Multi-robot cooperative path planning method based on multi-strategy improved whale optimization algorithm

Abstract

The application provides a multi-unmanned aerial vehicle cooperative path planning method based on a multi-strategy improved whale optimization algorithm, and the method comprises the following steps: acquiring geographic parameters, constructing an unmanned aerial vehicle flight environment based on the geographic parameters; determining constraint conditions of a multi-unmanned aerial vehicle path planning problem according to the unmanned aerial vehicle flight environment, and constructing a multi-unmanned aerial vehicle cooperative path cost function; using the improved whale optimization algorithm to solve the value of the multi-unmanned aerial vehicle cooperative path cost function at the minimum time, so as to obtain an optimal path point sequence, and performing smooth connection to obtain an optimal flight route of the unmanned aerial vehicle. The application improves the optimization performance by fusing multiple optimization strategies on the whale optimization algorithm, balances the strength of global exploration and local development by designing a nonlinear convergence factor, introduces a competitive differential mutation strategy, generates and screens candidate solutions by using Cauchy mutation and Levy flight, accelerates the convergence speed, and further balances exploration and development and improves the ability to jump out of the local optimum by fusing a thinking innovation strategy.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path planning technology, and in particular to a multi-UAV cooperative path planning method based on a multi-strategy improved whale algorithm. Background Technology

[0002] Unmanned Aerial Vehicle (UAV) technology has been widely applied in civilian fields such as disaster relief, logistics distribution, and environmental monitoring in recent years. In complex application scenarios such as urban low-altitude logistics and forest fire monitoring, the limited sensing range, small payload, low mission efficiency, and low fault tolerance of a single UAV restrict its ability to perform complex tasks. However, multiple UAVs operating in formation offer numerous advantages, including a wider sensing range, higher efficiency, and greater flexibility, making them more adaptable to complex environments and multi-tasking requirements. Path planning is one of the main tasks of UAV swarm operations, requiring all UAVs to reach the target location along a continuous trajectory from the starting point to the endpoint while satisfying relevant constraints. This problem exhibits complex characteristics such as high dimensionality, non-convexity, multimodality, and multiple constraints, making it a typical NP-Hard (Nondeterministic Polynomial-time Hard) problem and a hot research topic in multi-UAV cooperative operations.

[0003] Traditional path planning algorithms such as A Algorithms such as Rapidly-exploring RandomTree (RRT) suffer from drawbacks in high-dimensional problems, including low search efficiency and accuracy, and high time complexity. In contrast, metaheuristic algorithms inspired by biological behavior in nature offer advantages such as simple structure, strong global search capability, and ease of implementation. However, mainstream intelligent optimization algorithms currently applied to path planning, such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Grey Wolf Optimizer (GWO), generally suffer from low convergence performance and poor optimization performance. Therefore, exploring optimization algorithms with higher optimization performance and greater adaptability has become an important research direction in the field of path planning.

[0004] The Whale Optimization Algorithm (WOA), with its unique predation mechanism and adaptive shrinking encirclement strategy, achieves a good balance between global exploration and local exploitation, and has been widely used in feature selection, fault diagnosis, image segmentation, and other fields. However, WOA still suffers from drawbacks such as insufficient convergence performance and susceptibility to getting trapped in local optima. Summary of the Invention

[0005] In view of the above situation, the main objective of this invention is to propose a multi-UAV cooperative path planning method based on a multi-strategy improved whale algorithm to solve the above-mentioned technical problems.

[0006] This invention proposes a multi-UAV cooperative path planning method based on a multi-strategy improved whale algorithm, the method comprising the following steps:

[0007] Step 1: Obtain geographic parameters and construct the UAV flight environment based on the geographic parameters;

[0008] Step 2: Determine the constraints of the multi-UAV path planning problem based on the UAV flight environment;

[0009] Step 3: Based on the constraints of the multi-UAV path planning problem, a multi-UAV cooperative path cost function is constructed. The multi-UAV cooperative path cost function includes UAV flight path length cost, UAV flight threat cost, UAV flight terrain threat cost, UAV flight path smoothing cost, UAV flight safety distance cost, and UAV flight time cooperative constraint cost.

