Unmanned aerial vehicle path planning method based on improved farthest best worst optimization algorithm

Abstract

The application provides a UAV path planning method and device based on an improved farthest optimal nearest worst optimization algorithm, which comprises complex three-dimensional terrain modeling, UAV motion constraints and a comprehensive cost minimization path to construct a fitness function as an optimization target, introduces an adaptive proportional tent chaos hybrid initialization mechanism to improve population diversity and ergodicity, embeds an adaptive elite individual local development strategy to improve the late development accuracy of an original farthest optimal nearest worst algorithm (FNO), and uses a cosine continuous nonlinear dynamic balance factor to construct an improved farthest optimal nearest worst algorithm (PCFNO) to realize adaptive dynamic balance of exploration and development and improve the accuracy, convergence speed and safety in a UAV path planning task.

Description

Technical Field

[0001] This paper belongs to the field of UAV technology, specifically involving a UAV path planning method based on an improved farthest-best-nearest optimization algorithm. Background Technology

[0002] With the rapid development of artificial intelligence, communication technology, and 5G technology, unmanned aerial vehicles (UAVs) have begun to play a crucial role in agricultural plant protection, logistics transportation, and military reconnaissance. Faced with complex spatial scenarios and variable weather conditions, finding a highly efficient and low-cost flight path during the UAV planning process is of paramount importance for UAV mission execution.

[0003] Unmanned aerial vehicle (UAV) path planning algorithms aim to plan the optimal flight path for a UAV under the current task. UAV path planning involves both 2D and 3D environments. 2D environments have simple structures and impose fewer constraints on the UAV, thus limiting their practicality. 3D environments present greater spatial complexity and higher constraints on the UAV itself. Furthermore, 3D path planning also faces computational challenges. Therefore, finding the most stable and safest path for the UAV in a 3D environment is particularly important. The Farthest Better or Nearest Worse Optimizer (FNO) algorithm searches based on a "location distance + fitness" method. Its unique "distance + fitness" guiding mechanism gives it an advantage over other intelligent algorithms; however, it still suffers from drawbacks such as insufficient initial population diversity, insufficient optimization accuracy in later stages, and an imbalance between exploration and development.

[0004] Therefore, there is an urgent need for a solution that can improve the efficiency of drone path planning. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this paper aims to provide a UAV path planning method based on an improved farthest-best-nearest optimization algorithm, which can improve the efficiency of UAV path planning.

[0006] To solve the above-mentioned technical problems, the specific technical solution presented in this paper is as follows: On the one hand, this paper provides a UAV path planning method based on an improved farthest-best-nearest optimization algorithm, the method comprising: Construct a three-dimensional terrain environment model, which includes at least spatial boundary constraints, terrain elevation constraints, no-fly zone threat constraints, and mission start and end point constraints. Design a motion constraint model for a UAV, which includes at least safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. A path planning mathematical model for unmanned aerial vehicles (UAVs) is established, comprising a segmented path encoding and a fitness function. Based on the three-dimensional terrain environment model and the UAV motion constraint model, the fitness function is optimized using an improved farthest-first-last-inferior optimization algorithm to obtain the UAV three-dimensional flight path with the minimum fitness value. The improved farthest-first-last-inferior optimization algorithm introduces an adaptive proportional tent chaotic hybrid initialization mechanism, a cosine continuous nonlinear dynamic balance factor, and an adaptive elite individual local development strategy.

[0007] Furthermore, the segmented path coding adopts segmented spherical coordinate coding, and each flight path segment is represented by three sets of parameters: distance, pitch angle, and azimuth angle.

[0008] Furthermore, the fitness function is expressed by the following formula: ; in, Let be the fitness function, which represents the total cost of the path. For the cost of the voyage; As a threat at cost; To smooth out costs; At a high cost; , , , These are the weighting coefficients for each cost item; ; in, , For the first j Waypoint coordinates , For the first j +1 waypoint coordinates For the first j The actual flight altitude after adding terrain elevation to each waypoint For the first j The actual flight altitude is calculated by adding the terrain altitude to one waypoint. This represents the total number of waypoints along the entire route. For the cost of the voyage; ; in, The horizontal distance from the path segment to the center of the obstacle; The radius of the obstacle; For drone dimensions; For safety margin; This is the penalty coefficient; ; in, For the first i Segment path pitch angle; For the first i Horizontal turning angle of the path segment; ; in, For the first j The altitude coordinates of each waypoint in actual three-dimensional space Minimum safe height; This is the highest safe altitude.

[0009] Furthermore, the fitness function is optimized using an improved farthest-best-nearest-worst optimization algorithm, including: The initial population is generated using chaotic mapping, resulting in multiple initial planned paths. Calculate the fitness value for each initial planned path; The fitness values ​​are sorted, and elite individuals and ordinary individuals are selected using a differentiated search strategy. Ordinary individuals are updated using the original dual-guided method of farthest best and nearest worst. The exploration and development phase of the string-continuous nonlinear dynamic balance factor balancing algorithm was adopted, and an elite local development strategy was implemented on the elite path to optimize the path quality and obtain the final UAV three-dimensional flight path.

[0010] Furthermore, chaotic mapping is used to initialize and generate the initial population, resulting in multiple initial planning paths: a chaotic initialization ratio λ is set, a chaotic sequence is generated using tent chaotic mapping, and mapped to the actual exploration space of the optimization problem through linear scaling transformation; during population initialization, initial individuals are generated according to the ratio λ using tent chaotic mapping, and the remaining ratio 1-λ is generated randomly to enhance the spatial ergodicity and diversity of the initial population.

