An unmanned aerial vehicle path planning method based on an artificial vole optimization algorithm

Abstract

The application belongs to the technical field of unmanned aerial vehicle path planning, and particularly relates to an unmanned aerial vehicle path planning method based on an artificial traveling wave optimization algorithm, which comprises the following steps: S1, initializing algorithm parameters; S2, adopting Tent chaotic mapping; S3, calculating the fitness of all individuals; S4, comparing the fitness of each individual with a currently recorded global optimal value; S5, calculating an energy coefficient E by using a nonlinear factor; S6, judging whether the energy coefficient E is greater than 1; S7, combining the original strategy of Levy flight with the inverse cumulative distribution of Cauchy; S8, judging whether a termination condition is met; and S9, returning a global optimal solution. The application has good initial diversity, stable exploration / exploitation balance and stronger local jumping capacity, so that the optimization precision and convergence stability are significantly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle path planning, in particular to an unmanned aerial vehicle path planning method based on an artificial lemming optimization algorithm. BACKGROUND

[0002] Unmanned aerial vehicle path planning refers to planning an optimal or feasible flight trajectory from a starting point to an ending point for an unmanned aerial vehicle according to a task target, a flight environment and physical limitations.

[0003] Currently, classical path planning algorithms include a particle swarm algorithm and a grey wolf algorithm. In recent years, there are a whale algorithm and an artificial lemming algorithm. The artificial lemming algorithm is a new meta-heuristic algorithm (intelligent optimization algorithm), which is inspired by four different behaviors of lemmings in nature: long-distance migration, hole digging, foraging and predator avoidance.

[0004] Currently, the artificial lemming algorithm ALA has the following defects: firstly, the initial diversity is insufficient. If the randomness of the initial population is not sufficient, or the initial population is generated near a powerful local optimal solution, the algorithm may quickly converge in the wrong direction from the beginning. Secondly, the conversion from exploration to exploitation is completely controlled by the energy factor E(t). This may cause the algorithm behavior pattern to be out of line with the actual situation of the population, fall into a local optimal solution, and be difficult to balance between path optimality and computational efficiency. In order to solve these problems, we provide an unmanned aerial vehicle path planning method based on an artificial lemming optimization algorithm. SUMMARY

[0005] This section aims to summarize some aspects of the embodiments of the present application and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of the specification to avoid obscuring the purpose of this section, the abstract and the title, and such simplifications or omissions cannot be used to limit the scope of the present application.

[0006] To solve the above technical problems, according to one aspect of the present application, the present application provides the following technical solutions:

[0007] An unmanned aerial vehicle path planning method based on an artificial lemming optimization algorithm, comprising the following steps:

[0008] S1: initializing algorithm parameters, population size N, maximum iteration number Max_iter, search boundary lb / ub, and handle fobj of a function to be optimized;

[0009] S2: using Tent chaotic mapping, setting the chaotic coefficient to 0.9, first randomly generating a column, and then traversing the [0, 1] interval according to the Tent recursive relationship;

[0010] S3: Calculate the fitness of all individuals, get a one-dimensional vector about the evaluation results of the whole population, compare the fitness obtained in the evaluation process with the optimal value recorded at present, if better, save the position of the individual and update the optimal value;

[0011] S4: Compare the fitness of each individual with the global optimal value recorded at present, if the fitness is smaller, save the position of the individual and update the fitness;

[0012] S5: Calculate the energy coefficient E using a nonlinear factor;

[0013] S6: Judge whether the energy coefficient E is greater than 1, when greater than 1, the algorithm will tend to a large range treaty to expand the global search, enter the hole digging or long distance migration strategy; when E is less than or equal to 1, adopt foraging or avoiding predator strategy;

[0014] S7: When the energy coefficient E is less than 1, the local development of the avoiding predator strategy combines the Levy flight of the original strategy with the inverse cumulative distribution of Cauchy;

[0015] S8: Judge whether the termination condition is met, when the current iteration number Iter is less than or equal to the maximum iteration number MaxIter, return to step 5 and enter the loop, otherwise enter the next step to output the global optimal solution;

[0016] S9: Return the global optimal solution, at this time, the global optimal fitness, the global optimal position and the historical optimal value sequence recorded will be directly output.

