Unmanned aerial vehicle path planning method and system based on enhanced multi-strategy whale migration optimization

Abstract

The application discloses an enhanced multi-strategy whale migration optimization UAV path planning method and system, and belongs to the technical field of civil path planning. The method comprises the following steps: constructing a three-dimensional path planning model of a mountainous environment; establishing a comprehensive objective function, wherein a highly relevant dynamic threat range model is adopted for threat cost, a flight height is adopted for dynamic adjustment of a threat source influence radius, and a flight stage is adopted for adaptive adjustment of weight coefficients of each cost item; S3 adopts an initialization strategy based on a good point set theory to generate an initial candidate path, and adopts a golden section ratio to generate an initial population with uniform distribution; S4 adopts an enhanced multi-strategy whale migration optimization algorithm for iterative optimization, calculates a population diversity index D(t), and adaptively selects a Lévy flight strategy or a Cauchy distribution disturbance strategy according to comparison between D(t) and a preset threshold value and a current iteration number; and S5 judges a termination condition and outputs an optimal path. The application improves the safety and efficiency of path planning.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of civil route planning, and particularly relates to an enhanced multi-strategy whale migration optimization UAV route planning method and system. BACKGROUND

[0002] UAV mountain route planning is a key technology for improving its autonomous operation capability, aiming to plan a safe and efficient flyable path under complex three-dimensional terrain and threat constraints. Intelligent optimization algorithms, such as particle swarm optimization and grey wolf optimization, are widely used because they are good at handling such nonlinear problems.

[0003] Whale optimization algorithm is a new meta-heuristic algorithm that simulates the social behavior of whales. The standard version and some preliminary improved algorithms have shown good performance in solving ordinary optimization problems. However, when applied to this specific scenario of complex mountain route planning, the existing technology has obvious shortcomings. First, the traditional initialization method leads to poor population diversity, making it difficult to fully perceive the complex solution space. Second, the algorithm lacks the ability to balance global exploration and local development during the search process, especially when facing multi-peak and discontinuous cost functions caused by terrain, it is easy to fall into local optimum, and the convergence speed is difficult to meet the real-time planning requirements. In addition, the existing methods also have shortcomings in threat modeling and target function weight configuration. On the one hand, the traditional fixed threat radius model cannot truly reflect the impact of flight height on threat range, leading to inaccurate safety margin evaluation. On the other hand, fixed weight configuration cannot adapt to the differentiated needs of different flight stages such as take-off, cruising, and threat avoidance, making it difficult to balance safety and economy in the planning results.

[0004] Therefore, there is an urgent need for a new route planning method that can specifically address the above bottleneck problems. SUMMARY

[0005] To solve the technical problems of existing technology that easily falls into local optimum and has low convergence accuracy in mountain route planning, the present application provides an enhanced multi-strategy whale migration optimization UAV route planning method and system. The present application constructs a multi-stage collaborative optimization framework combining high-quality initialization, intelligent global exploration and reinforced local development, and through the organic integration of good point set strategy, Lévy flight strategy and Cauchy distribution disturbance strategy, it produces a synergistic effect, thereby significantly improving the comprehensive performance of the algorithm in complex environments.

[0006] To achieve the above purpose, the present application adopts the following key technical solutions:

[0007] In a first aspect, the present application provides an enhanced multi-strategy whale migration optimization UAV route planning method, comprising the following steps:

[0008] S1: Construct a three-dimensional flight path planning model for the mountainous environment, acquire terrain elevation data, and set the starting point, ending point, and multiple flight path points for the UAV;

[0009] S2: Establish a comprehensive objective function, which is a weighted sum of track length cost, altitude cost, smoothness cost, and threat cost, wherein:

[0010] The threat cost is described using a highly correlated dynamic threat range model, where the influence radius of the threat source is dynamically adjusted based on the flight altitude of the waypoint.

[0011] The weighting coefficients of the trajectory length cost, altitude cost, smoothness cost, and threat cost are adaptively adjusted according to the flight phase, with different weighting configurations used for different flight phases;

[0012] S3: N initial candidate tracks are generated using an initialization strategy based on the optimal point set theory, where the optimal point set theory uses the golden ratio to generate a uniformly distributed initial population.

[0013] S4: An enhanced multi-strategy whale migration optimization algorithm is used to iteratively optimize candidate routes, including:

[0014] Calculate the diversity index of the current population The diversity index characterizes the degree of dispersion of candidate tracks in a population;

[0015] According to the diversity index With preset threshold The comparison, and the current iteration number. With maximum number of iterations Relationship, adaptive selection of search strategy:

[0016] when and At that time, the Lévy flight strategy was adopted;

[0017] when or At that time, the Cauchy distribution perturbation strategy is adopted;

[0018] Calculate the fitness value of each candidate track after the update;

[0019] Update the current best candidate track;

[0020] S5: Determine if the termination condition is met. If it is, output the optimal trajectory. If not, continue iterative optimization.

[0021] As a further embodiment of the planning method of the present invention, the formula for calculating the dynamic influence radius of the threat source is:

[0022] ,

[0023] wherein:

[0024] is the basic threat radius of the th threat source;

[0025] is the flight altitude of the th waypoint;

[0026] and are the minimum and maximum altitudes of the planning space, respectively;

[0027] is the altitude impact factor, with a value range of 0.1-0.3;

[0028] The calculation formula of the threat cost is:

[0029] ,

[0030] wherein, is the total number of waypoints, is the total number of threat sources, is the shortest distance from the th waypoint to the boundary of the th threat source.

