Unmanned aerial vehicle path planning method based on hybrid strategy improved Kepler algorithm

Abstract

Along with continuous development of the technology, the autonomous path planning problem of an unmanned aerial vehicle in a three-dimensional space becomes a big problem. The invention provides an unmanned aerial vehicle path planning method based on a hybrid strategy improved Kepler algorithm. The improved content of the method comprises the following steps: firstly, initializing a population by using Latin hypercube sampling; a self-adaptive parameter adjustment mechanism is used for balancing exploration and development, and a Levy jump mechanism and a dynamic disturbance mechanism are used for expanding the search range; using a multi-target gravitation mechanism to guide the current solution to move towards a better direction; and convergence is accelerated by using a local fine tuning strategy and an elite cross recombination mechanism. According to the method, the global search precision of the algorithm is effectively improved, compared with a Kepler optimization algorithm, the hybrid improvement strategy effectively improves the global search capability, the flight distance of the Kepler optimization algorithm on a three-dimensional path is effectively shortened, and the method is successfully applied to a three-dimensional path planning task of the unmanned aerial vehicle; and a new thought is provided for subsequent research and engineering application.

Description

Technical Field

[0001] This invention relates to an intelligent unmanned aerial vehicle (UAV) path planning method, belonging to the field of UAV path planning technology. Background Technology

[0002] With the continuous development of technology, drones are widely used in daily life. Their flexible movement and independence from ground traffic rules significantly reduce time consumption, bringing considerable application value and enabling drones to shine in fields such as agricultural planting, geological surveying, logistics transportation, fire fighting, disaster relief, and road inspection. As the application areas continue to expand, two-dimensional path planning for drones is insufficient to handle the complex tasks of today's society; therefore, three-dimensional path planning for drones has become an important research direction.

[0003] The UAV 3D path planning problem involves finding the optimal path in a complex 3D space. Solving this problem primarily employs traditional algorithms and heuristic algorithms. Traditional algorithms, such as the A* algorithm, can find the optimal path through precise state-space search, but they easily become computationally complex and memory-intensive in large-scale, high-dimensional environments. In contrast, heuristic algorithms (such as genetic algorithms, particle swarm optimization, and ant colony optimization) simulate natural optimization processes, enabling them to quickly find the optimal path in a 3D environment. With further research, improved heuristic algorithms have been proposed, addressing the problem of traditional heuristic algorithms getting trapped in local optima, thereby improving the efficiency and accuracy of path planning.

[0004] CN202511300826.4 discloses a UAV 3D path planning method based on an improved artificial lemming optimization algorithm, belonging to the technical field of UAV path planning methods. This method enables UAVs to navigate autonomously in complex environments, avoid obstacles, find the optimal path, and improve mission efficiency and safety. The method maps the constraints and objective function of UAV 3D path planning to the search space and fitness function of the optimization algorithm. The artificial lemming optimization algorithm is used to search for the optimal flight path, and the path is optimized by combining UAV performance constraints, terrain features, and weather conditions. For the UAV 3D path planning problem under complex conditions, the artificial lemming algorithm is adaptively improved. The algorithm parameters and structure are adjusted according to the mathematical characteristics of the problem model in the initialization, exploration, and development stages. Based on real-time environmental changes and the UAV's own state information perceived by sensors, the flight path is adjusted to meet safety and mission requirements.

[0005] CN202511026474.8 discloses a method and system for UAV path planning. The method includes: S1. Constructing an environmental model for UAV operation; S2. Setting the objective function and constraints for UAV path planning; S3. Based on the environmental model, objective function, and constraints, using an ant colony algorithm to determine information about an approximately optimal path; S4. Applying the information about the approximately optimal path to a sequential quadratic programming algorithm to determine the optimal path. The UAV path planning method provided by this invention, based on the ant colony algorithm, integrates a sequential quadratic programming algorithm (SQP) for secondary optimization. This solves the problems of traditional ant colony algorithms easily getting trapped in local optima and having slow convergence speed. It successfully shortens the path length of UAV path planning, reduces the number of iterations, and achieves more efficient and accurate path optimization. The optimized algorithm has strong adaptability and robustness.

