Unmanned aerial vehicle path planning method based on improved differential evolution algorithm

Abstract

The application discloses a kind of methods for unmanned aerial vehicle path planning based on improved differential evolution algorithm, comprising the following steps: 1) model is built;1-1) the representation method of unmanned aerial vehicle flight path is built;1-2) three-dimensional environment model is built, and the three-dimensional environment model includes terrain model and threat area model;1-3) constraint condition model is established according to unmanned aerial vehicle flight performance and terrain constraint condition;1-4) cost function is constructed according to distance, height, height variation and corner index;2) improved algorithm, the multi-variation strategy of self-adaptive weight adjustment is introduced in standard differential evolution algorithm, and scaling factor F is dynamically adjusted according to iteration number, and the standard differential evolution algorithm is improved;3) the flight path of unmanned aerial vehicle is obtained;3-1) the model parameters built in step 1) and the task parameters of unmanned aerial vehicle are loaded;3-2) improved standard differential evolution algorithm is used to obtain the flight path of unmanned aerial vehicle;3-3) the flight path of unmanned aerial vehicle is smoothed, and the final flight path of unmanned aerial vehicle is obtained.

Description

Technical Field

[0001] This invention relates to the field of UAV trajectory planning, and specifically to a UAV trajectory planning method based on an improved differential evolution algorithm. Background Technology

[0002] With the continuous development of drone-related technologies, such as more intelligent autonomous flight technology, drone swarm collaboration technology, and high-precision guidance and control technology, drones are being used more and more widely in fields such as civilian exploration, environmental monitoring, and logistics transportation. However, the operating environment of drones is becoming increasingly complex. To ensure that drones can complete their tasks efficiently and stably, scientific and reasonable trajectory planning has become particularly important for drones.

[0003] Path planning is primarily used to solve the problem of calculating a feasible or optimal path from a starting point to a target point under known or unknown conditions. Compared to high-altitude flight, low-altitude flight is better suited to complex terrain conditions, effectively avoids obstacles, reduces external environmental interference, and improves the operational safety and mission completion quality of UAVs. Therefore, it is widely used in various low-altitude operational scenarios. During low-altitude operations, to ensure that the automatic planning of the UAV's three-dimensional path can complete the task efficiently, accurately, and quickly, an optimal path planning method needs to be found. However, finding the optimal path is a complex optimization problem considering multiple constraints. The complexity of the problem increases rapidly with the scale of the operational range and environmental complexity, which greatly affects the determination of the optimal path planning and hinders the smooth progress of UAV operations.

[0004] Although there are existing UAV trajectory planning schemes based on improved differential evolution algorithms, such as the invention patent application CN 114721429A entitled "Three-dimensional UAV trajectory planning method and device based on improved differential evolution algorithm", this method still has obvious limitations:

[0005] 1. Its 3D environment modeling only focuses on natural environmental factors such as terrain and landforms, and does not fully consider the human threats commonly encountered in low-altitude operations, resulting in insufficient adaptability to complex operation scenarios;

[0006] 2. The algorithm improvement focuses on single-dimensional optimization, which is lacking in balancing the global search range and local optimization accuracy. When facing trajectory planning problems under multiple constraints, it is prone to low optimization efficiency or getting trapped in local optima.

[0007] 3. The trajectory planning results do not fully take into account the stability and feasibility of the actual flight of the UAV, and lack systematic consideration of the trajectory geometry characteristics and flight attitude related indicators. This may result in problems such as drastic attitude adjustment and insufficient safety redundancy in actual applications, making it difficult to meet the requirements of UAVs to complete tasks efficiently and stably in complex low-altitude environments.

[0008] Therefore, there is an urgent need for a UAV trajectory planning method that can adapt to complex threat environments and balance optimization accuracy with trajectory practicality. Summary of the Invention

[0009] To address the aforementioned problems, this invention provides a UAV trajectory planning method based on an improved differential evolution algorithm. It improves the standard differential evolution algorithm by employing a multi-mutation strategy and an adaptive scaling factor adjustment method, thereby enhancing the algorithm's optimization capability, robustness, and convergence. In complex mission environments, it can provide the optimal flight path for the UAV.