[0031] As a further scheme of the planning method of the present application, the division of the flight phases and the adaptive adjustment rule of the weight coefficients are as follows:

[0032] Take-off or landing phase: the flight segment from the starting point to the point where the flight altitude reaches a 30% altitude increment of the preset cruising altitude, or the flight segment from the point where the flight altitude starts to be lower than a 30% altitude increment of the preset cruising altitude to the ending point, which is assigned a height cost weight .

[0033] Cruising phase: other flight segments except the take-off or landing phase and the threat area phase, which is assigned a waypoint length cost weight and a smoothness cost weight .

[0034] Threat area crossing phase: the flight segment where the distance between a waypoint and the boundary of any threat source is less than 1.5 times the basic radius of the threat source, which is assigned a threat cost weight .

[0035] As a further scheme of the planning method of the present application, in step S3, the generation formula of the initialization strategy based on the optimal point set theory is as follows:

[0036] ,

[0037] wherein:

[0038] is the individual index, ;

[0039] is the dimension index, ;

[0040] is the golden section ratio, ;

[0041] and are the upper and lower bounds of the jth dimension search space, respectively;

[0042] denotes the fractional part of the extraction .

[0043] As a further scheme of the planning method of the present application, in step S4, the calculation formula of the diversity index D(t) is:

[0044] ,

[0045] wherein:

[0046] is the population size of the candidate track;

[0047] is the position vector of the ith candidate track at the tth iteration;

[0048] is the center position of the population at the tth iteration;

[0049] denotes the Euclidean distance norm.

[0050] As a further scheme of the planning method of the present application, the candidate track position update formula of the Lévy flight strategy is:

[0051] ,

[0052] wherein is the average position of the high-quality individuals in the population, is the current optimal candidate track position, is a random vector in the interval [0, 1], denotes the Hadamard product, is the Lévy flight step length;

[0053] The candidate track position update formula of the Cauchy distribution disturbance strategy is:

[0054] ,

[0055] wherein is a uniformly distributed random vector, is the inverse cumulative distribution function of the Cauchy distribution.

[0056] As a further scheme of the planning method of the present application, the complete expression of the comprehensive objective function is:

[0057] ,

[0058] wherein:

[0059] is the length cost of the flight path, calculated as the sum of the distances between adjacent flight path points;

[0060] is the height cost, calculated as the standard deviation of the flight height of each flight path point from the mean;

[0061] is the smoothness cost, calculated as the sum of the absolute values of the changes in the heading angle of adjacent flight segments;

[0062] is the threat cost;

[0063] is the weight coefficient of each cost term, which is adaptively adjusted according to the flight phase, and the specific adjustment rules are:

[0064] Takeoff or landing phase: give the height cost a weight ;

[0065] Cruise phase: give the length cost of the flight path a weight , and the smoothness cost a weight ;

[0066] Threat zone crossing phase: give the threat cost a weight .

[0067] In a second aspect, the present application provides an enhanced multi-strategy whale migration optimization UAV flight path planning system, which comprises the following modules:

[0068] a processor and a memory, the memory storing a computer program, and the processor implementing the functions of the following modules when executing the computer program:

[0069] an environment modeling module for constructing a three-dimensional flight path planning model of a mountainous environment;

[0070] A target function construction module is configured to establish a comprehensive target function, wherein a threat cost adopts a highly relevant dynamic threat range model, and each cost term weight coefficient is adaptively adjusted according to a flight phase;

[0071] A good point set initialization module is configured to generate an initial candidate track population by using an initialization strategy based on a good point set theory;

[0072] An enhanced multi-strategy optimization module is configured to:

[0073] Calculate a population diversity index D(t);

[0074] According to a comparison of the diversity index D(t) with a preset threshold value and a relationship between a current iteration number and a maximum iteration number, a search strategy is adaptively selected; wherein: When D(t) < D(threshold value), the current iteration number is less than the maximum iteration number, and the search strategy is a Lévy flight strategy; When D(t) > D(threshold value) or the current iteration number is equal to the maximum iteration number, the search strategy is a Cauchy distribution disturbance strategy;

[0075] When D(t) < D(threshold value), the current iteration number is less than the maximum iteration number, and the search strategy is a Lévy flight strategy; When D(t) > D(threshold value) or the current iteration number is equal to the maximum iteration number, the search strategy is a Cauchy distribution disturbance strategy;

[0076] Iteratively update a candidate track and record an optimal solution; An iteration update module is configured to iteratively update a candidate track and record an optimal solution;

[0077] A judgment output module is configured to judge whether a termination condition is met and output an optimal track.

[0078] The present application has the following beneficial effects:

[0079] 1、The present application organically integrates good point set initialization, a Lévy flight strategy and a Cauchy distribution disturbance strategy to construct a synergistically enhanced optimization framework. The good point set provides a high-diversity initial population for optimization and avoids premature algorithm; the Lévy flight enhances global search capability by long-step jumping in the exploration stage and quickly locates a potential optimal area; the Cauchy disturbance effectively disturbs the current optimal solution by using its heavy-tailed characteristics to make it jump out of a local optimal trap. The synergistic effect of the three makes the algorithm have stronger global optimization capability and higher convergence accuracy in a multi-peak, nonlinear cost function caused by a complex mountainous environment.

