Unmanned aerial vehicle flight path planning method based on improved Harris eagle optimization algorithm

Abstract

The invention discloses an unmanned aerial vehicle flight path planning method based on an improved Harris eagle optimization algorithm, and the method comprises the steps: setting peak parameter information, constructing a threat equivalent terrain simulation map through a peak function, and carrying out the modeling of a flight environment; establishing a corresponding cost function according to the length cost, the threat cost and the smoothness cost of the flight path, and converting a flight path planning problem into an optimization problem of minimizing the cost function; and solving the optimization problem of the minimum cost function by using an improved Harris eagle optimization algorithm fusing a labor division mechanism and an elimination selection strategy, and carrying out iterative optimization to obtain the optimal flight path of the unmanned aerial vehicle. According to the invention, the feasible track can be explored and developed as much as possible in the flight space, collision and track jitter can be avoided, and smooth execution of the flight task of the unmanned aerial vehicle is facilitated.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) trajectory planning, and in particular to a UAV trajectory planning method based on an improved Harris Hawk optimization algorithm. Background Art

[0002] In recent years, drone technology has developed rapidly. With its advantages of low cost and fast response speed, it has been widely used in military and civilian fields. Track planning is an important research field in drone technology. Its purpose is to plan a flight path to ensure that the drone can avoid threat areas and reach its destination smoothly while meeting its own constraints. An excellent track can not only maintain the safety of the drone flight process, but also ensure the drone's endurance. Therefore, a good drone track planning method is an important guarantee for the successful execution of drone flight missions.

[0003] The research solutions of domestic and foreign scholars on the trajectory planning problem can be divided into two categories: ① Traditional algorithms, including A* algorithm, RRT algorithm, artificial potential field method, etc. ② Intelligent optimization algorithms, including particle swarm optimization algorithm [5], gray wolf algorithm, whale optimization algorithm, etc. Compared with traditional algorithms, intelligent algorithms have the advantages of fast optimization speed and strong stability, and are more adaptable to the increasingly complex UAV planning problems.

[0004] Among the intelligent optimization algorithms, the Harris Hawk Optimization algorithm (HHO) has the advantages of simple principle, few parameters and easy implementation, and can better adapt to the UAV trajectory planning problem. However, its disadvantages are low convergence accuracy, slow convergence speed and easy to fall into local optimality, which can easily cause redundant flight of the UAV and affect the endurance performance of the UAV. Summary of the invention

[0005] The purpose of the present invention is to provide a UAV trajectory planning method based on an improved Harris Hawk optimization algorithm, which can improve the convergence accuracy and greatly improve its stability on the basis of the original Harris Hawk optimization algorithm, and more effectively handle the UAV trajectory planning problem.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0007] A UAV trajectory planning method based on an improved Harris Hawk optimization algorithm, the UAV trajectory planning method comprising the following steps:

[0008] S1, set the peak parameter information, use the peak function to construct the threat equivalent terrain simulation map, and model the flight environment;

[0009] S2, according to the length cost, threat cost and smoothness cost of the track, a corresponding cost function is established to transform the track planning problem into an optimization problem of minimizing the cost function;

[0010] S3, using the improved Harris Eagle optimization algorithm that integrates the division of labor mechanism and elimination selection strategy, solves the optimization problem of minimizing the cost function, and iteratively optimizes to obtain the optimal trajectory of the UAV.

[0011] Furthermore, in step S1, the mathematical model of the flight environment is:

[0012]

[0013] In the formula, z(x,y) represents the terrain height corresponding to the point (x,y) on the horizontal plane; p represents the number of peaks; h(i) represents the peak height of the i-th peak; x ci and ci Respectively represent the horizontal and vertical coordinates of the ith peak vertex; x ki and ki Represents the peak attenuation coefficient, which is inversely proportional to the slope.