[0006] CN202510964697.2 discloses a UAV 3D path planning method and system based on a multi-strategy improved black-winged kite optimization algorithm. The method includes: generating an initial population through Latin hypercube sampling to improve the population's distribution uniformity and diversity; introducing an adaptive weighting factor to achieve a dynamic balance between exploration and exploitation capabilities; combining a dynamic back-learning strategy to effectively enhance global search capabilities and avoid premature convergence; and further improving algorithm performance by integrating the watchdog position update formula from the sparrow search algorithm. This invention addresses the problems of traditional path planning problems, such as being prone to local optima, slow convergence, and path instability. It can efficiently plan shorter and safer optimal flight paths.

[0007] CN202510855850.8 discloses a path planning method based on a genetic algorithm, comprising: establishing a UAV path planning model; initializing a candidate population and an adversarial population; calculating the first fitness of each candidate solution in the candidate population under all adversarial solutions in the adversarial population, selecting candidate solutions from the candidate population, performing crossover and mutation operations to generate a new candidate population; calculating the second fitness of each adversarial solution in the adversarial population under all candidate solutions in the new candidate population, selecting adversarial solutions from the adversarial population, performing crossover and mutation operations to generate a new adversarial population; when the maximum number of iterations is reached, determining the optimal candidate solution based on the candidate solution corresponding to the smallest first fitness; calculating the third fitness of the optimal candidate solution under all adversarial solutions in the new adversarial population, determining the maximum adversarial perturbation based on the largest third fitness; and determining the final planned path based on the optimal candidate solution and the maximum adversarial perturbation.

[0008] CN202510811137.3 discloses a method for UAV path planning and obstacle avoidance optimization based on an improved elite ant colony algorithm, including the following steps: 3D grid environment modeling and obstacle generation, obtaining a discrete model of the entire 3D space using a "layered + 2D grid" method; elite strategy and path generation, where ants use a random proportional strategy to select paths, setting a transition probability function and introducing a fluctuation coefficient to prevent excessive concentration of path weights caused by pheromone evaporation; dynamic evaporation rate adaptive adjustment, adaptively adjusting based on pheromone distribution to construct a dynamic evaporation rate model; path cost calculation and dynamic constraint integration, using a multi-objective programming method to simultaneously optimize path length and flight stability, and constructing a path cost function; path post-processing and smoothing optimization, including processing balanced paths to improve flyability and collision detection, thereby establishing a UAV dynamic constraint model to ensure flight safety under the premise of path optimization.

[0009] Kepler optimization is a key method for solving many engineering problems, and it has excellent research value in UAV path planning tasks. However, traditional Kepler optimization algorithms suffer from slow convergence speed, low convergence accuracy, and a tendency to get trapped in local optima. Therefore, multiple strategies should be introduced to improve the Kepler optimization algorithm through hybrid approaches. Summary of the Invention

[0010] This invention provides a UAV path planning method based on a hybrid strategy-improved Kepler algorithm. The improvements to this method may include: First, the population is initialized using Latin hypercube sampling to enhance its diversity. An adaptive parameter adjustment mechanism balances exploration and development. A Levy jump mechanism expands the search range. A dynamic perturbation factor further expands the search range, allowing the population to escape local optima initially and accelerating convergence later. A multi-objective gravity mechanism, combining the positional information of multiple high-quality individuals, guides the current solution towards a better direction. A local fine-tuning strategy generates an alternative solution near the current solution, enhancing population diversity. Finally, an improved elite crossover mechanism prevents the loss of elite individuals and updates the population through crossover combinations. Comparative experiments with seven different algorithms were conducted in CEC2017, CEC2020, CEC2022 tests and UAV 3D path planning experiments. This invention effectively improves global search accuracy and provides new ideas for subsequent research and engineering applications of the Kepler optimization algorithm.

[0011] This invention provides a UAV path planning method based on a hybrid strategy improved Kepler algorithm, including... 1: Initialize the population using Latin hypercube sampling; 2: Using an adaptive periodic function instead of the traditional periodic iteration mechanism allows for dynamic adjustment of both the exploration and development phases; 3: Use the Levy flight mechanism to increase the search mode, so as to achieve most small perturbations and a few large jumps to escape the local optimum; 4: Use dynamic perturbation factors to expand the search range. In the early stage, the value of the dynamic adjustment factor is relatively large, which can help escape local optima; in the later stage, the value of the dynamic adjustment factor is relatively small, which can accelerate convergence. 5: Using a multi-objective gravity mechanism, by controlling the number of excellent solutions, the resultant force of multiple excellent solutions on the current solution is calculated, and the gravitational direction of the individual is adjusted according to this resultant force; 6: Use a local fine-tuning mechanism to refine the current solution. This mechanism generates an alternative solution near the current solution, enhancing population diversity. 7: Introduce an improved elite crossover mechanism. The improved elite crossover mechanism prevents the loss of elite individuals and renews the population through crossover combinations.

