Multi-unmanned aerial vehicle cooperative flight path planning method based on improved GWO algorithm

Abstract

The invention relates to the technical field of unmanned aerial vehicle cooperation, and particularly discloses a multi-unmanned aerial vehicle cooperation route planning method based on an improved GWO algorithm, and the method comprises the following steps: carrying out the constraint analysis of an unmanned aerial vehicle group; analyzing the flight path cost of the unmanned aerial vehicle; a GWO algorithm and improvement are carried out; and finally carrying out simulation experiment and algorithm performance analysis. According to the multi-unmanned aerial vehicle cooperative flight path planning method based on the improved GWO algorithm, aiming at the condition that the initialization effect of the GWO algorithm is poor, a greedy algorithm and a variation strategy are used, and the fitness value during unmanned aerial vehicle flight path initialization is reduced; a clustering method is introduced, the flight path of the unmanned aerial vehicle is divided into a plurality of sub-populations, each sub-population is independently optimized, and through comparison of the improved GWO algorithm, the MP-GWO algorithm and the GWO algorithm, the result shows that the flight path calculated by the improved GWO algorithm is lower in flight path cost and higher in convergence precision compared with the flight path calculated by the other two algorithms.

Description

Technical Field

[0001] The invention relates to the technical field of unmanned aerial vehicle cooperation, and in particular to a method for cooperative trajectory planning of multiple unmanned aerial vehicles based on an improved GWO algorithm. Background Art

[0002] With the complexity of today's wars, cooperative operations of unmanned aerial vehicle formations have been favored by various countries. In cooperative operations, cooperative trajectory planning technology for unmanned aerial vehicle formations has become a key research direction. Trajectory planning refers to the process of planning a feasible flight trajectory from the starting point to the target point at the lowest cost based on cooperative situational awareness of combat environment information, on the basis of the cooperative target allocation plan of multiple unmanned combat aircraft, taking into account the cooperative constraints between unmanned aerial vehicles and trajectory planning constraints, so that each unmanned combat aircraft can complete the target strike or identification mission and improve the overall survivability and combat effectiveness of multiple unmanned combat aircraft.

[0003] The current research on multi-unmanned aerial vehicle trajectory planning is still in the exploratory stage, mainly studying the collaborative relationship between the members within the unmanned aerial vehicle formation. Tang Song proposed a single-parent genetic algorithm model to solve the problem of large scale and low efficiency of multi-unmanned aerial vehicle collaborative trajectory planning; Wei Ming optimized the collaborative trajectory planning of unmanned aerial vehicles based on the joint use of deep reinforcement learning and A* algorithm; Tang Miao improved the particle swarm algorithm, added the idea of ​​extreme value variation, and introduced the alpha wolf call and survival of the fittest mechanism, thereby improving the algorithm's optimization performance; Sui Dong proposed an enhanced multi-strategy dung beetle algorithm UAV trajectory planning method to solve the three-dimensional trajectory planning problem. In summary, when solving the problem of collaborative trajectory planning of unmanned aerial vehicle formations, the algorithm used is prone to cause the function to fall into a local optimum, resulting in poor stability of the result. Therefore, the present invention uses the gray wolf optimization algorithm to solve this problem.

[0004] The Gray Wolf Optimization (GWO) algorithm is a meta-heuristic algorithm proposed by Mirjalili, which imitates the leadership hierarchy and hunting mechanism of gray wolves in nature. The GWO algorithm has the advantages of simple structure, few parameters to be adjusted, strong stability, and good ability to avoid falling into local optimum. The existing GWO model has been widely used in the planning field, but the existing GWO algorithm is relatively simple, and the initial solution has a great influence on the optimization result. Therefore, the present invention proposes to perform multi-unmanned aerial vehicle collaborative trajectory planning based on the improved GWO algorithm. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-unmanned aerial vehicle collaborative trajectory planning method based on an improved GWO algorithm. The task of a group of unmanned aerial vehicles crossing a dangerous area and collaboratively reaching a designated target location is taken as the background. The unmanned aerial vehicle routes are optimized while minimizing the loss. The improved gray wolf optimization algorithm is used to perform trajectory planning for the unmanned aerial vehicle group under multiple constraints. The effectiveness of the improved gray wolf algorithm is verified through simulation experiments, and this algorithm is effectively compared with the MP-GWO and GWO algorithms. The results show that the algorithm of the present invention has a better effect.

[0006] To achieve the above object, the present invention provides a multi-unmanned aerial vehicle collaborative trajectory planning method based on an improved GWO algorithm, 1. The multi-unmanned aerial vehicle collaborative trajectory planning method based on the improved GWO algorithm is characterized by comprising the following steps:

[0007] S1. Unmanned aerial vehicle group constraint analysis, wherein the constraints include range constraint, flight spacing constraint, flight altitude constraint and time constraint;

[0008] S2. Unmanned aerial vehicle track cost analysis, wherein the track cost includes fuel consumption cost, flight altitude cost, dangerous area cost, collision cost and time cost;

[0009] S3, GWO algorithm and its improvement, and generate the initial wolf pack based on greedy thinking and mutation strategy;

[0010] S4. Conduct simulation experiments and algorithm performance analysis.

