Three-dimensional path planning method, device, equipment and storage medium

Abstract

This invention discloses a three-dimensional path planning method, apparatus, device, and storage medium, relating to the field of swarm intelligence optimization algorithm technology. The method includes: acquiring a UAV flight area map and constructing a path planning objective function; initializing a population and determining target individuals through quasi-backward learning combined with chaotic mapping and boundary awareness strategies; determining a nonlinear cosine convergence factor and updating the position of the target individuals to obtain candidate positions; applying flight perturbations to the candidate positions and resetting the boundaries to obtain updated individual positions; maintaining the population containing the updated individual positions and determining iterative target individuals based on the path planning objective function; and generating a three-dimensional flight path through path interpolation based on the iterative target individuals. This effectively improves the quality of the initial population and the convergence speed, while enhancing global optimization capabilities and suppressing local optimum traps through flight perturbations and boundary resetting.

Description

Technical Field

[0001] This invention relates to the field of swarm intelligence optimization algorithm technology, and in particular to a three-dimensional path planning method, apparatus, device and storage medium. Background Technology

[0002] With the widespread application of drones in complex three-dimensional scenarios such as power line inspection, emergency rescue, and logistics delivery, how to quickly search for the least costly feasible flight path under multiple constraints such as obstacle avoidance, safe flight altitude, and threat area avoidance has become a key requirement that needs to be addressed in the field of drone autonomous navigation.

[0003] Existing whale optimization algorithms employ uniform random initialization, resulting in low initial population quality and slow convergence. Furthermore, the linearly decreasing convergence factor leads to an overly uniform transition between global exploration and local development, resulting in insufficient early global exploration. Simultaneously, they are prone to getting trapped in local optima in high-dimensional complex terrain path planning, leading to poor result stability. In addition, existing improvement strategies are mostly isolated applications of single methods such as chaotic mapping, back learning, or flight perturbation, lacking systematic combination design and ablation verification for 3D path planning scenarios. This makes it difficult to collaboratively address the issues of initial population quality, convergence speed, and local optimum traps.

[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The main objective of this invention is to provide a three-dimensional path planning method, apparatus, device, and storage medium, aiming to solve the technical problem of how to improve the initial population quality, convergence speed, and global optimization capability of the whale optimization algorithm in three-dimensional path planning, and suppress local optimum traps.

[0006] To achieve the above objectives, the present invention provides a three-dimensional path planning method, which includes the following steps: Obtain a map of the UAV's flight area and construct a path planning objective function based on the flight area map; The population is initialized by combining quasi-backward learning with chaotic mapping and boundary awareness strategies, and the target individual is determined according to the objective function of the path planning. Determine the nonlinear cosine convergence factor for the current iteration, and update the position based on the nonlinear cosine convergence factor and the target individual to obtain candidate positions; The candidate positions are subjected to flight perturbations and the boundaries are reset to obtain the updated individual positions; The current population containing the updated individual positions is maintained, and the fitness of the maintained population is calculated according to the path planning objective function to determine the iterative target individual; Based on the iterative target individual, path interpolation is performed to generate a three-dimensional flight path.

[0007] In one embodiment, the step of initializing the population through quasi-backward learning combined with chaotic mapping and boundary-aware strategies, and determining the target individual according to the path planning objective function, includes: Original candidate solutions are generated based on chaotic mapping, wherein the control parameters of the chaotic mapping are preset chaotic parameter values, and the number of iterations is greater than the preset number of chaotic entries; Quasi-backward learning is performed on the original candidate solutions to obtain quasi-backward solutions; The original candidate solutions and the quasi-reverse solutions are merged to obtain merged candidate solutions, and the merged candidate solutions are filtered according to the path planning objective function to obtain an initial set of individuals; Boundary-aware individuals are sampled from the boundary region of the search space, and these boundary-aware individuals are merged with the initial set of individuals to obtain an initial population. The fitness of the initial population is calculated based on the path planning objective function to determine the target individual.

[0008] In one embodiment, the step of determining the nonlinear cosine convergence factor of the current iteration and updating the position based on the nonlinear cosine convergence factor and the target individual to obtain candidate positions includes: The nonlinear cosine convergence factor is determined based on the current iteration number and the maximum iteration number. The convergence coefficient is determined based on the nonlinear cosine convergence factor. Select an individual to be updated from the population, and when the convergence coefficient satisfies the preset shrinkage condition, update the first candidate position according to the distance between the target individual and the individual to be updated; When the convergence coefficient satisfies the preset exploration conditions, a random individual is selected from the population, and the second candidate position is updated according to the distance between the random individual and the individual to be updated. Generate a random number for behavior selection, and when the random number for behavior selection meets the preset attack conditions, perform a spiral attack update based on the distance between the target individual and the individual to be updated to obtain a third candidate position; Based on the convergence coefficient and the behavior, a random number is selected to determine the target candidate position from the first candidate position, the second candidate position, and the third candidate position. In one embodiment, the step of applying flight perturbations to the candidate locations and resetting the boundaries to obtain updated individual locations includes: The flight disturbance step size is generated based on the ratio of two normally distributed random numbers; The flight disturbance step size is superimposed on the candidate position to obtain the disturbed candidate position; The candidate positions after the disturbance are judged to be out of bounds; When the candidate position after the perturbation exceeds the boundary of the search space, the out-of-bounds dimension is reset to a random value within the boundary to obtain the updated individual position.

[0009] In one embodiment, the step of maintaining the current population containing the updated individual positions and calculating the fitness of the maintained population according to the path planning objective function to determine the iterative target individual includes: The current target individual is determined from the current population, which includes the updated individual location. Apply periodic perturbations to the current target individual to obtain a refined target individual; Individuals with poor fitness are eliminated from the current population to obtain the remaining population; The remaining population is merged with the newly generated individuals to obtain the maintained population. The fitness of the maintained population is calculated based on the path planning objective function to determine the target individual for iteration.

[0010] In one embodiment, the step of acquiring a UAV flight area map and constructing a path planning objective function based on the flight area map includes: Acquire terrain elevation information and threat area location information from the drone flight area map; A three-dimensional simulation map is constructed based on the terrain elevation information and the location information of the threat area; Determine the starting and ending points on the three-dimensional simulation map; The path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost are determined based on the starting point and the ending point. The path planning objective function is obtained by weighted summing of the path length cost, the threat area cost, the terrain collision cost, the path smoothing cost, the boundary constraint cost, the progress guidance cost, the safety height cost, and the corridor constraint cost.

[0011] In one embodiment, the step of generating a three-dimensional flight path by performing path interpolation based on the iterative target individual includes: Extract the coordinates of the path control points in the target individual being iterated; Cubic spline interpolation is performed on the coordinates of the path control points to obtain a smooth trajectory curve; Determine whether the interpolation points on the smooth trajectory curve meet the preset safety height conditions and preset threat avoidance conditions; When the interpolation point satisfies the preset safe altitude condition and the preset threat avoidance condition, the smooth trajectory curve is determined as the three-dimensional flight path.

[0012] Furthermore, to achieve the above objectives, the present invention also proposes a three-dimensional path planning device for unmanned aerial vehicles (UAVs), the device comprising: The objective function construction module is used to obtain a map of the UAV's flight area and construct a path planning objective function based on the flight area map. The population initialization module is used to initialize the population by combining quasi-backward learning with chaotic mapping and boundary awareness strategies, and to determine the target individual according to the path planning objective function. The iterative optimization module is used to determine the nonlinear cosine convergence factor of the current iteration, and update the position of the target individual based on the nonlinear cosine convergence factor to obtain candidate positions; apply flight perturbation to the candidate positions and reset the boundaries to obtain updated individual positions; maintain the current population containing the updated individual positions, and calculate the fitness of the maintained population based on the path planning objective function to determine the iterative target individual; The path generation module is used to perform path interpolation based on the iterative target individual to generate a three-dimensional flight path.

[0013] Furthermore, to achieve the above objectives, the present invention also proposes a three-dimensional path planning device, the device comprising: a memory, a processor, and a three-dimensional path planning program stored in the memory and executable on the processor, the three-dimensional path planning program being configured to implement the steps of the three-dimensional path planning method as described above.

[0014] Furthermore, to achieve the above objectives, the present invention also proposes a storage medium storing a three-dimensional path planning program, which, when executed by a processor, implements the steps of the three-dimensional path planning method described above.

[0015] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the three-dimensional path planning method described above.

