Multi-constraint route planning method for searching air target by multi-radar platform

Abstract

The invention discloses a multi-constraint flight path planning method for searching an air target by a plurality of radar platforms, which comprises the following steps of: firstly, establishing a cost function by combining constraint conditions of the radar platforms and considering threats suffered by the radar platforms in a motion airspace and height threats of a digital elevation model; a multi-radar platform track planning problem is converted into an optimization problem for ensuring feasible and safe operation of a radar platform, finally, a PSO algorithm is utilized to systematically search corresponding relations between particle positions and turning angles, climbing angles and diving angles of the radar platform, and a configuration space of the multi-radar platform is effectively searched. And finding an optimal track which minimizes the cost function. According to the method, the track planning capability of a multi-radar platform is improved, the method is suitable for track planning in a dangerous and complex airspace, and effective search of an air target is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-radar platform track planning, and in particular relates to a multi-constraint track planning method for multi-radar platform aerial target search. Background Art

[0002] Radar platforms play a key role in target reconnaissance, strike, and rescue, providing important functions of target positioning and monitoring. With the introduction of multiple radar platforms, their collaborative search capabilities have been significantly enhanced. The trajectory planning design of multiple radar platforms plays a key role in their applications. By analyzing the constraints of the radar platform itself and the threats encountered in the trajectory, the target benefit function is established, a multi-constrained optimization problem is formed, the collaborative search route is planned, the radar platform trajectory is adjusted, and the trajectory planning of multiple radar platforms is completed. For the trajectory planning problem of a single platform, the literature "L. Ma, Y. Tian, ​​Y. Zhang and P. Chu, "Trajectory Optimization of Aircraft for A Continuous Descent Continuous Procedure," 2020 Chinese Automation Congress (CAC), Shanghai, China, 2020, pp. 2063-2067" focuses on the problem of descending aircraft platforms and constructs performance indicators related to minimum fuel consumption and delay time. In the document "Y. Yang, Y. Nan and H. Chen, "Trajectory optimization in stochastic environment based on original natural computation," 2018 Chinese Control And Decision Conference (CCDC), Shenyang, China, 2018, pp. 6027-6031", original natural computation is used to solve the trajectory problem for an aircraft platform in a random environment.

[0003] In summary, although the above-mentioned trajectory planning methods can optimize the trajectory to a certain extent, none of the above methods considers the terrain threat constraints and potential threats in the airspace. An effective trajectory planning algorithm is crucial to the operation of a multi-radar platform. The trajectory planning algorithm not only needs to consider the constraints of the radar platform itself, but also the terrain threats. In addition, it must be able to cope with potential threats in the airspace, adjust the trajectory to avoid threats and ensure safe arrival at the target point. By continuously optimizing and improving the trajectory planning algorithm, the multi-radar platform can be made more flexible and better adapt to various complex combat environments and mission requirements, thereby providing more reliable support and guarantee for specific operations. Summary of the invention

[0004] To solve the above technical problems, the present invention provides a multi-constraint trajectory planning method for searching aerial targets by multiple radar platforms, which improves the trajectory planning capability of multiple radar platforms, is suitable for planning trajectories in dangerous and complex airspaces, and realizes effective search for aerial targets.

[0005] The technical solution adopted by the present invention is: a multi-constraint trajectory planning method for multi-radar platform air target search, the specific steps are as follows:

[0006] S1, import the digital elevation model DEM and obtain the starting point location information and target location information of the track;

[0007] First, import the digital elevation model DEM, that is, import the DEM file by specifying the path of the DEM file and using the read function in the simulation software; and give the starting position information of the track (x start ,y start ,z start ) and target location information (x end ,y end ,z end ).

[0008] S2. Model the threat areas in the airspace such as radars in the flight track of the radar platform and establish the denied airspace;

[0009] The threat area in the airspace existing in the flight track of the radar platform is modeled as denied airspace, and the denied airspace is modeled as a cone shape.

[0010] S3, according to the location information obtained in step S1 and the DEM model constraints, the radar platform constraints and the airspace threat constraints, establish the multi-radar platform trajectory planning optimization problem, and assign different weights to different constraints according to the specific tasks;

[0011] Among them, the radar platform's own constraints include: track length constraints and dynamic constraints.