[0080] 1、The present application organically integrates good point set initialization, a Lévy flight strategy and a Cauchy distribution disturbance strategy to construct a synergistically enhanced optimization framework. The good point set provides a high-diversity initial population for optimization and avoids premature algorithm; the Lévy flight enhances global search capability by long-step jumping in the exploration stage and quickly locates a potential optimal area; the Cauchy disturbance effectively disturbs the current optimal solution by using its heavy-tailed characteristics to make it jump out of a local optimal trap. The synergistic effect of the three makes the algorithm have stronger global optimization capability and higher convergence accuracy in a multi-peak, nonlinear cost function caused by a complex mountainous environment.

[0081] ​​​​2、The application introduces a dynamic threat radius model and a stage-adaptive weight coefficient adjustment mechanism in the objective function. The dynamic threat radius makes the threat cost more realistically reflect the influence of height change on security; the adaptive weight allows the algorithm to intelligently adjust the priority of each cost in different flight stages, and the joint improvement of the two improves the final planned flight path not only mathematically optimal, but also more in line with the actual flight task requirements, significantly improving the safety and task reliability of the unmanned aerial vehicle flight in complex mountainous environments.

[0082] 3、Compared with the standard whale optimization algorithm and other traditional improved algorithms, the good point set initialization adopted by the application avoids the blind distribution of the initial population in the solution space, laying a good foundation for rapid convergence. Meanwhile, the application innovatively introduces a diversity index-driven adaptive strategy switching mechanism, intelligently selects the global exploration or local development strategy by monitoring the population diversity index D(t) in real time and combining the iteration process. Compared with the traditional fixed iteration number switching method, the mechanism can dynamically adjust the search strategy according to the actual optimization state; compared with the complex fuzzy logic controller, the parameter setting is extremely simple, only a threshold coefficient p is needed, and the calculation efficiency is high and the generalization ability is strong. This adaptive mechanism ensures that the algorithm can maintain high search performance and stable convergence characteristics in different complexity problems.

[0083] Synergistic effect description:

[0084] The application constructs a synergistic optimization framework by organically integrating the good point set initialization, Lévy flight strategy and Cauchy distribution disturbance strategy. The specific synergistic mechanism is as follows:

[0085] The good point set initialization provides a high-diversity initial population for optimization, avoids premature convergence, and provides a good search starting point for subsequent strategies;

[0086] The Lévy flight strategy enhances the global search ability through long-step jumping in the exploration stage, quickly locates the potential optimal area, and forms a wide coverage and deep exploration synergy with the good point set;

[0087] The Cauchy disturbance strategy utilizes its heavy-tailed characteristics to effectively disturb the current optimal solution in the development stage, so that it can jump out of the local optimal trap and form a complement of global exploration and local jumping with Lévy flight;

[0088] The diversity index-driven adaptive switching mechanism intelligently selects the strategy by monitoring the population state in real time, so that the three strategies dynamically synergize in the iteration process, thereby showing stronger global optimization ability and higher convergence accuracy in the multi-peak, nonlinear cost function brought by the complex mountainous environment. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1A flowchart of the enhanced multi-strategy whale migration optimization UAV path planning method proposed in the present application is shown in the figure.

[0090] Figure 2 An algorithm flowchart of the enhanced multi-strategy whale migration optimization UAV path planning method proposed in the present application is shown in the figure.

[0091] Figure 3 A UAV path planning comparison diagram of the enhanced multi-strategy whale migration optimization UAV path planning method proposed in the present application is shown in the figure.

[0092] Figure 4 A target function convergence result comparison diagram of the enhanced multi-strategy whale migration optimization UAV path planning method proposed in the present application is shown in the figure. DETAILED DESCRIPTION

[0093] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0094] Embodiment one:

[0095] In the first embodiment of the present application, the present application provides an enhanced multi-strategy whale migration optimization UAV path planning method, as shown in the figure, comprising the following steps: Figures 1-4

[0096] A three-dimensional path planning model of a complex mountainous environment is constructed, and the starting point, end point and path point parameters of the UAV are set.

[0097] Further, the construction process of the three-dimensional path planning model includes:

[0098] Obtain the geographic elevation data of the target area;

[0099] Based on the geographic elevation data, a three-dimensional geographic model for representing the ups and downs of the mountain, the changes of the slope and the terrain obstacles is constructed by using an elevation matrix;

[0100] The starting point and the end point of the UAV are set in the three-dimensional geographic model;

[0101] N path points are set between the starting point and the end point to generate a three-dimensional path planning model.

