A hippopotamus optimization algorithm-based multi-unmanned aerial vehicle path planning method

Abstract

The application discloses a kind of multi-unmanned aerial vehicle path planning methods based on hippo optimization algorithm, belong to unmanned aerial vehicle path planning field.The method includes: establishing environment model;Parameter is initialized;The position vector of all path points of unmanned aerial vehicle is encoded as a hippo individual, and population is initialized using Latin hypercube sampling;Define the fitness function including path length cost, multi-machine flight time coordination cost and collision cost;In the exploration stage, the first new candidate solution is generated using the Levy flight strategy of group elite learning mechanism, and the second new candidate solution is generated using the quadratic interpolation strategy in the development stage, which is compared with the original candidate solution respectively, and the collision path point is processed;After each iteration, the fitness value is calculated and the global optimal solution is updated;The optimal individual corresponding to the multi-machine path planning scheme is outputted after iteration is finished.The application can improve the uniformity of population initialization, enhance the ability to jump out of local optimum, and consider the multi-machine coordination constraint, to realize efficient and safe path planning in complex environment.

Description

Technical Field

[0001] This invention belongs to the field of UAV path planning technology, specifically relating to a multi-UAV path planning method based on an improved Hippo optimization algorithm. More specifically, it relates to an improvement of the Hippo optimization algorithm through Latin hypercube sampling, a Levy flight strategy with a swarm elite learning mechanism, and a quadratic interpolation strategy, in order to achieve efficient and collaborative planning of multi-UAV flight paths in complex environments. Background Technology

[0002] With the rapid development of technologies such as multi-agent control, information interaction, and anti-interference, unmanned aerial vehicles (UAVs) are increasingly widely used in fields such as surveillance and inspection, emergency communication, logistics and transportation, agricultural plant protection, and search and rescue. In multi-UAV collaborative missions, how to plan a safe, feasible, and optimal flight path for each UAV from its starting position to its target position, while effectively avoiding obstacles, meeting dynamic constraints, and multi-UAV collision avoidance requirements, has become one of the key issues that urgently need to be addressed in the UAV field.

[0003] Currently, multi-UAV path planning methods mainly include traditional path planning algorithms, intelligent optimization algorithms, and machine learning-based methods. Among these, traditional path planning algorithms primarily include the artificial potential field method, Algorithms, etc.; Intelligent optimization algorithms mainly include genetic algorithms, particle swarm optimization algorithms, and the hippo optimization algorithm proposed in recent years. Existing research has made certain improvements to the hippo optimization algorithm. For example, the paper "Hippo Optimization Algorithm Improved by Integrating Multiple Strategies and Its Application" in the Journal of Taiyuan Normal University (Natural Science Edition), 2025, No. 4, improves the algorithm performance by adopting a hierarchical random initialization strategy to enhance population diversity, combining a dynamic cooperative search mechanism to adjust the search direction, and introducing an adaptive escape strategy to escape local optima. The paper "Agricultural UAV Path Planning Based on Improved Hippo Algorithm" in the Journal of Agricultural Machinery, 2026, No. 1, proposes a dynamic improved hippo optimization algorithm, which comprehensively uses Levy flight, growth ratio mechanism, prism opposition learning algorithm with adaptive learning rate, and random diffusion strategy to improve the global search and exploration capabilities of the algorithm, and applies it to agricultural UAV path planning. The paper "Hippo Optimization Algorithm Improved by Integrating Multiple Strategies and Dimensions" in Computer Science, 2025, Vol. 52, No. 6A, improves the performance of the original algorithm by adopting a quasi-backward learning initialization, sine and cosine optimization strategy, and a combination of tangent flight and PID search factor. However, the existing improved Hippo algorithm still has the following problems in solving the multi-UAV path planning problem:

[0004] I. In the population initialization stage, although existing improved methods have introduced some random reinforcement or reverse learning mechanisms, the population individual distribution is not uniform enough, resulting in limited coverage of the initial solution space. In complex three-dimensional environments, early search concentration is likely to occur, which affects the subsequent global optimization performance.

[0005] Second, in the path search process, most existing improvement strategies simply switch between different optimization strategies based on the algorithm search stage, without fully considering the dynamic evolution characteristics of the population state as the number of iterations changes. They lack an adaptive update mechanism for the search process, resulting in limited improvement in the algorithm's local fine search capability. In complex obstacle environments, the algorithm is still prone to getting stuck in local optima, and the algorithm's convergence stability and path quality still need to be further improved.

[0006] Third, for multi-UAV path planning scenarios, existing methods still do not adequately consider the path coupling relationship between multiple UAVs, dynamic collision avoidance constraints, and collaborative safety. Especially in complex environments, it is difficult to simultaneously take into account path length, path smoothness, and multi-UAV collaborative safety requirements.