[0010] Step 4: Improve the whale algorithm by using Sine-Cubic hybrid chaotic mapping, nonlinear convergence factor, competitive difference mutation strategy and innovative thinking strategy to obtain the improved whale algorithm. Use the improved whale algorithm to solve for the value that minimizes the cost function of multi-UAV cooperative path to obtain the optimal path point sequence.

[0011] Step 5: Smoothly connect the optimal path point sequence to obtain the optimal flight route for the UAV.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] This invention improves optimization performance by integrating multiple optimization strategies into the whale algorithm. It uses a Sine-Cubic hybrid chaotic mapping to initialize the population, designs a nonlinear convergence factor to balance the intensity of global exploration and local exploitation, introduces a competitive differential mutation strategy, and uses Cauchy mutation and Lévy flight to generate and screen candidate solutions to accelerate the convergence speed. It also incorporates innovative thinking strategies to further balance exploration and exploitation and improve the ability to escape local optima.

[0014] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by means of embodiments of the invention. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the steps of a multi-UAV cooperative path planning method based on a multi-strategy improved whale algorithm proposed in this invention.

[0016] Figure 2 The overall framework diagram of the improved whale algorithm;

[0017] Figure 3 This is a graph showing the changing trend of the nonlinear convergence factor.

[0018] Figure 4 A 3D example of the path optimization results from the standard whale optimization algorithm;

[0019] Figure 5 A 3D example diagram showing the path optimization results of the improved whale optimization algorithm that incorporates multiple strategies. Detailed Implementation

[0020] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0021] These and other aspects of the embodiments of the present invention will become clear from the following description and accompanying drawings. In these descriptions and drawings, some specific embodiments of the present invention are specifically disclosed to illustrate some ways of implementing the principles of the embodiments of the present invention; however, it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0022] Please see Figure 1 This embodiment provides a multi-UAV cooperative path planning method based on a multi-strategy improved whale algorithm, the method including the following steps:

[0023] Step 1: Obtain geographic parameters and construct the UAV flight environment based on the geographic parameters.

[0024] In step 1, geographic parameters are obtained, and the UAV flight environment is constructed based on these parameters. This includes the following sub-steps:

[0025] Obtain geographic parameters and construct a basic terrain model based on these parameters. The following relationship exists in the corresponding process:

[0026] ;

[0027] in, A mathematical model representing the basic terrain. This represents the coordinates of the point projected onto the horizontal plane. Represents the x-coordinate, Represents the ordinate, This indicates taking the sine value. This indicates taking the cosine value. All of these represent constants used to simulate different terrain surfaces;

[0028] In this invention, take .

[0029] The obstacle terrain model is constructed based on geographic parameters, and the following relationship exists in the corresponding process:

[0030] ;

[0031] in, Mathematical models representing obstacle terrain, Indicates the number of obstacles. Indicates the first The elevation of the obstacle, Represents an exponential function. Indicates the first The coordinates of the center point of each obstacle Indicates the first An obstacle along The slope of the axis, Indicates the first An obstacle along The slope of the axis;

[0032] The basic terrain model and the obstacle terrain model are superimposed to determine the UAV flight environment. The following relationship exists in the corresponding process:

[0033] ;

[0034] in, A mathematical model representing the flight environment of a drone.

[0035] Step 2: Determine the constraints of the multi-UAV path planning problem based on the UAV flight environment.

[0036] Step 3: Based on the constraints of the multi-UAV path planning problem, construct the multi-UAV cooperative path cost function. The multi-UAV cooperative path cost function includes UAV flight path length cost, UAV flight threat cost, UAV flight terrain threat cost, UAV flight path smoothing cost, UAV flight safety distance cost, and UAV flight time cooperative constraint cost.