[0102] ​Specifically, first, the geographical elevation data of the target mountainous area is obtained, which can be obtained from a digital elevation model (DEM) database or by airborne radar, laser radar and other surveying and mapping means. Based on the geographical elevation data, a three-dimensional geographical model is constructed in the spatial coordinate system using the elevation matrix. This model can accurately represent the ups and downs, slope changes and terrain obstacles of the mountainous environment, providing accurate spatial reference for the UAV. The three-dimensional geographical model can be represented as:

[0103] ,

[0104] wherein the variables and represent the coordinate components on the horizontal projection plane in the geographical environment model, represents the elevation value of the corresponding projection point, and the three variables , and correspond to the maximum boundary values of the terrain in the spatial three-dimensional direction;

[0105] Then, the task parameters of the UAV are set in the three-dimensional geographical model, and the starting point and the ending point of the UAV are defined. These two points define the fixed endpoints of the flight path, wherein the starting point and the ending point of the UAV are and ;

[0106] Finally, N flight points are set between the starting point and the ending point. These flight points together with the starting and ending points form the skeleton of the UAV flight path, forming a complete flight path to be optimized. Thus, the three-dimensional flight path planning model integrating the terrain environment (three-dimensional geographical model) and the flight task (starting and ending points, flight points) is constructed, providing a clear object and spatial constraint for subsequent flight path optimization.

[0107] According to the dynamic constraints and task requirements of the UAV, a comprehensive objective function is established, which integrates the flight path length cost, height cost, smoothness cost and threat cost.

[0108] Further, the establishment process of the comprehensive objective function includes:

[0109] A flight path length cost function is constructed to measure the rationality and feasibility of the flight path;

[0110] A height cost function is constructed to improve terrain fitting and avoid collision risks;

[0111] A smoothness cost function is constructed to ensure that the flight path planning meets the performance constraints of the UAV itself;

[0112] A safety threat cost function is constructed to achieve effective obstacle avoidance;

[0113] The trajectory length cost function, altitude cost function, smoothness cost function, and threat cost function are weighted and fused together, and a penalty coefficient is introduced to construct a comprehensive objective function.

[0114] Specifically, a trajectory length cost function is first constructed to measure the rationality and feasibility of a flight path. Given that the UAV is limited by the capacity of its fuel tank or battery and its weight during mission execution, it needs to complete the mission efficiently while meeting the maximum range constraint. This cost function aims to plan a trajectory with a shorter total length, and its mathematical expression is as follows:

[0115] ,

[0116] Where n represents the total number of waypoints. This represents the total number of additional, evenly distributed waypoints between two adjacent waypoints. Indicates the first The first waypoint and the first +1 Euclidean distance between waypoints;

[0117] Next, an altitude cost function is constructed to improve terrain fit and avoid collision risks. To better adapt to complex mountainous environments, UAVs should fly at the lowest possible altitude to improve terrain fit and inspection accuracy; however, excessively low flight altitudes increase the risk of collisions. This function aims to maintain a reasonable and stable flight altitude, and its mathematical expression is as follows:

[0118] ,

[0119] in, Indicates the first The flight altitude of each waypoint;

[0120] Then, a smoothness cost function is constructed to ensure that the trajectory planning conforms to the performance constraints of the UAV itself. Due to the performance constraints of the UAV, its turning and climbing angles are limited. This function ensures the feasibility of the trajectory by penalizing excessive yaw angles. Its mathematical expression is as follows:

[0121] ,

[0122] in, For the first The deflection angle of each waypoint ;

[0123] Next, a safety threat cost function is constructed to achieve effective obstacle avoidance. During the trajectory planning process, not only the influence of terrain but also threat sources such as no-fly zones need to be considered. This function aims to improve the safety of UAV trajectory planning, and its mathematical expression is as follows:

[0124] ,

[0125] where n represents the total number of track points, m represents the total number of additional evenly distributed track points between two track points, represents the total number of threat sources, represents the radius of the threat source, and respectively represent the mapping points of the i th track point and the i+1 th track point, represents the center of the i+1 th threat source, when the minimum distance on the line segment from to is greater than , it is considered as successful obstacle avoidance, otherwise it is determined that the obstacle is crossed;

[0126] In this embodiment, the threat cost function is optimized, and a highly relevant dynamic threat range model is adopted. Specifically, the fixed threat radius is replaced by which dynamically changes with the height of the track point, and the calculation formula is as follows:

[0127] ,

[0128] wherein:

[0129] is the basic threat radius of the i th threat source;

[0130] is the flight height of the i th track point; and

[0131] are the minimum and maximum heights of the planning space, and in this embodiment , ; ;

[0132] is the height influence factor, the value range is 0.1-0.3, and in this embodiment =0.2.

[0133] The physical meaning of this dynamic threat model is that in mountainous environment, the detection distance of threat sources such as ground radar is significantly affected by flight height. When flying at low altitude, the terrain obstruction reduces the threat range; when flying at high altitude, the clear line of sight leads to an increase in the threat range. The dynamic threat model truly reflects this physical law, and compared with the fixed radius model, the threat assessment accuracy is improved and the safety margin is increased.

[0134] The modified threat cost function is:

[0135] ,

[0136] wherein is the shortest distance from the i-th waypoint to the j-th threat source boundary.

[0137] Meanwhile, the weight coefficient in the comprehensive objective function is implemented by the flight phase adaptive adjustment strategy, specifically:

[0138] (1) Take-off or landing phase: the flight segment from the starting point to the flight height reaching , or the flight segment from the flight height below to the end point. This phase is to ensure safety, and a higher weight is given to the height cost θ, and the weight configuration is: , , , .

[0139] (2) Cruise phase: other flight segments except the take-off / landing phase and the threat area phase. This phase is to optimize economy and flight efficiency, and a higher weight is given to the waypoint length cost σ and the smoothness cost ω, and the weight configuration is: , , , .