[0010] To achieve the above objectives, the technical solution of the present invention is: a UAV trajectory planning method based on an improved differential evolution algorithm, comprising the following steps: 1) Constructing a model; 1-1) Constructing a method for representing the flight path of an unmanned aerial vehicle (UAV); 1-2) Construct a three-dimensional environment model, which includes a terrain model and a threat area model; 1-3) Establish a constraint model based on the UAV's flight performance and terrain constraints; 1-4) Construct a cost function based on distance, altitude, altitude change, and turning angle indicators; 2) Improve the algorithm by introducing an adaptive weight adjustment multi-mutation strategy into the standard difference evolution algorithm, dynamically adjusting the scaling factor F according to the number of iterations, and thus improving the standard difference evolution algorithm; 3) Obtain the flight path of the drone; 3-1) Load the model parameters and UAV mission parameters constructed in step 1); 3-2) An improved standard difference evolutionary algorithm is used to obtain the UAV track; 3-3) Smooth the drone's trajectory to obtain the drone's final trajectory.

[0011] Preferably, in step 1-1), the method for constructing the representation of the UAV flight path specifically involves: assuming that all environmental information is known and fixed, defining the coordinates of the starting point P0 as P0:(x0, y0, z0), and the target point P... n+1 The coordinates are P n+1 :(x n+1 , y n+1 , zn+1 The track consists of n navigation points {P1, P2, P3, ..., P...} n The elements} together form a set P: {P0, P1, P2, P3, ..., P} n , P n+1} is used to represent information about the entire flight path.

[0012] Preferably, in step 1-2), the specific steps for constructing the three-dimensional environment model are as follows:

[0013] 1-2-1) A terrain model is constructed using the digital elevation modeling method to describe the height information of the terrain surface and form various different terrain features;

[0014] 1-2-2) Construct a threat area model, which includes radar and no-fly zones;

[0015] a) Construct a model of radar detection of UAVs, specifically:

[0016] ;

[0017] In the formula, P R R represents the radar detection probability. Rmax d is the maximum detection radius of the radar. R This represents the distance from the drone to the center of the radar.

[0018] b) Construct a no-fly zone model, specifically as follows:

[0019] ;

[0020] In the formula, For threat probability, , The coordinates represent the length of the no-fly zone. , The coordinates represent the width of the no-fly zone.

[0021] Preferably, the cost function includes distance cost, altitude cost, altitude change cost, and corner cost.

[0022] Preferably, the cost function formula for the UAV trajectory is:

[0023] ;

[0024] Among them, J C For the total cost of the flight path, For the cost of distance, For a high price, At the cost of high change, For the cost of turning the corner, , , , These are the weighting coefficients for each cost;

[0025] The distance cost function formula is as follows:

[0026] ;

[0027] in,( , , ) as navigation point The coordinates, ( , , ) as navigation point coordinates navigation point With navigation points The straight-line distance between them As a cost of distance;

[0028] The formula for the height cost function is:

[0029] ;

[0030] in, At a high cost, z i This represents the height of the i-th navigation point;

[0031] The formula for the cost function of height change is:

[0032] ;

[0033] Among them, J H Represents the cost function of high variability. z is the average flight altitude of the navigation points. i This represents the height of the i-th navigation point;

[0034] The formula for the corner cost function is:

[0035] ;

[0036] Among them, J T a represents the cost of turning. i For navigation point P i-1 To navigation point P i The resulting vector, For navigation point P i To navigation point P i+1 The resulting vector, Let vector a i sum vector The corner between them.

[0037] Preferably, the constraint model includes terrain constraints, map constraints, turning angle constraints, climb / descent constraints, and minimum track length constraints.

[0038] Preferably, the formula for the terrain constraint is:

[0039] ;

[0040] Among them, H safe For the minimum safe flight altitude, z i H represents the height of the i-th navigation point. ter (x i ,y i ) is (x i ,y i ) ground level;

[0041] The formula for the map constraint is:

[0042] ;

[0043] Among them, L OutMap Indicates the length of the drone's flight path outside the map;

[0044] The formula for the turning angle constraint is:

[0045] ;

[0046] Among them, b i The horizontal projection of the i-th segment of the track. The maximum permissible turning angle;

[0047] The formula for the climb / descent constraint is:

[0048] ;

[0049] Among them, b i Let z be the horizontal projection of the i-th segment of the track. i This represents the height of the i-th navigation point. The maximum allowable angle of ascent or descent;

[0050] The formula for the minimum track length constraint is:

[0051] ;

[0052] in, navigation point With navigation points The straight-line distance between them, l min This is the minimum track length.

