Multi-unmanned aerial vehicle cooperative route planning method based on improved grey wolf optimization algorithm

Abstract

The invention discloses an improved grey wolf optimization algorithm-based solution for multi-unmanned aerial vehicle cooperative flight path planning, and belongs to the field of unmanned aerial vehicle flight path planning. According to the method, a multi-aircraft cooperative flight path planning model is established in a three-dimensional space, and the provided algorithm not only needs to consider self-factor limitations such as a pitch angle, a yaw angle, a navigation height and a navigation distance of an aircraft course, but also needs to consider areas where radars, artillery fire coverage areas and meteorological equipment in avoidance space are located, and external factors such as inter-aircraft cooperation. An original grey wolf optimization algorithm is improved by using a method of combining global search and local search, a fitness function loss value is quickly reduced by adopting multiple strategies, and a local search range can be expanded to a certain extent. The improved grey wolf optimization algorithm adopted by the invention is relatively high in parameter adjustment effectiveness and high in convergence speed, and can plan a track with relatively small loss according to different types of three-dimensional space constraints, so that a collaborative track optimization scheme of the unmanned aerial vehicle group is given.

Description

Technical Field

[0001] The invention relates to a multi-UAV collaborative track planning method based on an improved grey wolf optimization algorithm, and belongs to the field of UAV track planning. Background Art

[0002] The application of unmanned equipment has expanded the vision and business scope of manned vehicles, especially providing higher safety and fault tolerance when performing tasks in dangerous environments. With the technological progress and continuous upgrading of business needs in fields such as materials, energy and telecommunications, efficient multi-UAV task coordination is gradually becoming a trend, which requires reasonable trajectory planning to achieve a high degree of spatiotemporal coordination between the various aircraft. Trajectory planning generally aims at the shortest path problem, that is, finding the shortest flight path for a UAV from its starting point to its destination, which allows the UAV to avoid obstacles and always maintain a safe distance from other UAVs.

[0003] To solve the path planning problem, it is necessary to first constrain the state of the drone itself and the environment. Environmental constraints generally include terrain restrictions, wireless channel fading, meteorological equipment obstacles, and the setting of no-fly zones such as radar and artillery fire. The modeling process will compile such information into an effective and appropriate configuration space. The state constraints of the drone itself generally include dynamic constraints such as flight altitude, instantaneous rate, pitch angle, yaw angle, maximum load, maximum range, remaining power, hovering ability, and fuselage spacing. Secondly, since solving the trajectory planning problem can actually be reduced to solving a type of nonlinear optimization problem. The existing solution methods mainly include traditional search algorithms such as A* search and high-order B-spline search, as well as intelligent optimization algorithms such as heuristic algorithms and multi-layer neural networks. Since the trajectory planning problem of drones in three-dimensional space involves a large number of parameters and faces multiple constraints, traditional methods often cannot obtain accurate analytical solutions. In this case, the intelligent optimization algorithm can give a suboptimal solution within an acceptable computational cost range.

[0004] Gray Wolf Optimization (GWO) is a swarm intelligence optimization algorithm based on bionics. It simulates the hunting behavior of gray wolf populations to explore an optimization path to the goal in multi-dimensional space and under the constraints of many conditions. It improves the shortcomings of traditional algorithms such as particle swarm optimization (PSO) and genetic algorithm (GA), such as falling into local optimality too quickly and iterative convergence too slowly. It draws on the social organization and hunting mode of gray wolves and has strong exploration capabilities. The improvement of the original algorithm can be started from three aspects: population initialization, optimal convergence factor and improvement of local optimization ability, to help the algorithm achieve faster, more flexible and reasonable intelligent search. Summary of the invention

[0005] (I) Purpose of the invention

[0006] The purpose of the present invention is to provide a multi-UAV collaborative trajectory planning method based on an improved gray wolf optimization algorithm. In view of the slow convergence speed of existing multi-UAV path planning algorithms, the traditional algorithm is improved from three aspects: the calculation method of the convergence factor, the iterative update condition of the population, and the selection of the initial point.

