Unmanned aerial vehicle three-dimensional flight path planning method based on LBDBO algorithm

Abstract

The invention discloses an unmanned aerial vehicle three-dimensional flight path planning method based on an LBDBO algorithm, and relates to the technical field of unmanned aerial vehicle three-dimensional flight path planning. According to the technical scheme, an unmanned aerial vehicle flight environment is established; establishing a fitness function; an improved LBDBO algorithm is adopted to carry out unmanned aerial vehicle global path planning; and cubic spline interpolation is adopted to obtain a smooth path curve. The method has the beneficial effects that uniformly distributed populations are obtained through Logistic-Tent chaotic mapping initialization, so that the algorithm has better global search capability; variation disturbance is performed on individuals by using a strategy combining Levy flight and Brownian motion, so that a local optimal solution of an algorithm is avoided, and global search and local development capabilities are balanced; and finally, a smooth and stable track is generated through a cubic B-spline curve fitting path. By improving algorithm initialization, variation strategy, path fitting and other aspects, the quality and efficiency of unmanned aerial vehicle flight path planning are effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of three-dimensional trajectory planning of unmanned aerial vehicles, and relates to a three-dimensional trajectory planning method of unmanned aerial vehicles based on LBDBO algorithm. Background Art

[0002] Unmanned aerial vehicle (UAV) refers to an aircraft that can be operated remotely or autonomously without human piloting and relies on its own perception of the environment. Its advantages are low cost, wide application scenarios, and no casualties. In modern warfare, UAVs have become indispensable reconnaissance and strike weapons, and their development has received widespread attention. Trajectory planning is an important research in the application of UAVs, which has a key impact on improving the combat effectiveness of UAVs in complex battlefield environments. UAV trajectory planning refers to designing an optimal flight path for UAVs to avoid obstacles given a starting point and a target point. This process needs to consider various constraints, such as obstacles in the environment, flight altitude restrictions, UAV dynamics, shortest flight time, and lowest energy consumption. The main goal of trajectory planning is to ensure that UAVs can complete their tasks safely and efficiently in an increasingly complex environment. This has become a key research topic for countries around the world to adapt to the needs of future battlefields.

[0003] At present, there are many mature algorithms applied to path planning, including traditional classical algorithms such as A* algorithm, artificial potential field method and Dijkstra algorithm, and swarm intelligence algorithms such as particle swarm optimization (PSO) algorithm, sparrow search algorithm (SSA), grey wolf optimization (GWO) algorithm, etc. Reference [1] applied the A* algorithm to UAV trajectory planning, but only considered a two-dimensional model. Reference [2] applied the artificial potential field method to UAV trajectory planning, but the model constraints were limited. Reference [3] applied the ant colony algorithm to the UAV trajectory planning problem and improved the local optimum, but it could not be applied to a three-dimensional environment. In short, the search space of the path planning problem is large and there are many constraints. The above improvements have improved the path planning quality to a certain extent.

[0004] The Dung beetle optimizer (DBO) algorithm was proposed in 2023. The algorithm draws on the social behaviors of dung beetles, including ball rolling, dancing, foraging, reproduction, and stealing. By simulating these behaviors, the DBO algorithm is divided into four roles: ball rolling dung beetles, breeding dung beetles (breeding balls), small dung beetles, and stealing dung beetles to adapt to different survival tasks and optimization problems. However, the No Free Lunch (NFL) theorem proves that no metaheuristic algorithm can be applied to all optimization problems. Therefore, the present invention must continue to develop new algorithms to solve different problems. The dung beetle optimization algorithm has demonstrated strong global exploration capabilities in many optimization problems, so it also has certain application potential in fields such as drone trajectory planning. However, despite the above advantages, the DBO algorithm still has the following significant deficiencies when dealing with complex UAV trajectory planning problems: 1) Local optimality problem: Although the DBO algorithm has strong global search capabilities in the early stage, it is easy to fall into local optimality in complex obstacle environments and lacks an effective mechanism to jump out of local optimality, resulting in insufficient global path planning accuracy. 2) Imbalance between global exploration and local development: UAV trajectory planning requires global exploration and local rapid response. The DBO algorithm is difficult to balance the two in a high-dimensional complex environment, resulting in a decrease in global search capabilities and limited local development effects, affecting the path quality. 3) Insufficient path smoothness: The trajectory generated by the DBO algorithm lacks smoothness, resulting in unstable flight and increased energy consumption, and it is difficult to meet the requirements for smooth paths in complex environments. In view of the above deficiencies, the present invention first adopts Logistic-Tent initialization to enable the algorithm to have better global search capabilities, and then uses a mutation strategy that combines Levy flight and Brownian motion to enhance the algorithm's ability to jump out of local optimality and development performance, and finally fits the path through a cubic B-spline curve to generate a smoother and more stable trajectory for the UAV.

