Unmanned aerial vehicle three-dimensional path planning method for improving dung beetle algorithm

Abstract

The invention discloses an unmanned aerial vehicle three-dimensional path planning method based on an improved dung beetle algorithm, and relates to the technical field of unmanned aerial vehicle path planning. According to the technical scheme, an unmanned aerial vehicle flight environment is modeled; establishing constraint conditions; establishing a target function; and performing unmanned aerial vehicle global path planning by adopting an improved dung beetle optimization algorithm. The method has the beneficial effects that initialization is carried out by utilizing a good point set strategy, so that the population diversity is improved; an improved sine algorithm is combined with a variation strategy of Levy flight and Brownian motion to be embedded into position updating of dung beetles, so that the search range is expanded, and the global optimization ability of the algorithm is improved; a simplex method and a self-adaptive reverse learning strategy are added for disturbance, and the algorithm is helped to jump out of a local optimal solution; the efficiency and accuracy of unmanned aerial vehicle path planning are remarkably improved, the robustness and adaptability of the algorithm are enhanced, the flight path of the unmanned aerial vehicle is optimized, and further development of the unmanned aerial vehicle technology is promoted.

Description

Technical Field

[0001] The invention belongs to the technical field of unmanned aerial vehicle path planning, and relates to a three-dimensional path planning method for an unmanned aerial vehicle by improving a dung beetle algorithm. Background Art

[0002] With the rapid development of Unmanned Aerial Vehicle (UAV) technology, their role in modern military strategy is becoming increasingly important. UAVs not only show unique advantages in reconnaissance, surveillance and strike missions, but also undertake key tasks in complex battlefield environments. However, effective path planning is one of the core challenges to ensure the successful execution of UAV missions, especially when multiple constraints such as navigation distance, altitude and radar are involved. How to plan the best path from the starting point to the target point is particularly critical.

[0003] Currently, there are many algorithms applied to UAV path planning, which are mainly divided into classical algorithms and swarm intelligence algorithms. Classical algorithms include A* algorithm, artificial potential field algorithm, Dijkstra algorithm, etc. Swarm intelligence algorithms include particle swarm optimization algorithm, ant colony optimization algorithm, gray wolf optimization algorithm, etc. Since most swarm intelligence algorithms have the advantages of fast convergence speed, high search accuracy and strong inspiration, they have become the most widely studied methods in the field of UAV path planning.

[0004] The Dung Beetle Optimizer (DBO) algorithm is a new optimization algorithm based on swarm intelligence proposed by XUE J et al. in 2023. The algorithm simulates different survival strategies of dung beetles and divides them into four roles: rolling dung beetles, breeding dung beetles (breeding balls), small dung beetles, and stealing dung beetles. The DBO algorithm has the characteristics of fast convergence and high solution accuracy and is widely used. However, the dung beetle optimization algorithm is also difficult to completely avoid falling into local optimality during the search process, and there is a defect of imbalance between global search and local development. Summary of the invention

[0005] In order to solve the technical problems existing in the above-mentioned prior art, the present invention provides a three-dimensional path planning method for a UAV based on an improved dung beetle algorithm, which uses a good point set strategy for initialization to improve population diversity; an improved sinusoidal algorithm and a mutation strategy combining Levy flight and Brownian motion are embedded in the position update of the dung beetle to expand the search range and improve the global optimization ability of the algorithm; the simplex method and an adaptive reverse learning strategy are added for perturbation to help the algorithm escape from the local optimal solution.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A three-dimensional path planning method for UAV based on an improved dung beetle algorithm, the steps are as follows:

[0008] S1. Modeling the UAV flight environment;

[0009] S2. Establish constraints;

[0010] S3, establish the objective function;

[0011] S4. Use the improved dung beetle optimization algorithm to perform global path planning for the UAV.

[0012] Furthermore, the environment modeling in step S1 includes:

[0013] S1.1. Benchmark terrain modeling: The peak function is used, and the mathematical expression is as follows:

[0014]

[0015] Where: z(x,y) is the terrain height at (x,y), h i is the height of the ith peak, (x i ,y i ) is the center coordinate of the i-th peak, x ni and ni are the attenuation of the i-th peak in the x-direction and the y-direction respectively;

[0016] S1.2. Radar threat area modeling: The model uses a hemispherical model, and the mathematical expression is as follows:

[0017]

[0018] Where: W j (x, y, z) is the jth radar threat area, (x j ,y j ,z j ) is the center coordinate of the jth radar threat area, R wj is the radius of the jth radar threat area.

