Low-altitude airspace aircraft three-dimensional path planning method based on enhanced particle swarm optimization
By enhancing the particle swarm optimization algorithm and combining adaptive adjustment of inertial weights and learning factors with a local perturbation mechanism, the problems of local optima and premature convergence in path planning for low-altitude aircraft are solved, achieving high-precision and high-stability path planning results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHENYANG AEROSPACE UNIVERSITY
- Filing Date
- 2026-02-13
- Publication Date
- 2026-05-05
AI Technical Summary
Existing low-altitude aircraft path planning algorithms are prone to getting stuck in local optima in complex low-altitude airspace, lack a global escape mechanism, suffer from reduced group diversity, low initial path quality, and limited local search capabilities, making it difficult to achieve high-precision and high-stability path planning.
An enhanced particle swarm optimization algorithm is adopted, which optimizes the path planning process by adaptively adjusting the inertia weight, individual learning factor and global learning factor, combined with local perturbation and stagnation perception mechanism. Dynamic greedy search and continuous domain ant colony algorithm initialization are introduced to improve the global exploration and local development capabilities of the path.
It achieves high-precision and high-stability path planning in complex low-altitude environments, and can quickly and accurately generate the optimal flight path, meeting the comprehensive requirements of safety, continuity and energy consumption control.
Smart Images
Figure CN121977573A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of autonomous navigation technology for low-altitude aircraft, and in particular to a three-dimensional path planning method for low-altitude airspace aircraft based on enhanced particle swarm optimization. This method can be widely applied to autonomous path planning of low-altitude aircraft in complex low-altitude airspace, as well as intelligent flight decision-making and path optimization in low-altitude economic scenarios. Background Technology
[0002] With the rapid development of low-altitude aircraft and related autonomous systems in low-altitude economic scenarios such as logistics distribution, inspection and monitoring, and emergency rescue, path planning technology in low-altitude airspace environments has become a key link in achieving safe flight and efficient operation. The goal of low-altitude path planning is to search for an optimal or suboptimal feasible flight path from the starting point to the target point in a known or partially known low-altitude environment. This path must simultaneously satisfy multiple constraints such as terrain and obstacle avoidance, flight smoothness, path length, and energy consumption. Traditional deterministic planning algorithms (such as A* algorithm and Dijkstra's algorithm) have high computational efficiency in low-dimensional, regularized environments, but they are prone to limitations such as computational explosion and poor path quality when facing complex low-altitude environments, dense obstacles, and high-dimensional search spaces. In recent years, swarm intelligence optimization algorithms (such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Ant Colony Optimization (ACO)) have been gradually applied to the field of low-altitude aircraft path planning due to their global search capabilities and adaptive characteristics. However, the standard particle swarm optimization algorithm still has several shortcomings under complex low-altitude airspace conditions: First, the algorithm is prone to getting trapped in local optima in multi-constraint environments and lacks an effective global escape mechanism; second, as the iteration process progresses, the diversity of the population decreases rapidly, which can easily lead to premature convergence and a decline in search capability; third, the traditional random initialization method is difficult to guarantee the feasibility and uniformity of the initial path, resulting in low quality of the initial solution; and fourth, the local search capability is limited, making it difficult to further refine the optimization of high-quality low-altitude flight paths.
[0003] Therefore, proposing a novel path planning method for low-altitude airspace environments, which takes into account both global exploration and local development capabilities in the path optimization process, and achieving high-precision and high-stability path planning in complex low-altitude environments, has become an urgent problem to be solved. Summary of the Invention
[0004] In view of this, the present invention provides a three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization, in order to solve the problems existing in the prior art.
[0005] This invention provides a three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization, comprising:
[0006] Modeling the low-altitude airspace environment yields a low-altitude airspace environment model.
[0007] Construct a fitness function for evaluating the comprehensive cost of a path;
[0008] An enhanced particle swarm optimization algorithm is used to iteratively solve for the global optimal solution vector within the feasible space of the low-altitude airspace environment model. During the iteration process, the inertia weight gradually decreases, the individual learning factor gradually decreases, and the global learning factor gradually increases. When the swarm tends to converge, local perturbations are applied to the positions of multiple well-performing particles, centered on the global optimal position. When the overall convergence speed of the swarm slows down or the changes in particle positions tend to stabilize, the swarm is determined to be in a stagnant state. If stagnation is detected for the first time, the velocities of some particles are updated by random perturbation. If stagnation is still detected after multiple iterations, the particle positions are slightly adjusted and boundary corrections are performed. The position vector of each particle in the particle swarm represents the encoding of a flight path.
