Waypoint screening and path planning method for near-field measurement of antenna of unmanned aerial vehicle

Abstract

The invention relates to a waypoint screening and path planning method for near-field measurement of an unmanned aerial vehicle antenna, and the method comprises the steps: carrying out the waypoint screening of a measurement plane through employing an adaptive sampling strategy based on electromagnetic induction, and carrying out the correction of a phase through combining wavefront curvature correction with data-driven residual error modeling. A more accurate electromagnetic propagation matrix is constructed; the contribution of each to-be-selected measurement point on an antenna pattern is evaluated by constructing an electromagnetic propagation matrix, and a certain number of measurement points are selected as waypoints of the unmanned aerial vehicle by setting a threshold value; local search and global search are balanced by combining an improved tabu search algorithm and a north pole sea parrot optimization algorithm. The method can effectively reduce the number of measurement points and the length of a scanning path, solves the problems that an existing path planning algorithm is liable to fall into local optimum, is long in planning time, and is closer to the reality.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) antenna measurement, and in particular to a waypoint screening and path planning method for UAV antenna near-field measurement. The method uses a UAV to perform waypoint screening in the antenna near-field measurement area based on an adaptive sampling strategy of electromagnetic induction, and implements UAV path planning based on an improved tabu search Arctic Puffin optimization algorithm. Background Art

[0002] Antenna measurement technology plays a crucial role in many fields, including modern communications, radar, and satellite navigation. As key components for transmitting and receiving electromagnetic waves, precise measurement of antenna performance is invaluable for ensuring stable system operation, improving signal transmission quality, and optimizing system compatibility. Traditional antenna measurement methods primarily include near-field and far-field methods. While traditional near-field measurement offers high accuracy, it suffers from high equipment costs, data redundancy, and limited adaptability to large antennas or complex measurement scenarios.

[0003] With the rapid development of drone technology, drones have demonstrated tremendous potential for antenna measurement and have gradually become a hot research topic. Compared with traditional measurement methods, drones offer numerous advantages, including high maneuverability, flexibility, and the ability to easily reach complex areas. These advantages effectively overcome the spatial limitations of traditional measurement methods, providing a new, efficient, and flexible solution for antenna measurement. Path planning is a key step in drone antenna measurement. Its core lies in accurately planning the drone's flight trajectory to achieve comprehensive coverage of the antenna measurement area while ensuring the accuracy and integrity of the measurement data. Current algorithms for solving the traveling salesman problem (TSP) using drones often suffer from the problem of being prone to local optima and struggling to balance global and local search capabilities. While precise algorithms can yield optimal solutions, their complexity increases exponentially, and their efficiency needs to be improved. Furthermore, the performance of many algorithms is highly sensitive to parameter selection, making the quality of the solution difficult to guarantee without extensive experimentation and precise tuning.

[0004] Considering the low efficiency of traditional antenna near-field measurement methods and the many shortcomings of drone path planning algorithms, the present invention proposes an efficient and accurate drone antenna near-field measurement solution. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a waypoint screening and path planning method for near-field measurements of UAV antennas. This method constructs an electromagnetic propagation matrix to evaluate the contribution of each candidate measurement point to the antenna pattern. A threshold is set to select a certain number of measurement points as UAV waypoints. By combining an improved tabu search algorithm with the Arctic Puffin optimization algorithm to balance local and global search, this method overcomes the problems of existing path planning algorithms, such as the tendency to fall into local optimality and the long planning time.

[0006] The technical solution adopted by the present invention to solve the technical problem is:

[0007] A waypoint screening and path planning method for near-field measurement of UAV antennas, comprising the following contents:

[0008] Control the size of the vertical plane measurement area of ​​the antenna near-field measurement by setting the maximum confidence angle and measurement distance;

[0009] A source point p is randomly generated in the area of ​​the antenna under test s , generate measurement point p in the measurement area above the antenna m ;

[0010] The electromagnetic propagation matrix B is constructed according to formula (2):

[0011]

[0012] Among them, d m,s is the measurement point p m With the source point p s The Euclidean distance between them; k0 is the wave number, j is the imaginary unit; B m,s is an element in the electromagnetic propagation matrix; is the basic spherical wave propagation term; is the phase correction factor:

[0013]

[0014] Among them, f θ (x m ,y m ) is a residual neural network with learnable parameters, θ is a learnable parameter of the neural network, which is used to reduce the phase residual; is the wavefront curvature correction factor; h represents the height difference between the measurement point and the source point; r is the radial distance between the measurement point and the source point;

[0015] The input of the residual neural network with learnable parameters is the two-dimensional plane coordinates (x m ,y m), the output is the phase correction of the corresponding point in the x, y, and z directions The loss function for training the residual neural network is:

[0016]

[0017] Where N is the number of training samples, φ real,i is the phase actually measured at the i-th measurement point in a certain direction; (x i ,y i ) is the coordinate of the i-th measurement point; φ model,i The propagation model is used for the i-th measurement point in this direction. Calculated theoretical phase;

[0018] Perform QR decomposition on the electromagnetic propagation matrix B. QR decomposition transforms the matrix B into T Decompose into an orthogonal matrix Q and an upper triangular matrix R, and calculate the absolute value of the diagonal elements of the upper triangular matrix R

[0019] Perform QR decomposition on the electromagnetic propagation matrix B. QR decomposition transforms the matrix B into T Decompose into an orthogonal matrix Q and an upper triangular matrix R, calculate the absolute value of the diagonal elements of the upper triangular matrix R, set the dynamic threshold τ and the lower limit num_waypoints of the number of measurement points required for actual antenna measurement, and obtain the key waypoint when the ratio of the absolute value of the last diagonal element to the first diagonal element of the upper triangular matrix is ​​not less than the dynamic threshold and the number of screened waypoints is not less than num_waypoints;

[0020] The drone path is planned based on the obtained key waypoints.

[0021] Furthermore, during training, the residual neural network with learnable parameters uses data of all measurement points of the antenna as training samples, and each sample includes three-dimensional coordinates, phase and amplitude data of a measurement point.

[0022] Furthermore, the path planning adopts the improved tabu search-based Arctic Puffin optimization algorithm and the K-Means clustering algorithm. All cities are divided into several city clusters based on the Euclidean distance between cities, and each city cluster is solved separately. The K-Means algorithm iteratively optimizes the cluster center and cluster members to minimize the total distance between cities in the cluster. That is, the improved tabu search-based Arctic Puffin optimization algorithm is run on each city cluster. The specific process is:

[0023] Set initial parameters and initialize the taboo list;

[0024] Use a greedy strategy to generate an initial solution for the tabu search algorithm. Repeat the greedy initialization process multiple times, selecting a different random starting city each time. Finally, from the multiple initial paths generated, the solution with the shortest path length is selected as the initial path of the tabu search algorithm.