[0012] S4, solving the optimization problem of step S3 by particle swarm PSO algorithm, and outputting the optimal track;

[0013] First, the PSO algorithm is initialized and the initialization parameters are set, including: the number of particles used in the search space, the position and velocity of each particle, the inertia weight, the acceleration coefficient and the number of iterations.

[0014] Then, according to the established trajectory planning optimization problem, the starting position information and the target position information, the PSO algorithm is used to update the particle position and velocity, search the multi-radar platform configuration space, and determine whether the termination condition is met, that is, whether the maximum number of iterations is reached. If the termination condition is met, the optimal trajectory that minimizes the cost function is output; if the termination condition is not met, the solution is repeatedly updated.

[0015] Furthermore, the step S3 is specifically as follows:

[0016] First, the DEM model constraints, radar platform constraints, and airspace threat constraints are analyzed. The radar platform constraints include: track length constraints and dynamic constraints, as follows:

[0017] (1) Track length constraint;

[0018] Considering the fuel consumption of the radar platform, shortening the flight track of the radar platform, and taking the Euclidean distance between two nodes as the length of each segment, the track length constraint C1(X i ) is expressed as follows:

[0019]

[0020] Among them, X i Represents the decision variable, that is, N track points P ij Each track point represents the position and track information of the radar platform; ij =(x ij ,y ij ,z ij ) represents the track node in the search map, i represents the i-th particle in the search space, that is, the dimension of the search space, the upper limit number of particles is M, and j represents the j-th track node among N track points.

[0021] (2) DEM model constraints;

[0022] Considering the flight altitude of the radar platform and the terrain height, the flight altitude of the radar platform should satisfy the following inequality:

[0023]

[0024] Among them, C2(X i ) represents the height constraint relative to DEM in modeling, H ij Indicates the height loss relative to the DEM at the current j-th track node, h ij Indicates that the radar platform is at (x ij ,y ij ) at a height of h DEM (i,j) means in (x ij ,y ij) is the height of the DEM at .

[0025] (3) Dynamic constraints;

[0026] Considering that the radar platform needs to satisfy dynamic constraints in actual flight, the dynamic constraints of the radar platform should satisfy the following inequality:

[0027]

[0028] Among them, C3(X i ) represents the dynamic constraints, namely the pitch climb angle and horizontal turn angle costs, φ ij represents the horizontal steering angle between the current position and the previous position, ψ ij Indicates the climbing angle, φ max represents the maximum horizontal steering angle, ψ max represents the maximum pitch climb angle, α and β represent the penalty coefficients of the horizontal steering angle and the pitch climb angle respectively.

[0029] (4) airspace threat constraints;

[0030] Considering the radar threat area of ​​the radar platform in the flight environment, the radar platform should satisfy the following inequality:

[0031]

[0032] Among them, C4(X i ) represents the airspace threat constraint, i.e., the search threat of the adversary’s radar. ij represents the center coordinates of the projection surface of the threat airspace, that is, the center coordinates of the denied airspace, R ij Indicates the radius of the threat airspace at the current location, R safe Indicates the safe distance, that is, the distance that needs to be maintained between the radar platform and the denied airspace.

[0033] Based on the above constraints, the multi-radar platform trajectory planning optimization problem is established, and the expression is as follows:

[0034]

[0035] Among them, C k (·) represents the kth cost function; b k represents the kth cost function C k (·) weight coefficient, C(X i ) represents the total cost function, and different weights are assigned to different constraints according to the actual situation.

[0036] Furthermore, the step S4 is specifically as follows:

[0037] First, the PSO algorithm is initialized and the initialization parameters are set, that is, the number of particles M used in the search space, the position and velocity of each particle, the inertia weight w, the acceleration coefficient and the maximum number of iterations K.

[0038] Among them, each particle represents a potential solution, and the particle searches for the optimal solution through iteration in the multi-dimensional search space; the acceleration coefficients include: local learning coefficient η1 and global learning coefficient η2.

