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

Abstract

The invention discloses an unmanned aerial vehicle group path planning method based on dual-population multi-constraint evolution. The method comprises the following steps: determining a first population and a second population according to unmanned aerial vehicle paths; generating filial generations based on the first population and the second population to obtain a first combined population and a second combined population; and sequentially determining the number of feasible solutions in the first combined population and the second combined population, performing updating in combination with a contribution value threshold, performing path planning on the unmanned aerial vehicle group, and judging whether a termination condition is reached, if not, returning to continue iteration, and if yes, outputting a non-dominated solution according to the updated first combined population and the second combined population. Based on the population contribution degree, an appropriate constraint calculation mode is adaptively selected to obtain a feasible solution mode, the solution efficiency and the solution quality can be remarkably improved, and meanwhile the stability and adaptability of the algorithm are enhanced.

Description

Technical Field

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

[0002] Drones have been widely used in military reconnaissance, environmental monitoring, and cargo transportation due to their portability and flexibility. Path planning is the key to ensuring that drones can successfully perform these tasks. The core of drone path planning is to effectively and safely guide drones to their destinations, including avoiding obstacles during flight and ensuring the feasibility and optimization of the path. At the same time, when planning the paths of multiple drones, attention should also be paid to the coordination between drones.

[0003] Typically, multi-UAV path planning problems can be modeled as constrained multi-objective optimization problems, where objectives may include minimizing total flight time, maximizing coverage, avoiding obstacles, etc. At the same time, constraints that need to be considered include altitude restrictions, no-fly zones, battery life, etc. When solving multi-UAV path planning problems, the paths of multiple UAVs are encoded into one solution.

[0004] However, in general, existing solutions only consider the total constraint value violated when solving feasible solutions, which leads 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. This solution will only be abandoned by the algorithm due to its large constraint, but this infeasible path is easy to repair, making this solution a feasible solution; in the second case, two paths are infeasible due to violating multiple constraints. Although the total constraint value violated is small and is retained by the algorithm, it is difficult to repair this solution into a feasible individual due to violating multiple constraints.

[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 optimal path finally obtained 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 solution:

[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 according to the drone path;

[0010] S2, generating 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, after updating with the contribution value threshold ∈·N, the path planning is performed for the drone group, where ∈ is the contribution rate and N represents the number of individuals in each population. The updating 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 first combined population and the second combined population are updated 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 non-dominated sorting and Hausdorff distance;

[0015] S4. Determine whether the termination condition is met. If not, return to S2 to continue iterating. If so, output a non-dominated solution based on the updated first combined population and the 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 by using B-spline sampling based on the three-dimensional environment terrain, and the UAV path is constructed through the path points.

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

[0020] The first offspring, the second offspring, and the first population are combined to obtain a first combined population, and the first offspring, the second offspring, 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 independent variables violate boundary conditions, the boundary conditions are used to repair them.

[0024] Preferably, S2 further includes, after obtaining the combined population, continuously updating the contribution value Ctr1 of the first population and the contribution value Ctr2 of the second population.

[0025] Preferably, the population is updated based on the overall violation according to the following criteria:

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

[0027] If two individuals are respectively a feasible solution and an infeasible solution, then the feasible solution individual dominates the infeasible solution individual;

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

[0029] And based on the number of constraint violations, the population is updated as follows:

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

[0031] If two individuals are respectively a feasible solution and an infeasible solution, then the feasible solution individual dominates the infeasible solution individual;

[0032] If both individuals are infeasible solutions, the individual with fewer constraint violations dominates the other individual.

[0033] Preferably, the objective function includes the total path length objective function of the UAV and the risk factor objective function, and the constraint function includes the path height constraint, the safety height constraint, the safety distance constraint, and the turning radius constraint.

[0034] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a UAV swarm path planning method based on dual-population multi-constraint evolution, which is used to adaptively select appropriate constraint calculation methods for the two populations according to the contribution of the two populations to obtain a feasible solution.

[0035] This application significantly improves the solution efficiency and solution quality by dividing the solutions in the multi-UAV path planning problem into two populations: easy-to-repair and difficult-to-repair, and adaptively selects the constraint calculation method to update the population, while enhancing the stability and adaptability of the algorithm, making it suitable for path planning problems under complex constraint environments.

[0036] At the same time, according to the contribution of the population, the appropriate constraint calculation method is adaptively selected, which can handle different types of solutions more flexibly, and will not easily abandon those solutions that are easy to repair, nor will it overly retain those solutions that are difficult to repair;

[0037] In addition, this application uses B-spline curves to represent the path, which can ensure the smoothness and continuity of the generated path and meet the dynamic constraints of the drone. It avoids the sharp turns and discontinuities that may be caused by traditional broken line paths. Compared with other interpolation methods, B-spline curves have extremely strong local controllability, that is, moving a control point will only affect the nearby curve part, and will not cause significant changes to 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying 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 It is a flow chart of the present invention for adaptively selecting constraint calculation method 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 It is a comparison chart of the convergence trend of HV (hyper volume matrix) values ​​of the algorithm of the present invention and other algorithms during iteration. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0047] In view of the current situation that existing methods cannot effectively deal with the violation of constraints by infeasible individuals, the present invention proposes an improved multi-constraint processing technology and a contribution mechanism based on feasible solutions in two populations. After integration, a multi-UAV path planning method in a three-dimensional scenario based on the improved multi-constraint processing technology and a dual-population evolutionary algorithm is proposed. The planning method proposed in the present invention can effectively solve the path planning problem of UAV swarms.