[0011] Furthermore, the mapping formula for tent chaos is: ; In the formula, Let p be the initial position vector of the p-th individual in the population. To optimize the upper bound vector of variables, To optimize the lower bound vector of variables; For normalized tent chaotic sequences; Initialize the proportions for chaos. The random numbers are uniformly distributed in the range [0,1]. This is a function for generating uniformly random locations.

[0012] Furthermore, the cosine continuous nonlinear dynamic equilibrium factor is obtained through the following formula: ; in, Let be the cosine continuous nonlinear dynamic equilibrium factor for the t-th iteration of the algorithm, where t is the current iteration number. This represents the maximum number of iterations for the algorithm.

[0013] Furthermore, the adaptive elite individual local development strategy includes: using a local perturbation model based on the individual's historical best to perform a refined search on the elite individual; the local perturbation model introduces a linearly increasing adaptive learning factor, which dynamically adjusts the local development intensity as the number of iterations increases.

[0014] Furthermore, a refined search is performed on the elite individuals using a local perturbation model based on their historical best performance, including: Design a linearly increasing adaptive learning factor, expressed as: ; in, Let be the learning factor for the t-th iteration. This is the lower limit of the learning factor. The upper limit of the learning factor, The coefficients for the current iteration. This represents the maximum number of iterations for the algorithm. Based on the linearly increasing adaptive learning factor, a local perturbation model is constructed for elite individuals to obtain their local search offset, expressed as: ; In the formula, Let be the local search offset of the elite individual p in the t-th iteration. Let be the historical optimal vector of the p-th individual. It is a random vector of dimension [0,1]. This represents the position of the p-th individual in the current t-th generation population. The new position of the elite individual is updated based on its local search offset, as shown below: ;in, This is the local search step size coefficient. Let p be the new position of the elite individual in the t-th iteration. This represents the position of the p-th individual in the current t-th generation population.

[0015] In addition, this paper also provides a UAV path planning device based on an improved farthest-best-nearest optimization algorithm, the device comprising: A 3D terrain environment model construction module is used to construct a 3D terrain environment model, which includes at least spatial boundary constraints, terrain elevation constraints, no-fly zone threat constraints, and mission start and end point constraints. The UAV motion constraint model design module is used to design a UAV motion constraint model, which includes at least safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. The path planning mathematical model building module establishes a path planning mathematical model for the UAV, which includes a segmented path encoding and a fitness function. The optimization module is used to optimize the fitness function based on the three-dimensional terrain environment model and the UAV motion constraint model, using an improved farthest-best-nearest-worst optimization algorithm to obtain the UAV three-dimensional flight path with the minimum fitness value. The improved farthest-best-nearest-worst optimization algorithm introduces an adaptive proportional tent chaotic hybrid initialization mechanism, a cosine continuous nonlinear dynamic balance factor, and an adaptive elite individual local development strategy.

[0016] By adopting the above technical solution, the UAV path planning method and device based on the improved farthest-nearest-dominant optimization algorithm described in this paper improves population diversity and ergodicity by introducing an adaptive proportional tent chaotic hybrid initialization mechanism; it also improves the later development accuracy of the original farthest-nearest-dominant algorithm (FNO) by embedding an adaptive elite individual local development strategy; and further utilizes a cosine continuous nonlinear dynamic balance factor to construct an improved farthest-nearest-dominant algorithm (PCFNO) to achieve an adaptive dynamic balance between exploration and development, thereby improving the accuracy, convergence speed, and safety of UAV path planning tasks.

[0017] To make the above and other objects, features and advantages of this document more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments or prior art described herein, the accompanying drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this article. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This document illustrates the steps of the UAV path planning method based on the improved farthest-best-nearest optimization algorithm provided in the embodiments of this paper. Figure 2 A schematic diagram of the three-dimensional terrain environment model in the embodiments of this paper is shown; Figure 3 The flowchart of the improved farthest best and nearest worst algorithm in the embodiments of this paper is shown; Figure 4a The comparison of ablation experiment iteration curves in the embodiments of this paper is shown. Figure 1 ; Figure 4b The comparison of ablation experiment iteration curves in the embodiments of this paper is shown. Figure 2 ; Figure 4c The comparison of ablation experiment iteration curves in the embodiments of this paper is shown. Figure 3 ; Figure 4d Figure 4 shows a comparison of the ablation experiment iteration curves in the embodiments described in this paper; Figure 5a This document shows a schematic diagram of the main view of the UAV's 3D path planning in an embodiment of the invention. Figure 5b This document shows a schematic diagram of the UAV 3D path planning in an embodiment of the invention. Figure 5c shows a schematic side view of the UAV three-dimensional path planning in the embodiment of this paper; Figure 6 This paper presents a schematic diagram showing the convergence comparison curves of multiple algorithm path iterations in the embodiments described herein. Figure 7 This diagram illustrates a UAV path planning device based on an improved farthest-best-nearest optimization algorithm provided in the embodiments of this paper. Figure 8 A schematic diagram of the structure of the computer device provided in the embodiments of this article is shown. Detailed Implementation

[0020] The technical solutions in the embodiments described below will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments described herein, and not all of the embodiments. Based on the embodiments described herein, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this document.

