Unmanned aerial vehicle route planning method and system based on improved grey wolf optimization algorithm

Abstract

The invention discloses an unmanned aerial vehicle route planning method based on an improved grey wolf optimization algorithm. The method comprises the following steps: 1, environment modeling and parameter setting; 2, designing constraint conditions and a target function; 3, initializing an algorithm and generating a population; 4, improving an algorithm and updating a track; and step 5, iteration termination and result output. The flight path of the unmanned aerial vehicle is efficiently coded in a spherical vector coding mode, and the flexibility and the calculation efficiency of flight path representation are remarkably improved; by introducing the Levy flight strategy, the global search capability of the algorithm is enhanced, and falling into a local optimal solution is avoided; meanwhile, a parameter adaptive adjustment strategy is combined, so that the convergence speed and precision of the algorithm are remarkably improved. According to the method, the problem of flight path planning in a complex mountain environment and a threat area is effectively solved, a safer and more efficient flight path is planned for the unmanned aerial vehicle, and the method has higher practicability and reliability.

Description

Technical Field

[0001] The present invention belongs to the technical field of UAV path planning, and particularly relates to a UAV path planning method and system based on an improved grey wolf optimization algorithm. Background Art

[0002] UAV path planning is one of the key technologies to ensure flight safety and improve mission efficiency. The goal of UAV path planning is to select an optimal flight path for the UAV in a complex environment, avoid obstacles, meet flight constraints, and optimize performance indicators such as flight time and energy consumption as much as possible. Currently, common UAV path planning methods mainly include methods based on graph search algorithms: such as the A* algorithm, Dijkstra algorithm, etc. These algorithms establish a graph model of the environment and then search for the shortest path from the starting point to the ending point. Although these algorithms perform well in a static environment, in a dynamic environment or under complex obstacle distributions, the efficiency and quality of path planning are poor. Sampling-based methods: such as Rapidly-exploring Random Tree (RRT) and its variants. These methods construct a search tree through random sampling and are applicable to high-dimensional spaces and dynamic environments. Although the RRT algorithm can handle complex environments, in a high-dimensional space, the continuity and smoothness of the path are poor, and it is easily interfered by environmental factors during the path planning process. Methods based on optimization algorithms: such as particle swarm optimization (PSO), ant colony algorithm (ACO), and genetic algorithm (GA), etc. These algorithms seek the optimal path by simulating biological behaviors in nature (such as swarm search, reproduction, etc.). Although these methods have strong global search capabilities, there are often large uncertainties in convergence speed and accuracy, and they are easily trapped in local optimal solutions.

[0003] Among these methods, the grey wolf optimization algorithm (GWO) has received extensive attention in recent years. The grey wolf optimization algorithm is a nature-inspired optimization algorithm that simulates the social structure and hunting behavior of grey wolves. Its main advantages are strong global search capabilities, simple algorithm implementation, and few parameters. GWO can effectively guide the search process and avoid being trapped in local optimal solutions by simulating the leadership hierarchy of grey wolves (Alpha wolves, Beta wolves, Delta wolves, etc.). However, although the grey wolf optimization algorithm has achieved good results in many optimization problems, there are still some disadvantages. In practical applications, the grey wolf optimization algorithm is easily affected by the initial population, and in a complex environment with many constraint conditions, the convergence speed is slow, and it is easily trapped in local optimal solutions, resulting in unsatisfactory optimization effects. Summary of the Invention

[0004] In order to overcome the deficiencies of the above-mentioned existing technologies, the purpose of the present invention is to provide a UAV trajectory planning method and system based on an improved grey wolf optimization algorithm. The spherical vector coding method is used to efficiently code the UAV trajectory, significantly improving the flexibility and computational efficiency of trajectory representation; by introducing the Levy flight strategy, the global search ability of the algorithm is enhanced to avoid falling into local optimal solutions; at the same time, combined with the parameter adaptive adjustment strategy, the convergence speed and accuracy of the algorithm are significantly improved. The present invention effectively solves the problem of trajectory planning in complex mountainous environments and threat areas, and plans a safer and more efficient flight path for the UAV, with higher practicability and reliability.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A UAV trajectory planning method based on an improved grey wolf optimization algorithm, comprising the following steps;

[0007] Step 1, environmental modeling and parameter setting:

[0008] Construct a UAV trajectory environmental model based on the complex model of the real mountain environment and the distribution characteristics of threat areas, and set parameter information such as the starting point, ending point, and number of waypoints of the UAV;

[0009] Step 2, constraint condition and objective function design:

[0010] Set the condition constraints of the UAV according to the performance of the UAV itself, the flight safety requirements in the mountain environment, and the distribution characteristics of threat areas, and at the same time design the objective function of the UAV trajectory according to the evaluation index of trajectory planning;

[0011] Step 3, algorithm initialization and population generation:

[0012] Initialize the parameters of the improved grey wolf optimization algorithm, including the grey wolf population size, search space dimension, and maximum number of iterations; randomly generate an initial grey wolf population according to the starting point, ending point, and number of waypoints information of the UAV in Step 1; calculate the fitness value of each grey wolf according to the objective function designed in Step 2, and record the optimal solution of the current population;

[0013] Step 4, improved algorithm and trajectory update:

[0014] Iteratively update the population position through the improved grey wolf optimization algorithm, simulate the social hierarchy, hunting behavior, and encirclement mechanism of grey wolves. The whole process strictly follows the constraint conditions set in Step 2, introduce the Levy flight strategy to enhance the global search ability of the algorithm to avoid falling into local optimal solutions, and combine the parameter adaptive adjustment strategy to further improve the convergence speed and accuracy of the algorithm, so as to generate an updated feasible solution of the trajectory;

[0015] Step 5, Iteration Termination and Result Output:

[0016] After each iteration, determine whether the current iteration count reaches the preset maximum iteration count or meets the convergence condition; if so, output the current optimal trajectory planning result in the environment model established in Step 1 and end the algorithm; otherwise, return to Step 4 to continue iterative optimization until an optimal trajectory planning scheme that meets the conditions is obtained.