[0007] (II) Technical solution

[0008] Problem description: Establish three-dimensional space and obstacle space The three-dimensional trajectory planning problem of UAV can be described as o An optimal continuous path from the starting point to the end point that satisfies the constraints is found as the trajectory planned by the UAV in three-dimensional space.

[0009] Fitness function and constraints: The fitness curve of the UAV path planning quantifies the cost generated by the optimization algorithm after each iteration. The lower the cost, the lower the fitness function value, and the closer the resulting path is to the global optimal path. The constraints of the optimization problem include space constraints and cost constraints. Among them, the cost constraints include fuel consumption cost L1, threat cost L2, and heading change cost L3.

[0010] Assuming that the UAV moves at a constant speed, the calculation formula of the fuel consumption cost is related to the flight mileage, and its calculation formula can be written as

[0011]

[0012] In the formula, k1 represents the fuel consumption coefficient, l t It represents the distance between the tth track point and the t+1th track point. The maximum number of track points planned on the entire route is t. max .

[0013] Assume that the drone needs to avoid a maximum of M radar or artillery coverage areas during navigation, and model these areas as areas with a radius of r m The threat level of different regions to the UAV is different. The cost function of the t-th track point being threatened by the m-th region is:

[0014]

[0015] In the formula, k 2,m represents the threat factor of area m to track point t, s t,m represents the distance between the tth track point and the center of the sphere of area m. The calculation formula of the threat cost is:

[0016]

[0017] Considering the performance limitations of the drone, in order to prevent it from climbing, descending and turning too sharply, the pitch angle of the drone needs to be adjusted. and yaw angle θ. The cost of heading change in UAV path planning mainly includes the yaw angle cost L θ and pitch angle cost Two parts.

[0018]

[0019] In formula (5), L θ,t is the yaw angle cost of the t-th track point, θ t is the yaw angle of the t-th track point, θ thr θ is the maximum yaw angle allowed by the drone. t The calculation formula is

[0020]

[0021] Among them, l a,t represents the horizontal projection length of track point t and track point t+1, l b,t represents the horizontal projection length of track point t and track point t-1, l c,t represents the horizontal projection length of track point t-1 and track point t+1, and

[0022]

[0023] In formula (8), is the pitch angle cost of the t-th track point, is the pitch angle of the t-th track point, The maximum pitch angle allowed for the drone. The calculation formula is

[0024]

[0025] Among them, l z,t represents the vertical projection length of track point t and track point t+1. Therefore, the total cost of heading change is

[0026]

[0027] Wherein, k3 represents the heading change coefficient.

[0028] The evaluation criteria for the quality of UAV route planning are related to the total cost of the path. The lower the total cost, the better the path planning. The weighted calculation formula for the total cost of UAV route planning is:

[0029] L总 =μ1L1+μ2L2+(1-μ1-μ2)L3 (11)

[0030] Among them, μ1 and μ2 are the weight coefficients of fuel consumption cost and threat cost respectively.

[0031] The spatial constraints of the path planning problem include environmental constraints and coordination constraints. Among them, the environmental constraints mainly stipulate that the maximum altitude of the UAV is h max , the minimum height is h min ; The coordination constraint stipulates that the minimum distance between any two drones is d min .

[0032] Among the many algorithms for solving multi-constrained optimization problems, the GWO algorithm is a swarm intelligence search algorithm with a simple principle and easy convergence. The gray wolf population obeys a pyramid-shaped social hierarchy. The alpha wolf is the head wolf, located at the highest level, responsible for overall affairs such as final decision-making; the beta wolf is at the second level, assisting the alpha wolf in decision-making as an auxiliary role, and is responsible for commanding other low-level wolves; the delta wolf is at the third level, obeying the orders of the alpha and beta wolves, and is responsible for reconnaissance, sentry and other affairs; most wolves are at the lowest level of ω to balance the hunting behavior within the wolf pack. In the GWO algorithm, each gray wolf will give a candidate solution for hunting decisions. According to the population hierarchy, α is the optimal solution, β is the second-best solution, δ is the third-best solution, and the remaining solutions are called ω.

