An unmanned aerial vehicle cluster target attack path planning method based on optimization algorithm

Abstract

The application discloses a kind of based on optimization algorithm's unmanned aerial vehicle cluster target attack path planning method, comprising the following steps: comprising the following steps:(1) according to the characteristics of complex urban environment using elevation diagram modeling method and MATLAB processing obtains three-dimensional complex urban environment model;(2) establish unmanned aerial vehicle constraint condition under complex urban environment model(3) establish unmanned aerial vehicle path cost function under complex urban environment model, obtain path evaluation result;(4) using optimization algorithm obtains the optimal route of unmanned aerial vehicle cluster in complex urban environment path planning.The application is based on complex urban environment model, unmanned aerial vehicle constraint condition and path evaluation result using optimization algorithm for unmanned aerial vehicle to plan a reasonable target attack trajectory in complex urban environment, so that the path planning of unmanned aerial vehicle has higher path planning efficiency and stability, and the consumed path cost is minimum and converges faster.

Description

Technical Field

[0001] This invention belongs to the field of trajectory planning technology, and specifically relates to a method for planning the trajectory of UAV swarm target attack based on an optimization algorithm. Background Technology

[0002] One of the key technologies for UAV urban warfare is UAV trajectory planning in urban environments. Currently, there is limited research on UAV trajectory planning in urban environments. (Javier) Some researchers have used Coverage Path Planning (CPP) algorithms for path planning, but this requires a comprehensive exploration of the urban environment, is time-consuming, and lacks real-time performance. In contrast, the Snake Optimizer (SO) algorithm is more efficient in handling real-time path generation. Jianfa Wu et al. proposed a path planning framework for Solar Unmanned Aerial Vehicles (SUAVs), solving the problem of accurate solar energy modeling. However, this method has limitations in planning under dim lighting conditions, while the Sine Cosine Algorithm (SCA) performs stably under various lighting conditions. Xinting Hu et al. proposed a risk-cost-based path planning method, which, although considering various risks, relies on a pre-set environmental model and lacks real-time performance. Therefore, researching how to avoid reliance on pre-set environmental models and achieve a highly adaptable, time-efficient, and real-time-responsive method for UAV urban environment path planning is a hot topic. Summary of the Invention

[0003] To address the shortcomings of the prior art, this invention provides a method for planning the trajectory of UAV swarm target attack based on an optimization algorithm.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for planning the trajectory of UAV swarm target engagement based on an optimization algorithm includes the following steps:

[0006] (1) Based on the characteristics of complex urban environments, a three-dimensional complex urban environment model was obtained using the elevation map modeling method and MATLAB processing.

[0007] (2) Establish UAV constraints under a complex urban environment model, wherein the UAV constraints are safe flight altitude area constraints, maximum range constraints, and waypoint obstacle avoidance area constraints.

[0008] (3) Establish a UAV trajectory cost function for complex urban environment model, evaluate the trajectory of UAV swarm, and obtain trajectory evaluation results;

[0009] (4) The optimal route for UAV swarm trajectory planning in complex urban environment is obtained by combining the optimization algorithm with the complex urban environment model, UAV constraints and trajectory evaluation results.

[0010] Furthermore, the complex urban environment model includes urban building hazard area modeling and threat area modeling. The urban building hazard area modeling and threat area modeling are constructed by using the 3D elevation map modeling method to realistically restore the urban building topography, threat areas and other enemy defense measures.

[0011] Furthermore, the urban building hazard zone modeling involves treating urban buildings as cylinders, with drones entering this area considered to be in a hazardous state. The modeling formula is as follows:

[0012]

[0013] The parameters of the nth cylindrical city building are represented as (a 1n ,b 1n ,h 1n ,R 1n ), (a 1n ,b 1n ) represents the coordinates of the building's central area, h 1n R represents the building height. 1n The radius of the building is represented by 1, n is a non-zero natural number, and (x,y,z) are the coordinates of the UAV's flight path.

[0014] Furthermore, the threat region modeling involves setting the threat region as a hemisphere, and the modeling expression formula is as follows:

[0015]

[0016] The m-th ground threat area is represented as (a 2m ,b 2m ,R 2m ), (a 2m ,b 2m ) represents the coordinates of the threat center, 2 represents the threat point, m is a non-zero natural number, and R 2m Indicates the radius corresponding to the threat point.