[0016] One or more technical solutions proposed in this application have at least the following technical effects: By initializing the population using quasi-backward learning combined with chaotic mapping and boundary awareness strategies, the quality of the initial population is significantly improved and the convergence speed is accelerated. The introduction of a nonlinear cosine convergence factor allows the algorithm to retain sufficient global exploration capability in the early stages of iteration and accelerate precise local development in the later stages, effectively balancing exploration and development. The combination of flight perturbation and boundary reset mechanisms endows the algorithm with long-distance random jump capability, effectively escaping local optima traps. A population maintenance mechanism periodically refines the target solution and restores population diversity during iteration, further improving convergence accuracy and result stability. Finally, smooth and continuous 3D flight paths are generated through path interpolation, ensuring excellent smoothness and engineering feasibility under multiple constraints. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating an embodiment of the three-dimensional path planning method of this application. Figure 2 The fitness convergence curve provided for Embodiment 1 of the three-dimensional path planning method of this application; Figure 3 This is a flowchart illustrating Embodiment 2 of the three-dimensional path planning method of this application. Figure 4 This is a schematic diagram of the module structure of the three-dimensional path planning device according to an embodiment of this application; Figure 5 This is a schematic diagram of the device structure of the hardware operating environment involved in the three-dimensional path planning method in the embodiments of this application.

[0020] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0022] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0023] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device or three-dimensional path planning device capable of performing the above functions. The following description uses a three-dimensional path planning device as an example to illustrate this embodiment and the subsequent embodiments.

[0024] Based on this, embodiments of this application provide a three-dimensional path planning method, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the three-dimensional path planning method of this application.

[0025] In this embodiment, the three-dimensional path planning method includes steps S10 to S60: Step S10: Obtain the UAV flight area map and construct the path planning objective function based on the flight area map; It should be understood that obtaining a map of the UAV flight area involves creating a 3D model of the flight area environment, setting spherical threat areas and terrain elevation information in the map, and constructing a 3D simulation map for algorithm optimization.

[0026] It should be noted that a UAV flight area map refers to a spatial data set containing information on the terrain, topography, and obstacle distribution of the flight area. This map provides basic geographic information support for subsequent path planning. Furthermore, the path planning objective function is a mathematical expression used to comprehensively evaluate the quality of a path; it is a single evaluation index obtained by weighted summation of multiple cost terms.

[0027] Understandably, compared to existing technologies, the 3D path planning method provided in this embodiment first acquires a map of the UAV's flight area and constructs an objective function for path planning of the moving target on that map. It then uses QOBL quasi-backward learning combined with a boundary awareness strategy to initialize the initial positions of individual whales in the population, thereby significantly improving the initial population quality and increasing the algorithm's convergence speed. Based on the objective function, it calculates the initial optimal fitness value and the optimal individual whale position, and guides individual position updates based on a nonlinear cosine convergence factor, effectively balancing global exploration and local development. This invention employs flight disturbance, periodic local refinement, and population diversity restoration mechanisms to determine the updated optimal fitness value and optimal whale individual position. Based on the updated optimal whale individual position, a three-dimensional flight path is generated through spline interpolation to determine the optimal path planning result. Building upon the whale optimization algorithm, this invention significantly improves the initial population quality by adopting a QOBL quasi-backward learning strategy. The introduction of a nonlinear cosine convergence factor allows for thorough global exploration in the early stages and precise local development in the later stages. Combined with multiple improvement mechanisms, it effectively avoids getting trapped in local optima, thereby improving the efficiency and quality of path planning in three-dimensional space.

[0028] It should be noted that this invention applies to path planning in three-dimensional space. It is understood that this invention is also applicable to any scenario requiring path planning; simply replace the objective function according to the specific scenario.

[0029] In one feasible implementation, step S10 includes steps A11 to A15: Step A11: Obtain terrain elevation information and threat area location information from the drone flight area map; It should be noted that terrain elevation information refers to data describing the changes in altitude at various points on the Earth's surface, that is, three-dimensional terrain height data reflecting the undulations of the ground. Furthermore, threat area location information refers to the spatial coordinates and extent of hazardous areas that need to be avoided within the flight area, i.e., the location information of areas that pose a potential threat to the flight safety of UAVs.

[0030] Understandably, step A11 involves acquiring terrain elevation information and threat area location information from the UAV flight area map, i.e., collecting surface height data and hazardous area distribution data of the flight area to provide raw input for constructing a 3D simulation map.

[0031] Step A12: Construct a 3D simulation map based on terrain elevation information and the location information of the threatened area; It should be noted that a 3D simulation map refers to a virtual 3D spatial model built based on real geographic data for algorithm simulation, that is, a computable environment that includes terrain and threat areas reconstructed in a computer.

[0032] Understandably, step A12 involves constructing a three-dimensional simulation map based on terrain elevation information and the location information of threat areas. In other words, it uses the acquired surface elevation data and dangerous area distribution data to establish a three-dimensional environment model in virtual space that can be used by the path planning algorithm.

[0033] Step A13: Determine the starting and ending points on the 3D simulation map; It should be noted that the starting point location refers to the initial spatial coordinates of the UAV flight mission, that is, the geographical location from which the UAV departs during path planning. Conversely, the ending point location refers to the destination spatial coordinates of the UAV flight mission, that is, the geographical location where the UAV needs to reach during path planning.

[0034] Understandably, step A13 involves determining the starting and ending points on the 3D simulation map, that is, marking the starting and ending points of the drone's flight in the constructed virtual 3D environment.

[0035] Step A14: Determine the path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost based on the starting and ending locations; It should be noted that path length cost refers to the cost indicator that measures the total length of the planned path, i.e., the path length reflected by the cumulative distances between control points along the path. Threat area cost refers to the penalty indicator that measures the proximity of the path to threat areas, i.e., the safety risk cost incurred when the path intrudes into or approaches dangerous areas. Furthermore, terrain collision cost refers to the cost indicator that measures the distance between the path and the terrain surface, i.e., the risk cost of colliding with the terrain when the flight altitude is below safety requirements. Additionally, path smoothing cost refers to the cost indicator that measures the degree of curvature change of the path, i.e., the flight stability cost reflected by the drastic changes in the path's turning angle and direction. Furthermore, boundary constraint cost refers to the penalty indicator that measures the degree to which the path exceeds the flight area boundary, i.e., the violation cost incurred when the path crosses the boundary. Additionally, progress guidance cost refers to the guidance indicator that measures the progress of the path towards the destination, i.e., the effective progress cost of the path approaching the destination in the forward direction. Finally, safe altitude cost refers to the cost indicator that measures the safety margin of the path's flight altitude, i.e., the risk cost when the altitude difference between the path points and the terrain surface is insufficient. Additionally, corridor constraint cost refers to the penalty metric that measures the degree to which a path deviates from the predetermined flight corridor, i.e., the constraint violation cost incurred when the path exceeds the permitted flight channel range.

[0036] Understandably, step A14 involves determining the path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safe altitude cost, and corridor constraint cost based on the starting and ending locations. In other words, it calculates the various costs of the path from eight dimensions: path length, threat avoidance, terrain safety, flight stability, area boundaries, direction of travel, altitude margin, and corridor range.

[0037] Step A15: Weight the path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost to obtain the path planning objective function.

[0038] It should be noted that weighted summation is a calculation method that involves assigning different weights to multiple different indicators according to their respective importance and then summing them up. In other words, it is a process of distinguishing the priority of each indicator by weight and combining them into a single value.

[0039] Understandably, step A15 involves a weighted summation of the path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost to obtain the path planning objective function. This means that the eight cost indicators are superimposed according to their respective weights to form a single objective value that comprehensively evaluates the path's merits. In this embodiment, the weight coefficient for path length cost is 8, for threat area cost it is 35, for terrain collision cost it is 30, for path smoothing cost it is 18, for boundary constraint cost it is 12, for progress guidance cost it is 8, for safety height cost it is 6, and for corridor constraint cost it is 10.

[0040] By constructing a path planning objective function that includes multiple constraints, the overall quality of a three-dimensional flight path can be comprehensively evaluated, achieving a balance between path length, safety, smoothness, and constraint satisfaction.