[0005] [1] Wei Ruixuan, Xu Zhuofan, Wang Shulei, et al. Self-optimizing A-Star UAV path planning algorithm based on Laguerre graph[J]. Systems Engineering and Electronics, 2015, 37(3): 577-582.

[0006] [2] Chen Haiyun, Chen Huazhou, Liu Qiang. Path planning of multi-UAV three-dimensional formation based on improved artificial potential field method[J]. Journal of System Simulation, 2020, 32(3): 414-420.

[0007] [3]ZHENGY,WANGL,PENGX,etal.An improvedantcolony algorithm for multi-agentpathplanning in dynamic environments[J].Computer Engineering andScience,2019,41(6):1078-1085. Summary of the invention

[0008] In order to solve the technical problems existing in the above-mentioned prior art, the present invention provides a three-dimensional trajectory planning method for a UAV based on the LBDBO algorithm. By initializing the Logistic-Tent chaotic mapping, a uniformly distributed population is obtained, so that the algorithm has better global search ability; a strategy combining Lévy flight and Brownian motion is used to mutate and perturb the individuals, thereby avoiding the local optimal solution of the algorithm and balancing the global search and local development capabilities; finally, a path is fitted by a cubic B-spline curve to generate a smooth and stable trajectory.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] A three-dimensional trajectory planning method for UAV based on LBDBO algorithm, the steps are as follows:

[0011] S1. Establish UAV flight environment;

[0012] S2, establish fitness function;

[0013] S3, using the improved LBDBO algorithm for UAV global path planning;

[0014] S4. Use cubic spline interpolation to obtain a smooth path curve.

[0015] Furthermore, in step S1, the function method is used to simulate the flight environment of the UAV, considering flying in a mountainous area, and the reference terrain and obstacle terrain are as follows:

[0016] z=sin(y+a)+b×sin(x)+c×cos(d×(y 2 +x 2 ))+e×cos(y)+f×sin(f×(y 2 +x 2 ))+g×cos(y);

[0017]

[0018] Where: z is the base terrain, h is the peak model, a, b, c, d, e, f, g are constants used in terrain generation to adjust the characteristics and appearance of the terrain; x and y represent coordinate points on the map; A is a matrix containing the coordinate points of the peaks, where A i,1 and A i,2 are the x and y coordinates of the ith peak; h i is the height of the ith peak; a i and b i are the slopes of the ith peak in the x and y directions respectively; h 0 It is the height of the lowest point of the mountain, usually set to 0 to represent the lowest terrain height.

[0019] Furthermore, in step S2, the fitness function is used to evaluate the quality of the path generated by the algorithm, considering the three aspects of path length, height and deflection angle. The constructed fitness function is as follows:

[0020] f=w 1 ×f 1 +w 2 ×f 2 +w 3 ×f 3

[0021] Among them, f 1 is the length evaluation index, f 2 is a high evaluation index, f 3 is the deflection angle evaluation index; w 1 、w 2 、w 3 is the weight coefficient of each indicator. The smaller f is, the higher the path quality is. 1、 f 2 、f 3 The calculation formula is as follows:

[0022]

[0023] f 3 =∑(cos(φ)-C(i))

[0024] Among them, X i , Y i , Z i are the coordinates of the i-th point on the path in the X, Y, and Z directions respectively; is the average height of all points on the path; φ is a reference angle; the angle Calculated using dot product.

[0025] Furthermore, in step S3, the DBO algorithm includes the following steps:

[0026] Assume that the dung beetle has a specific moving direction in the entire space, and the intensity of the light source will also affect the trajectory of the dung beetle; when there are no obstacles, the position update of the rolling dung beetle is expressed as follows:

[0027] x i (t+1)=x i (t)+α×k×x i (t-1)+b×Δx

[0028] Δx=|x i (t)-X W |

[0029] Where: t is the current number of iterations, x i (t) is the position of the i-th dung beetle at the t-th iteration, k∈(0,0.2] is a constant, i.e., the deflection coefficient, b is a constant belonging to (0,1), α is a natural coefficient, assigned a value of -1 or 1, and Δx is used to represent the degree of change in light intensity, where X W is the worst position in the current population;

[0030] When the dung beetle encounters an obstacle, it changes its direction by dancing to find a new path to continue rolling the ball forward. The algorithm uses the tangent function to simulate the dancing behavior, and the position update is expressed as follows:

[0031] x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)|

[0032] Where: |x i (t)-x i (t-1)| is the difference between the position of the i-th dung beetle at the t-th iteration and the position at the t-1-th iteration. Where θ∈[o,π], if θ is equal to 0, π / 2 or π, the position of the dung beetle will not be updated;

[0033] A boundary selection strategy is used to establish spawning areas, which are defined as follows:

[0034] Lb * =max(X * ×(1-R),Lb),

[0035] Ub * =min(X * ×(1+R),Ub)

[0036] Where: X * is the current local optimal position, Lb * and Ub *are the lower and upper limits of the spawning area, respectively, R = 1-t / T max , T max is the maximum number of iterations, Lb and Lb are the lower and upper bounds of the optimization problem respectively;

[0037] The boundary range of the spawning area changes dynamically due to the R value, and the position update of the hatching ball is expressed as follows:

[0038] B i (t+1)=X * +b 1 ×(B i (t)-Lb * )+b 2 ×(B i (t)-Ub * )

[0039] Where: B i (t) is the position information of the ith brooding ball at the nth iteration, b 1 and b 2 are two independent random vectors of size 1×D, where D is the dimension of the optimization problem.

[0040] The boundaries of the optimal foraging area are defined as follows:

[0041] Lb b =max(X b ×(1-R),Lb),

[0042] Ub b =min(X b ×(1+R),Ub)

[0043] In the formula: X b is the global optimal position, Lb b and Lb b are the lower and upper bounds of the optimal foraging area, respectively;

[0044] The updated positions of these dung beetles are shown below:

[0045] x i (t+1)=x i (t)+C 1 ×(x i (t)-Lb b )+C 2 ×(x i (t)-Ub b )

[0046] In the formula, x i (t) is the position information of the i-th dung beetle at the n-th iteration, C 1 is a random number that follows a normal distribution, C2 is a random vector belonging to (0,1);

[0047] Assume that X in the algorithm b It is the best place for the thief dung beetle to steal. The position update of the thief dung beetle is shown as follows:

[0048] x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |)

[0049] In the formula, x i (t) is the position information of the i-th thief at the n-th iteration, g is a random vector of size 1×D that obeys the normal distribution, and S is a constant.

[0050] Furthermore, in step S3, the LBDBO algorithm is improved by using Logistic-Tent chaotic mapping, and the following steps are performed:

[0051] When x∈[0,1] is in the range, its output sequence is evenly distributed, which is far more prominent than the chaotic characteristics of Logistic and Tent mapping in this range. Its mathematical formula is defined as follows:

[0052]

[0053] Where: x is the system variable; r is the control parameter; x∈[0,1], r∈(0,4).

[0054] Further, in step S3, the Levy flight improved LBDBO algorithm is used to perform the following steps:

[0055] The step size formula of Levy distribution is as follows:

[0056]

[0057] Where: β is in the range of 1≤β≤3, and the present invention takes 1.5, u~N(0,σ 2 ), σ and v~N(0,1) obey normal distribution; the value of σ is as follows:

[0058]

[0059] Where: Γ is the standard gamma function.

[0060] Furthermore, in step S3, the position is updated by combining Lévy flight and Brownian motion: the optimal individual is mutated and disturbed by combining the strategies of Lévy flight and Brownian motion. If the new solution generated by the strategy is better than the optimal solution, a new position is selected to enter the next iteration.

[0061] x i (t+1)=R(t)×[L×x i (t)+B×Δx]

[0062] ΔX=|x i (t)-x i (t-1)|

[0063] Where: x i (t+1) is the position of the optimal individual i after the mixed disturbance of Levy flight and Brownian motion, R(t) = e -t / M , called the attenuation factor, L is Levy flight, and B is Brownian motion.

[0064] Furthermore, it is characterized in that, in step S4, after the control points are solved by the LBDBO algorithm, cubic spline interpolation is used in combination with the starting point and the end point given by the problem to obtain a smooth path curve.

[0065] Beneficial effects of the present invention:

[0066] Compared with the prior art, the three-dimensional trajectory planning method for unmanned aerial vehicles based on the LBDBO algorithm described in the present invention has the following technical characteristics or beneficial effects:

[0067] The beneficial effects of the present invention are mainly reflected in the following aspects:

[0068] (1) Enhanced global search capability: By using Logistic-Tent chaotic mapping initialization, the present invention enables the algorithm to obtain a uniformly distributed population in the initial stage, which greatly improves the global search capability of the algorithm. Compared with traditional initialization methods, Logistic-Tent chaotic mapping can more effectively explore the solution space, laying a solid foundation for the subsequent optimization process.

[0069] (2) Avoiding local optimal solutions: By combining the mutation strategies of Lévy flight and Brownian motion, the present invention provides the algorithm with a powerful ability to jump out of the local optimal solution. Lévy flight, with its long-distance jump characteristics, helps the algorithm to achieve a large-scale search in the solution space, while Brownian motion can perform detailed searches in local areas. This combination strategy effectively balances global search and local development, avoiding the algorithm from falling into the local optimal solution.

[0070] (3) Improve path quality: By fitting the path with a cubic B-spline curve, the present invention generates a smooth and stable track for the UAV. This path not only meets the dynamic performance requirements of the UAV, but also reduces energy consumption and unstable factors during flight, thereby improving the combat effectiveness and safety of the UAV.