[0017] The specific process of the environmental modeling and parameter setting in Step 1 is as follows:

[0018] Step 1.1: Construct a mountain environment simulation model based on three-dimensional elevation map data, extract the elevation information of the terrain and the distribution characteristics of threat areas, and set the three-dimensional map area in the rectangular coordinate system. Its environmental model is shown in Equation (1):

[0019] Ω = {(x, y, z)|0 ≤ x ≤ X, 0 ≤ y ≤ Y, 0 ≤ z ≤ Z} (1)

[0020] Among them, x and y are the coordinates of the projection points on the horizontal plane in the environmental model, z is the elevation value corresponding to the projection point, and X, Y, and Z are the maximum boundary values in the map coordinate system; according to the distribution characteristics of the threat areas, set the specific position coordinates of the cylindrical threat areas in the simulation environment. Its center coordinates are (x i , y i ), the radius is r i , and the height is h i , as shown in Equation (2):

[0021] T i = {(x, y, z)|(x - x i ) 2 + (y - y i ) 2 ≤ r i 2 , 0 ≤ z ≤ h i} (2)

[0022] Among them, T i represents the i-th threat area;

[0023] Step 1.2: Set the starting point coordinates of the UAV as (x start , y start , z start ), the termination point coordinates as (x end , y end , z end ), and initialize the number of waypoints and other relevant parameter information to provide basic data support for subsequent trajectory planning.

[0024] The specific process of the constraint condition and objective function design in Step 2 is as follows:

[0025] Step 2.1: The shorter the flight path planned by the UAV, the shorter the time required for the UAV to complete the task, the higher the execution efficiency of the task. The extra path length cost is used to measure the difference between the actual flight path of the UAV and the theoretical shortest path; this cost is evaluated by calculating the ratio of the total length of the UAV's flight path to the straight-line distance from the starting point to the ending point, and finally normalized to a relative value, as shown in Equation (3):

[0026]

[0027] where p i =(x i , y i , z i ) represents the i-th point on the path, p s =(x s , y s , z s ) is the starting point, p f =(x f , y f , z f ) is the ending point, J k is a constant used to amplify the cost; N represents the total number of path points.

[0028] Step 2.2: The threat cost is used to evaluate the risk degree of the UAV passing through or approaching the threat area during flight. The threat cost is inversely proportional to the distance between the UAV and the threat area. The closer the distance, the higher the cost;

[0029] Step 2.3: The collision cost is used to evaluate the risk of the UAV colliding with the mountain terrain or other obstacles; this cost is closely related to the flight altitude of the UAV, the terrain undulation, and the distribution of obstacles;

[0030] Step 2.4: The target cost is used to measure the consistency between the direction of the path segment and the target direction. If the direction of the path segment is consistent with the target direction, the cost is 0. If the direction of the path segment deviates from the target direction, the cost gradually increases. Through such a design, the path optimization algorithm can guide the path towards the target direction and reduce unnecessary detours; the specific calculation of the target cost is shown in Equation (7):

[0031]

[0032] θ is the angle between the direction of the path segment and the target direction;

[0033] Step 2.5: The smoothness cost measures the smoothness of the path and consists of two parts: the horizontal turning angle cost and the vertical climbing angle cost. Through a piecewise linear cost function, sharp turns, sharp climbs, and descents of the path are penalized, thereby effectively guiding the path optimization algorithm to generate a smooth flight path and reducing unnecessary turns and climbs;

[0034] Step 2.6: Considering the additional path length cost, threat cost, collision cost, target cost, and smoothness cost of the UAV comprehensively, a target function reflecting the UAV flight path quality is constructed, as shown in Equation (11):

[0035] J = ω1·J1 + ω2·J2 + ω3·J3 + ω4·J4 + ω5·J5 (11)

[0036] where ω1, ω2, ω3, ω4, ω5 are the weights corresponding to each cost function, and J1, J2, J3, J4, J5 represent the additional path length cost, threat cost, collision cost, target cost, and smoothness cost of the UAV, respectively.

[0037] In the said Step 2.2:

[0038] The calculation of the threat cost is as shown in Equation (4):

[0039]

[0040] where N is the total number of path points, N threat is the total number of threats, t k =(x k , y k , z k ) is the center position and danger radius of the k-th threat, and Cost threat (p i , p i+1 , t k ) is the cost function between the path segment (p i , p i+1 ) and the threat t k . The specific cost function is as shown in Equation (5):

[0041]

[0042] d is the minimum distance from the path segment (p i , p i+1 ) to the threat t k , r k is the threat radius of the threat t k , is a weight factor used to smoothly transition between the warning distance and the danger distance. When d > 1.1r k it is in the safe area and the cost is 0 at this time. When rk k d ≤ 1.1r k In the warning area, the cost gradually increases as d decreases. When d ≤ r k In the dangerous area, the cost directly takes the maximum value;

[0043] In step 2.3:

[0044] The specific cost function is shown in Equation (6):

[0045]

[0046] Z L represents the height of the path segment (p i , p i+1 ) at any position. Z represents the terrain height. Z max , Z min represent the maximum and minimum heights of the terrain. 0.1·(Z max - Z min ) is the safety height threshold. When the height Z L of the path segment is higher than the terrain height Z and maintains the safety height threshold, it is a safe situation. When the height Z L of the path segment is lower than the terrain height Z or does not reach the safety height threshold, a collision is considered to have occurred.

[0047] Step 2.5 is specifically:

[0048] Regarding the specific calculation of the smoothing cost, as shown in Equation (8):

[0049]

[0050] θ i is the horizontal turning angle between the path segment (p i , p i+1 ) and (p i+1 , p i+2 ). φ i is the vertical climbing angle between the path segment (p i , p i+1 ) and (p i+1 , p i+2 ). Cost turn (θ i ) is the cost function of the horizontal turning angle. Cost climb (φ i ) is the cost function of the vertical climbing angle; the specific cost functions are shown in Equations (9) and (10):

[0051]

[0052] θ1 and θ2 are respectively the starting tolerance angle for path smoothing and the starting angle for sharp path turning, and φ1 and φ2 are respectively the starting tolerance angle for path smooth climbing and the starting angle for sharp path climbing.