[0041] Step S20: Initialize the population by combining quasi-backward learning with chaotic mapping and boundary awareness strategies, and determine the target individual based on the path planning objective function; It should be noted that quasi-backward learning is an optimization strategy that improves the initial quality of the population by generating reverse candidate solutions to the original solution; that is, it is a method of generating new solutions by interpolation between the original solution and its symmetric point about the center of the search space. Additionally, chaotic mapping is a mathematical method that utilizes the ergodicity and randomness of chaotic systems to generate uniformly distributed sequences; that is, it generates pseudo-random sequences that are non-repeating and uniformly covered within the search space through nonlinear iteration. Furthermore, boundary-aware strategies are initialization methods that force sampling in the boundary regions of the search space; that is, a sampling strategy that enhances the population's ability to cover the boundary regions by generating individuals near the boundary. Additionally, the population refers to the set of multiple candidate solutions in an optimization algorithm; that is, the total number of potential path schemes maintained by the algorithm simultaneously. Furthermore, the target individual refers to the candidate solution with the best fitness in the population; that is, the path scheme individual with the minimum overall path cost in the current population.

[0042] Understandably, step S20 initializes the population by combining quasi-backward learning with chaotic mapping and boundary awareness strategies, and determines target individuals based on the path planning objective function. Specifically, it first uses chaotic mapping to generate initial candidate solutions, then uses quasi-backward learning to generate backward solutions and select high-quality individuals, while simultaneously supplementing the initial population from the boundary region. Finally, it calculates the fitness to determine the current optimal path scheme. In this embodiment, the control parameter for chaotic mapping is 4, the number of iterations is greater than 5, the high-quality individuals selected by quasi-backward learning account for 80% of the population, and the boundary-aware individuals account for 20%.

[0043] By initializing the population using quasi-backward learning combined with chaotic mapping and boundary awareness strategies, the quality and diversity of the initial population are significantly improved, and the convergence speed of the algorithm is accelerated.

[0044] It should be understood that, based on the Logistic chaotic mapping ( )produce The initial candidate solutions are given by the chaotic mapping formula: Generated according to the quasi-reverse learning formula A quasi-reverse solution; Merge 2 The candidate solutions are sorted in ascending order of fitness, and the top [number] solutions are selected. The individuals with the best quality are selected as the QOBL portion (accounting for 80% of the population). 20% of the boundary-aware individuals were added from the boundary region of the search space and merged with the QOBL portion to form a complete initial population; The quasi-reverse learning formula is:

[0045] in Let the j-th dimension be the center of the search space. The numbers are independent and uniformly random numbers in each dimension. , Let be the lower and upper bounds of the j-th dimension variable, respectively. The j-th dimension component of the original candidate solution; the boundary-aware individual is sampled according to the following formula: when hour, ;when hour, ,in .

[0046] In the specific implementation, a QOBL quasi-backward learning combined with a boundary-aware strategy is used to initialize the population, including: Based on Logistic chaotic mapping One original candidate solution ; Generate a corresponding quasi-inverse solution for each original solution. Merge 2N candidate solutions; Sort by fitness in ascending order 2 1 candidate solution, before screening The highest quality individual is selected as the QOBL component; 0.2 is added from the boundary region of the search space. A boundary-aware individual, combined with the QOBL portion, constitutes the complete initial population. ; Calculate the fitness values ​​of all individuals to determine the initial optimal fitness value and the optimal location of the whale individual.

[0047] Step S30: Determine the nonlinear cosine convergence factor of the current iteration, and update the position based on the nonlinear cosine convergence factor and the target individual to obtain the candidate position; It should be noted that the nonlinear cosine convergence factor refers to a parameter used to control the balance between the exploration and development of the algorithm, calculated through the nonlinear decrease of the cosine function. Specifically, it is a convergence control value that changes with the number of iterations, decreasing slowly in the early stages and contracting sharply in the later stages. Additionally, the candidate position refers to the intermediate position to be further perturbed after position update calculations, i.e., the coordinates of the preliminary path scheme determined in this iteration.

[0048] It should be understood that the formula for the nonlinear cosine convergence factor is: ,in This represents the current iteration number. The maximum number of iterations; the nonlinear cosine convergence factor decreases linearly compared to the original WOA method. In the early stages of iteration The value decreases slowly, then contracts sharply in the later stages of iteration, effectively balancing the relationship between global exploration and local development.

[0049] In one feasible implementation, step S30 includes steps A21 to A26: Step A21: Determine the nonlinear cosine convergence factor based on the current iteration number and the maximum iteration number; It should be noted that the current iteration count refers to the number of iterations completed during the algorithm's operation, i.e., the generation at which the position is updated. Conversely, the maximum number of iterations refers to the maximum number of generations the algorithm is allowed to run, i.e., the total number of iterations the algorithm is permitted to run.

[0050] Understandably, step A21 determines the nonlinear cosine convergence factor based on the current iteration number and the maximum iteration number. That is, the convergence control value corresponding to the current algebra is calculated by using the cosine function. This value decreases slowly in the early stage of the iteration to preserve the global exploration capability, and shrinks sharply in the later stage to accelerate local development.

[0051] Step A22: Determine the convergence coefficients based on the nonlinear cosine convergence factor; It should be noted that the convergence coefficient is a parameter used to control the position update amplitude, determined based on the nonlinear cosine convergence factor, that is, the scaling factor that determines whether an individual moves closer to or further away from the target individual.

[0052] Understandably, step A22 determines the convergence coefficient based on the nonlinear cosine convergence factor, that is, the coefficient controlling the individual's step size is derived from the convergence factor. This coefficient changes dynamically with the iteration process to balance exploration and development.

[0053] In the specific implementation, a nonlinear cosine convergence factor is used to guide the position update of individual whales. The original WOA convergence factor decreases linearly. The initial exploration was insufficient. This invention changes the convergence factor to a cosine nonlinear decreasing one, as shown in equation (3). For example, when... When = 0.3, the cosine factor linear factor It retains more comprehensive global exploration capabilities; in the later stages The value shrinks sharply, accelerating precise local development and effectively balancing the relationship between exploration and development.

[0054] Step A23: Select individuals to be updated from the population, and update the first candidate position based on the distance between the target individual and the individual to be updated when the convergence coefficient meets the preset shrinkage condition; It should be noted that the "individual to be updated" refers to the candidate solutions in the population that currently require position adjustment, i.e., the path schemes that will be optimized and updated in this iteration. Additionally, the preset contraction condition refers to the criterion for triggering the contraction and encirclement behavior, i.e., the local development condition executed when the absolute value of the convergence coefficient is less than a preset threshold. Furthermore, the first candidate position refers to the contraction and encirclement update position calculated based on the distance between the target individual and the individual to be updated, i.e., the candidate path scheme that moves closer to the current optimal solution.

[0055] Understandably, step A23 involves selecting individuals to be updated from the population, and updating the first candidate position based on the distance between the target individual and the individual to be updated when the convergence coefficient meets the preset shrinkage condition. That is, when the algorithm is in the local development stage, it makes the individual move closer to the current optimal path scheme.

[0056] Step A24: When the convergence coefficient meets the preset exploration conditions, select a random individual from the population and update the second candidate position according to the distance between the random individual and the individual to be updated; It should be noted that the preset exploration conditions refer to the criteria for triggering random walk behavior, i.e., the global exploration conditions executed when the absolute value of the convergence coefficient is greater than or equal to a preset threshold. Additionally, a random individual refers to a candidate solution randomly selected from the population to guide the position update; that is, an individual with any path scheme unrelated to the individual to be updated. Furthermore, the second candidate position refers to the random walk update position calculated based on the distance between the random individual and the individual to be updated; that is, a candidate path scheme moving closer to the random individual.

[0057] Understandably, step A24 involves selecting a random individual from the population when the convergence coefficient meets the preset exploration conditions, and updating the second candidate position based on the distance between the random individual and the individual to be updated. That is, when the algorithm is in the global exploration phase, the individual is moved to the randomly selected path scheme to expand the search range.

[0058] Step A25: Generate a random number for behavior selection, and when the random number for behavior selection meets the preset attack conditions, perform a spiral attack update based on the distance between the target individual and the individual to be updated to obtain the third candidate position; It should be noted that the behavior selection random number refers to the random value used to determine whether to adopt a contraction encirclement or a spiral attack behavior; that is, a uniformly distributed random number between 0 and 1. Furthermore, the preset attack condition refers to the criterion for triggering the spiral attack behavior; that is, the spiral update condition executed when the behavior selection random number is greater than or equal to a preset probability threshold. Further, the spiral attack update refers to the spiral position update mechanism simulating the predatory behavior of humpback whales in bubble nets; that is, the position adjustment method by which an individual approaches the target individual along a logarithmic spiral curve. Additionally, the third candidate position refers to the spiral update position calculated based on the spiral attack mechanism; that is, the candidate path schemes that approach the optimal solution along the spiral trajectory.