[0011] Preferably, step S1 specifically includes the following steps:

[0012] S11. Range constraints:

[0013] Assume that the flight distance of each segment of the UAV is l i , the longest range that can ensure safe return is L max , the total flight segment is n, therefore, the range of the UAV shall not be greater than the maximum safe distance, that is:

[0014]

[0015] S12. Flight spacing constraints:

[0016] The minimum distance between UAVs shall not be less than the minimum safe flight distance. If it is less than the minimum safe distance, it will be regarded as a UAV collision, that is:

[0017] d ij ≥d s (2)

[0018] In the above formula: d ijis the minimum distance between the track points of the i-th UAV and the j-th UAV; d s The minimum safe flying distance between unmanned aerial vehicles is considered as stipulated;

[0019] S13. Flight altitude constraints:

[0020] Assume that the maximum flight altitude of the UAV is H max , the minimum is H min , so the flight altitude constraint is:

[0021] H min ≤H i ≤H max (3);

[0022] S14. Time constraints:

[0023] The UAV needs to reach the target within a specified time. Assume that the task needs to be completed within t max The time constraint is:

[0024] t i ≤t max (4).

[0025] Preferably, in step S2, the track cost, also called fitness, includes fuel consumption cost, flight altitude cost, collision cost and danger zone cost; the track cost calculation formula for a single unmanned aerial vehicle is as follows:

[0026] Total cost of fuel consumption:

[0027] Total cost of flight altitude:

[0028] Total cost of hazardous area:

[0029] Total collision cost:

[0030] Total time cost:

[0031] Total cost per machine:

[0032]

[0033] In the above formula: h i is the altitude of the ith track; f O represents the fuel cost function related to the track length; f H represents the flight altitude cost function related to the flight altitude; f D A danger cost function representing the danger level of the voyage; The collision cost function representing the number of collisions between the i-th segment of the UAV’s trajectory; Represents the time cost function related to the flight time of the i-th segment of the UAV track; represents the total fuel cost of the jth aircraft; represents the total cost of the flight altitude of the jth aircraft; represents the total cost of the dangerous area for the jth aircraft; represents the total collision cost of the jth aircraft; represents the total time cost of the j-th aircraft; ω1, ω2, ω3, ω4, ω5 are weighted coefficients, ω1+ω2+ω3+ω4+ω5=1;

[0034] The calculation formula of the track cost of multiple unmanned aerial vehicles is:

[0035]

[0036] In the above formula: N is the number of unmanned aerial vehicles; ω1, ω2, ω3, ω4, ω5 are the weights of each cost;

[0037] The speed of the UAV in flight is expressed as the average speed of the total voyage, so the fuel cost function fO of a single aircraft is expressed as a fixed proportion of the flight distance, that is:

[0038]

[0039] In the above formula: ρ is the fuel consumption per kilometer, k is the waypoint, x k ,y k , z k are the horizontal, vertical and vertical coordinates of the kth waypoint respectively;

[0040] If the drone flies too high or too low, it will pass f H The function increases the cost, namely:

[0041]

[0042] In the above formula: a1, a2 are the increase factors;

[0043] If the UAV passes through the danger zone, it will pass through the f D The function increases the risk cost, namely:

[0044]

[0045] In the above formula: dgr j is the danger level of the danger zone; M xj , M yj is the center coordinate of the jth dangerous area. If dgr jIf it is smaller than the radius of the danger zone, it means that the UAV has flown into the danger zone;

[0046] If a UAV collides, it will pass through f E The function increases the cost, namely:

[0047]

[0048] If the UAV takes too long to reach the target, it will pass f T The function increases the cost, namely:

[0049]

[0050] Preferably, in step S3, the GWO algorithm optimizes the search target by simulating the hierarchical structure and hunting behavior of the gray wolf population, and uses four types of gray wolves, α, β, δ and ω, to simulate social hierarchical relationships;

[0051] Specific:

[0052] The GWO algorithm first randomly generates a population of gray wolves in the search space;

[0053] The solutions with the best, second best, and third best fitness values ​​are considered as α wolf, β wolf, and δ wolf, respectively, while the remaining solutions are considered as ω wolf;

[0054] Then the alpha wolf, beta wolf and delta wolf will be responsible for leading the hunt, and the omega wolf will follow the first three types of wolves;

[0055] When a gray wolf searches for prey, it gradually approaches the prey. The mathematical model of this behavior is as follows:

[0056] D=|C*X p (t)-X(t)| (19)

[0057] X(t+1)=X p (t)-A*D (20)

[0058] A=2a*r1-a (21)

[0059] C=2r2 (22)

[0060] In the above formula: t is the current iteration number; A and C are the synergy coefficient vectors; X p (t) represents the position vector of the prey; X(t) is the current position vector of the gray wolf; a decreases linearly from 2 to 0 during the entire bagging process; r1 and r2 are random vectors in [0, 1];