[0033] In the process of wolf hunting, the behavior of searching and surrounding prey can be defined as

[0034]

[0035] Formula (12) is the distance formula between individual wolves and the target (prey), and formula (13) calculates the updated position of the wolves at the next moment. and are the position vectors of the target and the gray wolf respectively; t is the number of iterations, which can also be regarded as the current moment; and is the coefficient vector, which is calculated as

[0036]

[0037] Among them: Parameter is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases; and is a random vector between [0,1]; t max The preset maximum number of iterations.

[0038] In a hunting trip of the gray wolf population, the α wolf, β wolf, and δ wolf belonging to the first three levels are the groups closest to the target and most sensitive to prey information, and the position of the ω gray wolf is determined by the decisions of the first three wolves. In practical problems, the α wolf, β wolf, and δ wolf may represent the three best path planning schemes currently obtained. The program can use the positions of these three to determine the future action vector, and then determine the action plan of the ω gray wolf, thereby updating the position of the entire wolf pack. The mathematical model is

[0039]

[0040]

[0041] Formula (17) obtains the distance between wolf α, wolf β, wolf δ and other individuals by solving the modulus of the vector. Corresponding to the current position vectors of α wolf, β wolf, and δ wolf respectively, is the current position vector of the ω gray wolf; formula (18) defines the step length and distance that the ω gray wolf moves to the α wolf, β wolf, and δ wolf; formula (19) is the final position of the ω wolf.

[0042] In order to make the traditional gray wolf search algorithm more suitable for path planning problems, the proposed new gray wolf optimization algorithm improves the traditional heuristic search in three main directions: first, by introducing a new weighting factor calculation formula to improve the convergence speed; second, by fine-tuning the iterative strategy to improve the fitness of the local search; third, trying to make the selection of the initial solution closer to the optimal solution.

[0043] For the first direction, a nonlinear convergence factor adjustment strategy can be used for improvement. The traditional gray wolf optimization algorithm is based on a linearly changing convergence factor. To distinguish the global search and local search process, when When , the gray wolf population has the opportunity to jump out of the current local optimal solution to search for the global optimal solution; when When , the gray wolf population conducts local optimal search, that is, attacks the target prey. The use of nonlinear convergence factor adjustment is conducive to timely group intelligence decision-making updates when the target prey (roadblocks, etc.) suddenly changes, making the optimization process more realistic. Make the following nonlinear adjustments:

[0044]

[0045] In the formula, and The parameters are The initial and final values ​​of ; k1 and k2 are used as adjustment coefficients.

[0046] For the second direction, we can refer to the idea of ​​survival of the fittest that is prevalent in biology and adjust the iterative process according to the elite retention strategy. After updating the position for ω according to formula (19), a certain proportion of ω individuals are randomly selected to calculate the cost value. If the cost function value of the corresponding individual in the previous generation is smaller, the elite individual of the previous generation is selected.

[0047] For the third direction, consider initializing the track points of individuals who have not selected the elite retention strategy according to the greedy strategy. The specific approach is that the current gray wolf individual will use the coordinates of the previous track point as the lower bound of the probability distribution interval, and the coordinates of the target end point as the upper bound. The initialized individual track points should obey a uniform distribution within the specified interval, that is,

[0048] x t+1 ~U(x t ,e x ) (twenty one)

[0049] y t+1 ~U(y t ,e y ) (twenty two)

[0050] z t+1 ~U(z t ,e z ) (twenty three)

[0051] In the formula, (x t ,y t ,z t ) and (x t+1 ,y t+1 ,z t+1 ) are the coordinates of two adjacent track points, (e x ,e y ,e z ) is the coordinate of the target endpoint, and U indicates that the coordinates of each track point are uniformly distributed. The track point initialization method based on the greedy strategy sacrifices population diversity in exchange for the improvement of individual average fitness. Individuals that do not adopt this strategy will still choose a random strategy that can ensure population diversity to complete the initialization process.