[0012] This application may yield one or more beneficial effects: (1) To enhance population diversity and improve global search capabilities by using Latin hypercube sampling to initialize the population; (2) Introduce an adaptive parameter adjustment mechanism to balance development and exploration, and improve global search capabilities; (3) To address the problem that the original algorithm is prone to getting trapped in local optima, the Levy flight mechanism is introduced to allow feasible solutions to jump out of the current search range and prevent them from getting trapped in local optima. (4) Introduce a dynamic disturbance factor to expand the search range. In the early stage, the value of the dynamic adjustment factor is relatively large, which can help to escape the local optimum; in the later stage, the value of the dynamic adjustment factor is relatively small, which can accelerate convergence. (5) Replace the original gravity mechanism with a multi-objective gravity mechanism, and optimize the movement direction of the current solution through multiple elite solutions to improve the global search accuracy. (6) Introduce a local fine-tuning strategy, generate candidate solutions around the current solution through dynamic scaling factor and step size factor, and judge the candidate solutions to improve local search capability; (7) An improved elite crossover mechanism is proposed, which selects multiple elite solutions for crossover strategy to generate offspring elite solutions. If the fitness of the offspring elite solution is less than the fitness of the global worst solution, it replaces the global worst solution, thereby enhancing the search accuracy and accelerating convergence. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application; Figure 2This application provides a comparative diagram of initialization methods for UAV path planning methods based on hybrid strategies and improved Kepler algorithms. Figure 3 A schematic diagram illustrating how the adaptive parameters of the UAV path planning method based on the hybrid strategy improved Kepler algorithm change with the periodicity is provided for this application. Figure 4 A schematic diagram illustrating the variation of the dynamic perturbation factor with the periodicity in the UAV path planning method of the hybrid strategy improved Kepler algorithm provided in this application; Figure 5 This application provides a schematic diagram of the Levy flight mechanism, which is a UAV path planning method based on a hybrid strategy to improve the Kepler algorithm. Figure 6 A schematic diagram illustrating the multi-elite gravity mechanism of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application; Figure 7 This application provides renderings of the UAV's 3D spatial environment model; Figure 8 A comparison diagram of the UAV's three-dimensional flight curves is provided for this application; Figure 9 A comparison chart of test results for the UAV path planning method with hybrid strategy improved Kepler algorithm in UAV 3D path planning experiments is provided for this application; Figure 10 The test results of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application are shown in the CEC2017 (F1-F16) test set; Figure 11 The test results of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application are shown in the CEC2017 (F17-F30) test set; Figure 12 The test results of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application are shown in the CEC2020 test set. Figure 13 The test results of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application are shown in the CEC2022 test set. Detailed Implementation

[0014] To facilitate a clearer understanding and use of this application, the following detailed description, in conjunction with the accompanying drawings and embodiments, will enhance the understanding of those skilled in the art and those who use the application. These embodiments are merely partial illustrative examples of this application. Any other embodiments of this application obtained by the recipient without inventive effort are within the scope of this application and are protected.

[0015] Figure 1This is a schematic diagram of the UAV path planning method based on the hybrid strategy improved Kepler algorithm provided in this application.

[0016] Step S1 involves initializing various parameters using Latin hypercube sampling to initialize the population. Specific steps include: Step S1-1. Initialize basic parameters, including population size, maximum number of iterations, initial value of the adaptation factor, number of multi-objective gravity targets, and number of elite individuals. Parameter values ​​are shown in Table 1. Table 1 Experimental settings parameters for the Improved Kepler Optimization Algorithm (SPKOA) Step S1-2. Initialize the population using Latin hypercube sampling. Figure 2 A comparative diagram of initializing populations for random sampling and Latin hypercube sampling; Steps S1-3. Calculate the fitness function value for each feasible solution, and design corresponding fitness functions for different types of engineering problems; Step S1-4. Based on the fitness function value, select the solution with the smallest fitness as the current optimal solution.

