Unmanned aerial vehicle swarm path planning method based on double population multi-constraint evolution

Abstract

The application discloses a kind of based on double population multi-constraint evolution UAV group path planning method, including determining first population and second population according to UAV path;First combination population and second combination population are obtained after generating offspring based on first population and second population;The number of feasible solutions in first combination population and second combination population is determined in turn, and is updated in combination with contribution value threshold, the path of UAV group is planned, and whether to reach termination condition is judged, if no, continue iteration is returned, if yes, non-dominated solution is exported according to updated first combination population and second combination population.This application is based on population contribution degree, and feasible solution mode is obtained by adaptively selecting suitable constraint calculation mode, can significantly improve solving efficiency and solution quality, and simultaneously enhance the stability and adaptability of algorithm.

Description

Technical Field

[0001] The present invention relates to the field of path planning technology, and more particularly to a method for unmanned aerial vehicle (UAV) swarm path planning based on dual-population multi-constraint evolution. Background Art

[0002] Drones, due to their portability and flexibility, have been widely used in fields such as military reconnaissance, environmental monitoring, and cargo transportation. Path planning is crucial for ensuring the successful execution of these missions. The core of drone path planning lies in effectively and safely guiding drones to their destinations, including avoiding obstacles during flight and ensuring the feasibility and optimization of the path. Furthermore, when planning paths for multiple drones, coordination and collaboration between them is crucial.

[0003] Typically, multi-UAV path planning can be modeled as a constrained multi-objective optimization problem. Objectives in this type of problem might include minimizing total flight time, maximizing coverage, and avoiding obstacles. Constraints that need to be considered include altitude restrictions, no-fly zones, and battery life. When solving a multi-UAV path planning problem, the paths of the multiple UAVs are encoded into a single solution.

[0004] However, existing solutions typically only consider the total constraint value violated when finding a feasible solution, which can lead to the following two situations. In the first case, when a solution consists of three drone paths, only one of the paths is infeasible and has a large total constraint value. Due to its large constraint, this solution will be discarded by the algorithm, but this infeasible path can be easily repaired, making it a feasible solution. In the second case, two paths are infeasible due to multiple constraint violations. Although the total constraint value is small and is retained by the algorithm, it is difficult to repair this solution into a feasible individual due to multiple constraint violations.

[0005] Therefore, if only the total constraint value violated is considered when solving the feasible solution in the multi-UAV path planning problem, it may lead to a slow solution process and the final optimal path may be difficult to meet the actual flight requirements. Summary of the Invention

[0006] In view of this, in order to at least partially solve the above technical problems, the present invention provides a UAV swarm path planning method based on dual-population multi-constraint evolution;

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A UAV swarm path planning method based on dual-population multi-constraint evolution, comprising:

[0009] S1, determine the first population and the second population based on the drone path;

[0010] S2. Generate offspring based on the first population and the second population to obtain a first combined population and a second combined population;

[0011] S3. Determine the number of feasible solutions in the first combined population and the second combined population in turn |S i |, i = 1, 2, combined with the contribution value threshold ∈ N, path planning is performed for the drone group, where ∈ is the contribution rate and N represents the number of individuals in each population. The update steps include:

[0012] When |S i When |≤∈·N, the first combined population updates the population based on the overall violation degree, and the second combined population updates the population based on the number of violated constraints;

[0013] When |S i |>∈·N and |S i |<N, the update mode of the first combined population and the second combined population is determined according to the contribution value of the first population and the contribution value of the second population;

[0014] When |S i When |≥N, both the first combined population and the second combined population update their populations according to the non-dominated sorting and Hausdorff distance;

[0015] S4. Determine whether the termination condition is met. If not, return to S2 to continue iteration. If so, output a non-dominated solution based on the updated first combined population and second combined population.

[0016] Preferably, the first population is randomly generated according to the drone path, and the second population is obtained by copying the first population.