[0007] In summary, existing methods still have shortcomings in terms of population initialization uniformity, adaptive update capability of the search process, path smoothness, and multi-machine cooperative constraint handling, making it difficult to simultaneously guarantee global optimization performance, convergence efficiency, and multi-machine cooperative security in complex environments. Summary of the Invention

[0008] The purpose of this invention is to address the problems of insufficient population initialization uniformity, lack of adaptive update mechanism in the search process leading to local optima, insufficient path smoothness, and insufficient consideration of multi-drone cooperative constraints in existing multi-drone path planning methods. This invention proposes an improved Hippo optimization algorithm that uses Latin hypercube sampling to uniformly initialize the initial population, incorporates a Levy flight strategy with a swarm elite learning mechanism to enhance global exploration capabilities, and introduces a quadratic interpolation strategy to strengthen local development capabilities. This enables the efficient generation of flight paths in complex environments that meet the requirements of global optimization performance, convergence efficiency, path smoothness, and multi-drone cooperative safety.

[0009] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0010] A multi-UAV path planning method based on the Hippo Optimization Algorithm is provided, including the following steps:

[0011] Step 1: Create an environment model that includes obstacles;

[0012] Step 2: Initialize the relevant parameters of the hippo optimization algorithm;

[0013] Step 3: Encode all waypoints of multiple drones into the position vector of a single hippopotamus individual. Each hippopotamus individual represents a multi-drone path planning scheme. Use the Latin hypercube sampling strategy to initialize the hippopotamus population composed of multiple hippopotamus individuals.

[0014] Step 4: Define a fitness function, which includes at least path length cost, multi-aircraft flight time coordination cost, and collision cost, to evaluate the merits of the multi-aircraft path planning scheme for each hippopotamus individual.

[0015] Step 5 involves iteratively updating the positions of individual hippos in the hippo population in stages to update the corresponding multi-aircraft path planning scheme. Specifically, during the exploration phase, a first new candidate solution is generated using the Levy flight strategy with a swarm elite learning mechanism. This first new candidate solution is compared with the original candidate solutions from the exploration phase, and the solution with the better fitness value is selected as the new position for that hippo individual. During the development phase, a second new candidate solution is generated using a quadratic interpolation strategy. This second new candidate solution is compared with the original candidate solutions from the development phase, and the solution with the better fitness value is selected as the new position for that hippo individual. During the iterative update process, path points that collide with obstacles are processed.

[0016] Step 6: After the iteration is completed, calculate the fitness value of each hippopotamus individual in the hippopotamus population, and update the information of the current global best hippopotamus individual based on the fitness value;

[0017] Step 7: Determine if the maximum number of iterations has been reached. If not, return to step 5. If it has been reached, output the information of the optimal hippo individual. The multi-drone path planning scheme corresponding to the optimal hippo individual is the optimal flight path of the multi-drone.

[0018] Furthermore, in step 1, the environment model includes a grid model and a non-grid model; in step 2, the relevant parameters of the Hippo optimization algorithm include the maximum number of iterations, the number of individuals in the population, the total number of drones, and the number of waypoints for each drone.

[0019] Furthermore, in step 3, the location of the hippopotamus population is initialized using the following formula:

[0020]

[0021] In the formula, For the first The location of each individual hippopotamus and These are the lower and upper bounds for location sampling, respectively. It is a Latin hypercube sampling function. Let be the dimension of the position vector, and ,in The total number of drones, The number of waypoints for each drone. is the dimension of the coordinate space.

[0022] Furthermore, the fitness function defined in step 4 is determined by the following formula:

[0023]

[0024] In the formula, , , , This indicates the optimization of weight parameters. , , , These are parameters for the expression, used for normalization. This represents the total actual flight distance of all drones. This indicates the maximum total flight range set for all drones. This indicates the total number of environmental risk zones. and They represent the first The horizontal and vertical coordinates of the drone. and They represent the first The central x-coordinate and y-coordinate of each environmental risk zone Indicates the first Flight time of the drone This indicates the set cooperative flight time. Indicates the number of collisions.

[0025] Furthermore, in step 5, the exploration phase includes a water gathering phase and a predator defense phase, while the development phase is a predator escape phase.