[0053] The specific process of the algorithm initialization and population generation in step 3 is as follows:

[0054] Step 3.1: Initialize the algorithm parameters and set the relevant parameters:

[0055] The size n of the gray wolf population, the maximum number of iterations M, and the initialization of the population individuals are shown in Equation (12):

[0056] X = X1 + rand × (X u -X l ) (12)

[0057] where X is the initialized population, X u is the upper boundary of the population, X l is the lower boundary of the population, and rand represents a random number between [0, 1]; each individual in the population corresponds to a candidate path solution;

[0058] Step 3.2: Initialize the population X = {Xi, i = 1, 2,..., n}, and the position of the i-th gray wolf Xi represents a path composed of N path points. In the encoding of path points, the spherical vector encoding form is adopted, and each path is encoded as a group of vectors. Each vector describes the movement of the UAV from one waypoint to another waypoint. These vectors are represented in the spherical coordinate system and have three components, including the amplitude ρ ∈ (0, path l length), the elevation angle ψ ∈ (-π / 2, π / 2), and the azimuth angle φ ∈ (-π, π). Then, the flight path X i with N nodes is represented by a 3N-dimensional spherical vector:

[0059] X i = (ρ i1 , ψ i1 , φ i1 , ρ i2 , ψ i2 , φ i2 ,..., ρ iN , ψ iN , φ iN ), N = n - 2 (13)

[0060] To evaluate the quality of the path, it is necessary to map the vector-based flight path X i to the direct path x i , and the vector u ij = (ρ ij , ψij , φ ij ) ∈ X i to waypoint P ij = (x ij , y ij , z ij ) ∈ x i The mapping to is shown in Equation (14):

[0061]

[0062] Step 3.3: Generate a flyable flight path according to the initialization result X = {Xi, i = 1, 2,..., n}, calculate the fitness of each individual in the initial population using the cost function, and determine the role of the leading wolf according to the fitness value. Select the individual with the best fitness as the Alpha wolf, the individual with the second-best fitness as the Beta wolf, and the individual with the third-best fitness as the Delta wolf. The positions of the Alpha wolf, Beta wolf, and Delta wolf are defined as: X α , X β , X δ .

[0063] The specific process of the improved algorithm and flight path update in Step 4 is as follows:

[0064] Step 4.1: Surround the prey. During hunting, simulate the behavior of gray wolves surrounding the prey as shown in Equations (16) and (15). In the process of UAV flight path planning, each gray wolf individual represents a UAV flight path, and the flight path consists of multiple waypoints. The process of surrounding the prey is to continuously search for the optimal flight path in the solution space;

[0065] X(t + 1) = X p (t) - A · D (15)

[0066] D = ∣C · X p (t) - X(t)∣ (16)

[0067] Equation (16) represents the distance between an individual and the prey, and Equation (15) is the position update formula for gray wolves. t is the current iteration number. The coefficients A and C are used to control the movement of gray wolves in the search space. Among them, A determines whether the gray wolf individual approaches or moves away from the prey. When A > 1, the gray wolf individual moves away from the prey, which is the global search stage; otherwise, it is the local search stage. The role of C is to help enhance the diversity of the algorithm. Through the above formulas, the gray wolf individual can continuously adjust the waypoint coordinates in the search space, thereby realizing the dynamic update of the UAV flight path and simulating its behavior of approaching the optimal flight path. The coefficients A and C are respectively expressed as:

[0068] A = 2a · r1 - a (17)

[0069]

[0070] C = 2r2 (19)

[0071] Where: r1 and r2 are random variables on the interval [0, 1], m is the current iteration number, M is the maximum iteration number, and a determines the global search ability and local development ability of the grey wolf optimization algorithm; however, the parameter a of the traditional grey wolf optimization algorithm decreases linearly, making it difficult to balance the global and local search abilities of the grey wolf optimization algorithm. This application proposes a non-linear control adjustment strategy to balance the global and local search abilities of the algorithm;

[0072] Step 4.2: Chase the prey;

[0073] When a grey wolf individual identifies the current optimal trajectory, the three optimal individuals in the group are respectively used as the Alpha wolf, Beta wolf, and Delta wolf to guide the remaining grey wolves to conduct collaborative search around the optimal trajectory. The specific position update formula is as follows:

[0074] X1 = X α (t) - A1·D α , D α = |C1·X α (t) - X(t)| (20)

[0075] X2 = X β (t) - A2·D β , D β = |C2·X β (t) - X(t)| (21)

[0076] X3 = X δ (t) - A3·D δ , D δ = |C3·X δ (t) - X(t)| (22)

[0077]

[0078] Where: X1, X2, and X3 are the step lengths of the grey wolf individuals affected by the α wolf, β wolf, and δ wolf respectively, and V i The speed adjustment term calculated through the Laiwu flight model. The specific calculation formula is as follows:

[0079]

[0080] Among them, X i and X αrespectively represent the position of the current individual and the position of the Alpha wolf. u and v are random variables of the standard normal distribution, and β is the control parameter for the flight in Laiwu. Through the above update mechanism, each grey wolf individual continuously adjusts the encoding representation of its path points, and conducts collaborative search under the guidance of the three high-quality flight paths of Alpha, Beta, and Delta, so as to continuously approximate and iteratively optimize the global optimal flight path.

[0081] The specific process of the iteration termination and result output in step 5 is as follows:

[0082] Step 5.1: Judge the positions of all individuals in the population, and adjust the individuals that cross the boundary.

[0083] Step 5.2: By comparing the current iteration number with the maximum iteration number, judge whether the algorithm has reached the iteration termination condition. If the maximum iteration number has not been reached, return to step 4 to continue the iteration; if the maximum iteration number has been reached, stop the iteration.

[0084] Step 5.3: After the iteration stops, output the optimal fitness value, and draw the corresponding flight path map according to the position of the optimal individual.