[0019] Furthermore, in step S2, detailed constraints are proposed for the UAV path planning to ensure that the UAV can fly stably in a complex environment, including

[0020] S2.1. Turning Angle Constraint

[0021] Limit the maximum turning angle μ of the drone during flight max and the minimum turning angle μ min , turning angle μ i satisfy:

[0022]

[0023] Where: a i =[xi -x i-1 ,y i -y i-1 ] T is the vector of the i-th path, (x i ,y i ,z i ) and (x i+1 ,y i+1 ,z i+1 ) represent the coordinates of the i-th path node and the i+1-th path node respectively;

[0024] S2.2, Maximum climb angle constraint

[0025] Set the maximum climb angle β max , turning angle β i satisfy:

[0026]

[0027] S2.3. Height Constraint

[0028] Set the minimum ground clearance to H min , the flight altitude of the drone is z i satisfy:

[0029] z i >H min #.

[0030] Furthermore, in step S3, the range cost, altitude cost and threat area cost are comprehensively considered:

[0031] S3.1. Flight cost: Considering the flight distance required by the drone from the starting point to the end point, the mathematical expression is:

[0032]

[0033] S3.2, Altitude cost: Ensure that the UAV maintains a stable flight trajectory and reduce frequent adjustments to the flight altitude. The mathematical expression is:

[0034]

[0035] S3.3, Threat area cost: Prevent the drone from colliding with the mountain and entering the enemy's radar detection area; by keeping a safe distance from the mountain and radar, the drone can ensure smooth flight, effectively reduce the probability of being discovered and attacked, and ensure the successful completion of the mission;

[0036]

[0037] Based on the above analysis, the overall objective function of the UAV is:

[0038] f=min{ω 1 L+ω 2 H+ω 3 T}

[0039] Where: 1 ,ω 2 ,ω 3 is the weight coefficient of each cost function, and satisfies ω 1 +ω 2 +ω 3 =1.

[0040] Further, in step S4, the dung beetle algorithm includes:

[0041] (1) Ball-rolling dung beetle

[0042] When there are no obstacles, the position update of the rolling dung beetle is expressed as follows:

[0043] x i (t+1)=x i (t)+α×k×x i (t-1)+b×Δx

[0044] Δx=|x i (t)-X W |

[0045] 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;

[0046] The tangent function is used to simulate dancing behavior, and the position update is expressed as follows:

[0047] x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)|

[0048] 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;

[0049] (2) Breeding dung beetles

[0050] Spawning areas are simulated using a boundary selection strategy, which is defined as follows:

[0051] Lb * =max(X * ×(1-R),Lb),

[0052] Ub * =min(X * ×(1+R),Ub)

[0053] 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 ma x is the maximum number of iterations, Lb and Lb are the lower and upper bounds of the optimization problem respectively;

[0054] The position update of the breeding ball is expressed as follows:

[0055] B i (t+1)=X * +b 1 ×(B i (t)-Lb * )+b 2 ×(B i (t)-Ub * )

[0056] 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;

[0057] (3) Small dung beetle

[0058] The boundaries of the optimal foraging area are defined as follows:

[0059] Lb b =max(X b ×(1-R),Lb),

[0060] Ub b =min(X b ×(1+R),Ub)

[0061] 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;

[0062] The updated positions of these dung beetles are shown below:

[0063] x i (t+1)=x i (t)+C 1 ×(x i (t)-Lb b )+C 2 ×(x i (t)-Ub b )

[0064] 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, C 2 is a random vector belonging to (0,1);

[0065] (4) Stealing Dung Beetles

[0066] X b is the optimal food source, X in the algorithm b Nearby represents the best place to compete for food. The position update of the thief dung beetle is shown below:

[0067] x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |)

[0068] 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.