[0140] (3) Crossing threat area phase: the flight segment in which the distance between the waypoint and any threat source boundary is less than 1.5 times the threat source basic radius . This phase is to prioritize obstacle avoidance, and the highest weight is given to the threat cost ϕ, and the weight configuration is: , , , .

[0141] In this embodiment, the starting point height , the end point height , and the cruising height .

[0142] To comprehensively measure the optimization effect of the flight path planning in terms of length, height, safety, and smoothness, the flight path length cost, the height cost, the smoothness cost, and the threat cost are weighted and fused in this paper to construct the comprehensive cost function of the UAV global flight path, and the mathematical formula is:

[0143] ,

[0144] wherein, , and ,​​ This represents the penalty coefficient.

[0145] The population position of the whale optimization algorithm is initialized using the best point set strategy, and the population fitness is calculated to generate an initial feasible solution for the trajectory.

[0146] Furthermore, the process for generating the initial feasible solution includes:

[0147] Set the number of individuals and the maximum number of iterations for the whale population;

[0148] Using the optimal point set strategy, the initial positions of a uniformly distributed whale population are generated within the search space defined by the upper and lower bounds of the population.

[0149] Decode the location information of each individual whale into a complete three-dimensional track;

[0150] Substitute each decoded 3D track into the comprehensive objective function to calculate its corresponding fitness value;

[0151] Compare the fitness values ​​of all individuals and record the position of the individual with the best fitness. Use the trajectory corresponding to that position as the initial feasible solution for the trajectory.

[0152] Specifically, first, initialize the basic parameters of the algorithm, setting the number of individuals in the whale population to N, and the maximum number of iterations to... Next, the population positions are initialized using the optimal point set strategy. This strategy can generate more evenly distributed initial solutions in the search space, thereby effectively avoiding the problem of over-clustering or over-dispersion of the population in the initial stage and enhancing the algorithm's ability to cover the solution space. The optimal point set strategy is used for population initialization, and its mathematical expression is as follows:

[0153] ,

[0154] in:

[0155] Indicate extraction The decimal part;

[0156] The golden ratio, ;

[0157] Indicates the first The first individual whale in the... The actual position of the dimension;

[0158] and They represent the first The upper and lower bounds of a dimension;

[0159] For population size, For search space dimensions ( ).

[0160] The optimal point set strategy utilizes the golden ratio from number theory to generate uniformly distributed initial positions, which can significantly improve the quality of initial solutions and the proportion of feasible solutions compared to random initialization.

[0161] The location information of each individual whale is decoded into a complete 3D track. The position of the i-th whale in the search space is... ,in Let represent the coordinates of the i-th individual whale at the n-th track point. Substitute the whale population location information into the formula of the objective function. The first third are used as the position points on the x-axis, the middle third as the position information on the y-axis, and the last third as the position information on the z-axis. Connect the starting point and the track point to form a complete track line.

[0162] Next, the population fitness is calculated. Each 3D track obtained from the above decoding steps is substituted into the comprehensive objective function established according to the aforementioned method to calculate its corresponding function value. This value is the fitness value of each whale individual's position. Finally, an initial feasible solution is generated. The fitness values ​​of all N individuals in the population are compared, and the individual with the best fitness value is found and its position is recorded. The 3D track corresponding to the position of the best individual is used as the initial feasible solution for this track planning, providing a starting point for the subsequent iterative optimization process.

[0163] An enhanced multi-strategy whale migration optimization algorithm is used to iteratively optimize the initial feasible solution to update the feasible solution of the trajectory. In the exploration and development phases of the algorithm, the Lévy flight strategy and the Cauchy distribution inverse accumulation strategy are introduced to update the position of individual whales.

[0164] In this embodiment, a diversity index-driven adaptive strategy switching mechanism is used as the judgment condition for the algorithm to enter the development stage from the exploration stage.

[0165] The specific steps are as follows:

[0166] (1) Calculate the diversity index of the current population. :

[0167] ,

[0168] in:

[0169] Population size (in this embodiment) );

[0170] For the first The candidate track in the first Position vector at the next iteration;

[0171] The population center position is calculated as ,

[0172] Euclidean distance norm is denoted as

[0173] (2) Calculate the diversity threshold

[0174] ,

[0175] wherein is a threshold coefficient, and the value range is 0.05-0.15, and the value in the embodiment is ; is the search space dimension.

[0176] (3) According to the diversity index, the search strategy is adaptively selected:

[0177] When and , the Lévy flight strategy is used for global exploration;

[0178] When or , the Cauchy distribution disturbance strategy is used for local development.

[0179] In the embodiment, the maximum iteration number , and after about 80 iterations, the value is reduced below the threshold value, and the algorithm is automatically switched to the local development stage.

[0180] Compared with the fixed iteration number switching, the diversity index mechanism can effectively improve the convergence speed, and the parameter setting is simple, and only one parameter needs to be set.

