Three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization

Abstract

The invention discloses a three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization, models the three-dimensional environment of the UAV low-altitude penetration to obtain a model; determines the penetration cost function for the model; obtains a sparrow search algorithm; improves the obtained sparrow search algorithm according to the UAV low-altitude penetration to obtain an improved sparrow search algorithm; and plans the three-dimensional path of the UAV low-altitude penetration using the improved sparrow search algorithm. The invention has a better path planning effect when facing different environments, that is, improves the optimization accuracy of the improved sparrow search algorithm and finds the optimal path.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) path planning, and in particular to a UAV low-altitude penetration three-dimensional path planning method optimized by a sparrow search algorithm with adaptive leader sparrow guidance and central variation-evolution factor. Background Art

[0002] Low-altitude penetration is an important part of UAV combat and is also a hot topic in current research. In order to find a safe path from the starting point to the end point that can avoid the threat source, the penetration target is based on an effective route planning method to find the optimal solution under the constraint problem. The key depends on the quality of the optimization algorithm. In recent years, scholars have conducted in-depth research and proposed a variety of low-altitude penetration path planning algorithms, which can be mainly divided into two categories: (1) conventional algorithms, such as artificial potential field method, A* algorithm, etc.; (2) intelligent algorithms, such as genetic algorithms (GA), particle swarm optimization (PSO), grey wolf optimization (GWO), moth-flame optimization (MFO), etc. Compared with conventional algorithms, intelligent algorithms have fast convergence speed and strong robustness. In particular, the use of swarm intelligence optimization algorithms to solve the problem of UAV penetration paths is a hot topic in current research. In order to solve the problem of UAV low-altitude penetration, Zhang Honghong et al. used an improved ant colony algorithm to generate a path with lower risk, which improved the optimization efficiency, but the path accuracy was not high. Song Yu et al. proposed an improved particle swarm optimization method based on three-dimensional planning, which improved the search performance. However, the threat field was considered relatively simply and factors such as terrain were not considered, so the actual application effect was not ideal. Xu Jiangbo et al. improved the fish swarm algorithm through adaptive strategies and used its global optimization ability to solve the path planning problem, but the search time was too long. Although the above studies have achieved the trajectory planning of UAVs, there is still room for further improvement in the path planning effect and iterative convergence speed. Sparrow Search Algorithm (SSA) is a new swarm intelligence optimization algorithm proposed by XUE in 2020. It simulates the foraging process of sparrows and has the characteristics of fast convergence speed, strong adaptability, and easy model modification. It is suitable for UAV path planning. Tang Andy et al. proposed a trajectory planning method based on the chaotic sparrow search algorithm, which can quickly obtain a safe and feasible trajectory. However, this algorithm is applied to two-dimensional scenes and has certain limitations. SSA itself still has problems such as easy to fall into local optimality and rapid reduction of population diversity, and still needs further improvement. Summary of the invention

[0003] The purpose of the present invention is to provide a three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization, so as to solve the problems of complex environment and large amount of path planning calculation in the prior art when the UAV is penetrating at three-dimensional low altitude, as well as the defects of insufficient path search ability of the existing sparrow search algorithm and easy to fall into local optimum. The present invention has better path planning effect when facing different environments, that is, improves the optimization accuracy of the improved sparrow search algorithm and finds the optimal path.

[0004] In order to achieve the above object, the present invention adopts the following technical scheme:

[0005] The three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization includes the following steps:

[0006] Step 1: Model the three-dimensional environment of the UAV low-altitude penetration to obtain a model;

[0007] Step 2: Determine the penetration cost function for the model obtained in step 1;

[0008] Step 3: Get the sparrow search algorithm;

[0009] Step 4: Improve the sparrow search algorithm obtained in step 3 according to the UAV low-altitude penetration to obtain an improved sparrow search algorithm;

[0010] Step 5: Use the improved sparrow search algorithm obtained in step 4 to plan the three-dimensional path of the UAV's low-altitude penetration.

[0011] Furthermore, the three-dimensional environment modeling of the UAV low-altitude penetration in step 1 includes terrain constraints and threat source model constraints:

[0012] The mountain modeling in a three-dimensional environment with terrain constraints is as follows:

[0013]

[0014] In the formula, (x, y) is the coordinate of the terrain, (x0, y0) is the coordinate of the center point of the mountain terrain, h is the height parameter, and λ1 and λ2 reflect the steepness of the mountain.