[0021] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings herein are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, apparatus, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0022] In existing technologies, path planning is becoming increasingly important for UAVs performing tasks. For example, the Farthest Better or Nearest Worse Optimizer (FNO) algorithm searches based on a combination of location distance and fitness. Its unique "distance + fitness" guidance mechanism gives it an advantage over other intelligent algorithms. However, this algorithm still suffers from drawbacks such as insufficient initial population diversity, insufficient optimization accuracy in later stages, and an imbalance between exploration and development.

[0023] To address the aforementioned issues, this paper presents an embodiment of a UAV path planning method based on an improved farthest-best-nearest optimization algorithm, which can improve the efficiency of UAV 3D path planning. Figure 1 This document illustrates the steps of a UAV path planning method based on an improved farthest-first-last-inferior optimization algorithm, as provided in the embodiments. While this specification provides the operational steps described in the embodiments or flowcharts, conventional or non-inventive methods may include more or fewer steps. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only possible order. In actual system or device products, the methods shown in the embodiments or accompanying drawings can be executed sequentially or in parallel. Specifically, as shown in the embodiments or accompanying drawings... Figure 1 As shown, the method may include: S101: Construct a three-dimensional terrain environment model, which includes at least spatial boundary constraints, terrain elevation constraints, no-fly zone threat constraints, and mission start and end point constraints. S102: Design a motion constraint model for the UAV, which includes at least safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. S103: Establish a path planning mathematical model for the UAV, wherein the path planning mathematical model includes a segmented path encoding and a fitness function; S104: Based on the three-dimensional terrain environment model and the UAV motion constraint model, the fitness function is optimized using the improved farthest-best-nearest-inferior optimization algorithm to obtain the UAV three-dimensional flight path with the minimum fitness value. The improved farthest-best-nearest-inferior optimization algorithm introduces an adaptive proportional tent chaotic hybrid initialization mechanism, a cosine continuous nonlinear dynamic balance factor, and an adaptive elite individual local development strategy.

[0024] In other words, the embodiments in this specification improve population diversity and ergodicity by introducing an adaptive proportional tent chaotic hybrid initialization mechanism; improve the later development accuracy of the original farthest-better-nearest-worse algorithm (FNO) by embedding an adaptive elite individual local development strategy; and further improve the accuracy, convergence speed, and safety of UAV path planning tasks by utilizing a cosine continuous nonlinear dynamic balance factor to construct an improved chaotic farthest-better-nearest-worse algorithm (PCFNO).

[0025] This invention constructs an integrated three-dimensional terrain model that includes mountain peaks, landforms, physical obstacles, and elevation mapping functions. It relies on a program to complete data parsing, landform reconstruction, obstacle placement, and elevation numerical calculation, providing a simulation environment for UAV path planning tasks.

[0026] This invention uses standardized topographic elevation data to construct a continuously undulating mountainous terrain. The original elevation data is scaled and normalized to obtain a topographic elevation matrix with uniform accuracy. The elevation correction formula is as follows: ; In the formula, This is the original terrain elevation data. This results in a usable terrain elevation matrix. A planar grid coordinate system is constructed based on this elevation matrix to reproduce undulating terrain and build mountain models. Simultaneously, airspace boundaries are defined to regulate the scope of flight activities.

[0027] Furthermore, in a mountainous environment, six sets of cylindrical three-dimensional obstacles were laid out to simulate a complex no-fly zone with multiple obstacles. Each of the six sets of obstacles was independently configured with its center coordinates and effective radius parameters, and was staggered throughout the mountainous environment to simulate obstacles such as mountain protrusions and no-fly zones in the airspace. Simultaneously, warning zones were delineated based on the obstacle boundaries, providing a foundation for UAV obstacle avoidance constraints.

[0028] Some embodiments in this specification construct complex three-dimensional mountain flight environments for UAV path planning. The environment includes spatial boundaries, terrain elevation, cylindrical no-fly zones, flight safety redundancy, mission start point, and trajectory smooth motion constraints. These constraints are coupled to form the flight space.

[0029] Specifically, it includes: Horizontal spatial boundary constraints restrict the horizontal coordinates of all waypoints of the UAV to within the map and prevent them from going out of bounds, as shown below.

[0030] ; In the formula, The lateral coordinates of the waypoints The longitudinal coordinates of the waypoints , This represents the maximum horizontal and vertical dimensions of the map. Waypoints outside this range cannot be included in the feasible set.

[0031] Three-dimensional elevation constraints can include terrain obstacle avoidance constraints, relative ground clearance range constraints, and global maximum absolute height constraints.

[0032] The terrain obstacle avoidance constraint requires that the absolute flight altitude of the UAV be derived from the superposition of the ground elevation and the relative altitude above the ground. The relative altitude above the ground should always be greater than 0 so that the flight path will not penetrate the mountain. The form is shown below.

[0033] ; In the formula, For the absolute altitude of the drone, For the drone's altitude relative to the ground, It represents the ground elevation.

[0034] To simulate the flight of a drone around mountainous obstacles, a relative altitude range constraint is imposed, limiting the drone's altitude relative to the ground. The form is shown below.

[0035] ; In the formula, This refers to the drone's altitude relative to the ground.

[0036] Global maximum absolute altitude constraint: Set a global absolute flight altitude limit, where any waypoint satisfies the following formula.

[0037] ; In the formula, This refers to the absolute altitude of the drone.