[0053] Preferably, the specific steps of the improved algorithm are as follows:

[0054] 2-1) Determine the individual dimension based on the number of navigation points, and randomly initialize the population using the following formula:

[0055] ;

[0056] in, Let x represent the i-th individual in the 0th generation population, and rand() represents a uniformly random number in the range [0, 1]. min and x max These are the upper and lower bounds for the value of variable x, respectively, and NP represents the population size.

[0057] 2-2) For each target individual, perform mutation operations, selecting DE / rand / 1, DE / rand / 2, and DE / current-to-best / 1 as mutation strategies:

[0058] DE / rand / 1:

[0059] ;

[0060] DE / rand / 2:

[0061] ;

[0062] DE / current-to-best / 1:

[0063] ;

[0064] in, for The corresponding mutated individuals, , , , and These are randomly selected, distinct index numbers, i.e. , , , and These are 5 individuals from the parent population, where F and λ are both scaling factors. It is the individual with the lowest cost in the current population;

[0065] Calculate the weights of each mutation strategy:

[0066] ;

[0067] in, Here, k represents the weight, k represents the ranking corresponding to the mutation strategy, and N represents the number of subpopulations.

[0068] Calculate the scaling factor:

[0069] ;

[0070] Where it is the current iteration number, and MaxIt is the total number of iterations. This is the scaling factor;

[0071] 2-3) Perform crossover operations to generate experimental individuals, calculate the track cost of the target individual and the experimental individual, and ensure that the generated track satisfies the flight constraints and threat constraints. Then select the better individual to retain to the next generation and record the minimum cost of the current iteration.

[0072] 2-4) If the maximum number of iterations is reached, output the optimal solution, record the position of each navigation point at this time, and obtain the planned trajectory. If the maximum number of iterations is not reached, return to step 2-3) and proceed to the next iteration.

[0073] Preferably, in step 3-3), cubic spline interpolation is used to smooth the UAV trajectory to obtain the final UAV trajectory.

[0074] The beneficial effects of this invention are as follows:

[0075] 1. The three-dimensional environment model constructed by this invention not only restores the natural environment model such as terrain and landforms, but also specifically adds models of man-made threat areas such as radar detection areas and no-fly zones. By quantifying the probability of radar detection and the probability of threat in no-fly zones, the flight path planning can fully avoid various risk sources, significantly improve the flight safety of UAVs in complex threat environments, and facilitate UAVs to meet the complex operation needs of multiple scenarios such as detection and environmental monitoring. It fills the gap in the existing technology that only focuses on natural terrain and ignores common man-made threats in low-altitude operations.

[0076] 2. The cost function of this invention comprehensively considers four major indicators: distance, altitude, altitude change, and turning angle. It minimizes energy consumption by using distance cost to ensure the shortest possible flight path, ensures low-altitude flight of the UAV by using altitude cost, reduces abrupt ascents and descents by using altitude change cost, and avoids sudden attitude changes by using turning angle cost, thus achieving a precise balance between flight path economy and flight stability. Compared to existing technologies that insufficiently consider flight path geometry and flight attitude, the flight path planned by this invention provides smoother attitude adjustments, more sufficient safety redundancy, and greater executability during actual flight.

[0077] 3. This invention effectively solves the problem of the standard difference evolutionary algorithm's difficulty in simultaneously achieving global search and local optimization by introducing an adaptive weight adjustment multi-mutation strategy combined with dynamically adjusting the scaling factor F based on the number of iterations. A larger F value in the initial iteration stage ensures global exploration capability and avoids getting trapped in local optima; the gradually decreasing F value in later iterations accelerates convergence and improves optimization accuracy. Simultaneously, the adaptive weight strategy dynamically adjusts the weights based on the actual performance of each mutation strategy, further enhancing the algorithm's adaptability to complex constraints and significantly improving trajectory planning efficiency and optimal solution quality.

[0078] 4. The constraint model of this invention covers five constraints: terrain, map, turning angle, climb / descent, and minimum track length, comprehensively conforming to the flight performance limits and environmental constraints of UAVs. Terrain constraints ensure that the flight altitude exceeds the minimum safety threshold; turning angle and climb / descent constraints prevent exceeding the UAV's maneuverability; and map constraints prevent the track from exceeding the operational range. This multi-dimensional approach ensures the physical feasibility of the track, completely solving the problem of insufficient safety redundancy in existing technologies and providing a solid guarantee for UAVs to complete missions efficiently and stably.