[0025] A neighborhood search is performed on the initial path to generate multiple candidate solutions. The optimal solution is selected and a tabu search algorithm is executed. The latest historical optimal solution is sorted and mapped to update the Arctic puffin population and enter the iteration process of the Arctic puffin algorithm. The Arctic puffin algorithm:

[0026] Establish a sorting mapping between continuous space and discrete space: Let the discrete path of discrete cities be path={c0,c1,…,c n-1}, where c i represents the i-th visited city, and i∈{0,1,…,n-1}, n is the total number of cities; define the mapping function Convert the discrete path into a continuous position vector pos, whose components pos[c i ] is defined as:

[0027] pos[c i ]=i,i=0,1,…,n-1 (12)

[0028] This continuous position vector pos preserves the sequential information of the path, but is represented in a way suitable for continuous optimization;

[0029] When evaluating the path, define the mapping function Restore the vector to a legal arrangement according to its numerical size;

[0030] The Arctic puffin population is updated after sorting and mapping the historical optimal solution of tabu search. Individuals in the Arctic puffin population dynamically adjust their exploration or foraging tendencies according to the behavior conversion factor B. The expression of the behavior conversion factor B is formula (13);

[0031]

[0032] Among them, f i is the fitness value of the current individual, which is calculated by minimizing the total path length; f best is the fitness value of the best individual in the current population; f mean is the average value of the current population fitness, representing the overall level of the current search group, and is calculated once per round in the program; α is the fitness difference amplification coefficient; FAAT i is the fitness perception weighting factor

[0033] If B is greater than parameter C, it enters the flight exploration phase, otherwise it enters the underwater foraging phase;

[0034] The Arctic Puffin optimization algorithm based on improved tabu search solves the TSP path of the cluster center point and obtains the rough optimization solution of the inter-cluster order. Finally, according to the order of the cluster center TSP path, the optimal paths within each cluster are spliced ​​in sequence to form an overall path and obtain the optimal path.

[0035] Furthermore, a piecewise uniform B-spline curve is used to smooth the optimal path output by the Arctic Puffin optimization algorithm based on improved tabu search. The path is divided into multiple segments, each segment is fitted using a uniform B-spline curve, and interpolation is performed at the path turns.

[0036] Furthermore, in the Arctic Puffin algorithm, the first and third stages of underwater foraging introduce a weighted cooperation factor F i , weighted disturbance factor β i To update the location,

[0037] In the first stage, the aggregation and foraging position update formula is (23):

[0038]

[0039] In formula (23), L(D) is the flight step function generated by introducing the Lévy flight strategy; D is the spatial dimension; r1, r2, and r3 are three randomly selected individual indices, and the three are not equal to each other; Indicates the update of the aggregation foraging position of the i-th candidate solution in the t+1th iteration;

[0040] Indicates the position update of the r1th candidate solution in the tth iteration; Indicates the position update of the r2th candidate solution in the tth iteration; Indicates the position update of the r3th candidate solution in the tth iteration;

[0041] Weighted cooperation factor F i The mathematical expression is:

[0042]

[0043] Note f mean is the average fitness value of all individuals at present, then f avg1 With f avg2 satisfy:

[0044] f avg1 =f mean +λ1·σ (25)

[0045] f avg2 =f mean +λ2·σ (26)

[0046] Where λ1 = -0.5, λ2 = 0.5, σ is the global fitness standard deviation;

[0047] In the third stage, the position update formula for avoiding predators is:

[0048]

[0049] in, is the predator-avoiding position update of the i-th candidate solution in the t+1th iteration; Indicates the position update of the i-th candidate solution in the t-th iteration; β i is the weighted disturbance factor, β i The mathematical expression is:

[0050]

[0051] The present invention also protects a computer-readable storage medium having a computer program stored therein, wherein the computer program is adapted to execute the method when loaded by a computer.

[0052] The present invention deploys the planning method on the onboard computer of the UAV, uses the ROS robot operating system and the Airsim simulation platform to complete the UAV path planning and perform the near-field measurement task of the antenna to be measured.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) An adaptive sampling strategy based on electromagnetic induction is used to screen waypoints on the measurement plane. The wavefront curvature correction is combined with data-driven residual modeling to correct the phase, and then a more accurate electromagnetic propagation matrix is ​​constructed. Based on this, waypoint screening is performed. Compared with the traditional methods of antenna near-field measurement: standard half-wavelength scanning and spiral scanning, the method of the present invention can effectively reduce the number of measurement points and the length of the scanning path.

[0055] (2) The Arctic Puffin optimization algorithm based on improved tabu search is used to quickly traverse the selected key waypoints. The experimental results of the comparison with similar path planning algorithms show that the Arctic Puffin optimization algorithm based on improved tabu search can better balance local search and global search, overcoming the problems of existing path planning algorithms such as being prone to falling into local optimality and long planning time.

[0056] (3) Using the AirSim simulation platform built on Unreal Engine, which supports multiple tool chains and is controlled by the ROS robot operating system, it can generate highly realistic visual effects and accurate physical simulations that are closer to reality. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] For a clearer and more specific description, the embodiments of the present invention are further explained below with reference to the accompanying drawings:

[0058] Figure 1 The figure is a flow chart of an embodiment of a method for waypoint screening and path planning for near-field measurement of UAV antennas according to the present invention.

[0059] Figure 2 Schematic diagram of the algorithm flow of the adaptive sampling strategy based on electromagnetic induction according to an embodiment of the present invention.

[0060] Figure 3 This is a result diagram of screening measurement points according to an embodiment of the present invention.

[0061] Figure 4 This is a flow chart of the Arctic Puffin optimization algorithm based on improved tabu search according to an embodiment of the present invention.

[0062] Figure 5 This is an overall problem modeling diagram for an embodiment of the present invention.

[0063] Figure 6 Schematic diagram of the path before and after smoothing according to the embodiment of the present invention.

[0064] Figure 7 This is an Airsim simulation flight experiment diagram of an embodiment of the present invention.

[0065] Figure 8 Schematic diagram of a UAV antenna near-field measurement system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The present invention is further explained below with reference to the embodiments and drawings, but they are not intended to limit the scope of protection of the present application.

[0067] The present invention is a waypoint screening and path planning method for UAV antenna near-field measurement, which includes two parts: an adaptive sampling strategy based on electromagnetic induction for efficient screening of antenna near-field measurement points and an Arctic Puffin optimization algorithm based on improved tabu search for path planning.