[0085] An unmanned aerial vehicle (UAV) flight path planning system based on an improved grey wolf optimization algorithm, including an environment modeling and parameter setting module, a constraint condition and objective function design module, an algorithm initialization and population generation module, an improved algorithm and flight path update module, and an iteration termination and result output module;

[0086] The environment modeling and parameter setting module constructs the flight path environment model of the UAV according to the complex model of the real mountain environment and the distribution characteristics of the threat areas, and sets the parameter information such as the starting point, ending point, and the number of waypoints of the UAV. This module provides the environmental input basis for the subsequent constraint condition setting and objective function design module, and at the same time provides the basic path planning space for the algorithm initialization and individual encoding;

[0087] The constraint condition and objective function design module sets the condition constraints of the UAV according to the performance of the UAV itself, the flight safety requirements in the mountain environment, and the distribution characteristics of the threat areas. At the same time, it designs the objective function of the UAV flight path according to the evaluation index of the flight path planning. The designed objective function will be used as the core basis for the evaluation of the fitness of the algorithm population and directly participate in the population evolution and flight path update process;

[0088] The algorithm initialization and population generation module initializes the parameters of the improved grey wolf optimization algorithm according to the flight environment parameters and path dimension information set by the environment modeling and parameter setting module, including the grey wolf population size, search space dimension, maximum iteration number, etc., and randomly generates the initial grey wolf population. Then, it calculates the fitness value of each grey wolf according to the objective function designed in the constraint condition and objective function design module, and records the optimal solution of the current population;

[0089] Improved Algorithm and Trajectory Update Module: Based on the combination of the set objective function and the fitness evaluation results, this module uses the improved Grey Wolf Optimization algorithm to iteratively update the population position. The optimization process includes simulating the social hierarchy structure, encirclement mechanism, and hunting behavior of grey wolves, and introducing the Levy flight strategy to enhance the global search ability of the algorithm and increase the possibility of jumping out of local optima. At the same time, combined with the parameter adaptive adjustment mechanism, the convergence efficiency and solution accuracy of the algorithm are further improved. The obtained updated trajectory solution will be used for fitness evaluation and serve as the basis for judging whether the termination condition is met, thus forming a feedback relationship with the Iterative Termination and Result Output Module.

[0090] Iterative Termination and Result Output Module: After each iteration, it judges whether the current iteration number reaches the preset maximum iteration number or meets the convergence condition. If so, it outputs the current optimal trajectory planning result and ends the algorithm; otherwise, it returns to the Improved Algorithm and Trajectory Update Module to continue iterative optimization until an optimal trajectory planning scheme that meets the conditions is obtained.

[0091] Advantages of the present invention:

[0092] 1. In step 1 of the present invention, by constructing a more realistic and accurate trajectory environment model based on the complex model of the real mountain environment and the distribution characteristics of threat areas, it can better adapt to complex environmental conditions and ensure the safety and reliability of UAV trajectory planning.

[0093] 2. In step 2 of the present invention, according to the flight performance of the UAV itself and the flight safety requirements in the mountain environment, more reasonable constraint conditions are designed. At the same time, combined with the evaluation index of the flight mission, the design of the objective function is optimized, making the trajectory planning more in line with the actual application requirements and improving the effectiveness of the UAV flight path.

[0094] 3. In step 4 of the present invention, by introducing the Levy flight strategy into the grey wolf position update formula, according to the definition of the speed adjustment term, the long jump characteristic of the Levy distribution is used to enhance the ability of the search individual to jump out of the local optimum, thus significantly improving the global search performance of the algorithm. This strategy enables the grey wolf individuals to form a large-scale search step with uncertain perturbations between the current position and the Alpha wolf, effectively avoiding the dilemma of the search falling into the local optimum. In addition, the present invention improves the adjustment factor for controlling the search range and intensity of individuals, and proposes a dynamic adjustment mechanism based on non-linear decreasing. This mechanism enables the population to have stronger global exploration ability in the initial stage of the search and stronger local exploitation ability in the later stage, thus improving the path quality and convergence speed.

[0095] In summary, compared with the prior art, by introducing an improved grey wolf optimization algorithm, optimized environmental modeling, constraint condition design, and Lévy flight strategy, the present invention not only improves the global search ability and convergence accuracy of the algorithm, but also can effectively adapt to complex environments, generate safer and more reliable UAV trajectory planning results, and enhance the overall efficiency and safety of flight missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 It is a flowchart of a UAV trajectory planning method based on an improved grey wolf optimization algorithm of the present invention.

[0097] Figure 2 It is a flowchart of the improved grey wolf optimization algorithm in the present invention.

[0098] Figure 3 It is a three-dimensional route map and top view of UAV trajectory planning implemented using the improved grey wolf optimization algorithm in the present invention.

[0099] Figure 4 It is a convergence curve graph showing the change of the objective function value of the improved grey wolf optimization algorithm in the present invention with the number of iterations. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0100] The present invention will be further described in detail below with reference to the accompanying drawings.

[0101] Refer to Figure 1 , a UAV trajectory planning method based on an improved grey wolf optimization algorithm, includes the following steps:

[0102] Step 1, environmental modeling and parameter setting: Construct a UAV trajectory environmental model based on the complex model of the real mountain environment and the distribution characteristics of threat areas, and set parameter information such as the starting point, ending point, and number of waypoints of the UAV. By modeling the flight environment, a real and effective simulation space is provided for subsequent optimization, improving the usability of the path planning results and the adaptability of the application scenarios;

[0103] Step 2, constraint condition and objective function design: Set the condition constraints of the UAV according to the UAV's own performance, flight safety requirements in the mountain environment, and the distribution characteristics of threat areas, and design the objective function of the UAV trajectory according to the evaluation index of trajectory planning. The design of this step ensures that the generated trajectory not only meets the task objectives, but also conforms to flight safety and operation feasibility, improving the comprehensive performance of the planning results.

[0104] Step 3, Algorithm Initialization and Population Generation: Initialize the parameters of the improved Grey Wolf Optimization algorithm, including the Grey Wolf population size, search space dimension, maximum number of iterations, etc., and randomly generate the initial Grey Wolf population. Calculate the fitness value of each Grey Wolf and record the optimal solution of the current population. This step covers the search space through a diverse initial population, providing a good foundation for subsequent global search and helping to avoid the algorithm falling into local optimal solutions in the early stage.

