Unmanned aerial vehicle cluster path planning method based on improved green bird optimization algorithm

Abstract

The invention belongs to the technical field of unmanned aerial vehicle cluster safety path planning, and discloses an unmanned aerial vehicle cluster safety path planning method based on an improved kinger optimization algorithm, which comprises the following steps: S1, according to a path optimal constraint, a safety and feasibility constraint, a flight height constraint, a path smoothness constraint and an unmanned aerial vehicle cluster anti-collision constraint, determining an unmanned aerial vehicle cluster safety path according to the path optimal constraint, the safety and feasibility constraint, the flight height constraint and the path smoothness constraint; constructing a total cost function of a single unmanned aerial vehicle; and S2, taking the total cost function of the unmanned aerial vehicle as a fitness function, and constructing and adopting an improved turnip optimization algorithm to optimize the fitness function to obtain a cost optimal path. According to the mirror reflection algorithm, the randomness and diversity of the algorithm can be improved, and premature convergence of the algorithm is avoided; a falling mechanism model is introduced, occurrence of an accidental obstacle or an enemy target can be considered in a path planning process, and a flight strategy is adjusted in time, so that the adaptability of an algorithm is enhanced, and the survivability of an unmanned aerial vehicle group in a complex environment is also enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of safe path planning for unmanned aerial vehicle (UAV) swarms, and particularly to a method for path planning of UAV swarms based on an improved pied kingfisher optimization algorithm. Background Art

[0002] The goal of UAV path planning is to ensure the safety of the aircraft body while finding the path with the lowest cost in the shortest possible time under the conditions that meet its own performance and environmental constraints. Safe path planning is a very crucial link in the process of UAVs performing tasks, and the research on the safe path planning problem of UAV swarms is of great importance. In the tasks of UAV swarms, in the face of complex environments and dynamically changing obstacles, how to effectively plan safe and effective paths for each UAV to ensure the cooperative combat ability of the swarm is one of the current research hotspots. How to plan such paths is still a complex and challenging problem.

[0003] Safe path planning is a very crucial link in the process of performing tasks, and the research on the safe path planning problem of UAV swarms is of great importance. In the tasks of UAV swarms, in the face of complex environments and dynamically changing obstacles, how to effectively plan safe and effective paths for each UAV to ensure the cooperative combat ability of the swarm is one of the current research hotspots, but how to plan such paths is still a complex and challenging problem. The UAV swarm problem can be regarded as an extension of the single-UAV problem, that is, the same constraint conditions are imposed on each UAV to minimize the total cost of all UAVs.

[0004] The existing UAV path planning cost function mainly consists of four parts: path optimization constraint, safety and feasibility constraint, flight altitude constraint, and path smoothing constraint. The collision safety problem between two or more UAVs is not considered. Secondly, the problem of solving the total cost function of path planning is essentially a multi-objective optimization problem. As a novel population-based metaheuristic algorithm, the pied kingfisher optimizer (PKO) has achieved certain success in simulating the hunting behavior of the white-breasted kingfisher, but there are still some problems: during the iterative process of the kingfisher optimization algorithm, as the number of iterations increases, the influence of the standard normal distribution random perturbation on the update of the discoverer's position gradually weakens, which may lead to a slowdown in the convergence speed of the algorithm in the later stage and affect the global search ability. Summary of the Invention

[0005] To solve the problem that in the above-mentioned existing technologies, the path planning of unmanned aerial vehicles (UAVs) does not consider the collision safety issues between two or more UAVs, and in the iterative process of the pied kingfisher optimization algorithm, as the number of iterations increases, the influence of the standard normal distribution random perturbation on the update of the discoverer's position gradually weakens, which may lead to a slowdown in the convergence speed of the algorithm in the later stage and affect the global search ability, the present invention proposes a method for safe path planning of UAV swarms based on an improved pied kingfisher optimization algorithm.

[0006] The present invention is implemented through the following technical solutions: including the following steps

[0007] S1. According to the path optimality constraint F1, safety and feasibility constraint F2, flight altitude constraint F3, path smoothness constraint F4, and UAV swarm anti-collision constraint F5, construct the total cost function F of a single UAV;

[0008] S2. Use the total cost function F of the UAV as the fitness function, construct and adopt an improved pied kingfisher optimization algorithm IPKO (Improved Pied Kingfisher Optimizer) to optimize the fitness function, and obtain the cost-optimal path.

[0009] Further, the specific steps of step S1 are as follows:

[0010] S11. According to the path points, construct the path optimality constraint F1, and the formula is as follows:

[0011]

[0012] In the formula, P ij and P i,(j+1) are respectively two adjacent path points; the sum of the n - 1 line segments of the n path points is the path optimality constraint F1;

[0013] S12. According to the center coordinate of the obstacle projection being C k , the radius being R k , the diameter R of the UAV, the distance d between the UAV and C k , and the danger zone S, construct the safety and feasibility constraint F2, and the formula is as follows: k In UAV path planning, it is also necessary to guide the UAV to safely pass through the threats caused by obstacles. Let K be the set of all threats, and each threat is represented by a cylinder. Let the center coordinate of the obstacle projection be C k k

[0014] k k

[0015] , due to the relatively small size of the UAV, most studies approximate the UAV as a particle. To make the threat cost of the UAV more accurate, the size of the UAV is considered here. Let the diameter of the UAV be R, and define d k as the distance between the UAV and C k . When d k ≤R + R k , the distance between the UAV and the obstacle is less than its own diameter, and a collision is bound to occur. When R + R k < d k ≤S + R + R k , due to reasons such as the operating environment and positioning accuracy, there is still a probability of collision between the UAV and the obstacle. Therefore, the area at a distance S from the collision area is called the dangerous area.

[0016] S13. Construct the flight altitude constraint F3 according to the flight altitude. The formula is as follows:

[0017]

[0018] F3(X i ) = H ij In formula (5), h ij represents the flight altitude of the UAV relative to the ground; h min and h max are the minimum and maximum altitudes of the UAV flight respectively; H ij is the penalty value. The H ij obtained according to formula (5) can keep the UAV at the average altitude and penalize the values beyond the range.

