Unmanned aerial vehicle cluster safety path planning method based on improved black-wing plinary optimization algorithm

Abstract

The invention discloses an unmanned aerial vehicle cluster safety path planning method based on an improved black-wing optimization algorithm, and the method comprises the steps: introducing an anti-collision constraint for each unmanned aerial vehicle in an unmanned aerial vehicle cluster, and forming a multi-factor constraint flight total cost function of the unmanned aerial vehicle cluster; introducing a good point set theory, an optimal value guide differential mutation strategy and an elite learning mechanism to improve a black wing plinary optimization algorithm; taking a multi-factor constraint flight total cost function of the unmanned aerial vehicle cluster as a fitness function, and solving the fitness function by adopting an improved black wing plinth algorithm; and simulating the path planning of the unmanned aerial vehicle, and verifying the effectiveness of the proposed algorithm. According to the algorithm, better performance can be obtained in the face of complex problems; the algorithm has flexible adjustment capability, the path is updated according to the information obtained in real time, learning can be carried out by comparing the difference between the algorithm and elite individuals and the difference between the algorithm and the population average value in the path planning process, and the algorithm performance is improved.

Description

Technical Field

[0001] The present invention relates to the safe path planning of unmanned clusters, and particularly to a method for safe path planning of unmanned aerial vehicle (UAV) clusters based on an improved black-winged kite optimization algorithm. Background Art

[0002] The goal of UAV path planning is to ensure the safety of the airframe 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 clusters is of great importance. In UAV cluster tasks, in the face of complex environments and dynamically changing obstacles, how to effectively plan safe and effective paths for each UAV to ensure the collaborative combat ability of the cluster 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 clusters is of great importance. In UAV cluster tasks, in the face of complex environments and dynamically changing obstacles, how to effectively plan safe and effective paths for each UAV to ensure the collaborative combat ability of the cluster is one of the current research hotspots, but how to plan such paths is still a complex and challenging problem. The UAV cluster 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 constraints, safety and feasibility constraints, flight altitude constraints, and path smoothing constraints. 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 meta-heuristic algorithm, although the black-winged kite optimization algorithm has achieved certain success in simulating the hunting behavior and migration behavior of black-winged kites, there are still some problems: during the iterative process of the black-winged kite optimization algorithm, as the number of iterations increases, it is found that the algorithm still has problems such as low convergence accuracy, slow convergence speed, and being easily trapped in local optima. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a method for safe path planning of UAV clusters based on an improved black-winged kite optimization algorithm.

[0006] Technical Solution: The method described in the present invention includes the following steps:

[0007] (1) Introduce anti-collision constraints for each unmanned aerial vehicle (UAV) in the UAV swarm to form a multi-factor constrained flight total cost function for the UAV cluster;

[0008] (2) Introduce the good point set theory, the optimal value-guided differential mutation strategy, and the elite learning mechanism to improve the black-winged kite optimization algorithm;

[0009] (3) Use the multi-factor constrained flight total cost function of the UAV cluster as the fitness function, and adopt the improved black-winged kite algorithm to solve the fitness function;

[0010] (4) Simulate the path planning of the UAV and verify the effectiveness of the proposed algorithm.

[0011] Furthermore, the anti-collision constraint is expressed as:

[0012]

[0013] Among them, F5(X i ) represents the anti-collision constraint, l ij represents the distance between the i-th and j-th UAVs, l ij =||x i -x j ||, 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 UAV.

[0014] Furthermore, the total cost of the UAV is expressed as:

[0015] F(X i )=b1F1(X i )+b2F2(X i )+b3F3(X i )+b4F4(X i )+b5F5(X i )

[0016] Among them, F is the total cost, F1 is the optimal path cost, F2 is the safety and feasibility cost, F3 is the flight altitude cost, F4 is the path smoothness cost, F5 is the anti-collision cost constraint of the UAV swarm, and the total cost is the linear weighted sum of the above costs, b n is the weighting coefficient.

[0017] Furthermore, the step (2) includes:

[0018] (2.1) Population initialization, which is initialized by the improved black-winged kite optimization algorithm;

[0019] (2.2) Evaluate particles, and use the constraint conditions in the threat environment to evaluate the fitness value of particles;

[0020] (2.3) Update the optimal value. According to the obtained fitness value, find the optimal position of the individual and the global optimal position;

[0021] (2.4) Update the positions of the particles;

[0022] (2.5) Calculate the average value and update the leader position. At the same time, based on the Black-winged Kite optimization algorithm, introduce an elite learning mechanism;

[0023] (2.6) Repeat steps (2.3) to (2.5) until the maximum number of iterations is reached.