[0105] Step 4, Improved Algorithm and Trajectory Update: By introducing various improvement strategies of the Grey Wolf Optimization algorithm, iteratively update the population positions, specifically including simulating the social hierarchy structure, hunting behavior, and encirclement mechanism of Grey Wolves, and combining with the Levy flight strategy to enhance the jumping ability and exploration diversity of the population, thereby effectively improving the global search ability of the algorithm and avoiding falling into local optima. At the same time, use the adaptive weight mechanism to dynamically adjust the population search intensity, realizing the contraction of the search range from large to small, so that the algorithm is more focused on wide-area exploration in the initial stage of iteration and on fine search in the later stage, further accelerating the convergence speed and improving the optimization accuracy. Through the synergistic effect of these mechanisms, it is possible to continuously generate higher-quality feasible trajectory solutions, significantly improving the optimization effect and stability of the overall path planning;

[0106] Step 5, Iteration Termination and Result Output: After each iteration, judge whether the current number of iterations reaches the preset maximum number of iterations or meets the convergence condition. If so, output the current optimal trajectory planning result and end the algorithm; otherwise, return to Step 4 to continue iterative optimization until an optimal trajectory planning scheme that meets the conditions is obtained. This step ensures a balance between the convergence and efficiency of the optimization algorithm, and finally obtains a high-quality trajectory planning scheme.

[0107] See Figure 2 , the specific processes of the above Step 3 and Step 4 are as follows:

[0108] Step 3.1: Initialize the algorithm parameters, set the relevant parameters: Grey Wolf population size n, maximum number of iterations M, and the initialization of population individuals is shown in Equation (1):

[0109] X = X1 + rand × (X u - X l ) (1)

[0110] where X is the initialized population, X u is the upper bound of the population, X l is the lower bound of the population, and rand represents a random number between [0, 1]. This process ensures that the population individuals have good distribution diversity in the search space, helps the algorithm to fully cover the solution space in the initial stage, lays a foundation for subsequent global search, and improves the ability of the algorithm to jump out of local optimal solutions and the overall convergence performance.

[0111] Step 3.2: Initialize the population X = {Xi, i = 1, 2, …, n}, where the position of the i-th gray wolf Xi represents a path composed of N path points. In the encoding of path points, a spherical vector encoding form is adopted, and each path is encoded as a set of vectors. Each vector describes the movement of the UAV from one waypoint to another, and these vectors are represented in the spherical coordinate system and have three components, including amplitude ρ ∈ (0, path l ength), elevation angle ψ ∈ (-π / 2, π / 2), and azimuth angle φ ∈ (-π, π). This path modeling method not only enhances the flexibility and continuity of flight path expression but also provides a structural basis for subsequent path optimization and feasibility evaluation. The flight path X with N nodes i is represented by a 3N-dimensional spherical vector:

[0112] X i =(ρ i1 ,ψ i1 ,φ i1 ,ρ i2 ,ψ i2 ,φ i2 ,...,ρ iN ,ψ iN ,φ iN ), N = n - 2 (2)

[0113] To evaluate the quality of the path, it is necessary to map the vector-based flight path X i to the direct path x i . The mapping of the vector u ij =(ρ ij ,ψ ij ,φ ij ) ∈ X i to the waypoint P ij =(x ij ,y ij ,z ij ) ∈ x i is as shown in the formula:

[0114]

[0115] Step 3.3: Generate a flyable flight path according to the initialization result, calculate the fitness of each individual in the initialized population using the cost function, and determine the role of the leading wolf according to the fitness value. Select the individual with the best fitness as the Alpha wolf, the individual with the second-best fitness as the Beta wolf, and the individual with the third-best fitness as the Delta wolf. Their positions are respectively defined as: X α ,X β ,X δThis process effectively guides the subsequent position update direction in the algorithm, ensuring that the population evolution moves towards a more optimal solution set, thereby improving the overall convergence speed and track quality of the algorithm.

[0116] Step 4.1: Surround the prey. When hunting, the behavior of gray wolves surrounding the prey is simulated as shown in Equations (4) and (5):

[0117] X(t + 1) = X p (t) - A·D (4)

[0118] D = ∣C·X p (t) - X(t)∣ (5)

[0119] Equation (5) represents the distance between an individual and the prey, and Equation (4) is the position update formula for gray wolves. t is the current iteration number. The coefficients A and C are used to control the movement of gray wolves in the search space. Among them, A determines whether the gray wolf individual approaches or moves away from the prey. When A > 1, the gray wolf individual moves away from the prey, which is the global search stage; otherwise, it is the local search stage. The role of C is to help enhance the diversity of the algorithm. Through the above formulas, the gray wolf individual can continuously adjust the path point coordinates in the search space, thereby realizing the dynamic update of the UAV track and simulating its behavior of approaching the optimal track. The coefficients A and C are respectively expressed as:

[0120] A = 2a·r1 - a (6)

[0121]

[0122] C = 2r2 (8)

[0123] In the formula: r1, r2 are random variables in the interval [0, 1], m is the current iteration number, M is the maximum iteration number, and a determines the global search ability and local development ability of the gray wolf optimization algorithm. However, the parameter a of the traditional gray wolf optimization algorithm decreases linearly, and it is difficult to balance the global and local search abilities of the gray wolf optimization algorithm. This paper proposes a non-linear control adjustment strategy to balance the global and local search abilities of the algorithm;

[0124] Step 4.2: Chase the prey. When a gray wolf individual identifies the current optimal track, the three optimal individuals in the group are respectively used as Alpha wolf, Beta wolf, and Delta wolf to guide the remaining gray wolves to conduct cooperative search around the optimal track. The specific update formula for the gray wolf individual is as follows:

[0125] X1 = X α (t) - A1·D α , D α = |C1·X α (t) - X(t)| (9)

[0126] X2 = X β (t) - A2·D β , D β = |C2·X β (t) - X(t)| (10)

[0127] X3 = X δ (t) - A3·D δ , D δ = |C3·X δ (t) - X(t)| (11)

[0128]

[0129] Where: X1, X2, and X3 are the step lengths of the gray wolf individuals affected by the α wolf, β wolf, and δ wolf respectively when moving, and V i The speed adjustment term calculated through the Laiwu flight model, and the specific calculation formula is shown in the following formula (13):

[0130]

[0131] Among them, X i and X α represent the position of the current individual and the position of the Alpha wolf respectively, u and v are random variables of the standard normal distribution, and β is the control parameter of the Laiwu flight. Through the above update mechanism, each gray wolf individual continuously adjusts the encoded representation of its path points, and conducts cooperative search under the guidance of the three high-quality flight paths of Alpha, Beta, and Delta, so as to achieve continuous approximation and iterative optimization of the global optimal flight path.