[0014] Step S2 further comprises:

[0015] Assume that p i (x i ,y i ,z i ) represents a track point, track Path = {p 0 ,p 1 ,p 2 ,...,p n-1 ,p n} represents the set of all points on the track, p 0 is the starting point, p n As the target point, the length cost model of the track is:

[0016]

[0017] Take 5 segmentation points at equal distances for each track, and determine the threat size of the track segment by the height difference between the segmentation points and the terrain. The threat cost model of the track is:

[0018]

[0019] Among them, T j h represents the height threat of the jth segment point in each track; j represents the height of the jth segment point; z j Indicates the terrain height corresponding to the jth segment point; h safe Indicates safe height; T const It means that the terrain cannot be crossed;

[0020] According to the constraints of turning angle and climb / descent angle, the smoothness cost model of the track is obtained as follows:

[0021]

[0022] Among them, S i represents the smoothing cost at the i-th track point; φ i and θ i They represent the turning angle and climb / descent angle at the i-th track point respectively; φ max and θ max Respectively represent the maximum turning angle and the maximum climbing / gliding angle;

[0023] According to the length cost, threat cost and smoothness cost of the track, the cost function of the track is established as:

[0024] C=α 1 C 1 +α 2 C 2 +α 3 C 3

[0025] Where C represents the total cost of the track, C 1 , C 2 and C 3 They represent the length cost, threat cost and smoothness cost of the track respectively, α 1 , α 2 and α 3 Represents the weight of each cost.

[0026] Step S3 further comprises:

[0027] Set the population size N and the maximum number of iterations T;

[0028] Determine the starting and ending points of the track, randomly generate N tracks, and each Harris hawk individual corresponds to a random track;

[0029] At the beginning of each iteration, the prey escape energy is calculated and selected in two stages:

[0030] If entering the exploration phase, the Harris hawk individual adopts the chance equal strategy to complete the exploration behavior according to the random position and its own position, or according to the optimal position and the average position, and uses convex lens learning to obtain the mirror solution of the exploration behavior, and introduces the greedy strategy to save the better solution in the population;

[0031] If entering the development stage, a division of labor mechanism is introduced to update the prey's physical strength, and a strategy is selected from the soft siege strategy, hard siege strategy, progressive dive soft siege strategy and progressive dive hard siege strategy for iteration; during the iteration process, an elimination selection mechanism is introduced to abandon the invalid position, and an adaptive step size is set for Levi flight to update the flight position;

[0032] After each iteration, the cost function is used to calculate the fitness value, and the minimum fitness that occurs in the iterative process is stored until the maximum number of iterations is reached, and the optimal trajectory is output.

[0033] Furthermore, the update formula of the prey escape energy E is:

[0034]

[0035] Among them, E 0 represents the initial energy of the prey, which is a random number between (0,10; t represents the current number of iterations; T represents the maximum number of iterations; if |E| < 1, it enters the development phase; if |E| ≥ 1, it enters the exploration phase.

[0036] Furthermore, in the exploration phase, the position update formula is:

[0037]

[0038] Among them, h i (t) and h i (t+1) represents the position of the i-th individual in the t-th generation and the t+1-th generation respectively; h rand (t) represents the position of a random individual in the tth generation; h rabbit (t) represents the position of the best individual in the tth generation; h m (t) represents the average position of the t-generation population; q, r 1 、r 2 、r 3 、r 4 is a random number in (0,1); ub and lb represent the upper and lower bounds of the search space;

[0039] Convex lens learning is used to improve the diversity of solutions. The convex lens learning method is as follows:

[0040]

[0041] Where ζ is the ratio between the object and the image, which is set to a random number in (0,1), h is the solution h(t+1) obtained by the exploration behavior, and h * For h, use the convex lens to learn the mirror solution h * (t+1);

[0042] A greedy strategy is introduced to save the better solution in the population. The final result obtained in the exploration phase is as follows:

[0043]

[0044] Where F(·) is the fitness function.