[0026] Furthermore, in step 5, the update formulas for the water gathering stage, the predator defense stage, and the predator escape stage are as follows:

[0027] Water accumulation stage:

[0028]

[0029]

[0030]

[0031]

[0032] In the formula, and Let represent the candidate solutions for male and female hippos before the update, respectively. and These represent the updated candidate solutions for male and female hippos, respectively. The best candidate solution in the representative population; and These represent the current iteration number and the maximum iteration number, respectively. Indicates the number of individuals in a population; and An integer between 1 and 2; , , and A random value between 0 and 1. , , and Between 0 and 1 3D random vector; and To pass A randomly selected numerical value or vector; A random integer that is either 0 or 1; This represents the mean of several randomly selected candidate solutions;

[0033] The predator defense phase:

[0034] First, the predator locations are randomly generated. :

[0035]

[0036] Calculate the first Distance between an individual hippopotamus and a predator:

[0037]

[0038] Then, new candidate solutions are generated. :

[0039]

[0040] In the formula, A random vector that obeys Levy's flight; This indicates element-wise addition; The fitness function; , , and The parameter is random. and A random vector between 0 and 1;

[0041] Escape from the predator phase:

[0042] First, calculate the local boundaries:

[0043]

[0044] Then new candidate solutions are generated:

[0045]

[0046] in, The parameters are random and generated using the following formula:

[0047]

[0048] In the formula, and These represent the lower bound and upper bound of the local search in the current iteration, respectively. and A random number between 0 and 1 A random vector between 0 and 1 These are random numbers that follow a standard normal distribution.

[0049] Furthermore, in step 5, the Levy flight strategy of the swarm elite learning mechanism specifically generates the first new candidate solution according to the following three-branch approach. :

[0050]

[0051] In the formula, This represents the random step size generated by the Levy flight strategy. and This represents two randomly selected distinct elite candidate solutions. and These represent the second and third candidate solutions ranked in the overall algorithm, respectively. For dynamic parameters, .

[0052] Furthermore, in step 5, the quadratic interpolation strategy is specifically as follows:

[0053] For each dimension of the position vector , The second new candidate solution is generated according to the following formulas respectively. The Dimensional components :

[0054]

[0055] In the formula, and This indicates that two distinct individuals randomly selected from the population are on the [missing information - likely a date or time]. Positional components in the dimension, Indicates the current best candidate solution In the Positional components in the dimension; if the denominator is zero, then... Assigned value .

[0056] Furthermore, in step 6, if the fitness value of the newly generated individual is less than the fitness value of the current global optimal solution, then the information of the global optimal solution is replaced with the information of the newly generated individual; if the fitness value of the newly generated individual is greater than or equal to the fitness value of the current global optimal solution, then the information of the current global optimal solution is retained.

[0057] The advantages of this invention are:

[0058] 1. To address the problem of insufficient initialization uniformity, this invention employs a Latin hypercube sampling strategy to initialize the hippopotamus population. This strategy enables the initial candidate solutions to be evenly distributed in the search space, avoiding individual clustering or blind spots, and improving the coverage of the initial solution space, thus laying a solid foundation for subsequent global optimization.

[0059] 2. To address the issues of lacking an adaptive update mechanism and being prone to getting trapped in local optima, this invention, in the exploration phase, utilizes a Levy flight strategy with a swarm elite learning mechanism to generate a first new candidate solution. This solution is then compared with the original candidate solutions from the exploration phase, and the better one is selected as the new position for the hippopotamus individual. This process effectively expands the search range and enhances the algorithm's ability to escape local optima. In the development phase, a second new candidate solution is generated using a quadratic interpolation strategy. This solution is then compared with the original candidate solutions from the development phase, and the better one is selected as the new position. This process utilizes information from the current optimal solution for refined local search, improving convergence accuracy. Through phased optimization in the exploration and development phases and a competitive selection mechanism for candidate solutions, a balance is effectively struck between global search and local development. This allows for faster convergence of solutions with better fitness and automatic adjustment of search behavior based on the iteration process, overcoming the shortcomings of existing strategies that simply switch and lack dynamic adaptability.

[0060] 3. To address the issues of insufficient consideration for multi-drone collaboration and inadequate path smoothness, this invention encodes all path points of multiple UAVs into a single "hippopotamus" individual. The fitness function comprehensively incorporates path length cost, multi-drone flight time collaboration cost, and collision cost, enabling the algorithm to simultaneously minimize total distance, ensure simultaneous arrival of multiple drones, and guarantee collision avoidance safety during optimization. Simultaneously, the quadratic interpolation strategy, by fusing the positional information of the optimal solution and random solutions, makes the transitions between generated path points smoother, avoiding abrupt changes. The swarm elite learning mechanism's guidance towards multiple elite solution centers also naturally suppresses path point fluctuations. The combined effect of these mechanisms results in a smooth final output path. Through comprehensive evaluation and optimization of these costs, the final multi-drone path planning scheme effectively shortens the overall flight distance, achieves multi-drone time collaboration, avoids collisions, and ensures smooth and continuous flight trajectories. This achieves high global optimization performance, fast convergence efficiency, and reliable multi-drone collaborative safety in complex environments. Attached Figure Description

[0061] The above and other features and advantages of the present invention will become more readily understood from the following description with reference to the accompanying drawings, in which:

[0062] Figure 1 This is a flowchart of a multi-UAV path planning method based on the hippo optimization algorithm according to an embodiment of the present invention;

[0063] Figure 2 The following is a comparison of simulation results of the embodiments of the present invention and the comparative algorithms in multi-UAV path planning, wherein (a) is the path planning diagram of the improved Hippo optimization algorithm of the present invention; (b) is the path planning diagram of the Gray Wolf optimization algorithm; (c) is the path planning diagram of the Sled Dog optimization algorithm; (d) is the path planning diagram of the Particle Swarm Optimization algorithm; and (e) is the path planning diagram of the existing Hippo optimization algorithm.