[0132] By continuously updating the positions of the gray wolves and performing calculations until the maximum number of iterations is reached. During this process, the optimal flight path planning result is output according to the final positions of the gray wolves (see Figure 3 ). From the appendix Figure 3 It can be seen that after the algorithm processing of each link in steps 3 and 4, the system successfully generates a high-quality optimal flight path in three-dimensional space. This path not only meets the task flight requirements between the starting point and the ending point, but also strictly follows the flight performance constraints of the UAV in terms of path configuration, such as the maximum climb angle, turning radius, and smoothness requirements, and effectively avoids all threat areas, fully reflecting the effective avoidance ability of terrain obstacles and threat sources. The overall path has high smoothness and spatial continuity, showing good feasibility and safety. This result fully verifies the rationality and effectiveness of the proposed algorithm in the links of parameter initialization, path encoding, fitness evaluation, and simulating the social hierarchy and encirclement mechanism of gray wolves, and can scientifically and efficiently plan the UAV flight path in complex mountain environments.

[0133] Meanwhile, according to the changes in the fitness value during the iterative process, a convergence curve graph of the objective function value with respect to the number of iterations is plotted (see Figure 4 ). As can be seen from the appendix Figure 4 , as the number of iterations increases, the optimal fitness value shows a trend of rapid decline and finally stable convergence. In the initial stage, the optimal fitness drops rapidly from a relatively high value, indicating that the algorithm has good global exploration ability in the initial search stage and can quickly lock in high-quality solutions in the solution space. Subsequently, the fitness curve gradually flattens out and stabilizes near a relatively low value, indicating that the algorithm has strong convergence and can effectively approximate the global optimal solution within a limited number of iterations, avoiding being trapped in the local optimal dilemma. During the entire optimization process, the fitness curve does not show obvious fluctuations or stagnation, further reflecting the advantages of the algorithm in terms of stability and reliability. It can continuously and efficiently evolve towards the optimal solution, demonstrating good optimization performance and engineering applicability.

[0134] In summary, compared with the existing technologies, the present invention, by introducing an improved grey wolf optimization algorithm, optimized environmental modeling, constraint condition design, and Levy flight strategy, not only improves the global search ability and convergence accuracy of the algorithm, but also can effectively adapt to complex environments, generate safer and more reliable UAV trajectory planning results, and improve the overall efficiency and safety of flight missions.

[0135] A UAV trajectory planning system based on an improved grey wolf optimization algorithm, comprising:

[0136] An environmental modeling and parameter setting module: constructs a UAV trajectory environment model based on the complex model of the real mountain environment and the distribution characteristics of threat areas, and sets parameter information such as the starting point, ending point, and the number of waypoints of the UAV;

[0137] A constraint condition and objective function design module: sets the condition constraints of the UAV according to the UAV's own performance, flight safety requirements in the mountain environment, and the distribution characteristics of threat areas, and designs the objective function of the UAV trajectory according to the evaluation index of trajectory planning;

[0138] An algorithm initialization and population generation module: initializes the parameters of the improved grey wolf optimization algorithm, including the grey wolf population size, search space dimension, maximum number of iterations, etc., randomly generates an initial grey wolf population, calculates the fitness value of each grey wolf, and records the optimal solution of the current population;

[0139] An improved algorithm and trajectory update module: iteratively updates the positions of the grey wolf population through the improved grey wolf optimization algorithm, including simulating the social hierarchy, hunting behavior, and encirclement mechanism of grey wolves, introducing the Levy flight strategy to enhance the global search ability of the algorithm, avoiding being trapped in local optimal solutions, and further improving the convergence speed and accuracy of the algorithm by combining the parameter adaptive adjustment strategy, thereby generating updated feasible trajectory solutions;

[0140] Iteration termination and result output module: After each iteration, it is judged whether the current iteration count reaches the preset maximum iteration count or meets the convergence condition. If it is satisfied, the current optimal trajectory planning result is output and the algorithm ends; otherwise, it returns to the improved algorithm and trajectory update module to continue iterative optimization until an optimal trajectory planning scheme that meets the conditions is obtained.

Claims

1. An unmanned aerial vehicle trajectory planning method based on an improved grey wolf optimization algorithm, characterized in that, Including the following steps; Step 1: Construct a trajectory environment model for the UAV based on the complex model of the real mountain environment and the distribution characteristics of threat areas, and set the parameter information of the starting point, ending point and the number of waypoints of the UAV; Step 2: Set the condition constraints of the UAV according to the UAV's own performance, flight safety requirements in the mountain environment and the distribution characteristics of threat areas, and design the objective function of the UAV trajectory according to the evaluation index of trajectory planning; Step 3: Initialize the parameters of the improved grey wolf optimization algorithm, including the grey wolf population size, search space dimension, maximum number of iterations; randomly generate an initial grey wolf population according to the starting point, ending point and the number of waypoints information of the UAV; calculate the fitness value of each grey wolf according to the objective function, and record the optimal solution of the current population; Step 4: Iteratively update the population position through the improved grey wolf optimization algorithm, simulate the social hierarchy, hunting behavior and encirclement mechanism of grey wolves, introduce the Lévy flight strategy based on the constraint conditions, and combine with the parameter adaptive adjustment strategy to generate an updated feasible solution of the trajectory; Step 5: After each iteration, judge whether the current iteration number reaches the preset maximum iteration number or meets the convergence condition; If satisfied, output the current optimal trajectory planning result in the environment model established in Step 1 and end the algorithm; otherwise, return to Step 4 to continue iterative optimization until an optimal trajectory planning scheme that meets the conditions is obtained.