[0019] S14. Construct the path smoothness constraint F4 according to the turning angle and climbing angle. The formula is as follows:

[0020]

[0021] In the formula, P ij P i,j+1 is the current path, and P ij+1 P ij+2 is the next path; is the projection vector of the path P ij P i,j+1 ; is the turning angle; ψ ij is the climbing angle; Z i is the Z - direction coordinate of the node on the current path i; Z i,j+1 is the Z - direction coordinate of the next node j + 1 on the path i; α1 and α2 are the penalty coefficients of the turning angle and climbing angle respectively;

[0022] S15. Construct the anti - collision constraint F5 for the UAV swarm according to the distance between UAVs. The formula is as follows:

[0023]

[0024] Wherein, l ij represents the distance between the i-th and j-th UAVs;

[0025] S16. According to the path-optimal constraint F1, the safety and feasibility constraint F2, the flight altitude constraint F3, the path-smoothing constraint F4, and the UAV swarm anti-collision constraint F5, construct the total cost function F of the UAVs, and the formula is as follows:

[0026] F(X i ) = b1F1(X i ) + b2F2(X i ) + b3F3(X i ) + b4F4(X i ) + b5F5(X i ) (11)

[0027] Wherein, b1, b2, b3, b4, and b5 are the weighting coefficients of the path-optimal constraint, the safety and feasibility constraint, the flight altitude constraint, the path-smoothing constraint, and the UAV swarm anti-collision constraint, respectively.

[0028] Furthermore, the specific steps of the step S2 are as follows:

[0029] S21. Introduce a specular reflection learning model in the initialization stage of the kingfisher optimization algorithm to increase the particle population;

[0030] S22. Use the total cost function F of the UAV to evaluate the fitness value PKO-Fitness of the particles;

[0031] S23. According to the fitness value obtained in the step S22, obtain the optimal position of the UAV individual and the global optimal position F 优 ;

[0032] S24. Improve the exploration stage of the original kingfisher fishing process into an exploration stage and a mining stage, and update the position and velocity of the particles;

[0033] S25. Update the fishing position and the fish-eating position, make a greedy selection for them, and add a falling mechanism to keep the population size unchanged;

[0034] S26. Repeat the steps S23 to S25 until the maximum number of iterations is reached, and output the optimal solution.

[0035] Furthermore, the specific steps of the step S21 are as follows:

[0036] S211. Construct a specular reflection learning model, and rewrite the reverse number as:

[0037]

[0038] The reverse point is rewritten as:

[0039]

[0040] In the formula, λ is the mixing parameter or attenuation coefficient, which controls the weight ratio of the mirror image information to the current solution. Its value is a real number greater than 0, and its value affects the dependence degree of the algorithm on the mirror point (reverse solution) and the attenuation intensity of the current solution. V L,i and V U,i represent the lower bound and upper bound of the i-th variable respectively. In specular reflection, these boundaries are used to generate the reverse solution. The reference value in the formula may correspond to the reverse point. D represents the number of variables in the optimization process.

[0041] S212. Based on formulas (12) and (13), the reverse solution of the solution is obtained through specular reflection. The formulas are as follows:

[0042]

[0043] where U max =(U max,1 , U max,2 , …, U max,D ) and L min =(L min,1 , L min,2 ,...L min,D ) are the upper limit and lower limit of the current population;

[0044] S213. The position of the spotted kingfisher is updated according to the following formula:

[0045] X i (t + 1)=X i (t)+α*T×(X j (t)-X i (t)), i, j = 1, 2, …, N and j≠i (15)

[0046] where X i (t + 1) represents the solution of the next iteration; X i (t) represents the position of the current iteration; α is a parameter, and its calculation formula is α = 2×randn(1, Dim)-1, where randn represents a random number in the normal distribution; Dim represents the dimension of the problem under consideration; N represents the overall scale; T is the strategy parameter.

[0047] Furthermore, the specific process of step S24 is as follows:

[0048] S241. The pied kingfisher regards the individuals with fitness values higher than its own as fish, and the formula is as follows:

[0049] fish_pos = find(fit < fit(i)) (16)

[0050] In the formula, fish_pos is the subscript set of the fish position; the find function is used to find the subscripts of the pied kingfishers with fitness values higher than its own; fit is the set of fitness values of all pied kingfisher individuals, and fit(i) is the fitness value of the i-th pied kingfisher.

[0051] S242. If the find function in step S241 does not find a pied kingfisher that meets the conditions, the position of the fish is the position of the best pied kingfisher individual; otherwise, the position of the fish is selected with equal probability according to the random number r1 in the interval (0, 1), and the formula is as follows:

[0052]

[0053] where selected_fish is the determined position of the fish; xbest is the position of the pied kingfisher with the best fitness value; X is the population matrix of the pied kingfisher positions; r1 is the selection factor, and its value is a random number in the range (0, 1); k is the position index value of a random fish.

[0054] S243. According to the position of the fish determined in step S242, the fishing position of the pied kingfisher is obtained, and the formula is as follows:

[0055]

[0056] where is the j-th dimension of the position of the i-th pied kingfisher after fishing; X i,j is the j-th dimension of the current position of the i-th pied kingfisher; rand i,j is the degree of position offset, and its value is a random number in the interval (0, 1); selectedfish i,j is the j-th dimension of the position of the fish determined by the i-th pied kingfisher; I i,j is the direction of the predation behavior, randomly taking values of 1 or 2.

[0057] S244. According to the fishing position of the pied kingfisher obtained in step S243, the fitness value is recalculated. If the fitness value of the fishing position is higher than the current position, the current position is replaced with the fishing position; otherwise, it is not replaced, and the formula is as follows:

[0058]

[0059] In the formula, X i is the position of the i-th pied kingfisher; is the fishing position of the i-th pied kingfisher;

[0060] S245. The pied kingfisher searches for a fish-eating position and calculates the fitness value. If the fitness value of the fish-eating position is higher than the current position, the current position is replaced by the fish-eating position; otherwise, it is not replaced. The formula is as follows:

[0061]

[0062] Where is the j-th dimension of the fish-eating position found by the i-th pied kingfisher, lb is the lower limit, ub is the upper limit, and t is the current iteration number.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] 1. The present invention introduces a specular reflection algorithm, which can increase the randomness and diversity of the algorithm and avoid premature convergence of the algorithm.

[0065] 2. The present invention combines the pied kingfisher optimization algorithm PKO and the specular reflection algorithm to obtain an improved pied kingfisher optimization algorithm IPKO (Improved Pied Kingfisher Optimizer). While maintaining the fast convergence advantage of the pied kingfisher optimization algorithm PKO, it can improve the quality and robustness of the solution. This enables the algorithm to obtain better performance when facing complex problems; the algorithm has flexible adjustment capabilities, updates the path according to the information obtained in real time, and the precise predation strategy of the pied kingfisher provides an effective reference for this, enabling the unmanned aerial vehicle to achieve efficient target tracking and risk avoidance in path planning.

[0066] 3. The present invention introduces a fall mechanism model, which can consider the appearance of unexpected obstacles or hostile targets during the path planning process and adjust the flight strategy in a timely manner. This not only enhances the adaptability of the algorithm but also strengthens the survival ability of the unmanned aerial vehicle swarm in a complex environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a schematic diagram of the dangerous area division in the present invention.

[0068] Figure 2 is a schematic diagram of the flight altitude constraint in the present invention.

[0069] Figure 3 is a schematic diagram of the flight corner and climbing angle constraints in the present invention.