[0045] Furthermore, in the development stage, a division of labor mechanism is introduced, and the improved prey strength update method is as follows:

[0046]

[0047] In the formula, r i represents the physical strength of the prey corresponding to the i-th individual; rank(·) represents the ascending ranking of fitness; N represents the total number of individuals in the population; h i (t) represents the position of the i-th individual in the t-th generation;

[0048] If 0.5≤|E|≤1 and r i ≥0.5, select the soft siege strategy, if |E|<0.5 and r i ≥0.5, choose the hard siege strategy, if 0.5≤|E|≤1 and r i <0.5, choose the progressive dive soft siege strategy, if |E| < 0.5 and r i <0.5, select the progressive dive hard siege strategy; E is the prey escape energy;

[0049] The position update formula of the soft siege strategy is:

[0050] h(t+1)=Δh(t)-E|Jh rabbit (t)|h(t)|

[0051] Δh(t)=h rabbit (t)-h(t)

[0052] Where, J represents the jumping energy of the prey, which is a random number within (0,2); h rabbit is the position of the best individual of the tth generation; ×h(t) is the best individual of the tth generation h rabbit The position difference with the Harris Hawk individual h(t);

[0053] The position update formula of the hard siege strategy is:

[0054] h(t+1)=h rabbit (t)-E|Δh(t)|;

[0055] The position update formula Y of the progressive dive soft siege strategy is:

[0056] Y=h rabbit(t)-E|Jh rabbit (t)-h(t)|;

[0057] The progressive dive hard siege position update formula Y is:

[0058] Y=h rabbit (t)-E|Jh rabbit (t)-h m (t)|;

[0059] The elimination selection mechanism is introduced to abandon the invalid position, and an adaptive step size is set for Levy flight. The position update formula of the improved progressive dive strategy is:

[0060]

[0061]

[0062] Where ω is a non-zero constant; F(·) is the fitness function; d is the dimension of the problem to be optimized; S is a d-dimensional random vector; LF(d) is the Levy flight function, and Y is the original update formula of the progressive dive strategy algorithm.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] First, the UAV trajectory planning method based on the improved Harris Hawk optimization algorithm of the present invention corresponds the individual positions of the Harris Hawk to the UAV trajectory, and improves the algorithm using multiple strategies. It can improve the convergence accuracy and greatly improve its stability on the basis of the original Harris Hawk optimization algorithm, and more effectively handle the UAV trajectory planning problem.

[0065] Second, the UAV trajectory planning method based on the improved Harris Hawk optimization algorithm of the present invention introduces convex lens learning to enhance exploration efficiency and improve the algorithm's search performance; proposes a division of labor mechanism to adjust the prey's physical strength to avoid blind selection of strategies; proposes an elimination selection strategy and integrates Levy flight with adaptive step length to enhance the algorithm's ability to jump out of local optimality in the early stage and perform precise search in the later stage. The present invention can explore and develop feasible trajectories in the flight space as much as possible, and can also avoid collisions and trajectory jitters, which is more conducive to the smooth execution of UAV flight missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 A flowchart of the specific steps of improving the Harris Hawk optimization algorithm of the present invention;

[0067] Figure 2The graphs are comparison graphs of convergence curves of some functions of the improved Harris Eagle optimization algorithm and three other algorithms, wherein (a) is a comparison graph of the F1 function, (b) is a comparison graph of the F3 function, (c) is a comparison graph of the F5 function, and (d) is a comparison graph of the F8 function;

[0068] Figure 3 The path planning comparison diagram of the improved Harris Hawk optimization algorithm of the present invention and other five algorithms, wherein (a) is the path planning diagram of the PSO algorithm, (b) is the path planning diagram of the GWO algorithm, (c) is the path planning diagram of the HHO algorithm, (d) is the path planning diagram of the DHHO algorithm, (e) is the path planning diagram of the EHHO algorithm, and (f) is the path planning diagram of the DEHHO algorithm;

[0069] Figure 4 A top view of the path planning for different algorithms;

[0070] Figure 5 A comparison chart of 10 independent path planning convergence curves of the improved Harris Eagle optimization algorithm of the present invention and other five algorithms;

[0071] Figure 6 Box plots of 10 independent path planning for the improved Harris Hawk optimization algorithm and five other algorithms of the present invention. DETAILED DESCRIPTION

[0072] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0073] like Figure 1 As shown, the present invention discloses a UAV trajectory planning method based on an improved Harris Hawk optimization algorithm, and the specific steps are as follows:

[0074] Step 1: Set the peak parameter information, use the peak function to construct the threat equivalent terrain simulation map, realize the modeling of the flight environment, and adopt the threat equivalent terrain simulation method. The mathematical model is:

[0075]

[0076] In the formula, z(x,y) represents the terrain height corresponding to the point (x,y) on the horizontal plane; p represents the number of peaks; h(i) represents the peak height of the i-th peak; x ci ,y ci Respectively represent the horizontal and vertical coordinates of the ith peak vertex; x ki ,y ki Represents the peak attenuation coefficient, which is inversely proportional to the slope.