[0059] Understandably, step A25 generates a random number for behavior selection, and when the random number for behavior selection meets the preset attack conditions, a spiral attack is performed to update the target individual based on the distance between the individual to be updated, resulting in a third candidate position. That is, when the random judgment value meets the attack probability, the individual moves closer to the current optimal path along the spiral trajectory.

[0060] Step A26: Select random numbers based on the convergence coefficient and behavior to determine the target candidate position from the first candidate position, the second candidate position, and the third candidate position.

[0061] It should be noted that the target candidate position refers to the position finally determined from the three candidate positions for the next perturbation, that is, the position update result determined after behavior selection in this round.

[0062] Understandably, step A26 involves selecting random numbers based on the convergence coefficient and behavior, determining the target candidate position from the first, second, and third candidate positions, that is, selecting the final position to update the output based on the current iteration state from three update results: shrinking encirclement, random walk, and spiral attack.

[0063] By guiding the dynamic switching of three position update mechanisms through a nonlinear cosine convergence factor, the algorithm effectively balances global exploration and local development, and avoids premature convergence.

[0064] In the specific implementation, a periodic local refinement and population diversity restoration mechanism is introduced. Every 10 generations, an adaptive Gaussian perturbation is applied to the current global optimal solution (the perturbation amplitude decreases linearly with the iteration progress) to achieve a fine search of the neighborhood of the optimal solution; every 15 generations, the worst 10% of individuals are eliminated and replaced with new individuals from a chaotic elite mixture.

[0065] in, To reserve a proportion for the elite This is the current globally optimal solution. The random positions generated based on the Logistic chaotic mapping restore population diversity while preserving elite information, thus preventing the algorithm from converging prematurely to a local optimum.

[0066] Step S40: Apply flight perturbation to the candidate positions and reset the boundaries to obtain the updated individual positions; It should be noted that flight perturbation refers to a random jump operation applied to candidate positions based on a heavy-tailed distribution with a random step size; this is a random perturbation mechanism used to help the algorithm escape local optima. Boundary reset refers to the process of reassigning individual coordinates that are outside the search space to random values ​​within the valid range; this is a correction mechanism to ensure that individuals remain within the valid search range. Furthermore, the updated individual position refers to the final individual coordinates determined after flight perturbation and boundary reset, i.e., the final position update result within the valid search space.

[0067] It should be understood that, Flight disturbances are generated using the Mantegna algorithm, with the step size formula as follows: ,in , , For hyperparameters, Calculated using the Mantegna formula; the perturbation step size is adaptively matched with the difference between the current individual position and the global optimal position.

[0068] In one feasible implementation, step S40 includes steps A31 to A34: Step A31: Generate the flight disturbance step size based on the ratio of two normally distributed random numbers; It should be noted that a normally distributed random number refers to a random sample value that follows a Gaussian distribution, that is, a continuous random variable whose values ​​are symmetrically distributed around its mean. Furthermore, the flight perturbation step size refers to the random movement distance superimposed on the candidate position, that is, the random jump amplitude used to escape local optima. Further, the distribution index is a parameter that controls the distribution shape of the flight perturbation step size, that is, the characteristic index that determines the thickness of the tail of the random step size probability density function. Additionally, the preset distribution index value refers to a pre-set specific value of the distribution index, which is set to 1.5 in this embodiment to balance the probability of large and small step sizes.

[0069] Understandably, step A31 generates the flight disturbance step size based on the ratio of two normally distributed random numbers, where the distribution index is a preset distribution index value, i.e., a random step size with heavy-tailed characteristics is calculated by the ratio of two Gaussian distributed random variables. In this embodiment, the preset distribution index value is 1.5.

[0070] Step A32: Superimpose the flight disturbance step size onto the candidate position to obtain the disturbed candidate position; It should be noted that the candidate position after perturbation refers to the middle position after superimposing the flight perturbation step size, that is, the candidate path scheme after random jumps but before boundary checks.

[0071] Understandably, step A32 involves superimposing the flight disturbance step size onto the candidate position to obtain the disturbed candidate position, which means adding the generated random jump distance to the target candidate position to form a new intermediate position.

[0072] Step A33: Perform boundary check on the disturbed candidate positions; It should be noted that boundary judgment refers to the judgment operation that checks whether the position of an individual exceeds the allowed range of the search space, that is, the review process that verifies whether the coordinates of each dimension of the candidate path solution are within the legal boundary.

[0073] Understandably, step A33 is to perform an out-of-bounds judgment on the candidate positions after perturbation, that is, to check whether the positions after random perturbation exceed the legal search range defined by the 3D simulation map.

[0074] Step A34: When the perturbed candidate position exceeds the boundary of the search space, reset the out-of-bounds dimension to a random value within the boundary to obtain the updated individual position.

[0075] It should be noted that the search space boundary refers to the spatial extent within which the optimization algorithm allows individuals to exist; that is, the minimum and maximum value boundaries defined in each dimension of the 3D simulation map. Additionally, the random value within the boundary refers to a reset value randomly generated within the legal range of the search space, i.e., a compliant random coordinate used to replace out-of-bounds dimensions.

[0076] Understandably, step A34 involves resetting the out-of-bounds dimension to a random value within the boundary when the perturbed candidate position exceeds the search space boundary, thus obtaining the updated individual position. In other words, when a coordinate exceeds the allowed range, the coordinate is reassigned to a random number within the legal range, forming the final position update result of this iteration.

[0077] By using flight perturbations, the algorithm is given the ability to make long-distance random jumps, effectively escaping local optima traps. At the same time, boundary resets ensure that individuals are always within the legal search space.

[0078] Step S50: Maintain the current population containing the updated individual positions, and calculate the fitness of the maintained population according to the path planning objective function to determine the iterative target individual; It should be noted that the current population refers to the set containing all updated individuals in this iteration, i.e., the complete candidate solution population after position updates and perturbation resets. Furthermore, the maintained population refers to the complete population after local refinement and diversity restoration, i.e., the updated population containing the refined target individual, remaining high-quality individuals, and newly added individuals. Further, the iterative target individual refers to the optimal individual in the population determined after this round of population maintenance operations, i.e., the path scheme with the minimum overall path cost after this round of maintenance.

[0079] It should be understood that the objective function of path planning comprehensively considers path length and cost. Threatened areas and costs Terrain collision cost The cost of heading towards the end Path smoothing cost Boundary constraint cost Progress-guided costs Safety is highly costly and corridor constraint costs The overall cost function is ,in These are the weighting coefficients for each cost item; the path uses... The real-number encoding of each intermediate control point is used to generate a smooth three-dimensional flight trajectory through cubic spline interpolation. It should be noted that the periodic local refinement strategy refers to a local search strategy that applies adaptive random perturbations to the current global optimum at a fixed iteration period, with the perturbation amplitude decreasing as the iteration progresses. In other words, it's an optimization technique that performs a refined search near the optimum every preset number of generations to improve convergence accuracy. Conversely, the population diversity restoration strategy refers to a global control strategy that eliminates inferior individuals and replenishes new individuals at a fixed iteration period to maintain the population's breadth. In other words, it's an optimization technique that removes low-quality solutions and introduces new solutions every preset number of generations to prevent premature convergence of the population.

[0080] Understandably, in this embodiment, the periodic local refinement strategy is as follows: every 10 iterations, an adaptive Gaussian perturbation is applied to the current global optimum, with the perturbation amplitude decreasing linearly with the iteration progress; the population diversity restoration strategy is as follows: every 15 iterations, the 10% of individuals with the worst fitness are eliminated, and then... Add new individuals, among which This is the current globally optimal solution. These are random locations generated based on the Logistic chaotic mapping.

[0081] In the specific implementation, a Logistic chaotic mapping combined with QOBL quasi-backward learning and boundary awareness strategy is used to initialize the initial position of individual whales.

[0082] First, a Logistic chaotic mapping is used to generate... One original candidate solution The specific formula is as follows:

[0083] in, For the first At that moment, For the first The position value at each time point ranges from (0, 1]. For control parameters, take The system then enters a state of complete chaos. Different The chaotic distribution of values ​​also differs. Initial value Randomly selected solutions are iterated at least 5 times to fully enter a chaotic state, thereby generating a uniformly distributed, non-repeating chaotic sequence in the search space. Based on the chaotic sequence and a diagonal-guided strategy, N high-quality original candidate solutions are generated. .

[0084] Then, based on the reverse learning strategy pair Each original candidate solution generates a corresponding quasi-inverse solution. Compare the quasi-inverse solution with the original solution Merge, total Each candidate solution is evaluated using the objective function, and then sorted in ascending order of fitness. The remaining solutions are then selected for further evaluation. The highest quality individuals are selected as the QOBL portion (representing 80% of the population); this ultimately yields the initial elite whale individual positions.