[0064] Figure 3 This is a comparison chart of the fitness convergence curves of the embodiment of the present invention and the comparison algorithm during the iteration process. Detailed Implementation

[0065] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments thereof. It should be noted that the following detailed description of the present invention is for illustrative purposes only and is not intended to limit the scope of the invention.

[0066] The multi-UAV path planning method based on the Hippo optimization algorithm provided by this invention is used to plan the optimal flight path for multiple UAVs in complex environments containing obstacles and unfavorable weather conditions. This path has the advantages of short total flight distance, coordinated flight time, and no collisions, thereby improving the execution efficiency and safety of UAV missions.

[0067] Reference Figure 1 As an exemplary embodiment of the present invention, a multi-UAV path planning method based on the Hippo optimization algorithm includes the following steps.

[0068] Step S1: Establish an environment model

[0069] First, a three-dimensional spatial model containing obstacles is constructed based on the actual flight environment. This environment model can be a grid model or a non-grid model. In this embodiment, a 100m×60m×50m three-dimensional terrain environment is established based on a digital elevation model, and multiple cuboid obstacles and spherical no-fly zones are set as environmental risk areas. The coordinates and dimensions of the specific obstacles and no-fly zones are shown in Tables 1 and 2. Table 1 shows the X-region, Y-region, and height range of multiple cuboid obstacles, such as X-region 43:50, Y-region 40:44, and height 13, etc. These obstacles simulate insurmountable entities such as buildings and mountains. Table 2 shows two no-fly zones, a spherical region with a radius of 8 centered at (55,10,20) and a spherical region with a radius of 5 centered at (70,50,30), used to simulate areas with unfavorable weather conditions such as electromagnetic interference and severe weather. Through the above settings, a representative complex multi-obstacle three-dimensional environment is obtained to verify the path planning performance of the present invention.

[0070] Table 1 Obstacle Information

[0071]

[0072] Table 2 No-fly zone information

[0073]

[0074] Step S2: Initialize the relevant parameters of the hippo optimization algorithm.

[0075] Initialize the maximum number of iterations (set to 100 in this embodiment), the number of individuals in the population (set to 50 in this embodiment), the total number of drones (set to 3 in this embodiment), and the number of waypoints for each drone (each drone in this embodiment includes a start point, an end point, and several intermediate waypoints, for a total of 8 waypoints). Additionally, the dimension of the position vector needs to be set. Calculation method: In the formula, The total number of drones, The number of waypoints for each drone. The dimension of the coordinate space, in a two-dimensional scene. In a 3D scene This embodiment is planned in three-dimensional space, with the coordinate space dimension number... Therefore, the dimension of the position vector of each individual hippopotamus is... .

[0076] Step S3, Population Initialization

[0077] All waypoints of multiple drones are encoded into the position vector of a single hippopotamus individual, with each hippopotamus individual representing a multi-drone path planning scheme. A Latin hypercube sampling strategy is used to initialize a hippopotamus population composed of multiple hippopotamus individuals.

[0078] The core idea of ​​this step is to transform the multi-UAV path planning problem into a hippo population optimization problem: the flight path of each UAV is represented by a series of waypoints (including the starting point, intermediate points, and the ending point). The coordinates of all waypoints of all UAVs are arranged sequentially to form a high-dimensional vector, which represents the position of a hippo individual. A single hippo individual completely describes a multi-UAV path planning scheme. Multiple such individuals constitute a hippo population.

[0079] Latin hypercube sampling (LHS) was used for population initialization, and the initialization formula is as follows:

[0080]

[0081] In the formula, For the first The location of each individual hippopotamus and These are the lower and upper bounds for location sampling, respectively. The value is a column vector , The value is a column vector , It is a Latin hypercube sampling function. Let be the dimension of the position vector. Specifically, first, the value range of each dimension is divided into equal parts. A small interval, The number of individuals in the population is 50 in this embodiment. Then, a sample is randomly drawn from each small interval, and it is ensured that the combination of each sample in different dimensions is random.

[0082] This initialization method enables the initial population to uniformly cover the entire search space, avoiding population clustering or search blind spots that may be caused by traditional random initialization. This improves the coverage of the initial solution space, effectively prevents early search concentration in complex 3D environments, and provides a good starting point for subsequent global searches.