[0037] In step 3, a multi-UAV cooperative path cost function is constructed based on the constraints of the multi-UAV path planning problem. This function includes the cost of UAV flight path length, UAV flight threat, UAV flight terrain threat, UAV flight path smoothing, UAV flight safety distance, and UAV flight time cooperative constraint cost. The expression for the multi-UAV cooperative path cost function is as follows:

[0038] ;

[0039] in, This represents the cost function for multi-drone cooperative paths. Indicates the first A cost function Indicates drone The set of waypoints that the flight needs to pass through. Indicates the first The weighting coefficients of each cost function, and ;

[0040] The functional expression for the cost of the UAV flight path length is as follows:

[0041] ;

[0042] in, This represents the cost of the drone's flight path length. Indicates drone The coordinates of each waypoint This represents the Euclidean distance between two points. Indicates a path segment;

[0043] The functional expression for the cost of drone flight threats is as follows:

[0044] ;

[0045] in, Indicates the cost of drone flight threats, Represents the set of all obstacles. Indicates the threat cost operator;

[0046] The expression for the threat cost operator is as follows:

[0047] ;

[0048] in, Indicates the distance from the threat zone to the collision zone. Indicates the diameter of the drone. Indicates the radius of the obstacle. This indicates the distance between the drone and the center coordinates of the obstacle. Indicates a fixed penalty cost, and ;

[0049] The functional expression for the cost of terrain threats during drone flight is:

[0050] ;

[0051] in, Indicates the cost of drone flight terrain threats. Indicates the penalty factor. Indicates the altitude of the drone. Indicates terrain elevation. Indicates a fixed penalty cost, and ;

[0052] The functional expression for the smoothing cost of the UAV flight path is:

[0053] ;

[0054] in, Indicates the cost of smoothing the drone's flight path. The penalty coefficient representing the steering angle. Indicates the steering angle. The penalty coefficient representing the pitch angle. and Both represent pitch angles;

[0055] The functional expression for the cost of safe flight distance for drones is:

[0056] ;

[0057] in, Indicates the cost of safe flight distance for drones. Indicates the number of drones, Indicates the penalty factor;

[0058] The expression for the penalty factor is:

[0059] ;

[0060] in, Indicates a fixed penalty cost, and ; Indicates drone With drones Safe distance between them;

[0061] The functional expression for the collaborative constraint cost of UAV flight time is:

[0062] ;

[0063] in, Indicates the penalty factor. Indicates a fixed penalty cost, and ; Indicates the total flight time. Indicates the time range required for the task. This represents the cost of coordinating flight time constraints for drones.

[0064] Step 4: Improve the whale algorithm by using Sine-Cubic hybrid chaotic mapping, nonlinear convergence factor, competitive difference mutation strategy and innovative thinking strategy to obtain the improved whale algorithm. Use the improved whale algorithm to solve for the value that minimizes the cost function of multi-UAV cooperative path to obtain the optimal path point sequence.

[0065] Please see Figure 2 and Figure 3 In step 4, the improved whale algorithm is used to find the value that minimizes the cost function of the multi-UAV cooperative path, so as to obtain the optimal path point sequence. This includes the following sub-steps:

[0066] A whale population is generated using a Sine-Cubic hybrid chaotic mapping. The individual with the lowest cost value in the whale population is calculated based on the multi-UAV cooperative path cost function. The individual with the lowest cost value is taken as the current optimal solution. The following relationship exists in the corresponding process:

[0067] ;

[0068] in, Indicates the first The value of the Sine mapping in the next iteration Represents the natural constant. This represents the Sine mapping control parameters. Indicates the first The value of the Sine mapping in the next iteration Indicates the Cubic mapping control parameters. Indicates the first The value of the Cubic mapping in the next iteration, This indicates a modulo operation on 1. Indicates the first The value of the Cubic mapping in the next iteration;

[0069] S401. The nonlinear convergence factor is calculated based on the current iteration number, and the following relationship exists in the corresponding process:

[0070] ;

[0071] in, Denotes the nonlinear convergence factor, and As the iteration process progresses, the value decreases nonlinearly from 2 to 0. Indicates the current iteration number. Indicates the maximum number of iterations;

[0072] It should be noted that, by Figure 3 It can be seen that the nonlinear convergence factor decreases relatively slowly in the early stage of iteration, which can effectively maintain a high exploration intensity; in the middle stage, it accelerates the transition from global exploration to local development; and in the later stage, it gradually decreases to avoid oscillation near the optimal solution due to excessive step size.