[0070] Figure 4 is a schematic diagram of the anti-collision constraint of the unmanned aerial vehicle swarm in the present invention.

[0071] Figure 5a is a schematic diagram of the three-dimensional space path of five unmanned aerial vehicles after path planning by the Arctic puffin optimization algorithm APO in the comparative experiment of the present invention.

[0072] Figure 5b This is the schematic diagram of the three-dimensional space paths of five drones after path planning by the Goose Optimization Algorithm (GOOSE) in the comparative experiment of the present invention.

[0073] Figure 5c This is the schematic diagram of the three-dimensional space paths of five drones after path planning by the Red-billed Blue Magpie Optimization Algorithm (RBMO) in the comparative experiment of the present invention.

[0074] Figure 5d This is the schematic diagram of the three-dimensional space paths of five drones after path planning by the Secretarybird Optimization Algorithm (SBOA) in the comparative experiment of the present invention.

[0075] Figure 5e This is the schematic diagram of the three-dimensional space paths of five drones after path planning by the Improved Kingfisher Optimization Algorithm (IPKO) designed in the present invention in the comparative experiment of the present invention.

[0076] Figure 6a This is the schematic diagram of the two-dimensional space paths of five drones after path planning by the Atlantic Puffin Optimization Algorithm (APO) in the comparative experiment of the present invention.

[0077] Figure 6b This is the schematic diagram of the two-dimensional space paths of five drones after path planning by the Goose Optimization Algorithm (GOOSE) in the comparative experiment of the present invention.

[0078] Figure 6c This is the schematic diagram of the two-dimensional space paths of five drones after path planning by the Red-billed Blue Magpie Optimization Algorithm (RBMO) in the comparative experiment of the present invention.

[0079] Figure 6d This is the schematic diagram of the two-dimensional space paths of five drones after path planning by the Secretarybird Optimization Algorithm (SBOA) in the comparative experiment of the present invention.

[0080] Figure 6e This is the schematic diagram of the two-dimensional space paths of five drones after path planning by the Improved Kingfisher Optimization Algorithm (IPKO) designed in the present invention in the comparative experiment of the present invention.

[0081] Figure 7a This is the bar chart of the cost function of five drones after path planning by the Atlantic Puffin Optimization Algorithm (APO) in the comparative experiment of the present invention.

[0082] Figure 7b This is the bar chart of the cost function of five drones after path planning by the Goose Optimization Algorithm (GOOSE) in the comparative experiment of the present invention.

[0083] Figure 7c This is the bar chart of the cost function of five drones after path planning by the Red-billed Blue Magpie Optimization Algorithm (RBMO) in the comparative experiment of the present invention.

[0084] Figure 7d This is a bar chart of the cost function of five drones in the comparative experiment of the present invention after path planning by the Secretarybird Optimization Algorithm (SBOA).

[0085] Figure 7e This is a bar chart of the cost function of five drones in the comparative experiment of the present invention after path planning by the Improved Pied Kingfisher Optimization Algorithm (IPKO) designed in the present invention.

[0086] Figure 8 This is the overall flowchart of the path planning method of the present invention. Detailed Implementation Manner

[0087] The advantages and features of the present invention will be illustrated and explained by the following non-restrictive description of preferred embodiments, which are given only as examples with reference to the accompanying drawings.

[0088] The method for path planning of an unmanned aerial vehicle (UAV) cluster based on an improved pied kingfisher optimization algorithm according to the present invention includes introducing a collision avoidance constraint for each UAV in the UAV cluster, improving the pied kingfisher optimization algorithm (PKO), introducing a specular reflection algorithm, improving the fishing process, and finally introducing a fall mechanism model to minimize the total cost of all UAVs in the UAV cluster.

[0089] As Figure 8 shown, this is the overall flowchart of the UAV cluster path planning method of the present invention. The UAV cluster problem is actually an extension of a single UAV, that is, the same constraint conditions are adopted for each UAV, and finally the total cost of all UAVs is minimized for optimization. The method for path planning of an unmanned aerial vehicle (UAV) cluster based on an improved pied kingfisher optimization algorithm according to the present invention includes the following specific steps:

[0090] S1. Construct the total cost function F of a single UAV according to the path optimal constraint F1, safety and feasibility constraint F2, flight altitude constraint F3, path smoothness constraint F4, and UAV cluster anti-collision constraint F5.

[0091] S11. Construct the path optimal constraint F1 according to the path points, and the formula is as follows:

[0092]

[0093] In the formula, P ij and P i,(j+1) are two adjacent path points respectively; the sum of n - 1 line segments of n path points is the path optimal constraint F1;

[0094] The primary objective of UAV path planning is to find the flight path plan with the shortest distance between the takeoff point and the target point. Generally, the flight path points of the UAV are denoted as W ij =(xij , y ij , z ij ), that is, the three-dimensional spatial position of the UAV at the j-th path point in the i-th flight path. Then the entire flight path x i can be expressed as a three-dimensional array containing n path points. The path length cost is composed of the Euclidean distance sum between adjacent path points, and the calculation formula is shown in Equation (1):

[0095] S12. The center coordinate of the obstacle projection is C k , and the radius is R k . The diameter of the UAV is R, the distance between the UAV and C k is d k . Construct the safety and feasibility constraint F2, and the formula is as follows:

[0096]

[0097] In UAV path planning, it is also necessary to guide the UAV to safely pass through the threats caused by obstacles. As Figure 1 shown, Figure 1 shows the safety constraint conditions. The UAV needs to avoid tall obstacles on the ground during flight. The path safety and feasibility cost F2 is calculated by Equations (2) and (3). Let K be the set of all threats, and each threat is represented by a cylinder. Let the center coordinate of the obstacle projection be C k , and the radius is R k . Since the size of the UAV is relatively small, most studies approximate the UAV as a point mass. To make the threat cost of the UAV more accurate, the size of the UAV is considered here. Let the diameter size of the UAV be R, and define d k as the distance between the UAV and C k . When d k ≤R + R k , the distance between the UAV and the obstacle is less than its own diameter size, and a collision will surely occur. When R + R k < d k ≤S + R + R k , due to reasons such as the operating environment and positioning accuracy, the UAV still has a probability of colliding with the obstacle. Therefore, the area at a distance of S from the collision area is called the dangerous area. When the distance d k ≤S + R + R k , the total cost is 0, and at this time the UAV path is the most ideal. The safety and feasibility constraint F2 described here is the safety and feasibility cost F2.

[0098] S13. According to the flight altitude, construct the flight altitude constraint F3, and the formula is as follows:

[0099]

[0100] F3(X i ) = H ij (5)

[0101] Wherein, h ij represents the flight altitude of the UAV relative to the ground; h min and h max are respectively the minimum and maximum altitudes of the UAV flight; H ij is the penalty value, and the H obtained according to formula (5) ij can keep the UAV at the average altitude and penalize the values outside the range.

