A novel multi-unmanned aerial vehicle cooperative path planning method

Abstract

This invention proposes a novel multi-UAV cooperative route planning method based on the Anas Platyrhynchos Optimizer (APO) algorithm. When multiple UAVs are used to cooperate in attacking a known target, the method first mathematically models the cooperative route planning process. Then, it proposes the Platyrhynchos Optimizer algorithm and applies it to solve the route planning problem, obtaining a three-dimensional cooperative route that meets the planning requirements. Finally, simulation experiments are conducted to verify the effectiveness of the proposed method through comparison with several other algorithms. This invention can significantly improve the quality of the optimal solution and the convergence speed, is simple in principle, and is not limited by spatial size or potential parallelism.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) route planning, and in particular to a novel multi-UAV collaborative route planning method. Background Technology

[0002] Multi-UAV cooperative route planning is a key technology for achieving collaborative operations among multiple UAVs. The multi-UAV cooperative route planning problem is characterized by high dimensionality, multiple constraints, and spatiotemporal coordination, making it a very challenging problem. To address this problem, researchers have proposed various methods, including route planning algorithms, obstacle avoidance techniques, and route adjustment strategies. Current research methods on route planning can be categorized into several types: potential field-based methods, such as the Artificial Potential Field (APF) method, are simple in principle and fast in computation, suitable for solving route planning problems with high real-time requirements; however, they are prone to stagnation in certain situations, leading to plan failure; random sampling-based methods can quickly search for a route in complex environments with known or dynamically unknown elements, but this method is costly, and the planned route is not always optimal; and heuristic search algorithms are simple and efficient, but prone to getting stuck in infinite loops and have many planned route folding points.

[0003] American biologists have discovered that mallards have a habit of controlling one part of their brain to remain asleep while another part remains awake. Even while sleeping, mallards can keep one eye open and the other closed. This research provides the first evidence that animals can control their sleep states. This semi-asleep habit helps mallards evade predators in dangerous environments. During mallard migration, a lead duck can be observed within the flock, and other ducks will flock to it. Finally, the entire flock will migrate towards its destination. When a duck is not in the flock, the lone duck can find its mate by calling out and moving towards them, eventually migrating with the group. As a group, mallards can coordinate themselves to become part of the flock. This swarm intelligence can be relevant to target problems that require optimization. Inspired by the collective behavior of mallards, a new swarm intelligence algorithm can be designed and applied to the multi-UAV route planning problem. This approach can better achieve multi-UAV cooperative combat technology than traditional route planning methods. Summary of the Invention

[0004] This invention addresses the problems of unreliable optimal solution quality and unsatisfactory convergence speed in traditional swarm intelligence algorithms. Based on the characteristics of multi-UAV cooperative route planning, a multi-constraint route planning model is established, and a novel multi-UAV cooperative route planning method is proposed. This method is based on the mallard optimization algorithm, which has the advantages of simple algorithm principle, fast planning speed, and no limitation by spatial size and potential parallelism.

[0005] In order to solve the above problems, the present invention provides, as follows: Figure 1 As shown, a novel multi-UAV cooperative route planning method is designed, and the following technical solution is adopted:

[0006] Step 1: Establish a 3D environment for multi-UAV route planning;

[0007] In flight path planning, an appropriate planning space must be established based on the flight environment and mission requirements. In the current mission environment with a mountainous background, a stochastic function is used to build a digital model to simulate peaks and other threatening obstacles. The mountain model function consists of raw data and a threat-equivalent terrain model. The former is expressed as:

[0008]

[0009] Where x and y refer to the coordinates of a point on the horizontal projection plane; z1 refers to the height coordinates corresponding to the coordinate point on the horizontal plane; a, b, c, d, e, f, and g are coefficients, and terrain models of other terrains can be obtained by changing the parameters.

[0010] The threat equivalent terrain model is:

[0011]

[0012] Where x and y refer to the coordinates of a point on the horizontal projection plane; z2 refers to the peak height; h(i) refers to the height of the highest point of peak i on the basic terrain; x 0i and y 0i The coordinates of the highest point of peak i; x si and y si This refers to the variables related to the slope of peak i along the x and y axes. If x si and y si If the slope is large, the peak will have a flat and steep gradient.