[0017] Step S2 introduces an adaptive factor mechanism to replace the original iterative mechanism and updates the adaptive factor value and gravity value. This allows the improved Kepler optimization algorithm, based on an adaptive periodicity factor, to balance the exploration and exploitation states and adopt a more reasonable position update strategy in response to changes in the number of iterations. The specific method is as follows: Step S2-1: Calculate the gravitational force value for each feasible solution. Each feasible solution also possesses a certain gravitational force, the magnitude of which is proportional to its mass. It is worth noting that the current solution's speed is closely related to the gravitational force exerted by the optimal solution: the closer to the optimal solution, the stronger the gravitational force and the faster the speed; the farther away, the weaker the gravitational force and the slower the speed. The formula for the gravitational force value is as follows: Where μ is the gravitational parameter, r1 is a randomly selected value in [0,1], and β is a local minimum. and M represents the mass of the sun. s and planetary mass m i The normalized value, Represents X s and X i The Euclidean distance R between time t i The normalized value is expressed as follows: Where r2 is a randomly selected value in [0,1], used to diverge the mass values ​​of each planet. μ(t) is a function that decreases exponentially with time t, used to control the search accuracy, and is defined as follows: Where γ is a constant, μ0 is an initial value, both of which are preset values; t and T max These represent the current iteration number and the maximum iteration number, respectively. Step S2-2: Calculate the value of the adaptive factor. First, set the initial value and maximum value of the adaptive factor. Adjust the adaptive factor value by varying the number of iterations and the maximum number of iterations. Traditional periodic functions typically maintain the same decay pattern throughout the optimization process, while adaptive periodic functions dynamically adjust according to the current search state, allowing the algorithm to adopt different strategies at different optimization stages. Figure 3 This diagram illustrates how the adaptive factor changes with the number of iterations. The formula is as follows: w = w min +(w max -w min )*(t / T max ) 2 (7)

[0018] Step S3 introduces the Levy flight mechanism to update the position of solutions entering the exploration phase; this expands the search range, increases global search accuracy, and prevents getting trapped in local optima. Step S3-1. For each feasible solution, perform the following operation: determine whether the value of the random number r is less than the value of the adaptive parameter w. If it is less, proceed to step S3-2; otherwise, proceed to step S4-2. Step S3-2. Enter the exploration phase and determine whether the value of the current random number r is less than the preset value. If it is greater than the preset value, add Levy flight disturbance and update the position of the current solution using Formula 3. Otherwise, proceed to S4-1. Figure 4 This is a schematic diagram of the flight trajectory of the Levy flight mechanism within a certain space. Where α(t) is the perturbation scaling factor, α max Let α be the initial disturbance amplitude. min The formula for the minimum value of the final disturbance is as follows: Where L i (t) is the Levy jump vector, expressed as follows: Where u jThe amount of Levy's jump is controlled, primarily determining its direction and amplitude; v j To control jump decay and amplify extreme jumps, β is a stable distribution parameter, and the standard deviation σ is defined as follows:

[0019] Step S4 introduces a dynamic perturbation factor to expand the search range. Initially, the value of the dynamic adjustment factor is relatively large, which can help escape local optima; later, the value of the dynamic adjustment factor is relatively small, which can accelerate convergence. Step S4-1. Introduce a dynamic disturbance factor and update the position of the current solution using a formula. Figure 5 This is a schematic diagram illustrating how dynamic disturbances change with a periodicity. Where r represents a randomly generated value in [0,1], and η is a linearly decreasing factor from 1 to -2, expressed as follows: η=(a2-1)×r4+1 (14) Where a2 is a cyclic control parameter with a value ranging from -1 to -2. Step S4-2. Enter the development stage. Determine whether the normalized value of the relative distance between the current solution and the optimal solution is less than 0.5. If it is less, calculate the value of the velocity magnitude V using the formula. Otherwise, calculate the value of the velocity V using the formula, and update the position of the current solution using the velocity and gravity values ​​of each feasible solution using the formula. in This represents the velocity of planet i at time t. Let r3 and r4 be probability variables that are randomly generated between [0,1]. and Two binary vectors, which can only be 0 or 1. and M represents a random solution selected from the overall solution. s and m i X s and X i The mass; μ(t) represents the gravitational constant, ε is the minimum value to prevent division by zero, R i (t) represents the optimal solution X at time t. s and X i The distance between them, a i (t) represents the semi-major axis of the elliptical orbit of planet i at time t, and is calculated using the following formula: Where T i Ri represents the period of planet i.-norm(t) Indicates that X s and X i The distances between them are normalized. The definition is as follows:

[0020] Step S5 introduces a multi-objective gravity mechanism to expand the search range and guides the current solution toward convergence towards the optimal solution: Step S5-1. Through a multi-elite gravity mechanism, Figure 6 This is a schematic diagram illustrating the multi-elite gravitational mechanism, which guides the current solution to move towards the elite group, seeking a better solution, and updates the current solution using a formula; Where V i F is the differential perturbation term, f is the direction scaling factor, and F g (i) represents the gravitational intensity factor, and U is the dimension selection mask. This is a standard Gaussian perturbation, used to improve local escape capability. (D) i To enhance the diversity of search directions (rotation invariance) by applying the rotation matrix R. The rotation matrix is ​​given by the following formula:

[0021] Step S6 introduces a local fine-tuning mechanism to refine the current solution. This mechanism generates an alternative solution near the current solution, enhancing the diversity of the population. Step S6-1. Generate candidate solutions around the current solution using a local fine-tuning mechanism. Calculate whether the fitness of a candidate solution can replace the current solution. If the fitness of a candidate solution is less than that of the current solution, then it replaces the current solution. Candidate solutions are generated using a dynamic scaling factor and a step size factor. The formula is as follows:

[0022] Step S7 updates the elite population using an improved elite crossover mechanism. Specifically, this mechanism prevents the loss of elite individuals and updates the population through crossover combinations, thus accelerating convergence. The specific method is as follows: Step S7-1: An improved elite crossover mechanism is adopted. Multiple elite solutions are selected and crossover operations are performed multiple times. The resulting offspring solutions are compared with the worst solution. If the fitness of the offspring solution is less than that of the worst solution, it replaces the worst solution, thereby preserving high-quality solutions and guiding the convergence direction. The formula is as follows: Step S7-2: Sort all solutions by fitness and select the solution with the smallest fitness as the optimal solution; Step S7-3: Determine the current iteration number. If it is less than the maximum iteration number, proceed to S2-1 and update t according to t = t + 1; otherwise, proceed to S7-4 and output the current optimal solution. Step S7-4: Output the optimal solution as the final solution of the method.