[0061] The gray wolf can identify the potential location of the prey. The hunting is guided by the α wolf, but the gray wolf does not know the exact location of the prey. In order to simulate the hunting behavior of the gray wolf, it is assumed that the α wolf, the β wolf and the δ wolf have more information about the potential location of the prey. Therefore, in each iteration, the three optimal solutions obtained so far are recorded, forcing the ω wolf to update its position according to the following formula:

[0062]

[0063] Where X α , X β , X δ represents the position vector of α wolf, β wolf and δ wolf in the current iteration, C1, C2, C3 are random vectors, D α , D β , D δ represents the distance between other individuals and wolf α, wolf β, and wolf δ, and X(t+1) is the updated position vector;

[0064] After generating a new group, the boundary of the group elements is controlled and a round of iteration is completed; the above steps are repeated until the termination condition of the algorithm is met, that is, the preset maximum number of iterations is reached, and then the best solution is output;

[0065] The function model of fitness value is:

[0066]

[0067] The process of cluster analysis is:

[0068] First, select k = 5 initial cluster centers; then calculate the distance between each data point and each cluster center using formula (27), and assign each data point to the nearest cluster center; secondly, recalculate the center of each cluster using formula (28); finally, iterate until the maximum number of iterations is reached.

[0069]

[0070] In the above formula, x is the data point, c is i is the i-th cluster center, d is the dimension of the data, x j and c ij They are x, c i The value in the jth dimension.

[0071]

[0072] In the above formula, S i is the set of data points of the ith cluster, |S i | is the number of data points in the set.

[0073] Preferably, the GWO algorithm is improved, specifically comprising the following steps:

[0074] S31, setting the size of the gray wolf population and the maximum number of iteration steps, generating the initial wolf group by adopting a greedy idea and introducing a mutation strategy, and initializing the parameters a, α wolf, β wolf and δ wolf;

[0075] S32, performing K-means clustering on all track populations;

[0076] S33, calculating the fitness value of each individual gray wolf in the subpopulation according to formula (26);

[0077] S34, comparing the best fitness value in each sub-population with the fitness values ​​of wolf α, wolf β and wolf δ, screening out the best solution α, optimal solution β and suboptimal solution δ of each sub-population during the current iteration, and recording their corresponding waypoint positions;

[0078] S35, each individual gray wolf in the subpopulation updates its position according to formula (25);

[0079] S36. Calculate a, A and C of three optimal solutions of each subpopulation according to formula (21) and formula (22);

[0080] S37. When the preset maximum number of iterations is reached, the best cooperative track and the corresponding optimal fitness value are output; otherwise, the process returns to step S32.

[0081] Therefore, the present invention adopts the above-mentioned multi-unmanned aerial vehicle collaborative trajectory planning method based on the improved GWO algorithm, and the beneficial effects are as follows:

[0082] (1) Aiming at the situation that the initialization effect of the GWO algorithm is poor, the present invention uses a greedy algorithm and a mutation strategy to reduce the fitness value of the unmanned aerial vehicle during track initialization.

[0083] (2) The present invention introduces the K-means clustering method, which divides the UAV tracks into multiple sub-populations and allows each sub-population to be optimized separately. This method can find solutions in different areas of the search solution space. As the iteration proceeds, information exchange and migration between individuals in different populations are allowed to enhance the global search capability and avoid falling into the local optimal solution.

[0084] (3) By comparing the improved GWO, MP-GWO and GWO algorithms, the results show that the track calculated by the improved GWO algorithm proposed in the present invention has a smaller track cost and higher convergence accuracy than those of the other two algorithms.

[0085] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is the unmanned aerial vehicle group trajectory simulation result of the improved GWO algorithm of the embodiment of the multi-unmanned aerial vehicle collaborative trajectory planning method based on the improved GWO algorithm of the present invention;

[0087] Figure 2 is a fitness curve of an improved GWO algorithm in an embodiment of a method for collaborative trajectory planning of multiple unmanned aerial vehicles based on an improved GWO algorithm of the present invention;

[0088] Figure 3 is the fitness curve of the MP-GWO algorithm of the embodiment of the method for collaborative trajectory planning of multiple unmanned aerial vehicles based on the improved GWO algorithm of the present invention;

[0089] Figure 4 It is the fitness curve of the GWO algorithm of the embodiment of the multi-unmanned aerial vehicle collaborative trajectory planning method based on the improved GWO algorithm of the present invention. DETAILED DESCRIPTION

[0090] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0091] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0092] The multi-UAV collaborative trajectory planning method based on the improved GWO algorithm includes the following steps:

[0093] Problem description and assumptions:

[0094] Assume that there is a three-dimensional environment of a×b×c as the battlefield. Each aircraft in the UAV group has an attack target. The set of UAV groups is U = {U i ,i=1,2,...,N},T={T i , i = 1, 2, ..., N} is the target set corresponding to the UAV, M = {M j , j = 1, 2, ..., N} is a set of dangerous areas, and each dangerous area is spherical in the three-dimensional coordinate system.