[0069] Furthermore, the dung beetle algorithm is optimized by using the good point set:

[0070] G S is a unit cube of S-dimensional Euclidean space, that is, S∈G S , X=(x 1 ,x 2 ,x 3 ,…,x s ), where 0≤x i ≤1,i=1,2,…S,G S The point r in 1 ,r 2 ,…,r s ), let r∈G S , in the form of P n (k) = {(r 1 (k),…r s(k)),k=1,2,…n} satisfy Where C(r,ε) is a constant that is only related to r,ε(ε>0), then P n (k) is the set of good points, and r is a good point.

[0071] Furthermore, the dung beetle algorithm is optimized by the sine algorithm:

[0072] The information of the optimal position of individual i so far and the global optimal position is introduced. When encountering an obstacle in the rolling stage, the sine operation is used to guide the dung beetle to update its position. The mathematical expression is as follows:

[0073] x i (t+1)=x i (t)+Asin(θ)|Bx i,best (t)-x i (t)|+C|x best (t)-x i (t)|

[0074]

[0075] Where a is a constant, B represents the weight, C is a uniformly distributed random number between 0 and 1, and x i,best (t) is the optimal position of individual i so far; x best (t) is the global optimal position;

[0076] In the modified sine function, Asin(θ)|x i,best (t)-x i (t)|Contribution to the cognition in the search process becomes, B|x best (t)-x i (t)|Contribute social components, combining the best of individuals and the best of the group in the search process.

[0077] Furthermore, the strategy of combining Levy flight and Brownian motion is used to optimize the dung beetle algorithm:

[0078] The step size formula of Levy distribution is as follows:

[0079]

[0080] 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:

[0081]

[0082] Where: Γ is the standard gamma function;

[0083] Introducing Lévy flight and Brownian motion in the position update of the stealing dung beetle, the improved mathematical expression is as follows:

[0084] x i (t+1)=ω×Levy×X b +Bl×S×g×(x i (t)-X * |+|x i (t)-X b |)

[0085] Where: Levy is Levy flight, Bl is Brownian motion;

[0086] Introducing the nonlinear adjustment parameter ω, the expression is:

[0087]

[0088] Furthermore, the dung beetle algorithm is optimized by the simplex method:

[0089] Assume x c is the optimal point x g and the suboptimal value x b The center of x s It’s the worst point;

[0090] Reflection operation: x r =x c +α(x c -x s ), x r is the reflection point, and the reflection coefficient α is 1;

[0091] Expansion operation: x e =x c +γ(x r -x c ), x e is the expansion point, and the expansion coefficient γ is 2;

[0092] External contraction operation: x t =x c +β(x s -x c ), x t It is the external contraction point, and the external contraction coefficient β is 0.5;

[0093] Inner contraction operation: x w =x c -β(x s -x c ), x w is the internal contraction point, and the internal contraction coefficient β is 0.5;

[0094] The basic steps of the simplex method are:

[0095] Step 1: Calculate the midpoint: Find the worst position x s , calculate the current optimal position x g and the second best position x b The midpoint x c , this midpoint is used for the following reflection and extension operations;

[0096] Step 2: Reflection operation: Calculate the reflection point x using the reflection formula r , if the fitness of the reflection point is better than the current optimal solution, then the expansion operation is performed;

[0097] Step 3: Extension operation: If the fitness of the reflection point is better than the current optimal solution, calculate the extension point x e ; If the fitness of the extension point is better, choose x e as the new position, otherwise select the reflection point x r ;

[0098] Step 4: External contraction operation: If the fitness of the reflection point is not better than the current optimal solution, calculate the external contraction point x t ; If the fitness of the external contraction point is better than the worst position x s , then select x t As a new location;

[0099] Step 5: Internal contraction operation: If the fitness of the reflection point is between the current optimal solution and the worst solution, calculate the internal contraction point x w ; If the fitness of the internal contraction point is better than the worst position x s , then select x w as the new position, otherwise choose the external contraction point x t .

[0100] Furthermore, the dung beetle algorithm is optimized through adaptive reverse learning:

[0101] For a solution x=(x 1 ,x 2 ,…,x D ), its reverse point is defined as:

[0102]

[0103] Where: i∈[1,2,…D], a i and b i are the lower and upper bounds of the i-th dimension respectively;

[0104] The quasi-reverse solution is defined as:

[0105]

[0106] The quasi-reflective solution is defined as follows:

[0107]

[0108] Adaptive reversal point The definition is as follows:

[0109]

[0110] Where: d(x 1 -x 2 )=|x 1 -x 2 | is the distance calculation function.