[0017] Furthermore, the safe flight altitude area constraint is as follows:

[0018] H min ≤H≤H max

[0019] Where H represents the current flight altitude of the drone, H min For the minimum safe flight altitude, H maxMaximum safe flight altitude;

[0020] The maximum range constraint is:

[0021]

[0022] Among them, l max l represents the maximum range. e The total number of flight paths for each segment of the flight path is represented by {l1, l2, l3…l... e It consists of a total of e flight paths;

[0023] The waypoint obstacle avoidance area constraints are as follows:

[0024] z n >A(x,y,z) or z m >B(x,y)

[0025] Among them, z n z represents the elevation of the UAV waypoint n. m This indicates the elevation of the drone's flight path point m.

[0026] Furthermore, the evaluation of the flight paths of the drone swarm specifically involves:

[0027] (1) Set the performance indicators for the target strike trajectory planning of UAV swarms: range cost, altitude change cost, and turning angle cost;

[0028] (2) The trajectory cost function is obtained by using the range cost function, altitude change cost function, and turning angle cost function:

[0029] J cost =D cost +H cost +Q cost

[0030] Among them, J cost It is the total trajectory cost function, D cost H is the range cost function. cost For a highly variable cost function, Q cost It is the turning angle cost function;

[0031] The range cost function is the actual flight distance of a UAV in the UAV swarm from waypoint k to waypoint k+1, and its expression is:

[0032]

[0033] The cost function for the height change is:

[0034]

[0035] Among them, C is the number of waypoints, is the average value of the waypoint heights, and Z is the flight altitude of the UAV;

[0036] The turning angle cost function is:

[0037]

[0038] By solving and processing the trajectory cost function, a trajectory composed of line segments is obtained, and then the cubic B-spline method is used to smooth it, and finally the trajectory evaluation result that the UAV can actually fly is obtained.

[0039] Furthermore, the specific steps of the optimization algorithm are as follows:

[0040] S1: The UAV trajectory planning control system automatically obtains the starting point coordinates, target point coordinates, complex urban environment model, UAV constraint conditions, trajectory evaluation results, maximum iteration number T, and UAV population number g of the aircraft group;

[0041] S2: Calculate the energy factor E, and the formula for calculating E is:

[0042] By

[0043] Among them, t represents the current iteration number, T represents the maximum iteration number, and r is a random number within (0, 1);

[0044] If E > 1, each UAV represents a candidate solution, the best solution in each step of the UAV is regarded as the target point coordinates, each UAV interacts with other UAVs through position information, can interact with any UAV in the aircraft group, and the interaction between UAVs is marked by churning. Then, update the UAV position according to the navigation interaction behavior, and the calculation formula is:

[0045]

[0046] Among them, in the navigation stage, V i (t + 1) represents the position vector of UAV i at the (t + 1)-th iteration, V j (t) represents the position vector of UAV j at the t-th iteration, j is the position of a UAV randomly selected from the current UAV group and j ≠ i, F represents a random matrix, and 0 and 1 can be randomly generated, represents the average position vector of the UAVs, and p1 represents a random number within (0, 1);

[0047] If 2 / 3 < E < 1, the UAV explores a new area:

[0048] V i (t + 1) = -r × U i (t + 1) + r × H r(t + 1)-L×(H r (t + 1)-V i (t))

[0049] Among them, in the exploration stage, H r (t + 1) represents the random position of the UAV in the exploration area, r is a random number within (0, 1), and L is the Levy flight function, which is used to expand the search space;

[0050] If 1 / 3 < E < 2 / 3, the UAV's flight path is corrected for local optimization to approach the target path. The expression formula is:

[0051] U i (t + 1) = W(t)+α×|W(t)-x prey (t)|

[0052]

[0053] Among them, in the correction stage, U i (t + 1) represents the corrected position vector of UAV i in the (t + 1)-th iteration, W(t) represents the projected position vector of the current UAV in the normalized search space, and x prey (t) represents the position of the current optimal solution of the target UAV, and α represents the scale of the resting area, which controls the intensity of local optimization;

[0054] According to the correction behavior, the UAV's navigation updates its position according to the formula:

[0055] V i (t + 1) = U i (t + 1)+n1×(U i (t + 1)round(rand)×V i (t))

[0056] Among them, n1 represents a random number within (0, 1), and round(rand) represents a random function that generates 0 or 1;

[0057]

[0058] In the strike stage, H prey (t + 1) represents the position of the target UAV in the (t + 1)-th iteration, β is the reduction coefficient for controlling the locking area, and the scale β makes the range of the strike area become smaller over time.