[0015] Threat source model constraints include radar detection, air defense artillery, and surface-to-air missiles;

[0016] The threat source is equivalent to a terrain model. Assuming that the closer to the center of the threat source, the greater the threat cost and the higher the terrain, and vice versa, the lower the threat cost, therefore, the threat source is equivalent to:

[0017]

[0018] In the formula, K thr is the threat source correction coefficient, and the horizontal coordinate of the center of the pth threat source is (xp ,y p ), the maximum radius R of the pth threat source max,p , R is the distance from the three-dimensional environment coordinate point (x, y) to the center of the threat source.

[0019] Furthermore, the penetration cost function of step 2 includes:

[0020] 1) During flight, the altitude of 0.05-2.5km above the ground is suitable for flight. The terrain threat cost of the track point is as follows:

[0021]

[0022] In the formula, K Z ,K′ z is the terrain threat factor, h j is the altitude of the jth track point, Z j is the terrain height of the jth track point, f Z,j is the threat cost corresponding to the j-th track point;

[0023] 2) Low-altitude penetration needs to consider the elevation cost. The elevation cost of track point j is as follows:

[0024] f H,j =h j

[0025] In the formula, f H,j is the elevation cost corresponding to the j-th track point;

[0026] 3) Terrain constraints also need to consider the flight boundary range and maximum flight altitude to ensure the controllability of the drone. The flight level range is set to (x min ,y min )=(0,0) and (x max ,y max )=(100,100), the maximum flight height is z max =5;

[0027] In the radar area, the simplified radar detection probability model is as follows:

[0028] P0=1 / r 4

[0029] In the formula, r is the distance from the track point to the center of the threat source;

[0030] In the anti-aircraft artillery zone, the probability of damage is expressed as:

[0031] P G =1 / r

[0032] The probability of being hit within the missile zone radius is:

[0033]

[0034] In the formula, R max is the maximum radius of the threat source;

[0035] The restrictions in the no-fly zone are:

[0036] P J =K J

[0037] In the formula, K J is the threat cost of the no-fly zone, P J The cost of restraint in no-fly zones;

[0038] The calculation cost of each track point in each threat area is defined as follows:

[0039]

[0040] In the formula, r j,p is the straight-line distance from the jth track point to the center of the threat source p, P0, P G , P M and P J are the cost functions of radar, artillery, missile, and no-fly zone, respectively, T,jp is the cost from track point j to the center of threat source p;

[0041] 4) UAV constraints are the physical constraints imposed on the UAV during flight, including turning angle α, descent and climb angle β, and fuel cost. The physical constraints are:

[0042]

[0043]

[0044]

[0045] In the formula, K α and K β are the threat factors of turning angle and pitch angle respectively, and is the cost function of α and β corresponding to the jth track point, J L,j is the flight distance corresponding to the j-th track point. Combining various cost functions, the UAV self-constraint cost function of the j-th track point is obtained as follows:

[0046] f J,j =J α_angle,j +J β_angle,j +J L,j

[0047] 5) The track cost function is a weighted combination of terrain constraints, elevation costs, threat source model constraints, and the costs of the UAV's own physical constraints to form the final UAV cost function. The formula is as follows:

[0048]

[0049] Where F is the cost of the entire track, σ1, σ2, σ3 and σ4 are the weights of each cost, d is the total number of track points, and w is the total number of threat sources.

[0050] Furthermore, the sparrow search algorithm in step 3 includes the following steps:

[0051] Step 3.1: Randomly initialize the sparrow population;

[0052] Step 3.2: Finder location update;

[0053] Step 3.3: Joiner location update;

[0054] Step 3.4: Sentinel position update.

[0055] Furthermore, the finder in the sparrow population in step 3.2 is responsible for foraging and guiding the movement of the entire population, and the finder position is updated as follows:

[0056]

[0057] In the formula, represents the j-th position of the ith individual in the tth generation in the population, ζ is a uniform random number in (0,1], Q is a standard normal distribution random number, L is a multi-dimensional all-one matrix with one row, R2 is a uniform random number in [0,1], and ST is the warning threshold;

[0058] In step 3.3, the joiners are the individuals in the population except the discoverer, and the position update formula of the joiners is as follows:

[0059]

[0060] In the formula, is the best position occupied by the discoverer of the tth generation population, represents the current global worst position, A is a 1×d matrix containing only 1 or -1 elements, and the matrix operation A is defined + The calculation method is as follows:

[0061] A + =A T (AA T ) -1

[0062] In step 3.4, 20% of the individuals in the sparrow population are randomly selected as sentinels. The sentinel update formula is as follows:

[0063]

[0064] In the formula, represents the current global optimal position, δ is the step size control parameter that conforms to the normal distribution, with a mean of 0 and a variance of 1, and k is a random number in the range of [-1,1]; f i Indicates the fitness of the sparrow’s current position; f g With f w are the global optimal and worst fitness respectively; ε is the minimum value that is not zero.