[0095] For each unmanned aerial vehicle, the track from the starting point to the target point is composed of a series of track points connected in sequence, and the distance between two adjacent track points is a segment l. i . Assume a single unmanned aerial vehicle U i The total flight distance is L i , the speed is v i , the flight altitude is H i , the flight time is t i The flight starting point is S i, the target point is G i , the track point is T i-k , (k=1,2,...,n-1), so U i The trajectory can be expressed as Where F(q) is the constraint condition and q is the constraint parameter.

[0096] S1. Unmanned aerial vehicle group constraint analysis, specifically including the following steps:

[0097] S11. Range constraints:

[0098] The UAV has a maximum range. Assume that the flight distance of each segment of the UAV is l i , the longest range that can ensure safe return is L max , the total flight segment is n, therefore, the range of the UAV shall not be greater than the maximum safe distance, that is:

[0099]

[0100] S12. Flight spacing constraints:

[0101] The flight spacing constraint means that there is no collision between UAVs. Therefore, the minimum distance between UAVs must not be less than the minimum safe flight distance. If it is less than the minimum safe distance, it is considered a UAV collision, that is:

[0102] d ij ≥d s (2)

[0103] In the above formula: d ij is the minimum distance between the track points of the i-th UAV and the j-th UAV; d s The minimum safe flying distance between unmanned aerial vehicles is considered to be specified.

[0104] S13. Flight altitude constraints:

[0105] If the UAV flies too low, it is easy to be hit by ground targets and may crash into the hillside. If it flies too high, the cost of a single flight will increase. Therefore, the flight altitude needs to be constrained within a certain range. Assume that the maximum flight altitude of the UAV is H max , the minimum is H min , so the flight altitude constraint is:

[0106] H min ≤H i ≤H max (3).

[0107] S14. Time constraints:

[0108] The UAV needs to reach the target within a specified time. Assume that the task needs to be completed within t max The time constraint is:

[0109] t i ≤t max (4).

[0110] S2, Unmanned aerial vehicle trajectory cost analysis;

[0111] The quality of the UAV track is judged by a variety of indicators. The track cost, also known as fitness, mainly includes fuel consumption cost, flight altitude cost, collision cost and danger zone cost. The calculation formula of the track cost of a single UAV is as follows (in this embodiment, only the cost of the UAV attacking the target is considered, and the cost of the return flight after the attack is completed is not considered for the time being):

[0112] Total cost of fuel consumption:

[0113] Total cost of flight altitude:

[0114] Total cost of hazardous area:

[0115] Total collision cost:

[0116] Total time cost:

[0117] Total cost per machine:

[0118]

[0119] In the above formula: h i is the altitude of the ith track; f O represents the fuel cost function related to the track length; f H represents the flight altitude cost function related to the flight altitude; f D A danger cost function representing the danger level of the voyage; The collision cost function representing the number of collisions between the i-th segment of the UAV’s trajectory; Represents the time cost function related to the flight time of the i-th segment of the UAV track; represents the total fuel cost of the jth aircraft; represents the total cost of the flight altitude of the jth aircraft; represents the total cost of the dangerous area for the jth aircraft; represents the total collision cost of the jth aircraft; represents the total time cost of the j-th aircraft; ω1, ω2, ω3, ω4, ω5 are weighted coefficients, ω1+ω2+ω3+ω4+ω5=1.

[0120] The calculation formula for the track cost of multiple unmanned aerial vehicles forming a formation is to add the single-machine costs of all unmanned aerial vehicles according to a certain weight. The calculation formula for the track cost of multiple unmanned aerial vehicles is:

[0121]

[0122] In the above formula: N is the number of unmanned aerial vehicles; ω1, ω2, ω3, ω4, ω5 are the weights of each cost;

[0123] The speed of the UAV in flight is expressed as the average speed of the total flight distance, so the fuel cost function fO of a single aircraft can be expressed as a fixed proportion of the flight distance, that is:

[0124]

[0125] In the above formula: ρ is the fuel consumption per kilometer, k is the waypoint, x k ,y k , z k are the horizontal, vertical and vertical coordinates of the kth waypoint respectively;

[0126] If the drone flies too high or too low, it will pass f H The function increases the cost, namely:

[0127]

[0128] In the above formula: a1, a2 are the increase factors;

[0129] If the UAV passes through the danger zone, it will pass through the f D The function increases the risk cost, namely:

[0130]

[0131] In the above formula: dgr j is the danger level of the danger zone; M xj , M yj is the center coordinate of the jth dangerous area. If dgr j If it is smaller than the radius of the danger zone, it means that the UAV has flown into the danger zone;

[0132] If a UAV collides, it will pass through f E The function increases the cost, namely:

[0133]

[0134] If the UAV takes too long to reach the target, it will pass f T The function increases the cost, namely:

[0135]

[0136] S3, GWO algorithm and improvements;