[0102] Restricted by natural conditions and application scenarios, the flight altitude of the UAV is restricted. For example: in measurement and inspection tasks, due to the specific resolution and field of view requirements of cameras and inspection equipment, the flight is restricted, and the altitude is adjusted every time. As Figure 2 shown, the minimum altitude during UAV flight is h min , and the maximum altitude is h max The altitude cost associated with the waypoint P j is shown in formulas (4) and (5). In formula (4), h ij represents the flight altitude of the UAV relative to the ground. It can be seen from Figure 2 that H ij maintains the average altitude and penalizes the values outside the range. Summing up all H ij waypoints gives the altitude cost.

[0103] S14. According to the turning angle and climbing angle, construct the path smoothing constraint F4, and the formula is as follows:

[0104]

[0105] Wherein, P ij P i,j+1 is the current path, and P ij+1 P ij+2 is the next path; is the projection vector of the path P ij P i,j+1 ; is the turning angle; ψ ij is the climbing angle; Z i is the Z-direction coordinate of the node on the current path i; Z i,j+1 is the Z-direction coordinate of the next node j + 1 on the path i; α1 and α2 are respectively the penalty

[0106] coefficients of the turning angle and the climbing angle;

[0107] As Figure 3As shown in the figure, to ensure the stable flight of the drone, its turning angle and climbing angle are restricted. Figure 3 The current path P in ij P i,j+1 The projection vector of P onto the XOY plane is calculated by Equation (6). The turning angle calculation formula is as shown in Equation (7). The path P ij P i,j+1 and P ij+1 P ij+2 The projection results of P onto the XOY plane are P′ ij P′ i,j+1 and P′ ij+1 P′ i,j+2 . The climbing angle calculation formula is as shown in Equation (8). The path smoothing constraint F4 in this step is the smoothing cost.

[0108] S15. According to the distance between drones, construct the anti-collision constraint F5 for the drone swarm, and the formula is as follows:

[0109]

[0110] In the formula, l ij represents the distance between the i-th and j-th drones; the calculation formula of l ij is where the spatial position of the drone is represented by three-dimensional coordinates. Assume the coordinates of the i-th drone are (x i , y i , z i ), and the coordinates of the j-th drone are (x j , y j , z j ).

[0111] As Figure 4 shown, r c,i and R c,i are two fixed circular regions, which are respectively called the collision region and the anti-collision region of the i-th drone. When r c,i ≤ l ij ≤ R c,i , the j-th drone is considered an anti-collision neighbor of the i-th drone Once l ij ≤ r c,i occurs, it can be considered that a collision has occurred in the formation system. Encourage the drone to keep moving forward during exploration, solve the problem of sparse rewards, promote the rapid convergence of the algorithm, and the safety constraint conditions for multi-drone anti-collision are as shown in Equation (10).

[0112] S16. Construct the total cost function F of the UAV according to the path optimal constraint F1, safety and feasibility constraint F2, flight altitude constraint F3, path smoothness constraint F4, and UAV swarm anti-collision constraint F5. The formula is as follows:

[0113] F(X i ) = b1F1(X i ) + b2F2(X i ) + b3F3(X i ) + b4F4(X i ) + b5F5(X i ) (11)

[0114] In the formula, b1, b2, b3, b4, and b5 are the weighting coefficients of the path optimal constraint, safety and feasibility constraint, flight altitude constraint, path smoothness constraint, and UAV swarm anti-collision constraint respectively. Their values are preferably b1 = 5, b2 = 1, b3 = 10, b4 = 1, b5 = 1.

[0115] S2. Take the total cost function F of the UAV as the fitness function, construct and adopt the improved kingfisher optimization algorithm IPKO to optimize the fitness function, and obtain the cost-optimal path.

[0116] When performing the path planning of the unmanned cluster, the selection of the fitness function is very important. In the present invention, the total cost function during navigation in a complex environment with multiple threats in the unmanned cluster is used as the fitness function. Next, the improved kingfisher optimization algorithm IPKO is used to solve the fitness function.

[0117] As a novel population-based metaheuristic algorithm, although the kingfisher optimization algorithm has achieved certain success in simulating the hunting behavior of the white-breasted kingfisher, there are still some problems. First, during the iteration process of the kingfisher optimization algorithm, as the number of iterations increases, the influence of the standard normal distribution random perturbation on the update of the discoverer's position gradually weakens, which may lead to a slowdown in the convergence speed of the algorithm in the later stage and affect the global search ability. To solve these problems, the present invention improves the original kingfisher optimization algorithm from three aspects: introducing mirror reflection learning to increase the population size, optimizing the kingfisher fishing process, and adding a falling mechanism.

[0118] S21. Introduce the mirror reflection learning model in the initialization stage of the kingfisher optimization algorithm to increase the particle population size.

[0119] S211. Construct the mirror reflection learning model and rewrite the reverse number as:

[0120]

[0121] Rewrite the reverse point as:

[0122]

[0123] In the formula, λ is the mixing parameter or attenuation coefficient, which controls the weight ratio of the mirror image information to the current solution. Its value is a real number greater than 0, and its value affects the dependence degree of the algorithm on the mirror image point (reverse solution) and the attenuation intensity of the current solution. V L,i and V U,i represent the lower bound and upper bound of the i-th variable respectively. In specular reflection, these boundaries are used to generate reverse solutions. The possible reference values corresponding to the reverse points in the formula. D represents the number of variables in the optimization process.

[0124] The value of λ can be obtained by the following formula:

[0125]

[0126] where k1 and k2 are two random numbers uniformly distributed between 0 and 1, R0 can be called the neighborhood radius, and can be called the elastic factor. In addition, set to [0, 1] to obtain all possible values within the neighborhood radius R0.

[0127] S212. Based on formulas (12) and (13), the reverse solution of the solution is obtained through specular reflection, and the formula is as follows:

[0128]

[0129] where U max =(U max,1 , U max,2 , …, U max,D ) and L min =(L min,1 , L min,2 ,...L min,D ) are the upper and lower limits of the current population.

[0130] Similar to the opposition-based learning method, specular reflection learning is also used as a mutation operator, through the jump rate J r to improve the metaheuristic method. In addition, some elements generated by formula (15) may exceed the boundaries, and the elements exceeding the boundaries can be restricted by the following formula:

[0131]

[0132] where l i is the lower boundary; u i is the upper boundary.

[0133] S213. The position of the spotted kingfisher is updated according to the following formula:

[0134] X i(t + 1)=X i (t)+α*T×(X j (t)-X i (t)), i, j = 1, 2, …, N and j ≠ i (17)

[0135] During the iteration process, the solution of the next iteration is represented by X i (t + 1), and the position of the current iteration is represented by X i (t). α is a parameter, and its calculation formula is α = 2×randn(1, Dim)-1, where randn represents a random number in the normal distribution; Dim represents the dimension of the problem under consideration; N represents the overall scale; T is the strategy parameter.