[0038] Cylindrical no-fly zone threat constraints: Static cylindrical obstacles are laid out on complex three-dimensional terrain to serve as no-fly zones in the environment, which are divided into basic access constraints and engineering safety distance constraints.

[0039] First, the geometric definition of a no-fly zone: the coordinates of the center of a single circular obstacle are... The radius of a single cylindrical obstacle is There are a total of 6 obstacles.

[0040] The basic no-entry constraint requires that the Euclidean distance between each waypoint of the UAV and the center of the obstacle in the horizontal angle must be greater than the radius of the obstacle itself, prohibiting entry into the cylinder. The form is shown below.

[0041] ; In the formula, The x-coordinate of the center of a single cylindrical obstacle, The ordinate of the center of a single cylindrical obstacle, Let be the radius of a single cylindrical obstacle.

[0042] To account for both the UAV's physical dimensions and emergency buffer distance, a two-level safety compensation parameter is set. Taking into account the fuselage dimensions and avoidance margin, a minimum safe distance constraint between the waypoint and the obstacle center is constructed. The form is shown below.

[0043] ; In the formula, The x-coordinate of the center of a single cylindrical obstacle, The ordinate of the center of a single cylindrical obstacle, Where is the radius of a single cylindrical obstacle, D is the radius of the UAV fuselage, and S is the emergency safety redundancy distance.

[0044] The mission start and end point constraints indicate that the UAV path planning should satisfy fixed start and end point constraints. A complete trajectory is constructed by sequentially piecing together the start point, intermediate discrete points, and the end point. Let the start point coordinates be... End point coordinates track sequence The complete path must meet the following requirements.

[0045] ; In the formula, the starting point and the ending point are given in advance, and the spatial, height and safety distance constraints mentioned above must be met.

[0046] In this embodiment of the specification, step S102 involves determining the constraints for the UAV's path flight based on its own characteristics and flight safety considerations. These constraints may include safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. Specifically: Safety distance constraints can be used to determine the positional relationship between the drone and obstacles by comparing the shortest distance from a point to a line segment with the radius of the obstacle. The formula for determining the constraint relationship is shown below: ; In the formula, The horizontal distance from the path to the center of the obstacle; The radius of the obstacle; For drone dimensions; For safety margin.

[0047] Collision threat constraint, when the horizontal distance from the path to the center of the obstacle and the radius of the obstacle satisfy... When a relationship is established, it is determined to be a collision, at which point the cost function becomes infinite.

[0048] Maximum pitch angle constraint: To match the drone's climb and fall maneuver limits, the pitch angle variation between consecutive flight segments is limited. The relationship is shown below: ; In the formula, The pitch angle of the preceding flight path. The pitch angle for the latter part of the flight path.

[0049] The maximum turning angle constraint uses the method of limiting the horizontal turning angle to constrain the minimum turning radius, as shown in the following formula: ; In the formula, This is the turning angle within the horizontal plane of the adjacent flight paths. If the drone makes a sharp turn, unreasonable trajectories are filtered out by adding a penalty cost.

[0050] Path length constraint and range cost are used to constrain the formation length of the UAV, as shown below. ; In the formula, , Let i be the coordinates of the i-th waypoint. This represents the actual flight altitude after overlaying terrain elevation with the corresponding waypoints. This represents the total number of waypoints along the entire route. The cost of the journey.

[0051] Furthermore, the UAV path planning of this invention adopts a segmented spherical coordinate encoding method. Each segment of the UAV's flight path is described by three sets of parameters: distance, pitch angle, and azimuth angle. The parameters of all segments are arranged in sequence to form the input of the optimization algorithm, thereby discretizing the continuous path.

[0052] In the embodiments described in this specification, the fitness function is represented by the following formula: ; in, Let be the fitness function, which represents the total cost of the path. For the cost of the voyage; As a threat at cost; To smooth out costs; At a high cost; , , , These are the weighting coefficients for each cost item; ; in, , For the first j Waypoint coordinates , For the first j +1 waypoint coordinates For the first j The actual flight altitude after adding terrain elevation to each waypoint For the first j The actual flight altitude is calculated by adding the terrain altitude to one waypoint. This represents the total number of waypoints along the entire route. For the cost of the voyage; ; in, The horizontal distance from the path segment to the center of the obstacle; The radius of the obstacle; For drone dimensions; For safety margin; This is the penalty coefficient; ; in, For the first i Segment path pitch angle; For the first i Horizontal turning angle of the path segment; ; in, For the first j The altitude coordinates of each waypoint in actual three-dimensional space Minimum safe height; This is the highest safe altitude.

[0053] This specification's embodiments utilize an improved farthest-nearest-inferior optimization algorithm to optimize the fitness function. This algorithm is a novel population-based metaheuristic optimization algorithm. The algorithm's core idea is to rely on the dual information of the fitness of individuals in the population and their Euclidean distance, enabling individuals to expand towards distant high-quality regions, thereby strengthening global exploration capabilities. At the same time, it encourages individuals to actively move away from nearby low-quality regions, avoiding premature local convergence and improving algorithm efficiency. Through this mechanism of establishing differentiated search guidance, a balance between global exploration and local development is achieved.

[0054] Among them, the Farthest Nearest Odd (FNO) algorithm does not blindly search for high-quality individuals but instead aims for individuals with better fitness at greater distances. By focusing on high-quality individuals at greater distances, it transcends local limitations and enhances global exploration capabilities. The current set of excellent individuals is selected as follows: ; In the formula, This can be either the p-th individual in the current t-th generation of the population, or it can be the position vector corresponding to the p-th individual in the current t-th generation of the population. It refers to the individual fitness of the minimization problem. Let be the fitness value of the p-th individual in the t-th generation of the population. For all individuals with fitness values ​​better than the current individual N is the set of other superior individuals, where N is the total number of individuals in the population of generation t.