[0068] The adaptive sampling strategy based on electromagnetic induction includes the following:

[0069] First, set the global parameters and generate the antenna source point and measurement point. s Randomly generated in the antenna area under test, the position of each source point is converted from polar coordinates to Cartesian coordinates and then calculated. m Distributed in the measurement area above the antenna, the measurement point is above the source point. Calculate each measurement point p according to formula (1) m With the source point p s The Euclidean distance d between m,s :

[0070]

[0071] Among them, (x m ,y m ,z m ) is the Cartesian coordinate position of the measuring point, (x s ,y s ,z s ) is the Cartesian coordinate position of the source point,

[0072] Then d m,s Substitute into formula (2) to construct the electromagnetic propagation matrix B:

[0073]

[0074] Where k0 is the wave number,

[0075]

[0076] j is the imaginary unit; λ is the wavelength; B m,s is an element in the electromagnetic propagation matrix; is the basic spherical wave propagation term; is the phase correction factor:

[0077]

[0078] Among them, f θ (x m ,y m ) is a residual neural network with learnable parameters, θ is a learnable parameter of the neural network, which is used to reduce the phase residual; is the wavefront curvature correction factor; h = z m -z s , represents the height difference between the measurement point and the source point; r is the radial distance between the measurement point and the source point; in formula (5) represents the phase correction term, represents the high-order curvature compensation term.

[0079] The first term in formula (4) The introduction of the basic spherical wave propagation term The wavefront curvature correction is added to achieve high-precision propagation modeling in the near field. The traditional spherical wave propagation model only considers the propagation from the source point p s To the measuring point p m The distance propagation term is more suitable for far-field propagation, but in near-field antenna modeling, the measurement distance is far from enough to approximate far-field propagation, and this model will have the defect of insufficient accuracy, especially in the focal area near the main lobe. The second term f θ (xm ,y m ) is a residual neural network with learnable parameters, the purpose of which is to reduce the phase residual:

[0080]

[0081] The input of the residual neural network with learnable parameters is the two-dimensional coordinates of the measurement point on the measurement plane (x m ,y m ), the output is the phase correction of the corresponding point in the x, y, and z directions Define the loss function for training residual neural network:

[0082]

[0083] Among them, θ is the learnable parameter of the neural network, N is the number of training samples, φ real,i is the phase actually measured at the i-th measurement point in a certain direction; (x i ,y i ) is the coordinate of the i-th measurement point; φ model,i The propagation model is used for the i-th measurement point in this direction. The calculated theoretical phase, φ real,i -φ model,i It is expressed as propagation phase residual and fitted using a neural network function, with the goal of minimizing the propagation phase residual prediction error.

[0084] When training the residual neural network with learnable parameters, the data of all measurement points of the antenna are used as training samples. Each sample contains the three-dimensional coordinates, phase and amplitude data of a measurement point. The phase at this time is the measured phase.

[0085] In order to select key waypoints from a large number of measurement points, the electromagnetic propagation matrix B is subjected to QR decomposition. T Decomposed into an orthogonal matrix Q and an upper triangular matrix R:

[0086] B T =QR (8)

[0087] Among them, Q is an orthogonal matrix that satisfies Q T Q = I, its column vectors are linearly independent, which ensures that the decomposed matrix has good numerical stability and computational efficiency. R is an upper triangular matrix, and the diagonal elements R i,i Indicates the importance of each measurement point's contribution to the electromagnetic field.

[0088] Compute the absolute values ​​of the diagonal elements of the upper triangular matrix R:

[0089] diag(R)=[|R1,1 |,|R 2,2 |,…,|R n,n |] (9)

[0090] Where n represents the number of rows and columns of the upper triangular matrix;

[0091] During the point selection process, the matrix dimension affects the number and distribution of measurement points. A threshold τ is set as the criterion for whether to adopt a measurement point. The diagonal elements are arranged in descending order. The number of measurement points is determined when the last diagonal element and the first diagonal element of the upper triangular matrix meet the conditions of formula (10):

[0092]

[0093] If the number of points that meet the conditions of formula (10) is less than num_waypoints, where num_waypoints is the lower limit of the number of measurement points required for the actual antenna measurement, and the number of measurement points is too small for the actual antenna measurement needs, the threshold τ is dynamically adjusted and appropriately lowered to screen out the waypoint indexes that meet the conditions.

[0094] The proposed Arctic Puffin optimization algorithm based on improved tabu search can achieve rapid traversal of key waypoints. It is an efficient drone path planning method that can solve the typical traveling salesman problem (TSP). The typical TSP problem requires returning to the starting point after reaching the last measurement point to form a closed path, facilitating the drone's return after completing the mission. Specifically, it includes the following:

[0095] Set initial parameters and initialize the taboo list;

[0096] Using the K-Means clustering algorithm, all cities are divided into several clusters based on the Euclidean distance between them. Each cluster is then solved separately, using the improved tabu search-based Arctic Puffin optimization algorithm. The K-Means algorithm iteratively optimizes cluster centers and cluster members to minimize the sum of the distances between cities within a cluster. Mathematically, the objective function of the K-Means algorithm is:

[0097]

[0098] Where K is the number of clusters, C j represents the jth cluster, μ j It is cluster C j The center of mass, x i is the coordinate of the i-th city, ||x i -μ j || is the city point x i To cluster center μ j The Euclidean distance of .

[0099] A greedy strategy is added to the early tabu search operation to generate an initial solution. To reduce the randomness of the initial solution, the greedy initialization process is repeated multiple times, each time selecting a different random starting city. Finally, from the multiple initial paths generated, the solution with the shortest path length is selected as the initial path of the tabu search algorithm.

[0100] Perform neighborhood search on the initial path, generate multiple candidate solutions, select the optimal solution, and complete an update of the optimal solution;

[0101] Check whether the update to the optimal solution is in the taboo list. If not, accept this solution as the optimal solution. If it is, further determine whether the pardon condition is met. If the pardon condition is met, accept this solution as the optimal solution. Otherwise, delete the solution and return to reselect the optimal solution.

[0102] If the taboo list is full, the earliest update to the optimal solution is removed first, and then this update is moved to the taboo list; if the taboo list is not full, this update is directly moved to the taboo list.

[0103] The purpose of the taboo list is to record the solutions that have been visited recently or certain specific update operations. Its purpose is to prevent the algorithm from repeatedly returning to the explored areas during the search process, thereby avoiding circular search and enabling the algorithm to jump out of the local optimal solution and explore a wider solution space.

[0104] The latest historical optimal solution finally obtained is sorted and mapped, and used to update the Arctic Puffin population, entering the iterative process of the Arctic Puffin Algorithm (APO algorithm).