[0181] Further, the updating process of the feasible solution of the track includes:

[0182] In the exploration stage of the algorithm, the position of the whale individual is updated according to the average position of the experienced individuals in the current population and the Lévy flight strategy;

[0183] When the iteration number is greater than half of the total iteration number, the algorithm enters the development stage;

[0184] In the development stage of the algorithm, the position of the whale individual is updated according to the optimal position of the current iteration number and the Cauchy distribution inverse cumulative strategy;

[0185] ​After each position update, the new whale individual position is re-decoded into a three-dimensional track and its fitness value is calculated;

[0186] The optimal individual position in the current population is updated according to the fitness value, thereby completing an iterative update of the feasible solution of the track.

[0187] Further, the output of the optimal track and the initial feasible solution continue the iterative optimization process, which includes:

[0188] After each iteration of updating the feasible solution of the track, it is determined whether the current iteration number has reached the preset maximum iteration number;

[0189] If the current iteration number has reached the maximum iteration number, the iteration process is terminated, and the current recorded optimal whale individual position is decoded into the final three-dimensional track as the output of the optimal track;

[0190] If the current iteration number has not reached the maximum iteration number, return to execute the iterative optimization step to continue the next iteration update.

[0191] Specifically, according to the above planning, a three-dimensional track planning model of the unmanned aerial vehicle is constructed in the complex mountain environment, the starting point, the termination point and the track point of the unmanned aerial vehicle are set as parameter information, and the whale population position is initialized according to the best point set strategy. This strategy can generate more uniform initial solutions in the search space, thereby effectively avoiding the problem of over-concentration or over-dispersion of the population in the initial stage, and enhancing the coverage ability of the algorithm to the solution space. Its mathematical expression is:

[0192] ,

[0193] wherein, represents the decimal part of , is the golden section ratio, is the optimal irrational number proved in number theory, which ensures that the generated sequence has the best uniformity and no periodicity;

[0194] In the exploration stage, the Lévy flight strategy is introduced. Compared with the standard random walk, the Lévy flight can jump out of the local optimum through some large step jumps, and enhance the global search ability. The random step length in the Lévy flight strategy obeys the Lévy distribution of The position update formula is:

[0195] ,

[0196] wherein, represents the average position information of experienced individuals in the whale population, represents the number of random generations between , and This represents the positions of the (i-1)th and ith whale individuals. This indicates the optimal position for the current iteration. This represents the Lévy flight strategy, and its mathematical expression is:

[0197] ,

[0198] in, and It means that in A number randomly generated within the range. =1.5, It is a gamma function;

[0199] The definition of a high-quality individual is: the population is sorted in ascending order of fitness value, and the top [number] individuals are selected. Each individual is considered a high-quality individual (in this embodiment) ).

[0200] The calculation formula is: ,

[0201] in The first one, sorted in ascending order of fitness value Individual location.

[0202] Lévy flight combines long-step jumps with short-step local searches, enabling it to escape local optima and enhance global search capabilities. The Lévy exponent β ranges from 1.3 to 1.7; in this embodiment, β = 1.5 is used.

[0203] When the number of iterations exceeds half of the total number of iterations, a development phase is initiated. During this phase, a Cauchy distribution inverse accumulation strategy is introduced to leverage the heavy-tailed nature of the Cauchy distribution to generate a larger perturbation step size, enhancing global search capabilities and thus improving the algorithm's search performance. This Cauchy distribution-based perturbation strategy employs the inverse accumulation function of the standard Cauchy distribution. Generate the perturbation step size. The position update formula is as follows:

[0204] ,

[0205] in:

[0206] For the first Current position of each candidate track;

[0207] for Random numbers within a range;

[0208] For interval of uniformly distributed random variable;

[0209] denotes Hadamard product (element-wise multiplication);

[0210] is the inverse cumulative distribution function of the Cauchy distribution:

[0211] ,

[0212] where:

[0213] is a location parameter that defines the position of the peak of the distribution;

[0214] is a scale parameter that defines the half-width at half-maximum;

[0215] When , it is called the standard Cauchy distribution (the standard Cauchy distribution is used in this embodiment);

[0216] is a uniformly distributed random number in the interval [0,1].

[0217] The Cauchy distribution has a fat-tailed property and has a certain ability to jump out while maintaining local search, and is suitable for the local development stage.

[0218] After each position update, the new whale individual position is decoded into a three-dimensional track according to the mapping rule described above, and then the track is substituted into the comprehensive objective function to calculate its fitness value. The fitness values of all individuals are compared, and if the fitness value of a new position is better than the fitness value of the current optimal solution, the position is updated, thereby completing an iterative update of the feasible solution of the track.

[0219] Determine whether the iteration process meets the termination condition. If it meets the termination condition, output the optimal track. If it does not meet the termination condition, continue to iteratively optimize the initial feasible solution.

[0220] Further, after outputting the optimal track, the following steps are further included:

[0221] According to the track point coordinates of the optimal track, an optimal flight track of the unmanned aerial vehicle is constructed and generated in the three-dimensional geographic model;

[0222] The optimal flight track and the three-dimensional geographic model are plotted together into a track planning result map through a visualization tool.

[0223] Specifically, after each population position update and fitness evaluation is completed, it is determined whether the current iteration number has reached the preset maximum iteration number. If the termination condition is met, the iteration optimization process is terminated, at this time, the optimal whale individual position recorded by the algorithm is the global optimal solution, the position vector is decoded, and the decoding rule is consistent with the rule adopted in the initialization and iteration process. Specifically, the first third component is used as the X-axis coordinate of the track point, the middle third component is used as the Y-axis coordinate, and the last third component is used as the Z-axis coordinate. The track points obtained by decoding are connected in order, and a three-dimensional geographic model is constructed to generate the final optimal flight path of the unmanned aerial vehicle. If the termination condition is not met, the previous iteration optimization step is returned to continue the next iteration to find a better feasible solution.