[0017] As a preferred scheme of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm, in the S2, the Tent chaotic mapping formula is:

[0018]

[0019] Wherein, the chaotic coefficient is , The current value of the kth mapping is taken from the chaotic sequence element generated in the last column or the last iteration, and the range is (0, 1); The next value obtained by the Tent mapping is also the number used for initialization in the next column or dimension, which is also limited to (0, 1); the conditions And Determine which linear formula to use, so that the sequence switches between the two mappings, ensuring chaotic ergodicity; The initial value is the initial value randomly generated in the first column, which needs to fall within (0, 1).

[0020] As a preferred scheme of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm, when the current value is less than linearly enlarged, and greater than or equal to, mapped back to the interval (0, 1) according to symmetric linear mapping, the two kinds of piecewise linear mapping have typical chaotic ergodic characteristics, and when the population is initially generated, the values of the previous column are iterated column by column, and finally, the individual distribution covering more uniform and sequence correlation is obtained.

[0021] As a preferred scheme of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm, in the S5, the calculation formula of the energy coefficient E is as follows:

[0022]

[0023]

[0024] wherein indicates a nonlinear time adjustment factor of the current iteration, used for dynamically adjusting the energy coefficient; Iter is the current iteration number accumulated from 1 to MaxIter; MaxIter is the maximum iteration number set by the algorithm; E is the energy coefficient, which determines whether the algorithm is inclined to global exploration or local development in the current iteration; r is a random number uniformly generated between 0 and 1; ln(1 / r) maps the random disturbance to an amplification coefficient of E.

[0025] As a preferred scheme of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm, the specific mathematical formula of the S7 is as follows:

[0026] (1)

[0027] (2)

[0028] (3)

[0029] (4)

[0030] (5)

[0031] wherein, in the formula (1), rand is a random number randomly generated between 0 and 1; indicates that a random direction is given to the disturbance in the current round, with 0.5 as the boundary to return +1 or -1; indicates that the strength coefficient of the enemy-avoiding strategy linearly decreases with the iteration, and converges with time; the obtained G is an adjustment factor with random direction and strength decaying with iteration, which is used to control the jumping scale of the individual around the optimal solution together with the Levy step length;

[0032] Equation (2) is the inverse cumulative distribution of Cauchy, where is a random variable within arctangent function, which is equivalent to generate random disturbance of Cauchy distribution; is a translation and scaling to get the inverse cumulative distribution of standard Cauchy distribution; determines the center of disturbance, controls the amplitude of disturbance, the larger the value, the more dispersed the generated scaling factor; and is a scaling vector corresponding to each dimension, which is used in Equation (3) is the generation of stable parameters of Levy flight step,

[0033] represents the characteristic exponent of Levy stable distribution, which is 1.5; is the Gama function, which is used to calculate the scale parameter of stable distribution , , to ensure that the generated step length meets the required Levy distribution;

[0034] Equation (4) is the generation of Levy step, where is the generated Levy flight step vector; is the numerator of Levy step; is a random vector subject to standard normal distribution; represents the absolute value of element-wise power when is very small, the denominator becomes small, which will cause to jump larger; , as described in equation 3, represents the characteristic exponent of Levy stable distribution;

[0035] Equation (5) is the predator avoidance strategy of Cauchy and Levy fusion, represents the position vector of the individual in the next generation; represents the global optimal position of the current iteration; is the Cauchy disturbance vector; is the direction mark with value {+1, -1}, is the energy adjustment factor with random positive and negative signs; is the Levy flight step vector; is the difference vector of the current individual pointing to the global optimum; is the Hadamard product, which represents element-wise multiplication, used to apply disturbance and step length independently by dimension.