[0085] Finally, for the remaining 20% ​​of individuals, a boundary-aware initialization strategy is adopted, which forces uniform sampling within the boundary regions of each dimension of the search space to form the QOBL individual population. With boundary-aware individual populations Merging to form a complete initial population This ensures that the population fully covers the central region and the area near the boundary of the search space, and the quality of the initial population is significantly better than that of the original WOA with uniform random initialization.

[0086] In one feasible implementation, step S50 includes steps A41-A45: Step A41: Determine the current target individual from the current population containing the updated individual locations; It should be noted that the current target individual refers to the individual with the best fitness in the current population, that is, the path scheme with the minimum overall path cost in the population after this round of iteration.

[0087] Understandably, step A41 involves determining the current target individual from the current population containing the updated individual positions, that is, selecting the individual with the best fitness from all candidate path schemes after position updates.

[0088] Step A42: Apply periodic perturbations to the current target individual to obtain the refined target individual; It should be noted that periodic perturbation refers to applying small, random perturbations to the target individual at fixed intervals, that is, a perturbation operation that performs a fine-tuning search of the neighborhood of the current optimal solution every certain number of iterations. Furthermore, the refined target individual refers to the optimal individual after periodic perturbation, that is, a better or similar path scheme obtained within the neighborhood of the current optimal solution.

[0089] Understandably, step A42 involves applying a periodic perturbation to the current target individual to obtain a refined target individual. This means that a small, random perturbation is applied to the vicinity of the current optimal path at fixed intervals to explore whether a better solution exists in its neighborhood. In this embodiment, the periodic perturbation period is 10 generations, and the perturbation amplitude decreases linearly with the iteration progress.

[0090] Step A43: Eliminate individuals with poor fitness from the current population to obtain the remaining population; It should be noted that an individual with poor fitness refers to a low-quality candidate solution in the population with the highest overall path cost, i.e., the individual with the worst path quality and the smallest contribution to population evolution. Furthermore, the remaining population refers to the set of candidate solutions retained after eliminating low-quality individuals, i.e., the main part of the population after removing the worst individual.

[0091] Understandably, step A43 involves eliminating individuals with poor fitness from the current population to obtain the remaining population. This means sorting by fitness, removing the individuals with the worst path quality, and retaining the initial candidate solutions. In this embodiment, the elimination rate is 10%.

[0092] Step A44: Merge the remaining population with the newly generated individuals to obtain the maintained population; It should be noted that new individuals refer to new candidate solutions generated based on a mixture of elite information and chaotic positions, that is, new path schemes used to fill the gaps left by eliminated individuals.

[0093] Understandably, step A44 involves merging the remaining population with the newly generated individuals to obtain the maintained population, that is, combining the retained initial candidate solutions with the newly added candidate solutions to form a new complete population. In this embodiment, the newly generated individuals are generated by mixing 20% ​​of the current best individual information and 80% of chaotic random positions.

[0094] Step A45: Calculate the fitness of the maintained population based on the path planning objective function to determine the target individual for iteration.

[0095] Understandably, step A45 involves calculating the fitness of the maintained population based on the path planning objective function, determining the target individual for the iteration, that is, evaluating the comprehensive cost of each path scheme for the complete population after the maintenance operation, and determining the optimal path scheme for the final iteration.

[0096] By periodically refining local conditions, a fine search of the neighborhood of the optimal solution is achieved. By eliminating inferior individuals and adding new individuals, the diversity of the population is restored, preventing the algorithm from converging to a local optimum too early, thus improving the convergence accuracy and result stability.

[0097] Step S60: Perform path interpolation based on the iterative target individual to generate a three-dimensional flight path.

[0098] It should be noted that path interpolation refers to the process of using mathematical methods to supplement intermediate points between discrete path control points to generate a continuous path, that is, a technique for transforming sparse control points into a smooth, continuous trajectory. Additionally, a three-dimensional flight path refers to the continuous flight trajectory that a UAV actually follows in three-dimensional space, that is, the final executable route connecting the starting point and the ending point and satisfying all constraints.

[0099] In one feasible implementation, step S60 includes steps A51 to A54: Step A51: Extract the coordinates of path control points in the target individual during iteration; It should be noted that the coordinates of the path control points refer to the coordinates of the key spatial points that constitute the flight path, that is, the three-dimensional spatial node position data used to define the path direction.

[0100] Understandably, step A51 involves extracting the coordinates of path control points in the iterative target individual, that is, decoding the coordinates of each key spatial point constituting the path from the finally determined optimal path scheme.

[0101] Step A52: Perform cubic spline interpolation on the coordinates of the path control points to obtain a smooth trajectory curve; It should be noted that cubic spline interpolation is a method to generate a smooth curve by connecting discrete points using piecewise cubic polynomials. In other words, it's an interpolation technique that constructs cubic functions between adjacent control points to make the path continuously differentiable. Furthermore, a smooth trajectory curve refers to a continuous and smooth flight path obtained after interpolation, i.e., a three-dimensional curve without abrupt changes and satisfying flight dynamics constraints.

[0102] Understandably, step A52 involves performing cubic spline interpolation on the coordinates of the path control points to obtain a smooth trajectory curve. This involves constructing a piecewise cubic polynomial function between adjacent path control points to generate a continuous, smooth, and gently curvature-changing three-dimensional flight trajectory. In this embodiment, the number of intermediate control points on the path is 10.

[0103] Step A53: Determine whether the interpolation points on the smooth trajectory curve meet the preset safety height conditions and preset threat avoidance conditions; It should be noted that interpolation points refer to intermediate points calculated through interpolation on a smooth trajectory curve, i.e., points along the trajectory that are supplemented between adjacent path control points. Additionally, the preset safe altitude condition refers to the constraint requirement that path points must be above the terrain surface with a certain safety margin, i.e., the minimum ground clearance standard that the flight altitude must meet. Furthermore, the preset threat avoidance condition refers to the constraint requirement that path points must maintain a safe distance from threat areas, i.e., the avoidance standard that the flight trajectory must not encroach on the danger zone.

[0104] Understandably, step A53 is to determine whether the interpolation points on the smooth trajectory curve meet the preset safety height conditions and preset threat avoidance conditions, that is, to check whether each point on the interpolated trajectory simultaneously meets the dual safety constraints of sufficient ground clearance and distance from the threat area.

[0105] Step A54: When the interpolation point meets the preset safe altitude condition and preset threat avoidance condition, the smooth trajectory curve is determined as the three-dimensional flight path.

[0106] Understandably, step A54 determines the smooth trajectory curve as the three-dimensional flight path when the interpolation points meet the preset safety altitude conditions and preset threat avoidance conditions. That is, after all interpolation points pass the safety check, the final usable three-dimensional flight path scheme is output.

[0107] A smooth and continuous three-dimensional flight path is generated by cubic spline interpolation, avoiding the flight instability caused by path polyline. At the same time, the feasibility of the path and flight safety are ensured by dual verification of safe altitude and threat avoidance.

[0108] Furthermore, this embodiment compares the QCWOA algorithm with the original WOA, PSO, and ACO algorithms using standard benchmark functions to verify the general effectiveness of the core improvements. The test functions include eight classic functions, among which... It is a unimodal function used to evaluate the optimization accuracy and convergence speed of the algorithm; The test function is a multi-peaked function, which provides a better test of the algorithm's global exploration capability. The test functions are shown in Table 1: Table 1

[0109] The proposed QCWOA algorithm (an improved whale optimization algorithm) was compared with the standard WOA, PSO, and ACO algorithms to verify its performance. The experimental results, including the optimal value, worst value, average fitness value, and standard deviation of 10 runs, are shown in Table 2. Table 2:

[0110] As shown in Table 2, the QCWOA algorithm proposed in this invention outperforms the WOA, PSO, and ACO algorithms in terms of average fitness values ​​across all eight test functions. From the single-peak function test results, QCWOA demonstrates significant advantages in optimization accuracy and convergence speed; from the multi-peak function test results, QCWOA exhibits stronger global exploration capabilities, effectively avoiding getting trapped in local optima. Therefore, for solving extremum problems, QCWOA possesses better overall performance, validating the universal effectiveness of the two core improvements: QOBL initialization and cosine convergence factor.

[0111] This embodiment applies the QCWOA algorithm to a 3D simulation map for specific path planning. The detailed steps are as follows: Set the QCWOA algorithm parameters. Set the population size nPop = 120, the maximum number of iterations MaxIt = 200, the number of independent runs RunNum = 8, and the number of intermediate control points PointNum = 10. Flight hyperparameters The local refinement cycle is 10 generations, the diversity restoration cycle is 15 generations, and the diversity restoration elite mixing ratio is [not specified]. .