[0065] Furthermore, in step 4, the sparrow search algorithm obtained in step 3 is improved according to the low-altitude penetration of the UAV to obtain an improved sparrow search algorithm, and the specific steps include:

[0066] Step 4.1: Initialize the sparrow population based on random tent mapping in the three-dimensional environment model obtained in step 1, and each sparrow represents a penetration path;

[0067] Step 4.2: Adopt the adaptive leader sparrow guidance strategy to update the position of the discoverer in the sparrow population;

[0068] Step 4.3: Joiner location update;

[0069] Step 4.4: Update the position of the sentinel;

[0070] Step 4.5: Update the position of the sparrow population based on the central variation-evolution factor;

[0071] Step 4.6: Calculate the fitness of the sparrow population and select the best sparrow according to the fitness;

[0072] Step 4.7: Determine whether the maximum number of iterations has been reached. If so, output the optimal sparrow, i.e. the optimal penetration track point. If not, return to step 4.2.

[0073] Furthermore, in step 4.1, the sparrow population is initialized based on the random tent mapping, and the formula is as follows:

[0074]

[0075] In the formula, i is the population size, i = 1, 2...n; j is the individual dimension, j = 1, 2...d; s is a random number (0, 1), ψ is the chaotic parameter. After taking the initial value of the above formula, n×d chaotic sequences are obtained. Substituting the chaotic sequence into the individual position formula to obtain the individual position of the population, the formula is as follows:

[0076] x i,j =Lbj +v i,j (Ub j -Lb j )

[0077] In the formula, Ub j and Lb j are the upper and lower boundaries of the j-dimensional three-dimensional terrain search space respectively.

[0078] Furthermore, in step 4.2, the adaptive leader guidance strategy is used to update the discoverer position. The specific formula is:

[0079]

[0080] In the formula, represents the best individual in the tth generation in the population, ω is the weight factor, and the update formula is as follows:

[0081]

[0082] In the formula, ω max ,ω min are the maximum and minimum values ​​of the weight factor respectively.

[0083] Furthermore, in step 4.5, the position is updated based on the central variation-evolution factor, specifically:

[0084] In order to speed up the iteration, only the best individuals are selected for central mutation. Let X = [x1, x2, ..., x d ] are d points with unit mass, then a discrete uniform overall center G is:

[0085]

[0086] Then a point x in the whole j The central variation point of is defined as:

[0087]

[0088] The evolution part is designed based on the principle of the survival of the fittest. The population is sorted by the fitness value and evolves in order. Individuals with good fitness are likely to be retained, while individuals with poor fitness are likely to evolve. The formula is as follows:

[0089]

[0090] In the formula, t1 and t2 are random individuals in the sparrow population and are different from each other; x1 is the optimal individual; rand and s are random numbers between 0 and 1; P(i) is the fitness level corresponding to the i-th individual in the population, and the calculation formula is:

[0091]

[0092] The calculation formula for generating new solutions through the central mutation-evolution factor is expressed as:

[0093]

[0094] In the formula, g1(x) is the central mutation; g2(x) is the evolution; τ is the probability of selecting central mutation or evolution, and the calculation formula is as follows:

[0095]

[0096] After using the central mutation-evolution factor to obtain a new solution, the new population is updated according to the greedy principle.

[0097] Furthermore, in step 5, the obtained improved sparrow search algorithm is used to plan the three-dimensional path of the UAV low-altitude penetration, and the specific method is as follows:

[0098] Each path is a line formed by connecting multiple track points, defining a sparrow in the population That is, a path. The sparrow with the lowest cost represents the optimal path. Each track point has three-dimensional attributes (x, y, z). When using ALCE-SSA to plan the three-dimensional penetration path of the UAV, the specific steps include:

[0099] Step 5.1: Using the method in step 4.1 to obtain the initial sparrow population on the three-dimensional environment model obtained in step 1;

[0100] Step 5.2: Calculate the fitness of each sparrow in the initial sparrow population using the cost function obtained in step 2, sort the sparrow population according to the fitness, and select the best sparrow;

[0101] Step 5.3: Update the position of the sparrow population using the method in steps 4.2-4.5, calculate the fitness of each sparrow, and sort the sparrow population according to the size of the fitness;

[0102] Step 5.4: Determine whether the maximum number of iterations has been reached. If so, output the optimal sparrow, i.e. the optimal penetration track point. Otherwise, return to step 5.3.

[0103] Step 5.5: Optimize the optimal track points obtained in 5.4 by cubic spline interpolation to obtain the final three-dimensional penetration path of the UAV.