2. The method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 1, characterized in that, The specific process of the environmental modeling and parameter setting in Step 1 is as follows: Step 1.1: Construct a mountain environment simulation model based on the three-dimensional elevation map data, extract the elevation information of the terrain and the distribution characteristics of threat areas, and set the three-dimensional map area in the rectangular coordinate system. Its environmental model is shown in Equation (1): Ω={(x,y,z)|0≤x≤X,0≤y≤Y,0≤z≤Z} (1) Among them, x and y are the coordinates of the projection points on the horizontal plane in the environmental model, z is the elevation value corresponding to the projection point, and X, Y, and Z are the maximum boundary values in the map coordinate system; according to the distribution characteristics of the threat area, the specific position coordinates of the cylindrical threat area are set in the simulation environment, and its center coordinates are (x i , y i ), the radius is r i , and the height is h i , as shown in Equation (2): Among them, T i represents the i-th threat area; Step 1.2: Set the starting point coordinates of the drone as (x start , y start , z start ), the ending point coordinates as (x end , y end , z end ), and initialize the number of waypoints and other relevant parameter information.

3. A method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 1, characterized in that, The specific process of the constraint condition and objective function design in Step 2 is as follows: Step 2.1: The shorter the flight trajectory planned by the UAV, the shorter the time required for the UAV to complete the task, the higher the execution efficiency of the task, and the additional path length cost is used to measure the difference between the actual flight path of the UAV and the theoretical shortest path; The length cost is evaluated by calculating the ratio of the total length of the UAV trajectory to the straight-line distance from the starting point to the ending point, and finally normalized to a relative value; Step 2.2: The threat cost is used to evaluate the risk degree of the UAV passing through or approaching the threat area during flight. The threat cost is inversely proportional to the distance between the UAV and the threat area. The closer the distance, the higher the cost; Step 2.3: The collision cost is used to evaluate the risk of the UAV colliding with the mountain terrain or other obstacles; this cost is closely related to the flight height of the UAV, the terrain undulation and the distribution of obstacles; Step 2.4: The target cost is used to measure the consistency between the path segment direction and the target direction. If the path segment direction is consistent with the target direction, the cost is 0. If the path segment direction deviates from the target direction, the cost gradually increases; Step 2.5: The smooth cost consists of two parts: the horizontal turning angle cost and the vertical climbing angle cost. Through the piecewise linear cost function, it punishes the sharp turning, sharp climbing and descending of the path. Step 2.6: Comprehensively consider the extra path length cost, threat cost, collision cost, target cost, and smoothness cost of the UAV, and then construct an objective function reflecting the UAV flight path quality, as shown in Equation (11): J = ω1·J1 + ω2·J2 + ω3·J3 + ω4·J4 + ω5·J5 (11) where ω1, ω2, ω3, ω4, and ω5 are the weights corresponding to each cost function, and J1, J2, J3, J4, and J5 represent the extra path length cost, threat cost, collision cost, target cost, and smoothness cost of the UAV, respectively.

4. A UAV flight path planning method based on an improved grey wolf optimization algorithm according to claim 3, characterized in that in the said Step 2.1; as shown in Equation (3): where p i = (x i , y i , z i ) represents the i-th point on the path, p s = (x s , y s , z s ) is the starting point, p f = (x f , y f , z f ) is the ending point, J k is a constant used to amplify the cost; N represents the total number of path points. in the said Step 2.2: the calculation of the threat cost is as shown in Equation (4): Among them, N is the total number of path points, N threat is the total number of threats, t k =(x k , y k , z k ) is the center position and danger radius of the k-th threat, Cost threat (p i , p i+1 , t k ) is the cost function between the path segment (p i , p i+1 ) and the threat t k . The specific cost function is shown in Equation (5): d is the minimum distance from the path segment (p i , p i+1 ) to the threat t k . r k is the threat radius of the threat t k , and is a weight factor used to smoothly transition between the warning distance and the danger distance. When d > 1.1r k , it is in the safe area and the cost is 0 at this time. When r k < d ≤ 1.1r k , it is in the warning area and the cost gradually increases as d decreases. When d ≤ r k , it is in the danger area and the cost directly takes the maximum value.

5. The method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 3, characterized in that, in the said Step 2.3: the specific cost function is as shown in Equation (6): Z L represents the height of the path segment (p i , p i+1 ) at any position, Z represents the terrain height, Z max , Z min represent the maximum and minimum heights of the terrain, 0.1·(Z max - Z min ) is the safety height threshold. When the height Z of the path segment L is higher than the terrain height Z and maintains the safety height threshold, it is a safe situation. When the height Z of the path segment L is lower than the terrain height Z or does not reach the safety height threshold, a collision is considered to have occurred; in the said Step 2.4; the specific calculation of the target cost is as shown in Equation (7): θ is the angle between the path segment direction and the target direction; J k is a constant used to amplify the cost.

6. The method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 3, characterized in that, the said Step 2.5 is specifically: the specific calculation of the smoothness cost is as shown in Equation (8): θ i is the horizontal turning angle between the path segments (p i , p i+1 ) and (p i+1 , p i+2 ), φ i is the vertical climbing angle between the path segments (p i , p i+1 ) and (p i+1 , p i+2 ), Cost turn (θ i ) is the cost function of the horizontal turning angle, Cost climb (φ i ) is the cost function of the vertical climbing angle; the specific cost functions are shown in Equations (9) and (10) as follows: θ1 and θ2 are the starting tolerance angles for path smoothness and the starting angle for sharp path turning, respectively, and φ1 and φ2 are the starting tolerance angles for path smooth climbing and the starting angle for sharp path climbing, respectively.

7. A method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 1, characterized in that The specific process of the said Step 3 algorithm initialization and population generation is: Step 3.1: Initialize the algorithm parameters and set the relevant parameters: the grey wolf population size n, the maximum number of iterations M, and the initialization of the population individuals are as shown in Equation (12): X = X1+rand×(X u -X l ) (12) Among them, X is the initialized population, X u is the upper boundary of the population, X l is the lower boundary of the population, rand represents a random number between [0, 1]; each individual in the population corresponds to a candidate path solution; Step 3.2: Initialize the population X = {Xi, i = 1, 2, …, n}, where the position of the i-th grey wolf Xi represents a path composed of N path points. In the encoding of path points, the spherical vector encoding form is adopted, and each path is encoded as a set of vectors. Each vector describes the movement of the UAV from one waypoint to another waypoint. These vectors are represented in the spherical coordinate system and have three components, including the amplitude ρ ∈ (0, path l length), the elevation angle ψ ∈ (-π / 2, π / 2), and the azimuth angle φ ∈ (-π, π). Then, the flight path X of N nodes i is represented by a 3N-dimensional spherical vector: X i = (ρ i1 , ψ i1 , φ i1 , ρ i2 , ψ i2 , φ i2 ,..., ρ iN , ψ iN , φ iN ), N = n - 2 (13) Map the vector-based flight path X i to the direct path x i , the vector u ij =(ρ ij , ψ ij , φ ij ) ∈ X i to the waypoint P ij =(x ij , y ij , z ij ) ∈ x i is shown in Equation (14) as follows: Step 3.3: Generate flyable flight paths according to the initialization result X = {Xi, i = 1, 2, …, n}, calculate the fitness of each individual in the initialized population using the cost function, and determine the role of the leading wolf according to the fitness value. Select the individual with the optimal fitness as the Alpha wolf, the individual with the second-best fitness as the Beta wolf, and the individual with the third-best fitness as the Delta wolf. The positions where the Alpha wolf, Beta wolf, and Delta wolf are located are defined as: X α , X β , X δ .