[0024] Furthermore, the construction of the good point set model includes:

[0025] Let G s be the unit cube in the s-dimensional space. Let r ∈ G s , which is expressed as:

[0026]

[0027] where φ(n) = C(r, ε)n -1+e is the deviation, C(r, ε)n -1+e is a constant related only to r and ε. ε is an arbitrarily small positive number, and {a} represents the fractional part of a. Then P n (k) is the good point set and r is the good point;

[0028] Furthermore, step (2.1) includes applying the good point set theory to the population initialization of the Black-winged Kite algorithm, which is expressed as:

[0029] x i (j) = (BK ub - BK lb ) * {r j (i) * k} + BK lb

[0030] where r = {2cos(2πk / p)}, 1 ≤ k ≤ s, p is the smallest prime number satisfying (p - 3) / 2 ≥ s. Map it to the space. BK lb and BK ub are respectively the lower bound and upper bound of the j-th dimension of the i-th black-winged kite.

[0031] Furthermore, in step (2.4), the improved Black-winged Kite predation and migration process is used to update the positions of the particles.

[0032] Furthermore, the predation process of the Black-winged Kite simulates the state of the Black-winged Kite hovering in the air and spreading its wings to maintain balance and the scene of quickly attacking.

[0033] The attack position of the black-winged kite is updated according to the following formula:

[0034]

[0035] where respectively represent the positions of the i-th black-winged kite at the j-th dimension in the t-th and (t + 1)-th iteration steps; rand is a random number between [0, 1]; p is a constant of 0.9; n is a non-linear factor:

[0036]

[0037] t is the number of iterations that have been completed, and T is the total number of iterations.

[0038] Furthermore, the migration position of the black-winged kite is updated according to the following formula:

[0039]

[0040] where, represents the current optimal position of the j-th dimension of the black-winged kite at the t-th iteration; l, s ∈ {1, 2,... N}, s ≠ l ≠ i; respectively represent the positions of the i-th black-winged kite at the j-th dimension in the t-th and t + 1-th iteration steps; F i represents the fitness value of the black-winged kite at the t-th iteration, F rj is the fitness value of the random position at the t-th iteration; La(0, 1) is the Laplace distribution.

[0041] Furthermore, the elite learning mechanism model is expressed as:

[0042]

[0043] where, is the elite individual in the population, s = rand(1, j) is the learning step size, and j is the dimension; X mean is the average value of the learning individuals, N is the number of individuals in the population, tf is the learning factor, and it randomly takes the value of 1 or 2.

[0044] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: Firstly, the present invention applies the good point set theory to the population initialization stage of the black-winged kite algorithm, aiming to improve the utilization rate of the entire search space of the algorithm and enhance the population diversity; Secondly, in the migration stage, it is proposed to replace the Cauchy distribution with the Laplace distribution and introduce an optimal value-guided differential mutation strategy to change the search space to avoid the occurrence of local extreme value problems, thereby ensuring the global exploration ability and accuracy of the algorithm in the search space; Finally, an elite learning mechanism is introduced to further strengthen the interaction between elites and learning individuals and improve the overall performance. This enables the algorithm to obtain better performance when facing complex problems; the algorithm has flexible adjustment ability and updates the path according to the information obtained in real time. The precise attack and migration behaviors of the black-winged kite provide an effective reference for this, enabling the unmanned aerial vehicle to achieve efficient target tracking and risk avoidance in path planning; introducing the elite learning mechanism model can learn by comparing the differences between itself and elite individuals as well as the population average during the path planning process to improve the algorithm performance. Description of the Drawings

[0045] Figure 1 It is a comparison diagram of the results of good point set initialization and random initialization;

[0046] Figure 2 It is a schematic diagram of dangerous area division;

[0047] Figure 3 It is a schematic diagram of flight altitude constraint;

[0048] Figure 4 It is a schematic diagram of flight corner and climbing angle constraints;

[0049] Figure 5 It is a schematic diagram of anti-collision constraints for a group of unmanned aerial vehicles;

[0050] Figure 6 Iteration number diagram:

[0051] Figure 7 It is a top view of a three-dimensional space;

[0052] Figure 8 It is a comparison diagram of two-dimensional space paths;

[0053] Figure 9 It is a comparison diagram of total costs;

[0054] Figure 10 It is a comparison diagram of each cost;

[0055] Figure 11 It is a comparison diagram of the overall cost cost function and four cost functions. Detailed implementation manners

[0056] The technical solution of the present invention will be further described below in conjunction with the drawings.