[0104] Compared with the prior art, the present invention has the following beneficial technical effects:

[0105] The present invention proposes an adaptive leading sparrow guide and center mutation-evolution factor sparrow search algorithm (ALCE-SSA), which obtains the optimal path for the UAV penetration under the premise of ensuring rapid optimization. The present invention has a better path planning effect when facing different environments, that is, it improves the optimization accuracy of the improved sparrow search algorithm and finds the optimal path.

[0106] Furthermore, the present invention designs a random tent mapping to initialize the population and improve the quality of the initialized population; adopts an adaptive leader bird guidance strategy in the update of the discoverer position to solve the adverse effects of the parent generation on the update position of the bird flock discoverer, and can simultaneously improve the ability of early global exploration and later local optimization; adopts a central variation-evolution factor to improve population diversity, prevent the population from falling into the local optimum, expand the search space, and improve the global optimization ability. Therefore, ALCE-SSA can more accurately and quickly enable the drone to autonomously avoid dangerous areas and select the optimal path to achieve low-altitude penetration.

[0107] Compared with the gray wolf algorithm, the moth-to-fire algorithm and the sparrow search algorithm, the present invention has better energy consumption, smoother paths, faster convergence speed, can enable the UAV to effectively use the terrain advantages to avoid threat sources, and exhibits better optimization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] The drawings in the specification are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0109] Figure 1 It is a schematic diagram of the process of the present invention;

[0110] Figure 2 It is a flow chart of the improved sparrow search algorithm involved in the present invention;

[0111] Figure 3 is a path planning diagram of the present invention in terrain 1;

[0112] Figure 4 It is the path planning diagram of the present invention in terrain 2. DETAILED DESCRIPTION

[0113] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0114] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0115] See also Figure 1 The flowchart of the present invention is shown in FIG. 1 . The present invention optimizes and improves the basic sparrow search algorithm and proposes a sparrow search algorithm with adaptive leader sparrow guidance and central variation-evolution factor, such as Figure 2 , applied to the path planning of low-altitude UAV penetration. First, the relevant terrain model and threat source model are established; secondly, the sparrow search algorithm is improved. The position of the population is initialized by random tents, which improves the quality of the initialized population; then, in view of the deficiency of the discoverer position update in the sparrow search algorithm, an adaptive leading sparrow guidance strategy is designed to reduce the adverse effects of relying on a single parent update, and can simultaneously improve the early global exploration and later local optimization capabilities; finally, in view of the problem of insufficient population diversity and easy to fall into local optimality, a central mutation-evolution factor is designed to expand the search space and further improve the global optimization capability. From Figure 3 and Figure 4 It can be seen that compared with the gray wolf algorithm, the moth-to-fire algorithm and the sparrow search algorithm, ALCE-SSA has better energy consumption, smoother paths, faster convergence speed, and can enable drones to effectively use terrain advantages to avoid threat sources, showing better optimization capabilities.

[0116] The specific steps are as follows:

[0117] Step 1: The three-dimensional environment modeling of UAV low-altitude penetration includes: terrain constraints and threat source model constraints.

[0118] The mountain modeling in a three-dimensional environment with terrain constraints is as follows:

[0119]

[0120] In the formula, (x, y) is the coordinate of the terrain, (x0, y0) is the coordinate of the center point of the mountain terrain, h is the height parameter, and λ1 and λ2 reflect the steepness of the mountain.

[0121] During flight, the altitude of 0.05-2.5km above the ground is suitable for flying. The terrain threat cost of the track point is as follows:

[0122]

[0123] In the formula, K Z ,K′ z is the terrain threat factor, h j is the altitude of the jth track point, Z j is the terrain height of the jth track point, f Z,j is the threat cost corresponding to the jth track point. In addition, the low-altitude penetration needs to consider the elevation cost. The elevation cost of track point j is as follows:

[0124] f H,j =h j

[0125] Terrain constraints also need to consider the flight boundary range and maximum flight altitude to ensure the controllability of the drone. Set the flight level range to (x min ,y min )=(0,0) and (x max ,y max )=(100,100), the maximum flight height is z max =5.

[0126] The threat source model constraints include radar detection, air defense artillery, surface-to-air missiles, etc.

[0127] In the radar area, the simplified radar detection probability model is as follows:

[0128] P0=1 / r 4

[0129] Where r is the distance from the track point to the center of the threat source.

[0130] Anti-aircraft artillery threat

[0131] In the anti-aircraft artillery zone, the probability of damage can be expressed as:

[0132] P G =1 / r

[0133] Surface-to-air missile threat

[0134] The probability of a drone being hit within the missile zone radius is:

[0135]

[0136] In the formula, R max The maximum radius of the threat source.

[0137] No-fly zone threat

[0138] In reality, there are some areas with very bad climate and environment, which are called no-fly zones in this invention. The constraints of no-fly zones are:

[0139] P J =K J

[0140] In the formula, K J The cost of the no-fly zone threat.