[0039] Then, according to the multi-radar platform trajectory planning optimization problem established in step S3, the starting position information and target position information of the trajectory obtained in step S1 are updated through the PSO algorithm, and the position and speed of the particles are continuously adjusted to search the multi-radar platform configuration space and find the trajectory that minimizes the cost function, as follows:

[0040] Based on the initialization of the PSO algorithm, the position and velocity of each particle are updated. The update model expression of the particle swarm algorithm is as follows:

[0041]

[0042] Among them, Q i =(x i1 ,x i2 ,...,x iN ) represents the position vector of the ith particle, x iN represents the position of the i-th particle at dimension N, V i =(v i1 ,v i2 ,...,v iN ) represents the velocity vector of the ith particle, v iN represents the speed of the ith particle at dimension N, where N represents the dimension of the search space, i.e., the number of track nodes in track planning; L i =(l i1 ,l i2 ,...,l iN ) represents the local optimal position, l iN represents the local optimal position of the i-th particle in dimension N, L g =(L g1 ,L g2 ,...,L gN ) represents the global optimal position, L gN represents the global optimal position of the i-th particle in dimension N; k represents the k-th iteration, w k represents the inertia weight coefficient, M represents the number of particles; r 1j and r 2j Represents a random number in the range [0,1].

[0043] After updating the particle position and velocity, evaluate the function fitness value of each particle, and update the global optimal position of the group. Repeat the updating steps to determine whether the maximum number of iterations is met. If the maximum number of iterations is reached, stop the iteration, update the position and velocity of the global best particle, and output the optimal trajectory. Otherwise, re-update the particle position and velocity until the iteration is completed.

[0044] The optimal trajectory expression is as follows:

[0045] E=(x i1 ,y i1 ,z i1 ,x i2 ,y i2 ,z i2 ,...,x iN ,y iN ,z iN ) (8)

[0046] Where E represents a track consisting of N nodes.

[0047] Beneficial effects of the present invention: The method of the present invention first combines the constraints of the radar platform itself, and considers the threats in the airspace where the radar platform moves and the height threat of the digital elevation model, establishes a cost function, and transforms the multi-radar platform trajectory planning problem into an optimization problem to ensure the feasibility and safe operation of the radar platform. Finally, the PSO algorithm is used to systematically search for the correspondence between the particle position and the turning angle, climbing angle and dive angle of the radar platform, effectively search the configuration space of the multi-radar platform, and find the optimal trajectory that minimizes the cost function. The method of the present invention introduces the digital elevation model height constraint and considers the constraints of the radar platform itself, as well as the denial airspace threat from the enemy search radar that may be faced during the search for air targets. Taking the above factors into consideration, the multi-radar platform configuration planning problem is transformed into a multi-constraint optimization problem to ensure the feasibility and safe operation of the radar platform, and then the PSO algorithm is used to effectively avoid the threat area, obtain the multi-radar platform trajectory planning result, improve the trajectory planning capability of the multi-radar platform, adapt to planning trajectories in dangerous and complex airspace, and realize effective search for air targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The present invention is a flow chart of a multi-constraint trajectory planning method for multi-radar platform aerial target search.

[0049] Figure 2 It is the digital elevation model, starting point location information, target location information and denied airspace simulation in the embodiment of the present invention.

[0050] Figure 3 The flowchart of the particle swarm optimization algorithm in the embodiment of the present invention is shown in FIG.

[0051] Figure 4 1 is a diagram showing simulation results of two radar platforms in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention adopts simulation experiments to demonstrate the effectiveness of the proposed method, and all steps and conclusions of the present invention are verified on the Matlab2022a simulation platform. The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0053] like Figure 1 As shown, a flow chart of a multi-constraint trajectory planning method for multi-radar platform air target search of the present invention, the specific steps are as follows:

[0054] S1, import the digital elevation model DEM and obtain the starting point location information and target location information of the track;

[0055] like Figure 2 As shown in the figure, in order to be more suitable for practical applications, the digital elevation model is selected as the trajectory planning model, the radar platform is approximated as a particle model, and the position coordinates of the radar platform in three-dimensional space are represented by (x, y, z).

[0056] First, import the digital elevation model DEM, that is, specify the path of the DEM file and use the imread function in MATLAB to read it; and give the starting position information of the track (x start ,y start ,z start ) and target location information (x end ,y end ,z end ).