[0105] The Arctic Puffin Algorithm (APO) consists of two phases: aerial flight (exploration) and underwater foraging (exploitation). During the aerial flight (exploration) phase, the algorithm introduces Levy flight and a speed factor mechanism to enhance its ability to escape local optima and improve convergence speed. During the underwater foraging (exploitation) phase, it employs strategies such as synergy effects and adaptive change factors to ensure the algorithm effectively utilizes the current best solution and guides search direction. Furthermore, a behavior conversion factor enables dynamic transitions between the exploration and exploitation phases, effectively balancing global search and local exploitation. The APO algorithm is typically used to solve continuous problems, while path planning problems typically involve finding the optimal path between discrete cities or nodes. By establishing a sorting mapping between continuous and discrete spaces, solutions can be converted between the two spaces. Otherwise, it would be difficult to generate valid neighborhoods and maintain path legitimacy.

[0106] Let the discrete path be path={c0,c1,…,c n-1}, where c iDenotes the i-th visited city, and i∈{0,1,…,n-1}, n is the total number of cities. Define the mapping function Convert the discrete path into a continuous position vector pos, whose components are defined as:

[0107] pos[c i ]=i,i=0,1,…,n-1 (12)

[0108] The position vector pos retains the order information of the path, but is expressed in a way suitable for continuous optimization, providing the APO algorithm with an optimizable continuous vector, which enables the algorithm to inherit the global search power of the continuous space. Finally, when evaluating the path, the mapping function is defined The vector is restored to a legal arrangement according to its numerical size. This mapping method enables APO and TS to play a role in their respective applicable spaces while working together in the overall framework.

[0109] The present invention adds the fitness perception weighting factor FAAT to the behavior conversion factor B i , enabling each individual to dynamically adjust its exploration or foraging tendency according to the current solution quality, fully considering the consistency of all individual behaviors and improving quality adaptability:

[0110]

[0111] where f i is the fitness value of the current individual, which is calculated by the objective function of the entire Arctic Puffin Optimization Algorithm based on Improved Tabu Search (APO-TS algorithm) stage (the objective function is to minimize the total path length); f best is the fitness value of the best individual in the current population, which is dynamically updated as the iteration progresses; f mean It is the average value of the current population fitness, representing the overall level of the current search group, and is calculated once per round in the program; α is the fitness difference amplification coefficient, which controls the weight of the fitness difference in this factor.

[0112] If B is greater than parameter C, it enters the flight exploration phase, otherwise it enters the underwater foraging phase. Here, parameter C is set by yourself, and its size directly affects the balance between the algorithm's global search and local optimization;

[0113] In the first stage of flight exploration, the Lévy flight strategy and the speed coefficient V are first introduced according to formula (15) to help explore the optimal solution;

[0114]

[0115] Among them, the speed coefficient V is defined as:

[0116] V=round(0.5*(0.05+rand))*η (16)

[0117]

[0118] Here, we use the MATLAB function rand to define the velocity coefficient V. The function generates a random decimal in the interval [0, 1), scales and translates the result, and then uses the round function to round the result. η is a random variable with a standard normal distribution and a mean of 0 and a standard deviation of 1.

[0119] Indicates the position update of the i-th candidate solution in the t+1th iteration;

[0120] Indicates the position update of the i-th candidate solution in the t-th iteration;

[0121] It represents the position of a candidate solution randomly selected from the current population in the tth iteration. The candidate solution number is m, where m is a random integer ranging from 1 to N-1, excluding i.

[0122] L(D) is the Lévy flight step vector generated in D-dimensional space, corresponding to formula (27). L(D) is a D-dimensional vector, where each component is the step size step generated by formula (27).

[0123] In the second stage of flight exploration, the speed coefficient S is introduced to quickly adjust the individual position, which is recorded as the new solution

[0124]

[0125] The speed coefficient S is defined as:

[0126] S=tan((rand-0.5)*π) (19)

[0127] Here, the function in MATLAB is used to represent the definition of the speed coefficient S. rand generates a random decimal in the interval [0,1). After scaling and translating the result, the tan function is used to calculate the tangent value of the above result.

[0128] In the third stage of flight exploration, the best individuals in the first two stages are merged as new candidate solutions.

[0129]

[0130]

[0131] sort represents a sorting operation, which sorts the merged candidate solution set from small to large according to the fitness value; new represents the sorted candidate solution set; It means selecting the first N individuals with the best fitness from new to form a new population.

[0132] In the first stage of underwater foraging, foraging is done in groups, and a weighted cooperation factor F is introduced. i To update the position, record it as the new solution

[0133]

[0134] In formula (23), L(D) is the flight step function generated by introducing the Lévy flight strategy. r1, r2, and r3 are three randomly selected individual indices, which are not equal to each other, that is, three different randomly selected individual indices, thus ensuring that three different individuals are randomly selected.

[0135] Weighted cooperation factor F i It is determined based on the comparison between the fitness value of individual i and the average fitness value of the population. i The mathematical expression is as follows:

[0136]

[0137] Note f mean is the average fitness value of all individuals at present, then f avg1 With f avg2 satisfy:

[0138] f avg1 =f mean +λ1·σ (225)

[0139] f avg2 =f mean +λ2·σ (26)

[0140] Where λ1 = -0.5, λ2 = 0.5, and σ is the global fitness standard deviation.

[0141] f avg1 Represents the lower bound of high-quality individuals, if f i ≤f avg1 , indicating that the individual is far from the optimal and needs to be F within a larger numerical range. i Take values ​​to enhance exploration; f avg2 Represents the upper bound of high-quality individuals, if f i ≥f avg2 , indicating that the individual has already been in the excellent ranks and needs to reduce disturbances and maintain stability.

[0142] In the global exploration phase, the Lévy flight strategy generates step sizes that enable new individuals to make long-distance jumps in the search space, effectively escaping the local optimal trap and expanding the search range. In the local development phase, the Lévy flight strategy is used to adjust the step size so that new individuals can conduct detailed searches in local areas.

[0143] The formula for generating the Lévy flight step length step is as follows:

[0144]

[0145] Among them, u and v are random variables that obey Gaussian distribution and satisfy:

[0146]

[0147] Where β is the characteristic index of the stable distribution and σ is the scaling factor of the Lévy flight, which is calculated as follows:

[0148]

[0149] The flight scaling factor σ controls the overall scale of the step sizes. Here, Γ(·) is the gamma function that ensures that the mathematical form of the step size distribution matches the physics of the Lévy flight, resulting in a reasonable search behavior for practical applications.

[0150] In the second stage of underwater foraging, the search is strengthened and the position is adjusted by the adaptive factor f, which is recorded as the new solution

[0151]

[0152] Where T is the total number of iterations.