[0009] Preferably, the low-altitude airspace environment modeling includes three-dimensional terrain modeling and static obstacle modeling.
[0010] Further preferably, the fitness function The formula is as follows:
[0011] ;
[0012] In the formula, Indicates the cost of the path length. Indicates the cost of path smoothness. Indicates the cost of flying altitude. Indicates the cost of obstacle avoidance. , , , These are the weighting coefficients.
[0013] Further optimization involves using the enhanced particle swarm optimization algorithm to iteratively solve for the global optimal solution vector within the feasible space of the low-altitude airspace environment model, as follows:
[0014] Initialize a containing A swarm of particles is generated, and the fitness function is used to evaluate the fitness of each particle. The position vector of each particle is used as its initial individual optimal solution vector. The position vector of the best-fit particle in the particle swarm is used as the initial global optimal solution vector. ,in, Indicates the size of the particle swarm;
[0015] Iteratively update each particle in the particle swarm to obtain the global optimal solution vector, where the i-th particle... The steps of this iteration are as follows:
[0016] Update the particle's velocity and position, including the inertial weights. Individual learning factors and global learning factor The formula is as follows:
[0017] ;
[0018] ;
[0019] ;
[0020] In the formula, This represents the current iteration number. The maximum number of iterations; This is the adjustment coefficient; , These are the upper and lower limits of the inertia weight, respectively. This represents the upper limit of the individual learning factor. This is the lower limit of the global learning factor;
[0021] Calculate the variance of group velocity And compare it with the preset population convergence threshold. If a comparison is made, At the current global optimal position A local perturbation is applied to several high-performing particles centered on the target particle. The perturbation model is as follows:
[0022] ;
[0023] in, For the first The original position vectors of each particle. For the first The new position vector of each particle after perturbation Let be a uniform random vector in the interval [-1, 1]. The current disturbance strength gradually decreases as the iteration progresses;
[0024] Calculate the normalized population velocity variance And compare it with the preset stagnation perception threshold. If a comparison is made, If the population is determined to be in a stagnant state, and stagnation is detected for the first time, the velocity of some particles is updated by random perturbation. If stagnation is still detected after multiple iterations, the particle positions are slightly adjusted and the boundary is corrected.
[0025] Further optimization involves initializing the particle swarm using a continuous domain ant colony algorithm.
[0026] Further optimization, current disturbance strength The formula is as follows:
[0027] ;
[0028] In the formula, and These are the upper and lower limits of the disturbance intensity, respectively. This represents the current iteration number. This represents the maximum number of iterations.
[0029] Further optimization, for the first The formula for perturbing and updating the velocity of each particle is as follows:
[0030] ;
[0031] in, For the first The original velocity vector of each particle. For the first The new velocity vector of each particle after the perturbation For the velocity disturbance intensity, Let be a random vector uniformly distributed in the interval [−1, 1]. For the first The maximum allowable velocity vector for a particle.
[0032] Further optimization, for the first The formula for making minute adjustments to the position of each particle is as follows:
[0033] ;
[0034] in, For the first The original position vectors of each particle. For the first The new position vector of each particle after perturbation Let be a uniform random vector in the interval [-1, 1]. The intensity of the positional disturbance. and These are the upper and lower boundary vectors of the search space, respectively.
[0035] Further optimization yields the following formula for boundary correction of particles:
[0036] ;
[0037] in, For the first The new position vector of each particle after perturbation For the first The corrected position vector of each particle. and These are the upper and lower boundary vectors of the search space, respectively.
[0038] Further preferably, the three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization also includes the following steps: smoothing the discrete waypoints corresponding to the global optimal solution vector using Bezier curves to obtain a continuous and smooth flight path.