[0057] S2. Model the threat areas in the airspace such as radars in the flight track of the radar platform and establish the denied airspace;

[0058] The threat area in the airspace existing in the flight track of the radar platform is modeled as a denied airspace, and the denied airspace is modeled as a cone shape (the radar threat existing in the airspace is abstracted as a conical search area). The cross section can be regarded as a circle with different radii. The threat area is as follows: Figure 2 As shown, Figure 2 The purple cone area is the denied airspace.

[0059] S3, according to the location information obtained in step S1 and the DEM model constraints, the radar platform constraints and the airspace threat constraints, establish the multi-radar platform trajectory planning optimization problem, and assign different weights to different constraints according to the specific tasks;

[0060] Among them, the DEM model constraints constrain the flight altitude of the radar platform, which can be converted into altitude constraints in multi-constraint optimization problems to ensure that the radar track is within a safe altitude range; the radar platform's own constraints include track length constraints and dynamic constraints, which can be converted into path length constraints and pitch and climb angle constraints that the radar needs to meet in multi-constraint optimization problems; the airspace threat constraints take into account the threat of the adversary's radar search and can be converted into constraints for avoiding the threat area in a multi-constraint optimization problem.

[0061] S4, solving the optimization problem of step S3 by particle swarm PSO algorithm, and outputting the optimal track;

[0062] First, the PSO algorithm is initialized and the initialization parameters are set, including: the number of particles used in the search space, the position and velocity of each particle, the inertia weight, the acceleration coefficient and the number of iterations.

[0063] Then, according to the established trajectory planning optimization problem, the starting position information and the target position information, the PSO algorithm is used to update the particle position and velocity, search the multi-radar platform configuration space, and determine whether the termination condition is met, that is, whether the maximum number of iterations is reached. If the termination condition is met, the optimal trajectory that minimizes the cost function is output; if the termination condition is not met, the solution is repeatedly updated.

[0064] In this embodiment, step S3 is specifically as follows:

[0065] First, the DEM model constraints, radar platform constraints, and airspace threat constraints are analyzed. The radar platform constraints include: track length constraints and dynamic constraints, as follows:

[0066] (1) Track length constraint;

[0067] Considering the fuel consumption of the radar platform, the radar platform track route should be as short as possible to reduce fuel consumption. Shortening the flight track of the radar platform can not only reduce fuel costs, but also improve the efficiency of track planning. Taking the Euclidean distance between two nodes as the length of each segment, the track length constraint C1(X i ) is expressed as follows:

[0068]

[0069] Among them, X i Represents the decision variable, that is, N track points P ij Each track point represents the position and track information of the radar platform; ij =(x ij ,y ij ,z ij) represents the track node in the search map, i represents the i-th particle in the search space, that is, the dimension of the search space, the upper limit number of particles is M, and j represents the j-th track node among N track points.

[0070] (2) DEM model constraints;

[0071] Considering the flight altitude and terrain height of the radar platform, in order to better adapt to the actual situation, reduce accidents caused by touching the ground, ensure the accuracy and reliability of the modeling, and more accurately simulate the terrain and ground features, the flight altitude of the radar platform should satisfy the following inequality:

[0072]

[0073] Among them, C2(X i ) represents the height constraint relative to DEM in modeling, H ij Indicates the height loss relative to the DEM at the current j-th track node, h ij Indicates that the radar platform is at (x ij ,y ij ) at a height of h DEM (i,j) means in (x ij ,y ij ) is the height of the DEM at .

[0074] (3) Dynamic constraints;

[0075] Considering that the radar platform needs to meet dynamic constraints in actual flight, that is, it needs to ensure that its pitch climbing angle and horizontal turning angle are limited to a certain range, so as to optimize the performance and safety of the platform, the dynamic constraints of the radar platform should satisfy the following inequality:

[0076]

[0077] Among them, C3(X i ) represents the dynamic constraints, namely the pitch climb angle and horizontal turn angle costs, φ ij represents the horizontal steering angle between the current position and the previous position, ψ ij Indicates the climbing angle, φ max represents the maximum horizontal steering angle, ψ max represents the maximum pitch climb angle, α and β represent the penalty coefficients of the horizontal steering angle and the pitch climb angle respectively. By limiting the climb angle, horizontal steering angle and pitch climb angle, and reasonably adjusting the horizontal steering angle and the pitch climb angle, it can ensure that the radar platform moves within a safe range during the air search track planning process, thereby improving stability.