[0077] Step 2: According to the length cost, threat cost, and smoothness cost of the track, a corresponding cost function is established to transform the track planning problem into an optimization problem of minimizing the cost function. The mathematical model expression of the track cost is as follows:

[0078] C=α 1 C 1 +α 2 C 2 +α 3 C 3

[0079] Where C represents the total cost of the track, C 1 , C 2 , C 3 They represent the length cost, threat cost and smoothness cost of the track respectively, α 1 , α 2 , α 3 represents the weight of each cost. The important goal of trajectory planning is to shorten the trajectory length as much as possible. Assuming p i (x i ,y i ,z i ) represents a track point, track Path = {p 0 ,p 1 ,p 2 ,...,p n-1 ,p n} represents the set of all points on the track, p 0 is the starting point, p n is the target point, where the track length cost model is:

[0080]

[0081] The planned track should avoid environmental threats. Five segmentation points are selected at equal distances for each track segment. The threat size of the track segment is determined by the height difference between these points and the terrain. The threat cost model is:

[0082]

[0083] Among them, T j h represents the height threat of the jth segment point in each track; j represents the height of the jth segment point; z j Indicates the terrain height corresponding to the jth segment point; h safe Indicates safe height; T const Should be as large as possible, indicating that the terrain cannot be traversed.

[0084] The constraints of turning angle and climb / descent angle are unified in the track smoothness cost. The smoothness cost model is:

[0085]

[0086] Among them, S i represents the smoothing cost at the i-th track point; φ i ,θ i represents the turning angle and climb / descent angle at the i-th track point; φ max ,θ max Indicates the maximum turning angle and the maximum climb / descent angle.

[0087] Step 3: Based on the established problem model, the improved Harris Eagle optimization algorithm with fusion division of labor mechanism and elimination selection strategy is used to iteratively optimize the optimal trajectory of the UAV, including the following sub-steps:

[0088] Step 31: Set the population size N and the maximum number of iterations T.

[0089] Step 32: determine the starting point and the end point of the track, randomly generate N tracks, and each Harris hawk individual corresponds to a random track.

[0090] Step 33: At the beginning of each iteration, calculate the prey escape energy and choose between two stages. The escape energy calculation formula is:

[0091]

[0092] Among them, E 0 represents the initial energy of the prey, which is a random number between (0,1); t represents the current number of iterations; T represents the maximum number of iterations. If |E|<1, it enters the development phase; if |E|≥1, it enters the exploration phase.

[0093] Step 34: If the exploration phase is entered, the Harris hawk individual adopts the opportunity equal strategy to complete the exploration behavior based on the random position and its own position, or based on the optimal position and the average position. The position update formula is:

[0094]

[0095] Among them, h i (t) and h i (t+1) represents the position of the i-th individual in the t-th generation and the t+1-th generation respectively; h rand (t) represents the position of a random individual in the tth generation; h rabbit (t) represents the position of the best individual in the tth generation; h m (t) represents the average position of the t-generation population; q, r 1 、r 2 、r 3 、r 4is a random number in (0,1); ub and lb represent the upper and lower bounds of the search space. Convex lens learning is used to improve the diversity of solutions. The convex lens learning method is as follows:

[0096]

[0097] Among them, ξ is the ratio between the object and the image, which is set to a random number in (0,1). After convex lens learning, a greedy strategy is added to save the better solution in the population. The final result obtained in the exploration phase is as follows:

[0098]

[0099] Among them, h is the solution h(t+1) obtained by the original exploration behavior, h * For h, use the convex lens to learn the mirror solution h * (t+1).