[0153] In the third stage of underwater foraging, avoiding predators, the dual strategy is also used to update the position, which is recorded as the new solution

[0154]

[0155] where β i is a weighted disturbance factor, which is determined based on the comparison between the fitness value of individual i and the average fitness value of the population, β i The mathematical expression is as follows:

[0156]

[0157] and weighted cooperation factor F i The setting is similar to that in which individuals with poor fitness are given greater disturbance, while individuals with good fitness are mainly stable.

[0158] Finally, the best individuals in the three stages of underwater foraging are merged as new candidate solutions:

[0159]

[0160] Following the above steps, the Arctic Puffin optimization algorithm based on improved tabu search is used to solve the TSP path of the cluster center, obtaining a coarse optimization solution for the inter-cluster order. Finally, the optimal paths within each cluster are sequentially spliced ​​together according to the order of the cluster center TSP paths to form the overall path.

[0161] In this embodiment of the present invention, a quadratic B-spline curve is used to smooth the planned path. B-spline curves are a flexible and powerful type of spline, widely used in fields such as computer graphics, data fitting, and numerical analysis. They overcome some limitations of Bezier curves, such as local control capabilities and the complexity of curve segment splicing.

[0162] Since the smoothed path will deviate from the original path points and produce position errors, in order to reduce this error, the path points are interpolated before smoothing, so that the smoothed path can be more consistent with the original path.

[0163] The total number of cities is n, and after one interpolation process, 2n-1 control points are generated (the control point index ranges from 0 to 2n-2), that is, the control point set is {Q0, Q1, ..., Q 2n-2}.

[0164] Given a node vector {p0,p1,…,p m The number of nodes is m+1 (node ​​vector indexes range from 0 to m). The number of nodes is related to the number of control points and the degree k of the B-spline curve, satisfying m+1=(2n-1)+k+1, that is, m+1=2n+k. Here, k is 2, so m=2n+2.

[0165] In summary, the formula of the quadratic B-spline curve is:

[0166]

[0167] Where C(p) represents a point on the quadratic B-spline curve, which is a function of parameter p. As p changes, C(p) moves along the curve. i,2 (p) represents the value of the ith quadratic B-spline basis function at parameter p, which determines the corresponding control point Q i The degree of influence on the curve point C(p). i Represents the control points, which define the shape of the curve. i is the index of the control point, ranging from 0 to 2n-2.

[0168] Example 1

[0169] like Figure 1 As shown, this embodiment of the method for waypoint screening and path planning for near-field measurement of UAV antennas includes the following steps:

[0170] Step 1:

[0171] The antenna near-field measurement area should be selected. Theoretically, its side length should be infinite. In actual measurement, the size of the measurement area is often controlled by setting the maximum confidence angle and measurement distance. Specifically, the following relationship should be satisfied:

[0172]

[0173] In formula (1), D is the antenna aperture, L is the side length of the measurement area, h is the measurement distance, and θ max is the maximum confidence angle,

[0174] To ensure the measurement plane is within the antenna's near-field, the vertical distance h between the measurement plane and the antenna plane should be greater than or equal to the antenna wavelength λ. To avoid interference from factors such as complex field distribution variations and phase center instability near the antenna aperture, and to facilitate the placement of the measurement equipment, h should be greater than 3λ. The maximum distance must consider both drone flight safety and measurement accuracy. Excessive distances will place the drone outside its flight zone or require special approval. Furthermore, measurement accuracy will decrease due to field strength attenuation, and phase measurement errors will increase.

[0175] Step 2:

[0176] The adaptive sampling strategy based on electromagnetic induction is used to efficiently screen the antenna near-field measurement points. The specific process is as follows: Figure 2 As shown, including the following:

[0177] The global parameter settings for the first part are shown in the table below:

[0178]

[0179] In the second part, the source point p s Randomly generated in the antenna area under test, the position of each source point is converted from polar coordinates to Cartesian coordinates (x, y, z) and then calculated. m Distributed in the measurement area above the antenna. Calculate each measurement point p m With the source point p s The Euclidean distance between:

[0180]

[0181] The electromagnetic propagation matrix B is constructed in this way:

[0182]

[0183] where k0 is the wave number, defined as:

[0184]

[0185] j is the imaginary unit; λ is the wavelength; B m,s is an element in the electromagnetic propagation matrix; is the basic spherical wave propagation term; is the phase correction factor:

[0186]

[0187] Item 1 In the basic spherical wave propagation term The wavefront curvature correction is added to achieve high-precision propagation modeling in the near field. The traditional spherical wave propagation model only considers the propagation from the source point p s To the measuring point p m The distance propagation term is more suitable for far-field propagation. However, in near-field antenna modeling, the measurement distance is far from enough to approximate far-field propagation. This model will have the defect of insufficient accuracy, especially in the focal area near the main lobe.

[0188] Note that the measurement point is above the source point, and the height difference is h = z m -z s ,but:

[0189] is the wavefront curvature correction factor; h represents the height difference between the measurement point and the source point; r is the radial distance between the measurement point and the source point. represents the phase correction term, represents the high-order curvature compensation term.

[0190] The second term f θ (x m ,y m ) is a residual neural network with learnable parameters, the purpose of which is to reduce the phase residual:

[0191]

[0192] The input of the residual neural network with learnable parameters is the two-dimensional coordinates of the measurement point on the measurement plane (x m ,y m ), the output is the phase correction of the corresponding point in the x, y, and z directions Define the loss function for training residual neural network:

[0193]

[0194] Among them, θ is the learnable parameter of the neural network, N is the number of training samples, φ real,i is the phase actually measured at the i-th measurement point in a certain direction; (x i ,y i ) is the coordinate of the i-th measurement point; φ model,i The propagation model is used for the i-th measurement point in this direction. The calculated theoretical phase, φ real,i -φ model,i It is expressed as propagation phase residual and fitted using a neural network function, with the goal of minimizing the propagation phase residual prediction error.

[0195] When training the residual neural network with learnable parameters, the data of all measurement points of the antenna are used as training samples. Each sample contains the three-dimensional coordinates, phase and amplitude data of a measurement point. The phase at this time is the measured phase.

[0196] In order to select key waypoints from a large number of measurement points, QR decomposition is performed on the matrix B. T Decomposed into an orthogonal matrix Q and an upper triangular matrix R:

[0197] B T =QR (9)

[0198] Among them, Q is an orthogonal matrix that satisfies Q T Q = I, its column vectors are linearly independent, which ensures that the decomposed matrix has good numerical stability and computational efficiency. R is an upper triangular matrix, and the diagonal elements R i,i Indicates the importance of each measurement point's contribution to the electromagnetic field.