[0112] Initial positions of whale populations are generated using Logistic chaotic mapping. (Initial values) Randomly selected, iterates more than 5 times, and then enters a chaotic state. Generated based on chaotic sequences. One original candidate solution Each individual is encoded as a coordinate vector of three-dimensional control points named PointNum. A diagonal guidance strategy is used to initially distribute the control points near the direction of the line connecting the start and end points.

[0113] Based on the original candidate solutions Quasi-reverse solutions are generated according to the quasi-reverse learning formula. The original solution X and the quasi-inverse solution Merge, total The candidate solutions are evaluated using the three-dimensional path objective function, and their fitness values ​​are calculated. The solutions are then sorted in ascending order of fitness, and the top-performing solutions are selected. The highest quality individual was selected; an additional 20% of boundary-aware individuals were added from the search space boundary region, and these were merged to form a complete initial population. Determine the initial optimal fitness value and the optimal location of the whale individual. .

[0114] Calculate the cosine convergence factor of the current generation. According to the standard WOA three-segment The position update mechanism iteratively updates the position of individual whales, and the position update equation is:

[0115] in, This represents the distance between the current individual and the optimal individual. It is the distance between the current individual and a random individual. It is the spiral attack range; It is a convergence coefficient vector. ; It is the oscillation coefficient vector. ; and It is a uniformly distributed random number. ; It is the helical shape constant, at which point ; It is a random number for the spiral parameter. ; It is the probability of behavioral choice. ; The definition is overlaid after each position update. Flight disturbance, i.e.

[0116] in For adaptive step size coefficient; The dimensions exceeding the boundary are then randomly reset, a process known as boundary reflection, as shown in the following formula:

[0117] in ; Calculate the path fitness value applied to the 3D simulation map. Specifically, this includes: The makima function in MATLAB is used to perform cubic spline interpolation on the x, y, and z coordinates of the path control points to fit a smooth three-dimensional flight trajectory. Determine each interpolation point in the path Terrain height corresponding to coordinates If the path point height z is lower than the safe height ( If the terrain collision penalty cost is J3, then the cumulative terrain collision penalty cost is J3. Calculate the Euclidean distance between each path point and the center of each threat region. If the distance is less than the threat radius, accumulate the threat cost. ; The cost is calculated based on the Euclidean distance between adjacent control points, accumulating the path length cost. ; The weighted sum is used to obtain the overall fitness value of the individual. A smaller fitness value indicates a better path quality.

[0118] Perform periodic local refinement (every 10 generations) and population diversity restoration (every 15 generations), retaining the best individuals of the current generation as elites, and determine whether the maximum number of iterations or the early stopping condition is met (fitness change less than 1×10 for 25 consecutive generations). - If the condition is met (³), the iteration stops; otherwise, return to step four and continue iterating until the optimal path planning result is obtained. Repeat the above steps for a total of RunNum = 8 independent runs, and output the globally optimal result.

[0119] This embodiment compares the QCWOA algorithm with the GA and GWO algorithms, where the parameter settings are: population size 120, maximum number of iterations 300, and number of independent runs 10. Other parameters are the same as described above, and the fitness convergence curve is shown below. Figure 2 As shown.

[0120] from Figure 2 As can be observed, the QCWOA algorithm demonstrates a significant advantage in improving fitness. During the iteration process, the fitness convergence speed of the QCWOA algorithm is significantly faster than that of the GA and GWO algorithms. After approximately 20 iterations, the fitness of the QCWOA algorithm approaches the optimal value; the GA algorithm remains at a high fitness level up to generation 150 and has not yet fully converged by generation 300; the GWO algorithm converges slowly in the first 150 generations, then gradually approaches the optimal value through a step-wise descent. From the final convergence value, the overall cost of the optimal path in QCWOA is significantly lower than that of GA and GWO, demonstrating the superiority of QCWOA in path planning for complex 3D terrain.

[0121] Furthermore, QCWOA's performance in actual 3D path planning also verified its effectiveness. In the 3D path planning experiment, QCWOA was able to effectively plan the optimal path that avoids all threat areas, flies at a safe altitude close to the terrain, and the path is smooth and continuous with no collisions from the start to the end, fully demonstrating the engineering practical value of the improved strategy proposed in this invention.

[0122] This embodiment provides a three-dimensional path planning method. By initializing the population using quasi-backward learning combined with chaotic mapping and boundary-aware strategies, the quality of the initial population is significantly improved and the convergence speed is accelerated. Introducing a nonlinear cosine convergence factor allows the algorithm to retain sufficient global exploration capability in the early stages of iteration, while rapidly contracting in the later stages to accelerate precise local development, effectively balancing exploration and development and avoiding premature convergence. Combining long-distance random step-size perturbation gives the algorithm the ability to make large-step jumps with a low probability, effectively escaping the local optimum trap. Applying adaptive Gaussian perturbation to the neighborhood of the current optimal solution through periodic local refinement achieves a fine search of the optimal solution's neighborhood, further improving convergence accuracy. A population diversity restoration mechanism eliminates inferior individuals and replenishes chaotic elite mixed individuals, restoring population diversity while preserving elite information, preventing the algorithm from prematurely converging to local optima, and improving result stability. Finally, a smooth and continuous three-dimensional flight path is generated through cubic spline interpolation, ensuring the path satisfies flight dynamics constraints and has excellent engineering feasibility.

[0123] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in the first embodiment described above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 3 Step S20 includes steps S201 to S205: Step S201: Generate original candidate solutions based on chaotic mapping, wherein the control parameters of chaotic mapping are preset chaotic parameter values, and the number of iterations is greater than the preset number of chaotic entries; It should be noted that the original candidate solutions refer to the individual potential path schemes initially generated based on the chaotic mapping, i.e., the initial population members that have not yet undergone screening and optimization. Furthermore, the control parameters refer to the numerical settings that adjust the iterative behavior of the chaotic mapping, i.e., the key variables that determine the distribution characteristics of the chaotic sequence. Further, the preset chaotic parameter value refers to the specific value of the pre-set control parameter, which is set to 4 in this embodiment to allow the system to enter a fully chaotic state. Additionally, the preset number of chaotic entry times refers to the pre-set minimum number of iterations for the chaotic mapping, i.e., the minimum number of iterations required to ensure the sequence fully enters a chaotic state.

[0124] Understandably, step S201 generates initial candidate solutions based on chaotic mapping, where the control parameters of the chaotic mapping are preset chaotic parameter values, and the number of iterations is greater than the preset number of chaotic entries. That is, it generates uniformly distributed and non-repeating initial path schemes through nonlinear iteration, ensuring sufficient iterations to enter a chaotic state. In this embodiment, the preset chaotic parameter value is 4, and the preset number of chaotic entries is 5.

[0125] Step S202: Perform quasi-backward learning on the original candidate solutions to obtain quasi-backward solutions; It should be noted that the quasi-reverse solution refers to the reverse candidate individual generated from the original candidate solution through the quasi-reverse learning strategy, that is, the new path scheme obtained by interpolation between the original solution and the central symmetric point of the search space.

[0126] Understandably, step S202 involves performing quasi-backward learning on the original candidate solutions to obtain quasi-backward solutions. That is, the quasi-backward learning strategy is used to generate corresponding reverse candidate individuals for each original candidate solution, so as to expand the search range and improve the quality of the initial solutions.

[0127] Step S203: Merge the original candidate solutions and quasi-reverse solutions to obtain merged candidate solutions, and then filter the merged candidate solutions according to the path planning objective function to obtain an initial set of individuals; It should be noted that the merged candidate solution refers to the set of candidate solutions formed by merging the original candidate solutions and the quasi-reverse solutions, that is, an expanded candidate group containing both the original and reverse solutions. Additionally, the initial individual set refers to the set of initial individuals selected from the merged candidate solutions, that is, the group of high-quality path solutions retained after fitness ranking.

[0128] Understandably, step S203 involves merging the original candidate solutions and quasi-reverse solutions to obtain merged candidate solutions, and then filtering the merged candidate solutions according to the path planning objective function to obtain an initial set of individuals. In other words, after merging the original solutions and reverse solutions, the solutions are sorted according to the comprehensive path cost, and the individuals with the best quality are retained to form an initial elite set.