[0036] Compared with the prior art, the application has the beneficial effects that: the application introduces Tent chaotic mapping initialization, so that the population coverage is more uniform, the initial exploration is more extensive, and the risk of early falling into local optimization is reduced from the source; a sine row nonlinear time factor is used to keep the periodic fluctuation of the energy coefficient, so as to ensure the dynamic balance of global exploration and local development, and avoid premature convergence caused by the monotone decline of the energy of the traditional algorithm; in the local stage, the inverse cumulative distribution of Cauchy and the Levy flight strategy are fused to give the heavy-tailed jumping ability around the optimal solution, and the probability of jumping out of the local extreme value is improved. The synergistic effect of the three improvements makes the algorithm have good initial diversity, stable exploration / development balance and stronger local jumping ability, thereby significantly improving the optimization precision and convergence stability. The application is especially suitable for the fields of intelligent agriculture and precision agriculture, such as unmanned aerial vehicle seeding coverage, unmanned aerial vehicle pesticide spraying path planning and the like application scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the application, the application will be described in detail below with reference to the drawings and detailed embodiments. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can also be obtained by those skilled in the art without creative labor. Among them:

[0038] Figure 1 The flowchart of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm of the application;

[0039] Figure 2 The simulation result comparison chart in embodiment 1 of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm of the application;

[0040] Figure 3 The path chart of the improved IALA algorithm and the original ALA algorithm in embodiment 2 of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm of the application;

[0041] Figure 4 The box plot of the result comparison of the improved IALA algorithm and the original ALA algorithm in embodiment 2 of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm of the application;

[0042] Figure 5 The convergence curve chart of the improved IALA algorithm and the original ALA algorithm in embodiment 2 of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm of the application;

[0043] Figure 6 The result chart of the performance comparison of the improved IALA algorithm and the original ALA algorithm in embodiment 2 of the unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm of the application;

[0044] Figure 7 Path diagram in embodiment 3 of the present application, a path planning method for unmanned aerial vehicle based on artificial vole optimization algorithm;

[0045] Figure 8 Convergence curve comparison diagram in embodiment 3 of the present application, a path planning method for unmanned aerial vehicle based on artificial vole optimization algorithm;

[0046] Figure 9 Performance comparison result diagram in embodiment 3 of the present application, a path planning method for unmanned aerial vehicle based on artificial vole optimization algorithm. DETAILED DESCRIPTION

[0047] In order to make the above object, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings.

[0048] Secondly, the present application is described in detail in combination with the schematic diagram, in the detailed description of the embodiments of the present application, the cross-sectional view of the device structure will be partially enlarged without the general proportion for the convenience of description, and the schematic diagram is only an example, which should not limit the scope of protection of the present application here. In addition, the three-dimensional spatial dimensions of length, width and depth should be included in actual manufacture.

[0049] In order to make the object, technical scheme and advantages of the present application more clear, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0050] A path planning method for unmanned aerial vehicle based on artificial vole optimization algorithm, comprising the following steps,

[0051] S1: initializing algorithm parameters, population size N, maximum iteration number Max_iter, search boundary lb / ub, and function handle fobj to be optimized;

[0052] S2: different from the uniform random initialization of the original ALA algorithm, the population is initialized using Tent chaotic mapping, Tent chaotic mapping is adopted, the chaotic coefficient is set to 0.9, a column is randomly generated first, and then the Tent recursive relationship is traversed in the interval [0, 1], so as to improve the dispersion degree of the initial solution, and the Tent chaotic mapping formula is:

[0053]

[0054] Wherein the chaotic coefficient is , is the current value of the kth mapping, which is taken from the last column or the chaotic sequence element generated in the last iteration, and the range is (0, 1); The next value obtained by Tent mapping is also the number used for the next column or the next dimensional initialization, which is also limited in (0, 1); With Decide which piece of linear formula, make the sequence switch between the two kinds of mapping, to ensure the ergodicity of chaos; The initial value of the initial value of the first column is randomly generated and needs to fall in (0, 1);