[0100] Step 35: If the development phase is entered, update the prey's physical strength and select a strategy from the soft siege strategy, hard siege strategy, progressive dive soft siege strategy and progressive dive hard siege strategy for iteration. First, introduce the division of labor mechanism to adjust the prey's physical strength. The improved prey physical strength update method is as follows:

[0101]

[0102] Among them, r i represents the physical strength of the prey corresponding to the i-th individual; rank(·) represents the ascending ranking of fitness; N represents the total number of individuals in the population. If 0.5≤|E|1 and r≥0.5, select the soft siege strategy; if |E|<0.5 and r≥0.5, select the hard siege strategy; if 0.5≤|E|≤1 and r<0.5, select the progressive dive soft siege strategy; if |E|<0.5 and r<0.5, select the progressive dive hard siege strategy.

[0103] The position update formula of the soft siege strategy is:

[0104] h(t+1)=Δh(t)-E|Jh rabbit (t)-h(t)|

[0105] Δh(t)=h rabbit (t)-h(t)

[0106] Where J represents the jumping energy of the prey, which is a random number in (0,2); Δh(t) is the position difference between the optimal individual of the tth generation and the Harris hawk individual.

[0107] The position update method of the progressive dive hard siege strategy is the same as the progressive dive soft siege strategy, but Y in the update formula of the progressive dive hard siege and the progressive dive soft siege is different (maintaining the original algorithm content), and Z is the common modified content of the present invention.

[0108] The position update formula Y of the progressive dive soft siege strategy is:

[0109] Y=h rabbit (t)-E|Jh rabbit (t)-h(t)|.

[0110] The progressive dive hard siege position update formula Y is:

[0111] Y=h rabbit (t)-El|Jh rabbit (t)-h(t)|.

[0112] An adaptive step-length Levy flight integrating elimination selection strategy is designed to improve its ability to jump out of local optimality in the early stage and convergence accuracy in the later stage; the position update formula of its adaptive step-length Levy flight is as follows:

[0113]

[0114] Among them, ω is a non-zero constant to avoid the Lévy flight from being almost ineffective in the late iteration. The position update formula of the improved progressive dive strategy is:

[0115]

[0116] Z=Y+S×LF(d)

[0117] Among them, F(·) is the fitness function; d is the dimension of the problem to be optimized; S is the d-dimensional random vector; LF(d) is the Levy flight function, and Y is the original update formula of the algorithm.

[0118] Step 36: The iterative process uses the cost function to calculate the fitness value, stores the minimum fitness that occurs in the iterative process, and outputs the optimal track until the maximum number of iterations.

[0119] In order to verify the improvement effect of the algorithm, the present invention uses 8 test functions and a three-dimensional trajectory planning map for verification.

[0120] The 8 test functions include 3 unimodal functions and 5 multimodal functions. The improved Harris Hawk optimization algorithm (DEHHO) is compared with the original algorithm, the Grey Wolf Optimization Algorithm (GWO) and the Particle Swarm Optimization Algorithm (PSO). The 8 test functions are shown in Table 1. Without loss of generality, some functions whose optimal values ​​appear at the origin are offset, and the search area adopts the corresponding offset.

[0121] Table 1 Test functions

[0122]

[0123] Figure 2 This is a comparison chart of the convergence curves of some functions of the improved Harris Eagle optimization algorithm and the other three algorithms. In the test, the population size of each algorithm is 30, the number of iterations is 300, and the independent statistics are 30 times. The statistical results are shown in Table 2:

[0124] Table 2 Comparison of test results

[0125]

[0126] The improved DEHHO algorithm of the present invention is compared with the original algorithm, GWO algorithm, PSO algorithm, Harris Hawk algorithm (DHHO) with division of labor mechanism to adjust prey strength, and adaptive Levy flying Harris Hawk algorithm (EHHO) with fusion elimination selection. The scale of each algorithm in the test is 30, the maximum iteration is 200, and the independent optimization is performed 10 times. The comparison data is shown in Table 3:

[0127] Table 3 Comparison of path planning results

[0128]

[0129]

[0130] Figure 3 This is a comparison chart of the path planning of the improved Harris Hawk optimization algorithm and other five algorithms. Figure 4 The top view of the path planning of different algorithms. Figure 5 This is a comparison chart of the convergence curve. Figure 6 The box plot is introduced to make an intuitive and comprehensive comparison of the algorithms. According to the results, the planning effects of the PSO and GWO algorithms are relatively unstable, and the solution accuracy is limited. Compared with the HHO algorithm, the DHHO and EHHO algorithms introduce a single strategy for improvement, and obvious optimization effects can be seen in indicators such as the median, quartiles, boundary values, and box area, proving the effectiveness of each strategy. DEHHO uses a fusion of multiple strategies to improve and can obtain the lowest median value among several algorithms, indicating its superiority in convergence accuracy. At the same time, the box area of ​​DEHHO is smaller, indicating that the algorithm solution is more centralized and stable. Overall, the improved DEHHO algorithm of the present invention has excellent optimization capabilities in path planning problems.

[0131] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0132] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0133] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0134] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0135] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0136] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A UAV trajectory planning method based on an improved Harris Hawk optimization algorithm, characterized in that: The UAV trajectory planning method comprises the following steps: S1, set the peak parameter information, use the peak function to construct the threat equivalent terrain simulation map, and model the flight environment; S2, according to the length cost, threat cost and smoothness cost of the track, a corresponding cost function is established to transform the track planning problem into an optimization problem of minimizing the cost function; S3, using the improved Harris Eagle optimization algorithm that integrates the division of labor mechanism and elimination selection strategy, solves the optimization problem of minimizing the cost function, and iteratively optimizes to obtain the optimal trajectory of the UAV.

2. The unmanned aerial vehicle trajectory planning method based on the improved Harris Hawk optimization algorithm according to claim 1 is characterized in that: In step S1, the mathematical model of the flight environment is: In the formula, z(x,y) represents the terrain height corresponding to the point (x,y) on the horizontal plane; p represents the number of peaks; h(i) represents the peak height of the i-th peak; x ci and ci Respectively represent the horizontal and vertical coordinates of the ith peak vertex; x ki and ki Represents the peak attenuation coefficient, which is inversely proportional to the slope.

3. The UAV trajectory planning method based on the improved Harris Hawk optimization algorithm according to claim 1 is characterized in that: Step S2 further comprises: Assume that p i (x i ,y i ,z i ) represents a track point, track Path = {p0, p1, p2, ..., p n-1 ,p n } represents the set of all points on the track, p0 is the starting point, p n As the target point, the length cost model of the track is: Take 5 segmentation points at equal distances for each track, and determine the threat size of the track segment by the height difference between the segmentation points and the terrain. The threat cost model of the track is: Among them, T j h represents the height threat of the jth segment point in each track; j represents the height of the jth segment point; z j Indicates the terrain height corresponding to the jth segment point; h safe Indicates safe height; T const It means that the terrain cannot be crossed; According to the constraints of turning angle and climb / descent angle, the smoothness cost model of the track is obtained as follows: Among them, S i represents the smoothing cost at the i-th track point; φ i and θ i They represent the turning angle and climb / descent angle at the i-th track point respectively; φ max and θ max Respectively represent the maximum turning angle and the maximum climbing / gliding angle; According to the length cost, threat cost and smoothness cost of the track, the cost function of the track is established as: C=α1C1+α2C2+α3C3 Where C represents the total cost of the track, C1, C2 and C3 represent the length cost, threat cost and smoothness cost of the track respectively, and α1, α2 and α3 represent the weights of each cost.