[0055] The spatial distance between any two dim-dimensional individuals is calculated using Euclidean distance, as shown below: ; In the formula, Let be the Euclidean distance between the p-th individual and the q-th individual. Let L2 be the symbolic representation of the L2 norm (or Euclidean norm), representing the length of the straight line between the p-th individual and the q-th individual.

[0056] In other words, it is possible to have a better set of individuals. In the process, the individuals with the greatest distance are selected using Euclidean distance, as shown in the following formula: ; In the formula, for The optimal individual in the set that is furthest from the p-th individual.

[0057] Since each individual may be surrounded by lower-quality individuals, the Farthest-Nearest-Inferior (FNO) algorithm can proactively identify these individuals, reducing the number of invalid searches and thus accelerating convergence. The current set of inferior individuals is selected as shown in the following formula: ; In the formula, For all individuals with fitness values ​​inferior to the current individual The set of other superior individuals.

[0058] A worse set of individuals In the process, the individuals with the greatest distance are selected using Euclidean distance, as shown in the following formula: ; In the formula, for The worst individual in the set that is closest to the p-th individual.

[0059] In the embodiments of this specification, the fitness function is optimized using an improved farthest-best-nearest-worst optimization algorithm, including: The initial population is generated using chaotic mapping, resulting in multiple initial planned paths. Calculate the fitness value for each initial planned path; The fitness values ​​are sorted, and elite individuals and ordinary individuals are selected using a differentiated search strategy. Ordinary individuals are updated using the original dual-guided method of farthest optimal and nearest worst. The exploration and development phase of the string-continuous nonlinear dynamic balance factor balancing algorithm was adopted, and an elite local development strategy was implemented on the elite path to optimize the path quality and obtain the final UAV three-dimensional flight path.

[0060] In this process, chaotic mapping is used to initialize and generate the initial population, resulting in multiple initial planning paths: a chaotic initialization ratio λ is set, a chaotic sequence is generated using tent chaotic mapping, and then mapped to the actual exploration space of the optimization problem through linear scaling transformation; when initializing the population, initial individuals are generated according to the ratio λ using tent chaotic mapping, and the remaining ratio 1-λ is generated randomly to enhance the spatial ergodicity and diversity of the initial population.

[0061] In other words, to address the problems of weak initialization traversal and poor population diversity in the farthest-best-nearest optimization algorithm, this invention introduces an adaptive proportional tent chaotic hybrid initialization mechanism. By setting a certain initial chaotic ratio, such as setting 80% of the initial individuals to be generated using tent chaos, and only retaining 20% ​​to randomly generate the remaining individuals, a hybrid initialization mode dominated by a high proportion of chaos is formed.

[0062] First, the chaotic sequence generated by the tent chaotic mapping is distributed in the interval [0,1], and is mapped to the actual exploration space of the optimization problem through linear scaling transformation. The mapping formula is shown below.

[0063] ; In the formula, Let p be the initial position vector of the p-th individual in the population. To optimize the upper bound vector of variables, To optimize the lower bound vector of variables, For normalized tent chaotic sequences.

[0064] Secondly, by adding a small number of random individuals, the spatial traversal during initialization is enhanced, greatly increasing the coverage of the population and fundamentally solving the problems of weak initial traversal and poor population diversity.

[0065] The adaptive scaling tent chaotic hybrid initialization mechanism is shown below.

[0066] ; In the formula, Let p be the initial position vector of the p-th individual in the population. To optimize the upper bound vector of variables, To optimize the lower bound vector of variables; For normalized tent chaotic sequences; The chaos initialization ratio can be 0.8 in the embodiments of this specification. The random numbers are uniformly distributed in the range [0,1]. This is a function for generating uniformly random locations.

[0067] In the embodiments of this specification, the original Farthest Best Nearest Odd (FNO) algorithm uses a square root nonlinear decay factor for switching between the exploration and development processes. However, this decay method results in a rapid decrease in the early iterations and a gradual decrease in the later iterations, leading to an overly abrupt transition between the early and late stages of the algorithm and making it difficult to achieve a smooth transition. This invention pioneers a cosine nonlinear decay control strategy. Relying on the continuous smoothness and nonlinear decreasing characteristics of the cosine function, the algorithm possesses a wide-ranging global exploration capability in the early iterations and focuses more on the development of local regions in the later iterations, enabling a smooth transition between exploration and development. Its form is shown below.

[0068] ; In the formula, Let be the cosine continuous nonlinear dynamic equilibrium factor for the t-th iteration of the algorithm, where t is the current iteration number. This represents the maximum number of iterations for the algorithm.

[0069] In the embodiments of this specification, the adaptive elite individual local development strategy includes: performing a refined search on the elite individual using a local perturbation model based on the individual's historical best; the local perturbation model introduces a linearly increasing adaptive learning factor, which dynamically adjusts the local development intensity as the number of iterations increases.