[0083] Step S4: Define the fitness function

[0084] The fitness function is a quantitative indicator for evaluating the performance of multi-aircraft path planning schemes. The fitness function used in this embodiment includes at least path length cost, multi-aircraft flight time coordination cost, and collision cost, and may also include environmental risk cost to enhance obstacle avoidance capabilities. The specific expression is as follows:

[0085]

[0086] In the formula, , , , In this embodiment, the weight parameters are optimized. Take 0.25, Take 0.15, Take 0.25, Take 0.35; , , , This is an expression parameter used for normalization processing. In this embodiment, Take 1, Take 10, Take 0.05, Take 1; This represents the total actual flight distance of all drones, which is the sum of the path lengths of each drone from the starting point to the destination. This indicates the maximum total flight range of all drones, which is set to 5km in this embodiment; Indicates the total number of environmental risk zones; and They represent the first The horizontal and vertical coordinates of the drone; and They represent the first The x-coordinate and y-coordinate of the center of each environmental risk zone; Indicates the first The flight time of a drone is obtained by dividing the path length by the average speed; This indicates the set cooperative flight time, which is the time when all drones arrive at the target point simultaneously. In this embodiment, it is set to 60 seconds. This indicates the number of collisions, including the number of collisions between drones and the number of collisions between drones and environmental risk areas.

[0087] The first term of the expression represents the path length cost, encouraging the algorithm to find the path with the shortest total distance. The second term represents the environmental risk cost, encouraging drones to stay away from the center of the risk zone. The third term represents the multi-drone flight time coordination cost, encouraging all drones to have flight times close to the set coordination time. The fourth term represents the collision cost, used to penalize path schemes that result in collisions; the more collisions, the higher the fitness value. A comprehensive fitness value is obtained through linear weighted summation; the smaller this value, the better the path planning scheme. By introducing path length cost, multi-drone flight time coordination cost, and collision cost, this invention can simultaneously consider the shortest total distance, simultaneous arrival of multiple drones, and collision avoidance safety requirements during algorithm optimization. It effectively solves the problem that existing methods do not adequately consider the path coupling relationship between multiple drones, dynamic collision avoidance constraints, and coordination safety. The fitness values ​​in subsequent stages are calculated using this function.

[0088] Step S5: Iteratively update the hippopotamus population in stages.

[0089] This step involves iteratively updating the positions of individual hippos within the hippo population in stages to update the corresponding multi-aircraft path planning scheme. The iterative update process includes an exploration phase and a development phase. The exploration phase is further subdivided into aquatic aggregation and predator defense phases, while the development phase involves escaping predators. During the iterative update process, path points that collide with obstacles are addressed to ensure flight path safety.

[0090] The update mechanism for each stage is described in detail below.

[0091] Water accumulation stage:

[0092] This phase simulates the aggregation behavior of hippopotamus groups in lakes or ponds. Individuals in the population are divided into male and female hippos (including calves). The number of male hippos is approximately half the total population, and their updates are guided by the globally optimal individual. Hippopotamus candidate solutions are updated using the following formula:

[0093]

[0094]

[0095]

[0096]

[0097] In the formula, and Let represent the candidate solutions for male and female hippos before the update, respectively. and These represent the updated candidate solutions for male and female hippos, respectively. The best candidate solution in the population is represented by the hippopotamus individual with the smallest fitness value in the current iteration. and These represent the current iteration number and the maximum iteration number, respectively. Indicates the number of individuals in a population; and An integer between 1 and 2; , , and A random value between 0 and 1. , , and Between 0 and 1 3D random vector; and To pass A randomly selected numerical value or vector; A random integer that is either 0 or 1; This represents the mean of several randomly selected candidate solutions.

[0098] After the update is complete, the newly generated male candidate solutions will be... Female candidate solutions Each solution is compared with the current candidate solutions, and the solution with the better fitness value is selected to proceed to the next stage. This competitive selection mechanism ensures that the quality of each generation of the population does not degenerate.

[0099] The predator defense phase:

[0100] This phase simulates the defensive behavior of a hippopotamus group when facing a predator. First, a predator's location is randomly generated within the search space. :

[0101]

[0102] Calculate the current distance between the individual hippopotamus and the predator:

[0103]

[0104] Then, based on the predator's fitness fitness of the current hippopotamus individual Based on the comparison results, new candidate solutions are generated using different defense strategies. :

[0105]

[0106] In the formula, A random vector that obeys Levy's flight; This indicates element-wise addition; The fitness function; and A random vector between 0 and 1; , , and The parameters are randomized and uniformly selected from the following intervals: , , , .