[0071] (4) Adaptability to complex environments: The algorithm of the present invention can adapt well to complex flight environments such as mountains. By establishing a terrain function that includes a mountain model, the algorithm can simulate obstacles and terrain undulations in the real environment and plan a flight path for the drone that is more in line with the actual situation.

[0072] (5) Improving algorithm robustness: The combination of Logistic-Tent chaos mapping, Lévy flight and Brownian motion, and cubic B-spline curve fitting and other strategies have jointly improved the robustness and adaptability of the algorithm. This enables the algorithm to perform well in different optimization problems and environments.

[0073] In summary, the present invention proposes a three-dimensional trajectory planning method for UAVs based on the LBDBO algorithm, which effectively improves the quality and efficiency of UAV trajectory planning by improving algorithm initialization, mutation strategy and path fitting. This not only provides strong support for UAV operations in complex battlefield environments, but also provides new ideas and methods for the research and development of path planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0075] Figure 1 It is a schematic diagram of the environmental model;

[0076] Figure 2 It is the LBDBO flow chart;

[0077] Figure 3 It is the result diagram of three-dimensional trajectory planning simulation;

[0078] Figure 4 It is the result diagram of two-dimensional trajectory planning simulation;

[0079] Figure 5 It is the trajectory planning cost convergence curve. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Figure 1-5 The three-dimensional trajectory planning method of a UAV based on the LBDBO algorithm is further explained, and the technical solutions in the embodiments of the present application are clearly and completely described; obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments, and all other embodiments obtained by ordinary technicians in this field without making creative work based on the embodiments in the present application are within the scope of protection of the present application.

[0081] Example 1

[0082] This embodiment provides a method for three-dimensional trajectory planning of a UAV based on the LBDBO algorithm, which includes the following steps: S1. Establishing a UAV flight environment; S2. Establishing a fitness function; S3. Using an improved LBDBO algorithm to perform global path planning of the UAV; S4. Using cubic spline interpolation to obtain a smooth path curve.

[0083] S1. The present invention uses a function method to simulate the flight environment of the UAV, only considering flying in mountainous areas, and the reference terrain and obstacle terrain are as follows:

[0084] z=sin(y+a)+b×sin(x)+c×cos(d×(y 2 +x 2 ))+e×cos(y)+f×sin(f×(y 2 +x 2 ))+g×cos(y);

[0085]

[0086] Where: z is the base terrain, h is the peak model, a, b, c, d, e, f, g are constants used in terrain generation to adjust the characteristics and appearance of the terrain; x and y represent coordinate points on the map; A is a matrix containing the coordinate points of the peaks, where A i,1 and A i,2 are the x and y coordinates of the ith peak; h i is the height of the ith peak; a i and b i are the slopes of the i-th peak in the x and y directions respectively; hi 0 It is the height of the lowest point of the mountain, usually set to 0 to represent the lowest terrain height.

[0087] S2. The present invention uses the fitness function to evaluate the quality of the path generated by the algorithm, considering the three aspects of path length, height and deflection angle. The constructed fitness function is as follows:

[0088] f=w 1 ×f 1 +w 2 ×f 2 +w 3 ×f 3

[0089] Among them, f 1 is the length evaluation index, f 2 is a high evaluation index, f 3 is the deflection angle evaluation index; w 1 、w 2 、w 3 is the weight coefficient of each indicator. The smaller f is, the higher the path quality is. 1、 f 2 、f 3 The calculation formula is as follows:

[0090]

[0091] f 3 =∑(cos(φ)-C(i))

[0092] Among them, X i , Y i , Z i are the coordinates of the i-th point on the path in the X, Y, and Z directions respectively; is the average height of all points on the path; φ is a reference angle; the angle It can be calculated using the dot product.

[0093] S3. The improved LBDBO algorithm is used for the global path planning of the UAV, where:

[0094] 1. DBO algorithm

[0095] (1) Ball-rolling dung beetle

[0096] Dung beetles use celestial cues to navigate, allowing them to roll their dung balls in a straight line. Assume that dung beetles have a specific direction of movement throughout space, and the intensity of the light source also affects the trajectory of the dung beetle. When there are no obstacles, the position update of the rolling dung beetle is expressed as follows:

[0097] x i (t+1)=x i (t)+α×k×x i (t-1)+b×Δx

[0098] Δx=|x i (t)-X W |

[0099] Where: t is the current number of iterations, x i (t) is the position of the i-th dung beetle at the t-th iteration, k∈(0,0.2] is a constant, i.e., the deflection coefficient, b is a constant belonging to (0,1), α is a natural coefficient, assigned a value of -1 or 1, and Δx is used to represent the degree of change in light intensity, where X W is the worst position in the current population.