[0070] A refined search is performed on the elite individuals using a local perturbation model based on their historical best performance, including: Design a linearly increasing adaptive learning factor, expressed as: ; in, Let be the learning factor for the t-th iteration. This is the lower limit of the learning factor. The upper limit of the learning factor, The coefficients for the current iteration. This represents the maximum number of iterations for the algorithm. Based on the linearly increasing adaptive learning factor, a local perturbation model is constructed for elite individuals to obtain their local search offset, expressed as: ; In the formula, Let be the local search offset of the elite individual p in the t-th iteration. Let be the historical optimal vector of the p-th individual. It is a random vector of dimension [0,1]. This represents the position of the p-th individual in the current t-th generation population, compared to the position mentioned earlier. Consistent; The new position of the elite individual is updated based on its local search offset, as shown below: ;in, This is the local search step size coefficient, for example, it can be 0.3. Let p be the new position of the elite individual in the t-th iteration. This represents the position of the p-th individual in the current t-th generation population.

[0071] Flowchart of the improved farthest nearest-inferior algorithm (PCFNO) attached Figure 3 As shown.

[0072] In the embodiments of this specification, to analyze the performance of the improved nearest-farthest-most-poor algorithm (PCFNO) and verify the effectiveness of the three improvements, benchmark function tests were conducted through ablation experiments. The PCFNO algorithm was compared with the original algorithm, the FNOS algorithm (which introduces an adaptive proportional tent chaotic hybrid initialization mechanism), and the FNOSS algorithm (which introduces an adaptive proportional tent chaotic hybrid initialization mechanism and an adaptive elite individual local development strategy). To confirm the effectiveness of the algorithm, the benchmark functions introduced included unimodal and multimodal benchmark functions.

[0073] These algorithms all share the same parameter settings: an initial set of 30 individuals and a total of 300 iterations. For each of the four algorithms, 30 independent experiments were conducted on each benchmark function to obtain the optimal value of the objective function. By comparing the convergence curves of each algorithm under the four test functions, the superiority of the improved farthest-nearest-inferior (PCFNO) optimization algorithm is visually demonstrated.

[0074] Specifically, the design process is as follows: Algorithm parameter settings The parameters for the improved farthest-nearest-inferior (PCFNO) algorithm are designed as follows: Population size (Popsize), maximum number of iterations (iter), variable dimension (dim), upper bound of search range (ub), lower bound of search range (lb), Tent chaos mapping coefficient (TENT_A), number of chaos warm-up iterations (CH_ITER), chaos initialization ratio (CHAOS_MIX_RATIO), elite ratio (elite_ratio), initial learning factor (c1), and PSO local search step size.

[0075] Population Individual Coding The three-dimensional path of the drone is abstracted into an individual, and each individual represents a complete path of the drone from the starting point to the destination.

[0076] Fitness function calculation The present invention aims to minimize the cost of drone flight.

[0077] Iterative optimization process based on the improved farthest nearest-inferior algorithm (PCFNO) (1) Initialize the population The initial population is generated using Tent chaotic mapping to ensure uniform path distribution and sufficient diversity.

[0078] (2) Fitness value calculation The fitness value of each individual is calculated for the corresponding path to obtain the fitness.

[0079] (3) Determining the farthest superiority and the nearest inferiority Sort by fitness, and then select the farthest and nearest individuals based on Euclidean distance.

[0080] (4) Improve the update strategy of the farthest nearest-inferior algorithm (PCFNO). First, an exploration and development phase was adopted using a nonlinear cosine dynamic decay factor balancing algorithm. Second, an elite local development strategy was implemented for elite paths to optimize path quality.

[0081] This invention is based on MATLAB 2023b, operating system: WIN11, 64-bit operating system, 16GB memory, CPU NVIDIA RTX 5060. The simulation is divided into two parts: benchmark test function ablation experiment and three-dimensional UAV environment path planning comparison experiment. The performance of the algorithm is verified by convergence iteration curve and three-dimensional path front, top and side views.

[0082] Step 1: Constructing a Mountainous Environment S11. Setting the location of mountain obstacles The mountain terrain dimensions of this invention are 450×450. It is 450m. The value is 450m. The position coordinates and radius settings of the cylindrical obstacle are shown in Table 1.

[0083] Table 1. Location coordinates and radius settings for cylindrical obstacles 1 （300,300,100） 30 2 （200,100,100） 20 3 （100,200,100） 30 4 （300,100,100） 20 5 （200,50,00） 20 6 （150,350,100） 30 Step 2: Design UAV Constraints S21. Set task start and end point constraints The starting and ending coordinates of the UAV of this invention are shown in Table 2.

[0084] Table 2 Coordinates of the UAV's Start and End Points (10,10,200) (400,400,150) S22. Set drone parameters This invention sets the number of intermediate waypoints to 10, the equivalent radius D of the UAV fuselage to 10, the emergency safety redundancy distance S to 20, and the pitch angle constraint range to [-π / 4, π / 4] to prevent the UAV from exhibiting large dives or climbs. The azimuth angle constraint range to [0, π / 2] prevents the UAV from flying in a specific direction.

[0085] Step 3: Design the fitness function This invention designs the total cost function as a weighted sum of four terms, with the optimization objective being to minimize the overall cost. The weights of each parameter in the fitness function can be: It is 10. It is 100. It is 10. It is 50.

[0086] Step 4: Benchmark Function Ablation Experiment To verify the effectiveness of the three improvements, this invention selected four sets of standard benchmark test functions, as shown in Table 3.