[0052] The improved path planning algorithm is used to solve the UAV trajectory planning problem in a complex three-dimensional environment, and a trajectory curve that meets the proposed constraints and has a high fitness level can be found.

[0053] (III) Beneficial effects

[0054] (1) The present invention aims at the problem of multi-machine cooperative trajectory planning under multi-dimensional constraints, optimizes the three-dimensional trajectory search problem of multiple UAVs by using the bionics concept, and gives a feasible path that meets all constraints. It also takes into account the spatiotemporal coordination between multiple UAVs during actual flight, ensuring that the fleet can reach the assembly point within the specified time range and spatial interval. The nonlinear weighting factor is introduced, which helps the gray wolf to escape from the local optimal solution on the one hand, and enables the algorithm to find a suboptimal iterative path under a controllable number of iterations on the other hand, achieving a certain trade-off in terms of algorithm search accuracy and stability. The elite retention strategy and the greedy strategy are adopted for some gray wolf individuals, respectively, which improve the individual fitness at the expense of population diversity in the iteration process and the initialization process.

[0055] (2) The improved gray wolf optimization algorithm adopted in the present invention can solve the three-dimensional space route planning problem that meets the constraints of different terrains, no-fly zones and self-state at a relatively low cost, and realize the optimal route search for the drone swarm. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a flow chart of the improved grey wolf optimization algorithm (Ameliorated GWO, AGWO) of the present invention.

[0057] Figure 2 This is the three-dimensional result diagram of the AGWO algorithm path planning of the present invention.

[0058] Figure 3 It is a two-dimensional top view of the path planning result of the AGWO algorithm of the present invention.

[0059] Figure 4 It is a comparison diagram of the fitness change curves of the AGWO algorithm of the present invention and the Grey Wolf Optimization Algorithm (GWO). DETAILED DESCRIPTION

[0060] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0061] like Figure 1 As shown, a multi-UAV collaborative trajectory planning method based on an improved gray wolf optimization algorithm includes the following steps:

[0062] Step 1: When searching for multi-UAV collaborative trajectories through the improved gray wolf optimization algorithm, first initialize the maximum search steps of the algorithm, the number of individuals in the gray wolf population, the individual positions of the population, and the individual activity range.

[0063] Step 2: Set the no-fly zone location, UAV start and end points, navigation fuel consumption, angle, altitude constraints and multi-machine coordination constraints, and give a cost evaluation function (fitness function). The costs generated by fuel consumption constraints, no-fly zone settings and angle constraints include fuel consumption cost L1, threat cost L2 and heading change cost L3.

[0064] Assuming that the drone moves at a constant speed, the calculation formula for the fuel consumption cost is related to the flight mileage, and its calculation formula can be written as

[0065]

[0066] In the formula, k1 represents the fuel consumption coefficient, l t It represents the distance between the tth track point and the t+1th track point. The maximum number of track points planned on the entire route is t. max .

[0067] Assume that the drone needs to avoid a maximum of M radar or artillery coverage areas during navigation, and model these areas as areas with a radius of r m The threat level of different regions to the UAV is different. The cost function of the t-th track point being threatened by the m-th region is:

[0068]

[0069] In the formula, k 2,m represents the threat factor of area m to track point t, s t,m It represents the distance between the tth track point and the center of the sphere of area m. The calculation formula of the threat cost is:

[0070]

[0071] Considering the performance limitations of the drone, in order to prevent it from climbing, descending and turning too sharply, the pitch angle of the drone needs to be adjusted. and yaw angle θ. The cost of heading change in UAV path planning mainly includes the yaw angle cost L θ and pitch angle cost Two parts.