[0013] The final mountain threat model is obtained by integrating the original digital terrain model into the threat-equivalent terrain model:

[0014] z(x,y)=max(z1(x,y),z2(x,y)) (3)

[0015] Different terrain models can be obtained by changing the parameters in the function. In the planning space, the flight path of a UAV can be represented by many waypoints. Therefore, waypoints are connected to form multiple flight paths, which are linked to the starting point and the target point to form a flight path. We set the starting point of a UAV as S(x0,y0,z0) and the target point as E(x... e ,y e ,z eThe number of waypoints is n, and the waypoints found can be represented as {S, P1, P2, ..., P...}. n ,E} represents; among these variables, the coordinates of the trajectory nodes are P. i =(x i ,y i ,z i ).

[0016] Step 2: Establish a multi-aircraft cooperative route planning model and determine the route cost function;

[0017] The goal of multi-UAV cooperative route planning is to ensure that each UAV can search for a suitable route while meeting the requirements of safe flight and spatiotemporal cooperation, and to minimize the overall route cost of the UAV fleet. Therefore, route planning requires establishing a route cost function as an indicator to evaluate route quality. This necessitates considering the dynamics and threat constraints of individual UAVs in multi-UAV cooperative route planning to satisfy the spatial and temporal cooperation constraints of the multi-UAVs. Therefore, given the planning objective, the following cost indicators are considered in the current work: individual UAV performance indicators include fuel consumption, maximum climb angle, flight altitude, peak threat, and multi-UAV temporal cooperation. Spatial cooperation is reflected in avoiding conflicts in multi-UAV routes, setting different flight altitudes that each UAV must avoid. The overall cost function is established as follows:

[0018]

[0019] Here, w1, w2, w3, w4, and w5 represent the weights of different cost indicators, and the sum of the weights is 1. Routes that meet different requirements can be obtained by adjusting the weights. To ensure that all cost indicators are included in route planning, the functions are normalized according to their range, and then a weighted sum is performed.

[0020] Fuel consumption costs are related to the length of the flight path and the flight speed. Assuming the drone always flies at a constant speed, the fuel cost can be replaced by the flight path length:

[0021]

[0022] Where (x) i+1 ,y i+1 ,z i+1 ) and (x i ,y i ,z i The coordinates correspond to the adjacent waypoints.

[0023] J angle The cost of the maximum climb angle is expressed as:

[0024]

[0025] Where, θ i It refers to the climb angle between adjacent points on a certain air route.

[0026] To meet flight safety and stealth requirements, flight altitude cannot be too low or too high. The cost of altitude can be expressed as...

[0027]

[0028] Among them, h i It refers to the altitude of route i on a certain air route, safth i This refers to the minimum safe altitude for each drone.

[0029] Collisions with mountains must be avoided during drone flight. The peak model is represented by a conical approximation, where the flight path is divided into m equal parts, with m-1 sampling points at the center. The threat cost of the entire flight path is expressed as...

[0030]

[0031] Where n represents the number of waypoints, K represents the number of peaks, and threshold(j,k) is the number of sampling points (x,k) in the current interval. i ,y i ,z i The threat cost at a certain peak is expressed as:

[0032]

[0033] R T (h)=(H(k)-h) / tan θ (10)

[0034] Where n represents the number of waypoints, K represents the number of peaks, H(k) represents the height of peak k, and R... T This refers to the maximum radius of extension. Additionally, h... j This is the current flight altitude of the drone, d T This refers to the distance d from the drone to the peak symmetry axis. Tmin This represents the minimum allowable distance on the terrain, where θ refers to the slope of the terrain. Terrain threats include... Figure 2 As shown.

[0035] The cooperation cost function implies time cooperation, requiring all drones to arrive at the target point as simultaneously as possible. If a flight path cannot meet the time cooperation constraint, the path must be corrected. Assume the flight speed of drone i is within [v...]. min ,v max Within the range, and the heading is in L i Within the range, its flight time is Similarly, assuming the flight time of drone j is in Within a certain range, if the flight times of two drones intersect, then temporal cooperation is feasible, that is...

[0036]

[0037] Based on the time cooperation evaluation formula between air routes, a time cooperation cost function was obtained based on the current planning model:

[0038]

[0039] Among them, T min T refers to the period of time within a flight path where the flight distance is relatively short. inter This indicates the point where the flight times of the two routes intersect.

[0040] Step 3: Propose an optimization algorithm for the mallard duck;

[0041] The mallard duck optimizer consists of two main steps: warning behavior and migration process, such as... Figure 3 As shown.