8. A method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 1, characterized in that The specific process of the said Step 4 improved algorithm and flight path update is: Step 4.1: Surround the prey. During hunting, simulate the behavior of grey wolf encirclement as shown in Equations (15) and (16). During the UAV flight path planning process, each grey wolf individual represents a UAV flight path, and the flight path consists of multiple path points. The process of surrounding the prey is to continuously search for the optimal flight path in the solution space; X(t + 1) = X p (t) - A·D(15) D = |C·X p (t) - X(t)| (16) Equation (16) represents the distance between the individual and the prey, and Equation (12) is the position update formula of the grey wolf. t is the current iteration number. The coefficients A and C are used to control the movement of the grey wolf in the search space. Among them, A determines whether the grey wolf individual approaches or moves away from the prey. When A > 1, the grey wolf individual moves away from the prey, which is the global search stage, and vice versa is the local search stage; the role of C is to help enhance the diversity of the algorithm; among them, the coefficients A and C are respectively expressed as: A = 2a·r1 - a (17) C＝2r2 (19) In the formula: r1, r2 are random variables in the interval [0, 1], m is the current iteration number, M is the maximum number of iterations, and a determines the global search ability and local development ability of the grey wolf optimization algorithm; Step 4.2: Chase the prey; When a grey wolf individual identifies the current optimal flight path, the three optimal individuals in the group are respectively used as the Alpha wolf, Beta wolf, and Delta wolf to guide the remaining grey wolves to conduct collaborative search around the optimal flight path. The specific position update formula is as follows: X1 = X α (t) - A1·D α , D α = |C1·X α (t) - X(t)| (20) X2 = X β (t) - A2·D β , D β = |C2·X β (t) - X(t)| (21) X3 = X δ (t) - A3·D δ , D δ = |C3·X δ (t) - X(t)| (22) where: X1, X2, and X3 are the step lengths of the grey wolf individuals affected by the α wolf, β wolf, and δ wolf respectively, and V i is the speed adjustment term calculated by the Laiwu flight model, and the specific calculation formula is as follows: Among them, X i and X α respectively represent the position of the current individual and the position of the Alpha wolf. u and v are random variables of the standard normal distribution, and β is the control parameter for flying in Laiwu. Through the above update mechanism, each gray wolf individual continuously adjusts the encoded representation of its path points, and conducts collaborative search under the guidance of the three high-quality flight paths of Alpha, Beta, and Delta, realizing the continuous approximation and iterative optimization of the global optimal flight path.

9. A method for unmanned aerial vehicle trajectory planning based on an improved grey wolf optimization algorithm according to claim 1, characterized in that, The specific process of the said Step 5 iteration termination and result output is: Step 5.1: Judge the positions of all individuals in the population and adjust the individuals that exceed the boundary; Step 5.2: Determine whether the algorithm has reached the iteration termination condition by comparing the current iteration number with the maximum iteration number. If the maximum iteration number has not been reached, return to Step 4 to continue the iteration; if the maximum iteration number has been reached, stop the iteration. Step 5.3: After the iteration stops, output the optimal fitness value and draw the corresponding flight path map according to the position of the optimal individual.

10. An unmanned aerial vehicle trajectory planning system based on an improved grey wolf optimization algorithm, characterized in that, It includes an environmental modeling and parameter setting module, a constraint condition and objective function design module, an algorithm initialization and population generation module, an improved algorithm and flight path update module, and an iteration termination and result output module. The environmental modeling and parameter setting module constructs the flight path environment model of the UAV based on the complex model of the real mountain environment and the distribution characteristics of threat areas, and sets parameter information such as the starting point, ending point, and number of waypoints of the UAV. The constraint condition and objective function design module sets the conditional constraints of the UAV according to the performance of the UAV itself, the flight safety requirements in the mountain environment, and the distribution characteristics of threat areas. At the same time, the objective function of the UAV flight path is designed according to the evaluation index of flight path planning. The algorithm initialization and population generation module initializes the parameters of the improved grey wolf optimization algorithm according to the flight environment parameters and path dimension information set by the environmental modeling and parameter setting module, including the grey wolf population size, search space dimension, and maximum iteration number, and randomly generates the initial grey wolf population. Then, according to the objective function designed in the constraint condition and objective function design module, calculates the fitness value of each grey wolf and records the optimal solution of the current population. Based on the combination of the set objective function and fitness evaluation results, the improved algorithm and flight path update module uses the improved grey wolf optimization algorithm to iteratively update the population position. The optimization process includes simulating the social hierarchy structure, encirclement mechanism, and hunting behavior of grey wolves, and introducing the Levy flight strategy to enhance the global search ability of the algorithm and increase the possibility of jumping out of the local optimum. At the same time, combined with the parameter adaptive adjustment mechanism, further improve the convergence efficiency and solution accuracy of the algorithm; the obtained updated flight path solution will be used for fitness evaluation and used as the basis for judging whether the termination condition is met, forming a feedback relationship with the iteration termination and result output module. The iteration termination and result output module determines whether the current iteration number reaches the preset maximum iteration number or meets the convergence condition after each iteration. If it is satisfied, output the current optimal flight path planning result and end the algorithm; otherwise, return to the improved algorithm and flight path update module to continue iterative optimization until an optimal flight path planning scheme that meets the conditions is obtained.

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