[0055] When the current value is less than Linear amplification, greater than or equal to, according to the symmetric linear mapping back to the interval (0, 1), the two kinds of piecewise linear mapping have typical ergodicity of chaos, when the initial population is generated, the value of the last column is iterated column by column, and the individual distribution with more uniform coverage and correlation is obtained;

[0056] S3: Calculate the fitness of all individuals, which will traverse the initialization population generated by the Tent chaotic sequence, for each, the fitness will be obtained by calling the objective function, and a one-dimensional vector about the evaluation result of the overall population is obtained. In the evaluation process, the fitness obtained is compared with the optimal value recorded at present, if it is better, the position of the individual is saved and the optimal value is updated, which lays a foundation for updating the global optimal solution S in the subsequent;

[0057] S4: Update the global optimal solution, after obtaining the fitness of all individuals in S3, the algorithm compares the fitness of each individual with the global optimal value recorded at present, if the fitness is smaller, the position of the individual is saved immediately, and the fitness is updated at the same time, which ensures that the best lemming individual in the current iteration is held before the process enters the main loop, providing a reliable reference for subsequent global optimal-based multiple update strategies;

[0058] S5: Calculate the energy coefficient E, the original ALA algorithm uses the inverse tangent type time factor, while the present application uses a nonlinear factor to calculate the energy coefficient, the specific formula is as follows:

[0059]

[0060]

[0061] Wherein Indicates the nonlinear time adjustment factor of the current iteration, which is used to dynamically adjust the energy coefficient; Iter is the current iteration number accumulated from 1 to MaxIter; MaxIter is the maximum iteration number set by the algorithm; E is the energy coefficient, which determines whether the algorithm is biased towards global exploration or local development in this round of iteration; r is a random number uniformly distributed between 0 and 1; ln(1 / r) maps the random disturbance to the amplification coefficient of E;

[0062] First calculate the nonlinear time adjustment factor , then get E through the energy coefficient formula, wherein E can be ensured to take a larger positive or negative value, combined with a nonlinear time adjustment factor The wave fluctuation enhances the dynamicity;

[0063] S6: Determine whether the energy coefficient E is greater than 1, when greater than 1, it means that the energy is high, the algorithm will tend to a large range of treaties to expand the global search, so enter the hole digging or long-distance migration strategy; When E is less than or equal to 1, the energy is low, emphasizing local development, so take foraging or avoiding predators strategy, the threshold 1 separates the high energy state from the low energy state, ensuring that the algorithm is dynamically balanced between exploration and development;

[0064] S7: The strategy adopted by the original ALA algorithm according to the energy coefficient is shown in S6, the application improves the local development of the avoiding predators strategy when the energy coefficient E is less than 1, and combines the original strategy of Levy flight and the inverse cumulative distribution of Cauchy, the specific mathematical formula is as follows:

[0065] (1)

[0066] (2)

[0067] (3)

[0068] (4)

[0069] (5)

[0070] Wherein in formula (1), rand is a random number between 0 and 1 generated randomly; Indicates that it returns +1 or -1 with 0.5 as the boundary, and gives a random direction to the disturbance of this round; Indicates that the strength coefficient of the avoiding predators strategy decreases linearly with iteration, and the obtained G is a regulation factor with direction randomness and strength decay with iteration, which is used to control the jumping scale of individuals around the optimal solution together with the Levy step length;

[0071] Formula (2) is the inverse cumulative distribution of Cauchy, wherein is a random variable in , which is used for the arctangent function, and is equivalent to generate random disturbance of Cauchy distribution; is a translation and scaling of , to obtain the inverse cumulative distribution of the standard Cauchy distribution; determines the disturbance center, controls the disturbance amplitude, the greater the value, the more dispersed the scaling factor generated;

[0072] And is a scaling vector corresponding to each dimension, which is used in formula (4) , select the candidate solution near the optimal position but with Cauchy heavy-tailed perturbation;