[0059] If 0 < E < 1 / 3, update the position according to the locking behavior. The calculation formula is:

[0060] V i (t + 1) = H prey (t + 1)+η×(Hprey (t+1)-round(rand)×V i (t))

[0061] Where η represents the curl factor;

[0062] S3: The drone's position is based on fitness (V) i (t) is used to decide whether to update:

[0063]

[0064] Where, fit(V) i (t) represents the current flight path adaptability of the UAV;

[0065] S4: After each iteration, update the current optimal solution x. prey (t) yields the optimal path in the UAV's flight path.

[0066] The beneficial effects of this invention are as follows: This invention uses an optimization algorithm based on a complex urban environment model, UAV constraints, and trajectory evaluation results to plan a reasonable target strike trajectory for UAVs in complex urban environments. This makes the UAV trajectory planning more efficient and stable, minimizes the trajectory cost, and converges faster. This achieves the optimal UAV target strike trajectory with a better convergence trend of the trajectory cost, the highest mission completion rate, and better performance. Attached Figure Description

[0067] Figure 1 This is a flowchart of a drone swarm target attack trajectory planning method based on an electric eel foraging optimization algorithm in a complex urban environment, according to the present invention.

[0068] Figure 2 This invention provides a schematic diagram of urban architecture.

[0069] Figure 3 A schematic diagram of the threat area provided by this invention;

[0070] Figure 4 A comparison chart of flight trajectories of EEFO, HHO, MFO, SCA, SO, and WOA algorithms for complex urban environments provided by this invention;

[0071] Figure 5 A line graph comparing the optimal fitness values ​​of the algorithm provided in this invention;

[0072] Figure 6 A histogram showing the difference in optimal fitness values ​​provided by the present invention;

[0073] Figure 7 A heat map showing the optimal fitness values ​​of the algorithm provided in this invention. Detailed Implementation

[0074] The present invention will now be described in detail with reference to the accompanying drawings:

[0075] A method for planning the trajectory of UAV swarm target engagement based on an optimization algorithm includes the following steps:

[0076] (1) Based on the characteristics of complex urban environments, a three-dimensional complex urban environment model is obtained using elevation map modeling and MATLAB processing. This complex urban environment model includes urban building hazard area modeling and threat area modeling. These models are constructed by realistically reproducing urban building topography, threat areas, and other enemy defense measures using three-dimensional elevation map modeling. Urban building hazard area modeling not only retains the main limiting factors that buildings pose to UAV flight but also significantly reduces computational complexity, enabling UAV path planning algorithms to process and find safe detour paths more efficiently. Threat area modeling can highly realistically simulate the all-round coverage and area of ​​effect of ground threats.

[0077] (2) Establish UAV constraints under a complex urban environment model, wherein the UAV constraints are safe flight altitude area constraints, maximum range constraints and waypoint obstacle avoidance area constraints.

[0078] (3) Establish a cost function for UAV trajectory under a complex urban environment model, evaluate the trajectory of UAV clusters, and obtain trajectory evaluation results.

[0079] (4) The optimal route for UAV swarm trajectory planning in complex urban environment is obtained by combining the optimization algorithm with the complex urban environment model, UAV constraints and trajectory evaluation results.

[0080] like Figure 2 As shown, the modeling of hazardous areas in urban buildings involves treating urban buildings as cylinders, with drones entering this area considered to be in a hazardous state. The modeling formula is as follows:

[0081]

[0082] The parameters of the nth cylindrical city building are represented as (a 1n ,b 1n ,b 1n ,R 1n ), (a 1n ,b 1n ) represents the coordinates of the building's central area, h 1n R represents the building height. 1nThis represents the radius corresponding to the building, where 1 represents the building, n is a non-zero natural number, and (x, y, z) are the coordinates of the UAV's flight path. By modeling urban buildings, UAVs can effectively avoid or discover new building hazard zones through model calculations, ultimately optimizing their flight paths.