[0042] 3.1 Warning Behavior

[0043] Prior to the warning behavior, based on the mallard duck behavior model, the population in the APO (Anas Platyrhynchos Optimizer, APO) is initialized as follows:

[0044] Pop i = rand·(up-low)+low (13)

[0045] Among them, Pop i Let N be the i-th population, N be the population size, and low and up be the upper and lower bounds of the search space.

[0046] rand is a random value selected from the range [0,1].

[0047] In the warning action, a dangerous flight operation implemented by the selection probability Pc is proposed; the main process of the warning action is described below:

[0048] (1) Calculate the probability of encountering danger, Pc;

[0049]

[0050] Among them, fit(Pop) i ) is Pop i The fitness value, rank(fit(Pop) i )) is considered Pop i The individual's ranking within the population of other individuals;

[0051] (2) If probability Pc is satisfied, the new individual is generated as follows:

[0052]

[0053] Where t represents the current iteration number, Pop best It is the leading duck; α0 > 0 is the step size scaling factor, and sign refers to the sign function; Levy flight is a type of random walk with a step size following a Levy distribution, and its distribution equation is as follows:

[0054] Levy~u=t -λ ,1<λ≤3 (16)

[0055] Where λ=1+β, Levying flight is a special type of random walk, and its step size probability distribution follows a heavy-tailed distribution. The Levying flight step size is defined as:

[0056]

[0057] Where s represents the Levy flight step size; u and υ are defined as follows:

[0058]

[0059] Here, α0 = 0.01 and β = 3 / 2 are set; u and υ follow a normal distribution. and Choose from.

[0060] 3.2 Migration Process

[0061] The migration process mainly includes the following:

[0062] (1) After defining the optimal particle, other search particles will attempt to move to the optimal particle; the mathematical model for this behavior is as follows:

[0063] Pop i (t+1)=Pop i (t)-A·|C·Pop best -Pop i (19)

[0064] Where A and C refer to the coefficient vector, the result is:

[0065] A = 2a·rand-a (20)

[0066] C = 2·rand (21)

[0067] Where 'a' refers to the coefficient vector that decreases linearly with iteration; the value of 'a' is:

[0068]

[0069] Where T is the maximum number of iterations;

[0070] The basic principles for solving two-dimensional problems are as follows: Figure 4 As shown; it can be determined based on the position of the current optimal solution (X). * ,Y * The position of the particle (X,Y) is updated using the coefficient vectors A and C; by adjusting the coefficient vectors A and C, an expansion search can be performed on different positions around the optimal solution based on the current position; the possible positions of the particle after the update in 3D space are as follows: Figure 5 As shown; due to the randomness of vectors A and C, the particle can reach any region between key points in the search space; therefore, updating the particle to the region near the optimal solution can be used as a means of simulating the behavior of moving to the leading duck.

[0071] (2) If the new individual is worse than the old solution, randomly select another particle;

[0072] (3) If Pop rand Superior to Pop i Then the i-th individual will move to the random particle Pop according to equation (23). rand ;

[0073]

[0074] Where l represents the distance between the random particle and the i-th individual;

[0075] (4) If Pop rand equals Pop i If so, the particle remains unchanged;

[0076] (5) If Pop rand Worse than Pop i Then the random particle will move to the i-th individual according to equation (24);

[0077]

[0078] Step 4: Multi-UAV collaborative route planning process;

[0079] As described in step 3, a multi-UAV route planning method based on the mallard duck optimization algorithm initializes the algorithm parameters and individual positions, calculates the fitness value of the current population individuals according to the cost function formula, and determines whether the termination condition has been met. If the termination condition is met, the best agent and the best route are output. If the termination condition is not met, the method returns to update the individual positions according to the APO.

[0080] In route planning, the fitness value of each route includes not only its own route cost information but also information on cooperation and interaction with other drones. In other words, each drone will refer to the route information of other drones when planning its route. By selecting routes with lower overall costs, routes with better coordination can be obtained while meeting the single-drone flight cost index. The planned routes can meet the collision avoidance and time constraints among multiple drones.

[0081] Compared with traditional route planning methods, this algorithm obtains the best solution with more reliable quality in multi-UAV collaborative route planning, has the ability to escape local optima, and has a faster convergence speed and higher stability. Attached Figure Description

[0082] Figure 1 This is a flowchart of multi-UAV route planning based on the mallard duck optimization algorithm.

[0083] Figure 2 This is a terrain threat map.

[0084] Figure 3 The warning behavior and migration process of mallard duck flocks.

[0085] Figure 4 This represents a 2D position vector and its subsequent possible positions.