[0078] (4) airspace threat constraints;

[0079] Considering the radar threat area of ​​the radar platform in the flight environment, the radar platform should satisfy the following inequality:

[0080]

[0081] Among them, C4(X i ) represents the airspace threat constraint, that is, the search threat of the adversary radar. By establishing constraints on airspace threats, the radar platform can assess airspace risks and improve the safety of trajectory planning tasks. ij It represents the center coordinates of the projection surface of the threat airspace, that is, the center coordinates of the denied airspace, which is used to determine the main source and concentration area of ​​the threat. ij Indicates the radius of the threat airspace at the current location. Through this radius, the radar platform can determine the proximity of potential threats and adjust the track. safe It represents the safe distance, that is, the distance that needs to be maintained between the radar platform and the denied airspace to avoid interference or denial. Maintaining an appropriate safe distance can reduce interference with the opponent's radar, ensure the normal operation of the radar platform, and protect the radar from attacks by the opponent.

[0082] Based on the above constraints, the multi-radar platform trajectory planning optimization problem is established, and the expression is as follows:

[0083]

[0084] Among them, C k (·) represents the kth cost function, which is used to evaluate the performance of trajectory planning schemes under different constraints; b k represents the kth cost function C k The weight coefficient of (·) is used to adjust the important coefficient of each cost function in the total cost function; C(X i ) represents the total cost function. Different weights are assigned to different constraints according to the actual situation. By adjusting the weight coefficients, the influence of different constraints can be balanced to obtain the optimal trajectory planning scheme. In this embodiment, the weight coefficients of each cost function are b1=5, b2=10, b3=1, and b4=5.

[0085] In this embodiment, step S4 is specifically as follows:

[0086] In this embodiment, the PSO algorithm is first initialized and the initialization parameters are set, that is, the number of particles used in the search space is set to M=500, the position and speed of each particle, the inertia weight w=1, the acceleration coefficient and the maximum number of iterations K=200.

[0087] Each particle represents a potential solution, and the particle searches for the optimal solution through iteration in the multidimensional search space; the acceleration coefficient includes: the local learning coefficient η1 and the global learning coefficient η2 (affecting the ability of the particle to obtain information). In this embodiment, the local learning coefficient and the global learning coefficient are uniformly set to 1.5.

[0088] Then, according to the multi-radar platform trajectory planning optimization problem established in step S3, the starting position information and target position information of the trajectory obtained in step S1 are updated through the PSO algorithm, and the position and speed of the particles are continuously adjusted to search the multi-radar platform configuration space and find the trajectory that minimizes the cost function, as follows:

[0089] Based on the initialization of the PSO algorithm, the position and velocity of each particle are updated. The process of the particle swarm optimization algorithm is as follows: Figure 3 As shown, the update model expression of the particle swarm algorithm is as follows:

[0090]

[0091] Among them, Q i =(x i1 ,x i2 ,...,x iN ) represents the position vector of the ith particle, x iN represents the position of the i-th particle at dimension N, V i =(v i1 ,v i2 ,...,v iN ) represents the velocity vector of the ith particle, v iN represents the speed of the ith particle at dimension N, where N represents the dimension of the search space, i.e., the number of track nodes in track planning; L i =(l i1 ,l i2 ,...,l iN ) represents the local optimal position, l iN represents the local optimal position of the i-th particle in dimension N, L g =(L g1 ,L g2 ,...,L gN ) represents the global optimal position, L gN represents the global optimal position of the i-th particle in dimension N; k represents the k-th iteration, w k represents the inertia weight coefficient, M represents the number of particles; r 1j and r 2j Represents a random number in the range [0,1], used to increase the randomness of the search.