[0073] Equation (3) is used to generate the stable parameter of the Levy flight step length, , which represents the characteristic exponent of the Levy stable distribution, and is set to 1.5; is the Gama function, which is used to calculate the scale parameter of the stable distribution , to ensure that the generated step length meets the required Levy distribution;

[0074] Equation (4) is used to generate the Levy step length, where is the generated Levy flight step length vector; is the numerator of the Levy step length; is a random vector subject to the standard normal distribution; represents the absolute value of element-wise power when is very small, the denominator becomes small, which will cause to jump too large; , as described in Equation 3, represents the characteristic exponent of the Levy stable distribution;

[0075] Equation (5) is the predator avoidance strategy that combines Cauchy and Levy, represents the position vector of the th individual in the next generation; represents the global optimal position of the current iteration; is the Cauchy perturbation vector; is the direction indicator with a value of {+1, -1}, is the energy adjustment factor with a random positive or negative sign; is the Levy flight step length vector; is the difference vector of the current individual pointing to the global optimum; is the Hadamard product, which represents element-wise multiplication, and is used to apply perturbation and step length independently by dimension;

[0076] The combined Cauchy and Levy avoidance strategy can not only maintain the attraction of the global optimum, but also allow individuals to make large jumps in the neighborhood;

[0077] S8: Determine whether the termination condition is met. When the current iteration number Iter is less than or equal to the maximum iteration number MaxIter, return to S5 and enter the loop, otherwise proceed to the next step to output the global optimal solution;

[0078] S9: Return the global optimal solution. At this time, the recorded global optimal fitness, global optimal position, and historical optimal value sequence will be directly output.

[0079] Embodiment 1

[0080] The simulation parameters for the improved Artificial Lemming Algorithm, the original Artificial Lemming Algorithm, Particle Swarm Optimization Algorithm, Gray Wolf Algorithm, and Whale Algorithm are set as follows: population size is set to 50, maximum number of iterations is set to 500, upper bound is set to 100, lower bound is set to -100, dimension is set to 30, and the test function is... The simulation results are as follows Figure 2 As shown;

[0081] The simulation results show that the improved Artificial Lemming Algorithm IALA has made significant progress compared to the original Artificial Lemming Algorithm ALA, improving both convergence accuracy and convergence speed. It also shows clear advantages over other algorithms such as Particle Swarm Optimization, Grey Wolf Algorithm, and Whale Algorithm.

[0082] Example 2

[0083] This example demonstrates drone path planning on a 20×20 grid map. The map uses 0 / 1 to represent fellow drones and obstacles, and white and black to distinguish them. The drone's starting point is (1, 1), and its ending point is (20, 20). In this example, the population size is set to 50, the maximum number of iterations is set to 300, the path length weight is set to 20, the path smoothness weight is set to 1, and the number of runs is set to 30.

[0084] For detailed simulation results of the improved IALA algorithm and the original ALA algorithm, please refer to the following: Figures 3-6 ,include Figure 3 Path map Figure 4 Box plots comparing results Figure 5 Convergence curve and Figure 6 The results of the performance comparison are shown in the graph.

[0085] Depend on Figure 3 The simulation results show that ALA involves numerous detours in areas with dense obstacles, resulting in a jagged route with multiple turns. The improved IALA, developed in this invention, utilizes an enhanced strategy to bypass obstacle zones in the middle section, resulting in a straighter overall path and avoiding redundant inflection points. Compared to ALA, IALA has a significantly shorter path length and better smoothness, reducing the UAV's travel distance and number of turns. This demonstrates the improvement in search efficiency brought about by Tent initialization and Cauchy-Gallover local jumps.

[0086] from Figure 5 The convergence curves show that IALA converges to low fitness around generation 40 and then tends to stabilize; while ALA undergoes three significant jumps and only achieves final improvement in generation 290. This indicates that the nonlinear energy factor and chaotic initialization of IALA accelerate the search process and reduce the time spent getting trapped in local optima.