[0100] When the dung beetle encounters an obstacle, it will use dancing behavior to change its direction of travel to find a new path to continue rolling the ball forward. The algorithm uses the tangent function to simulate the dancing behavior, and the position update is expressed as follows:

[0101] x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)|

[0102] Where: |x i (t)-x i (t-1)| is the difference between the position of the i-th dung beetle at the t-th iteration and the position at the t-1-th iteration. Where θ∈[o,π], if θ is equal to 0, π / 2 or π, the position of the dung beetle will not be updated.

[0103] (2) Breeding dung beetles (breeding balls)

[0104] Dung beetles will roll the dung balls to a safe place to hide, and female dung beetles want to provide a safe environment for their offspring, so they will carefully choose a suitable area for laying eggs. In the algorithm, a boundary selection strategy is used to establish the egg-laying area, which is defined as follows:

[0105] Lb * =max(X * ×(1-R),Lb),

[0106] Ub * =min(X * ×(1+R),Ub)

[0107] Where: X * is the current local optimal position, Lb * and Ub * are the lower and upper limits of the spawning area, respectively, R = 1-t / T max , T max is the maximum number of iterations, Lb and Lb are the lower and upper bounds of the optimization problem respectively.

[0108] Female dung beetles will start laying eggs after finding a safe place. In the algorithm, each female dung beetle only lays one egg in each iteration, and the boundary range of the egg-laying area changes dynamically due to the R value. The position update of the hatching ball is expressed as follows:

[0109] B i (t+1)=X * +b 1 ×(B i (t)-Lb * )+b 2 ×(B i (t)-Ub * )

[0110] Where: B i (t) is the position information of the ith brooding ball at the nth iteration, b 1 and b 2 are two independent random vectors of size 1×D, where D is the dimension of the optimization problem.

[0111] (3) Small dung beetle

[0112] Some grown-up dung beetles will come out to look for food, and the algorithm establishes an optimal foraging area to guide the foraging process of these dung beetles. The boundary of the optimal foraging area is defined as follows:

[0113] Lb b =max(X b ×(1-R),Lb),

[0114] Ub b =min(X b ×(1+R),Ub)

[0115] In the formula: X b is the global optimal position, Lb b and Lb b are the lower and upper bounds of the optimal foraging area, respectively.

[0116] The updated positions of these dung beetles are shown below:

[0117] x i (t+1)=x i (t)+C 1 ×(x i (t)-Lb b )+C 2 ×(x i (t)-Ub b )

[0118] In the formula, x i (t) is the position information of the i-th dung beetle at the n-th iteration, C1 is a random number that follows a normal distribution, C 2 is a random vector in (0,1).

[0119] (4) Stealing Dung Beetles

[0120] Some dung beetles do not try to push the ball, but choose to steal the dung ball. They are called thief dung beetles. Suppose X in the algorithm b is their best place to steal. The position update of the thief dung beetle is shown as follows:

[0121] x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |)

[0122] In the formula, x i (t) is the position information of the i-th thief at the n-th iteration, g is a random vector of size 1×D that obeys the normal distribution, and S is a constant.

[0123] 2. Improved LBDBO algorithm

[0124] The dung beetle algorithm uses random initialization, which will reduce the richness of the population; at the same time, although the algorithm has a certain optimization ability and convergence speed, it is also prone to fall into local optimality and lacks global exploration ability. To this end, the present invention improves the DBO algorithm to solve the global optimization problem, uses Logistic-Tent chaotic mapping initialization, updates the positions of the four dung beetle populations, and mutates the optimal position by combining Levy flight and Brownian motion strategies to determine the termination conditions. The improved algorithm is called LBDBO. The flowchart of the improved algorithm LBDBO is as follows: Figure 2 .

[0125] (1) Logistic-Tent Chaotic Mapping

[0126] The result of population initialization will affect the optimization performance of the algorithm and the quality of the optimal solution. Therefore, the Logistic-Tent chaotic mapping is introduced to improve the generation strategy of the initial dung beetle population. The Logistic-Tent composite chaotic mapping was proposed by Gupta et al. When x∈[0,1], its output sequence is evenly distributed, which is far more prominent than the chaotic characteristics of Logistic and Tent mapping in this range. Its mathematical formula is defined as follows:

[0127]

[0128] Where: x is the system variable; r is the control parameter; x∈[0,1], r∈(0,4).

[0129] (2) Levi Flight

[0130] Levi's Flight was created in 1982 by Benoit Mandelbrot It was proposed and named after the French mathematician Paul Levy. Levy flight is a special random walk process, and the probability distribution of its step length shows a heavy-tailed characteristic. The introduction of Levy flight will produce random movements with longer jumps and multiple mutation directions, thereby enhancing the global search ability of the algorithm and jumping out of the local optimal solution. The step length formula of Levy distribution is as follows:

[0131]

[0132] Where: β is in the range of 1≤β≤3, and the present invention takes 1.5, u~N(0,σ 2 ), σ and v~N(0,1) obey normal distribution; the value of σ is as follows:

[0133]

[0134] Where: Γ is the standard gamma function.