[0141] The threat source is equivalent to a terrain model, assuming that the closer to the center of the threat source, the greater the threat cost and the higher the terrain, and vice versa. Therefore, the threat source can be equivalent to:

[0142]

[0143] In the formula, K thr is the threat source correction coefficient, and the horizontal coordinate of the center of the pth threat source is (x p ,y p ), the maximum radius R of the pth threat source max,p , R is the distance from the coordinate point to the center of the threat source. The calculation cost of each track point in the threat area is defined as follows:

[0144]

[0145] In the formula, r j,p is the straight-line distance from the jth track point to the center of the threat source p, P0, P G , P M and P J are the cost functions of radar, artillery, missile, and no-fly zone, respectively, T,jp is the cost from track point j to the center of threat source p.

[0146] Drone constraints are the physical constraints that the drone is subject to during flight, including the turning angle α, the descent and climb angle β, and the fuel cost (distance). The physical constraints are:

[0147]

[0148]

[0149]

[0150] In the formula, K α and K β are the threat factors of turning angle and pitch angle respectively, and is the cost function of α and β corresponding to the jth track point, J L,j is the flight distance corresponding to the jth track point. Combining various cost functions, the UAV self-constraint cost function of the jth track point can be obtained as:

[0151] f J,j =J α_angle,j +J β_angle,j +J L,j

[0152] The track cost function is a weighted combination of terrain constraints, elevation costs, threat source model constraints, and the physical constraints of the drone itself, which constitutes the final drone cost function. The formula is as follows:

[0153]

[0154] Where F is the cost of the entire track, σ1, σ2, σ3 and σ4 are the weights of each cost, d is the total number of track points, and w is the total number of threat sources.

[0155] Step 2: The basic Mahjong search algorithm is divided into the following steps:

[0156] The finder in the sparrow population is responsible for foraging and guiding the movement of the entire population. The finder position is updated as follows:

[0157]

[0158] In the formula, represents the j-th dimensional position of the ith individual in the t-th generation in the population, ζ is a uniform random number in (0,1], Q is a standard normal distribution random number, L is a multi-dimensional all-one matrix with one row, R2 is a uniform random number in [0,1], ST is the warning threshold, and its value is 0.6.

[0159] Joiners are individuals with poor fitness except for the discoverer. The position update formula of joiners is as follows:

[0160]

[0161] In the formula, is the best position occupied by the discoverer of the tth generation population, represents the current global worst position, A is a 1×d matrix containing only 1 or -1 elements, and the matrix operation A is defined + The calculation method is as follows:

[0162] A + =A T (AA T ) -1

[0163] 20% of the individuals in the sparrow population are randomly selected as sentinels, and the sentinel update formula is as follows:

[0164]

[0165] In the formula, represents the current global optimal position, δ is the step size control parameter that conforms to the normal distribution, with a mean of 0 and a variance of 1, and k is a random number in the range of [-1,1]; f i Indicates the fitness of the sparrow’s current position; f g With f w are the global optimal and worst fitness respectively; ε is the minimum value that is not zero, set to 1 -8 , to prevent the denominator from being 0.

[0166] Step 3: Improve the sparrow search algorithm for drone penetration. The following steps are included:

[0167] In the three-dimensional terrain space obtained in step 1, the sparrow population is initialized based on random tent mapping. Each sparrow represents a penetration path. The formula for initializing the sparrow population based on random tent mapping is as follows:

[0168]

[0169] In the formula, i is still the population size (i = 1, 2 ... n), j is the individual dimension (j = 1, 2 ... d), s is a random number (0, 1), ψ is the chaotic parameter, and after taking the initial value of the formula, n × d chaotic sequences can be obtained. Substituting the chaotic sequence into the individual position formula to obtain the individual position of the population, the formula is as follows:

[0170] x i,j =Lb j +v i,j (Ub j -Lb j )

[0171] In the formula, Ub j and Lb j are the upper and lower boundaries of the j-dimensional search space respectively. Figure 2 As shown, the chaotic sequence generated by random Tent mapping has more uniform distribution in y and z dimensions.

[0172] An adaptive leader-guided strategy to update the discoverer:

[0173] The updated formula for the new discoverer is revised to:

[0174]

[0175] In the formula, represents the best individual in the tth generation in the population, ω is the weight factor, and the update formula is as follows:

[0176]

[0177] In the formula, ω max ,ω min are the maximum and minimum values ​​respectively. Update ω, ω for the individual y dimension of the population maxy ,ω miny Take 1 and 0.01, the update ω of the z dimension maxz and ω minz Take 0.1 and 0.005.

[0178] The position update formula for joiners and sentinels remains unchanged.