[0086] Figure 5 This represents the 3D position vector and its subsequent possible positions.

[0087] Figure 6 For scenario 1, three-dimensional flight path planning for each UAV.

[0088] Figure 7 Contour map of each drone for scenario 1.

[0089] Figure 8 This is the cost convergence curve for each drone in case 1.

[0090] Figure 9 The convergence curve of the synthetic route cost for each UAV in case 1.

[0091] Figure 10 For scenario 2, three-dimensional flight path planning for each UAV.

[0092] Figure 11 Contour map of each drone in scenario 2.

[0093] Figure 12 This is the cost convergence curve for each drone in case 2.

[0094] Figure 13 The convergence curve of the synthetic route cost for each UAV in case 2.

[0095] Figure 14 For scenario 3, three-dimensional flight path planning for each UAV.

[0096] Figure 15 Contour map for each drone in scenario 3.

[0097] Figure 16 The cost convergence curve for each drone in case 3 is shown.

[0098] Figure 17 The convergence curve of the synthetic route cost for each UAV in case 3.

[0099] Figure 18 For scenario 4, three-dimensional flight path planning for each UAV.

[0100] Figure 19 Contour map of each drone in scenario 4.

[0101] Figure 20 The cost convergence curve for each drone in case 4 is shown.

[0102] Figure 21 The convergence curve of the synthetic route cost for each UAV in case 4.

[0103] Figure 22 This is the convergence curve of the 3D integration path cost under case 1.

[0104] Figure 23 This is the convergence curve of the 3D integration path cost under case 2.

[0105] Figure 24 This is the convergence curve of the 3D integration path cost under case 3.

[0106] Figure 25 This is the convergence curve of the 3D integration path cost under case 4.

[0107] Figure 26 The distribution of the results of the operation in case 1 (tested 30 times).

[0108] Figure 27 The distribution of the results of the operation in case 2 (tested 30 times).

[0109] Figure 28 The distribution of the results of the operation in case 3 (tested 30 times).

[0110] Figure 29 The distribution of the results of the operation in case 4 (tested 30 times). Detailed Implementation

[0111] To verify the performance of the novel multi-UAV route planning method in this invention, simulation tests will be conducted based on the mallard optimization algorithm, and the results will be compared and analyzed with several other traditional intelligent algorithms.

[0112] Step 1: Simulation Environment Setup and Analysis;

[0113] The planning space was set to 100km × 100km × 500m, including 6 peaks. The parameters of the original digital terrain model were set to a = 0.1, b = 0.01, c = 1, d = 0.1, e = 0.2, f = 0.4, and g = 0.02. Table 1 lists the peak height, horizontal coordinates of the highest point, and slope parameters. Multi-UAV cooperative route planning was conducted under a known task allocation scheme. In the simulation experiment, the route subpopulation was initialized according to the number of UAVs. The number of individuals in the population, iterations, and waypoints were 50, 100, and 10, respectively. The weight coefficients of all cost functions corresponded to 0.4, 0.2, 0.1, 0.2, and 0.1, respectively, and the UAV flight speed ranged from 40 to 60 m / s.

[0114] Table 1 Model parameters of the peaks

[0115]

[0116] Scenario 1: Three drones start from the starting point and reach the designated target point to perform the mission. The coordinates of the starting point and the target point are shown in Table 2.

[0117] Table 2 Coordinates of all UAV start and target points

[0118]

[0119] The 3D flight path planning and contour map of each UAV are displayed. Figure 6 and Figure 7 In the middle. The convergence curves of the cost of each UAV and the synthetic route cost are in Figure 8 and Figure 9 Draw in the middle.

[0120] Figures 6-9 This demonstrates that all drones can effectively avoid threats and reach the target point. The cost function value of each drone gradually converges with increasing iteration time, thus verifying the effectiveness of the algorithm. The flight time interval (in seconds) and range (in kilometers) of each drone, obtained through simulation, are listed in Table 3. The time intersection point is [1828.9454, 2562.7885]. By setting different flight speeds for all drones, the time coordination requirement can be met.

[0121] Table 3 Flight time and range for each UAV

[0122]

[0123] Scenario 2: Four drones fly to two target points. Table 4 lists the coordinates of the starting point and the target point.

[0124] Table 4. Coordinates of the starting and target points of all UAVs

[0125]

[0126] like Figure 10 and Figure 11 As shown, the planned flight path of the UAV was obtained. Figure 12 and Figure 13 The route cost convergence and overall cost curves for each UAV were plotted.