[0135] (3) Brownian motion

[0136] Brownian motion was proposed by British biologist Brown in 1827. It was inspired by the phenomenon of pollen moving irregularly on the liquid surface. It is a scientific experiment of great significance. Brownian motion is a random motion with short steps and a random process that follows Gaussian distribution. Studies have shown that in some cases, a search strategy combining Lévy flight and Brownian motion may be more effective than a single strategy. Therefore, Lévy flight and Brownian motion are introduced in this paper.

[0137] (4) Position update combining Lévy flight and Brownian motion

[0138] In the late stage of the iteration of the dung beetle algorithm, the dung beetle population will quickly converge to a vicinity of an optimal position, but this position may not be the global optimal solution, which will result in the inability to find the true global optimal solution. The mutation perturbation strategy is an effective method to solve the problems of premature convergence and local optimality of the algorithm. By applying random perturbations to the individuals of the population in the late stage of the algorithm iteration, the richness of the population is increased, thereby helping the algorithm to jump out of the local optimal solution. The present invention selects a strategy combining Levy flight and Brownian motion to perform mutation perturbations on the optimal individuals. If the new solution generated by the strategy is better than the optimal solution, a new position is selected to enter the next iteration.

[0139] x i (t+1)=R(t)×[L×x i(t)+B×Δx]

[0140] ΔX=|x i (t)-x i (t-1)|

[0141] Where: x i (t+1) is the position of the optimal individual i after the mixed disturbance of Levy flight and Brownian motion, R(t) = e -t / M , called the attenuation factor, L is Levy flight, and B is Brownian motion.

[0142] S4. After the LBDBO algorithm solves the control points, cubic spline interpolation is used to obtain a smooth path curve based on the starting and ending points given in the problem.

[0143] Example 2

[0144] 1. Establish the UAV flight environment

[0145] For the three-dimensional trajectory planning of UAV, the environment and static obstacles need to be modeled. In the actual flight mission of UAV, it often faces terrain obstacles. There is a lot of threat information hidden in the mission space, including terrain, radar, anti-aircraft guns, etc., and these threats are often uncertain. Therefore, it is very difficult to obtain the threat information in the actual flight space in advance. In order to simplify the trajectory planning process, the present invention uses the function method to simulate the flight environment of the UAV, considering only flying in the mountains, and the reference terrain and obstacle terrain are as follows:

[0146] z=sin(y+a)+b×sin(x)+c×cos(d×(y 2 +x 2 ))+e×cos(y)+f×sin(f×(y 2 +x 2 ))+g×cos(y);

[0147]

[0148] Where: z is the base terrain, h is the peak model, a, b, c, d, e, f, g are constants used in terrain generation to adjust the characteristics and appearance of the terrain; x and y represent coordinate points on the map; A is a matrix containing the coordinate points of the peaks, where A i,1 and A i,2 are the x and y coordinates of the ith peak; h i is the height of the ith peak; a i and b i are the slopes of the ith peak in the x and y directions respectively; h 0 is the height of the lowest position of the mountain, usually set to 0 to represent the lowest terrain height. Figure 1 shown.

[0149] 2. Establish fitness function

[0150] In actual application requirements, flight distance, flight altitude, and path smoothness are key considerations. A shorter flight path means that the task can be completed more quickly, while the flight altitude affects the stealth of the drone. The present invention uses the fitness function to evaluate the quality of the path generated by the algorithm, considering the three aspects of path length, altitude, and deflection angle. The constructed fitness function is as follows:

[0151] f=w 1 ×f 1 +w 2 ×f 2 +w 3 ×f 3

[0152] Among them, f 1 is the length evaluation index, f 2 is a high evaluation index, f 3 is the deflection angle evaluation index; w 1 、w 2 、w 3 is the weight coefficient of each indicator. The smaller f is, the higher the path quality is. 1、 f 2 、f 3 The calculation formula is as follows:

[0153]

[0154] f 3 =∑(cos(φ)-C(i))

[0155] Among them, X i , Y i , Z i are the coordinates of the i-th point on the path in the X, Y, and Z directions respectively; is the average height of all points on the path; φ is a reference angle; the angle It can be calculated using the dot product.

[0156] 3. Use the improved LBDBO algorithm for UAV global path planning

[0157] The invention improves the DBO algorithm to solve the global optimization problem. Firstly, the Logistic-Tent chaotic mapping is used for initialization to obtain the positions of four dung beetle populations. Secondly, the optimal position is mutated by combining the Lévy flight and Brownian motion strategies. Finally, the termination condition is determined.