[0057] The UAV swarm safety path planning method based on the improved Black-winged Kite optimization algorithm described in the present invention includes introducing anti-collision constraints for each UAV in the UAV swarm and improving the Black-winged Kite optimization algorithm. The good point set theory is introduced to replace the random generation of the initial position, improving the utilization rate of the search space and enhancing the population diversity. The Laplace distribution is introduced to replace the Cauchy distribution in the migration stage, and the optimal value-guided differential mutation strategy is introduced to change the search space and avoid the problem of local extrema. Finally, an elite learning mechanism is introduced to improve the overall performance of the algorithm.

[0058] (1) Anti-collision constraints are introduced for each UAV in the UAV swarm to form a multi-factor constrained flight total cost function for the UAV swarm;

[0059] The UAV swarm 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.

[0060] (1.1) Modeling method

[0061] The UAV swarm 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 modeling method for a single UAV is as follows:

[0062] 1.1 Path optimal constraint F1

[0063] The primary goal of UAV path planning is to find a 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 =(x ij , 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 represented as a three-dimensional array containing n path points. The path length cost is composed of the Euclidean distance sum between adjacent two path points, and the calculation formula is as follows:

[0064]

[0065] In the above formula, P ij and P i，(j+1) are respectively adjacent two path points, and the sum of the n - 1 line segments of the n path points is the path length cost.

[0066] (1.2) Safety and feasibility constraint F2

[0067] During the flight of the drone, it is necessary to avoid tall obstacles on the ground. The path safety and feasibility cost F2 is calculated by equations (2) and (3), as Figure 2 shown, which presents the safety constraint conditions.

[0068]

[0069] Among them, the diameter D of the drone and the dangerous distance S from the danger zone to the collision area. It can be seen from equations (3) and Figure 2 that when the distance d k is less than the radius R k + D of the danger zone, the cost F2 is infinite, that is, the drone must fly far away from the danger zone. When the distance d k is within the safety buffer zone, the closer the drone is to the obstacle, the higher the cost. When the distance d k is greater than R k + D + S, the safety cost is 0, and at this time the drone path is the most ideal.

[0070] (1.3) Flight altitude constraint F3

[0071] Restricted by natural conditions and application scenarios, the flight altitude of the drone 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 altitude is restricted, and each altitude is pulled. As Figure 3 shown, the minimum altitude during the flight of the drone is h min , and the maximum altitude is h max The altitude cost associated with the waypoint P j is:

[0072]

[0073] F3(X i ) = H ij (5)

[0074] In the above formula, h ij represents the flight altitude of the drone relative to the ground. It can be seen from Figure 3 that H ij maintains the average altitude and penalizes values outside the range. Summing up all H ij waypoints gives the altitude cost, as follows:

[0075] (1.4) Path smoothness constraint F4

[0076] To ensure the smooth flight of the drone, its turning angle and climbing angle are restricted. As Figure 4 shown, the projection vector is calculated by the following formula:

[0077]

[0078] Turning angle calculation formula:

[0079]

[0080] Among them, P ij P i，j+1 is the current path, P ij+1 P ij+2 is the next path, path P ij P ij+1 and P ij+1 P ij+2 projected onto the XOY plane results in P j P T，j+1 and P ij+1 P i，j+2 . The climb angle ψ ij is the angle between the ascending trajectory of the UAV and the horizontal line.

[0081] The climbing angle calculation formula is:

[0082]

[0083] In Equation (8), Z i is the z-direction coordinate of the node on the current path i, Z ij+1 is the z-direction coordinate of the next node j + 1 on path i, and the calculation formula for the smoothing cost is:

[0084]

[0085] In the above formula, a1 and a2 are the penalty coefficients for the turning angle and the climbing angle respectively.