[0048] In one embodiment, the method for UAV group path planning based on dual-population multi-constraint evolution disclosed in the present invention comprises the following steps: Figure 1 ,include:

[0049] S1, determine the first population and the second population according to the drone 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, determine the number of feasible solutions in the first combined population and the second combined population in turn | S i |, combined with the contribution value threshold ∈·N for updating, the path planning of the drone group is carried out, where ∈ is the contribution rate, N represents the number of individuals in each population,

[0052] S4. Determine whether the termination condition is met. If not, return to S2 to continue iterating. If so, output a non-dominated solution based on the updated first combined population and the second combined population.

[0053] In an exemplary embodiment,

[0054] In step S1, the drone path is obtained as follows:

[0055] Obtain the three-dimensional environment terrain of the flight area, determine the path points based on the three-dimensional environment terrain using B-spline sampling, and construct the UAV path through the path points;

[0056] In this embodiment, a digital elevation model (DEM) of a real environment may be first obtained, 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 the sample area;

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

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

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

[0061] Then, based on the three-dimensional environment terrain, the path points are determined by B-spline sampling, and then 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 a uniform B-spline curve. These control points are regarded as decision variables of the proposed algorithm, which are expressed as:

[0062] CN 0 (x 0 ,y 0 , z 0 ), CN 1 (x 1 ,y 1 , z 1 ), ..., 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] PN 0 (x′ 0 , y′ 0 , z′ 0 ), PN 1 (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 the present application, the path points are determined by the following formula according to the control points on the B-spline curve:

[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 nIt represents the nth sampling value among 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] In the formula, w j ∈V={w 0 , w 1 , ..., w i}, represents the jth node of the B-spline curve, satisfying:

[0074]

[0075] In one embodiment, after obtaining the drone path, a first population is randomly generated according to the drone path, and a second population is obtained by replicating the first population. Preferably, a first population is randomly generated according to the drone path, and a 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 perform initialization, 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 ∈ 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 is generated by 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] Among them, in S21, the step of generating offspring includes:

[0087] S211. Based on the obtained three paired parents, a child o is generated by 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 ith 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, continuously updating the contribution value Ctr1 of the first population and the contribution value Ctr2 of the second population, 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 drone group is carried out, where ∈ is the contribution rate and N represents the number of individuals in each population.

[0099] In the present invention, for and The overall constraint violation degree and the number of constraint violations 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, select different constraint calculation methods to update the population.

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

[0101] When |S 1 |≤∈·N, the first combined population updates the population based on the overall violation degree, when |S 2 When |≤∈·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 a 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 The decision will be based on the number of constraints violated. The first N individuals enter

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

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

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

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

[0111] When |S 1 |>∈·N and |S 1 |<N, the first combined population determines the update mode according to the contribution value of the first population and the contribution value of the second population; and when |S 2 |>∈·N and |S 2 |<N, the second combined population determines the update method 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 CDP (Constraint Dominance Principle), select The first N individuals enter

[0114] If Ctr2>Ctr1, for According to the number of constraints violated, select The first N individuals enter

[0115] If Ctr1=Ctr2, for According to CDP (Constraint Dominance Principle), select The first N individuals enter for According to the number of constraints violated, select The first N individuals enter

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

[0117] Specifically, S i Merge with Arcpop to form a temporary population right The individuals in the non-dominated sort are sorted, the Hausdorff distance HD(x) is calculated, and the first N uniformly distributed individuals are selected according to the non-dominated sort and HD(x) to enter At the same time, the archive population Arcpop is updated to keep its size below the preset size.

[0118] To further optimize the above technical solution, when constructing the objective and constraint functions in this application, the decision vector is composed of control points CN, that is, x = (CN 1，0 , CN 1，1 ,…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 the UAV path 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, take 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] In the formula, h i，j is the height of the jth path point on the ith 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] In the formula, is the terrain height corresponding to the path point, h min The minimum height of the ground that needs to be maintained, 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 ith UAV path and the oth path point on the kth 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: 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] In the formula, r min is the minimum UAV turning radius, r i，j is the turning radius calculated using three consecutive points, i.e. PN i，j-1 , PN i，j and PN i，j+1 Three points, g and denote the gravitational acceleration and the maximum load factor of the i-th UAV at the j-th path point respectively.