[0087] from Figure 4 Box plot and Figure 6The performance comparison result chart shows that the average fitness of IALA is improved by 44.67% compared with ALA, which indicates that the comprehensive cost, i.e., the length and smoothness, is significantly reduced; the path length of IALA is shortened by about 19.3% compared with ALA, and the variance is smaller, and the stability is better; the average smoothness of IALA is reduced by 58% compared with ALA, which indicates that the turning penalty is greatly reduced, and the path is smoother.

[0088] Example 3

[0089] This example performs single-UAV path planning on a 1000x1000x120 three-dimensional map, and the starting point of the UAV is [40, 129, 5] and the ending point is [951, 833, 10]. The algorithm parameters of this example are as follows: the population size is 50, the maximum number of iterations is 100, the path length weight is 1, and the path height weight is 0.1. The simulation results are shown in the path chart, Figure 7 the convergence curve comparison chart, and Figure 8 the performance comparison result chart. Figure 9

[0090] From the path chart and the convergence curve chart, it can be seen that the blue curve is the IALA optimal path, the control points along the way are lifted to a higher height, and a large-span arc is formed near the peak, which always dominates the terrain column; the red curve is the ALA optimal path, the control points are distributed lower, and the path is close to the terrain, almost close to the ground in the peak area.

[0091] From the convergence curve chart, it can be seen that the comprehensive fitness of IALA is quickly reduced from about 2500 to about 1600 in the first 20 generations, and the subsequent iterations continue to steadily decline and finally approach 1500; ALA slowly declines, and until 100 generations, it still stays at about 2000. This shows that the improvement strategy of IALA can help it quickly find a high-quality solution, and can continue to optimize to a lower target value.

[0092] From the performance comparison result chart, it can be seen that the comprehensive fitness of IALA is much lower than that of ALA, and the overall solution is better; at the same time, the path length is also shorter than that of ALA, which indicates that the trajectory found by the improved algorithm is more compact; the average height cost of IALA is higher than that of ALA, but because the height weight is only 0.1, it cannot offset the advantage in length, and the comprehensive fitness is still significantly lower; the collision flag is 1 for terrain collision and 0 for no collision in this example, and the ALA result has one terrain collision, while the IALA result has no collision, which indicates that the IALA algorithm is more reliable under the obstacle avoidance constraint.

[0093] ​Although the present application has been described with reference to the embodiments above, various changes and modifications can be suggested to one skilled in the art, and it is intended that the present application encompass such changes and modifications as fall within the scope of the appended claims. Particularly, each feature disclosed in the description and / or the claims can be used in the combination with each of the features disclosed in the description and / or the claims, unless specifically stated otherwise. Therefore, the present application is not intended to be limited to the particular embodiments disclosed in the description and / or the claims.

Claims

1. An unmanned aerial vehicle path planning method based on an artificial vole optimization algorithm, characterized in that, The method comprises the following steps: S1: initialize algorithm parameters, population size N, maximum iteration number Max_iter, search boundary lb / ub, and function handle fobj to be optimized; S2: adopt Tent chaotic mapping, set chaotic coefficient to 0.9, first randomly generate a column, and then traverse the [0, 1] interval according to the Tent recursive relationship; S3: calculate the fitness of all individuals to obtain a one-dimensional vector about the evaluation result of the whole population, and compare the obtained fitness with the current recorded optimal value in the evaluation process, if the fitness is better, save the position of the individual and update the optimal value; S4: compare the fitness of each individual with the current recorded global optimal value, if the fitness is smaller, save the position of the individual and update the fitness; S5: calculate the energy coefficient E by using a nonlinear factor; S6: judge whether the energy coefficient E is greater than 1, when greater than 1, the algorithm will tend to a large range treaty to expand the global search, enter the hole digging or long distance migration strategy; when E is less than or equal to 1, adopt the foraging or avoiding predator strategy; S7: when the energy coefficient E is less than 1, the local development of the avoiding predator strategy combines the original strategy of Levy flight and the inverse cumulative distribution of Cauchy; S8: judge whether the termination condition is met, when the current iteration number Iter is less than or equal to the maximum iteration number MaxIter, return to step 5 and enter the loop, otherwise enter the next step to output the global optimal solution; S9: return the global optimal solution, at this time, the global optimal fitness, global optimal position and historical optimal value sequence recorded will be directly output.