[0179] Update the position of the sparrow population based on the central variation-evolution factor to increase population diversity:

[0180] In order to speed up the iteration, only the best individuals are selected for central mutation. Let X = [x1, x2, ..., x d ] are d points with unit mass, then the center of a discrete uniform system is G:

[0181]

[0182] Then a point x in the whole j The central variation point of is defined as:

[0183]

[0184] The evolution part is designed based on the principle of the survival of the fittest. The population is sorted by the fitness value and evolves in order. It can be seen that individuals with good fitness are more likely to be retained, and individuals with poor fitness are more likely to choose to evolve. The formula is as follows:

[0185]

[0186] In the formula, t1 and t2 are random individuals in the sparrow population and are different from each other; x1 is the optimal individual; rand and s are random numbers between 0 and 1; P(i) is the fitness level corresponding to the i-th individual in the population, and the calculation formula is:

[0187]

[0188] The calculation formula for generating new solutions through the central mutation-evolution factor can be expressed as:

[0189]

[0190] In the formula, g1(x) is the central mutation; g2(x) is the evolution; τ is the probability of selecting central mutation or evolution, and the calculation formula is as follows:

[0191] The calculation formula is as follows:

[0192]

[0193] After using the central mutation-evolution factor to obtain a new solution, the new population is updated according to the greedy principle.

[0194] Calculate the fitness of the new sparrow population and select the best sparrow according to the fitness;

[0195] Determine whether the maximum number of iterations has been reached. If so, output the optimal sparrow, that is, the optimal penetration track point.

[0196] Step 5: Combine the improved sparrow search algorithm with the UAV low-altitude penetration three-dimensional path planning. The specific method is:

[0197] Each path is a line connected by multiple track points, defining a sparrow x in the population. d i That is, a path, the sparrow with the lowest cost represents the optimal path, and each track point has three-dimensional attributes (x, y, z). When using ALCE-SSA to plan the three-dimensional penetration path of the UAV, the specific steps include:

[0198] Step 5.1: Using the method in step 4.1 to obtain the initial sparrow population on the three-dimensional environment model obtained in step 1;

[0199] Step 5.2: Calculate the fitness of each sparrow in the initial sparrow population using the cost function obtained in step 2, sort the sparrow population according to the fitness, and select the best sparrow;

[0200] Step 5.3: Update the position of the sparrow population using the method in steps 4.2-4.5, calculate the fitness of each sparrow, and sort the sparrow population according to the size of the fitness;

[0201] Step 5.4: Determine whether the maximum number of iterations has been reached. If so, output the optimal sparrow, i.e. the optimal penetration track point. Otherwise, return to step 5.3.

[0202] Step 5.5: Optimize the optimal track points obtained in 5.4 by cubic spline interpolation to obtain the final three-dimensional penetration path of the UAV.

[0203] Figure 3 For the specific path planning diagram in terrain 1, Figure 4 It is a specific path planning map in terrain 2.

[0204] Figure 3 It is composed of mountains, threat sources (circled areas) and paths. By comparing the algorithm ALCE-SSA of the present invention with SSA, GWO and MFO in the trajectory diagram of the UAV penetration route, it can be seen that the planned route of GWO (path with + label) generally has a high flight altitude and does not avoid the threat source; the late optimization ability of GWO is poor, resulting in large errors in some dimensions of the path points; the moth update mechanism in MFO (path with △ label) makes the global optimization ability stronger, and the path planning in the three-dimensional path diagram does avoid the threat source and finds a relatively optimal path, but the path is not smooth enough overall and the flight difficulty is large; the flight altitude in the path planned by SSA (path with ○ label) fluctuates up and down, and the path is not smooth enough; the ALCE-SSA algorithm (without label) of the present invention can effectively avoid the threat source, and is similar to generating a better path along the diagonal of the map, which is smoother and reduces the flight difficulty, and can achieve low-altitude flight and complete the low-altitude penetration target.

[0205] Figure 4 Verified Figure 3 The conclusion drawn is verified. It verifies that the SSA algorithm obtained in model 1 has a fast update speed but is prone to fall into local optimality, the GWO algorithm has poor late optimization ability, resulting in poor accuracy of some path point dimensions, and the MFO algorithm has strong global optimization ability but slow update speed. The algorithm in this paper is superior in update speed and accuracy.

[0206] Finally, it should be noted that the above embodiments are only preferred embodiments of the present invention to illustrate the technical solutions of the present invention, rather than limiting them, and certainly not limiting the patent scope of the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention. In other words, any changes or modifications made to the main design concept and spirit of the present invention that have no substantive significance, and the technical problems they solve are still consistent with the present invention, should be included in the protection scope of the present invention. In addition, the direct or indirect application of the technical solutions of the present invention in other related technical fields is also included in the patent protection scope of the present invention.