[0073] S402. Based on the nonlinear convergence factor, the predation behavior of whales is simulated, and the individuals in the whale population are calculated through shrinking encirclement, random search and spiral approximation to obtain the initially updated individuals. The following relationship exists in the corresponding process:

[0074] ;

[0075] in, Represents a coefficient vector. This indicates the individual after the initial update. This represents the current optimal solution. Indicates the first In the nth iteration The location of the whale This represents a random number within the interval (0,1). Both represent random numbers within the interval [0,1]. Indicates different individuals, This represents the logarithmic spiral shape constant. This represents a random number within the interval (-1, 1);

[0076] S403. Repeat steps S401 and S402 for all individuals in the whale population to obtain the whale population after the first update.

[0077] S404. Based on the competitive differential mutation strategy, Cauchy mutation and Lévy flight are used to enhance the initially updated individuals to obtain individuals after Cauchy mutation and individuals after Lévy flight, respectively. Using the multi-UAV cooperative path cost function, the cost values ​​of the initially updated individuals, the Cauchy-mutated individuals, and the Lévy-flying individuals are calculated, and a greedy selection is performed to obtain the individuals optimized by the competitive differential mutation strategy. The following relationship exists in the corresponding process:

[0078] ;

[0079] in, This represents the Euclidean distance between the initially updated individual and the current optimal solution. This indicates taking the Euclidean distance. Indicates the angle of dynamic disturbance. This represents the dynamic disturbance coefficient. This represents the maximum distance between an individual in the population and the optimal solution. This represents a very small constant, used to avoid division by zero errors; This refers to an individual that has undergone Cauchy mutation. Indicates Cauchy mutation, Both indicate differences And each individual is different. This refers to the individual after Levi's flight. Indicates Levi's flight, Both represent random numbers within the interval [0,1]. This represents the worst-case solution in the whale population. This represents the individual optimized through a competitive differential mutation strategy. This represents the minimum value. This represents the independent variable that reaches its minimum value;

[0080] It should be noted that when making a greedy choice, the individual with the lowest cost value is selected as the individual after the greedy choice.

[0081] S405. Repeat step S404 for all initially updated individuals in the whale population after the first update to obtain the whale population after the second update.

[0082] S406. Based on the innovative thinking strategy, the new individual optimized by the competitive differential mutation strategy is merged with the exploration direction guided by the current optimal solution to obtain the individual optimized by the innovative thinking strategy. Using the multi-UAV cooperative path cost function, the cost values ​​of the individual optimized by the innovative thinking strategy and the individual optimized by the competitive differential mutation strategy are calculated respectively, and greedy selection is performed to obtain the final updated individual. The following relationship exists in the corresponding process:

[0083] ;

[0084] in, It represents imagination. Represents a random number within the interval [0,1]. Representing deep knowledge, This refers to individuals who have undergone optimization through innovative thinking strategies. This indicates taking the tangent value. Indicates an information event;

[0085] S407. Repeat step S406 for all individuals in the whale population after the second update that have been optimized by the competitive differential mutation strategy, to obtain the whale population after the third update.

[0086] S408. The cost value of all the finally updated individuals in the whale population after the third update will be calculated by using the multi-UAV cooperative path cost function. Based on the cost value of all the finally updated individuals in the whale population after the third update and the cost value of the current optimal solution, the individual with the lowest cost value will be selected as the updated optimal solution.