[0129] Step S204: Sample boundary-sensing individuals from the boundary region of the search space, and merge the boundary-sensing individuals with the initial individual set to obtain the initial population; It should be noted that the search space boundary region refers to the area near the boundary of the allowed value range of each dimension variable in the optimization problem, that is, the narrow interval close to the boundary between the maximum and minimum values. Additionally, boundary-aware individuals refer to candidate individuals specifically sampled and generated in the search space boundary region; that is, special path schemes that are forcibly distributed near the boundary to enhance boundary coverage.

[0130] Understandably, step S204 involves sampling boundary-aware individuals from the boundary region of the search space, merging these boundary-aware individuals with the initial individual set to obtain the initial population. This involves generating special individuals near the boundary and merging them with the selected initial individuals to form a complete initial population that covers both the center and the boundary regions.

[0131] Step S205: Calculate the fitness of the initial population based on the path planning objective function to determine the target individual.

[0132] It should be noted that fitness calculation refers to the quantitative process of evaluating the merits of each individual's path in the population based on the objective function of path planning, that is, the operation of calculating the fitness value of each path scheme through the comprehensive cost function.

[0133] Understandably, step S205 involves calculating the fitness of the initial population based on the path planning objective function, determining the target individual, that is, evaluating the comprehensive cost of all path schemes in the merged initial population, and determining the optimal path scheme with the minimum cost as the target individual.

[0134] By initializing the population using chaotic mapping combined with quasi-backward learning and boundary awareness strategies, the quality of the initial population was significantly improved, enabling the population to fully cover the center and boundary regions of the search space. This laid a high-quality initial foundation for subsequent iterative optimization and accelerated the convergence speed of the algorithm.

[0135] In the specific implementation, it was retained and optimized. Flight disturbance mechanism. Each individual position update is followed by a superposition based on the Mantegna algorithm, when... , generated Flight stride:

[0136] in , , Calculated using the Mantegna formula, as follows:

[0137] in For hyperparameters, It is a gamma function; The flight step size is adaptively matched with the difference between the current individual position and the global optimal position, giving the algorithm the ability to make large step jumps with a low probability, effectively escaping the local optimum trap.

[0138] This embodiment provides a three-dimensional path planning method. By initializing the population using quasi-backward learning combined with chaotic mapping and boundary awareness strategies, the quality of the initial population is significantly improved, and the convergence speed is accelerated, enabling the population to fully cover the central region and the area near the boundary of the search space. A nonlinear cosine convergence factor is introduced to guide position updates, allowing the algorithm to retain more global exploration capabilities in the early stages of iteration and then rapidly contract in the later stages to accelerate precise local development, effectively balancing the relationship between global exploration and local development and preventing premature convergence. Flight perturbations endow the algorithm with the ability to make large-step jumps with a low probability, effectively escaping the local optimum trap. Periodic local refinement applies adaptive perturbations to the neighborhood of the current optimal solution, achieving a fine search of the optimal solution's neighborhood and further improving convergence accuracy. A population diversity restoration mechanism eliminates inferior individuals and replenishes chaotic elite individuals, restoring population diversity while preserving elite information, preventing premature convergence to local optima, and improving result stability. Finally, a smooth and continuous three-dimensional flight path is generated through cubic spline interpolation, ensuring that the path satisfies flight dynamics constraints and has excellent engineering feasibility.

[0139] It should be noted that the above examples are only for understanding this application and do not constitute a limitation on the three-dimensional path planning method of this application. Any simple modifications based on this technical concept are within the protection scope of this application.

[0140] This application also provides a three-dimensional path planning device, please refer to... Figure 4 The three-dimensional path planning device includes: Objective function construction module 10 is used to obtain the UAV flight area map and construct the path planning objective function based on the flight area map; Population initialization module 20 is used to initialize the population through quasi-backward learning combined with chaotic mapping and boundary awareness strategies, and to determine the target individual according to the path planning objective function; The iterative optimization module 30 is used to determine the nonlinear cosine convergence factor of the current iteration, and update the position based on the nonlinear cosine convergence factor and the target individual to obtain candidate positions; apply flight perturbation to the candidate positions and reset the boundaries to obtain the updated individual positions; maintain the current population containing the updated individual positions, and calculate the fitness of the maintained population based on the path planning objective function to determine the iterative target individual; The path generation module 40 is used to perform path interpolation based on the iterative target individual to generate a three-dimensional flight path.

[0141] The three-dimensional path planning device provided in this application, employing the three-dimensional path planning method in the above embodiments, can solve the technical problem of how to improve the initial population quality, convergence speed, and global optimization ability of the whale optimization algorithm in three-dimensional path planning, while suppressing local optimum traps. Compared with the prior art, the beneficial effects of the three-dimensional path planning device provided in this application are the same as those of the three-dimensional path planning method provided in the above embodiments, and other technical features in the three-dimensional path planning device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0142] In one embodiment, the population initialization module 20 is further configured to generate original candidate solutions based on the chaotic mapping, wherein the control parameters of the chaotic mapping are preset chaotic parameter values, and the number of iterations is greater than the preset number of chaotic entries; Quasi-backward learning is performed on the original candidate solutions to obtain quasi-backward solutions; The original candidate solutions and quasi-reverse solutions are merged to obtain merged candidate solutions, and the merged candidate solutions are filtered according to the path planning objective function to obtain an initial set of individuals; Boundary-aware individuals are sampled from the boundary region of the search space, and these boundary-aware individuals are merged with the initial set of individuals to obtain the initial population. The fitness of the initial population is calculated based on the objective function of path planning to determine the target individual.

[0143] In one embodiment, the iterative optimization module 30 is further configured to determine a nonlinear cosine convergence factor based on the current iteration number and the maximum iteration number; The convergence coefficient is determined based on the nonlinear cosine convergence factor. Select individuals to be updated from the population, and update the first candidate position based on the distance between the target individual and the individual to be updated when the convergence coefficient meets the preset shrinkage condition; When the convergence coefficient meets the preset exploration conditions, a random individual is selected from the population, and the second candidate position is updated according to the distance between the random individual and the individual to be updated. Generate a random number for behavior selection, and when the random number for behavior selection meets the preset attack conditions, perform a spiral attack update based on the distance between the target individual and the individual to be updated to obtain the third candidate position; Based on the convergence coefficient and behavior, random numbers are selected to determine the target candidate position from the first, second, and third candidate positions.

[0144] In one embodiment, the iterative optimization module 30 is further configured to generate a flight disturbance step size based on the ratio of two normally distributed random numbers; The flight disturbance step size is superimposed on the candidate position to obtain the disturbed candidate position; Perform boundary checks on the disturbed candidate positions; When the perturbed candidate position exceeds the boundary of the search space, the out-of-bounds dimension is reset to a random value within the boundary to obtain the updated individual position.

[0145] In one embodiment, the iterative optimization module 30 is further configured to determine the current target individual from the current population containing the updated individual positions; Apply periodic perturbations to the current target individual to obtain a refined target individual; Individuals with poor fitness are eliminated from the current population to obtain the remaining population; The remaining population is merged with the newly generated individuals to obtain the maintained population. The fitness of the maintained population is calculated based on the path planning objective function to determine the target individual for iteration.

[0146] In one embodiment, the objective function construction module 10 is also used to obtain terrain elevation information and threat area location information in the UAV flight area map; A three-dimensional simulation map is constructed based on terrain elevation information and the location information of the threatened area; Determine the starting and ending points on the 3D simulation map; The path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost are determined based on the starting and ending locations. The objective function for path planning is obtained by weighted summation of path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost.

[0147] In one embodiment, the path generation module 40 is further configured to extract the coordinates of path control points in the iterative target individual; A smooth trajectory curve is obtained by performing cubic spline interpolation on the coordinates of the path control points; Determine whether the interpolation points on the smooth trajectory curve meet the preset safety height conditions and preset threat avoidance conditions; When the interpolation point meets the preset safe altitude conditions and preset threat avoidance conditions, the smooth trajectory curve is determined as the three-dimensional flight path.

[0148] This application provides a three-dimensional path planning device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the three-dimensional path planning method in Embodiment 1 above.

[0149] The following is for reference. Figure 5This document illustrates a structural schematic diagram of a three-dimensional path planning device suitable for implementing embodiments of this application. The three-dimensional path planning device in these embodiments may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), and in-vehicle terminals (e.g., in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 5 The illustrated 3D path planning device is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0150] like Figure 5 As shown, the 3D path planning device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in ROM (Read Only Memory) 1002 or a program loaded from storage device 1003 into RAM (Random Access Memory) 1004. RAM 1004 also stores various programs and data required for the operation of the 3D path planning device. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via bus 1005. Input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touch screens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. The communication device 1009 allows the 3D path planning device to communicate wirelessly or wiredly with other devices to exchange data. Although the figure shows a 3D path planning device with various systems, it should be understood that it is not required to implement or have all of the systems shown. More or fewer systems may be implemented alternatively.