Claims

1. A three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization is characterized by: The following steps are involved: Step 1: Model the three-dimensional environment of the UAV low-altitude penetration to obtain a model; Step 2: Determine the penetration cost function for the model obtained in step 1; Step 3: Get the sparrow search algorithm; Step 4: Improve the sparrow search algorithm obtained in step 3 according to the UAV low-altitude penetration to obtain an improved sparrow search algorithm; the specific steps include: Step 4.1: Initialize the sparrow population based on random tent mapping in the three-dimensional environment model obtained in step 1, and each sparrow represents a penetration path; Initialize the sparrow population based on random tent mapping, the formula is as follows: In the formula, i is the population size, i = 1, 2...n; j is the individual dimension, j = 1, 2...d; s is a random number (0, 1), ψ is the chaotic parameter. After taking the initial value of the above formula, n×d chaotic sequences are obtained. Substituting the chaotic sequence into the individual position formula to obtain the individual position of the population, the formula is as follows: x i,j =Lb j +v i,j (Ub j -Lb j ) In the formula, Ub j and Lb j are the upper and lower boundaries of the j-dimensional three-dimensional terrain search space respectively; Step 4.2: Adopt the adaptive leader sparrow guidance strategy to update the position of the discoverer in the sparrow population; the specific formula is: In the formula, represents the best individual in the tth generation in the population, ω is the weight factor, and the update formula is as follows: In the formula, ω max ,ω min are the maximum and minimum values ​​of the weight factor respectively; Step 4.3: Joiner location update; Step 4.4: Update the position of the sentinel; Step 4.5: Update the position of the sparrow population based on the central variation-evolution factor; specifically: In order to speed up the iteration, only the best individuals are selected for central mutation. Let X = [x1, x2, ..., x d ] are d points with unit mass, then a discrete uniform overall center G is: Then a point x in the whole j The central variation point of is defined as: The evolution part is designed based on the principle of the survival of the fittest. The population is sorted by the fitness value and evolves in order. Individuals with good fitness are likely to be retained, while individuals with poor fitness are likely to evolve. The formula is as follows: In the formula, t1 and t2 are random individuals in the sparrow population and are different from each other; x1 is the optimal individual; rand and s are random numbers between 0 and 1; P(i) is the fitness level corresponding to the i-th individual in the population, and the calculation formula is: The calculation formula for generating new solutions through the central mutation-evolution factor is expressed as: In the formula, g1(x) is the central mutation; g2(x) is the evolution; τ is the probability of selecting central mutation or evolution, and the calculation formula is as follows: After using the central mutation-evolution factor to find a new solution, the new population is updated according to the greedy principle; Step 4.6: Calculate the fitness of the sparrow population and select the best sparrow according to the fitness; Step 4.7: Determine whether the maximum number of iterations has been reached. If so, output the optimal sparrow, i.e. the optimal penetration track point. If not, return to step 4.

2. Step 5: Use the improved sparrow search algorithm obtained in step 4 to plan the three-dimensional path of the UAV's low-altitude penetration.

2. The three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization according to claim 1 is characterized in that: In step 1, the three-dimensional environment modeling of the UAV low-altitude penetration includes terrain constraints and threat source model constraints: The mountain modeling in a three-dimensional environment with terrain constraints is as follows: In the formula, (x, y) is the coordinate of the terrain, (x0, y0) is the coordinate of the center point of the mountain terrain, h is the height parameter, and λ1 and λ2 reflect the steepness of the mountain. Threat source model constraints include radar detection, air defense artillery, and surface-to-air missiles; The threat source is equivalent to a terrain model. Assuming that the closer to the center of the threat source, the greater the threat cost, the higher the terrain, and vice versa, the lower the threat cost. Therefore, the threat source is equivalent to: In the formula, K thr is the threat source correction coefficient, and the horizontal coordinate of the center of the pth threat source is (x p ,y p ), the maximum radius R of the pth threat source max,p , R is the distance from the three-dimensional environment coordinate point (x, y) to the center of the threat source.