[0137] GWO Algorithm

[0138] The GWO algorithm optimizes the search target by simulating the hierarchical structure and hunting behavior of the gray wolf population, and uses four types of gray wolves, namely α, β, δ, and ω, to simulate social hierarchical relationships;

[0139] Specific:

[0140] The GWO algorithm first randomly generates a population of gray wolves in the search space;

[0141] To construct the social hierarchy model of gray wolves, the solutions with the best, second-best, and third-best fitness values ​​were considered as α-wolves, β-wolves, and δ-wolves, respectively, while the remaining solutions were considered as ω-wolves;

[0142] Then the alpha wolf, beta wolf and delta wolf will be responsible for leading the hunt, and the omega wolf will follow the first three types of wolves;

[0143] When a gray wolf searches for prey, it gradually approaches the prey. The mathematical model of this behavior is as follows:

[0144] D=|C*X p (t)-X(t)| (19)

[0145] X(t+1)=X p (t)-A*D (20)

[0146] A=2a*r1-a (21)

[0147] C=2r2 (22)

[0148] In the above formula: t is the current iteration number; A and C are the synergy coefficient vectors; X p (t) represents the position vector of the prey; X(t) is the current position vector of the gray wolf; a decreases linearly from 2 to 0 during the entire bag-sticking process; r1 and r2 are random vectors in [0, 1].

[0149] The gray wolf can identify the potential location of the prey. The hunting is guided by the α wolf, but the gray wolf does not know the exact location of the prey. In order to simulate the hunting behavior of the gray wolf, it is assumed that the α wolf, the β wolf and the δ wolf have more information about the potential location of the prey. Therefore, in each iteration, the three optimal solutions obtained so far are recorded, forcing the ω wolf to update its position according to the following formula:

[0150]

[0151] Where X α , X β , X δ represents the position vector of α wolf, β wolf and δ wolf in the current iteration, C1, C2, C3 are random vectors, D α , D β , D δ represents the distance between other individuals and wolf α, wolf β, and wolf δ, and X(t+1) is the updated position vector.

[0152] After generating a new group, the boundaries of the group elements are controlled and a round of iteration is completed; the above steps are repeated until the termination condition of the algorithm is met, that is, the pre-set maximum number of iterations is reached, and then the best solution is output.

[0153] The function model of fitness value is:

[0154]

[0155] The process of cluster analysis is:

[0156] First, select k = 5 initial cluster centers; then calculate the distance between each data point and each cluster center using formula (27), and assign each data point to the nearest cluster center; secondly, recalculate the center of each cluster using formula (28); finally, iterate until the maximum number of iterations is reached.

[0157]

[0158] In the above formula, x is the data point, c is i is the i-th cluster center, d is the dimension of the data, x j and c ij They are x, c i The value in the jth dimension.

[0159]

[0160] In the above formula, S i is the set of data points of the ith cluster, |S i | is the number of data points in the set.

[0161] In the collaborative trajectory planning of three-dimensional unmanned aerial vehicles, the Gray Wolf Optimization Algorithm has some shortcomings: when the Gray Wolf Optimization Algorithm randomly initializes individuals, the generated initial points are disordered, resulting in low individual fitness; when there are too many indicators, it is easy to fall into local optimality.

[0162] In view of the shortcomings of the GWO algorithm, the present invention makes the following improvements to the GWO algorithm:

[0163] The use of a greedy initialization method can help improve the fitness of a single machine. Specifically, to ensure that the distribution of individual waypoints roughly matches the direction of the track, the point selection range of a single machine is limited to the range with the previous waypoint coordinates as the lower bound and the target coordinates as the upper bound. However, this initialization method will reduce the diversity of the group, so the mutation strategy is introduced. When the group is initialized, each individual will choose the initialization method based on whether the mutation parameter m is less than the threshold to decide whether to use a greedy algorithm or a random initialization method.

[0164] The initialization method based on greedy thinking is:

[0165] x i+1 ~U(x i , e x ) (29)

[0166] y i+1 ~U(y i , e y ) (30)

[0167] In the above formula, x i , x i+1 is the horizontal coordinate of two adjacent waypoints in an individual, y i ,y i+1 is the ordinate of two adjacent waypoints in an individual, e x , e y are the horizontal and vertical coordinates of the target point coordinates; U is the function of limiting the waypoint coordinates.

[0168] For collaborative trajectory planning, K-means clustering analysis can be performed on the UAV trajectory:

[0169] Firstly, the movement tracks of the UAV formation at the same time are regarded as an individual track, thus forming a track population;

[0170] Secondly, the evaluation index is applied to the track population. By evaluating the performance of each track individual separately, the advantages and disadvantages of each individual can be fully understood from multiple perspectives.

[0171] Thirdly, the track population is divided into several sub-populations, which usually contain track individuals that perform relatively well on certain evaluation indicators;

[0172] Finally, the individuals with the best performance under multiple evaluation indicators are further screened out from the sub-population.

[0173] This method can find solutions in different areas of the search solution space. As the iteration proceeds, information exchange and migration between individuals in different populations are allowed to enhance the global search capability and avoid falling into the local optimal solution.