[0023] Step S8 tests the improved Kepler optimization algorithm (SPKOA) against the Kepler optimization algorithm (KOA), Great Wall Construction Worker optimization algorithm (GWCA), Snake optimization algorithm (SO), Crayfish optimization algorithm (COA), Termite Life Cycle optimization algorithm (TLCO), Porcupine optimization algorithm (CPO), and Parrot optimization algorithm (PO) in the UAV 3D path planning. The improved Kepler optimization algorithm achieved first place in multiple tests and has strong global optimization ability. Step S8-1: Establish a three-dimensional flight environment model for the UAV. Figure 7 A rendering of a 3D spatial environment model for a drone. Drones often prioritize avoiding terrain obstacles such as mountains during flight missions; therefore, modeling mountains and other terrain features is crucial. In a mathematical model, mountains can be represented as: Where (x) i ,y i ) represents the center coordinates of the i-th mountain, h i The parameter controlling the height of this mountain peak is 'n', which is the total number of mountains in the terrain. The parameter x... si and y si These represent the attenuation coefficients of the i-th mountain in the x-axis and y-axis directions, respectively, which are used to control the slope changes of the mountain in each direction and reflect the steepness of its terrain changes. Step S8-2: Use a cubic B-spline curve as the flight curve of the UAV. Figure 8 This image shows a comparison of the flight curves of a UAV in three-dimensional space. The B-spline curve is determined by a set of ordered spatial control points and their corresponding node vectors. Interpolation within each interval using a cubic polynomial generates a continuously differentiable spatial trajectory, achieving global path smoothing and effectively avoiding sharp angles or abrupt bends at node connections. Assume the path control point sequence is: P0, P1, ... P n-1 ,P n It contains a total of n+1 control points. Where P0 represents the coordinates of the UAV's takeoff point in three-dimensional space, P... n Indicate the coordinates of the termination point, P1,...P n-1 This represents an intermediate control point in the path. In the parameter interval t∈[t3,t... n+1 The cubic B-spline path can be constructed along the coordinate axes as follows: Where N i,3 (t) is a cubic B-spline basis function, and the nodal vector {t} is a cubic B-spline basis function. j The specific value of} can be selected according to application requirements. A cubic B-spline curve can ensure global path smoothness while crossing all control points; Step S8-3: Establish the fitness function. To more comprehensively evaluate path quality, the fitness function is constructed by comprehensively considering six aspects: path length cost, terrain cost, boundary cost, yaw angle cost, elevation / depression angle cost, and altitude cost, thereby achieving a joint evaluation of path feasibility and efficiency. Path cost C1 primarily reflects the total length of the flight path required for the UAV to travel from the starting point to the destination. The shorter the path, the lower the corresponding cost. Assuming the generated path consists of n+1 waypoints (including the starting and ending points), its path length cost can be modeled as follows: Terrain cost primarily considers the potential threats posed by terrain obstacles (such as mountains) to the UAV during flight. This cost term penalizes portions of the path where terrain collisions may occur. By controlling the value of C2, the cost of terrain on the UAV is calculated, thereby guiding the UAV to automatically avoid terrain obstacles during path planning, improving flight safety and reliability. When altitude Z... i Above obstacle height Z min (x i y i When ), the drone is not threatened, C 2(i) The value is set to 0; when the height is lower than the obstacle height Z. min (x i y i When the drone receives a terrain threat, C 2(i) The value is set to λ c1 *|Z i -Z min (x i ,y i )|, where λ c1 The expression for the single-point terrain cost, representing the penalty intensity, is as follows: β c1 The terrain penalty coefficient, and the expression for the cumulative terrain cost are: Boundary cost c3 is used to constrain the UAV to perform flight missions within a specified spatial range, avoiding unreasonable flight behavior caused by path deviating from the boundary. A soft constraint mechanism is adopted for planning, allowing the path planning process to guide the solution space towards the legal boundary region through dynamic penalties without completely eliminating out-of-bounds solutions, thus balancing convergence and solution diversity. A penalty function C is introduced.3(i) To measure the waypoint (x) i ,y i ,z i Whether a boundary is exceeded, the expression for its soft boundary cost is: Where, x max y max , z max Let λ represent the maximum flyable boundaries of the UAV in the x, y, and z directions, respectively. c2 λ represents the boundary penalty strength on the x-axis and y-axis. c3 Let x_penalty represent the boundary penalty strength on the z-axis, y_penalty represent the deviation distance of point i from the boundary on the x-axis, y_penalty represent the deviation distance of point i from the boundary on the y-axis, and z_penalty represent the deviation distance of point i from the boundary on the z-axis. When a pathpoint is within the valid region, the boundary cost is 0. When a pathpoint deviates from the boundary, the penalty term increases with the magnitude of the deviation, thus achieving flexible suppression of illegal solutions. The total boundary cost of the UAV can be obtained by summing the boundary costs of all pathpoints. The maximum deflection angle cost C4 is primarily used to limit the change in the UAV's turning angle along the path, avoiding overly sharp turns and thus improving path smoothness and flightability. When the deflection angle θ... i When the maximum permissible yaw angle θ is exceeded, a penalty mechanism is activated, the cost of which is defined as follows: Where β c4 This is the deflection angle penalty coefficient. This cost term can effectively suppress sharp turns in the path, improving the stability and control feasibility of the aircraft; The maximum pitch angle cost C5 is used to limit the drone's uphill and downhill angles between consecutive path segments, ensuring its flight attitude remains within a controllable range. To prevent excessively steep ascents or descents, a maximum permissible pitch angle threshold is set. If the pitch angle of the path exceeds this threshold, a penalty cost term is introduced, defined as follows: Where β c5 This is the pitch angle penalty intensity. This constraint can effectively suppress steep ascents or descents in the flight path, ensuring that the path is within the allowable range of aircraft dynamics, thereby improving the feasibility of the path and flight safety; The maximum altitude cost C6 is used to limit the flight altitude of the drone. During flight, the maximum altitude difference of the drone is often a very critical limiting condition. Therefore, ensuring that the drone's flight altitude difference does not exceed the maximum altitude difference can guarantee the drone's flight safety. C6=β c6 ·Δh=βc 3( max(z r )-min(z r )), Δh>h (41) Where β c6 The penalty intensity for altitude difference is given by h, which is a fixed value for altitude difference. If the altitude difference Δh of the drone exceeds the value h, the altitude difference penalty is activated to ensure the safety of the drone flight. The overall fitness function of the UAV is expressed as follows: min(C)=min(w1C1+w2C2+w3C3+w4C4+w5C5+w6C6) (42) Where C1 is the path length cost, C2 is the terrain cost, C3 is the boundary cost, C4 is the maximum deflection angle cost, C5 is the maximum depression and elevation angle cost, C6 is the maximum altitude cost, and w1, w2, w3, w4, w5, and w6 are weighting coefficients. Step S8-4: Set the experimental parameters for each algorithm, and set the iteration period to 500 and the population size to 50. Table 2 shows the main parameter settings for the Improved Kepler Optimization Method (SPKOA) compared to the other seven algorithms. Step S8-5 Figure 9 Table 3 shows a comparison of test results from SPKOA and seven other UAV 3D path planning experiments. Figure 9 The results of the comparative experiment are presented, showing that SPKOA performed best among the eight algorithms compared. In terms of cost, SPKOA's cost of 214.66 is lower than algorithms such as KOA (255.78) and SO (248.37). SPKOA was used as the benchmark algorithm in the Wilcoxon statistical test, demonstrating a significant performance advantage over other algorithms. Although SPKOA's running time is approximately twice that of other algorithms, its superior performance in cost control and stability makes it the best-performing algorithm in this comparison. Table 2. Main parameter settings of the Improved Kepler Optimization Method (SPKOA) compared to the other seven algorithms. Table 3. Experimental results of the Improved Kepler Optimization Algorithm (SPKOA) and seven other algorithms in 3D path planning.

