); In the formula, x w ,y w 、z w , R w They represent the x, y, z axis coordinates and radius of the center of the cylinder base circle in the standard coordinate system, respectively. w represents the height of the cylinder, and w is the number of the obstacle.

3. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 1 is characterized in that: The step S2 specifically includes: The azimuth angle and the uniqueness of the target ship are used as the basis for division. The azimuth relationship between the area where each anti-ship missile launch platform is located and the target ship determines the division of the sub-problem. All the divided anti-ship missile multi-base cross-domain unilateral n-to-1 route planning sub-problems are required to meet the following two conditions: Same-side launch: In each unilateral n-to-1 routing subproblem, all launch platforms must be located on the same side of the target ship; Unique target ship: In each sub-problem, the target ship targeted by all launch platforms must be the same and unique.

4. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 1 is characterized in that: The step S3 specifically includes: The projection position of the launch platform far from the target ship on the horizontal plane is selected as the origin, and a new three-dimensional coordinate system is established, the axis direction of which points to the target ship; Next, according to the semi-grid modeling method, the environment is divided into multiple grid planes parallel to the y-axis. Each grid plane is parallel to the straight line where the target ship is located, and multiple route planning areas are established based on each launch platform. On these grid planes, the route turning points of the anti-ship missiles are planned, and these route turning points are distributed and adjusted according to the geographical locations of the target ships and launch platforms to ensure that the path planning can accurately cover all possible flight trajectories.

5. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 1, characterized in that: Step S3 converts the coordinate parameters under the standard coordinates in step S2 to the relative coordinate system, which is expressed as: In the formula, (xyz) T is the coordinate in the standard coordinate system, R0 is the rotation matrix from the standard coordinate system to the relative coordinate system, (x g_far y g_far z g_far ) T are the coordinates of the launch platform farthest from the target ship.

6. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 1 is characterized in that: The step S4 specifically includes: S41, obtaining environmental parameters in the relative coordinate system, including obstacle-related information, coordinates of each launch platform, coordinate information of the target ship, and flight parameters of the anti-ship missile, the flight parameters including range, maximum turning angle, minimum route segment, maximum number of route turning points, ideal flight altitude range, extreme flight altitude, and coordinated incidence angle between missiles; S42, taking the largest minimum route segment distance of each anti-ship missile as the area distance L, dividing the combat area according to the distance, and after dividing the areas, using the semi-grid environment modeling method to determine the number of route turning points of all routes and their y-axis coordinates; S43, all particles are initialized according to the geometric knowledge of anti-ship missile route planning and the spatial geometric gradient law. At this time, if the route turning point in a certain route does not conform to the spatial geometric gradient law, a new route turning point is randomly generated in the correction window formed by the intersection of the previous turning point and the straight line where the launch platform is located and the grid plane as the center, until it conforms to the spatial geometric gradient law; S44, calculating the cooperative fitness function values ​​of all first-generation particles, and calculating the current optimal and global optimal of the first-generation particles; S45, during the particle swarm optimization process, selecting a suitable initial velocity range to initialize the particle velocity according to a predetermined updating rule; S46. Update particles according to the particle update formula. After each particle update, use the avoidance operator, the coordination operator and the smoothing operator for optimization. S47, after each optimization, recalculate the collaborative fitness function value of the updated particles, and update the current optimal solution and the global optimal solution of each particle; S48, as the iteration proceeds, the particle speed is updated and the parameters thereof are adjusted according to the current number of iterations and a preset particle update formula; S49, repeating the operations of steps S45 to S48 until the maximum number of iterations is reached. When the maximum number of iterations is reached, outputting the global optimal particle as the final planning result of the multi-base cross-domain unilateral n-to-1 route planning sub-problem of the anti-ship missile.

7. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 6 is characterized in that: The step S43 uses the correction window to generate a new route turning point, and the generation process includes: Ship A launches an anti-ship missile to attack target ship B. When planning the reverse route, the route turning point P i Deviating from the spatial geometric functional area, the previous turning point P i-1 The intersection of the line where the launching ship A is located and the grid plane is taken as the center of the circle, and a circular area with a fixed radius r is generated on the grid plane, as shown in the area marked by the black solid line in the figure. This area is the correction window; a new route turning point P is randomly generated in the correction window. i ′, until it conforms to the law of spatial geometric gradual change, let P i-1 (x i-1 ,y i-1 ,z i-1 ), P i (x i ,y i ,z i ), A(x A ,y A ,z A ), the center coordinate W of the correction window can be expressed as: The correction window range can be expressed as:

8. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 6, characterized in that: The collaborative fitness function of step S44 is set to the difference between the objective function and the penalty function; The objective function is expressed as: f=a1a L +a2a d +a3a Num +a4a Z +a5a s ; Among them, a1~a5 are the coefficients of each indicator, α L is the total route length, α d represents the sum of the cooperative incident angle deviations, α Num is the total number of turning points, α s is the mean square error of the absolute value of the steering angle; The sum of the deviations of the incident angles α d The expression is: In the formula, α real is the route cooperative incident angle, α syn is the set cooperative incident angle, U is the number of cooperative incident angles, G is the number of routes, u is the subscript of the cooperative incidence angle; Each index of the objective function needs to be normalized so that the sum of a1 to a5 is 1. The normalized objective function f is expressed as F; The penalty function is expressed as: v=b1β1+b2β2+b3β3+b4β4; Where v is the penalty function, b1~b4 are the index coefficients, β1~β4 are the penalty function indexes indicating the degree of collision, the penalty function index indicating the degree of route intersection, the penalty function index indicating the degree of unreasonable flight altitude, and the penalty function index indicating the degree of steering angle exceeding the maximum steering angle limit; Each index of the penalty function needs to be normalized so that the sum of the index coefficients b1 to b4 is 1. The normalized penalty function v is expressed as V; The fitness function of the multi-base cross-domain anti-ship missile can be expressed as the difference between the normalized objective function F and the penalty function V, expressed as: fit(X j )=F-V; Where fit is the fitness function of the multi-base cross-domain anti-ship missile, X is the particle, and j is the particle number.

9. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 8, characterized in that: The penalty function index indicating the degree of collision is expressed as: Where β1 is the penalty function indicator of the collision degree, which represents the count and number of collisions; μ gs is the collision mark, if a collision occurs, it is marked as 1, otherwise it is marked as 0; G is the number of routes, g is the route subscript, where S g is the number of route segments of the g-th route, and s is the route segment subscript; The penalty function index indicating the degree of route intersection is expressed as: In the formula, β2 is an index indicating the degree of route intersection, γ dt If a route crossing occurs, mark γ dt is 1, otherwise it is marked as 0; the detection of route intersection involves permutations and combinations, D is the number of areas involved, d is the number of areas, T d is the number of pairwise combinations of route segments in the dth area, and t is the number of the combination results in the area; The penalty function index indicating the unreasonable degree of flight altitude is expressed as: In the formula, β3 represents the index of unreasonable flight altitude; G is the number of routes, g is the route subscript, and I g is the number of route turning points contained in the g-th route, i is the subscript of the route turning point of the route; h gi Used to indicate the degree to which a single anti-ship missile's flight altitude is within the ideal altitude range, h gi The calculation formula can be expressed as: Among them, (h min ,h max ) is the ideal flight altitude range of the anti-ship missile, H is the maximum flight altitude of the missile, z gi is the height of the i-th route turning point of the g-th route; The indicator indicating the degree to which the steering angle exceeds the maximum steering angle limit is expressed as: Where β4 is an indicator of the degree to which the steering angle exceeds the maximum steering angle limit, and is a sign of whether all steering angles are within the limit. If the steering angle is within the limit, is 0, otherwise it is 1.

10. The anti-ship missile multi-base cross-domain route planning method based on particle swarm optimization algorithm as claimed in claim 6, characterized in that: The particle update formula in step S46 is expressed as: Among them, X represents the particle position, k represents the current iteration number, and V represents the particle speed, which is calculated by the following speed calculation formula: Among them, ω is the inertia weight; c1 and c2 are learning factors; r1 and r2 are random factors, which are randomly generated in [0,1).

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