2. The unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm according to claim 1, characterized in that, In the S2, the Tent chaotic mapping formula is: ； where the chaotic coefficient is , is the current value of the kth mapping, taken from the previous column or the previous iteration of the chaotic sequence element, ranging from (0, 1); is the next value from the Tent mapping, also used in the next column or the next dimension initialization, also limited to (0, 1); condition and determine which segment of the linear formula to use, switching the sequence between the two mappings to ensure chaotic ergodicity; is the initial value, i.e. the first column of randomly generated initial values, which needs to fall within (0, 1).

3. The unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm according to claim 2, characterized in that, When the current value is less than linearly amplified, and greater than or equal to is mapped back to the interval (0, 1) according to the symmetric linear mapping, both of which have typical chaotic ergodic characteristics. When the population is initially generated, the values of the previous column are iterated column by column, and ultimately the individual distribution covering more uniform and sequence correlation is obtained.

4. The unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm according to claim 1, characterized in that, In the S5, the calculation formula of the energy coefficient E is as follows: ； ； wherein represents the nonlinear time adjustment factor of the current iteration, used to dynamically adjust the energy coefficient; Iter is the current iteration number accumulated from 1 to MaxIter; MaxIter is the maximum iteration number set by the algorithm; E is the energy coefficient, which determines whether the algorithm is biased towards global exploration or local development in this iteration; r is a random number uniformly distributed between 0 and 1; ln(1 / r) maps the random disturbance to an amplification coefficient of E.

5. The unmanned aerial vehicle path planning method based on the artificial vole optimization algorithm according to claim 1, characterized in that, The specific mathematical formula of the S7 is as follows: （1）； （2）； （3）； （4）； （5）； wherein, in formula (1), rand is a random number between 0 and 1 randomly generated; represents returning +1 or -1 with 0.5 as a boundary, and giving a random direction to the disturbance in this round; represents that the strength coefficient of the predator avoidance strategy linearly decreases with iterations, and converges with time; the obtained G is an adjustment factor with random direction and strength decaying with iterations, which is used to control the jumping scale of the individual near the optimal solution together with the Levy step length; Formula (2) is the Cauchy inverse cumulative distribution, where yes The random variable within the arctangent function is equivalent to generating a random perturbation with a Cauchy distribution. Yes After translation and scaling, the inverse cumulative distribution of the standard Cauchy distribution is obtained; Determine the center of disturbance. The larger the value of the disturbance control, the more dispersed the resulting scaling factor becomes; and... It is a scaling vector corresponding to each dimension, used in formula (4). Candidate solutions near the optimal position but with Cauchy heavy-tail offset are selected; Equation (3) generates the stable parameter for the Lévy flight step size, characteristic exponent of the Lévy stable distribution, taken as 1.5; Gama function used to find the scale parameter of the stable distribution , ensures that the generated step size satisfies the required Lévy distribution; Formula (4) is used to generate the Lévy step size, where This is the generated Levi flight step size vector; For the Lévy step length molecule; It is a random vector that follows a standard normal distribution; Indicates to The absolute value is raised to the power of each element. When the denominator is very small, it will lead to A large jump occurs; As shown in Formula 3, this represents the characteristic index of the Lévy stable distribution; Equation (5) is the Lévy flight with the Cauchy distribution, represents the position vector of the i-th individual in the next generation; represents the global optimal position of the current iteration; is the Cauchy perturbation vector; is the direction indicator taking values in {+1, -1}, is the energy adjustment factor with random sign; is the Lévy flight step vector; is the difference vector of the current individual pointing to the global optimum; is the Hadamard product, representing the element-wise multiplication, used to apply the perturbation and step independently by dimension.​

Images