[0151] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0152] The three-dimensional path planning device provided in this application, employing the three-dimensional path planning method described in the above embodiments, can solve the technical problem of how to improve the initial population quality, convergence speed, and global optimization ability of the whale optimization algorithm in three-dimensional path planning, while suppressing local optimum traps. Compared with the prior art, the beneficial effects of the three-dimensional path planning device provided in this application are the same as those of the three-dimensional path planning method provided in the above embodiments, and other technical features of this three-dimensional path planning device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0153] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0154] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0155] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the three-dimensional path planning method in the above embodiments.

[0156] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, RAM (Random Access Memory), ROM (Read Only Memory), EPROM (Erasable Programmable Read Only Memory or Flash Memory), optical fibers, CD-ROM (CD-Read Only Memory), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0157] The aforementioned computer-readable storage medium may be included in the three-dimensional path planning device; or it may exist independently and not be assembled into the three-dimensional path planning device.

[0158] The aforementioned computer-readable storage medium carries one or more programs. When these programs are executed by a 3D path planning device, the 3D path planning device: acquires a map of the UAV's flight area and constructs a path planning objective function based on the flight area map; initializes a population using a quasi-backward learning strategy combined with chaotic mapping and boundary awareness, and determines a target individual based on the path planning objective function; determines the nonlinear cosine convergence factor for the current iteration and updates the position based on the nonlinear cosine convergence factor and the target individual to obtain candidate positions; applies flight perturbations to the candidate positions and resets the boundaries to obtain updated individual positions; maintains the current population containing the updated individual positions and calculates the fitness of the maintained population based on the path planning objective function to determine the iterative target individual; and performs path interpolation based on the iterative target individual to generate a 3D flight path.

[0159] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including LAN (Local Area Network) or WAN (Wide Area Network)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0160] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0161] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0162] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described three-dimensional path planning method. This solves the technical problem of how to improve the initial population quality, convergence speed, and global optimization ability of the whale optimization algorithm in three-dimensional path planning, while suppressing local optimum traps. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the three-dimensional path planning method provided in the above embodiments, and will not be repeated here.

[0163] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the three-dimensional path planning method described above.

[0164] The computer program product provided in this application can solve the technical problem of how to improve the initial population quality, convergence speed, and global optimization ability of the whale optimization algorithm in three-dimensional path planning, and suppress local optimum traps. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the three-dimensional path planning method provided in the above embodiments, and will not be repeated here.

[0165] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A three-dimensional path planning method, characterized in that, The method includes: Obtain a map of the UAV's flight area and construct a path planning objective function based on the flight area map; The population is initialized by combining quasi-backward learning with chaotic mapping and boundary awareness strategies, and the target individual is determined according to the objective function of the path planning. Determine the nonlinear cosine convergence factor for the current iteration, and update the position based on the nonlinear cosine convergence factor and the target individual to obtain candidate positions; The candidate positions are subjected to flight perturbations and the boundaries are reset to obtain the updated individual positions; The current population containing the updated individual positions is maintained, and the fitness of the maintained population is calculated according to the path planning objective function to determine the iterative target individual; Based on the iterative target individual, path interpolation is performed to generate a three-dimensional flight path.

2. The method as described in claim 1, characterized in that, The steps of initializing the population through quasi-backward learning combined with chaotic mapping and boundary awareness strategies, and determining the target individual based on the path planning objective function, include: Original candidate solutions are generated based on chaotic mapping, wherein the control parameters of the chaotic mapping are preset chaotic parameter values, and the number of iterations is greater than the preset number of chaotic entries; Quasi-backward learning is performed on the original candidate solutions to obtain quasi-backward solutions; The original candidate solutions and the quasi-reverse solutions are merged to obtain merged candidate solutions, and the merged candidate solutions are filtered according to the path planning objective function to obtain an initial set of individuals; Boundary-aware individuals are sampled from the boundary region of the search space, and these boundary-aware individuals are merged with the initial set of individuals to obtain an initial population. The fitness of the initial population is calculated based on the path planning objective function to determine the target individual.

3. The method as described in claim 1, characterized in that, The step of determining the nonlinear cosine convergence factor of the current iteration and updating the position based on the nonlinear cosine convergence factor and the target individual to obtain candidate positions includes: The nonlinear cosine convergence factor is determined based on the current iteration number and the maximum iteration number. The convergence coefficient is determined based on the nonlinear cosine convergence factor. Select an individual to be updated from the population, and when the convergence coefficient satisfies the preset shrinkage condition, update the first candidate position according to the distance between the target individual and the individual to be updated; When the convergence coefficient satisfies the preset exploration conditions, a random individual is selected from the population, and the second candidate position is updated according to the distance between the random individual and the individual to be updated. Generate a random number for behavior selection, and when the random number for behavior selection meets the preset attack conditions, perform a spiral attack update based on the distance between the target individual and the individual to be updated to obtain a third candidate position; Based on the convergence coefficient and the behavior, a random number is selected to determine the target candidate position from the first candidate position, the second candidate position, and the third candidate position.

4. The method as described in claim 1, characterized in that, The step of applying flight perturbations to the candidate locations and resetting the boundaries to obtain updated individual locations includes: The flight disturbance step size is generated based on the ratio of two normally distributed random numbers; The flight disturbance step size is superimposed on the candidate position to obtain the disturbed candidate position; The candidate positions after the disturbance are judged to be out of bounds; When the candidate position after the perturbation exceeds the boundary of the search space, the out-of-bounds dimension is reset to a random value within the boundary to obtain the updated individual position.

5. The method as described in claim 1, characterized in that, The steps of maintaining the current population containing the updated individual positions and calculating the fitness of the maintained population according to the path planning objective function to determine the iterative target individual include: The current target individual is determined from the current population, which includes the updated individual location. Apply periodic perturbations to the current target individual to obtain a refined target individual; Individuals with poor fitness are eliminated from the current population to obtain the remaining population; The remaining population is merged with the newly generated individuals to obtain the maintained population. The fitness of the maintained population is calculated based on the path planning objective function to determine the target individual for iteration.

6. The method as described in claim 1, characterized in that, The steps of acquiring the UAV flight area map and constructing a path planning objective function based on the flight area map include: Acquire terrain elevation information and threat area location information from the drone flight area map; A three-dimensional simulation map is constructed based on the terrain elevation information and the location information of the threat area; Determine the starting and ending points on the three-dimensional simulation map; The path length cost, threat area cost, terrain collision cost, path smoothing cost, boundary constraint cost, progress guidance cost, safety height cost, and corridor constraint cost are determined based on the starting point and the ending point. The path planning objective function is obtained by weighted summing of the path length cost, the threat area cost, the terrain collision cost, the path smoothing cost, the boundary constraint cost, the progress guidance cost, the safety height cost, and the corridor constraint cost.

7. The method as described in claim 1, characterized in that, The step of generating a three-dimensional flight path by performing path interpolation based on the iterative target individual includes: Extract the coordinates of the path control points in the target individual being iterated; Cubic spline interpolation is performed on the coordinates of the path control points to obtain a smooth trajectory curve; Determine whether the interpolation points on the smooth trajectory curve meet the preset safety height conditions and preset threat avoidance conditions; When the interpolation point satisfies the preset safe altitude condition and the preset threat avoidance condition, the smooth trajectory curve is determined as the three-dimensional flight path.

8. A three-dimensional path planning device for unmanned aerial vehicles (UAVs), characterized in that, The device includes: The objective function construction module is used to obtain a map of the UAV's flight area and construct a path planning objective function based on the flight area map. The population initialization module is used to initialize the population by combining quasi-backward learning with chaotic mapping and boundary awareness strategies, and to determine the target individual according to the path planning objective function. The iterative optimization module is used to determine the nonlinear cosine convergence factor of the current iteration, and update the position of the target individual based on the nonlinear cosine convergence factor to obtain candidate positions; apply flight perturbation to the candidate positions and reset the boundaries to obtain updated individual positions; maintain the current population containing the updated individual positions, and calculate the fitness of the maintained population based on the path planning objective function to determine the iterative target individual; The path generation module is used to perform path interpolation based on the iterative target individual to generate a three-dimensional flight path.

9. A three-dimensional path planning device, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the three-dimensional path planning method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the three-dimensional path planning method as described in any one of claims 1 to 7.

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