[0017] Preferably, in S1, the step of obtaining the drone path includes:

[0018] The three-dimensional environment terrain of the flight area is obtained, the path points are determined based on the three-dimensional environment terrain using B-spline sampling, and the UAV path is constructed through the path points.

[0019] Preferably, in S2, a first offspring generation is generated based on individuals in the first population, and a second offspring generation is generated based on individuals in the second population;

[0020] The first progeny, the second progeny, and the first population are combined to obtain a first combined population, and the first progeny, the second progeny, and the second population are combined to obtain a second combined population.

[0021] Preferably, the step of generating offspring comprises:

[0022] Obtain paired parents based on the first population or the second population, and generate offspring based on the mutation operator;

[0023] When the offspring population violates the boundary condition, the boundary condition is used to repair the violation.

[0024] As a preference, S2 further comprises continuously updating the contribution value Ctr1 of the first population and the contribution value Ctr2 of the second population after obtaining the combined population.

[0025] As a preference, the population is updated based on the total violation degree according to the following rules:

[0026] If both individuals are feasible solutions, the individual with a smaller objective function value dominates the other individual;

[0027] If both individuals are feasible solutions, the individual with a smaller objective function value dominates the other individual;

[0028] If both individuals are infeasible solutions, the individual with a smaller constraint violation value dominates the other individual;

[0029] and the population is updated based on the number of violated constraints according to the following rules:

[0030] If both individuals are feasible solutions, the individual with a smaller objective function value dominates the other individual;

[0031] If both individuals are feasible solutions, the individual with a smaller objective function value dominates the other individual;

[0032] If both individuals are infeasible solutions, the individual with a smaller constraint violation value dominates the other individual.

[0033] As a preference, the objective function comprises a total path length objective function of the UAV and a risk factor objective function, and the constraint function comprises a path height constraint, a safety height constraint, a safety distance constraint, and a turning radius constraint.

[0034] According to the technical solution described above, compared with the prior art, the application provides a UAV group path planning method based on double-population multi-constraint evolution, which is used for adaptively selecting a suitable constraint calculation method according to the contribution degrees of two populations to obtain a feasible solution.

[0035] The application divides the solutions in the multi-UAV path planning problem into two populations of easy-to-repair and difficult-to-repair solutions, and adaptively selects a constraint calculation method to update the population, which significantly improves the solution efficiency and solution quality, and enhances the stability and adaptability of the algorithm, and is suitable for path planning problems in a complex constraint environment.

[0036] Meanwhile, according to the contribution degrees of the populations, a suitable constraint calculation method is adaptively selected to more flexibly process different types of solutions, which neither easily discards the solutions easy to repair nor excessively retains the solutions difficult to repair;

[0037] Furthermore, this application uses B-spline curves to represent the path, ensuring smoothness and continuity of the generated path, meeting the UAV's dynamic constraints. This avoids the sharp turns and discontinuities that can occur with traditional broken-line paths. Compared to other interpolation methods, B-spline curves offer strong local controllability, meaning that moving a control point only affects the nearby curve portion without significantly altering the entire path. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0039] Figure 1 This is a flow chart of the UAV swarm path planning method based on dual-population multi-constraint evolution of the present invention;

[0040] Figure 2 is a schematic diagram of a three-dimensional environment terrain in an embodiment of the present invention;

[0041] Figure 3 This is an example flow chart of the UAV swarm path planning method based on dual-population multi-constraint evolution of the present invention;

[0042] Figure 4 This is a flow chart of the present invention's method for adaptively selecting constraint calculations based on population contribution;

[0043] Figure 5 is a schematic diagram of the objective function for calculating risk factors of the present invention;

[0044] Figure 6 This is a schematic diagram of the optimal UAV swarm planning path set obtained by the present invention;

[0045] Figure 7 This is a comparison chart of the convergence trends of HV (hyper volume matrix) values ​​of the algorithm of the present invention and other algorithms during iteration. DETAILED DESCRIPTION

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0047] The present application aims at the current situation that the existing method cannot effectively deal with the constraint violation of infeasible individuals, and proposes an improved multi-constraint processing technology and a contribution mechanism based on feasible solutions in two populations, and after integration, proposes a multi-UAV path planning method in a three-dimensional scene based on the improved multi-constraint processing technology of double-population evolutionary algorithm. The planning method proposed by the present application can effectively solve the UAV group path planning problem.