[0158] The present invention constructs a mountain terrain environment to simulate the flight scene of the UAV. In the flight area of ​​200×200×100, a mountain is simulated as an obstacle model, the starting point is (0, 0, 20), the target point is (200, 200, 40), and the number of intermediate nodes is 3. In this environment, the DBO algorithm, ABC algorithm, SSA algorithm, SOA algorithm and GWO algorithm are also selected for comparative experiments in the static environment of the UAV. When the algorithm is run independently 30 times, the optimal values ​​(Optimal) and average values ​​(Mean) of the six algorithms are listed, as shown in Table 1.

[0159] Figure 3 and Figure 4 The following are simulation diagrams of the drone's trajectory planning in a three-dimensional perspective and in a two-dimensional perspective of the xOy plane. It can be seen from the figure that several algorithms can generate their own flyable trajectories, effectively avoid threats, and successfully reach the target point, but the ABC, SSA, and SOA algorithms generate higher trajectories, which will make the drone easier to be discovered, while the improved LBDBO algorithm of the present invention plans a shorter trajectory, and the trajectory is less tortuous and smoother.

[0160] Figure 5 Iterative convergence diagrams of the six algorithms. As can be seen from the figure, the original DBO algorithm converges slowly, and the convergence value is higher than that of the GWO and LBDBO algorithms. The LBDBO algorithm has the smallest initial value and quickly finds the optimal value at the beginning of the iteration. Although the final convergence results of GWO and LBDBO are similar, LBDBO converges to the optimal value faster and has the lowest fitness value. The experimental results show that the LBDBO algorithm can find the optimal flight trajectory more quickly and stably, and has better performance indicators.

[0161] Table 1 Algorithm test results comparison

[0162] Statistics DBO LBDBO ABC SSA SOA GWO Optimal value 302.82 285.97 711.22 364.28 375.18 287.71 average value 303.96 302.04 727.22 371.17 380.66 303.40

[0163] Table 1 shows the results of 30 independent runs of the algorithm. The optimal value of LBDBO is the smallest, and the average value is close to DBO and GWO, but also lower than other algorithms. The above data show that LBDBO has significant advantages in convergence speed and stability.

[0164] 4. In the study of trajectory planning, since the UAV trajectory generated by the algorithm is composed of line segments and is not suitable for precise flight, after the track points are planned using the LBDBO algorithm, cubic B-spline interpolation is used to smooth the path to obtain a smooth path curve.

[0165] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A three-dimensional trajectory planning method for unmanned aerial vehicles based on LBDBO algorithm, characterized in that: Here are the steps: S1. Establish UAV flight environment; S2, establish fitness function; S3, using the improved LBDBO algorithm for UAV global path planning; S4. Use cubic spline interpolation to obtain a smooth path curve.

2. The method for three-dimensional trajectory planning of an unmanned aerial vehicle based on the LBDBO algorithm as claimed in claim 1, characterized in that: In step S1, the function method is used to simulate the flight environment of the UAV. Considering flying in a mountainous area, the reference terrain and obstacle terrain are as follows: z=sin(y+a)+b×sin(x)+c×cos(d×(y 2 +x 2 ))+e×cos(y)+f×sin(f×(y 2 +x 2 ))+g×cos(y); Where: z is the base terrain, h is the peak model, a, b, c, d, e, f, g are constants used in terrain generation to adjust the characteristics and appearance of the terrain; x and y represent coordinate points on the map; A is a matrix containing the coordinate points of the peaks, where A i,1 and A i,2 are the x and y coordinates of the ith peak; h i is the height of the ith peak; a i and b i are the slopes of the ith peak in the x and y directions respectively; h0 is the height of the lowest position of the peak, which is usually set to 0 to indicate the lowest terrain height.

3. The method for three-dimensional trajectory planning of unmanned aerial vehicle based on LBDBO algorithm as claimed in claim 1, characterized in that: In step S2, the fitness function is used to evaluate the quality of the path generated by the algorithm, considering three aspects: path length, height and deflection angle. The constructed fitness function is as follows: f=w1×f1+w2×f2+w3×f3 Among them, f1 is the length evaluation index, f2 is the height evaluation index, and f3 is the deflection angle evaluation index; w1, w2, and w3 are the weight coefficients of each index. The smaller f is, the higher the path quality is. The calculation formulas of f1, f2, and f3 are as follows: f3=∑(cos(φ)-C(i)) Among them, X i , Y i , Z i are the coordinates of the i-th point on the path in the X, Y, and Z directions respectively; is the average height of all points on the path; φ is a reference angle; the angle Calculated using dot product.