[0107] Levy flight is a type of random walk with a heavy-tailed distribution. Its step size is sometimes small, which is beneficial for fine-grained local searches, and sometimes large, which is beneficial for escaping local optima. Combining levy flight with predator location can generate diverse defensive behaviors, enhancing the algorithm's global search capability during the exploration phase. When the predator's fitness is better than the current individual, the hippo exhibits a stronger counterattack behavior (first branch); otherwise, it adopts a milder escape behavior (second branch). Then, it is compared with the current candidate solutions, and the one with the lower fitness is retained to enter the next stage.

[0108] Escape from the predator phase:

[0109] This phase simulates the behavior of a hippopotamus rapidly fleeing when encountering a predator at close range. First, the local search boundary is calculated; as the number of iterations increases, the search range gradually shrinks.

[0110]

[0111] Then new candidate solutions are generated:

[0112]

[0113] in, The parameters are random and generated using the following formula:

[0114]

[0115] In the formula, and These represent the lower bound and upper bound of the local search in the current iteration, respectively. and A random number between 0 and 1 A random vector between 0 and 1 These are random numbers that follow a standard normal distribution.

[0116] generate Then, it is compared with the current candidate solutions, and the one with the smaller fitness is retained for the next iteration. In this stage, because the local boundary decreases with the number of iterations, the search step size gradually becomes smaller in the later stages, which is conducive to fine-grained search near the optimal solution and improves convergence accuracy.

[0117] Levy's flight strategy based on a group elite learning mechanism:

[0118] This invention introduces an improved strategy—Levy flight with a swarm elite learning mechanism—in addition to the exploration phase, namely the water aggregation phase, and the predator defense phase. This strategy generates new candidate solutions independently of the aforementioned phases and competes with candidate solutions generated in the original phases for selection, thereby further enhancing global search capabilities. The specific method is as follows:

[0119] The first new candidate solution is generated using the following three-branch approach. :

[0120]

[0121] In the formula, This represents the random step size generated by the Levy flight strategy. and This represents two randomly selected distinct elite candidate solutions. and These represent the second and third candidate solutions ranked in the overall algorithm, respectively. The parameters are dynamic. The first branch moves the current individual towards the global optimum; the second branch moves the current individual towards the difference between the two random elites; the third branch moves the current individual towards the center formed by the optimal solution and the mean of the second and third elites. These three branches are controlled by dynamic parameters. Equal probability selection can generate diverse exploration directions. In this embodiment, This ensures the parameters As the iteration progresses, it exhibits a non-linear decreasing trend, achieving a natural transition from "coarse search" to "fine search".

[0122] generate Then, it is compared with the candidate solutions generated in the original exploration phase (gathering in the water and resisting predators), and the solution with the better fitness value is selected as the final candidate solution to enter the next phase.

[0123] Through the Levy flight strategy employing the aforementioned elite learning mechanism, this invention, during the exploration phase, leverages the random long jumps of Levy flight and the directional guidance of superior individuals to efficiently generate diverse candidate solutions within a broad search space. This effectively prevents the population from prematurely concentrating in local optima, reducing ineffective blind searches and thus lowering the computational complexity of a single iteration, while enhancing the algorithm's ability to escape local optima. Furthermore, this strategy automatically adjusts its search behavior according to the iteration process, achieving an adaptive transition from coarse to fine search, overcoming the shortcomings of existing strategies that rely on simple switching and lack dynamic adaptability. In addition, the guidance method in the third branch, which converges towards multiple elite solution centers, naturally suppresses drastic fluctuations in path points, facilitating the generation of continuous and smooth flight trajectories.

[0124] Quadratic interpolation strategy:

[0125] This invention introduces a quadratic interpolation strategy during the development phase, specifically the predator escape phase, to enhance local exploitation capabilities. This strategy performs quadratic interpolation on each dimension of the position vector. For each dimension of the position vector... , The second new candidate solution is generated according to the following formulas respectively. The Dimensional components :

[0126]

[0127] In the formula, and This represents two distinct individuals A and B randomly selected from the population on the [missing information - likely a date or time]. Positional components in the dimension, Indicates the current best candidate solution In the Positional components in the dimension. If the denominator is zero, then directly... Assigned value .

[0128] The geometric meaning of this formula is as follows: using the coordinates of three known points—the optimal individual, random individual A, and random individual B—in their respective dimensions and their global fitness, a quadratic interpolation function is constructed, and the minimum point of this quadratic function is used as the component of the new candidate solution in that dimension. Because global fitness is used instead of local fitness in that dimension, this strategy can integrate information from multiple excellent individuals, generating candidate positions closer to the global optimum. This generates a complete position vector. Then, it is compared with the original candidate solutions generated during the development phase of the Hippo optimization algorithm, and the solution with the better fitness value is retained for the next iteration. This fine-grained local search can improve the convergence accuracy of the algorithm.