[0086] (1.5) Anti-collision constraint F5 for UAV swarm

[0087] In this paper, l ij represents the distance between the i-th and j-th UAVs, where l ij = ||x i - x j ||. 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 UAV, and their differences are as Figure 5 shown. When r c，i ≤ l ij ≤ R c，i it is considered that the j-th UAV is the anti-collision neighbor of the i-th UAV Once l ij ≤ r c，iWhen this occurs, it can be considered that a collision has occurred in the formation system. UAVs are encouraged to keep moving forward during exploration to solve the problem of sparse rewards, promote the rapid convergence of the algorithm, and the safety constraint conditions for multi-UAV anti-collision are as follows:

[0088]

[0089] (1.6) Flight cost function F with multi-factor constraints

[0090] The total cost is obtained by linearly weighting the optimal path cost F1, the safety and feasibility cost F2, the flight altitude cost F3, the path smoothness cost F4, and the multi-UAV anti-collision cost F5. Where b is the weighting coefficient.

[0091] F(X i ) = b1F1(X i ) + b2F2(X i ) + b3F3(X i ) + b4F4(X i ) + b5F5(X i ) (11)

[0092] In the above formula, the weight values refer to the practices in other literatures, and the values are b1 = 5, b2 = 1, b3 = 10, b4 = 1, b5 = 1.

[0093] (2) Introduce the good point set theory, the optimal value-guided differential mutation strategy, and the elite learning mechanism to improve the black-winged kite optimization algorithm

[0094] (2.1) Population initialization. Initialize using the improved black-winged kite optimization algorithm.

[0095] Since the randomly generated population is not evenly distributed in the entire solution space, it is very concentrated in some areas and very scattered in some areas, resulting in low utilization of the entire search space by the algorithm and weak population diversity. Aiming at the problems caused by the random initialization method, the good point set is proposed. The good point set is a technique used for population initialization in optimization algorithms, as Figure 1 shown. It is a method for generating a uniformly distributed point set in a multi-dimensional space. These point sets are called good point sets, and the points in them are called good points.

[0096] Let Gs be the unit cube in the s-dimensional space, and let r ∈ G s , which is expressed as:

[0097]

[0098] Among them, φ(n) = C(r, ε)n -1+e is the deviation, C(r, ε)n -1+eis a constant related only to r and ε, where ε is an arbitrarily small positive number, and {a} represents the fractional part of a. Then P n (k) is a good point set and r is a good point.

[0099] This application applies the good point set theory to the population initialization stage of the black-winged kite algorithm and constructs a good point set by using the method of cyclotomic fields.

[0100] In Equation (13), r = {2cos(2πk / p)}, 1 ≤ k ≤ s, where p is the smallest prime number satisfying (p - 3) / 2 ≥ s, and it is mapped into space as follows:

[0101] x i (j) = (BK ub -BK lb ) * {r j (i) *k} + BK lb (13)

[0102] BKlb and BKub are respectively the lower bound and upper bound of the j-th dimension of the i-th black-winged kite.

[0103] (2.2) Evaluate the particle. Use the constraint condition F in the threat environment to evaluate the fitness value F(i) of the particle.

[0104] (2.3) Update the optimal value. According to the obtained fitness value, find the optimal position of the individual and the global optimal position X L .

[0105] (2.4) Update the particle. Update the position of the particle.

[0106] This application updates the position of the particle by improving the predation and migration processes of the black-winged kite. The original black-winged kite process includes the predation and migration stages. Based on this, this patent optimizes on the basis of migration and uses the Laplace distribution, which has strong perturbation ability or self-adjustment ability. The black-winged kite algorithm is more likely to jump out of the local optimal point, improve the quality of the solution, and improve the search speed. It comprehensively uses the global exploration of polynomial difference learning combined with the Baldwin learning operator to change the search space to avoid the occurrence of local extreme value problems, thereby ensuring the global exploration ability and accuracy of the algorithm in the search space.