[0136] Among them, the strategy parameter T is obtained separately according to different motion patterns.

[0137] Basis for strategy selection:

[0138] Perching strategy: In the early iteration stage of the algorithm, the kingfisher is more inclined to use the perching strategy because at this time the algorithm needs to conduct extensive exploration in the global scope to find potential optimization areas.

[0139] Hovering strategy: In the later iteration stage of the algorithm, the kingfisher is more inclined to use the hovering strategy because at this time the algorithm needs to conduct fine search in the local scope to improve the accuracy of the solution.

[0140] Mechanism for strategy switching:

[0141] During the iteration process of the algorithm, the position update of the kingfisher will be dynamically adjusted according to the current strategy (perching or hovering). The choice of strategy is usually based on the ratio of the current iteration number t to the maximum iteration number Max_Iter. As the iteration number increases, the algorithm will gradually shift from global exploration (perching strategy) to local exploitation (hovering strategy).

[0142] The calculation formula for the strategy parameter T in the perching strategy is as follows:

[0143]

[0144] Crest_angles = 2*pi*rand (19)

[0145] Among them, Max_Iter is the maximum iteration number; BF is a constant value; rand is a random value between 0 and 1; pi represents π;

[0146] The calculation formula for the strategy parameter T in the hovering strategy is as follows:

[0147]

[0148]

[0149] Among them, PKO_Fitness(i) and PKO_Fitness(j) respectively represent the fitness of the i-th and j-th kingfishers.

[0150] The strategy parameter T plays a key role in the method designed in the present invention. Its value is dynamically determined according to the current strategy and can be "perch" or "hover". The calculation of the parameter T is tailored for each strategy to ensure the best performance in different operating modes.

[0151] In order to accelerate the convergence speed of the algorithm and enable the algorithm to find the optimal solution faster and more accurately. On the basis of the original kingfisher optimization algorithm, the present invention adds a specular reflection learning model and increases the population size in its initialization stage.

[0152] For the specular reflection learning model, Ao and oB are the incident light and the reflected light respectively. The angle α between Ao and the normal is called the incident angle, and the angle β between oB and the normal is called the reflection angle. According to the law of reflection, α is equal to β, and o=(x0,0) is the midpoint of [V L ,V U , while x=(a,0) is a random variable within [V L ,V U . Therefore, can be expressed as the opposite number obtained by using x . In the proposed specular reflection learning, assuming that the obtained opposite number is , the following formula can be satisfied:

[0153]

[0154] As mentioned above, α is equal to β. Therefore, the relationship between formulas (22) and (23) can be expressed as:

[0155]

[0156] Assume B0 = λA0, where λ (λ>0) is a real number. Therefore, formula (25) can be rewritten as:

[0157]

[0158] It can be seen from formula (26) that when λ is set to different values, the value of b can be calculated as follows:

[0159]

[0160] where b1 and b2 satisfy b1∈(x0, 2x0 - a) and b2∈(2x0 - a, V u , respectively. In the designed specular reflection learning, λ can be calculated by formula (14).

[0161] Therefore, based on the specular reflection learning model, the reverse number can be rewritten in the form of formula (12), and the reverse point can be rewritten in the form of formula (13).

[0162] S22. Use the total cost function F of the UAV to evaluate the fitness value PKO_Fitness of the particle.

[0163] In the Kingfisher Optimization Algorithm (PKO), the fitness value PKO_Fitness is an index used to evaluate the quality of each particle (i.e., each UAV or each candidate solution). The calculation of the fitness value is usually based on the objective function of the problem. In the UAV path planning problem, the objective function is the total cost function F of the UAV. Therefore, the evaluation process of the fitness value can be understood as substituting the total cost function F of the UAV into the fitness evaluation formula to obtain the fitness value of each UAV.

[0164] The fitness value PKO_Fitness is usually inversely proportional to the total cost function F, that is, the lower the cost, the higher the fitness value. Therefore, the fitness value can be calculated by the following formula:

[0165]

[0166] The meaning of this formula is: the smaller the total cost F(X i ), the larger the fitness value PKO_Fitness(Xi), indicating that the path planning scheme of this UAV is better.

[0167] The fitness value PKO_Fitness is used to guide the update of particles in the Kingfisher Optimization Algorithm. For example, in the perching strategy and hovering strategy, the fitness value is used to calculate the strategy parameter T:

[0168] In the perching strategy, the fitness value is used to calculate Crest_angles and T.

[0169] In the hovering strategy, the fitness value is used to calculate beating_rate and T.

[0170] S23. Obtain the optimal position of the UAV individual and the global optimal position F according to the fitness value obtained in step S22 优 .

[0171] S24. Improve the exploration stage of the original kingfisher fishing process to an exploration stage and a mining stage, and update the position and velocity of the particles.

[0172] The present invention updates the position and velocity of particles by adopting an improved fishing process of the pied kingfisher. The original fishing process of the pied kingfisher only has an exploration stage. On this basis, the present invention divides it into an exploration stage and a mining stage. In the exploration stage, two actions of position identification and fishing are required, and greedy selection is adopted to optimize the fishing position.

[0173] S241. The pied kingfisher regards the individuals with fitness values higher than its own as fish, and the formula is as follows:

[0174] fish_pos = find(fit < fit(i)) (28)

[0175] In the formula, fish_pos is the subscript set of the fish position; the find function is used to find the subscript of the pied kingfisher with a higher fitness value than itself; fit is the set of fitness values of all pied kingfisher individuals, and fit(i) is the fitness value of the i-th pied kingfisher.

[0176] This step is the position identification in the exploration stage. The pied kingfisher has extremely powerful eyesight and can efficiently detect the position of fish in the air.

[0177] S242. If the find function in step S241 does not find a pied kingfisher that meets the conditions, the position of the fish is the position of the best pied kingfisher individual; otherwise, the position of the fish is selected with equal probability according to the random number r1 in the interval (0, 1), and the formula is as follows:

[0178]

[0179] Among them, selected_fish is the determined position of the fish; xbes is the position of the pied kingfisher with the best fitness value; X is the population matrix of the pied kingfisher positions; r1 is the selection factor, and its value is a random number in the interval (0, 1); k is the position index value of a random fish.

[0180] S243. According to the position of the fish determined in step S242, the fishing position of the pied kingfisher is obtained, and the formula is as follows:

[0181]

[0182] Among them is the j-th dimension of the position of the i-th pied kingfisher after fishing; X i,j is the j-th dimension of the current position of the i-th pied kingfisher; rand i,j is the offset degree of the position, and its value is a random number in the interval (0, 1); selectedfish i,j is the j-th dimension of the position of the fish determined by the i-th pied kingfisher; I i,j is the direction of the predation behavior, and the random value is 1 or 2;

[0183] This step is the fishing process in the exploration stage. After determining the position of the fish, the pied kingfisher will dive in one direction and plunge underwater to hunt it. During this process, the position of the pied kingfisher changes to a certain extent, and its mathematical model is shown in formula (30).