3. The three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization according to claim 1 is characterized in that: The penetration cost function of step 2 includes: 1) During flight, the altitude of 0.05-2.5km above the ground is suitable for flight. The terrain threat cost of the track point is as follows: In the formula, K Z ,K z ′ is the terrain threat coefficient, h j is the altitude of the jth track point, Z j is the terrain height of the jth track point, f Z,j is the threat cost corresponding to the j-th track point; 2) Low-altitude penetration needs to consider the elevation cost. The elevation cost of track point j is as follows: f H,j =h j In the formula, f H,j is the elevation cost corresponding to the j-th track point; 3) Terrain constraints also need to consider the flight boundary range and maximum flight altitude to ensure the controllability of the drone. The flight level range is set to (x min ,y min )=(0,0) and (x max ,y max )=(100,100), the maximum flight height is z max =5; In the radar area, the simplified radar detection probability model is as follows: P0＝1 / r 4 In the formula, r is the distance from the track point to the center of the threat source; In the anti-aircraft artillery zone, the probability of damage is expressed as: P G ＝1 / r The probability of being hit within the missile zone radius is: In the formula, R max is the maximum radius of the threat source; The restrictions in the no-fly zone are: P J =K J In the formula, K J is the threat cost of the no-fly zone, P J The cost of restraint in no-fly zones; The calculation cost of each track point in each threat area is defined as follows: In the formula, r j,p is the straight-line distance from the jth track point to the center of the threat source p, P0, P G , P M and P J are the cost functions of radar, artillery, missile, and no-fly zone, respectively, T,jp is the cost from track point j to the center of threat source p; 4) UAV constraints are the physical constraints imposed on the UAV during flight, including turning angle α, descent and climb angle β, and fuel cost. The physical constraints are: In the formula, K α and K β are the threat factors of turning angle and pitch angle respectively, J α_angle,j and J β_angle,j is the cost function of α and β corresponding to the jth track point, J L,j is the flight distance corresponding to the j-th track point. Combining various cost functions, the UAV self-constraint cost function of the j-th track point is obtained as follows: f J,j =J α_angle,j +J β_angle,j +J L,j 5) The track cost function is a weighted combination of terrain constraints, elevation costs, threat source model constraints, and the costs of the UAV's own physical constraints to form the final UAV cost function. The formula is as follows: Where F is the cost of the entire track, σ1, σ2, σ3 and σ4 are the weights of each cost, d is the total number of track points, and w is the total number of threat sources.

4. The three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization according to claim 1 is characterized in that: The sparrow search algorithm in step 3 includes the following steps: Step 3.1: Randomly initialize the sparrow population; Step 3.2: Finder location update; Step 3.3: Joiner location update; Step 3.4: Sentinel position update.

5. The three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization according to claim 4 is characterized in that: In step 3.2, the finder in the sparrow population is responsible for foraging and guiding the movement of the entire population. The finder position is updated as follows: In the formula, represents the j-th position of the ith individual in the tth generation in the population, ζ is a uniform random number in (0,1], Q is a standard normal distribution random number, L is a multi-dimensional all-one matrix with one row, R2 is a uniform random number in [0,1], and ST is the warning threshold; In step 3.3, the joiners are the individuals in the population except the discoverer, and the position update formula of the joiners is as follows: In the formula, is the best position occupied by the discoverer of the tth generation population, represents the current global worst position, A is a 1×d matrix containing only 1 or -1 elements, and the matrix operation A is defined + The calculation method is as follows: A + =A T (CHALLENGE ACCEPTED T ) -1 In step 3.4, 20% of the individuals in the sparrow population are randomly selected as sentinels. The sentinel update formula is as follows: In the formula, represents the current global optimal position, δ is the step size control parameter that conforms to the normal distribution, with a mean of 0 and a variance of 1, and k is a random number in the range of [-1,1]; f i Indicates the fitness of the sparrow’s current position; f g With f w are the global optimal and worst fitness respectively; ε is the minimum value that is not zero.

6. The three-dimensional UAV low-altitude penetration method based on ALCE-SSA optimization according to claim 1 is characterized in that: In step 5, the improved sparrow search algorithm is used to plan the three-dimensional path of the UAV low-altitude penetration. The specific method is as follows: Each path is a line connected by multiple track points, defining a sparrow x in the population. d i That is, a path. The sparrow with the lowest cost represents the optimal path. Each track point has three-dimensional attributes (x, y, z). When using ALCE-SSA to plan the three-dimensional penetration path of the UAV, the specific steps include: Step 5.1: Using the method in step 4.1 to obtain the initial sparrow population on the three-dimensional environment model obtained in step 1; Step 5.2: Calculate the fitness of each sparrow in the initial sparrow population using the cost function obtained in step 2, sort the sparrow population according to the fitness, and select the best sparrow; Step 5.3: Update the position of the sparrow population using the method in steps 4.2-4.5, calculate the fitness of each sparrow, and sort the sparrow population according to the size of the fitness; Step 5.4: Determine whether the maximum number of iterations has been reached. If so, output the optimal sparrow, i.e. the optimal penetration track point. Otherwise, return to step 5.

3. Step 5.5: Optimize the optimal track points obtained in 5.4 by cubic spline interpolation to obtain the final three-dimensional penetration path of the UAV.

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