[0048] In an embodiment, the UAV group path planning method based on double-population multi-constraint evolution disclosed by the present application has the steps as Figure 1 , comprising:

[0049] S1, determining a first population and a second population according to the UAV path;

[0050] S2, generating offspring based on the first population and the second population to obtain a first combined population and a second combined population;

[0051] S3, determining the number of feasible solutions |S i | in the first combined population and the second combined population in turn, updating in combination with the contribution value threshold ∈·N, and then performing path planning for the UAV group, wherein ∈ is the contribution rate, and N represents the number of individuals in each population,

[0052] S4, judging whether the termination condition is reached, if not, returning to S2 for iteration, and if yes, outputting non-dominated solutions according to the updated first combined population and second combined population.

[0053] In an exemplary embodiment,

[0054] In step S1, the UAV path is obtained by the following method:

[0055] Obtaining the three-dimensional environment terrain of the flight area, determining the path point based on the three-dimensional environment terrain using B-spline sampling, and constructing the UAV path through the path point;

[0056] In this embodiment, a digital elevation model (DEM) of a real environment can be obtained first, and the steps include:

[0057] 1) Find a suitable terrain on Google Earth Engine as the elevation data to be collected, and select a terrain as a sample area;

[0058] 2) Set the sampling accuracy to 25 units;

[0059] 3) Use JavaScript statements to obtain the elevation data at the sample area.

[0060] 4) Import the collected elevation data into software such as QGIS or Matlab for viewing, as shown in the attached Figure 2 ​

[0061] Then, B-spline sampling is used to determine the path points based on the three-dimensional environment terrain, and the UAV path is constructed through the path points. The present invention uses a t-order uniform B-spline curve to represent the multi-UAV path. The control points will be used to generate the uniform B-spline curve. These control points are regarded as the decision variables of the proposed algorithm and are expressed as:

[0062] CN0(x0,y0,z0),CN1(x1,y1,z1),...,CN cs-1 (x cs-1 ,y cs-1 , z cs-1 )

[0063] Where cs-1 represents the number of control points.

[0064] In a B-spline curve, path points are generated by control points, which can be represented as path points:

[0065] PN0(x′0,y′0,z′0), PN1(x′1,y′1,z′1),…,PN pp (x′ pp ,y pp , z pp )

[0066] Where pp represents the number of path points.

[0067] Furthermore, in this application, the path points are determined according to the control points on the B-spline curve using the following formula:

[0068]

[0069] Among them, (x′ j , y′ j , z′ j ) represents the coordinates of the path point, (x j ,y j , z j ) represents the coordinates of the control point, B k，t (·) represents the basis function of the jth segment of the t-order B-spline curve, with the domain being [0, cs+t], ζ n It represents the nth sampling value among the pp equally spaced sampling values ​​in [0, cs+t], where pp represents the number of path points in each path.

[0070] Among them, ζ satisfies the condition: B j，t (·) can be expressed by the following recursive expression:

[0071]

[0072]

[0073] Where w j ∈V={w0,w1,...,w i}, represents the j-th node of the B-spline curve, satisfying:

[0074]

[0075] In one embodiment, after obtaining the drone path, a first population is randomly generated based on the drone path, and a second population is obtained by replicating the first population. Preferably, the first population is randomly generated based on the drone path, and the second population is obtained by replicating the first population.