[0174] The K-means cluster analysis method is to improve the GWO algorithm, which specifically includes the following steps:

[0175] S31, setting the size of the gray wolf population and the maximum number of iteration steps, generating the initial wolf group by adopting a greedy idea and introducing a mutation strategy, and initializing the parameters a, α wolf, β wolf and δ wolf;

[0176] S32, performing K-means clustering on all track populations;

[0177] S33, calculating the fitness value of each individual gray wolf in the subpopulation according to formula (26);

[0178] S34, comparing the best fitness value in each sub-population with the fitness values ​​of wolf α, wolf β and wolf δ, screening out the best solution α, optimal solution β and suboptimal solution δ of each sub-population during the current iteration, and recording their corresponding waypoint positions;

[0179] S35, each individual gray wolf in the subpopulation updates its position according to formula (25);

[0180] S36. Calculate a, A and C of three optimal solutions of each subpopulation according to formula (21) and formula (22);

[0181] S37. When the preset maximum number of iterations is reached, the best cooperative track and the corresponding optimal fitness value are output; otherwise, the process returns to step S32.

[0182] S4. Conduct simulation experiments and algorithm performance analysis.

[0183] 1. Simulation environment settings

[0184] The present invention uses MATLAB to perform algorithm simulation. Assume that a UAV formation consisting of 5 UAVs attacks 5 targets. The starting coordinates of the UAVs and the coordinates of the targets are shown in Table 1. A total of 13 danger zones are set, including radar scanning zones, missile zones, ground artillery zones, weather impact zones, etc. Assuming the number of iterations is 50, the maximum range of the UAV is L max is 1.5 times the starting distance, and the flight speed is v i is [0.3Ma, 0.7Ma], and the flight altitude is H i The range is [0.02km, 20km], and the safety distance d between each unmanned aerial vehicle s The cost formula of cooperative trajectory of unmanned aerial vehicle formation is 0.5km. The fuel cost ω1=0.1, the flight altitude cost ω2=0.1, the dangerous area cost ω3=0.2, the collision cost ω4=0.4, and the time cost ω5=0.2. Meanwhile, compared with MP-GWO, the parameter settings of GWO algorithm are the same as those of the present invention, which is convenient for reference comparison between algorithms.

[0185] Table 1 Coordinates of UAV and attack targets

[0186] Unmanned aerial vehicle coordinates Target coordinates (1.5，1.5，15) (20，20，4) (0，1.5，15) (16，20，5) (1.5，0，15) (20，16，5) (0，3，15) (18，20，4.5) (3，0，15) (20，18，4.5)

[0187] 2. Experimental Analysis (Analysis of Algorithm Effectiveness)

[0188] like Figure 1 As shown, the improved GWO algorithm is experimented. Figure 1 The dark area in the figure indicates the radar danger zone, and the rest are missile, ground-based air defense artillery, weather and other danger zones. It can be seen that all five unmanned aerial vehicles can reach the target area.

[0189] Figure 2 The curve of the fitness function as the number of iterations increases is shown. It can be seen from the figure that as the number of iterations increases, the fitness gradually decreases and eventually tends to a constant value, that is, the cost of the unmanned aerial vehicle track becomes smaller, indicating that the optimal route has been found, verifying the effectiveness of the algorithm of the present invention.

[0190] Table 2 shows the flight speed, flight distance, number of collisions and other parameters of each UAV. It can be seen that all parameters are within the normal range, indicating that the damage degree of the UAV is very low.

[0191] Table 2 Parameters of unmanned aerial vehicle

[0192]

[0193] 3. Algorithm Comparison and Analysis

[0194] The improved GWO algorithm was simulated with the MP-GWO and GWO algorithms, and the algorithm running time, fitness convergence value, number of iterations to reach the optimal convergence value and number of flight collisions were compared. Table 3 shows the simulation results of each algorithm running 20 times.

[0195] Table 3 Comparison of simulation results of three algorithms

[0196] algorithm Run time Fitness convergence value Iterations Flight collision times Improved GWO 77s 28.78 44 0 MP-GWO 74s 30.07 40 0 GWO 72s 31.79 39 0

[0197] From Table 3, we can see that the improved GWO algorithm can achieve the optimal fitness value, and the convergence accuracy is better than that of the MP-GWO and GWO algorithms. At the same time, we can see that the running time of the improved GWO algorithm is long because the improved GWO algorithm optimizes more steps and requires more time to run. The high number of iterations to reach the optimal value is because more iterations are used to obtain a more accurate convergence value. The optimization effect of the MP-GWO algorithm is also better than that of the GWO algorithm.

[0198] pass Figure 2 and Figure 3 , Figure 4 From the comparison, it can be seen that the improved GWO algorithm has a faster convergence speed and higher convergence accuracy. In addition, due to the use of the greedy algorithm for track initialization, the fitness of the improved GWO algorithm in the initial iteration is much smaller than that of the other two algorithms, indicating the advantage of using the greedy algorithm for initialization.