[0039] This invention provides a three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization. It introduces a dynamic greedy search mechanism, adaptively adjusting the search radius and trigger probability according to the iteration progress. This enhances the algorithm's ability to find fine-grained paths in high-potential low-altitude areas with dense buildings and significant terrain undulations. Employing a stagnation-aware escape mechanism, it monitors population diversity to detect premature convergence and adaptive jump repair, improving the algorithm's ability to escape local optima under complex low-altitude airspace conditions. This method can plan paths quickly and accurately, effectively meeting the comprehensive requirements of low-altitude flight for safety, continuity, and energy consumption control. It can be widely applied to typical low-altitude economic application scenarios such as low-altitude vehicle logistics distribution, low-altitude inspection, urban low-altitude security, low-altitude emergency rescue, and low-altitude traffic management, demonstrating promising engineering application prospects and industrial promotion value.
[0040] The three-dimensional path planning method for low-altitude airspace aircraft based on enhanced particle swarm optimization provided by this invention can quickly and accurately plan the optimal flight path. Attached Figure Description
[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0042] Figure 1 A flowchart of the three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization provided by the present invention;
[0043] Figure 2 The optimal path three-view diagram generated by the method proposed in this invention in a complex terrain environment in low-altitude airspace is shown in (a) as a three-dimensional view, (b) as a top view, and (c) as a side view.
[0044] Figure 3The three views of the path generated using the traditional particle swarm optimization (PSO) algorithm in the same low-altitude airspace environment are shown, where (a) is a three-dimensional view, (b) is a top view, and (c) is a side view. Detailed Implementation
[0045] The present invention will be further described below with reference to specific embodiments.
[0046] like Figure 1 As shown, this invention provides a three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization, comprising the following steps:
[0047] S1: Model the low-altitude airspace environment to obtain a low-altitude airspace environment model;
[0048] The low-altitude airspace environment modeling includes three-dimensional terrain modeling and static obstacle modeling;
[0049] The 3D terrain information can be acquired through LiDAR, depth cameras, or pre-built digital elevation models (DEMs). This information includes the longitude, latitude, and altitude of the land surface, used to accurately reproduce real mountain ranges, canyons, and other landforms. Static obstacles include buildings, communication towers, no-fly zones, groups of trees, or other static structures. The geometry of static obstacles is described using cylinders, and the location of each obstacle is defined. Horizontal boundary and vertical height range Static obstacles are represented as follows: , Let the three-dimensional Cartesian coordinates of the obstacle be... This represents the total number of static obstacles.
[0050] S2: Construct a fitness function for evaluating the comprehensive cost of a path;
[0051] Preferably, the overall path cost takes into account path length, trajectory smoothness, and obstacle avoidance safety;
[0052] fitness function The formula is as follows:
[0053] ;
[0054] In the formula, Indicates the cost of the path length. Indicates the cost of path smoothness. Indicates the cost of flying altitude. Indicates the cost of obstacle avoidance. , , , These are weighting coefficients, used to balance path feasibility and optimization performance;
[0055] Regarding the fitness function mentioned above, the lower the fitness, the higher the path quality.
[0056] S3: An enhanced particle swarm optimization algorithm is used to iteratively solve for the global optimal solution vector within the feasible space of the low-altitude airspace environment model. During the iteration process, the inertia weight gradually decreases, the individual learning factor gradually decreases, and the global learning factor gradually increases to achieve an adaptive balance in the evolution of search capability over time. When the swarm tends to converge, local perturbations are applied to the positions of multiple well-performing particles, centered on the global optimal position, to concentrate the search in high-potential areas. When the overall convergence speed of the swarm slows down or the changes in particle positions tend to stabilize, the swarm is determined to be in a stagnant state. If stagnation is detected for the first time (in a mild stagnation), the velocity of some particles is updated by random perturbation. If stagnation is still detected after multiple iterations (in a deep stagnation), the particle positions are slightly adjusted and boundary corrections are performed to enhance the redispersibility of the swarm. The position vector of each particle in the particle swarm represents the encoding of a flight path.