[0107] Next, the attack position of the black-winged kite is updated according to the following formula:

[0108]

[0109] Equation (14) simulates the state of the black-winged kite hovering in the air and spreading its wings to maintain balance and quickly attack. Among them respectively represent the position of the \(i\)-th black-winged kite at the \(j\)-th dimension in the \(t\)-th and \((t + 1)\)-th iteration steps; rand is a random number between \([0, 1]\); \(p\) is a constant of \(0.9\); \(n\) is a non-linear factor:

[0110]

[0111] \(t\) is the number of iterations that have been completed so far, and \(T\) is the total number of iterations

[0112] Next, the migration position of the black-winged kite is updated according to the following formula:

[0113]

[0114] where represents the current optimal position of the \(j\)-th dimension of the black-winged kite in the \(t\)-th iteration; \(l, s\in\{1, 2, \ldots N\}\), \(s\neq l\neq i\); respectively represent the position of the \(i\)-th black-winged kite at the \(j\)-th dimension in the \(t\)-th and \((t + 1)\)-th iteration steps; \(F\) i represents the fitness value of the black-winged kite in the \(t\)-th iteration, \(F\) ri is the fitness value of the random position in the \(t\)-th iteration; \(La(0, 1)\) is the Laplace distribution.

[0115] (2.5) Calculate the average value and update the leader position. At the same time, to improve the overall performance of the algorithm, an elite learning mechanism is introduced on the basis of the black-winged kite optimization algorithm.

[0116] In the "elite learning" stage, the black-winged kite learning individuals actively learn from the elite individuals, aiming to improve their own status. This process not only promotes the mutual motivation between individuals, but also effectively combines the role of the population mean, further strengthening the interaction between the elite individuals and learning individuals of the black-winged kite. Specifically, the learning individuals learn by comparing the differences between themselves, the elite individuals of the black-winged kite, and the population average. First, calculate the average value of the current population, and then use this mean to determine the differences between the elite individuals and the learning individuals.

[0117]

[0118] where, is the elite individual in the population, \(s = rand(1, j)\) is the learning step size, and \(j\) is the dimension; \(X\) mean is the average value of the learning individuals, \(N\) is the number of population individuals, and \(tf\) is the learning factor, randomly taking values of 1 or 2.

[0119] (2.6) Repeat steps (2.3) - (2.5) until the maximum number of iterations is reached.

[0120] (3) Take the multi-factor constrained flight total cost function of the UAV swarm as the fitness function, and use the improved black-winged kite algorithm to solve the fitness function;

[0121] When conducting UAV swarm path planning, the selection of the fitness function is very important. This patent takes the optimal total cost function during navigation in a complex environment with multiple threats for the UAV swarm as the fitness function. Next, the improved black-winged kite algorithm is used to solve the fitness function.

[0122] As a novel population-based metaheuristic algorithm, the black-winged kite optimization algorithm has achieved certain success in simulating the attack behavior and migration behavior of black-winged kites, but there are still some problems. First, during the iteration process of the black-winged kite optimization algorithm, as the number of iterations increases, the randomly generated population leads to low utilization of the entire search space by the algorithm. In the early stage, the frequent use of Cauchy mutation increases the risk of falling into local optima. To solve these problems, this patent introduces the good point set theory to replace the random generation of the initial position, improves the utilization of the search space, and enhances the population diversity; in the migration stage, the Laplace distribution is introduced to replace the Cauchy distribution, and the optimal value-guided differential mutation strategy is introduced to change the search space and avoid the problem of local extrema; finally, an elite learning mechanism is introduced to improve the overall performance of the algorithm. The original black-winged kite optimization algorithm is improved in the above three aspects.

[0123] (4) Simulate the path planning of the UAV and verify the effectiveness of the proposed algorithm.

[0124] In this paper, the path planning of the UAV is simulated in the MATLAB R2022b environment, and the effectiveness of the proposed algorithm is verified. In this experiment, a UAV swarm consisting of 5 UAVs is used, and the optimization algorithm is 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 5 UAVs. The original BKA optimization algorithm for comparison:

[0125] A Basic Black-Winged Kite Optimization Algorithm (BKA) is an intelligent optimization algorithm proposed by Wang J et al. in 2024. This algorithm is inspired by the migration and predation behaviors of black-winged kites. Black-winged kites have a strong hovering ability and will adjust the angles of their wings and tails according to the wind speed, quietly hover and observe prey, and then quickly dive to attack.

[0126] A random experimental environment model is 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. Four 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 (150, 150, 50), and the target point coordinates are (900, 720, 50). 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 100 times, and the performance of each algorithm is evaluated and compared through the experimental results. The population size of the improved Black Kite Optimization Algorithm is set to 50, and the maximum number of iterations is set to 100.