[0127] The flight time intervals (in seconds) and ranges (in kilometers) for each UAV, based on simulations, are listed in Table 5. The time intersections are [1961.975, 2417.0379]. The planned routes and ranges are short, effectively avoiding obstacles. If the UAVs get too close to each other, collisions can be avoided by setting different flight altitudes.

[0128] Table 5 Flight time and range of each UAV

[0129]

[0130] Scenario 3: Six drones fly to six target points. Table 6 lists the coordinates of the starting point and the target points.

[0131] Table 6. Coordinates of the starting and target points of all UAVs

[0132]

[0133] The result of scenario 3 is as follows Figures 14-17 As shown in Table 7, the flight time interval (in seconds) and range (in seconds) for each UAV are listed in kilometers, based on simulation. The time intersection is [1924.111, 2481.215]. The planned routes and ranges are short, effectively avoiding obstacles. If the UAVs get too close to each other, collisions can be avoided by setting different flight altitudes.

[0134] Table 7 Flight time and range for each UAV

[0135]

[0136] Scenario 4: Eight drones fly to four target points. Table 8 lists the coordinates of the starting point and the target points.

[0137] Table 8. Coordinates of the starting and target points of all UAVs

[0138]

[0139] The result of scenario 4 is as follows Figures 18-21 As shown in the figure. The flight time intervals (in seconds) and ranges (in kilometers) for each UAV, based on simulation, are listed in Table 9. The time intersections are [1922.8382, 2493.2072]. The planned paths and distances are short, effectively avoiding obstacles.

[0140] Table 9 Flight time and range for each UAV

[0141]

[0142] Step 2: Comparison and verification;

[0143] Based on the above four scenarios, the Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Differential Evolution (DE) algorithm, and GWO algorithm were applied to multi-UAV cooperative route planning. Furthermore, the Mallard Optimizer algorithm was compared with the Static Average Grey Wolf Optimizer (IGWO) and the Grey Wolf Optimizer algorithm improved based on chaos theory (HGWO) to verify the effectiveness of the algorithms. The relevant parameter settings for the above algorithms are shown in Table 10.

[0144] Table 10. Parameter settings for the comparison algorithm

[0145]

[0146] Simulation results were compared with the proposed algorithm, validating the effectiveness of the improved strategy. Among these factors, the PSO algorithm parameters included a particle count of 50, learning factors c1 = c2 = 2, and an inertia factor linearly decreasing from 0.96 to 0.2; the DE algorithm parameters included a chromosome count of 50, an upper bound (0.6) and a lower bound (0.2) for the scaling factor, a mutation rate (0.5), and a crossover probability (0.6). To avoid the influence of randomness, each algorithm was run 30 times, with the total population set to 50 and the number of iterations set to 100. Fair comparisons were ensured by setting the same evaluation method for all general parameters (e.g., population size). Table 11 shows the average time for each algorithm in each scheme.

[0147] Table 11 Average time for each algorithm in each scheme

[0148]

[0149] The convergence curves of 3D integration path cost in each case are as follows: Figures 22-25 As shown, the distribution of the calculation results (tested 30 times) is as follows: Figures 26-29 As shown.

[0150] The results show that the cost function of each algorithm can converge to a certain value, meeting the practical requirements of planning. However, compared with PSO, DE, GWO, HGWO, and IGWO algorithms, the Mallard Optimization Algorithm achieves a significantly better final stable value and converges faster. Furthermore, the Mallard Optimization Algorithm outperforms other algorithms in convergence speed and accuracy, with a shorter running time. It can effectively solve the multi-UAV cooperative route planning problem and has greater advantages in solving practical engineering problems.