[0076] Step S2, generating offspring based on the first population and the second population to obtain a first combined population and a second combined population;

[0077] In this embodiment, Figure 3 As shown, first initialize, including:

[0078] 1) Initialize the number of iterations t to 1;

[0079] 2) Initialize the first population The size is N, and the first population is replicated Get the second population

[0080] 3) Setting the contribution rate ∈, which is used to determine the threshold of contribution value in environmental selection;

[0081] 4) Initialize the contribution values ​​of the two populations Ctr1 = 0 and Ctr2 = 0;

[0082] 5) Initialize the archive population The size is N, which is used to save the optimal solution during the evolution process.

[0083] Then perform the operation of selecting the parent and generating the child. The steps include:

[0084] S21. Based on the first population The first offspring of the individual Based on the second population The second generation of individuals In this embodiment, three individuals are selected from the first population and the second population respectively as paired parents to produce offspring, until the number of offspring reaches N / 2. If not, the process is repeated.

[0085] S22. Merge the first offspring, the second offspring, and the first population to obtain a first combined population Right now And merge the first offspring, the second offspring and the second population to obtain the second combined population Right now In this embodiment, an empty population is generated at the same time and Save the individuals of the new generation, size N.

[0086] In S21, the step of generating offspring includes:

[0087] S211. Based on the three paired parents obtained, generate an offspring o using the following mutation operator.

[0088]

[0089]

[0090] Among them, s m and ω are control parameters, representing the mutation rate and distribution index respectively; L i and R i are the lower and upper bounds of the ith decision variable, σ i is the scaling factor of the i-th decision variable, and p is a random number in the interval [0, 1];

[0091] S212. If the offspring population violates the boundary conditions, the following boundary conditions are used for processing:

[0092]

[0093] Where, L i and R i are the lower and upper bounds of the ith decision variable, respectively, o i represents the i-th decision variable of individual o.

[0094] In one embodiment, the dual population update operation is preferentially performed, including:

[0095] After obtaining the first combined population and the second combined population, the contribution value Ctr1 of the first population and the contribution value Ctr2 of the second population are continuously updated, including:

[0096] Indicates the offspring corresponding to the first population The number of feasible solutions in ;

[0097] Indicates the offspring corresponding to the second population The number of feasible solutions in .

[0098] Step S3, based on the first combined population and the second combined population Determine the number of feasible solutions |S i|, combined with the contribution value threshold ∈·N for updating, the path planning of the UAV swarm is performed, where ∈ is the contribution rate and N represents the number of individuals in each population.

[0099] In the present invention, and The overall constraint violation degree and the number of violated constraints are used as the calculation methods of constraint violation degree. Specifically, it includes constructing a feasible solution set. is a feasible solution}, i=1,2, according to |S i |The number of feasible solutions in, choose different constraint calculation methods to update the population.

[0100] Update method such as Figure 4 : Determine the number of currently feasible solutions;

[0101] When |S1|≤∈·N, the first combined population updates the population based on the overall violation degree, and when |S2|≤∈·N, the second combined population updates the population based on the number of violated constraints;

[0102] for Each individual uses the overall constraint violation CV(x) to calculate the constraint, Where k is the number of constraints, g i (x) is the constraint violation value of the i-th constraint, ε is the slack variable, and is determined according to the CDP (constraint dominance criterion) The first N individuals enter CDP is defined as follows:

[0103] 1) If both individuals are feasible solutions, the individual with the smaller objective function value dominates the other individual;

[0104] 2) If two individuals are respectively a feasible solution and an infeasible solution, then the feasible solution individual dominates the infeasible solution individual;

[0105] 3) If both individuals are infeasible solutions, the individual with the smaller constraint violation value dominates the other individual.

[0106] for The constraint is calculated using the number of constraint violations NV(x), where NV(x) = the number of constraints violated by the infeasible individual, and Will be determined based on the number of constraints violated The first N individuals enter

[0107] The violated constraint quantity rules include the following definitions:

[0108] 1) If both individuals are feasible solutions, the individual with the smaller objective function value dominates the other individual;

[0109] 2) If two individuals are feasible and infeasible, respectively, the feasible individual dominates the infeasible individual;

[0110] 3) If both individuals are infeasible, the individual with less constraint violations dominates the other individual.