[0057] The specific steps of using the enhanced particle swarm optimization algorithm to iteratively solve for the global optimal solution vector within the feasible space of the low-altitude airspace environment model are as follows:
[0058] S31: Initialize a containing A swarm of particles is constructed, and the fitness function is used to evaluate the fitness of each particle (i.e., each path). The position vector of each particle is used as its initial individual optimal solution vector. The position vector of the best-fit particle in the particle swarm is used as the initial global optimal solution vector. ,in, This represents the particle swarm size, where the position vector of each particle encodes a flight path. The position vector of each particle It is expressed as follows: , , Indicates the first The first path Three-dimensional Cartesian coordinates of intermediate waypoints , This represents the total number of intermediate waypoints in the path (excluding the starting and ending points);
[0059] To improve the diversity and global feasibility of the initial particle swarm under complex low-altitude airspace conditions, the continuous domain ant colony algorithm is preferred. Initialize the particle swarm;
[0060] Among them, the continuous domain ant colony algorithm ( Initializing the particle swarm includes the following steps:
[0061] Multiple initial paths are randomly generated within the feasible space of the low-altitude airspace environment model;
[0062] Each path is evaluated using the fitness function, and all paths are sorted according to their fitness.
[0063] High-quality paths are assigned higher sampling weights, and multiple rounds of "evaluation-screening-resampling" are repeated to generate high-quality initial paths as the initial positions of the particle swarm.
[0064] The above initialization method can significantly improve the distribution uniformity and global exploration capability of the initial population under conditions of multiple obstacles and height restrictions in low-altitude airspace, and effectively avoid the premature convergence problem that traditional random initialization is prone to occur in complex low-altitude environments.
[0065] S32: Update the velocity and position of each particle (dynamic greedy search mechanism), where the velocity and position update formulas are as follows:
[0066] ;
[0067] ;
[0068] ;
[0069] In the formula, For the first During the nth iteration, the 1st The first particle 1D velocity components; For the first During the nth iteration, the 1st The first particle Positional components of the dimension; For the first The first particle The individual optimal solution component of dimension; For the particle swarm The global optimal solution component of dimension; For inertial weights, , These are individual learning factors and global learning factors, respectively. , A random number between [0, 1]; This represents the current iteration number. The maximum number of iterations; This is the adjustment coefficient; , These are the upper and lower limits of the inertia weight, respectively. This represents the upper limit of the individual learning factor. This represents the lower bound of the global learning factor; as iterations proceed, the inertia weight... Gradually decrease, individual learning factor Gradually decreasing, while the global learning factor It gradually grows larger, thereby realizing an adaptive search strategy of "early exploration and later development";
[0070] S33: Calculate the group velocity variance The formula is as follows:
[0071] ;
[0072] In the formula, For the dimension of the particle, , This represents the total number of intermediate waypoints in the path (excluding the starting and ending points). For the first The first particle Dimensional speed; Indicates the first The variance of the velocity set of all particles in a dimension is used to measure the dispersion of the particle swarm velocity in that dimension, providing a basis for the algorithm's adaptation.
[0073] S34: Comparing group velocity variances With the preset population convergence threshold ,like (The value can be 0.05), indicating that the population tends to converge. A local greedy perturbation mechanism is then activated, strengthening the local search around the current global optimum. The specific steps are as follows:
[0074] At the current global optimal position Centered on a few high-performing particles, local perturbations are applied to concentrate the search on high-potential regions. The perturbation model is as follows:
[0075] ;
[0076] in, For the first The original position vectors of each particle. For the first The new position vector of each particle after perturbation , Let be a uniform random vector in the interval [-1, 1]. The current perturbation strength, which gradually decreases with the iteration progress, is defined as:
[0077] ;
[0078] in, and These are the upper and lower limits of the disturbance intensity, respectively, and can be 0.5 and 0.05.