[0079] 5. This invention smooths the initial planned trajectory using cubic spline interpolation, eliminating the defects of a broken-line trajectory caused by straight-line connections between navigation points. The smoothed trajectory not only better conforms to the dynamic characteristics of the UAV, reducing attitude adjustment losses during flight, but also reduces equipment wear and extends the UAV's endurance. Attached Figure Description

[0080] Figure 1 This is a flowchart of the present invention;

[0081] Figure 2 This is a three-dimensional view of the optimal flight path planning for a UAV using the improved differential evolution algorithm of this invention.

[0082] Figure 3 This is a vertical cross-sectional view of the optimal trajectory planning for a UAV using the improved differential evolution algorithm of this invention.

[0083] Figure 4 This is a comparison of the cost convergence curves of the improved differential evolution algorithm of this invention and the standard differential evolution algorithm of the prior art. Detailed Implementation

[0084] See Figures 1 to 4 A method for UAV trajectory planning based on an improved differential evolution algorithm includes the following steps:

[0085] 1) Constructing a model;

[0086] 1-1) The method for constructing the UAV flight path representation is as follows: In UAV flight path planning, it is assumed that the environmental information is known and fixed, including the location and size of mountainous terrain covering thousands of square kilometers, air defense radar search areas, and no-fly zones, etc. The task of the planning algorithm is to calculate a feasible path with the lowest possible cost. The coordinates of the starting point P0 are defined as P0:(x0, y0, z0), and the target point P... n+1 The coordinates are P n+1 : (x n+1 , y n+1 , z n+1 The track consists of n navigation points {P1, P2, P3, ..., P...} n The elements} together form a set P: { P0, P1, P2, P3, ..., P n ,P n+1 The} symbol is used to represent information about the entire flight path. This representation method allows for an accurate description of the UAV's flight path.

[0087] 1-2) Construct a three-dimensional environment model, which includes a terrain model and a threat area model. The specific steps are as follows:

[0088] 1-2-1) A terrain model is constructed using the digital elevation modeling method to accurately describe the height information of the terrain surface, thereby forming various different landforms, such as mountains, hills, and basins.

[0089] 1-2-2) Construct a threat area model, which includes radar and no-fly zones;

[0090] a) Construct a model of radar detection of UAVs. Considering the functional characteristics of radar, the main parameter is the radar's maximum detection radius R. Rmax Its simplified model is a circle with radius R Rmax Let d be the distance from the UAV to the center of the radar. R Radar detection probability P R The calculation formula is:

[0091] ;

[0092] In the formula, P R R represents the radar detection probability. Rmax d is the maximum detection radius of the radar. R This represents the distance from the drone to the center of the radar.

[0093] b) Construct a no-fly zone model. The no-fly zone (NFZ) model is simplified as a cuboid. The cross-section parallel to the horizontal plane where the UAV is located at a certain altitude is ABCD. Define the coordinates of A, B, C, and D as A: (x1, y1), B: (x2, y1), C: (x2, y2), and D: (x1, y2), respectively. It can be seen that the coordinate values ​​do not change with the altitude of the UAV. Threat probability The calculation formula is:

[0094] ;

[0095] In the formula, For threat probability, , The coordinates represent the length of the no-fly zone. , The coordinates represent the width of the no-fly zone.

[0096] 1-3) Establish a constraint model based on the UAV's flight performance and terrain constraints; the constraint model includes terrain constraints, map constraints, turning angle constraints, climb / descent constraints, and minimum track length constraints.

[0097] The formula for the terrain constraint is:

[0098] ;

[0099] Among them, H safe For the minimum safe flight altitude, z i H represents the height of the i-th navigation point. ter (x i ,y i ) is (x i ,y i ) ground level;

[0100] The formula for the map constraint is:

[0101] ;

[0102] Among them, L OutMap Indicates the length of the drone's flight path outside the map;

[0103] The formula for the turning angle constraint is:

[0104] ;

[0105] Among them, b i The horizontal projection of the i-th segment of the track. The maximum permissible turning angle;

[0106] The formula for the climb / descent constraint is:

[0107] ;

[0108] Among them, b i Let z be the horizontal projection of the i-th segment of the track. i This represents the height of the i-th navigation point. The maximum allowable angle of ascent or descent;

[0109] The formula for the minimum track length constraint is:

[0110] ;

[0111] in, navigation point With navigation points The straight-line distance between them, l min This is the minimum track length.