[0092] After updating the particle position and velocity, evaluate the function fitness value of each particle, and update the global optimal position of the group. Repeat the updating steps to determine whether the maximum number of iterations is met. If the maximum number of iterations is reached, stop the iteration, update the position and velocity of the global best particle, and output the optimal trajectory. Otherwise, re-update the particle position and velocity until the iteration is completed.

[0093] The optimal trajectory expression is as follows:

[0094] E=(x i1 ,y i1 ,z i1 ,x i2 ,y i2 ,z i2 ,...,x iN ,y iN ,z iN ) (8)

[0095] Where E represents a track consisting of N nodes.

[0096] The simulation results of the two radar platforms in this embodiment are as follows Figure 4 As shown in the figure, the purple area represents the search radar airspace threat area, that is, the denied airspace, the dot represents the starting position information, the star represents the target position information, and the black curve is the planned radar platform track planning result. From the results, it can be seen that the radar platform can effectively avoid the airspace threat area and will not touch the ground to cause an accident, and can fly in complex airspace. From the results, it can be seen that the radar platform can consider the height threat of the digital elevation model and better adapt to the actual situation. In addition, it can effectively avoid the denied airspace threat from the enemy search radar, and can complete the track planning in dangerous and complex airspace to achieve effective search for air targets.

[0097] In summary, the method of the present invention introduces the height constraint of the digital elevation model and considers the constraint conditions of the radar platform itself, as well as the denied airspace threat from the enemy search radar that may be faced during the search for air targets. Taking the above factors into consideration, the multi-radar platform configuration planning problem is transformed into a multi-constraint optimization problem that ensures the feasibility and safe operation of the radar platform. Then, the PSO algorithm is used to effectively avoid the threat area, and the multi-radar platform track planning results are obtained, thereby improving the track planning capability of the multi-radar platform, adapting to planning tracks in dangerous and complex airspace, and realizing effective search for air targets.

[0098] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A multi-constraint trajectory planning method for multi-radar platform air target search, the specific steps are as follows: S1, import the digital elevation model DEM and obtain the starting point location information and target location information of the track; First, import the digital elevation model DEM, that is, import the DEM file by specifying the path of the DEM file and using the read function in the simulation software; And given the starting position information of the track (x start ,y start ,z start ) and target location information (x end ,y end ,z end ); S2. Model the threat areas in the airspace such as radars in the flight track of the radar platform and establish the denied airspace; The threat area in the airspace existing in the flight track of the radar platform is modeled as denied airspace, and the denied airspace is modeled as a cone shape; S3, according to the location information obtained in step S1 and the DEM model constraints, the radar platform constraints and the airspace threat constraints, establish the multi-radar platform trajectory planning optimization problem, and assign different weights to different constraints according to the specific tasks; Among them, the radar platform's own constraints include: track length constraints, dynamic constraints; S4, solving the optimization problem of step S3 by particle swarm PSO algorithm, and outputting the optimal track; First, the PSO algorithm is initialized and the initialization parameters are set, including: the number of particles used in the search space, the position and velocity of each particle, the inertia weight, the acceleration coefficient, and the number of iterations; Then, according to the established trajectory planning optimization problem, the starting position information and the target position information, the PSO algorithm is used to update the particle position and velocity, search the multi-radar platform configuration space, and determine whether the termination condition is met, that is, whether the maximum number of iterations is reached. If the termination condition is met, the optimal trajectory that minimizes the cost function is output; if the termination condition is not met, the solution is repeatedly updated.