[0079] S35: Calculate the normalized population velocity variance The formula is as follows:
[0080] ;
[0081] in, For the dimension of the particle, , This represents the total number of intermediate waypoints in the path (excluding the starting and ending points). For the first The first particle Dimensional speed; Indicates the first The variance of the set of velocities of all particles in a given dimension is used to measure the dispersion of particle swarm velocities in that dimension, providing a basis for the algorithm's adaptability. For the first The maximum speed allowed by the dimension;
[0082] S36: Compare the normalized population velocity variance Compared with the preset stagnation perception threshold ,like The system determines that the group is in a stagnant state and performs velocity and / or position perturbations on the particles to allow them to escape. The value ranges from 0.03 to 0.08. The specific rules for achieving escape by perturbing the velocity and / or position of the particle are as follows:
[0083] (a) Mild stagnation: When stagnation is first detected, it is given a probability. (If we take 0.2) We perform random perturbation updates on the velocities of some particles, as shown in the following formula:
[0084] ;
[0085] in, For the first The original velocity vector of each particle. For the first The new velocity vector of each particle after the perturbation The velocity disturbance intensity is preferably measured in the range of 0.05 to 0.2. Let be a random vector uniformly distributed in the interval [−1, 1]. For the first The maximum allowable velocity vector for each particle;
[0086] (b) Deep Stagnation: If stagnation is still detected after K consecutive iterations (e.g., K=3), the particle positions are slightly adjusted to enhance population redispersibility. The adjustment formula is as follows:
[0087] ;
[0088] in, For the first The original position vectors of each particle. For the first The new position vector of each particle after perturbation Let be a uniform random vector in the interval [-1, 1]. The location disturbance intensity is preferably within the range of 0.01 to 0.05. and These are the upper and lower boundary vectors of the search space, respectively;
[0089] (c) Determine whether the perturbed particles exceed the search space boundary. If so, correct the particle position using mirror reflection, as shown in the following formula:
[0090] ;
[0091] in, For the first The new position vector of each particle after perturbation For the first The corrected position vector of each particle. and These are the upper and lower boundary vectors of the search space, respectively;
[0092] The above mechanism (stagnation perception escape mechanism) can detect and break the stagnation state of the population caused by multiple constraints under low-altitude complex airspace conditions through the dual correction of velocity perturbation and / or position perturbation and position reflection. It can effectively restore the diversity of the particle swarm under low-altitude complex airspace conditions and enhance the algorithm's ability to escape local optima.
[0093] S37: Use the fitness function to evaluate the updated particles and update the global optimal solution vector and the individual optimal solution vector;
[0094] S38: Repeat S32-S37 until the rate of change of the fitness function is less than 1%. Or, after reaching the maximum number of iterations, the current optimal solution vector is obtained, along with the waypoint coordinates of the corresponding optimal three-dimensional path;
[0095] To improve the continuity and feasibility of the final low-altitude flight path during actual flight, the following steps are included after obtaining the optimal solution vector:
[0096] S4: The discrete waypoints in the optimal solution vector are smoothed using Bézier curves to obtain a continuous and smooth flight path. This involves smoothing the continuous control nodes. Represented by a cubic Bézier curve, its parametric equation is:
[0097] ;
[0098] in, This indicates the interpolation ratio from the starting point to the ending point.
[0099] The present invention provides a three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization. By adopting a dynamic greedy search strategy and introducing a local greedy perturbation mechanism, it can strengthen global search in the early stage of iteration and enhance local development in the later stage, adaptively balancing exploration and development capabilities, and avoiding premature convergence or slow convergence. The stagnation-aware escape mechanism can detect whether the particle swarm is trapped in a local optimum stagnation and promptly trigger the perturbation strategy to allow the particles to jump out of the stagnation region, thereby improving optimization accuracy and global convergence capability.
[0100] Figure 2 To generate optimal path three-view diagrams in complex terrain environments in low-altitude airspace using the method proposed in this invention, Figure 3 To compare the path three-view diagrams generated by the traditional particle swarm optimization (PSO) algorithm in the same low-altitude airspace environment, it can be seen that in low-altitude complex terrain and obstacle-dense airspace environments, the path planned by the path planning method proposed in this invention is shorter and smoother than the path planned by the traditional PSO algorithm, and can effectively avoid terrain and obstacles, thus achieving efficient global optimization of aircraft path planning under low-altitude airspace conditions.
[0101] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.