[0199] Compute the absolute values ​​of the diagonal elements of the matrix R:

[0200] diag(R)=[|R 1,1 |,|R 2,2 |,…,|R n,n |] (10)

[0201] In the process of point selection, the matrix dimension will affect the number and distribution of measurement points. Here, the threshold τ is defined as the criterion for whether to adopt a measurement point. Arrange the diagonal elements in descending order, and the points R that meet the conditions nn Need to meet:

[0202]

[0203] If the number of points that meet the conditions exceeds the set num_waypoints value, the index corresponding to the first num_waypoints largest element is selected as the waypoint. If the number of points that meet the conditions is less than num_waypoints, there are too few measurement points for the actual antenna measurement needs, so the threshold τ is dynamically adjusted and appropriately lowered to filter out the waypoint indexes that meet the conditions. The number of points selected here is set to 250. The results of screening measurement points are as follows Figure 3 shown.

[0204] Step 3:

[0205] Construct an Arctic Puffin optimization algorithm based on improved tabu search. The algorithm flow chart is as follows: Figure 4 As shown;

[0206] Set initial parameters and initialize the taboo list;

[0207] Using the K-Means clustering algorithm, all cities are divided into several clusters based on the Euclidean distance between cities, and each cluster is solved separately. The K-Means algorithm iteratively optimizes cluster centers and cluster members to minimize the sum of the distances between cities within a cluster. Mathematically, the objective function of the K-Means algorithm is:

[0208]

[0209] Where K is the number of clusters, C j represents the jth cluster, μ j It is cluster C j The center of mass, x i is the coordinate of the i-th city, ||x i -μ j || is the city point x i To cluster center μ j The Euclidean distance of .

[0210] A greedy initialization strategy is added to the early tabu search operation. To reduce the randomness of the initial solution, the greedy initialization process is repeated multiple times, each time selecting a different random starting city. Finally, from the multiple initial paths generated, the solution with the shortest path length is selected as the initial path of the tabu search algorithm.

[0211] Perform neighborhood search on the initial path, generate multiple candidate solutions, select the optimal solution, and complete an update of the optimal solution;

[0212] Check whether the update to the optimal solution is in the taboo list. If not, accept this solution as the optimal solution. If it is, further determine whether the pardon condition is met. If the pardon condition is met, accept this solution as the optimal solution. Otherwise, delete the solution and return to reselect the optimal solution.

[0213] If the taboo list is full, the earliest update to the optimal solution is removed first, and then this update is moved to the taboo list; if the taboo list is not full, this update is directly moved to the taboo list.

[0214] The purpose of the taboo list is to record the solutions that have been visited recently or certain specific update operations. Its purpose is to prevent the algorithm from repeatedly returning to the explored areas during the search process, thereby avoiding circular search and enabling the algorithm to jump out of the local optimal solution and explore a wider solution space.

[0215] The latest historical optimal solution finally obtained is sorted and mapped, and used to update the Arctic Puffin population, entering the iterative process of the Arctic Puffin Algorithm (APO algorithm).

[0216] Establish a sorting mapping between continuous space and discrete space: Let the discrete path be path={c0,c1,…,c n-1}, where c i represents the i-th visited city, and c i ∈{0,1,…,n-1}, n is the total number of cities. Define the mapping function Convert the discrete path into a continuous position vector pos, whose components are defined as:

[0217] pos[c i ]=i,i=0,1,…,n-1 (13)

[0218] The position vector retains the order information of the path, but is expressed in a way suitable for continuous optimization, providing the APO algorithm with an optimizable continuous vector, which enables the algorithm to inherit the global search power of the continuous space. Finally, when evaluating the path, the mapping function is defined The vector is restored to a legal arrangement according to its numerical size. This mapping method enables APO and TS to play a role in their respective applicable spaces while working together in the overall framework.

[0219] Considering the problem that all individuals in the original APO algorithm behave in the same way and lack quality adaptation, the fitness perception weighting factor FAAT is added to the behavior conversion factor B. i , giving each individual the ability to dynamically adjust its exploration or foraging tendency based on the quality of the current solution:

[0220]

[0221] where f i is the fitness value of the current individual, which is calculated by the objective function of the entire Arctic Puffin Optimization Algorithm based on Improved Tabu Search (APO-TS algorithm) stage (the objective function is to minimize the total path length); fbest is the fitness value of the best individual in the current population, which is dynamically updated as the iteration progresses; f mean It is the average value of the current population fitness, representing the overall level of the current search group, and is calculated once per round in the program; α is the fitness difference amplification coefficient, which controls the weight of the fitness difference in this factor.

[0222] If B is greater than parameter C, it enters the flight exploration phase, otherwise it enters the underwater foraging phase. Here, parameter C is set by yourself, and its size directly affects the balance between the algorithm's global search and local optimization;

[0223] In the first stage of flight exploration, the Lévy flight strategy and the speed coefficient V are first introduced according to formula (8) to help explore the optimal solution;

[0224]

[0225] The velocity coefficient V is defined as:

[0226] V=round(0.5*(0.05+rand))*η (17)

[0227] η~Normal(0,1) (18)

[0228] Here, we use the MATLAB function rand to define the velocity coefficient V. The function generates a random decimal in the interval [0, 1), scales and translates the result, and then uses the round function to round the result. η is a random variable with a standard normal distribution and a mean of 0 and a standard deviation of 1.

[0229] Indicates the position update of the i-th candidate solution in the t+1th iteration;

[0230] Indicates the position update of the i-th candidate solution in the t-th iteration;

[0231] It represents the position of a candidate solution randomly selected from the current population in the tth iteration. The candidate solution number is m, where m is a random integer ranging from 1 to N-1, excluding i.

[0232] L(D) is the Lévy flight step vector generated in D-dimensional space, corresponding to formula (27). L(D) is a D-dimensional vector, where each component is the step size step generated by formula (27).

[0233] In the second stage of flight exploration, the speed coefficient S is introduced to quickly adjust the individual position, which is recorded as the new solution

[0234]

[0235] The speed coefficient S is defined as:

[0236] S=tan((rand-0.5)*π) (20)

[0237] Here, the function in MATLAB is used to represent the definition of the speed coefficient S. rand generates a random decimal in the interval [0,1). After scaling and translating the result, the tan function is used to calculate the tangent value of the above result.

[0238] In the third stage of flight exploration, the best individuals in the first two stages are merged as new candidate solutions.

[0239]

[0240] sort represents a sorting operation, which sorts the merged candidate solution set from small to large according to the fitness value; new represents the sorted candidate solution set; It means selecting the first N individuals with the best fitness from new to form a new population.

[0241] In the first stage of underwater foraging, aggregate foraging, the weighted cooperation factor F is designed i To update the position, record it as the new solution

[0242]

[0243] In formula (24), L(D) is the flight step function generated by introducing the Lévy flight strategy. r1, r2, and r3 are three randomly selected individual indices, which are not equal to each other, that is, three different randomly selected individual indices, thus ensuring that three different individuals are randomly selected.