[0129] The quadratic interpolation strategy significantly improves the search accuracy near the optimal solution, enabling the algorithm to converge with fewer fitness evaluations, further reducing overall computational overhead and improving convergence accuracy. In particular, because quadratic interpolation performs smooth interpolation between multiple elite solutions, the transitions between generated path points are smoother, effectively avoiding sharp turns or corners in the path, thus significantly improving the smoothness of the flight trajectory. Working synergistically with the Levy flight strategy, the algorithm can quickly approach the global optimum in fewer iterations while maintaining population diversity, resulting in faster convergence, stronger stability, lower computational complexity, and better path smoothness when solving multi-UAV path planning problems.

[0130] Collision detection and path correction:

[0131] After each new candidate solution is generated, i.e., after a new multi-drone path scheme is generated, collision detection needs to be performed on each waypoint of each drone. For any waypoint, its distance to all environmental risk zones is calculated. .like If the distance is greater than the safe distance, it is assumed that the drone will not collide; if If the distance is less than or equal to the safe distance, a collision is considered to have occurred. In this embodiment, the safe distance is set to the obstacle radius plus the drone's safe radius. For waypoints that collide, the algorithm performs correction processing to ensure they escape the obstacle area. Common processing methods include moving the collision point a certain distance away from the obstacle center or regenerating the point. In this way, the final output flight path can effectively avoid all obstacles and risk areas.

[0132] Step S6: Global Optimal Update

[0133] After each iteration, the fitness value of each hippopotamus in the population is calculated according to the fitness function defined in step S4, and compared with the fitness value of the current global optimum. If the fitness value of the newly generated individual is less than that of the current global optimum, the global optimum information is replaced with the new individual information; otherwise, the original global optimum is retained. In this way, the global optimum is continuously updated with iterations, gradually approaching the theoretical optimum.

[0134] Step S7, Termination and Output

[0135] Determine if the maximum number of iterations has been reached. If not, return to step S5. If it has been reached, output the information of the optimal hippo individual. The multi-drone path planning scheme corresponding to the optimal hippo individual is the optimal flight path of the multi-drone.

[0136] In this embodiment, the maximum number of iterations is 100. After 100 iterations, the algorithm terminates and outputs the sequence of 3D path points corresponding to the optimal individual. Connecting these path points yields the flight trajectory of each drone.

[0137] Following the steps outlined above, conduct simulation experiments in the established three-dimensional environment. Figure 2 The simulation results of the algorithm of this invention and other comparative algorithms in multi-UAV path planning are presented, including 3D path graphs and projection graphs on a 2D plane. It can be seen that the Latin hypercube sampling initialization of this invention makes the initial population more evenly distributed in the search space, avoiding early individual aggregation, and thus generating reasonable detour paths faster in complex obstacle environments. Compared with other algorithms, the path generated by the improved Hippo optimization algorithm of this invention exhibits superior smoothness and feasibility, avoiding problems such as redundant detours. Specifically, the sled dog optimization algorithm and the existing Hippo optimization algorithm have excessively curved paths and are close to obstacle boundaries in areas with dense obstacles, easily leading to potential collision risks, and the trajectory has obvious angles and insufficient smoothness. Although the gray wolf optimization algorithm and particle swarm optimization algorithm can effectively complete obstacle avoidance, they still exhibit the phenomenon of getting trapped in suboptimal solutions in some local environments. The algorithm of this invention enhances global exploration capabilities through Levy flight with a swarm elite learning mechanism and improves local development accuracy by combining quadratic interpolation. The quadratic interpolation strategy performs smooth interpolation between multiple elite solutions, making the transition between generated path points smoother and effectively avoiding sharp path changes, thereby significantly improving the smoothness of the flight trajectory. At the same time, the algorithm can effectively escape local optima, so it can still maintain strong global optimal performance and good path smoothness under complex obstacle distribution.

[0138] Figure 3 This figure compares the fitness convergence curves of the algorithm of this invention with those of other optimization algorithms during the iteration process. As can be observed from the figure, the adaptive update mechanism proposed in this invention, which combines the Levy flight strategy in the exploration phase with quadratic interpolation in the development phase, allows the algorithm to automatically adjust its search behavior according to the iteration process. This results in a significantly faster convergence speed compared to the comparison algorithms, and the lowest final fitness value. Specifically, the sled dog optimization algorithm exhibits significant fluctuations in fitness value in the early stages of iteration, demonstrating obvious instability. The particle swarm optimization algorithm and the gray wolf optimization algorithm basically converge after the first 10 iterations, but their final convergence values ​​are relatively high, indicating insufficient optimization accuracy. In contrast, the improved hippo optimization algorithm of this invention shows better convergence ability, and its final fitness value is lower than other comparison algorithms. This indicates that the improved hippo optimization algorithm proposed in this invention not only accelerates the convergence speed but also outperforms the comparison algorithms in both convergence speed and quality, demonstrating stronger global search and local development capabilities. It can efficiently meet the requirements of path length, time coordination, and collision safety for optimal multi-UAV cooperative flight.