[0072]

[0073] In formula (5), L θ,t is the yaw angle cost of the t-th track point, θ t is the yaw angle of the t-th track point, θ thr θ is the maximum yaw angle allowed by the drone. t The calculation formula is

[0074]

[0075] Among them, l a,t represents the horizontal projection length of track point t and track point t+1, l b,t represents the horizontal projection length of track point t and track point t-1, l c,trepresents the horizontal projection length of track point t-1 and track point t+1, and

[0076]

[0077] In formula (8), is the pitch angle cost of the t-th track point, is the pitch angle of the t-th track point, The maximum pitch angle allowed for the drone. The calculation formula is

[0078]

[0079] Among them, l z,t represents the vertical projection length of track point t and track point t+1. Therefore, the total cost of heading change is:

[0080]

[0081] Wherein, k3 represents the heading change coefficient.

[0082] The evaluation criteria for the quality of UAV route planning are related to the total cost of the path. The lower the total cost, the better the path planning. The weighted calculation formula for the total cost (fitness) of UAV route planning is:

[0083] L 总 =μ1L1+μ2L2+(1-μ1-μ2)L3 (11)

[0084] Among them, μ1 and μ2 are the weight coefficients of fuel consumption cost and threat cost respectively.

[0085] The spatial constraints of the path planning problem include environmental constraints and coordination constraints. Among them, the environmental constraints mainly stipulate that the maximum altitude of the UAV is h max , the minimum height is h min ; The coordination constraint stipulates that the minimum distance between any two drones is d min .

[0086] Step 3: Define a matrix to record the position and fitness of α, β, δ wolves and other individuals after each iteration. The specific update process includes the following steps:

[0087] Step 3.1: Definition During the wolf pack hunting process, the behaviors of searching and surrounding prey are described by equations (12) and (13).

[0088]

[0089] Formula (12) is the distance formula between individual wolves and the target (prey), and formula (13) calculates the updated position of the wolves at the next moment. and are the position vectors of the target and the gray wolf respectively; t is the number of iterations, which can also be regarded as the current moment; and is the coefficient vector, which is calculated as

[0090]

[0091]

[0092] Among them: Parameter is the convergence factor; and The parameters are The initial and final values ​​of ; k1 and k2 are used as adjustment coefficients; and is a random vector between [0,1]; t max The preset maximum number of iterations.

[0093] Step 3.2: In a hunting trip of the gray wolf population, the α wolf, β wolf, and δ wolf belonging to the first three levels are the groups closest to the target and most sensitive to prey information. The position of the ω gray wolf is determined by the decisions of the first three wolves. In practical problems, the α, β, and δ gray wolves may represent the three best path planning solutions currently obtained. The program can use the positions of these three to determine the future action vector, and then determine the action plan of the ω gray wolf, thereby updating the position of the entire wolf pack. The mathematical model is

[0094]

[0095] Formula (17) obtains the distance between α, β, δ and other individuals by solving the modulus of the vector. The current position vectors corresponding to α, β, and δ respectively, is the current position vector of ω; Equation (18) defines the step size and distance of ω moving to α, β, δ; Equation (19) is the latest position of ω.

[0096] Step 3.3: After updating the position for ω according to formula (19), randomly select a certain proportion of ω individuals to calculate the cost value. If the cost function value of the corresponding individual in the previous generation is smaller, then the elite individual of the previous generation is selected. The individuals that do not choose the elite retention strategy are initialized according to the greedy strategy. The specific approach is that the current gray wolf individual will use the coordinates of the previous track point as the lower bound of the probability distribution interval, and the coordinates of the target end point as the upper bound. The initialized individual track points should obey a uniform distribution within the specified interval, that is,

[0097] x t+1 ~U(xt ,e x ) (20)

[0098] y t+1 ~U(y t ,e y ) (twenty one)

[0099] z t+1 ~U(z t ,e z ) (twenty two)

[0100] In the formula, (x t ,y t ,z t ) and (x t+1 ,y t+1 ,z t+1 ) are the coordinates of two adjacent track points, (e x ,e y ,e z ) is the coordinate of the target end point, and U indicates that the coordinates of each track point obey uniform distribution.