[0087] Repeat steps S401-S408 iteratively until the preset maximum number of iterations is reached to obtain the final global optimal solution, which is then used as the optimal path point sequence.

[0088] It should be noted that, in Figure 2 middle, This represents the final updated individual.

[0089] Step 5: Smoothly connect the optimal path point sequence to obtain the optimal flight route for the UAV.

[0090] To verify the effectiveness of the improved Whale Optimization Algorithm (MSWOA) in path planning, a 3D simulation map environment was constructed, and a multi-UAV cooperative path planning experiment was conducted. The speed of the UAVs was set to 5~20m / s, and the minimum safe distance between UAVs was 5m. The path planning experiment parameters are shown in Table 1, and the obstacle location information in the map environment is shown in Table 2, where X and Y represent the planar coordinates of the obstacle, R is the radius of the obstacle, and H is the height of the obstacle.

[0091] Table 1. Experimental parameters for UAV path planning

[0092]

[0093] Table 2 Location information of threatening obstacles

[0094]

[0095] Based on the above parameter settings, simulation was performed in MATLAB R2020b software. Figure 4 and Figure 5 The figures shown are the path planning experimental results of the standard Whale Optimization Algorithm (WOA) and the improved Whale Optimization Algorithm (MSWOA), respectively.

[0096] Table 3 Comparison of Optimal Costs of 6 Algorithms

[0097]

[0098] As shown in Table 3 of the path planning solution results, the solution based on MSWOA is optimal, achieving a 56.02% improvement compared to the original WOA. Figure 4 and Figure 5It can be seen that when the three UAVs planned by MSWOA fly along their respective paths, they can effectively avoid terrain collisions and obstacle collisions, and do not collide with other UAVs. Moreover, the path is relatively smooth. In contrast, the path planned by WOA will collide with threatening obstacles.

[0099] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0100] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0101] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0102] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A multi-UAV cooperative path planning method based on a multi-strategy improved whale algorithm, characterized in that, The method includes the following steps: Step 1: Obtain geographic parameters and construct the UAV flight environment based on the geographic parameters; Step 2: Determine the constraints of the multi-UAV path planning problem based on the UAV flight environment; Step 3: Based on the constraints of the multi-UAV path planning problem, a multi-UAV cooperative path cost function is constructed. The multi-UAV cooperative path cost function includes UAV flight path length cost, UAV flight threat cost, UAV flight terrain threat cost, UAV flight path smoothing cost, UAV flight safety distance cost, and UAV flight time cooperative constraint cost. Step 4: Improve the whale algorithm using Sine-Cubic hybrid chaotic mapping, nonlinear convergence factor, competitive difference mutation strategy, and innovative thinking strategy to obtain the improved whale algorithm. Use the improved whale algorithm to solve for the value that minimizes the cost function of the multi-UAV cooperative path, so as to obtain the optimal path point sequence. The specific steps include the following: A whale population is generated using a Sine-Cubic mixed chaotic mapping. The individual with the lowest cost value in the whale population is calculated based on the multi-UAV cooperative path cost function, and the individual with the lowest cost value is taken as the current optimal solution. S401. Calculate the nonlinear convergence factor based on the current iteration number; S402. Simulate whale predation behavior based on nonlinear convergence factor, and calculate the individuals in the whale population through shrinking encirclement, random search and spiral approximation to obtain the preliminary updated individuals. S403. Repeat steps S401 and S402 for all individuals in the whale population to obtain the whale population after the first update. S404. Based on the competitive differential mutation strategy, the individuals after the initial update are enhanced by Cauchy mutation and Lévy flight respectively, so as to obtain individuals after Cauchy mutation and individuals after Lévy flight; using the multi-UAV cooperative path cost function, the cost values ​​of the individuals after the initial update, the individuals after Cauchy mutation, and the individuals after Lévy flight are calculated respectively, and greedy selection is performed to obtain individuals optimized by the competitive differential mutation strategy. S405. Repeat step S404 for all initially updated individuals in the whale population after the first update to obtain the whale population after the second update. S406. Based on the innovative thinking strategy, the individual optimized by the competitive differential mutation strategy is merged with the exploration direction guided by the current optimal solution to obtain the individual optimized by the innovative thinking strategy. Using the multi-UAV collaborative path cost function, the cost values ​​of individuals optimized by the thinking innovation strategy and those optimized by the competitive differential mutation strategy are calculated respectively, and a greedy selection is performed to obtain the final updated individuals. S407. Repeat step S406 for all individuals in the whale population after the second update that have been optimized by the competitive differential mutation strategy, to obtain the whale population after the third update. S408. Using the multi-UAV cooperative path cost function, calculate the cost value of all the finally updated individuals in the whale population after the third update. Based on the cost value of all the finally updated individuals in the whale population after the third update and the cost value of the current optimal solution, select the individual with the lowest cost value as the updated optimal solution. Repeat steps S401-S408 iteratively until the preset maximum number of iterations is reached to obtain the final global optimal solution, and use the final global optimal solution as the best path point sequence. Step 5: Smoothly connect the optimal path point sequence to obtain the optimal flight route for the UAV.

2. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 1, characterized in that, In step 1, geographic parameters are obtained, and the UAV flight environment is constructed based on the geographic parameters. This includes the following sub-steps: Obtain geographic parameters and construct a basic terrain model based on these parameters; An obstacle terrain model is constructed based on geographic parameters; The basic terrain model and the obstacle terrain model are overlaid to determine the UAV flight environment.

3. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 2, characterized in that, In the steps of obtaining geographic parameters and constructing a basic terrain model based on these parameters, the following relationship exists: ； in, A mathematical model representing the basic terrain. This represents the coordinates of the point projected onto the horizontal plane. Represents the x-coordinate, Represents the ordinate, This indicates taking the sine value. This indicates taking the cosine value. All represent constants; In the step of constructing an obstacle terrain model based on geographic parameters, the following relationship exists: ； in, Mathematical models representing obstacle terrain, Indicates the number of obstacles. Indicates the first The elevation of the obstacle, Represents an exponential function. Indicates the first The coordinates of the center point of each obstacle Indicates the first An obstacle along The slope of the axis, Indicates the first An obstacle along The slope of the axis; In the step of overlaying the basic terrain model and the obstacle terrain model to determine the UAV flight environment, the following relationship exists: ； in, A mathematical model representing the flight environment of a drone.

4. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 3, characterized in that, In step 3, a multi-UAV cooperative path cost function is constructed based on the constraints of the multi-UAV path planning problem. This function includes the cost of UAV flight path length, UAV flight threat, UAV flight terrain threat, UAV flight path smoothing, UAV flight safety distance, and UAV flight time cooperative constraint cost. The expression for the multi-UAV cooperative path cost function is as follows: ； in, This represents the cost function for multi-drone cooperative paths. Indicates the first A cost function Indicates drone The set of waypoints that the flight needs to pass through. Indicates the first Weighting coefficients for each cost function; The functional expression for the cost of the UAV flight path length is as follows: ； in, This represents the cost of the drone's flight path length. Indicates drone The coordinates of each waypoint This represents the Euclidean distance between two points. Indicates a path segment; The functional expression for the cost of drone flight threats is as follows: ； in, Indicates the cost of drone flight threats. Represents the set of all obstacles. Indicates the threat cost operator; The expression for the threat cost operator is as follows: ； in, Indicates the distance from the threat zone to the collision zone. Indicates the diameter of the drone. Indicates the radius of the obstacle. This indicates the distance between the drone and the center coordinates of the obstacle. Indicates a fixed penalty cost; The functional expression for the cost of terrain threats during drone flight is: ； in, Indicates the cost of drone flight terrain threats. Indicates the penalty factor. Indicates the altitude of the drone. Indicates terrain elevation. Indicates a fixed penalty cost; The functional expression for the smoothing cost of the UAV flight path is: ； in, Indicates the cost of smoothing the drone's flight path. The penalty coefficient representing the steering angle. Indicates the steering angle. The penalty coefficient representing the pitch angle. and Both represent pitch angles; The functional expression for the cost of safe flight distance for drones is: ； in, Indicates the cost of safe flight distance for drones. Indicates the number of drones, Indicates the penalty factor; The expression for the penalty factor is: ； in, Indicates a fixed penalty cost. Indicates drone With drones Safe distance between them; The functional expression for the collaborative constraint cost of UAV flight time is: ； in, Indicates the penalty factor. Indicates a fixed penalty cost. Indicates the total flight time. Indicates the time range required for the task. This represents the cost of coordinating flight time constraints for drones.

5. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 4, characterized in that, In the step of generating a whale population using a Sine-Cubic mixed chaotic mapping, calculating the individual with the lowest cost value in the whale population based on the multi-UAV cooperative path cost function, and taking the individual with the lowest cost value as the current optimal solution, the following relationship exists: ； in, Indicates the first The value of the Sine mapping in the next iteration Represents the natural constant. This represents the Sine mapping control parameters. Indicates the first The value of the Sine mapping in the next iteration Indicates the Cubic mapping control parameters. Indicates the first The value of the Cubic mapping in the next iteration, This indicates a modulo operation on 1. Indicates the first The value of the Cubic mapping in the next iteration.

6. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 5, characterized in that, In the step of calculating the nonlinear convergence factor based on the current iteration number, the following relationship exists in the corresponding process: ； in, Represents the nonlinear convergence factor. Indicates the current iteration number. Indicates the maximum number of iterations; In the process of simulating whale predation behavior based on nonlinear convergence factors, and calculating the individuals in the whale population through methods such as shrinking encirclement, random search, and spiral approximation to obtain a preliminary updated list of individuals, the following relationship exists: ； in, Represents a coefficient vector. This indicates the individual after the initial update. This represents the current optimal solution. Indicates the first In the nth iteration The location of the whale This represents a random number within the interval (0,1). Both represent random numbers within the interval [0,1]. Indicates different individuals, This represents the logarithmic spiral shape constant. This represents a random number within the interval (-1, 1).

7. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 6, characterized in that, In the steps of using a competitive differential mutation strategy to enhance initially updated individuals using Cauchy mutation and Lévy flight respectively, to obtain individuals after Cauchy mutation and individuals after Lévy flight; and using a multi-UAV cooperative path cost function to calculate the cost values ​​of initially updated individuals, individuals after Cauchy mutation, and individuals after Lévy flight respectively, and then performing greedy selection to obtain individuals optimized by the competitive differential mutation strategy, the following relationship exists: ； in, This represents the Euclidean distance between the initially updated individual and the current optimal solution. This indicates taking the Euclidean distance. Indicates the angle of dynamic disturbance. This represents the dynamic disturbance coefficient. This represents the maximum distance between an individual in the population and the optimal solution. This represents a very small constant, used to avoid division by zero errors; This refers to an individual that has undergone Cauchy mutation. Indicates Cauchy mutation, Both indicate differences And each individual is different. This refers to the individual after Levi's flight. Indicates Levi's flight, Both represent random numbers within the interval [0,1]. This represents the worst-case solution in the whale population. This represents the individual optimized through a competitive differential mutation strategy. This represents the minimum value. This represents the independent variable that reaches its minimum value.

8. The multi-UAV cooperative path planning method based on the multi-strategy improved whale algorithm according to claim 7, characterized in that, In the step of integrating individuals optimized by the competitive differential mutation strategy with the exploration direction guided by the current optimal solution based on the innovative thinking strategy to obtain individuals optimized by the innovative thinking strategy, the following relationship exists: ； in, It represents imagination. Represents a random number within the interval [0,1]. Representing deep knowledge, This refers to individuals who have undergone optimization through innovative thinking strategies. This indicates taking the tangent value. Indicates an information event.

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