[0199] In summary, the present invention constructs a new type of multi-unmanned aerial vehicle trajectory planning method by improving the GWO algorithm. The initial unmanned aerial vehicle group trajectory points are generated by greedy thinking and introducing mutation strategies. The unmanned aerial vehicle trajectories are then divided into multiple sub-populations and clustered. The fitness value of each individual in the sub-population is calculated, and the optimal fitness value of the sub-population is found. The optimal fitness value of the sub-population is compared with the α wolf, β wolf and δ wolf to screen out the optimal solution, the best solution and the suboptimal solution. Then the positions of the sub-population individuals are updated. When the pre-set maximum number of iterations is reached, the best collaborative trajectory and the corresponding optimal fitness value are output, otherwise the iteration continues. The application of this method in the collaborative trajectory planning of unmanned aerial vehicles can attack combat targets at a lower cost, which is beneficial to improving combat efficiency.

[0200] The present invention conducts effectiveness and comparative test analysis on the improved GWO algorithm. The results show that in terms of effectiveness, this method can find the optimal route at the lowest cost, and the damage degree of the unmanned aerial vehicle is very low. In terms of comparative analysis, the fitness convergence accuracy of the improved GWO algorithm is 28.78, which is much smaller than 30.07 and 31.79 of the MP-GWO and GWO algorithms; however, the running time of the improved GWO algorithm is longer than that of the other two algorithms, because the improved GWO algorithm optimizes more steps and requires more time to run. The research results are of certain significance for the expansion of the application of the GWO algorithm and the coordinated development of multi-unmanned aerial vehicle collaborative trajectory planning technology.

[0201] Therefore, the present invention adopts the above-mentioned multi-unmanned aerial vehicle collaborative trajectory planning method based on the improved GWO algorithm. Aiming at the situation that the initialization effect of the GWO algorithm is poor, the greedy algorithm and mutation strategy are used to reduce the fitness value of the unmanned aerial vehicle during trajectory initialization; at the same time, the K-means clustering analysis method is introduced to enhance the global search capability and avoid falling into the local optimal solution; the trajectory calculated by the improved GWO algorithm is compared with the other two algorithms. The trajectory cost of the method proposed in the present invention is smaller and the convergence accuracy is higher. The research results have certain significance for the expansion of the application of the GWO algorithm and the coordinated development of multi-unmanned aerial vehicle collaborative trajectory planning technology.

[0202] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-unmanned aerial vehicle collaborative trajectory planning method based on an improved GWO algorithm, characterized in that: The following steps are involved: S1. Unmanned aerial vehicle group constraint analysis, wherein the constraints include range constraint, flight spacing constraint, flight altitude constraint and time constraint; S2. Unmanned aerial vehicle track cost analysis, wherein the track cost includes fuel consumption cost, flight altitude cost, dangerous area cost, collision cost and time cost; S3, GWO algorithm and its improvement, and generate the initial wolf pack based on greedy thinking and mutation strategy; S4. Conduct simulation experiments and algorithm performance analysis.

2. The method for collaborative trajectory planning of multiple unmanned aerial vehicles based on the improved GWO algorithm according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S11. Range constraints: Assume that the flight distance of each segment of the UAV is l i , the longest range that can ensure safe return is L max , the total flight segment is n, therefore, the range of the UAV shall not be greater than the maximum safe distance, that is: S12. Flight spacing constraints: The minimum distance between UAVs shall not be less than the minimum safe flight distance. If it is less than the minimum safe distance, it will be regarded as a UAV collision, that is: d ij ≥d s (2) In the above formula: d ij is the minimum distance between the track points of the i-th UAV and the j-th UAV; d s The minimum safe flying distance between unmanned aerial vehicles is considered as stipulated; S13. Flight altitude constraints: Assume that the maximum flight altitude of the UAV is H max , the minimum is H min , so the flight altitude constraint is: H min ≤H i ≤H max (3); S14. Time constraints: The UAV needs to reach the target within a specified time. Assume that the task needs to be completed within t max The time constraint is: t i ≤t max (4)。 3. The method for collaborative trajectory planning of multiple unmanned aerial vehicles based on the improved GWO algorithm according to claim 2 is characterized in that: In step S2, the track cost, also called fitness, includes fuel consumption cost, flight altitude cost, collision cost and dangerous area cost; the track cost calculation formula for a single unmanned aerial vehicle is as follows: Total cost of fuel consumption: Total cost of flight altitude: Total cost of hazardous area: Total collision cost: Total time cost: Total cost per machine: In the above formula: h i is the altitude of the ith track; f O represents the fuel cost function related to the flight track length; fH represents the flight altitude cost function related to the flight altitude; fD represents the danger cost function related to the flight danger level; The collision cost function representing the number of collisions between the i-th segment of the UAV’s trajectory; Represents the time cost function related to the flight time of the i-th segment of the UAV track; represents the total fuel cost of the jth aircraft; represents the total cost of the flight altitude of the jth aircraft; represents the total cost of the dangerous area for the jth aircraft; represents the total collision cost of the jth aircraft; represents the total time cost of the j-th aircraft; ω1, ω2, ω3, ω4, ω5 are weighted coefficients, ω1+ω2+ω3+ω4+ω5=1; The calculation formula of the track cost of multiple unmanned aerial vehicles is: In the above formula: N is the number of unmanned aerial vehicles; ω1, ω2, ω3, ω4, ω5 are the weights of each cost; The speed of the UAV in flight is expressed as the average speed of the total flight distance, so the fuel cost function f of a single aircraft is O Expressed as a fixed ratio of flight distance, namely: In the above formula: ρ is the fuel consumption per kilometer, k is the waypoint, x k ,y k , z k are the horizontal, vertical and vertical coordinates of the kth waypoint respectively; If the UAV flies too high or too low, the cost will be increased through the fH function, that is: In the above formula: a1, a2 are the increase factors; If the UAV passes through the danger zone, it will pass through the f D The function increases the risk cost, namely: In the above formula: dgr j is the danger level of the danger zone; M xj , M yj is the center coordinate of the jth dangerous area. If dgr j If it is smaller than the radius of the danger zone, it means that the UAV has flown into the danger zone; If the UAV collides, the cost will be increased through the fE function, that is: If the UAV takes too long to reach the target, the cost will be increased through the fT function, that is:

4. The method for collaborative trajectory planning of multiple unmanned aerial vehicles based on the improved GWO algorithm according to claim 3 is characterized in that: In step S3, the GWO algorithm optimizes the search target by simulating the hierarchical structure and hunting behavior of the gray wolf population, and uses four types of gray wolves, α, β, δ and ω, to simulate social hierarchical relationships; Specific: The GWO algorithm first randomly generates a population of gray wolves in the search space; The solutions with the best, second best, and third best fitness values ​​are considered as α wolf, β wolf, and δ wolf, respectively, while the remaining solutions are considered as ω wolf; Then the alpha wolf, beta wolf and delta wolf will be responsible for leading the hunt, and the omega wolf will follow the first three types of wolves; When a gray wolf searches for prey, it gradually approaches the prey. The mathematical model of this behavior is as follows: D=|C*X p (t)-X(t)| (19) X(t+1)=X p (t)-A*D (20) A=2a*r1-a (21) C＝2r2 (22) In the above formula: t is the current iteration number; A and C are the synergy coefficient vectors; X p (t) represents the position vector of the prey; X(t) is the current position vector of the gray wolf; a decreases linearly from 2 to 0 during the entire bagging process; r1 and r2 are random vectors in [0, 1]; The gray wolf can identify the potential location of the prey. The hunting is guided by the α wolf, but the gray wolf does not know the exact location of the prey. In order to simulate the hunting behavior of the gray wolf, it is assumed that the α wolf, the β wolf and the δ wolf have more information about the potential location of the prey. Therefore, in each iteration, the three optimal solutions obtained so far are recorded, forcing the ω wolf to update its position according to the following formula: Where X α , X β , X δ represents the position vector of α wolf, β wolf and δ wolf in the current iteration, C1, C2, C3 are random vectors, D α , D β , D δ represents the distance between other individuals and wolf α, wolf β, and wolf δ, and X(t+1) is the updated position vector; After generating a new group, the boundary of the group elements is controlled and a round of iteration is completed; the above steps are repeated until the termination condition of the algorithm is met, that is, the preset maximum number of iterations is reached, and then the best solution is output; The function model of fitness value is: The process of cluster analysis is: First, select k = 5 initial cluster centers; then calculate the distance between each data point and each cluster center using formula (27), and assign each data point to the nearest cluster center; secondly, recalculate the center of each cluster using formula (28); finally, iterate until the maximum number of iterations is reached. In the above formula, x is the data point, c is i is the i-th cluster center, d is the dimension of the data, x j and c ij They are x, c i The value in the jth dimension. In the above formula, S i is the set of data points of the ith cluster, |S i | is the number of data points in the set.

5. The method for collaborative trajectory planning of multiple unmanned aerial vehicles based on the improved GWO algorithm according to claim 4 is characterized in that: The GWO algorithm is improved, specifically including the following steps: S31, setting the size of the gray wolf population and the maximum number of iteration steps, generating the initial wolf group by adopting a greedy idea and introducing a mutation strategy, and initializing the parameters a, α wolf, β wolf and δ wolf; S32, performing K-means clustering on all track populations; S33, calculating the fitness value of each individual gray wolf in the subpopulation according to formula (26); S34, comparing the best fitness value in each sub-population with the fitness values ​​of wolf α, wolf β and wolf δ, screening out the best solution α, optimal solution β and suboptimal solution δ of each sub-population during the current iteration, and recording their corresponding waypoint positions; S35, each individual gray wolf in the subpopulation updates its position according to formula (25); S36. Calculate a, A and C of three optimal solutions of each subpopulation according to formula (21) and formula (22); S37. When the preset maximum number of iterations is reached, the best cooperative track and the corresponding optimal fitness value are output; otherwise, the process returns to step S32.

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