[0101] Step 4: After each iteration, determine whether the algorithm meets the convergence conditions. If so, output the final navigation path; otherwise, continue to iterate until the algorithm converges.

[0102] Example

[0103] In order to verify the feasibility and effectiveness of the method, further explanation is given below in combination with simulation experiments.

[0104] The simulation test environment relies on three-dimensional space to set the starting point and the end point. The purpose of programming is to plan a global path for the drone to reach the target location. For convenience, consider using abstract points to represent the drone configuration in the simulation environment. The drone group gathers near the starting point in the form of a triangular formation, and regroups in the form of a triangular formation when it reaches the end point. The drone angle constraint is set to a pitch angle of not less than 35° and a yaw angle of not more than 60°. The drone height constraint is set to a maximum height of no more than 20km and a minimum height of no less than 0.02km. The minimum distance between drone formations during flight is 200m. There are preset artillery fire areas and radar coverage areas in the passing area of ​​the drone group. Since some areas may not be attacked at the first time, some drones are allowed to pass quickly with a certain probability after weighing the cost.

[0105] The AGWO algorithm was applied to the above simulation environment to conduct global path planning experiments. The planning results were as follows: Figure 2 and two Overlooking Figure 3 The algorithm was able to successfully avoid the no-fly zone, with only a few routes briefly passing through the radar search area. Figure 4 Comparison of the fitness curves of the AGWO algorithm of the present invention and the GWO algorithm shows that the fitness curve of the present invention decreases faster in the early stage. This is because the elite retention strategy and the greedy strategy make AGWO focus on obtaining displacement vectors with better fitness in the initial parameter setting. In the later stage of iteration, the nonlinear convergence factor gradually plays a role, making AGWO constantly try to explore the global optimal route when encountering complex obstacle environments, so the fitness obtained during this period is higher than that of GWO.