[0139] Finally, it should be noted that the features mentioned and / or shown in the above description of exemplary embodiments of the present invention can be combined in the same or similar manner with one or more other embodiments, combined with or substituted for corresponding features in other embodiments. These combined or substituted technical solutions should also be considered to be included within the scope of protection of the present invention.

Claims

1. A multi-UAV path planning method based on the Hippo Optimization Algorithm, characterized in that, Includes the following steps: Step 1: Create an environment model that includes obstacles; Step 2: Initialize the relevant parameters of the hippo optimization algorithm; Step 3: Encode all waypoints of multiple drones into a single hippopotamus individual's position vector; each hippopotamus individual represents a multi-drone path planning scheme. Initialize the hippopotamus population, composed of multiple hippopotamus individuals, using a Latin hypercube sampling strategy. In the formula, For the first The location of each individual hippopotamus and These are the lower and upper bounds for location sampling, respectively. It is a Latin hypercube sampling function. Let be the dimension of the position vector, and ,in The total number of drones, The number of waypoints for each drone. The dimension of the coordinate space; Step 4: Define a fitness function, which includes at least path length cost, multi-aircraft flight time coordination cost, and collision cost, to evaluate the merits of the multi-aircraft path planning scheme for each hippopotamus individual. Step 5: Iteratively update the positions of individual hippos in the hippo population in stages to update the corresponding multi-aircraft path planning scheme. Specifically, in the exploration phase, a first new candidate solution is generated using the Levy flight strategy with a swarm elite learning mechanism. This first new candidate solution is compared with the original candidate solutions from the exploration phase, and the solution with the better fitness value is selected as the new position for that hippo individual. In the development phase, a second new candidate solution is generated using a quadratic interpolation strategy. This second new candidate solution is compared with the original candidate solutions from the development phase, and the solution with the better fitness value is selected as the new position for that hippo individual. During the iterative update process, path points that collide with obstacles are processed. Step 6: After the iteration is completed, calculate the fitness value of each hippopotamus individual in the hippopotamus population, and update the information of the current global best hippopotamus individual based on the fitness value; Step 7: Determine if the maximum number of iterations has been reached. If not, return to step 5. If it has been reached, output the information of the optimal hippo individual. The multi-drone path planning scheme corresponding to the optimal hippo individual is the optimal flight path of the multi-drone.

2. The multi-UAV path planning method according to claim 1, characterized in that, In step 1, the environment model includes a grid model and a non-grid model; in step 2, the parameters related to the hippo optimization algorithm include the maximum number of iterations, the number of individuals in the population, the total number of drones, and the number of waypoints for each drone.

3. The multi-UAV path planning method according to claim 1, characterized in that, The fitness function defined in step 4 is determined by the following formula: In the formula, , , , This indicates the optimization of weight parameters. , , , These are parameters for the expression, used for normalization. This represents the total actual flight distance of all drones. This indicates the maximum total flight range set for all drones. This indicates the total number of environmental risk zones. and They represent the first The horizontal and vertical coordinates of the drone. and They represent the first The central x-coordinate and y-coordinate of each environmental risk zone Indicates the first Flight time of the drone This indicates the set cooperative flight time. Indicates the number of collisions.

4. The multi-UAV path planning method according to claim 3, characterized in that, In step 5, the exploration phase includes a water gathering phase and a predator defense phase, and the development phase is a predator escape phase.

5. The multi-UAV path planning method according to claim 4, characterized in that, In step 5, the Levy flight strategy of the swarm elite learning mechanism specifically generates the first new candidate solution according to the following three-branch method. : In the formula, This represents the random step size generated by the Levy flight strategy. The best candidate solution in the group. and This represents two randomly selected distinct elite candidate solutions. and These represent the second and third candidate solutions ranked in the overall algorithm, respectively. For dynamic parameters, , and These represent the current iteration number and the maximum iteration number, respectively.

6. The multi-UAV path planning method according to claim 4, characterized in that, In step 5, the quadratic interpolation strategy is specifically as follows: For each dimension of the position vector , The second new candidate solution is generated according to the following formulas respectively. The Dimensional components : In the formula, and This indicates that two different individuals randomly selected from the population are on the [missing information - likely a date or time]. Positional components in the dimension, For the fitness function, Indicates the current best candidate solution In the Positional components in the dimension; if the denominator is zero, then... Assigned value .

7. The multi-UAV path planning method according to any one of claims 1 to 6, characterized in that, In step 6, if the fitness value of the newly generated individual is less than the fitness value of the current global optimum, the information of the global optimum is replaced with the information of the newly generated individual; if the fitness value of the newly generated individual is greater than or equal to the fitness value of the current global optimum, the information of the current global optimum is retained.

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