4. The method for three-dimensional trajectory planning of an unmanned aerial vehicle based on the LBDBO algorithm as claimed in claim 1, characterized in that: In step S3, the DBO algorithm includes the following steps: Assume that the dung beetle has a specific moving direction in the entire space, and the intensity of the light source will also affect the trajectory of the dung beetle; when there are no obstacles, the position update of the rolling dung beetle is expressed as follows: x i (t+1)=x i (t)+α×k×x i (t-1)+b×Δx Δx=|x i (t)-X W | Where: t is the current number of iterations, x i (t) is the position of the i-th dung beetle at the t-th iteration, k∈(0,0.2] is a constant, i.e., the deflection coefficient, b is a constant belonging to (0,1), α is a natural coefficient, assigned a value of -1 or 1, and Δx is used to represent the degree of change in light intensity, where X W is the worst position in the current population; When the dung beetle encounters an obstacle, it changes its direction by dancing to find a new path to continue rolling the ball forward. The algorithm uses the tangent function to simulate the dancing behavior, and the position update is expressed as follows: x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)| Where: |x i (t)-x i (t-1)| is the difference between the position of the i-th dung beetle at the t-th iteration and the position at the t-1-th iteration; where θ∈[o,π], if θ is equal to 0, π / 2 or π, the position of the dung beetle will not be updated; A boundary selection strategy is used to establish spawning areas, which are defined as follows: Lb * =max(X * ×(1-R),Lb), Ub * =min(X * ×(1+R),Ub) Where: X * is the current local optimal position, Lb * and Ub * are the lower and upper limits of the spawning area, respectively, R = 1-t / T max , T max is the maximum number of iterations, Lb and Lb are the lower and upper bounds of the optimization problem respectively; The boundary range of the spawning area changes dynamically due to the R value, and the position update of the hatching ball is expressed as follows: B i (t+1)=X * +b1×(B i (t)-Lb * )+b2×(B i (t)-Ub * ) Where: B i (t) is the position information of the i-th brooding ball at the n-th iteration, b1 and b2 are two independent random vectors of size 1×D, and D is the dimension of the optimization problem; The boundaries of the optimal foraging area are defined as follows: Lb b =max(X b ×(1-R),Lb), Ub b =min(X b ×(1+R),Ub) In the formula: X b is the global optimal position, Lb b and Lb b are the lower and upper bounds of the optimal foraging area, respectively; The updated positions of these dung beetles are shown below: x i (t+1)=x i (t)+C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b ) In the formula, x i (t) is the position information of the ith dung beetle at the nth iteration, C1 is a random number that obeys the normal distribution, and C2 is a random vector belonging to (0,1); Assume that X in the algorithm b It is the best place for the thief dung beetle to steal. The position update of the thief dung beetle is shown as follows: x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |) In the formula, x i (t) is the position information of the i-th thief at the n-th iteration, g is a random vector of size 1×D that obeys the normal distribution, and S is a constant.

5. The method for three-dimensional trajectory planning of unmanned aerial vehicle based on LBDBO algorithm as claimed in claim 4, characterized in that: In step S3, the Logistic-Tent chaotic mapping is used to improve the LBDBO algorithm, and the following steps are performed: When x∈[0,1] is in the range, its output sequence is evenly distributed, which is far more prominent than the chaotic characteristics of Logistic and Tent mapping in this range. Its mathematical formula is defined as follows: Where: x is the system variable; r is the control parameter; x∈[0,1], r∈(0,4).

6. The method for three-dimensional trajectory planning of an unmanned aerial vehicle based on the LBDBO algorithm as claimed in claim 4, characterized in that: In step S3, the Levy flight improved LBDBO algorithm is used to perform the following steps: The step size formula of Levy distribution is as follows: Where: β is in the range of 1≤β≤3, and the present invention takes 1.5, u~N(0,σ 2 ), σ and v~N(0,1) obey normal distribution; the value of σ is as follows: Where: Γ is the standard gamma function.

7. The method for three-dimensional trajectory planning of an unmanned aerial vehicle based on the LBDBO algorithm as claimed in claim 4, characterized in that: In step S3, the position is updated by combining Lévy flight and Brownian motion: the optimal individual is mutated and disturbed by combining the strategies of Lévy flight and Brownian motion. If the new solution generated by this strategy is better than the optimal solution, a new position is selected to enter the next iteration. x i (t+1)=R(t)×[L×x i (t)+B×Δx] ΔX=|x i (t)-x i (t-1)| Where: x i (t+1) is the position of the optimal individual i after the mixed disturbance of Levy flight and Brownian motion, R(t) = e -t / M , called the attenuation factor, L is Levy flight, and B is Brownian motion.

8. The method for three-dimensional trajectory planning of an unmanned aerial vehicle based on the LBDBO algorithm according to any one of claims 1 to 7, characterized in that: In step S4, after the LBDBO algorithm solves the control points, cubic spline interpolation is used in combination with the starting point and end point given in the problem to obtain a smooth path curve.

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