[0083] like Figure 3 As shown, the threat region modeling involves setting the threat region as a hemisphere, and the modeling expression formula is as follows:

[0084]

[0085] The m-th ground threat area is represented as (a 2m ,b 2m ,R 2m ), (a 2m ,b 2m ) represents the coordinates of the threat center, 2 represents the threat point, m is a non-zero natural number, and R 2m This represents the radius corresponding to the threat point. The threat area consists of ground-deployed radar systems, electromagnetic interference devices, missile vehicles, etc. The hemispherical model, as an analysis tool, can realistically simulate the all-around coverage and area of ​​effect of ground threats.

[0086] When conducting precision strike missions in urban environments, while excessively high flight altitudes can broaden the field of view, they also increase the risk of detection by enemy radar; conversely, excessively low altitudes may make it difficult for drones to handle sudden obstacles, increasing the risk of collisions. Therefore, the safe flight altitude range is constrained as follows:

[0087] H min ≤H≤H max

[0088] Where H represents the current flight altitude of the drone, H min For the minimum safe flight altitude, H max This is the maximum safe flight altitude. Therefore, the maximum safe flight altitude H... max The lowest altitude at which enemy radar can detect the aircraft; the minimum safe flight altitude H. min It should be lower than h 1n Or the height of a point that is not within B(x,y).

[0089] Besides basic energy consumption, the complexity of maneuvering, the unpredictability of wind resistance, and variable environmental factors such as temperature and air pressure further exacerbate energy consumption, significantly weakening the UAV's endurance. Therefore, rationally setting the UAV's range constraint is crucial for optimizing its combat effectiveness and extending its mission execution time. The maximum range constraint is as follows:

[0090]

[0091] Among them, l max l represents the maximum range. e The total number of flight paths for each segment of the flight path is represented by {l1, l2, l3…l... e It consists of a total of e flight paths.

[0092] To ensure that drones maintain a safe distance when navigating urban areas and avoid any form of collision risk, the waypoint obstacle avoidance zone constraints are as follows:

[0093] z n >A(x,y,z) or z m >B(x,y)

[0094] Among them, z n z represents the elevation of the UAV waypoint n. m This indicates the elevation of the drone's flight path point m. This allows the drone to accurately avoid tall buildings and potentially threatening areas in the city.

[0095] In UAV trajectory planning, range cost is a key decision factor, and turning angle directly affects flight time, energy efficiency, and mission performance. Therefore, optimization strategies typically focus on minimizing the flight distance between waypoints. Thus, evaluating the trajectory of a UAV swarm specifically involves:

[0096] (1) Set the performance indicators for the target strike trajectory planning of UAV swarms: range cost, altitude change cost, and turning angle cost;

[0097] (2) The trajectory cost function is obtained by using the range cost function, altitude change cost function, and turning angle cost function:

[0098] J cost =D cost +H cost +Q cost

[0099] Among them, J cost It is the total trajectory cost function, D cost H is the range cost function. cost For a highly variable cost function, Q cost This is the turning angle cost function. The total trajectory cost function J cost The smaller the value, the better the trajectory planning optimization.

[0100] The range cost function is the actual flight distance of a drone in the drone swarm from waypoint k to waypoint k+1, expressed using Euclidean distance:

[0101]

[0102] By calculating the standard deviation of altitude during the flight, flight stability is assessed, and a basis for optimizing strategies and reducing unnecessary altitude adjustments is provided. The altitude change cost function is:

[0103]

[0104] Where C is the number of waypoints. Z is the average altitude of the waypoints, and Z is the flight altitude of the UAV.

[0105] The turning angle cost function is used as an evaluation metric to measure the turning frequency and smoothness of a path; therefore, the turning angle cost function is:

[0106]

[0107] By solving the trajectory cost function, a trajectory composed of line segments is obtained. Then, the cubic B-spline method is used to smooth it, and finally, the evaluation result of the actual flyable trajectory of the UAV is obtained.