[0127] For the convenience of comparative analysis, the iteration diagrams, top views, two-dimensional space diagrams, total cost display comparison diagrams, and individual cost comparison diagrams of the optimal UAV swarm paths generated by the two algorithms in 100 independent runs are respectively given, as Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 . The results show that the paths generated by the two algorithms can bypass the threats, and each path meets the requirements in terms of length, height, turning angle, climbing / diving angle, and the effect of the IBKA optimization algorithm is better.

[0128] As Figure 7 shown, by comparing and analyzing the performance of two UAV path planning algorithms (IBKA, BKA) in a 3D environment, the following differences can be observed:

[0129] 1. Path length and complexity

[0130] IBKA: All paths are relatively intuitive and concise, with the fewest number of turns.

[0131] BKA: The paths are relatively tortuous, especially for UAV2 and UAV4.

[0132] 2. Obstacle avoidance ability

[0133] BKA: When encountering obstacles, the path changes are diverse, and the obstacle avoidance path is relatively complex.

[0134] IBKA: The obstacle avoidance ability is the most prominent, the path planning is simple and effective, and the overall path looks the shortest.

[0135] 3. Overall path planning effect

[0136] BKA: The complexity of the path planning is relatively high, and the path looks less intuitive.

[0137] IBKA: The path is very direct, avoiding unnecessary detours, and the planning effect is the best.

[0138] Through the above comparison, the IBKA 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 IBKA algorithm is superior to the BKA algorithm. Therefore, the IBKA algorithm indeed exhibits the best comprehensive performance and is an excellent UAV path planning algorithm.

[0139] As Figure 8 shown, the performance comparison of the two algorithms in two-dimensional space path planning is presented. By comparing the two algorithms, it can be seen that:

[0140] 1. BKA:

[0141] The path is relatively fluctuating, and obviously several paths bypass large obstacle areas.

[0142] The paths of each UAV vary greatly, and the overall path is relatively long.

[0143] 2. IBKA:

[0144] As can be seen from the figure, the performance of the IBKA algorithm is superior to that of the BKA algorithm.

[0145] The paths of each UAV almost coincide, and the path is the shortest.

[0146] While avoiding obstacles, the path is the smoothest and most direct, and is more efficient and stable compared to the BKA algorithm.

[0147] As Figure 9 shown in the bar chart of the cost function of the unmanned cluster, we can compare and analyze the performance of the two algorithms (BKA and IBKA):

[0148] 1. BKA:

[0149] The cost of UAV1 to UAV5 is approximately between 1200 and 1800.

[0150] The fluctuation is relatively large. In particular, the cost of UAV4 is relatively low, while the cost of UAV2 is relatively high.

[0151] 2. IBKA:

[0152] The cost of UAV1 to UAV5 is between 1200 and 1600.

[0153] The overall cost is the lowest and the fluctuation is small. The costs of each UAV are relatively balanced.

[0154] As Figure 10 and Figure 11The overall cost cost functions of each UAV in the unmanned cluster and the bar charts of four cost functions including corner cost, altitude cost, threat cost, and path cost are shown respectively:

[0155] 1. BKA:

[0156] The corner cost of UAV4 is the lowest, and there is no threat cost at all. The path costs vary greatly

[0157] 2. IBKA:

[0158] The path costs of the UAV swarm are almost the same, the threat cost is basically 0, the corner costs of UAV2 and UAV3 are 0, and the paths are basically the same

[0159] From the above analysis, it can be seen that the IBKA algorithm performs best relative to BKA in terms of the cost cost function evaluation index of the unmanned cluster. IBKA not only has the lowest total cost, but also the cost performance of each UAV is very balanced without obvious fluctuations, which indicates that the algorithm can effectively reduce the cost of each UAV and maintain stability. In contrast, BKA has cost fluctuations to varying degrees and a relatively high total cost.