[0112] 1-4) Construct a cost function based on distance, altitude, altitude change, and turning angle indices; the cost function includes distance cost, altitude cost, altitude change cost, and turning angle cost.

[0113] The cost function formula for the UAV trajectory is:

[0114] ;

[0115] Among them, J C For the total cost of the flight path, For the cost of distance, For a high price, At the cost of high change, For the cost of turning the corner, , , , These are the weighting coefficients for each cost, which can be adjusted according to the actual task requirements.

[0116] The drone's flight path information can be obtained from a set P: { P0, P1, P2, P3, ..., P n , P n+1} indicates that the distance cost J L It is obtained by adding up n+1 segments of the trajectory. The distance cost function formula is:

[0117] ;

[0118] in,( , , ) as navigation point The coordinates, ( , , ) as navigation point coordinates navigation point With navigation points The straight-line distance between them As a cost of distance;

[0119] Height cost function J Z This causes the drone to tend to plan low-altitude routes, and the altitude cost function formula is:

[0120] ;

[0121] in, At a high cost, z i This represents the height of the i-th navigation point;

[0122] The formula for the cost function of height change is:

[0123] ;

[0124] Among them, J H Represents the cost function of high variability. z is the average flight altitude of the navigation points. i This represents the height of the i-th navigation point;

[0125] In three-dimensional space, there are 3 navigation points {P} i-1 , P i , P i+1 The corner is formed by point P. i-1 Point P i Get vector a i From point P i Point P i+1 Get vector a i+1 , Let be the turning angle between these two vector segments, and the formula for the turning angle cost function is:

[0126] ;

[0127] Among them, J T a represents the cost of turning. i For navigation point P i-1 To navigation point P i The resulting vector, For navigation point P i To navigation point P i+1 The resulting vector, Let vector a i sum vector The corner between them.

[0128] 2) Improve the algorithm by introducing an adaptive weight adjustment multi-mutation strategy into the standard difference evolution algorithm. The scaling factor F is dynamically adjusted based on the number of iterations, thus improving the standard difference evolution algorithm. The specific steps are as follows:

[0129] 2-1) Determine the individual dimension based on the number of navigation points, and randomly initialize the population using the following formula:

[0130] ;

[0131] in, Let x represent the i-th individual in the 0th generation population, and rand() represents a uniformly random number in the range [0, 1]. min and x max These are the upper and lower bounds for the value of variable x, respectively, and NP represents the population size.

[0132] 2-2) For each target individual, perform mutation operations, selecting DE / rand / 1, DE / rand / 2, and DE / current-to-best / 1 as mutation strategies:

[0133] DE / rand / 1:

[0134] ;

[0135] DE / rand / 2:

[0136] ;

[0137] DE / current-to-best / 1:

[0138] ;

[0139] in, for The corresponding mutated individuals, , , , and These are randomly selected, distinct index numbers, i.e. , , , and These are 5 individuals from the parent population, where F and λ are both scaling factors. It is the individual with the lowest cost in the current population;

[0140] After initializing the population, it is divided into three subpopulations. Each subpopulation randomly selects a policy for mutation based on the weights of each policy. Simultaneously, an adaptive weight adjustment policy is introduced to dynamically adjust the weights of each policy based on its performance. In each iteration, the minimum generation values ​​obtained from the evolution of the three subpopulations are sorted in ascending order. The original weights of the three policies are 1:1:1; the weights of each policy are recalculated according to the sorting order. The calculation formula is as follows:

[0141] ;

[0142] in, Here, k represents the ranking corresponding to the mutation strategy, and N represents the number of subpopulations. After updating the weights of each strategy, the next round of evolution can proceed. After multiple rounds of evolution, the weights of different strategies will adaptively change according to the changes in the individual fitness value to achieve better optimization results.