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

[0148] S4, determine whether the termination condition is met, if not, set t = t + 1, return to S2 to continue iteration, if so, output non-dominated solutions according to the updated first combined population and second combined population, and preferably, output all non-dominated solutions in the archived population Arcpop, which is a set of optimal solutions for the multi-UAV path planning obtained by optimization, such as Figure 6 shown.

[0149] By combining non-dominated sorting and Hausdorff distance to update the population, it is possible to gradually converge to the optimal solution while maintaining population diversity. This updating method makes the algorithm more adaptable when facing complex environments or constraints.

[0150] In order to further demonstrate the advantages of the UAV swarm path planning method based on dual-population multi-constraint evolution proposed in the present invention, the comparative experimental results of the UAV swarm path planning method of the present invention and other algorithms are analyzed.

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

[0152] Table 1

[0153]

[0154] Initialize the algorithm parameters, N: = 100, ∈ = 0.4; and conduct experimental comparisons on the test set between the path planning method of the present invention and the algorithms such as MOEA / D-CDP and PPS, and set the initialization parameters of these algorithms according to the original literature. The ratio of the number of times the algorithm of the present invention and each algorithm obtains a feasible solution after running 30 times in the three test problems is obtained, 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 shows the average values ​​and standard deviations of IGD and HV values ​​obtained after the algorithm of the present invention and other algorithms were run 30 times in three test problems, and the bold parts represent the optimal values ​​in the same test problem;

[0158] Table 3

[0159]

[0160]

[0161] The hypervolume matrix (HV), inverse generation distance matrix (IGD), and running number ratio (FR) of feasible solutions, which are three indicators commonly used to evaluate multi-objective optimization algorithms, are used to evaluate the experimental performance of each algorithm. 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] Attached Figure 7 The convergence trend comparison of the HV value during the iteration of the algorithm of the method of the present invention and each algorithm is shown.

[0164] Multiple experimental results 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 UAV swarm dynamics and task-related constraints in the UAV swarm path planning process, and obtain better solutions with fewer computing resources.

[0165] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0166] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be 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 will not be limited to the embodiments shown herein, but rather 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 in that: S1, determine the first population and the second population according to 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; S3, determine the number of feasible solutions in the first combined population and the second combined population in turn | S i |,i=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 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; When |S i | > ∈·N and |S i | < 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; When |S i When |≥N, both the first combined population and the second combined population update their populations according to non-dominated sorting and Hausdorff distance; S4. Determine whether the termination condition is met. If not, return to S2 to continue iterating. If so, output a non-dominated solution based on the updated first combined population and the second combined population.

2. A method for drone group path planning 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 replicating the first population.

3. A UAV swarm path planning method according to claim 1 or 2, characterized in that: In S1, the steps for obtaining the drone path include: Acquire the three-dimensional environment terrain of the flight area, determine the path points based on the three-dimensional environment terrain by using B-spline sampling, and construct the UAV path through the path points; determine the path points by using B-spline sampling, including determining the path points according to the control points on the B-spline curve by the following formula; 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 Represents the nth sampling value among pp equally spaced sampling values ​​in [0,cs+t], where pp represents the number of path points in each path.

4. A method for UAV group path planning 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 offspring, the second offspring, and the first population are combined to obtain a first combined population, and the first offspring, the second offspring, and the second population are combined to obtain a second combined population.

5. The method for UAV group path planning according to claim 1, characterized in that: In S2, the steps of generating offspring include: Get the paired parents based on the first population or the 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 ith 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. A method for UAV group path planning according to claim 1, characterized in that: S2 also includes continuously updating the contribution value Ctr1 of the first population and the contribution value Ctr2 of the second population after obtaining the combined 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.

7. A method for drone group path planning according to claim 1, characterized in that: In S3, the updating method is determined according to the contribution value of the first population and the contribution value of the second population, and the steps include: If Ctr1>Ctr2, both the first combined population and the second combined population update the population 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.

8. The method for drone group path planning according to claim 1, characterized in that: In S3, the population is updated based on the overall violation 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.

9. A method for UAV group path planning according to claim 8, characterized in that: The objective functions include: 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 i,j is the jth path point on the i-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 i,k,j is the distance between the jth path point and the kth grid point on the i-th path.

10. A UAV swarm path planning method according to claim 8, characterized in that: Constraint functions include: (1) Path height constraint, the expression is: c 1,i,j =max(h i,j +h max ,0) In the formula, h i,j is the height of the jth path point on the ith path, h max is the restricted maximum flight altitude; (2) Safety height constraint, expressed as: In the formula, is the terrain height corresponding to the path point, h min The minimum height of the ground that needs to be maintained, h i,j is the height of the current path point; (3) Safety distance constraint, expressed as: t sub =|t i,j -t k,o | Where, d i,k,j,o is the distance between the jth path point on the ith UAV path and the oth path point on the kth 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; (4) Turning radius constraint, expressed as: c 4,i,j =max(r min -r i,j ,0) In the formula, r min is the minimum UAV turning radius, r i,j is the turning radius, g and denote the gravitational acceleration and the maximum load factor of the i-th UAV at the j-th path point respectively.

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