Claims

1. A method for safe path planning of unmanned aerial vehicle clusters based on an improved black-winged kite optimization algorithm, characterized in that, It includes the following steps: (1) Introduce anti-collision constraints for each unmanned aerial vehicle (UAV) in the UAV swarm to form a multi-factor constrained flight total cost function of the UAV cluster; (2) Introduce the good point set theory, the optimal value-guided differential mutation strategy, and the elite learning mechanism to improve the black-winged kite optimization algorithm; (3) Use the multi-factor constrained flight total cost function of the UAV cluster as the fitness function, and use the improved black-winged kite algorithm to solve the fitness function; (4) Simulate the path planning of the UAV and verify the effectiveness of the proposed algorithm.

2. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 1, wherein The anti-collision constraint is expressed as: Among them, F5(X i ) represents the anti-collision constraint, l ij represents the distance between the i-th and j-th UAVs, l ij =||x i -x j ||, r c，i and R c，i are two fixed circular regions, respectively called the collision area and anti-collision area of the i-th UAV.

3. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 1, wherein The total cost of the UAV is expressed as: F(X i ) = b1F1(X i ) + b2F2(X i ) + b3F3(X i ) + b4F4(X i ) + b5F5(X i ) Among them, F is the total cost, F1 is the optimal path cost, F2 is the safety and feasibility cost, F3 is the flight altitude cost, F4 is the path smoothness cost, F5 is the anti-collision cost constraint of the UAV swarm, and the total cost is obtained by linearly weighting the above costs, where b n is the weighting coefficient.

4. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved elanus caeruleus optimization algorithm according to claim 1, wherein The step (2) includes: (2.1) Population initialization, initialized by using the improved black-winged kite optimization algorithm; (2.2) Evaluate particles, and use the constraint conditions in the threat environment to evaluate the fitness values of the particles; (2.3) Update the optimal value, and find the optimal position of the individual and the global optimal position according to the obtained fitness values; (2.4) Update the positions of the particles; (2.5) Calculate the average value, update the leader position, and at the same time, introduce the elite learning mechanism on the basis of the black-winged kite optimization algorithm; (2.6) Repeat steps (2.3) to (2.5) until the maximum number of iterations is reached.

5. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 1, wherein The construction of the good point set model includes: Let \(G_s\) be the unit cube in the \(s\)-dimensional space, and let \(r\in G\) s , which is expressed as: where φ(n) = C(r, ε)n -1+e is the deviation, and C(r, ε)n -1+e is a constant related only to r and ε. ε is an arbitrarily small positive number, and {a} represents the fractional part of a. Then P n (k) is the set of good points, and r is the good point.

6. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 4, wherein The step (2.1) includes applying the good point set theory to the population initialization of the black-winged kite algorithm, expressed as: where \(r = \{2\cos(2\pi k / p)\}\), \(1\leq k\leq s\), \(p\) is the smallest prime number satisfying \((p - 3) / 2\geq s\), and mapping it into space, \(BK\) lb and \(BK\) ub are respectively the \(j\)-dimensional lower bound and upper bound of the \(i\)th black-winged kite.

7. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 4, wherein In the step (2.4), the improved black-winged kite predation and migration processes are used to update the positions of the particles.

8. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 7, wherein The predation process of the black-winged kite simulates the state of the black-winged kite hovering in the air and spreading its wings to maintain balance and quickly attack; The attack position of the black-winged kite is updated according to the following formula: wherein respectively represent the position of the i-th black-winged kite at the j-th dimension in the t-th and (t + 1)-th iteration steps; rand is a random number between [0, 1]; p is a constant of 0.9; n is a non-linear factor: t is the number of iterations that have been completed so far, and T is the total number of iterations.

9. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 7, wherein The migration position of the black-winged kite is updated according to the following formula: Among them, represents the current optimal position of the j-th dimension of the black-winged kite in the t-th iteration; l, s ∈ {1, 2, … N}, s ≠ l ≠ i; respectively represent the positions of the i-th black-winged kite in the j-th dimension at the t-th and t + 1-th iteration steps; F i represents the fitness value of the black-winged kite in the t-th iteration, F ri is the fitness value of a random position in the t-th iteration; La(0, 1) is the Laplace distribution.

10. The method for safe path planning of an unmanned aerial vehicle cluster based on an improved black-winged kite optimization algorithm according to claim 1, wherein, The elite learning mechanism model is expressed as: Among them, is the elite individual in the population, s = rand(1, j) is the learning step size, and j is the dimension; X mean is the average value of the learning individuals, N is the number of population individuals, tf is the learning factor, and it is randomly taken as 1 or 2.

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