[0143] For the improved strategy of scaling factor F, it is dynamically adjusted according to the number of iterations. This method sets a minimum and a maximum value for the scaling factor, and then calculates the value to be used in the current iteration based on the ratio of the current iteration number it to the total number of iterations MaxIt. The calculation formula is as follows:

[0144] ;

[0145] Where it is the current iteration number, and MaxIt is the total number of iterations. This is the scaling factor.

[0146] When the number of iterations is small, the value of F is relatively large, which allows the differential evolution algorithm to try more explorations in the initial stage in order to better discover the global optimum. As the number of iterations gradually increases, the value of F decreases, which allows for more emphasis on utilizing existing information in later stages in order to converge to the optimum solution, i.e. the optimal trajectory of the UAV, more quickly.

[0147] 2-3) Perform crossover operations to generate experimental individuals, calculate the track cost of the target individual and the experimental individual, and ensure that the generated track satisfies the flight constraints and threat constraints. Then select the better individual to retain to the next generation and record the minimum cost of the current iteration.

[0148] 2-4) If the maximum number of iterations is reached, output the optimal solution, record the position of each navigation point at this time, and obtain the planned trajectory. If the maximum number of iterations is not reached, return to step 2-3) and proceed to the next iteration.

[0149] 3) Obtain the flight track;

[0150] 3-1) Load the model parameters and UAV mission parameters constructed in step 1), specifically including UAV environmental planning modeling and map elevation data; radar, no-fly zone location and size information; distance cost, altitude cost, altitude change cost, and turning cost corresponding to their respective weight coefficients; and the maximum turning angle, maximum climb or descent angle, minimum track length, etc. in the constraint modeling.

[0151] 3-2) An improved standard difference evolutionary algorithm is used to obtain the UAV track;

[0152] 3-3) The UAV trajectory is smoothed by cubic spline interpolation to obtain the final UAV trajectory.

[0153] Since the initial path formed by connecting navigation points generally does not meet flight conditions, cubic spline interpolation is introduced to smooth the path, resulting in a smooth path. Cubic spline interpolation is a mathematical technique used for data fitting and function approximation. It is a cubic polynomial function that can smoothly connect known data points and has a certain continuity of first and second derivatives at these data points.

[0154] It is defined as: given n+1 nodes on [a, b], a=x0 <x1<…<x n-1 <x n =b and the function values ​​f(x) at these points i )=y i (i=0, 1,…, n). Define s(x) as the function f(x) with respect to nodes x0, x1,…, xn. n A cubic spline function.

[0155] Solving cubic spline interpolation using the second derivative as a linear function:

[0156]

[0157] Where h j =x j+1 -x j M j =s"(x j ), j=0, 1,… , n.

[0158] The UAV trajectory is smoothed using cubic spline interpolation to obtain the final UAV trajectory.

[0159] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications made to the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for UAV trajectory planning based on an improved differential evolution algorithm, characterized in that: Includes the following steps: 1) Constructing a model; 1-1) Constructing a method for representing the flight path of an unmanned aerial vehicle (UAV); 1-2) Construct a three-dimensional environment model, which includes a terrain model and a threat area model; 1-3) Establish a constraint model based on the UAV's flight performance and terrain constraints; 1-4) Construct a cost function based on distance, altitude, altitude change, and turning angle indicators; 2) Improve the algorithm by introducing an adaptive weight adjustment multi-mutation strategy into the standard difference evolution algorithm, dynamically adjusting the scaling factor F according to the number of iterations, and thus improving the standard difference evolution algorithm; 3) Obtain the flight path of the drone; 3-1) Load the model parameters and UAV mission parameters constructed in step 1); 3-2) An improved standard difference evolutionary algorithm is used to obtain the UAV track; 3-3) Smooth the drone's trajectory to obtain the drone's final trajectory.

2. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 1, characterized in that: In step 1-1), the method for constructing the representation of the UAV flight path is as follows: assuming that all environmental information is known and fixed, the coordinates of the starting point P0 are defined as P0:(x0, y0, z0), and the target point P... n+1 The coordinates are P n+1 : (x n+1 , y n+1 , z n+1 The track consists of n navigation points {P1, P2, P3, ..., P...} n The elements} together form a set P: { P0, P1, P2, P3, ..., P n , P n+1 } is used to represent information about the entire flight path.

3. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 1, characterized in that: In steps 1-2), the specific steps for constructing the three-dimensional environment model are as follows: 1-2-1) A terrain model is constructed using the digital elevation modeling method to describe the height information of the terrain surface and form various different terrain features; 1-2-2) Construct a threat area model, which includes radar and no-fly zones; a) Construct a model of radar detection of UAVs, specifically: ； In the formula, P R R represents the radar detection probability. Rmax d is the maximum detection radius of the radar. R This represents the distance from the UAV to the center of the radar. b) Construct a no-fly zone model, specifically as follows: ； In the formula, For threat probability, , The coordinates represent the length of the no-fly zone. , The coordinates represent the width of the no-fly zone.

4. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 1, characterized in that: The cost function includes distance cost, altitude cost, altitude change cost, and corner cost.

5. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 4, characterized in that: The cost function formula for the UAV trajectory is: ； Among them, J C For the total cost of the flight path, For the cost of distance, For a high price, At the cost of high change, For the cost of turning the corner, , , , These are the weighting coefficients for each cost; The distance cost function formula is as follows: ； in,( , , ) as navigation point The coordinates, ( , , ) as navigation point coordinates navigation point With navigation points The straight-line distance between them As a cost of distance; The formula for the height cost function is: ； in, At a high cost, z i This represents the height of the i-th navigation point; The formula for the cost function of height change is: ； Among them, J H Represents the cost function of high variability. z is the average flight altitude of the navigation points. i This represents the height of the i-th navigation point; The formula for the corner cost function is: ； Among them, J T a represents the cost of turning. i For navigation point P i-1 To navigation point P i The resulting vector, For navigation point P i To navigation point P i+1 The resulting vector, Let vector a i sum vector The corner between them.

6. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 1, characterized in that: The constraint model includes terrain constraints, map constraints, turning angle constraints, climb / descent constraints, and minimum track length constraints.

7. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 6, characterized in that: The formula for the terrain constraint is: ； Among them, H safe For the minimum safe flight altitude, z i H represents the height of the i-th navigation point. ter (x i ,y i ) is (x i ,y i ) ground level; The formula for the map constraint is: ； Among them, L OutMap Indicates the length of the drone's flight path outside the map; The formula for the turning angle constraint is: ； Among them, b i The horizontal projection of the i-th segment of the track. The maximum permissible turning angle; The formula for the climb / descent constraint is: ； Among them, b i Let z be the horizontal projection of the i-th segment of the track. i This represents the height of the i-th navigation point. The maximum allowable angle of ascent or descent; The formula for the minimum track length constraint is: ； in, navigation point With navigation points The straight-line distance between them, l min This is the minimum track length.

8. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 1, characterized in that: The specific steps of the improved algorithm are as follows: 2-1) Determine the individual dimension based on the number of navigation points, and randomly initialize the population using the following formula: ； in, Let x represent the i-th individual in the 0th generation population, and rand() represents a uniformly random number in the range [0, 1]. min and x max These are the upper and lower bounds for the value of variable x, respectively, and NP represents the population size. 2-2) For each target individual, perform mutation operations, selecting DE / rand / 1, DE / rand / 2, and DE / current-to-best / 1 as mutation strategies: DE / rand / 1: ； DE / rand / 2: ； DE / current-to-best / 1: ； in, for The corresponding mutated individuals, , , , and These are randomly selected, distinct index numbers, i.e. , , , and These are 5 individuals from the parent population, where F and λ are both scaling factors. It is the individual with the lowest cost in the current population; Calculate the weights of each mutation strategy: ； in, Here, k represents the weight, k represents the ranking corresponding to the mutation strategy, and N represents the number of subpopulations. Calculate the scaling factor: ； Where it is the current iteration number, and MaxIt is the total number of iterations. This is the scaling factor; 2-3) Perform crossover operations to generate experimental individuals, calculate the track cost of the target individual and the experimental individual, while ensuring that the generated tracks meet the flight constraints and threat constraints, select the better individual to retain to the next generation, and record the minimum cost of the current iteration. 2-4) If the maximum number of iterations is reached, output the optimal solution, record the position of each navigation point at this time, and obtain the planned trajectory. If the maximum number of iterations is not reached, return to step 2-3) and proceed to the next iteration.

9. The UAV trajectory planning method based on the improved differential evolution algorithm according to claim 1, characterized in that: In step 3-3), cubic spline interpolation is used to smooth the UAV trajectory to obtain the final UAV trajectory.

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