[0108] The specific steps of the optimization algorithm are as follows:

[0109] S1: Automatically acquire the starting point coordinates, target point coordinates, complex urban environment model, UAV constraints, trajectory evaluation results, maximum number of iterations T, and UAV population size g in the UAV trajectory planning and control system;

[0110] S2: Calculate the energy factor E. The formula for calculating E is:

[0111]

[0112] Where t represents the current iteration number, T represents the maximum iteration number, and r is a random number within (0,1).

[0113] The energy factor is introduced to balance global and local searches. In the early stages, the energy factor is higher to promote global search; as iterations progress, the energy factor gradually decreases to focus more on local search and improve the accuracy of the solution.

[0114] If E > 1, then the UAV position is updated based on the navigation interaction behavior, calculated using the following formula:

[0115]

[0116] in,

[0117] During the navigation phase, V i (t+1) represents the position vector of drone i at iteration t+1, and the next position is determined by the interaction between drones; V j(t) represents the position vector of the drone j at the t-th iteration, where j is the position of a drone randomly selected from the current drone swarm and j ≠ i; F represents a random matrix that can randomly generate 0 and 1; represents the average position vector of the drones; V r (t) represents the position of a drone randomly selected from the current drone swarm; p1 represents a random number within (0, 1), which is used to determine whether the next updated position is based on the average position or the position of other randomly selected drones. Low and Up respectively represent the lower and upper limits of the solution space, which are used to define the search boundary of the drones.

[0118] If 2 / 3 < E < 1, the drone explores a new area:

[0119] V i (t + 1) = -r × U i (t + 1) + r × H r (t + 1) - L × (H r (t + 1) - V i (t))

[0120] Among them, in the exploration stage, H r (t + 1) represents a random position of the drone within the exploration area, r is a random number within (0, 1), and L is the Levy flight function, which has a heavy-tailed distribution and can generate long-distance jumps to avoid the search falling into local optima and is used to expand the search space.

[0121] Among them, H r (t + 1) is calculated based on x prey (t) in the target area and the correction scale coefficient. The specific calculation formula is:

[0122] [[ID=?]] [[ID=?]] [[ID=?]]

[0123] β = β0xsin(2πr)

[0124] [[ID=4?]] [[ID=4?]] [[ID=4?]]

[0125] β represents the scale coefficient of the hunting area, which controls the offset of the target position. β gradually decreases over time, making the search range gradually converge. β0 is the initial scale coefficient.

[0126] If 1 / 3 < E < 2 / 3, the drone's flight path is corrected for local optimization to approach the target path. The expression formula is:

[0127] U i (t + 1) = W(t) + α × |W(t) - x prey (t)|

[0128] α = α0×sin(2πr) Note: There seem to be some tags with "?" in the original text where the content is incomplete or unclear. The translation has been done as accurately as possible based on the available information.

[0129]

[0130] Among them, in the correction stage, U i (t + 1) represents the position vector corrected by the UAV i in the (t + 1)-th iteration, W(t) represents the projected position vector in the normalized search space of the current UAV, and x prey (t) represents the position of the current optimal solution of the target UAV. α represents the scale of the resting area and controls the intensity of local optimization; α0 is the initial scale.

[0131] Update the position of the UAV's navigation according to the correction behavior, according to the formula:

[0132] V i (t + 1) = U i (t + 1) + n1×(U i (t + 1)round(rand)×V i (t))

[0133] Among them, n1 represents a random number within (0, 1). This random perturbation term makes the position of the UAV fluctuate slightly in the correction stage to avoid over-concentration; round(rand) represents a random function that generates 0 or 1, which is used to randomly determine whether to introduce the influence of the current UAV position V i (t). If round(rand) = 1, the information of the current UAV position will be included. If round(rand) = 0, the included U i (t + 1) information.

[0134] If 0 < E < 1 / 3, update the position according to the locking behavior. The calculation formula is: <{

[0135] V[[ID=3--7]] i (t + 1) = H prey (t + 1) + η×(H prey (t + 1) - round(rand)×V i (t))

[0136] Among them, η represents the curling factor, which is used to control the random perturbation intensity when updating the UAV position. It changes with the advancement of time t;

[0137]

[0138] r is a random number within (0, 1), which determines the specific value of the curling factor to ensure the randomness and curling characteristics of the UAV path.