4. The UAV trajectory planning method based on the improved Harris Hawk optimization algorithm according to claim 1 is characterized in that: Step S3 further comprises: Set the population size N and the maximum number of iterations T; Determine the starting and ending points of the track, randomly generate N tracks, and each Harris hawk individual corresponds to a random track; At the beginning of each iteration, the prey escape energy is calculated and selected in two stages: If entering the exploration phase, the Harris hawk individual adopts the chance equal strategy to complete the exploration behavior according to the random position and its own position, or according to the optimal position and the average position, and uses convex lens learning to obtain the mirror solution of the exploration behavior, and introduces the greedy strategy to save the better solution in the population; If entering the development stage, a division of labor mechanism is introduced to update the prey's physical strength, and a strategy is selected from the soft siege strategy, hard siege strategy, progressive dive soft siege strategy and progressive dive hard siege strategy for iteration; during the iteration process, an elimination selection mechanism is introduced to abandon the invalid position, and an adaptive step size is set for Levi flight to update the flight position; After each iteration, the cost function is used to calculate the fitness value, and the minimum fitness that occurs in the iterative process is stored until the maximum number of iterations is reached, and the optimal trajectory is output.

5. The UAV trajectory planning method based on the improved Harris Hawk optimization algorithm according to claim 4 is characterized in that: The update formula of the prey escape energy E is: Among them, E0 represents the initial energy of the prey, which is a random number in (0,1); t represents the current number of iterations; T represents the maximum number of iterations; if |E|<1, it enters the development stage, and if |E|≥1, it enters the exploration stage.

6. The unmanned aerial vehicle trajectory planning method based on the improved Harris Hawk optimization algorithm according to claim 4 is characterized in that: In the exploration phase, the position update formula is: Among them, h i (t) and h i (t+1) represents the position of the i-th individual in the t-th generation and the t+1-th generation respectively; h rand (t) represents the position of a random individual in the tth generation; h rabbit (t) represents the position of the best individual in the tth generation; h m (t) represents the average position of the t-th generation population; q, r1, r2, r3, r4 are random numbers in (0,1); ub and lb represent the upper and lower bounds of the search space; Convex lens learning is used to improve the diversity of solutions. The convex lens learning method is as follows: Where ξ is the ratio between the object and the image, which is set to a random number between (0,10), h is the solution h(t+1) obtained by the exploration behavior, and h * For h, use the convex lens to learn the mirror solution h * (t+1); A greedy strategy is introduced to save the better solution in the population. The final result obtained in the exploration phase is as follows: Where F(·) is the fitness function.

7. The UAV trajectory planning method based on the improved Harris Hawk optimization algorithm according to claim 4 is characterized in that: During the development phase, a division of labor mechanism was introduced, and the improved prey strength update method is as follows: In the formula, r i represents the physical strength of the prey corresponding to the i-th individual; rank(·) represents the ascending ranking of fitness; N represents the total number of individuals in the population; h i (t) represents the position of the i-th individual in the t-th generation; If 0.5≤|E|≤1 and r i ≥0.5, select the soft siege strategy, if |E|<0.5 and r i ≥0.5, choose the hard siege strategy, if 0.5≤|E|≤1 and r i <0.5, choose the progressive dive soft siege strategy, if |E| < 0.5 and r i <0.5, select the progressive dive hard siege strategy; E is the prey escape energy; The position update formula of the soft siege strategy is: h(t+1)=Δh(t)-E|Jh rabbit (t)-h(t)| Δh(t)=h rabbit (t)-h(t) Where, J represents the jumping energy of the prey, which is a random number within (0,2); h rabbit is the position of the best individual of the tth generation; Δh(t) is the best individual of the tth generation h rabbit The position difference with the Harris Hawk individual h(t); The position update formula of the hard siege strategy is: h(t+1)=h rabbit (t)-EΔh(t)|; The position update formula Y of the progressive dive soft siege strategy is: Y=h rabbit (t)-EJh rabbit (t)-h(t)|; The progressive dive hard siege position update formula Y is: Y=h rabbit (t)-E|Jh rabbit (t)-h m (t)|; The elimination selection mechanism is introduced to abandon the invalid position, and an adaptive step size is set for Levy flight. The position update formula of the improved progressive dive strategy is: Where ω is a non-zero constant; F(·) is the fitness function; d is the dimension of the problem to be optimized; S is a d-dimensional random vector; LF(d) is the Levy flight function, and Y is the original update formula of the progressive dive strategy algorithm.

Images