[0106] The basic principles, main features and advantages of the present invention are described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A multi-UAV collaborative trajectory planning method based on an improved gray wolf optimization algorithm, characterized in that: The steps include: Step 1: When searching for multi-UAV collaborative tracks by improving the gray wolf optimization algorithm, first initialize the maximum number of algorithm search steps, the number of gray wolf individuals, the position of individuals in the population, and the activity range of individuals; Step 2: Set the no-fly zone location, UAV start and end points, navigation fuel consumption, angle, altitude constraints and multi-machine coordination constraints respectively, and give a cost evaluation function; the costs generated by fuel consumption constraints, no-fly zone settings and angle constraints include fuel consumption cost L1, threat cost L2 and heading change cost L3; Assuming that the drone moves at a constant speed, the calculation formula for the fuel consumption cost is related to the flight mileage, and its calculation formula is written as In the formula, k1 represents the fuel consumption coefficient, l t It represents the distance between the tth track point and the t+1th track point. The maximum number of track points planned on the entire route is t. max ; Assume that the drone needs to avoid a maximum of M radar or artillery coverage areas during navigation, and model these areas as areas with a radius of r m The threat level of different regions to the UAV is different. The cost function of the t-th track point being threatened by the m-th region is: In the formula, k 2,m represents the threat factor of area m to track point t, s t,m represents the distance between the tth track point and the center of the sphere of area m. The calculation formula of the threat cost is: Pitch angle of the drone and yaw angle θ, the heading change cost of the UAV path planning includes the yaw angle cost L θ and pitch angle cost Two parts; In formula (5), L θ,t is the yaw angle cost of the t-th track point, θ t is the yaw angle of the t-th track point, θ thr is the maximum yaw angle allowed by the drone; θ t The calculation formula is Among them, l a,t represents the horizontal projection length of track point t and track point t+1, l b,t represents the horizontal projection length of track point t and track point t-1, l c,t represents the horizontal projection length of track point t-1 and track point t+1, and In formula (8), is the pitch angle cost of the t-th track point, is the pitch angle of the t-th track point, The maximum pitch angle allowed for the drone; The calculation formula is Among them, l z,t represents the projection length of track point t and track point t+1 in the vertical direction; therefore, the total cost of heading change is Among them, k3 represents the heading change coefficient; The weighted calculation formula for the total cost of UAV route planning is: L 总 =μ1L1+μ2L2+(1-μ1-μ2)L3(11)where μ1 and μ2 are the weight coefficients of fuel consumption cost and threat cost respectively; The spatial constraints of the path planning problem include environmental constraints and coordination constraints. Among them, the environmental constraints mainly stipulate that the maximum altitude of the UAV is h. max , the minimum height is h min ; The coordination constraint stipulates that the minimum distance between any two drones is d min ; Step 3: Define a matrix to record the position and fitness of α wolf, β wolf, δ wolf and other individuals after each iteration; the specific update process includes the following steps: Step 3.1: Definition During the wolf pack hunting process, the behaviors of searching and surrounding prey are described by equations (12) and (13); Formula (12) is the distance formula between the wolf pack and the target, and formula (13) calculates the updated position of the wolf pack at the next moment; where: and are the position vectors of the target and the gray wolf respectively; t is the number of iterations; and is the coefficient vector, which is calculated as Among them: Parameter is the convergence factor; and The parameters are The initial and final values ​​of ; k1 and k2 are used as adjustment coefficients; and is a random vector between [0,1]; t max is the preset maximum number of iterations; Step 3.2: In a hunting trip of the gray wolf population, the α wolf, β wolf, and δ wolf belonging to the first three levels are the groups closest to the target and most able to perceive prey information, and the position of the ω gray wolf is determined by the decisions of the first three wolves; in the actual problem, the α wolf, β wolf, and δ wolf represent the three best path planning schemes currently obtained. The positions of the α wolf, β wolf, and δ wolf are used to determine the future action vector, and then the action plan of the ω gray wolf is determined, so as to update the position of the entire wolf pack. The mathematical model is Formula (17) obtains the distance between wolf α, wolf β, wolf δ and other individuals by solving the modulus of the vector. They correspond to the current position vectors of α wolf, β wolf, and δ wolf respectively. is the current position vector of the ω gray wolf; Formula (18) defines the step length and distance of the ω gray wolf moving toward the α wolf, β wolf, and δ wolf; Formula (19) is the latest position of the ω gray wolf; Step 3.3: After updating the position of the ω gray wolf according to formula (19), randomly select a certain proportion of ω gray wolf individuals to calculate the cost value; if the cost function value of the corresponding individual in the previous generation is smaller, then select the elite individual of the previous generation; the individuals that do not choose the elite retention strategy are initialized according to the greedy strategy; the specific method is that the current gray wolf individual will use the coordinates of the previous track point as the lower bound of the probability distribution interval, and the coordinates of the target end point as the upper bound. The initialized individual track points should obey a uniform distribution within the specified interval, that is, x t+1 ~U(x t ,e x ) (20) and t+1 ~U(y t ,and y ) (21) z t+1 ~U(z t ,e z ) (22) In the formula, (x t ,y t ,z t ) and (x t+1 ,y t+1 ,z t+1 ) are the coordinates of two adjacent track points, (e x ,e y ,e z ) is the coordinate of the target end point, and U indicates that the coordinates of each track point are uniformly distributed; Step 4: After each iteration, determine whether the trajectory planning method meets the convergence conditions. If so, output the final navigation path; otherwise, continue to iterate until the algorithm converges.

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