[0139] S3: Determine whether to update the position of the UAV based on the fitness fit(V i (t)):

[0140]

[0141] Where, fit(V) i (t) represents the current flight path adaptability of the UAV;

[0142] S4: After each iteration, update the current optimal solution x. prey (t) yields the optimal path in the UAV's flight path.

[0143] like Figure 4 As shown, this implementation compares five algorithms: EEFO (the calculation method of this invention), SCA (sine and cosine optimization algorithm), SO (snake optimization algorithm), WOA (whale optimization algorithm), MFO (moth flame optimization algorithm), and HHO (Harris Eagle optimization algorithm). In dense urban environments with enemy defenses, the target strike mission of the UAV faces particularly challenging conditions. The EEFO algorithm demonstrates exceptional navigation and avoidance capabilities. It not only accurately guides the UAV to effectively avoid all buildings but also bypasses potential threat areas, ultimately reaching the target location precisely for strike. The trajectories planned by the other five algorithms either cause the UAV to collide with buildings or increase mission risk due to improper path planning. Notably, the trajectories generated by the SCA and MFO algorithms exhibit severe deviations; their turning angles deviate directly from the preset three-dimensional environment, clearly failing to achieve effective target strike. Therefore, the EEFO algorithm significantly outperforms the other five algorithms in terms of safety, efficiency, and accuracy.

[0144] In scenarios involving 80 urban building obstacles and 10 radar threat zones, 50 experiments were conducted on the EEFO algorithm and five other algorithms. The average fitness results after each iteration are as follows: Figure 5-7 As shown in the figure, with the deepening of the iteration process and continuous optimization, the EEFO algorithm achieves higher efficiency in finding feasible solutions, exhibiting a lower fitness value for the flight path and a significant downward trend. Compared with other algorithms, the EEFO algorithm can explore and lock a better flight path with a higher probability, ensuring that the UAV can completely avoid all potential obstacles and threat areas. In contrast, the other five algorithms, after 50 iterations, have a lower success rate in overcoming obstacles and other constraints and cannot find a feasible path that meets the conditions. In complex and ever-changing dense urban environments, especially when facing challenges such as high-density obstacles and enemy defense areas, the EEFO algorithm can quickly find feasible solutions and is more adaptable to complex environmental scenarios.

[0145] Although the specific embodiments of the present invention have been described and illustrated in detail above, it should be noted that various changes and modifications can be made to the above embodiments without departing from the spirit of the present invention and the scope set forth in the appended claims.

Claims

1. A method for planning the trajectory of UAV swarm target attack based on an optimization algorithm, characterized in that... , including the following steps: (1) Using the elevation map modeling method and MATLAB processing according to the characteristics of complex urban environments to obtain a three-dimensional complex urban environment model; (2) Establishing the UAV constraints for the complex urban environment model, where the UAV constraints are the safe flight altitude area constraint, the maximum flight range constraint, and the waypoint obstacle avoidance area constraint; (3) Establishing the UAV trajectory cost function for the complex urban environment model, evaluating the trajectories of the UAV swarm, and obtaining the trajectory evaluation results; (4) Using an optimization algorithm combined with the complex urban environment model, UAV constraints, and trajectory evaluation results to obtain the optimal route for the UAV swarm's trajectory planning in the complex urban environment; The specific steps of the optimization algorithm are as follows: S1: Automatically obtaining the starting point coordinates, target point coordinates, complex urban environment model, UAV constraints, trajectory evaluation results, maximum number of iterations T, and UAV population number g in the UAV trajectory planning control system; S2: Calculating the energy factor E, and the formula for calculating E is: where t represents the current iteration number, T represents the maximum number of iterations, and r is a random number within (0, 1); If E > 1, then update the UAV position according to the navigation interaction behavior, and the calculation formula is: During the navigation phase, V i (t+1) represents the position vector of drone i at iteration t+1, V j (t) represents the position vector of drone j in the t-th iteration, where j is a position of a drone randomly selected from the current drone swarm and j ≠ i. E represents a random matrix that can be randomly generated with 0s and 1s. Let p1 represent the average position vector of the UAV, and p1 represent a random number within (0,1). If 2 / 3 < E < 1, the UAV explores new areas: V i (t+1)=-r×U i (t+1)+r×H r (t+1)-L×(H r (t+1)-V i (t)) In the exploration phase, (H) r (t+1) represents the random position of the UAV within the exploration area, r is a random number in (0,1), and L is the Levy flight function, used to expand the search space; If 1 / 3 < E < 2 / 3, perform trajectory correction on the UAV, and locally optimize to approach the target path, and the expression formula is: U i (t+1)=W(t)+α×|W(t)-x prey (t)| During the correction phase, U i (t+1) represents the position vector corrected by UAV i in iteration t+1, W(t) represents the projected position vector of the current UAV in the normalized search space, and x prey (t) represents the position of the target UAV's current optimal solution, and α represents the scale of the resting zone, which controls the intensity of local optimization; Update the UAV navigation position according to the correction behavior, according to the formula: V i (t+1)=U i (t+1)+n1×(U i (t+1)round(rand)×V i (t)) where n1 represents a random number within (0, 1), and round(rand) represents a random function that generates 0 or 1; During the strike phase, H prey (t+1) represents the position of the target UAV in the (t+1)th iteration, β is the shrinkage coefficient that controls the locking area, and the scale β makes the range of the strike area smaller over time; If 0 < E < 1 / 3, update the position according to the locking behavior, and the calculation formula is: V i (t+1)=H prey (t+1)+η×(H prey (t+1)-round(rand)×V i (t)) where η represents the curling factor; S3: The drone's position is based on fitness (V) i (t) is used to decide whether to update: Where, fit(V) i (t) represents the current flight path adaptability of the UAV; S4: After each iteration, update the current optimal solution x. prey (t) yields the optimal path in the UAV's flight path.