[0244] Weighted cooperation factor F i It is determined based on the comparison between the fitness value of individual i and the average fitness value of the population. i The mathematical expression is as follows:

[0245]

[0246] Note f mean is the average fitness value of all individuals at present, then f avg1 With f avg2 satisfy:

[0247] f avg1 =f mean +λ1·σ (26)

[0248] f avg2 =f mean +λ2·σ (27)

[0249] Where λ1 = -0.5, λ2 = 0.5, and σ is the global fitness standard deviation.

[0250] f avg1 Represents the lower bound of high-quality individuals, if f i ≤f avg1 , indicating that the individual is far from the optimal and needs to be F within a larger numerical range. i Take values ​​to enhance exploration; f avg2 Represents the upper bound of high-quality individuals, if f i ≥f avg2 , indicating that the individual has already been in the excellent ranks and needs to reduce disturbances and maintain stability.

[0251] L(D) in Equation (23) is the flight step length function generated by the Lévy flight strategy. In the global exploration phase, the Lévy flight strategy generates a step length that enables new individuals to make long-distance jumps in the search space, effectively escaping the local optimal trap and expanding the search range. In the local development phase, the Lévy flight strategy is used to adjust the step length, enabling new individuals to conduct a detailed search within the local area.

[0252] The formula for generating the Lévy flight step length is as follows:

[0253]

[0254] Among them, u and v are random variables that obey Gaussian distribution and satisfy:

[0255]

[0256] Where β is the characteristic index of the stable distribution and σ is the scaling factor of the Lévy flight, which is calculated as follows:

[0257]

[0258] The flight scaling factor σ controls the overall scale of the step sizes. Here, Γ(·) is the gamma function that ensures that the mathematical form of the step size distribution matches the physics of the Lévy flight, resulting in a reasonable search behavior for practical applications.

[0259] In the second stage of underwater foraging, the search is strengthened and the position is adjusted by the adaptive factor f, which is recorded as the new solution

[0260]

[0261] Where T is the total number of iterations.

[0262] In the third stage of underwater foraging, avoiding predators, the dual strategy is also used to update the position, which is recorded as the new solution

[0263]

[0264] where β i is a weighted disturbance factor, which is determined based on the comparison between the fitness value of individual i and the average fitness value of the population, β i The mathematical expression is as follows:

[0265]

[0266] and weighted cooperation factor F i The setting is similar to that in which individuals with poor fitness are given greater disturbance, while individuals with good fitness are mainly stable.

[0267] Finally, the best individuals in the three stages of underwater foraging are combined as new candidate solutions.

[0268]

[0269] Following the above steps, the Arctic Puffin optimization algorithm based on improved tabu search is used to solve the TSP path of the cluster center, obtaining a coarse optimization solution for the inter-cluster order. Finally, the optimal paths within each cluster are sequentially spliced ​​together according to the order of the cluster center TSP paths to form the overall path.

[0270] Step 4:

[0271] The planned path is smoothed using a quadratic B-spline curve. B-spline curves are a flexible and powerful type of spline, widely used in computer graphics, data fitting, and numerical analysis. They overcome some of the limitations of Bezier curves, such as local control and the complexity of curve segment splicing.

[0272] Since the smoothed path will deviate from the original path points and produce position errors, in order to reduce this error, the path points are interpolated before smoothing, so that the smoothed path can be more consistent with the original path.

[0273] The total number of cities is n, and after one interpolation process, 2n-1 control points are generated (the control point index ranges from 0 to 2n-2), that is, the control point set is {Q0, Q1, ..., Q 2n-2}.

[0274] Given a node vector {p0,p1,…,p mThe number of nodes is m+1 (node ​​vector indexes range from 0 to m). The number of nodes is related to the number of control points and the degree k of the B-spline curve, satisfying m+1=(2n-1)+k+1, that is, m+1=2n+k. Here, k is 2, so m=2n+2.

[0275] In summary, the formula of the quadratic B-spline curve is:

[0276]

[0277] Where C(p) represents a point on the quadratic B-spline curve, which is a function of parameter p. As p changes, C(p) moves along the curve. i,2 (p) represents the value of the ith quadratic B-spline basis function at parameter p, which determines the corresponding control point Q i The degree of influence on the curve point C(p). i Indicates the control points, which define the shape of the curve. In this case, i is the index of the control point, ranging from 0 to 2n-2.

[0278] The overall problem modeling idea is as follows Figure 5 The following diagrams represent the steps of selecting the measurement area, selecting the measurement points, path planning, and UAV flight. Considering the subsequent restoration of the antenna's far-field pattern, the altitude required for the UAV flight is the vertical distance h indicated in step 1 and (h + 0.1). For phase-free near-field measurements, data processing is performed using the amplitude information of the orthogonal polarization components of two parallel planes. A phase iteration algorithm is then used to restore the missing phase information based on the phase correlation between the two planes. This is then followed by the near-field to far-field transformation.

[0279] The paths before and after smoothing are as follows Figure 6 As shown in (a) and (b).

[0280] Step 5:

[0281] The method is deployed on the onboard computer of the UAV, and the UAV is controlled by the ROS robot operating system to perform path planning. The flight process is visualized using the Airsim simulation platform to complete the simulation verification work before the actual flight. Figure 7 shown.

[0282] Example 2

[0283] In this embodiment, the UAV antenna near-field measurement system is as follows: Figure 8As shown, the system includes a drone 1, a test probe 2, an antenna under test 3, a ground station 5, a remote control 6, and an RTK positioning module 7. The RTK positioning module receives signals from multiple satellites, including pseudorange and carrier phase observations, and also knows its own precise position coordinates. Based on the received satellite signals and the known position, it calculates the various errors incurred during satellite signal propagation and generates differential correction data. This differential correction data is then transmitted in real time to the rover on the drone via wireless communication. The rover receives both the satellite signals and the differential correction data sent by the base station, performs real-time comparison and calculations, eliminates most common errors, and determines the drone's precise position, thus achieving centimeter-level positioning accuracy.

[0284] In order to ensure the accuracy and reliability of the measurement data, it is necessary to accurately align the drone's position data with the timestamp, thereby achieving high-precision spatial positioning of the antenna's near-field electromagnetic field distribution, thereby improving the credibility and effectiveness of the antenna measurement results.

[0285] In summary, the method of using a drone to perform waypoint screening and path planning for the antenna near-field measurement area in the present invention can efficiently screen measurement points and perform path planning, complete the antenna near-field measurement task while satisfying constraints, and significantly improve task efficiency.