[0111] Beneficial effects of the present invention:

[0112] Compared with the prior art, the UAV three-dimensional path planning method of the improved dung beetle algorithm described in the present invention has the following technical characteristics or beneficial effects:

[0113] (1) Improved the efficiency and accuracy of UAV path planning: By introducing the good point set strategy for initialization, the population diversity of the dung beetle optimization algorithm is significantly improved, so that the algorithm can cover a wider search space in the initial stage, thereby increasing the possibility of finding the global optimal solution. The application of the improved sine algorithm, the mutation strategy combining Lévy flight and Brownian motion, and the simplex method and adaptive reverse learning strategy jointly enhance the algorithm's global search ability and local development ability, enabling the algorithm to quickly and accurately find the best path from the starting point to the target point.

[0114] (2) Enhanced algorithm robustness and adaptability: The proposed method can comprehensively consider various constraints during the flight of the UAV, such as turning angle constraints, maximum climbing angle constraints, and altitude constraints, ensuring the stable flight of the UAV in complex environments. By simulating the different survival strategies of dung beetles, the algorithm can adaptively adjust the search strategy, effectively avoiding the problem of falling into the local optimal solution, and improving the robustness and adaptability of the algorithm.

[0115] (3) Optimized the flight trajectory of the UAV: ​​By comprehensively considering the range cost, altitude cost, and threat area cost, a reasonable objective function was established, so that the algorithm can fully consider the flight efficiency and safety of the UAV when planning the path. Through refined environmental modeling and threat area modeling, the algorithm can accurately identify and avoid potential flight obstacles and threats, ensuring that the UAV can successfully complete the mission.

[0116] (4) Promoted the further development of UAV technology: The method proposed in this invention is not only applicable to the three-dimensional path planning of UAVs, but also can provide new solutions and methods for other similar optimization problems. By improving and optimizing the dung beetle optimization algorithm, it provides strong technical support and guarantee for the further development of UAV technology and promotes the widespread application of UAVs in military and civilian fields.

[0117] In summary, the present invention significantly improves the efficiency and accuracy of UAV path planning by improving and optimizing the dung beetle optimization algorithm, enhances the robustness and adaptability of the algorithm, optimizes the flight trajectory of the UAV, and promotes the further development of UAV technology. These beneficial effects make the present invention have broad application prospects and important research value in the field of UAV path planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] 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:

[0119] Figure 1 It is a schematic diagram of the search points of the simplex method;

[0120] Figure 2 It is the HDBO flow chart;

[0121] Figure 3 is a terrain-path planning simulation result diagram;

[0122] Figure 4 It is the terrain two path planning simulation result diagram;

[0123] Figure 5 It is a terrain-path planning convergence curve graph;

[0124] Figure 6 It is the terrain two path planning convergence curve. DETAILED DESCRIPTION

[0125] 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 1-6The three-dimensional path planning method for unmanned aerial vehicles based on the improved dung beetle 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 based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0126] Example 1

[0127] This invention proposes an improved dung beetle optimization algorithm (HDBO) for three-dimensional path planning of unmanned aerial vehicles. First, the optimal point set strategy is used for initialization to improve population diversity; secondly, the improved sine algorithm is used to replace the tangent dancing strategy in the rolling ball stage, and the position is updated in the stealing stage in combination with the Levy flight and Brownian motion strategies to improve the global optimization ability of the DBO algorithm; then the simplex method is used to improve the worst position, and the adaptive reverse learning strategy is used to help the algorithm effectively escape from the local optimum; finally, the HDBO algorithm is simulated in two groups of environments to verify its ability to optimize paths in complex environments. The specific scheme is as follows:

[0128] A three-dimensional path planning method for unmanned aerial vehicles (UAVs) based on an improved dung beetle algorithm includes the following steps: S1. Modeling the flight environment of the UAV; S2. Establishing constraint conditions; S3. Establishing an objective function; S4. Using the improved dung beetle optimization algorithm to perform global path planning for the UAV.