[0111] When |S1|>∈·N and |S1|<N, the first combined population determines the updating mode according to the contribution value of the first population and the contribution value of the second population; and when |S2|>∈·N and |S2|<N, the second combined population determines the updating mode according to the contribution value of the first population and the contribution value of the second population;

[0112] The specific steps include:

[0113] If Ctr1>Ctr2, for According to the CDP (constraint dominance principle), select top N individuals in S

[0114] If Ctr2>Ctr1, for According to the constraint violation number rule, select top N individuals in S

[0115] If Ctr1=Ctr2, for According to the CDP (constraint dominance principle), select top N individuals in S For According to the constraint violation number rule, select top N individuals in S

[0116] When |S i |≥N, the first combined population and the second combined population both update the population according to the non-dominated sorting and the Hausdorff distance;

[0117] Specifically, S i is merged with Arcpop to form a temporary population The individuals in S are non-dominated sorted, the Hausdorff distance HD(x) is calculated, and according to the non-dominated sorting and HD(x), the top N uniformly distributed individuals are selected into S and the archive population Arcpop is updated at the same time, and the size thereof is kept from exceeding the preset size.

[0118] To further optimize the above technical solutions, when constructing the target and constraint functions, the decision vector is composed of control points CN, that is, x=(CN 1，0 , CN1，1 ,…CN 1，cs-1 , CN 2，0 ,…CN UP，cs-1 ) T , whose dimension is UP×cs, where UP is the number of UAV paths and cs is the number of control points for each UAV path.

[0119] In one embodiment, the objective function of path planning includes:

[0120] The objective function of the total path length of the UAV is expressed as:

[0121]

[0122] Where UP is the number of UAV paths, pp is the number of waypoints in each path, and PP i，j is the jth path point on the i-th path;

[0123] The objective function of risk factors related to UAV paths is expressed as:

[0124]

[0125] Among them, mp is the number of grid points in the safe distance, that is, the path point AP j After projecting onto the horizontal plane, with the corresponding projection point as the center, d safe The number of projection points in a circular area with a radius of , which intersects with the terrain grid points; Figure 5 As shown, d sr is the safety distance radius, d i，k，j is the distance between the jth path point and the kth grid point on the i-th path.

[0126] Furthermore, the constraint functions of path planning include:

[0127] (1) Path height constraint, that is, regarding the height limit of the UAV, the path height must be guaranteed to be lower than the maximum height, expressed as:

[0128]

[0129] c 1，i，j =max(h i，j +h max ,0)

[0130] Where h i，j is the height of the jth path point on the i-th path, h max is the restricted maximum flight altitude;

[0131] (2) Safety altitude constraint, that is, the safety altitude that the UAV needs to maintain above the terrain, expressed as:

[0132]

[0133]

[0134] Where, is the terrain height corresponding to the path point, h min The minimum height that needs to be maintained on the ground, h i，j is the height of the current path point;

[0135] (3) Safety distance constraint, that is, the safety distance that each UAV must maintain from other UAVs, expressed as:

[0136]

[0137]

[0138] t sub =|t i，j -t k，o |

[0139] Where, d i，k，j，o is the distance between the jth path point on the i-th UAV path and the oth path point on the k-th UAV path, d min is the minimum safe distance allowed between each pair of UAVs, t sub is the time interval between the two UAVs arriving at the collision point in space, t i，j and t k，o is the time when the i-th and k-th UAVs arrive at the starting collision point;

[0140] (4) Turning radius constraint, that is, the turning radius of the UAV path must be greater than the minimum turning radius.

[0141] The expression is:

[0142]

[0143] C 4，i，j =max(r min -r i，j ,0)

[0144]

[0145]

[0146] Where r min is the minimum UAV turning radius, r i，j is the turning radius calculated using three consecutive points, PN i，j-1 , PN i，jand PN i，j+1 Three points, g and respectively represent the gravity acceleration and the maximum load factor of the ith unmanned aerial vehicle at the jth path point.