[0102] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0103] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0104] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0105] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0106] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
Claims
1. A three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization, characterized in that, include: Modeling the low-altitude airspace environment yields a low-altitude airspace environment model. Construct a fitness function for evaluating the comprehensive cost of a path; An enhanced particle swarm optimization algorithm is used to iteratively solve for the global optimal solution vector within the feasible space of the low-altitude airspace environment model. During the iteration process, the inertia weight gradually decreases, the individual learning factor gradually decreases, and the global learning factor gradually increases. When the swarm tends to converge, local perturbations are applied to the positions of multiple well-performing particles, centered on the global optimal position. When the overall convergence speed of the swarm slows down or the changes in particle positions tend to stabilize, the swarm is determined to be in a stagnant state. If stagnation is detected for the first time, the velocities of some particles are updated by random perturbation. If stagnation is still detected after multiple iterations, the particle positions are slightly adjusted and boundary corrections are performed. The position vector of each particle in the particle swarm represents the encoding of a flight path.
2. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 1, characterized in that: The low-altitude airspace environment modeling includes 3D terrain modeling and static obstacle modeling.
3. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 1, characterized in that: The fitness function The formula is as follows: ； In the formula, Indicates the cost of the path length. Indicates the cost of path smoothness. Indicates the cost of flying altitude. Indicates the cost of obstacle avoidance. , , , These are the weighting coefficients.
4. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 1, characterized in that: The specific steps of using the enhanced particle swarm optimization algorithm to iteratively solve for the global optimal solution vector within the feasible space of the low-altitude airspace environment model are as follows: Initialize a containing A swarm of particles is generated, and the fitness function is used to evaluate the fitness of each particle. The position vector of each particle is used as its initial individual optimal solution vector. The position vector of the best-fit particle in the particle swarm is used as the initial global optimal solution vector. ,in, Indicates the size of the particle swarm; Iteratively update each particle in the particle swarm to obtain the global optimal solution vector, where the i-th particle... The steps of this iteration are as follows: Update the particle's velocity and position, including the inertial weights. Individual learning factors and global learning factor The formula is as follows: ； ； ； In the formula, This represents the current iteration number. The maximum number of iterations; This is the adjustment coefficient; , These are the upper and lower limits of the inertia weight, respectively. This represents the upper limit of the individual learning factor. This is the lower limit of the global learning factor; Calculate the variance of group velocity And compare it with the preset population convergence threshold. If a comparison is made, At the current global optimal position A local perturbation is applied to several high-performing particles centered on the target particle. The perturbation model is as follows: ； in, For the first The original position vectors of each particle. For the first The new position vector of each particle after perturbation Let be a uniform random vector in the interval [-1, 1]. The current disturbance strength gradually decreases as the iteration progresses; Calculate the normalized population velocity variance And compare it with the preset stagnation perception threshold. If a comparison is made, If the population is determined to be in a stagnant state, and stagnation is detected for the first time, the velocity of some particles is updated by random perturbation. If stagnation is still detected after multiple iterations, the particle positions are slightly adjusted and the boundary is corrected.
5. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 4, characterized in that: The particle swarm is initialized using the continuous domain ant colony algorithm.
6. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 4, characterized in that: Current disturbance intensity The formula is as follows: ； In the formula, and These are the upper and lower limits of the disturbance intensity, respectively. This represents the current iteration number. This represents the maximum number of iterations.
7. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 4, characterized in that: For the The formula for perturbing and updating the velocity of each particle is as follows: ； in, For the first The original velocity vector of each particle. For the first The new velocity vector of each particle after the perturbation For the velocity disturbance intensity, Let be a random vector uniformly distributed in the interval [−1, 1]. For the first The maximum allowable velocity vector for a particle.
8. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 4, characterized in that: For the The formula for making minute adjustments to the position of each particle is as follows: ； in, For the first The original position vectors of each particle. For the first The new position vector of each particle after perturbation Let be a uniform random vector in the interval [-1, 1]. The intensity of the positional disturbance. and These are the upper and lower boundary vectors of the search space, respectively.
9. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 4, characterized in that: The formula for boundary correction of particles is as follows: ； in, For the first The new position vector of each particle after perturbation For the first The corrected position vector of each particle. and These are the upper and lower boundary vectors of the search space, respectively.
10. The three-dimensional path planning method for low-altitude airspace vehicles based on enhanced particle swarm optimization according to claim 1, characterized in that: It also includes the following steps: smoothing the discrete waypoints corresponding to the global optimal solution vector using Bézier curves to obtain a continuous and smooth flight path.