[0129] S1. The environmental modeling of the present invention includes two main parts: baseline terrain modeling and radar threat area modeling. The baseline terrain modeling is performed using the mountain function, and the mathematical expression is as follows:

[0130]

[0131] Where: z(x,y) is the terrain height at (x,y), h i is the height of the ith peak, (x i ,y i ) is the center coordinate of the i-th peak, x ni and ni are the attenuation of the i-th peak in the x-direction and the y-direction respectively.

[0132] The radar threat area modeling adopts a hemispherical model, and the mathematical expression is as follows:

[0133]

[0134] Where: W j (x, y, z) is the jth radar threat area, (x j ,y j ,zj ) is the center coordinate of the jth radar threat area, R wj is the radius of the jth radar threat area.

[0135] S2. The present invention proposes detailed constraint conditions for UAV path planning to ensure that the UAV can fly stably in complex environments.

[0136] (1) Turning angle constraint

[0137] Turning angle constraint is also an important consideration in path planning. It limits the maximum turning angle μ of the drone during flight. max and the minimum turning angle μ min To adapt to complex terrain and ensure flight flexibility and stability, the turning angle μ i Need to meet:

[0138]

[0139] Where: a i =[x i -x i-1 ,y i -y i-1 ] T is the vector of the i-th path, (x i ,y i ,z i ) and (x i+1 ,y i+1 ,z i+1 ) represent the coordinates of the i-th path node and the i+1-th path node respectively.

[0140] (2) Maximum climb angle constraint

[0141] The climbing angle is a key factor in controlling the vertical motion stability of the UAV. The present invention sets a maximum climbing angle β max This constraint prevents the drone from tilting its head too high or too low when ascending or descending, thereby avoiding affecting the efficiency of the power system or causing aerodynamic instability. The turning angle β i Need to meet:

[0142]

[0143] (3) Highly constrained

[0144] The altitude constraint is to ensure that the UAV remains above a safe flight altitude to avoid potential threats caused by terrain obstacles. The present invention sets the minimum altitude above the ground to H min In order to adapt to the ups and downs of different terrains and ensure that the drone operates within the specified flight altitude to avoid low-altitude obstacles, the drone's flight altitude is z iNeed to meet:

[0145] z i >H min #

[0146] S3. The present invention comprehensively considers the range cost, altitude cost and threat area cost, which are key factors in ensuring the flight performance and safety of the UAV.

[0147] (1) Voyage cost

[0148] The range cost considers the distance the drone needs to fly from the starting point to the end point. Optimizing the range can directly reduce energy consumption and flight time, which is crucial for mission efficiency and economy. The mathematical expression is:

[0149]

[0150] (2) High cost

[0151] The altitude cost is to ensure that the drone maintains a stable flight trajectory as much as possible. Reducing the frequency of adjusting the flight altitude can significantly reduce energy consumption and flight risks. The mathematical expression is:

[0152]

[0153] (3) Threatened area costs

[0154] The threat cost is to prevent the drone from colliding with the mountain and entering the enemy's radar detection area. By keeping a safe distance from the mountain and radar, the drone can ensure smooth flight, effectively reduce the probability of being discovered and attacked, and ensure the successful completion of the mission.

[0155]

[0156] Based on the above analysis, the overall objective function of the UAV is:

[0157] f=min{ω 1 L+ω 2 H+ω 3 T}

[0158] Where: 1 ,ω 2 ,ω 3 is the weight coefficient of each cost function, and satisfies ω 1 +ω 2 +ω 3 =1.

[0159] S4. The improved dung beetle optimization algorithm is used for the global path planning of the UAV, where:

[0160] 1. DBO algorithm

[0161] (1) Ball-rolling dung beetle

[0162] In nature, dung beetles can use celestial light sources to roll their dung balls to keep moving in a straight line. When there are no obstacles, the position update of a rolling dung beetle is expressed as follows:

[0163] x i (t+1)=x i (t)+α×k×x i (t-1)+b×Δx

[0164] Δx=|x i (t)-X W |

[0165] 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.

[0166] If the ball hits an obstacle during rolling, the dung beetle will adjust its direction by dancing. The tangent function is used to simulate the dancing behavior, and the position update is expressed as follows:

[0167] x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)|

[0168] 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.

[0169] (2) Breeding dung beetles (breeding balls)

[0170] In order to provide a safe environment for offspring, female dung beetles will select a suitable area as an egg-laying site, which is simulated using a boundary selection strategy, which is defined as follows:

[0171] Lb * =max(X * ×(1-R),Lb),

[0172] Ub * =min(X *×(1+R),Ub)

[0173] 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.