[0147] In one embodiment, when planning the path, the parameter h max , h min , cn, d safe , d min , v and DN are respectively set to 190, 10, 5, 10, 2, 25 and 2.

[0148] S4, determine whether the termination condition is reached, if not, let t = t + 1, return to S2 to continue iteration, if yes, output the non-dominated solution according to the updated first combined population and the second combined population, as preferred, output all non-dominated solutions in the archive population Arcpop, that is, a set of optimal solutions of the multi-unmanned aerial vehicle path planning obtained by optimization, as shown in formula (7). Figure 6

[0149] By combining non-dominated sorting and Hausdorff distance to update the population, the optimal solution can be gradually converged while maintaining the diversity of the population. This updating method makes the algorithm have strong adaptability when facing complex environment or constraints.

[0150] To further show the advantages of the multi-constraint evolutionary-based unmanned aerial vehicle group path planning method proposed in the present application, the comparative experimental results of the unmanned aerial vehicle group path planning method of the present application and other algorithms are analyzed.

[0151] First, a plurality of digital elevation models are obtained, and the parameters of the multi-objective optimization problem are adjusted to generate a plurality of test problems. As shown in Table 1:

[0152] Table 1

[0153]

[0154] Initialize the algorithm parameters, N: = 100, ∈ = 0.4; and compare the path planning method of the present application with the MOEA / D-CDP and PPS algorithms on the test set, set the initialization parameters of these algorithms according to the original literature. Get the running frequency ratio of the feasible solutions obtained by the algorithm of the present application and each algorithm after running 30 times in three test problems, as shown in Table 2.

[0155] Table 2

[0156] Test Questions MOEA / D-CDP PPS Algorithm of the present invention Terrain-1 1.00 0.50 1.00 Terrain-2 1.00 0.43 1.00 Terrain-3 0.93 0.60 1.00

[0157] Table 3 is the average value and standard deviation of IGD and HV values obtained by the algorithm of the present application and each algorithm after running 30 times in three test problems, and the bold part represents the optimal value in the same test problem;​

[0158] Table 3

[0159]

[0160]

[0161] The experimental performance of each algorithm was evaluated using the hypervolume matrix (HV), inverse generation distance matrix (IGD), and the run-time ratio (FR) of feasible solutions, three indicators commonly used to evaluate multi-objective optimization algorithms. Among them, the larger the HV, the smaller the IGD, and the larger the FR, the better the experimental performance.

[0162] Tables 2 and 3 show the FR, HV, and IGD values ​​obtained by the algorithm of the present invention and each algorithm after running 30 times on each test problem.

[0163] Attachment Figure 7 The convergence trend comparison of the HV value during the iteration of the algorithm of the present invention and each algorithm is shown.

[0164] The results of multiple experiments show that the algorithm of the method of the present invention can obtain feasible solutions earlier and more stably than other algorithms, and has better convergence and distribution in the iterative process. It can efficiently handle the dynamics and task-related constraints of the drone swarm in the process of drone swarm path planning, and obtain better solutions with fewer computing resources.