[0184] S244. Recalculate the fitness value according to the fishing position of the pied kingfisher obtained in step S243. If the fitness value of the fishing position is higher than the current position, the current position is replaced by the fishing position; otherwise, it is not replaced. The formula is as follows:

[0185]

[0186] In the formula, X i is the position of the i-th pied kingfisher; is the fishing position of the i-th pied kingfisher; F is the fitness function, that is, the total cost function of the UAV in step S16, which is used to calculate the fitness value of the pied kingfisher individual.

[0187] Steps S241 to S244 are the exploration stage in the improved pied kingfisher optimization algorithm.

[0188] S245. The pied kingfisher searches for a fish-eating position and calculates the fitness value. If the fitness value of the fish-eating position is higher than the current position, the current position is replaced by the fish-eating position; otherwise, it is not replaced. The formula is as follows:

[0189]

[0190] Among them is the j-th dimension of the fish-eating position found by the i-th pied kingfisher, lb is the lower limit, ub is the upper limit, and t is the current iteration number.

[0191] This step is the exploitation stage in the new improvement of the present invention compared with the original pied kingfisher optimization algorithm.

[0192] S25. Update the fishing position and the fish-eating position, make a greedy selection for them, and add a falling mechanism to keep the population size unchanged. The formula is as follows:

[0193]

[0194] Among them, r3, r4, and r5 are random numbers in the value range (0, 1); x step is the falling step size of the pied kingfisher; its formula is as follows:

[0195] x step =(ub - lb)exp(-C2t / T max ) (34)

[0196] C2 = 2W f ×n (35)

[0197] W f = 0.1 - 0.05t / T max (36)

[0198] wherein, ub and lb are the upper and lower bounds of the values in the i-th dimension; n is the dimension of the problem; C2 is the step size factor; W f is the probability of the kingfisher falcon falling; T max is the maximum number of iterations; t is the current number of iterations.

[0199] While updating the fishing position and the fish-eating position, the present invention also proposes a falling mechanism, that is, there is a certain probability that the kingfisher falcon will fall or be preyed on by other large birds during the flight and foraging processes. To ensure that the population size remains unchanged after the fall, we establish a falling mechanism model based on the position of the kingfisher falcon and the step size of the kingfisher falcon's descent.

[0200] S26. Repeat steps S23 to S25 until the maximum number of iterations is reached, and output the optimal solution.

[0201] The present invention conducts a simulation experiment on the path planning of unmanned aerial vehicles (UAVs) in the MATLAB R2019b environment, and verifies the effectiveness of the UAV swarm path planning method based on the improved kingfisher falcon optimization algorithm described in the present invention. The experiment uses five UAVs to form a UAV swarm, and five different optimization algorithms are used to simultaneously plan the paths of the five UAVs. The cost of each UAV consists of five parts: path cost, threat cost, altitude cost, smoothness cost, and anti-collision cost. The total cost of the UAV swarm is the sum of the costs of the five UAVs. The five optimization algorithms are respectively:

[0202] A The Goose Optimization Algorithm (GOOSE Algorithm for short) is an intelligent optimization algorithm proposed in 2024. This algorithm is inspired by the resting and foraging behaviors of geese. When geese hear any strange sound or movement, they will make a loud sound to wake up the individuals in the group and ensure their safety.

[0203] B The Arctic Puffin Optimization Algorithm (APO Algorithm for short) is an intelligent optimization algorithm proposed in 2024. This algorithm simulates the behaviors of puffins in two stages: flying in the air and foraging underwater, aiming to achieve a balance between exploration and exploitation.

[0204] C The Secretarybird Optimization Algorithm (SBOA Algorithm for short) was proposed by Fu Youfa et al. in 2024. This algorithm is inspired by the survival behaviors of secretarybirds in the natural environment.

[0205] The Red-billed Blue Magpie Optimizer (RBMO algorithm for short) is a new meta-heuristic algorithm designed by Shengwei Fu et al. This algorithm solves optimization problems by simulating the cooperative foraging behavior of red-billed blue magpies, including searching for, attacking prey, and storing food. The basic idea of the RBMO algorithm is to use individuals in the red-billed blue magpie population to find the optimal solution through information sharing and collaborative work. The social and cooperative nature of red-billed blue magpies during foraging, as well as their flexibility and adaptability in hunting behavior, inspire the algorithm. By simulating these behaviors, the algorithm achieves effective exploration and exploitation in the search space.

[0206] E The Improved Kingfisher Optimization Algorithm IPKO, which is the new optimization algorithm designed in this invention.

[0207] In the experiment, an experimental environment model is randomly constructed, and threats with a radius of r are established in these scenarios. The number and positions of the threats (represented by cylinders) are selected according to environments of different complexities. Five algorithms are used to draw the flight paths of the UAV swarm in the environment. Among them, the starting point coordinates of the UAV swarm are (200, 100, 0), and the target point coordinates are (900, 700, 150). The path planning of the UAV swarm needs to fly from the starting point coordinates around the threat area to the target point coordinates. Considering the randomness of the heuristic algorithm, each tested algorithm is independently executed 50 times, and the performance of each algorithm is evaluated and compared through the experimental results. The population size of the improved kingfisher optimization algorithm is set to 200, and the maximum number of iterations is set to 1000.

[0208] For the convenience of comparative analysis, the three-dimensional spatial diagrams, two-dimensional spatial diagrams, and cost function bar charts of the optimal UAV swarm paths generated by the five algorithms in 50 independent runs are respectively given. As Figures 5a to 5e shown, they are respectively the three-dimensional spatial path schematic diagrams of the UAV swarm after path planning by the APO algorithm, GOOSE algorithm, RBMO algorithm, SBOA algorithm, and the IPKO algorithm of this invention. As Figures 6a to 6e shown, they are respectively the two-dimensional spatial path schematic diagrams of the UAV swarm after path planning by the APO algorithm, GOOSE algorithm, RBMO algorithm, SBOA algorithm, and the IPKO algorithm of this invention. As Figures 7a to 7e shown, they are respectively the cost function bar charts of the UAV swarm after path planning by the APO algorithm, GOOSE algorithm, RBMO algorithm, SBOA algorithm, and the IPKO algorithm of this invention. The results show that the paths generated by the five algorithms can all bypass the threats, and each path meets the requirements in terms of length, height, turning angle, climbing / diving angle, and the effect of the IPKO algorithm is better.

[0209] Comparison Figures 5a to 5e , the following differences can be observed:

[0210] 1. Path length and complexity

[0211] APO algorithm: The path is relatively tortuous, especially the paths of the second UAV UAV2 and the fourth UAV UAV4.