[0224] After outputting the optimal flight path, in order to intuitively display and verify the planning result, the optimal flight path is drawn together with the three-dimensional geographic model into a flight path planning result graph by a visualization tool. In specific implementation, scientific computing and visualization tools such as MATLAB, Python Matplotlib library, etc. can be called. In a three-dimensional graphical interface, a three-dimensional geographic model based on the elevation matrix is first drawn for real terrain display, and then the optimal flight path generated in the above step is superimposed on the three-dimensional terrain model. The flight path is drawn in a prominent color (such as red) and line type (such as solid line) to distinguish from the background terrain. At the same time, the starting point and the ending point of the flight path are clearly marked in the graph. The finally generated flight path planning result graph can clearly show the safe and efficient three-dimensional flight path planned by the unmanned aerial vehicle in the complex mountainous environment, facilitating engineers to analyze and make decisions.

[0225] Embodiment two:

[0226] At present, the unmanned aerial vehicle flight path planning algorithm in the complex mountainous environment mainly includes two categories: one is the traditional optimization algorithm represented by the grey wolf algorithm and the scarab beetle algorithm, and the other is the intelligent optimization algorithm represented by the particle swarm algorithm and the giant lemur algorithm. Intelligent optimization algorithms are widely used in the field of flight path planning due to their flexible parameter setting and fast convergence speed. Whale migration optimization algorithm is a meta-heuristic optimization algorithm simulating the migration behavior of whales. This algorithm can balance the development and exploration stages in the optimization process and effectively prevent premature convergence of the algorithm. However, in the case of dense obstacles or complex terrain, the algorithm is prone to local optimum and difficult to ensure that the unmanned aerial vehicle reaches the specified target area stably, safely and quickly in the complex mountainous environment. To solve the above problems, the present application provides an enhanced multi-strategy whale migration optimization unmanned aerial vehicle flight path planning system, as shown in the structure of Figures 1-4 The specific implementation process of the system is as follows:

[0227] The system comprises a processor and a memory, the memory stores a computer program, and the processor implements the functions of the following modules when executing the computer program:

[0228] An environment modeling module is configured to construct a three-dimensional path planning model of a complex mountainous environment, and set a starting point, an ending point and path point parameters of the UAV.

[0229] A target function construction module is configured to establish a comprehensive target function integrating path length cost, height cost, smoothness cost and threat cost according to the dynamic constraints and task requirements of the UAV.

[0230] An initialization module is configured to initialize the population position of the whale optimization algorithm by using the best point set strategy, and calculate the population fitness to generate an initial feasible solution of the path.

[0231] An optimization solving module is configured to iteratively optimize the initial feasible solution by using the enhanced multi-strategy whale migration optimization algorithm to update the path feasible solution, and introduce a Lévy flight strategy and a perturbation strategy based on Cauchy distribution in the exploration stage and the development stage of the algorithm respectively to update the position of the whale individuals.

[0232] A judgment and output module is configured to judge whether the iteration process meets the termination condition, if yes, output the optimal path, and if not, continue to iteratively optimize the initial feasible solution.

[0233] Specifically, first, the environment modeling module constructs a three-dimensional path planning model containing terrain undulations, slope changes and obstacles, and sets the starting point, ending point and path point parameters of the UAV, thereby providing a spatial framework and input conditions for the planning task. On this basis, the target function construction module establishes a comprehensive target function integrating path length, height, smoothness and threat cost according to the dynamic constraints and task requirements of the UAV, thereby providing a quantitative evaluation standard for the pros and cons of the path. Subsequently, the initialization module generates uniformly distributed initial positions of the whale population in the search space by using the best point set strategy, and generates an initial feasible solution of the path through decoding and fitness calculation, thereby providing a high-quality starting point for the optimization algorithm. Then, the optimization solving module iteratively optimizes the initial feasible solution by using the enhanced multi-strategy whale migration optimization algorithm, thereby continuously updating the position of the whale individuals and driving the path feasible solution to evolve towards the optimal solution by introducing the Lévy flight strategy in the exploration stage to enhance the global exploration ability, and introducing the Cauchy distribution inverse cumulative strategy in the development stage to enhance the ability of local fine search and jumping out of the local optimum. Finally, the judgment and output module is responsible for monitoring the iteration process, and when the termination condition is met, decoding the current optimal individual position into the final three-dimensional path and outputting, thereby completing the whole automatic planning process from environment modeling to optimal path generation.

[0234] Finally, it should be noted that the above is only the preferred embodiment of the present application, and is not intended to limit the present application, although the foregoing embodiments of the present application are described in detail, for those skilled in the art, it still can be modified to the technical solution recorded in the foregoing embodiments, or equivalent replacement of some technical features, any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application, should be included in the protection scope of the present application.