[0151] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1.A method for multi-UAV cooperative path planning, characterized in that, Includes the following steps: Step 1: Establish a 3D environment for multi-UAV route planning; A digital model is built using a random function to simulate the mountain threat model function; the mountain threat model function consists of the original digital terrain model and the threat equivalent terrain model. The original digital terrain model is as follows: Where x and y refer to the coordinates of a point on the horizontal projection plane; These refer to the height coordinates corresponding to coordinate points on the horizontal plane: a, b, c, d, e, f, and g are terrain model coefficients; The threat equivalent terrain model is as follows: Where x and y refer to the coordinates of a point on the horizontal projection plane; Peak height: The height of the highest point of peak i on the basic terrain; and The coordinates of the highest point of peak value i; and Variables related to the slope of peak i along the x and y axes: Integrating the original digital terrain model into the threat-equivalent terrain model yields the following final mountain threat model: Set the starting point of a certain drone as Set the target point as The number of waypoints is n, and the waypoints found can be used... This indicates that, among these variables, the coordinates of the trajectory nodes are... ; Step 2: Establish a multi-aircraft cooperative route planning model and determine the route cost function; Establish a route cost function as an indicator for evaluating route quality, considering the performance indicators of individual UAVs, including fuel consumption, maximum climb angle, flight altitude, peak threat, and multi-UAV time cooperation; set different flight altitudes that each UAV must avoid; Establish the comprehensive cost function: in, , , , and These refer to the weights of different cost indicators, and the sum of the weights is 1. fuel cost Represented as: in and The coordinates corresponding to adjacent waypoints; The cost of the maximum climb angle is expressed as: in, It refers to the climb angle between adjacent points on a certain air route; The high cost is represented as: in, It refers to the altitude of route i on a certain air route. This refers to the minimum safe altitude for each drone; The threat cost of the entire route is expressed as: Where n represents the number of waypoints, and K represents the number of peak values. It is the sampling point in the current interval. The threat cost at a certain peak is expressed as: Where n represents the number of waypoints, K represents the number of peaks, and H(k) represents the height of peak k. This refers to the maximum radius of extension; in addition, This is the current flight altitude of the drone. This refers to the distance from the drone to the peak symmetry axis. This indicates the minimum distance allowed by the terrain. The slope of the terrain; Assume the flight speed of drone i is Within range, and the heading is Within the range, its flight time is Similarly, assume that the flight time of drone j is in Within a certain range, if the flight times of two drones intersect, then temporal cooperation is feasible, that is... The time collaboration cost function is expressed as follows: in, It refers to the period of time within a flight path where the flight distance is relatively small. Indicates the intersection of the flight times of two routes; Step 3: Propose an optimization algorithm for the mallard duck; The mallard duck optimizer consists of two main steps: warning behavior and migration process. 3.1 Warning behavior; Prior to the warning action, based on the mallard duck behavior model, the population in the APO is initialized as follows: in, It is the i-th population, and low and up are the upper and lower bounds of the search space; rand is a random value selected from the range [0,1]. In the warning action, a dangerous flight operation implemented by the selection probability Pc is proposed; the main process of the warning action is described below: (1) Calculate the probability of encountering danger ; in, yes fitness value, It is considered The ranking of an individual within a population of other individuals, where N is the population size; (2) If probability Pc is satisfied, the new individuals are generated as follows: Where t represents the current iteration number. It is the leading duck; It is the step size scaling factor, and sign refers to the sign function; A Levi's walk is a type of random walk whose step size follows a Levi distribution, and its distribution equation is as follows: in, The probability distribution of Levy's flight step size follows a heavy-tailed distribution, defined as: Where s represents Levy's flight step length; and The definition is as follows: Among the settings , ; and From normal distribution and Select from; 3.2 Migration process; The migration process mainly includes the following: (1) After defining the optimal particle, other search particles will attempt to move to the optimal particle; the mathematical model for this behavior is as follows: Where A and C refer to the coefficient vector, the result is: Where 'a' refers to the coefficient vector that decreases linearly with iteration; the value of 'a' is: Where T is the maximum number of iterations; The basic principle for solving two-dimensional problems is that the position of the current optimal solution can be used as a reference. The position of the particle (X,Y) is updated; by adjusting the coefficient vectors A and C, an expansion search can be performed on different positions around the optimal solution based on the current position; due to the randomness of vectors A and C, the particle can reach any region between key points in the search space; therefore, updating the particle to the region near the optimal solution can be used as a means of simulating the behavior of moving to the leading duck. (2) If the new individual is worse than the old solution, randomly select another particle; (3) If Superior Then the i-th individual will move to the random particle according to equation (23). ; Where 1 represents the distance between the random particle and the i-th individual; (4) If equal If so, the particle remains unchanged; (5) If worse than Then the random particle will move to the i-th individual according to equation (24); Step 4: Multi-UAV collaborative route planning process; As described in step 3, a multi-UAV route planning method based on the mallard duck optimization algorithm initializes the algorithm parameters and individual positions, calculates the fitness value of the current population individuals according to the cost function formula, and determines whether the termination condition has been met. If the termination condition is met, the best agent and the best route are output. If the termination condition is not met, the method returns to update the individual positions according to the APO. The planned route can meet the collision avoidance and time constraints among multiple UAVs.

Images