[0165] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0166] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A UAV swarm path planning method based on dual-population multi-constraint evolution, characterized by: S1, determine the first population and the second population based on the drone path; S2, generating offspring based on the first population and the second population to obtain a first combined population and a second combined population; after obtaining the combined population, continuously updating the contribution value Ctr1 of the first population and the contribution value Ctr2 of the second population, including: represents the number of feasible solutions in the corresponding offspring of the first population; represents the number of feasible solutions in the corresponding offspring of the second population; S3. Determine the number of feasible solutions in the first combined population and the second combined population in turn |S a |,a=1,2, and update it in combination with the contribution value threshold ∈·N to plan the path of the drone group, where ∈ is the contribution rate and N represents the number of individuals in each population. The update steps include: When |S a When |≤∈·N, the first combined population updates the population based on the overall violation degree, and the second combined population updates the population based on the number of violated constraints; When |S a | > ∈·N and |S a | < N, both the first metapopulation and the second metapopulation determine the update method according to the contribution value of the first population and the contribution value of the second population; the steps include: If Ctr1>Ctr2, both the first combined population and the second combined population update their populations based on the overall violation degree; If Ctr2>Ctr1, both the first combined population and the second combined population update their populations based on the number of violated constraints; If Ctr1 = Ctr2, the first combined population updates the population based on the overall violation degree, and the second combined population updates the population based on the number of violated constraints; When |S a When |≥N, both the first combined population and the second combined population update their populations according to the non-dominated sorting and Hausdorff distance; S4. Determine whether the termination condition is met. If not, return to S2 to continue iteration. If so, output a non-dominated solution based on the updated first combined population and second combined population.

2. The UAV swarm path planning method according to claim 1, characterized in that: In S1, the first population is randomly generated according to the drone path, and the second population is obtained by copying the first population.

3. The UAV swarm path planning method according to claim 1 or 2, characterized in that: In S1, the steps for obtaining the drone path include: Obtaining the three-dimensional environmental terrain of the flight area, determining path points based on the three-dimensional environmental terrain using B-spline sampling, and constructing a UAV path using the path points; determining the path points using B-spline sampling includes determining the path points using the following formula based on control points on the B-spline curve; Among them, (x' j ,y' j ,z' j ) represents the coordinates of the path point, (x j ,y j ,z j ) represents the coordinates of the control point, B j,t (·) represents the basis function of the jth segment of the t-order B-spline curve, with the domain being [0, cs+t], ζ n It represents the nth sampling value among the pp equally spaced sampling values ​​in [0, cs+t], where pp represents the number of path points in each path.

4. The UAV swarm path planning method according to claim 1, characterized in that: In S2, after generating offspring based on the first population and the second population, a first combined population and a second combined population are obtained, the steps include: Generate a first offspring based on individuals in the first population, and generate a second offspring based on individuals in the second population; The first progeny, the second progeny, and the first population are combined to obtain a first combined population, and the first progeny, the second progeny, and the second population are combined to obtain a second combined population.

5. The UAV swarm path planning method according to claim 1, characterized in that: In S2, the steps of generating offspring include: Get the paired parent based on the first or second population, and generate offspring through the following mutation operator: Among them, s m represents the mutation rate, ω represents the distribution index, σ i is the scaling factor of the i-th decision variable, and p is a random number in the interval [0,1]; When the offspring population independent variable violates the boundary conditions, the following boundary conditions are used to repair it: Where, L i and R i are the lower and upper bounds of the ith decision variable, respectively. i represents the i-th decision variable of individual o.

6. The UAV swarm path planning method according to claim 1, characterized in that: In S3, the population is updated based on the overall violation degree according to the following criteria: If both individuals are feasible solutions, the individual with the smaller objective function value dominates the other individual; If two individuals are respectively a feasible solution and an infeasible solution, then the feasible solution individual dominates the infeasible solution individual; If both individuals are infeasible solutions, the individual with the smaller constraint violation value dominates the other individual; And based on the number of constraint violations, the population is updated as follows: If both individuals are feasible solutions, the individual with the smaller objective function value dominates the other individual; If two individuals are respectively a feasible solution and an infeasible solution, then the feasible solution individual dominates the infeasible solution individual; If both individuals are infeasible solutions, the individual with fewer constraint violations dominates the other individual.

7. The UAV swarm path planning method according to claim 6, characterized in that: The objective function includes: The objective function of the total path length of the UAV is expressed as: Where UP is the number of UAV paths, pp is the number of waypoints in each path, and PP u,p is the p-th path point on the u-th path; The risk factor objective function is expressed as: Where mp is the number of grid points in the safety distance, d sr is the safety distance radius, d u,k,p is the distance between the p-th path point and the k-th grid point on the u-th path.

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