Claims

1. An enhanced multi-strategy whale migration optimization UAV trajectory planning method, characterized in that, Includes the following steps: S1: Construct a three-dimensional flight path planning model for the mountainous environment, acquire terrain elevation data, and set the starting point, ending point, and multiple flight path points for the UAV; S2: Establish a comprehensive objective function, which is a weighted sum of track length cost, altitude cost, smoothness cost, and threat cost, wherein: The threat cost is described using a highly correlated dynamic threat range model, where the influence radius of the threat source is dynamically adjusted based on the flight altitude of the waypoint. The weighting coefficients of the trajectory length cost, altitude cost, smoothness cost, and threat cost are adaptively adjusted according to the flight phase, with different weighting configurations used for different flight phases; S3: Generates an initialization strategy based on the theory of optimal point sets. An initial candidate trajectory is generated, and the optimal point set theory uses the golden ratio to generate a uniformly distributed initial population. S4: An enhanced multi-strategy whale migration optimization algorithm is used to iteratively optimize candidate routes, including: Calculate the diversity index of the current population The diversity index characterizes the degree of dispersion of candidate tracks in a population; According to the diversity index With preset threshold The comparison, and the current iteration number. With maximum number of iterations Relationship, adaptive selection of search strategy: when and At that time, the Lévy flight strategy was adopted; when or At that time, the Cauchy distribution perturbation strategy is adopted; Calculate the fitness value of each candidate track after the update, where the fitness value is the output of the comprehensive objective function; Update the current best candidate track; S5: Determine if the termination condition is met. If it is met, output the optimal trajectory. If not, continue iterative optimization. The formula for calculating the dynamic influence radius of the threat source is: ， in: For the first The basic threat radius of each threat source; For the first Flight altitude of each waypoint; and These are the minimum and maximum heights of the planned space, respectively; It is a high-impact factor, with a value range of 0.1 to 0.3; The formula for calculating the cost of the threat is as follows: ， in, The total number of waypoints. The total number of threat sources, For the first The first trackpoint to the second The shortest distance to the boundary of each threat source; In step S4, the diversity index The calculation formula is: ， in: The size of the candidate track population; For the first The candidate track in the first The position vector at the next iteration; For the population in the first The center position at the next iteration; This represents the Euclidean distance norm.

2. The method according to claim 1, characterized in that: The rules for dividing the flight phases and adaptively adjusting the weighting coefficients are as follows: Takeoff or landing phase: The segment from the starting point to an altitude increment of 30% of the preset cruise altitude, or the segment from an altitude increment below the preset cruise altitude to the ending point, is assigned an altitude cost weight. ; Cruise phase: The segments of flight other than the takeoff or landing phase and the threat zone phase, which are assigned a track length cost weight. Smoothness cost weight ; Threat zone crossing phase: Segments where the distance between the waypoint and the boundary of any threat source is less than 1.5 times the base radius of the threat source are assigned a threat cost weight. .

3. The method according to claim 1, characterized in that: In step S3, the generation formula for the initialization strategy based on the optimal point set theory is as follows: ， in: For individual serial numbers, ; For dimensional indexing, ; The golden ratio, ; and These are the upper and lower bounds of the j-th dimension search space, respectively; Indicate extraction The decimal part.

4. The method according to claim 1, characterized in that: The candidate track position update formula for the Lévy flight strategy is as follows: ， in This represents the average position of high-performing individuals in the population. This is the current optimal candidate track position. Let [a] be a random vector in the interval [0,1]. It represents the Hadamah accumulation. For Lévy's flight stride; The candidate track position update formula for the Cauchy distribution perturbation strategy is as follows: ， in For a uniformly distributed random vector, It is the inverse cumulative distribution function of the Cauchy distribution.

5. The method according to claim 1, characterized in that: The complete expression for the comprehensive objective function is: ， in: The cost of track length is calculated as the sum of the distances between adjacent track points; As a cost of altitude, it is calculated as the standard deviation of the flight altitude from the mean at each waypoint; As a smoothness cost, it is calculated as the sum of the absolute values ​​of the changes in heading angle between adjacent flight segments; As a threat at cost; The weighting coefficients for each cost item are adaptively adjusted based on the flight phase. The specific adjustment rules are as follows: Takeoff or landing phase: assigning weight to altitude costs ; Cruise Phase: Weighting the Cost of Track Length Weights of smoothness cost ; Threat Zone Traversal Phase: Assigning Weights to Threat Costs .

6. An enhanced multi-strategy whale migration optimization UAV trajectory planning system, used to execute the method according to any one of claims 1-5, characterized in that, include: A processor and a memory, the memory storing a computer program, the processor executing the computer program to perform the functions of the following modules: The environmental modeling module is used to construct a three-dimensional trajectory planning model for mountainous environments; The objective function construction module is used to build a comprehensive objective function, in which the threat cost adopts a highly correlated dynamic threat range model, and the weight coefficients of each cost item are adaptively adjusted according to the flight phase. The optimal point set initialization module is used to generate an initial candidate track population using an initialization strategy based on optimal point set theory. The enhanced multi-strategy optimization module is configured as follows: Calculate the population diversity index D(t); According to the diversity index With preset threshold The comparison, and the current iteration number. With maximum number of iterations The relationship between them allows for adaptive selection of search strategies; where: when and At that time, the Lévy flight strategy was adopted; when or At that time, the Cauchy distribution perturbation strategy is adopted; Iteratively update candidate tracks and record the optimal solution; The output module is used to determine whether the termination condition is met and output the optimal trajectory.

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