[0286] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A waypoint screening and path planning method for UAV antenna near-field measurement, characterized in that: The method includes the following: Control the size of the vertical plane measurement area of ​​the antenna near-field measurement by setting the maximum confidence angle and measurement distance; A source point p is randomly generated in the area of ​​the antenna under test s , generate measurement point p in the measurement area above the antenna m ; The electromagnetic propagation matrix B is constructed according to formula (2): Among them, d m,s is the measurement point p m With the source point p s The Euclidean distance between them; k0 is the wave number, j is the imaginary unit; B m,s is an element in the electromagnetic propagation matrix; is the basic spherical wave propagation term; is the phase correction factor: Among them, f θ (x m ,y m ) is a residual neural network with learnable parameters, θ is a learnable parameter of the neural network, which is used to reduce the phase residual; is the wavefront curvature correction factor; h represents the height difference between the measurement point and the source point; r is the radial distance between the measurement point and the source point; The input of the residual neural network with learnable parameters is the two-dimensional plane coordinates (x m ,y m ), the output is the phase correction of the corresponding point in the x, y, and z directions The loss function for training the residual neural network is: Where N is the number of training samples, φ real,i is the phase actually measured at the i-th measurement point in a certain direction; (x i ,y i ) is the coordinate of the i-th measurement point; φ model,i The propagation model is used for the i-th measurement point in this direction. Calculated theoretical phase; Perform QR decomposition on the electromagnetic propagation matrix B. QR decomposition transforms the matrix B into T Decompose into an orthogonal matrix Q and an upper triangular matrix R, and calculate the absolute value of the diagonal elements of the upper triangular matrix R; Perform QR decomposition on the electromagnetic propagation matrix B. QR decomposition transforms the matrix B into T Decompose into an orthogonal matrix Q and an upper triangular matrix R, calculate the absolute value of the diagonal elements of the upper triangular matrix R, set the dynamic threshold τ and the lower limit num_waypoints of the number of measurement points required for actual antenna measurement, and obtain the key waypoint when the ratio of the absolute value of the last diagonal element to the first diagonal element of the upper triangular matrix is ​​not less than the dynamic threshold and the number of screened waypoints is not less than num_waypoints; The drone path is planned based on the obtained key waypoints.

2. The method according to claim 1, characterized in that During training, the residual neural network with learnable parameters uses data from all measurement points of the antenna as training samples, and each sample contains three-dimensional coordinates, phase, and amplitude data of a measurement point.

3. The method according to claim 1, characterized in that The path planning adopts the improved tabu search-based Arctic Puffin optimization algorithm and the K-Means clustering algorithm. All cities are divided into several city clusters based on the Euclidean distance between cities. Each city cluster is solved separately. The K-Means algorithm iteratively optimizes the cluster center and cluster members to minimize the total distance between cities in the cluster. That is, the improved tabu search-based Arctic Puffin optimization algorithm is run on each city cluster. The specific process is: Set initial parameters and initialize the taboo list; Use a greedy strategy to generate an initial solution for the tabu search algorithm. Repeat the greedy initialization process multiple times, selecting a different random starting city each time. Finally, from the multiple initial paths generated, the solution with the shortest path length is selected as the initial path of the tabu search algorithm. A neighborhood search is performed on the initial path to generate multiple candidate solutions. The optimal solution is selected and a tabu search algorithm is executed. The latest historical optimal solution is sorted and mapped to update the Arctic puffin population and enter the iteration process of the Arctic puffin algorithm. The Arctic puffin algorithm: Establish a sorting mapping between continuous space and discrete space: Let the discrete path of discrete cities be path={c0,c1,…,c n-1 }, where c i represents the i-th visited city, and i∈{0,1,…,n-1}, n is the total number of cities; define the mapping function Convert the discrete path into a continuous position vector pos, whose components pos[c i ] is defined as: pos[c i ]=i,i=0,1,…,n-1 (12) This continuous position vector pos preserves the sequential information of the path, but is represented in a way suitable for continuous optimization; When evaluating the path, define the mapping function Restore the vector to a legal arrangement according to its numerical size; The Arctic puffin population is updated after sorting and mapping the historical optimal solution of tabu search. Individuals in the Arctic puffin population dynamically adjust their exploration or foraging tendencies according to the behavior conversion factor B. The expression of the behavior conversion factor B is formula (13); Among them, f i is the fitness value of the current individual, which is calculated by minimizing the total path length; f best is the fitness value of the best individual in the current population; f mean is the average value of the current population fitness, representing the overall level of the current search group, and is calculated once per round in the program; α is the fitness difference amplification coefficient; FAAT i is the fitness perception weighting factor If B is greater than parameter C, it enters the flight exploration phase, otherwise it enters the underwater foraging phase; The Arctic Puffin optimization algorithm based on improved tabu search solves the TSP path of the cluster center point and obtains the rough optimization solution of the inter-cluster order. Finally, according to the order of the cluster center TSP path, the optimal paths within each cluster are spliced ​​in sequence to form an overall path and obtain the optimal path.

4. The method according to claim 3, characterized in that The optimal path output by the Arctic Puffin optimization algorithm based on improved tabu search is smoothed using piecewise uniform B-spline curves. The path is divided into multiple segments, each segment is fitted using a uniform B-spline curve, and interpolation is performed at the path turns.

5. The method according to claim 3, characterized in that In the Arctic Puffin algorithm, the weighted cooperation factor F is introduced in the first and third stages of underwater foraging. i , weighted disturbance factor β i To update the location, In the first stage, the aggregation and foraging position update formula is (23): In formula (23), L(D) is the flight step function generated by introducing the Lévy flight strategy; D is the spatial dimension; r1, r2, and r3 are three randomly selected individual indices, and the three are not equal to each other; Indicates the update of the aggregation foraging position of the i-th candidate solution in the t+1th iteration; Indicates the position update of the r1th candidate solution in the tth iteration; Indicates the position update of the r2th candidate solution in the tth iteration; Indicates the position update of the r3th candidate solution in the tth iteration; Weighted cooperation factor F i The mathematical expression is: Note f mean is the average fitness value of all individuals at present, then f avg1 With f avg2 satisfy: f avg1 =f mean +λ1·σ (25) f avg2 =f mean +λ2·σ (26)where λ1=-0.5, λ2=0.5, σ is the global fitness standard deviation; In the third stage, the update formula for avoiding predators is: in, is the predator-avoiding position update of the i-th candidate solution in the t+1th iteration; Indicates the position update of the i-th candidate solution in the t-th iteration; β i is the weighted disturbance factor, β i The mathematical expression is:

6. A computer-readable storage medium, wherein a computer program is stored in the storage medium, and wherein the computer program is adapted to execute the method according to any one of claims 1 to 5 when loaded by a computer.

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