[0087] Table 3. Benchmark Functions Appendix: Experimental Results of Benchmark Function Test Figures 4a-4d As shown, in terms of the optimal value of the objective function and algorithm convergence, the improved farthest nearest-dominant algorithm (PCFNO) exhibits superior performance compared to the farthest nearest-dominant algorithm (FNO), FNOS, and FNOSS. Its convergence speed is significantly faster than other algorithms, and it converges to the optimal solution. This demonstrates that the three improvements in this invention improve the performance of the original algorithm, enrich the population diversity of the original algorithm, improve the late-stage convergence accuracy of the algorithm, and strengthen the balance between global exploration and local exploitation.

[0088] Step 5: UAV 3D path planning based on the improved farthest nearest-nothing algorithm (PCFNO) Algorithm parameter design To ensure the validity and public nature of the experimental results, this invention has standardized some parameters of various algorithms: Population size Popsize is 60, maximum number of iterations iter is 300, variable dimension dim is 30, and the fitness formula is unified as a four-item weighted cost.

[0089] In the improved farthest nearest-inferior algorithm (PCFNO), the tent mapping control coefficient TENT_A is 0.9, the number of chaotic preheating iterations is 10, the elite individual ratio is 0.3, the initial learning factor c1 dynamically changes from 1.2 to 2.0, and the PSO local search step size is 0.3.

[0090] In the Particle Swarm Optimization (PSO) algorithm, the individual cognitive learning factor c1 is 1.49, the global social learning factor c2 is 1.49, the upper limit of particle velocity Vmax is 5, and the lower limit of particle velocity Vmin is -5. The convergence factor of the Whale Optimization (WOA) algorithm is... The screw tightness coefficient b is 1, and the screw parameters are... The escape energy of the Harris Hawk algorithm (HHO) is The development boundary threshold is 0.5, the finder percentage (find) of the Sparrow Search Algorithm (SSA) is 0.4, the safety threshold (ST) is 0.8, the warning sparrow percentage (FD) is 0.2, the rolling ball dung beetle (DBO) percentage (rol_percent) is 0.25, the brooding ball dung beetle (egg_percent) is 0.25, the larval small dung beetle (bab_percent) is 0.25, the thieving dung beetle (ste_percent) is 0.25, and the rolling ball switching threshold is 0.9.

[0091] The comparison curves of the UAV 3D path planning diagram and the path iteration convergence of multiple algorithms are attached. Figure 5a -Figure 5c, Appendix Figure 6 As shown in the figure, the improved farthest-nearest-dominant algorithm (PCFNO) demonstrates superior performance compared to other algorithms in UAV 3D path planning, both in terms of UAV path and convergence speed. Therefore, the results indicate that the improved farthest-nearest-dominant algorithm (PCFNO) can reduce the cost of UAV path planning and find the ideal path planning scheme fastest in complex 3D multi-constraint environments.

[0092] Based on the methods provided above, this specification also provides an unmanned aerial vehicle (UAV) path planning device based on an improved farthest-best-nearest optimization algorithm, such as... Figure 7 As shown, the device includes: The three-dimensional terrain environment model construction module 710 is used to construct a three-dimensional terrain environment model, which includes at least spatial boundary constraints, terrain elevation constraints, no-fly zone threat constraints, and mission start and end point constraints. The UAV motion constraint model design module 720 is used to design a UAV motion constraint model, which includes at least safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. The path planning mathematical model establishment module 730 establishes a path planning mathematical model for the UAV, wherein the path planning mathematical model includes a segmented path encoding and a fitness function; The optimization module 740 is used to optimize the fitness function based on the three-dimensional terrain environment model and the UAV motion constraint model, using an improved farthest-best-nearest-worst optimization algorithm to obtain the UAV three-dimensional flight path with the minimum fitness value. The improved farthest-best-nearest-worst optimization algorithm introduces an adaptive proportional tent chaotic hybrid initialization mechanism, a cosine continuous nonlinear dynamic balance factor, and an adaptive elite individual local development strategy.

[0093] This embodiment provides a computer device, the internal structure of which can be shown in the following diagram. Figure 8 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used for communication with external terminals via a network connection.

[0094] Those skilled in the art will understand that Figure 8 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0095] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0096] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the above method embodiments.

[0097] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0098] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0099] It should also be understood that, in the embodiments herein, the term "and / or" is merely a description of the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following associated objects have an "or" relationship.

[0100] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this document.

[0101] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0102] In the embodiments provided herein, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through some interfaces, devices, or units, or they may be electrical, mechanical, or other forms of connection.

[0103] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments described herein, depending on actual needs.

[0104] This document uses specific embodiments to illustrate the principles and implementation methods of this document. The descriptions of the embodiments above are only for the purpose of helping to understand the methods and core ideas of this document. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this document. Therefore, the content of this specification should not be construed as a limitation of this document.

Claims

1. A UAV path planning method based on an improved farthest-first-last-inferior optimization algorithm, characterized in that, The method includes: Construct a three-dimensional terrain environment model, which includes at least spatial boundary constraints, terrain elevation constraints, no-fly zone threat constraints, and mission start and end point constraints. Design a motion constraint model for a UAV, which includes at least safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. A path planning mathematical model for unmanned aerial vehicles (UAVs) is established, comprising a segmented path encoding and a fitness function. Based on the three-dimensional terrain environment model and the UAV motion constraint model, the fitness function is optimized using an improved farthest-first-last-inferior optimization algorithm to obtain the UAV three-dimensional flight path with the minimum fitness value. The improved farthest-first-last-inferior optimization algorithm introduces an adaptive proportional tent chaotic hybrid initialization mechanism, a cosine continuous nonlinear dynamic balance factor, and an adaptive elite individual local development strategy.