[0024] Step S9 tests the improved Kepler optimization algorithm (SPKOA) against Kepler optimization algorithm (KOA), Great Wall Construction Worker optimization algorithm (GWCA), snake optimization algorithm (SO), crayfish optimization algorithm (COA), termite life cycle optimization algorithm (TLCO), porcupine optimization algorithm (CPO), and parrot optimization algorithm (PO) on the CEC2017 (F2 unstable and removed in this experiment), CEC2020, and CEC2022 test sets. The improved Kepler optimization algorithm achieved first place in multiple tests, demonstrating strong global optimization ability. Step S9-1: Select seven algorithms as comparison algorithms: Kepler Optimization Algorithm (KOA), Great Wall Construction Worker Optimization Algorithm (GWCA), Snake Optimization Algorithm (SO), Crayfish Optimization Algorithm (COA), Termite Life Cycle Optimization Algorithm (TLCO), Porcupine Optimization Algorithm (CPO), and Parrot Optimization Algorithm (PO). Step S9-2: Set the iteration period to 500 and the population size to 50. Set the parameter values ​​for each algorithm, as shown in Table 2. Step S9-3 Figure 10 , Figure 11 , Figure 12 , Figure 13 The figures show the experimental results from CEC2017 (D=50), CEC2020 (D=20), and CEC2022 (D=20). Analyzing the experimental results in the figures, we can conclude the effectiveness and superiority of the improved Kepler method.