2. The method for planning the target attack trajectory of an unmanned aerial vehicle swarm based on an optimization algorithm according to claim 1, characterized in that... , the complex urban environment model includes urban building dangerous area modeling and threat area modeling, and the urban building dangerous area modeling and threat area modeling are constructed by using the elevation map modeling method to truly restore the information of urban building topography, threat areas, and other enemy defense measures.

3. The method for planning the target attack trajectory of an unmanned aerial vehicle swarm based on an optimization algorithm according to claim 2, characterized in that... , the urban building dangerous area modeling is to set urban buildings as cylinders, and when the UAV is in this area, it is in a dangerous state, and the modeling expression formula is: The parameters of the nth cylindrical city building are represented as (a 1n ,b 1n ,h 1n ,R 1n ), (a 1n ,b 1n ) represents the coordinates of the building's central area, h 1n R represents the building height. 1n The radius of the building is represented by 1, n is a non-zero natural number, and (x,y,z) are the coordinates of the UAV's flight path.

4. The method for planning the trajectory of UAV swarm target attack based on an optimization algorithm according to claim 3, characterized in that... , the threat area modeling is to set the threat area as a hemisphere, and the modeling expression formula is: The m-th ground threat area is represented as (a 2m ,b 2m ,R 2m ), (a 2m ,b 2m ) represents the coordinates of the threat center, 2 represents the threat point, m is a non-zero natural number, and R 2m Indicates the radius corresponding to the threat point.

5. The method for planning the trajectory of UAV swarm target attack based on an optimization algorithm according to claim 4, characterized in that... [[ID= H min ≤H≤H max Where H represents the current flight altitude of the drone, H min For the minimum safe flight altitude, H max Maximum safe flight altitude; ​ Among them, l max l represents the maximum range. e The total number of flight paths for each segment of the flight path is represented by {l1, l2, l3…l... e It consists of a total of e flight paths; ​ z n >A(x, y, z) or z m >B(x, y) Among them, z n z represents the elevation of the UAV waypoint n. m This indicates the elevation of the drone's flight path point m.

6. A method for planning the trajectory of UAV swarm target attack based on an optimization algorithm according to claim 5, characterized in that... ​ ​ ​ J cost =D cost +H cost +Q cost Among them, J cost It is the total trajectory cost function, D cost H is the range cost function. cost For the highly variable cost function, Q cost It is the turning angle cost function; ​ ​ Where C is the number of waypoints. Z is the average altitude of the waypoints, and Z is the flight altitude of the UAV. ​ ​

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