2. The multi-constraint trajectory planning method for multi-radar platform air target search according to claim 1 is characterized in that: The step S3 is specifically as follows: First, the DEM model constraints, radar platform constraints, and airspace threat constraints are analyzed. The radar platform constraints include: Track length constraints and dynamic constraints are as follows: (1) Track length constraint; Considering the fuel consumption of the radar platform, shortening the flight track of the radar platform, and taking the Euclidean distance between two nodes as the length of each segment, the track length constraint C1(X i ) is expressed as follows: Among them, X i Represents the decision variable, that is, N track points P ij Each track point represents the position and track information of the radar platform; ij =(x ij ,y ij ,z ij ) represents the track node in the search map, i represents the i-th particle in the search space, that is, the dimension of the search space, the upper limit number of particles is M, and j represents the j-th track node among N track points; (2) DEM model constraints; Considering the flight altitude of the radar platform and the terrain height, the flight altitude of the radar platform should satisfy the following inequality: Among them, C2(X i ) represents the height constraint relative to DEM in modeling, H ij Indicates the height loss relative to the DEM at the current j-th track node, h ij Indicates that the radar platform is at (x ij ,y ij ) at a height of h DEM (i,j) means in (x ij ,y ij ) at the height of the DEM; (3) Dynamic constraints; Considering that the radar platform needs to satisfy dynamic constraints in actual flight, the dynamic constraints of the radar platform should satisfy the following inequality: Among them, C3(X i ) represents the dynamic constraints, namely the pitch climb angle and horizontal turn angle costs, φ ij represents the horizontal steering angle between the current position and the previous position, ψ ij Indicates the climbing angle, φ max represents the maximum horizontal steering angle, ψ max represents the maximum pitch climb angle, α and β represent the penalty coefficients of the horizontal steering angle and the pitch climb angle respectively; (4) airspace threat constraints; Considering the radar threat area of ​​the radar platform in the flight environment, the radar platform should satisfy the following inequality: Among them, C4(X i ) represents the airspace threat constraint, i.e., the search threat of the adversary’s radar; T ij represents the center coordinates of the projection surface of the threat airspace, that is, the center coordinates of the denied airspace, R ij Indicates the radius of the threat airspace at the current location, R safe Indicates the safe distance, that is, the distance that needs to be maintained between the radar platform and the denied airspace; Based on the above constraints, the multi-radar platform trajectory planning optimization problem is established, and the expression is as follows: Among them, C k (·) represents the kth cost function; b k represents the kth cost function C k (·) weight coefficient, C(X i ) represents the total cost function, and different weights are assigned to different constraints according to the actual situation.

3. The multi-constraint trajectory planning method for multi-radar platform air target search according to claim 1 is characterized in that: The step S4 is specifically as follows: First, the PSO algorithm is initialized and the initialization parameters are set, that is, the number of particles M used in the search space, the position and velocity of each particle, the inertia weight w, the acceleration coefficient and the maximum number of iterations K; Each particle represents a potential solution, and the particle searches for the optimal solution through iteration in the multidimensional search space; the acceleration coefficients include: local learning coefficient η1 and global learning coefficient η2; Then, according to the multi-radar platform trajectory planning optimization problem established in step S3, the starting position information and target position information of the trajectory obtained in step S1 are updated through the PSO algorithm, and the position and speed of the particles are continuously adjusted to search the multi-radar platform configuration space and find the trajectory that minimizes the cost function, as follows: Based on the initialization of the PSO algorithm, the position and velocity of each particle are updated. The update model expression of the particle swarm algorithm is as follows: Among them, Q i =(x i1 ,x i2 ,...,x iN ) represents the position vector of the ith particle, x iN represents the position of the i-th particle at dimension N, V i =(v i1 ,v i2 ,...,v iN ) represents the velocity vector of the ith particle, v iN represents the speed of the ith particle at dimension N, where N represents the dimension of the search space, i.e., the number of track nodes in track planning; L i =(l i1 ,l i2 ,...,l iN ) represents the local optimal position, l iN represents the local optimal position of the i-th particle in dimension N, L g =(L g1 ,L g2 ,...,L gN ) represents the global optimal position, L gN represents the global optimal position of the i-th particle in dimension N; k represents the k-th iteration, w k represents the inertia weight coefficient, M represents the number of particles; r 1j and r 2j Represents a random number in the range [0,1]; After updating the particle position and velocity, evaluate the function fitness value of each particle, and update the global optimal position of the group. Repeat the updating steps to determine whether the maximum number of iterations is met. If the maximum number of iterations is reached, stop the iteration, update the position and velocity of the global best particle, and output the optimal trajectory. If not, re-update the particle position and velocity until the iteration is completed. The optimal trajectory expression is as follows: E=(x i1 ,y i1 ,z i1 ,x i2 ,y i2 ,z i2 ,...,x iN ,y iN ,z iN ) (8) Where E represents a track consisting of N nodes.

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