[0212] GOOSE algorithm: The path is relatively straight, but there are many turns when encountering obstacles.

[0213] RBMO algorithm: The path is relatively smooth, and a few UAVs (such as the second UAV UAV2 and the third UAV UAV3) bypass more obstacles.

[0214] SBOA algorithm: The path is relatively uniform, but when the distance between some unmanned start and end points is relatively close, its path appears complex.

[0215] IPKO algorithm: All paths are relatively intuitive and concise, with the fewest number of turns.

[0216] 2. Obstacle avoidance ability

[0217] APO algorithm and GOOSE algorithm: When encountering obstacles, the path changes diversely, and the obstacle avoidance path is relatively complex.

[0218] RBMO algorithm and SBOA algorithm: The obstacle avoidance ability is relatively good, but the detour distance of the path is long.

[0219] IPKO algorithm: The obstacle avoidance ability is the most prominent, the path planning is simple and effective, and the overall path looks the shortest.

[0220] 3. Overall path planning effect

[0221] APO algorithm and GOOSE algorithm: The complexity of path planning is relatively high, and compared with other algorithms, the path looks less intuitive.

[0222] RBMO algorithm: The overall path is relatively uniform, and the obstacle avoidance ability is good.

[0223] SBOA algorithm: Try to bypass obstacles as much as possible, and the complexity of path planning is moderate.

[0224] IPKO algorithm: The path is very direct, avoiding unnecessary detours, and the planning effect is the best.

[0225] Through the above comparison, the IPKO algorithm performs the best in terms of the intuitiveness of path planning and obstacle avoidance ability. In this 3D environment, whether it is the simplicity of the path or the obstacle avoidance effect, the IPKO algorithm is superior to the other four algorithms. Therefore, the IPKO algorithm exhibits the best comprehensive performance and is the most excellent UAV path planning algorithm.

[0226] By comparison Figures 6a to 6e , it can be seen that:

[0227] 1. APO algorithm:

[0228] The path is relatively fluctuating, and it is obvious that several paths bypass large obstacle-free areas.

[0229] The paths of each UAV vary greatly, and the overall path is relatively long.

[0230] 2. GOOSE algorithm:

[0231] The path is relatively messy, and the paths of some UAVs have large detours.

[0232] Nevertheless, the paths of each UAV are still relatively consistent, but the overall path is not optimal.

[0233] 3. RBMO algorithm:

[0234] The path is relatively good, and the paths of the UAVs do not deviate significantly, and the path is relatively optimized.

[0235] However, it can still be seen that some paths are slightly more variable.

[0236] 4. SBOA algorithm:

[0237] The path is significantly shorter and more optimized, and the paths of the UAVs are very close and do not deviate significantly.

[0238] The paths are relatively consistent, indicating that the algorithm has good convergence.

[0239] 5. IPKO algorithm:

[0240] As can be seen from the figure, the IPKO algorithm performs the best.

[0241] The paths of each UAV almost coincide, and the path is the shortest.

[0242] While avoiding obstacles, the path is the smoothest and most direct, and is the most efficient and stable compared to other algorithms.

[0243] Among these five algorithms, the IPKO algorithm has obvious advantages in path planning, with the shortest path and the best consistency, and perfectly plans the obstacle avoidance path.

[0244] Comparison Figures 7a to 7e, the following conclusions can be drawn:

[0245] 1. APO algorithm:

[0246] The cost of five drones is approximately between 1500 and 2000.

[0247] The fluctuations are relatively large. In particular, the cost of the fourth drone (UAV4) is relatively low, while the cost of the fifth drone (UAV5) is relatively high.

[0248] 2. GOOSE algorithm:

[0249] The cost of five drones is between 1400 and 2000.

[0250] The costs of the first drone (UAV1) to the third drone (UAV3) are relatively low, while the costs of the fourth drone (UAV4) and the fifth drone (UAV5) are relatively high, showing an increasing trend.

[0251] 3. RBMO algorithm:

[0252] The cost of five drones is between 1500 and 2500.

[0253] The cost of the second drone (UAV2) is the lowest, while the costs of the first drone (UAV1) and the fourth drone (UAV4) remain high, and the overall fluctuations are relatively large.

[0254] 4. SBOA algorithm:

[0255] The cost of five drones is between 1200 and 1700.

[0256] The cost fluctuations are relatively small, but the cost of the second drone (UAV2) is relatively high.

[0257] 5. IPKO algorithm:

[0258] The cost of five drones is between 1000 and 1400.

[0259] The overall cost is the lowest and the fluctuations are relatively small, and the costs of each drone are relatively balanced.

[0260] As can be seen from the above analysis, the IPKO algorithm performs best in terms of the cost cost function evaluation index of the unmanned cluster. The IPKO algorithm described in the present invention not only has the lowest total cost, but also the cost performance of each UAV is very balanced without obvious fluctuations, indicating that the algorithm can effectively reduce the cost of each UAV and maintain stability. In contrast, the other four algorithms all have varying degrees of cost fluctuations and relatively high total costs. The fluctuations of the RBMO algorithm are particularly obvious, and the maximum cost is as high as 2500. The costs of the APO algorithm and the GOOSE algorithm are also relatively high for some UAVs.

[0261] In addition to the above embodiments, the present invention may also have other embodiments. Any technical solutions formed by equivalent replacement or equivalent transformation fall within the protection scope required by the present invention.

Claims

1. A UAV cluster path planning method based on an improved kingfisher optimization algorithm is characterized by: The steps include: S1, construct the total cost function F of a single UAV based on the path optimal constraint F1, safety and feasibility constraint F2, flight altitude constraint F3, path smoothness constraint F4 and UAV group collision avoidance constraint F5; S2. The total cost function F of the UAV is used as the fitness function, and the improved kingfisher optimization algorithm IPKO is constructed and used to optimize the fitness function to obtain the cost-optimal path.

2. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 1 is characterized in that: The specific steps of step S1 are as follows: S11. According to the path points, construct the path optimal constraint F1, the formula is as follows: Where P ij With P i,(j+1) are two adjacent path points respectively; the sum of n-1 line segments of n path points is the path optimal constraint F1; S12, according to the center coordinates C of the obstacle projection k , radius R k , the diameter R of the drone, the drone and C k The distance d k and the danger zone S, construct the safety and feasibility constraints F2, the formula is as follows: S13. According to the flight altitude, construct a flight altitude constraint F3, the formula is as follows: In the formula, h ij Indicates the flying height of the drone relative to the ground; h min and h max are the minimum and maximum flight altitudes of the drone; H ij is the penalty value; S14. Construct path smoothness constraint F4 according to the turning angle and climbing angle. The formula is as follows: Where P ij P i,j+1 is the current path, P ij+1 P ij+2 for the next path; For path P ij P i,j+1 The projection vector of is the turning angle; ψ ij is the climbing angle; Z i is the Z coordinate of the node on the current path i; Z i,j+1 is the Z-direction coordinate of the next node j+1 on path i; α1 and α2 are the penalty coefficients for the turning angle and the climbing angle respectively; S15. According to the distance between the drones, construct the drone group anti-collision constraint F5, the formula is as follows: In the formula, l ij represents the distance between the i-th and j-th drones; S16. According to the path optimal constraint F1, the safety and feasibility constraint F2, the flight altitude constraint F3, the path smoothness constraint F4 and the UAV group collision avoidance constraint F5, the total cost function F of the UAV is constructed. The formula is as follows: F(X i )=b1F1(X i )+b2F2(X i )+b3F3(X i )+b4F4(X i )+b5F5(X i ) (11) Where b1, b2, b3, b4, and b5 are the weighted coefficients of path optimal constraint, safety and feasibility constraint, flight altitude constraint, path smoothness constraint, and UAV swarm collision avoidance constraint, respectively.

3. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 2 is characterized in that: The specific steps of step S2 are as follows: S21, introduce the mirror reflection learning model in the initialization stage of the kingfisher optimization algorithm to increase the number of particle populations; S22, using the total cost function F of the drone to evaluate the fitness value PKO_Fintness of the particle; S23, according to the fitness value obtained in step S22, the optimal position of the individual drone and the global optimal position F are obtained. 优 ; S24, improving the exploration phase of the original kingfisher fishing process into an exploration phase and an exploitation phase, and updating the position and velocity of the particles; S25, update the fishing position and the fish-eating position, perform greedy selection on them, and add a falling mechanism to keep the population unchanged; S26. Repeat steps S23 to S25 until the maximum number of iterations is reached, and output the optimal solution.

4. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 3 is characterized in that: The specific steps of step S21 are as follows: S211. Build a mirror reflection learning model and rewrite the reverse number as: The reverse point is rewritten as: Where λ is the mixing parameter or attenuation coefficient, and its value is a real number greater than 0; V L,i and V U,i Represent the lower and upper bounds of the i-th variable respectively; D represents the number of variables in the optimization process; S212. Based on formulas (12) and (13), the inverse solution of the solution is obtained by mirror reflection, and the formula is as follows: Among them U max =(U max,1 ,U max,2 ,…,U max,D ) and L min =(L min,1 ,L min,2 ,...L min,D ) are the upper and lower limits of the current population; S213. The position of the kingfisher is updated according to the following formula: X i (t+1)=X i (t)+α*T×(X j (t)-X i (t)),i,j=1,2,…,N and j≠i (15) Among them, X i (t+1) represents the solution of the next iteration; X i (t) represents the position of the current iteration; α is a parameter, and the calculation formula is α=2×randn(1,Dim)-1, where randn represents a random number in a normal distribution; Dim represents the dimension of the problem under consideration; N represents the overall scale; and T is a strategy parameter.

5. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 4 is characterized in that: The specific process of step S24 is as follows: S241. Kingfishers regard individuals with higher fitness values ​​than themselves as fish. The formula is as follows: fish_pos = find(fit <fit(i) (16) Where fish_pos is the subscript set of fish positions; the find function is used to find the subscript of the kingfisher with a higher fitness value than itself; fit is the set of fitness values ​​of all kingfishers, and fit(i) is the fitness value of the i-th kingfisher; S242, if the find function in step S241 does not find a kingfisher that meets the conditions, the position of the fish is the position of the best kingfisher individual; otherwise, the position of the fish is selected with equal probability according to a random number r1 in the interval (0,1), and the formula is as follows: Among them, selected_fish is the position of the determined fish; xbest is the position of the kingfisher with the best fitness value; X is the population matrix of the kingfisher position; r1 is the selection factor, whose value is a random number within (0,1); k is the position index value of a random fish; S243, according to the position of the fish determined in step S242, the fishing position of the kingfisher is obtained, and the formula is as follows: in is the jth dimension of the position of the i-th kingfisher after catching fish; X i,j is the jth dimension of the current position of the i-th kingfisher; rand i,j is the degree of position deviation, and its value is a random number in the interval (0,1); selectedfish i,j is the jth dimension of the fish position determined by the i-th kingfisher; i,j is the direction of predation behavior, which is randomly assigned a value of 1 or 2; S244, according to the fishing position of the kingfisher obtained in step S243, recalculate the fitness value, if the fitness value of the fishing position is higher than the current position, then the current position is replaced with the fishing position; otherwise, it is not replaced, the formula is as follows: Where X i is the position of the i-th kingfisher; is the fishing position of the i-th kingfisher; S245, the kingfisher searches for a fish-eating position and calculates the fitness value. If the fitness value of the fish-eating position is higher than the current position, the current position is replaced with the fish-eating position; otherwise, the current position is not replaced. The formula is as follows: in is the j-th dimension of the fish-eating position found by the i-th kingfisher, lb is the lower limit, ub is the upper limit, and t is the current number of iterations.

6. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 5 is characterized in that: The value of λ in step S211 can be obtained by the following formula: Where κ1 and κ2 are two random numbers uniformly distributed between 0 and 1; R0 is the neighborhood radius; is the elasticity factor.

7. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 5 is characterized by: In step S212, the The value of is controlled by the following formula: Among them l i is the lower limit of the boundary; u i The upper boundary limit.

8. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 5 is characterized by: The strategy parameter T in step S213 includes the following two calculation formulas: The calculation formula of the strategy parameter T in the habitat strategy is as follows: Among them, Max_Iter is the maximum number of iterations; BF is a constant value; rand is a random value between 0 and 1; pi represents π; The calculation formula of the strategy parameter T in the hover strategy is as follows: Among them, PKO_Fitness(i) and PKO_Fitness(j) represent the fitness of the i-th and j-th kingfisher respectively.

9. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 5 is characterized in that: The falling mechanism formula in step S25 is as follows: x step =(ub-lb)exp(-C2t / T max ) (28) C2=2W f ×n (29) W f =0.1-0.05t / T max (30) Among them, r3, r4 and r5 are random numbers in the value interval (0,1); x step is the falling step length of the kingfisher; ub and lb are the upper and lower bounds of the value of the i-th dimension; n is the dimension of the problem; C2 is the step length factor; W f is the probability of Kingfisher falling; T max is the maximum number of iterations; t is the current number of iterations.

10. The UAV cluster path planning method based on the improved kingfisher optimization algorithm according to claim 5 is characterized in that: In step S15, ij The calculation formula is: The spatial position of the UAV is represented by three-dimensional coordinates. Assuming that the coordinates of the i-th UAV are (x i ,y i ,z i ), the coordinates of the jth drone are (x j ,y j ,z j ).

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