2. The method according to claim 1, characterized in that, The segmented path coding adopts segmented spherical coordinate coding, and each flight path segment is represented by three sets of parameters: distance, pitch angle, and azimuth angle.

3. The method according to claim 1, characterized in that, The fitness function is expressed by the following formula: ； in, Let be the fitness function, which represents the total cost of the path. For the cost of the voyage; As a threat at cost; To smooth out costs; At a high cost; , , , These are the weighting coefficients for each cost item; ； in, , For the first j Waypoint coordinates , For the first j +1 waypoint coordinates For the first j The actual flight altitude after adding terrain elevation to each waypoint For the first j The actual flight altitude is calculated by adding the terrain altitude to one waypoint. This represents the total number of waypoints along the entire route. For the cost of the voyage; ； in, The horizontal distance from the path segment to the center of the obstacle; The radius of the obstacle; For drone dimensions; For safety margin; This is the penalty coefficient; ； in, For the first i Segment path pitch angle; For the first i Horizontal turning angle of the path segment; ； in, For the first j The altitude coordinates of each waypoint in actual three-dimensional space Minimum safe height; This is the highest safe altitude.

4. The method according to claim 1, characterized in that, The fitness function is optimized using an improved farthest-best-nearest-worst optimization algorithm, including: The initial population is generated using chaotic mapping, resulting in multiple initial planned paths. Calculate the fitness value for each initial planned path; The fitness values ​​are sorted, and elite individuals and ordinary individuals are selected using a differentiated search strategy. Ordinary individuals are updated using the original dual-guided method of farthest optimal and nearest worst. The exploration and development phase of the string-continuous nonlinear dynamic balance factor balancing algorithm was adopted, and an elite local development strategy was implemented on the elite path to optimize the path quality and obtain the final UAV three-dimensional flight path.

5. The method according to claim 1, characterized in that, The initial population is generated using chaotic mapping, resulting in multiple initial planning paths: a chaotic initialization ratio λ is set, a chaotic sequence is generated using tent chaotic mapping, and then mapped to the actual exploration space of the optimization problem through linear scaling transformation; when initializing the population, initial individuals are generated using tent chaotic mapping according to the ratio λ, and the remaining ratio 1-λ is generated randomly to enhance the spatial ergodicity and diversity of the initial population.

6. The method according to claim 5, characterized in that, The mapping formula for tent chaos is: ； In the formula, Let p be the initial position vector of the p-th individual in the population. To optimize the upper bound vector of variables, To optimize the lower bound vector of variables; For normalized tent chaotic sequences; Initialize the proportions for chaos. The random numbers are uniformly distributed in the range [0,1]. This is a function for generating uniformly random locations.

7. The method according to claim 1, characterized in that, The cosine continuous nonlinear dynamic equilibrium factor is obtained by the following formula: ; in, Let be the cosine continuous nonlinear dynamic equilibrium factor for the t-th iteration of the algorithm, where t is the current iteration number. This represents the maximum number of iterations for the algorithm.

8. The method according to claim 1, characterized in that, The adaptive elite individual local development strategy includes: using a local perturbation model based on the individual's historical best to perform a refined search on the elite individual; the local perturbation model introduces a linearly increasing adaptive learning factor, which dynamically adjusts the local development intensity as the number of iterations increases.

9. The method according to claim 8, characterized in that, A refined search is performed on the elite individuals using a local perturbation model based on their historical best performance, including: Design a linearly increasing adaptive learning factor, expressed as: ; in, Let be the learning factor for the t-th iteration. This is the lower limit of the learning factor. The upper limit of the learning factor, The coefficients for the current iteration. This represents the maximum number of iterations for the algorithm. Based on the linearly increasing adaptive learning factor, a local perturbation model is constructed for elite individuals to obtain their local search offset, expressed as: ; In the formula, Let be the local search offset of the elite individual p in the t-th iteration. Let be the historical optimal vector of the p-th individual. It is a random vector of dimension [0,1]. This represents the position of the p-th individual in the current t-th generation population. The new position of the elite individual is updated based on its local search offset, as shown below: ;in, This is the local search step size coefficient. Let p be the new position of the elite individual in the t-th iteration. This represents the position of the p-th individual in the current t-th generation population.

10. A UAV path planning device based on an improved farthest-first-last-inferior optimization algorithm, characterized in that, The device includes: A 3D terrain environment model construction module is used to construct a 3D terrain environment model, which includes at least spatial boundary constraints, terrain elevation constraints, no-fly zone threat constraints, and mission start and end point constraints. The UAV motion constraint model design module is used to design a UAV motion constraint model, which includes at least safety distance constraints, collision threat constraints, maximum pitch angle constraints, maximum turning angle constraints, and path length constraints. The path planning mathematical model building module establishes a path planning mathematical model for the UAV, which includes a segmented path encoding and a fitness function. The optimization module is used to optimize the fitness function based on the three-dimensional terrain environment model and the UAV motion constraint model, using an improved farthest-best-nearest-worst optimization algorithm to obtain the UAV three-dimensional flight path with the minimum fitness value. The improved farthest-best-nearest-worst optimization algorithm introduces an adaptive proportional tent chaotic hybrid initialization mechanism, a cosine continuous nonlinear dynamic balance factor, and an adaptive elite individual local development strategy.

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