Claims

1. A method for unmanned aerial vehicle path planning based on hybrid policy improved Kepler algorithm, characterized in that, The method comprises the following steps: S1: initializing the population using a Latin hypercube sampling method; S2: using an adaptive periodic function to replace the traditional periodic iteration mechanism, which can dynamically adjust the exploration and development parts; S3: using the Levy flight mechanism to increase the search mode, realizing a few small perturbations and a few large jumps to jump out of the local optimal solution; S4: using a dynamic disturbance factor to expand the search range, the initial dynamic adjustment factor has a larger value, which can jump out of the local optimal solution; the value of the dynamic adjustment factor is smaller in the later stage, which can accelerate the convergence; S5: using a multi-objective gravity mechanism, by controlling the number of excellent solutions, calculating the force of multiple excellent solutions on the current solution, and adjusting the direction of the body's gravity according to the force; S6: using a local fine-tuning mechanism to perform fine-tuning on the current solution, the local fine-tuning mechanism generates a candidate solution near the current solution, enhancing the diversity of the population; S7: introducing an improved elite crossover mechanism, which prevents the loss of elite individuals and updates the population through crossover combination; S8: using a hybrid strategy to improve the UAV path planning method based on the Kepler algorithm to solve the three-dimensional path planning problem of the UAV. 2.The method of claim 1, wherein, S1: initializing the population using a Latin hypercube sampling method, comprising: S1-1: initializing basic parameters, including population size, maximum iteration number, initial value of adaptive factor, number of multi-objective gravity, number of elite individuals, etc.; S1-2: initializing the population by Latin hypercube sampling method; S1-3: calculating the fitness function value of each feasible solution, and designing the corresponding fitness function for different types of engineering problems; S1-4: selecting the solution with the smallest fitness value as the current optimal solution according to the fitness function value. 3.The method of claim 1, wherein, S2: the adaptive periodic function, comprising: S2-1: calculating the gravity value of each feasible solution; S2-2: calculating the value of the adaptive periodic function, according to the initial value and the maximum value of the adaptive periodic function set in S1-1, and adjusting the value of the adaptive periodic function through the maximum iteration number.

4. The method of claim 1, wherein, S3: introducing the Levy flight mechanism for position updating, comprising: S3-1: judging whether the random number is less than the adaptive parameter, if yes, entering S3-2, otherwise entering S4-2; S3-2: entering the exploration stage, judging whether the current random number is less than the preset value, if yes, using the Levy flight mechanism to update the position of the current solution; otherwise, entering S4-1.

5. The method of claim 1, wherein, S4: using a dynamic disturbance factor to expand the search range, comprising: S4-1: using a dynamic disturbance factor to update the position of the current solution; S4-2: entering the development stage, judging whether the normalized value of the relative distance between the current solution and the optimal solution is less than 0.5, then calculating the speed value through the formula in the original Kepler optimization algorithm, and updating the position of the current solution through the speed and gravity value of each feasible solution.

6. The method of claim 1, wherein, S5: using a multi-objective gravity mechanism, introducing the convergence of the current solution to the direction of the excellent solution, comprising: S5-1: using a multi-objective gravity mechanism, setting multiple excellent solutions, calculating the weighted force of multiple excellent targets on the current solution, and adjusting the gravity direction of the current solution according to the force, guiding the current solution to move in the direction of the excellent population, and finding a better solution.

7. The method according to claim 1, wherein, S6: the use of local fine-tuning mechanism for fine-tuning operation of the current solution, including: S6-1: using a local fine-tuning mechanism to generate candidate solutions around the current solution through dynamic scaling factor and step factor, calculating whether the fitness of the candidate solution is smaller than the fitness of the current solution, if the fitness of the candidate solution is smaller than the fitness of the current solution, replacing the current solution; otherwise, keeping the current solution.

8. The method of claim 1, wherein, S7: the use of improved elite crossover and recombination mechanism, including: S7-1: using an improved elite crossover mechanism, selecting multiple elite solutions, performing multiple crossover operations, and generating offspring solutions with fitness smaller than the worst solution, replacing the worst solution to keep the high-quality solution; otherwise, keeping the worst solution to speed up the population to the optimal direction; S7-2: sorting the fitness of all solutions, selecting the solution with the smallest fitness as the optimal solution; S7-3: judging the current iteration number, if less than the maximum iteration number, entering S2-1, and updating t according to t=t+1; otherwise, entering S7-4 to output the current optimal solution; S7-4: outputting the optimal solution as the final solution of the method.

9. The method of claim 1, wherein, S8: the use of mixed strategy improved Kepler algorithm for unmanned aerial vehicle path planning method to solve the problem of three-dimensional path planning of unmanned aerial vehicle, including: S8-1: establishing a three-dimensional flight environment model of unmanned aerial vehicle; S8-2: using a cubic B-spline curve as the flight curve of the unmanned aerial vehicle to make the flight curve of the unmanned aerial vehicle more realistic; S8-3: establishing a fitness function; S8-4: setting the experimental parameters of the algorithm, and setting the iteration period to 500 and the population size to 50; S8-5: verifying the superiority of the SPKOA algorithm according to the flight path under the three-dimensional path of the unmanned aerial vehicle and the experimental results.

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