[0174] After determining the egg-laying area, each female dung beetle only lays one egg in each iteration. This boundary range changes dynamically and is mainly determined by the R value. The position update of the breeding ball is expressed as follows:

[0175] B i (t+1)=X * +b 1 ×(B i (t)-Lb * )+b 2 ×(B i (t)-Ub * )

[0176] 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.

[0177] (3) Small dung beetle

[0178] When young dung beetles grow up, they will leave the safe area to look for food, so an optimal foraging area is established to guide them. The boundaries of the area are defined as follows:

[0179] Lb b =max(X b ×(1-R),Lb),

[0180] Ub b =min(X b ×(1+R),Ub)

[0181] 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.

[0182] The updated positions of these dung beetles are shown below:

[0183] x i (t+1)=x i (t)+C1 ×(x i (t)-Lb b )+C 2 ×(x i (t)-Ub b )

[0184] 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, C 2 is a random vector in (0,1).

[0185] (4) Stealing Dung Beetles

[0186] Some of these thief dung beetles will steal dung balls from other dung beetles. b is the optimal food source. b Nearby represents the best place to compete for food. The position update of the thief dung beetle is shown below:

[0187] x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |)

[0188] 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.

[0189] 2. Improved dung beetle optimization algorithm

[0190] Although the dung beetle algorithm has the characteristics of fast convergence speed and high solution accuracy, the random initialization method it adopts will reduce the diversity of the population; at the same time, its global exploration and local development capabilities are insufficient, and it is easy to fall into the local optimum. To this end, the present invention uses several strategies to enhance the optimization performance of DBO and avoid local optimal solutions. The improved algorithm is named HDBO, and the flow chart is as follows Figure 2 .

[0191] (1) Good Points Collection

[0192] Random initialization will lead to uneven distribution of individuals in the population, thus affecting the individuals' effective extraction of information from the solution space. The invention introduces the good point set to improve the generation strategy of the initial dung beetle population. The good point set method was proposed by Hua Luogeng et al., and its theory is:

[0193] G S is a unit cube of S-dimensional Euclidean space, that is, S∈GS , X=(x 1 ,x 2 ,x 3 ,…,x s ), where 0≤x i ≤1,i=1,2,…S,G S The point r in 1 ,r 2 ,…,r s ), let r∈G S , in the form of P n (k) = {(r 1 (k),…r s (k)),k=1,2,…n} satisfy Where C(r,ε) is a constant that is only related to r,ε(ε>0), then P n (k) is the set of good points, and r is a good point.

[0194] The optimal point set initialization can be used to uniformly and effectively select points, so that the individuals in the generated initial population are evenly distributed in the search space, and the population has the characteristics of diversity, and there is no crossover or overlap between individuals. Compared with random initialization, the initial position generated by this method is more uniform and converges faster.

[0195] (2) Improved sine algorithm

[0196] The sine algorithm (SA) is an optimization algorithm based on the mathematical sine function, which updates the position of the candidate solution by utilizing the periodic characteristics of the sine function. In the rolling ball dung beetle update rule, the tangent function is used to simulate the dancing behavior when there are obstacles. The position update strategy may be too random, and the position of the rolling ball dung beetle when θ is equal to 0, π / 2 or π is not taken into account. Based on the above situation, the present invention proposes an improved sine function, which replaces the tangent dancing strategy of the dung beetle. The improved sine function introduces the information of the optimal position of individual i so far and the global optimal position, which is conducive to enhancing the dung beetle's global and local exploration capabilities. Therefore, when encountering an obstacle in the rolling ball stage, the sine operation is used to guide the dung beetle to update its position, that is, the improved mathematical expression of formula (13) is as follows:

[0197] x i (t+1)=x i (t)+Asin(θ)|Bx i,best (t)-x i (t)|+C|x best (t)-x i (t)|

[0198]

[0199] Where a is a constant, B represents the weight, C is a uniformly distributed random number between 0 and 1, and x i,best (t) is the optimal position of individual i so far; x best (t) is the global optimal position.

[0200] In the modified sine function, Asin(θ)|x i,best (t)-x i (t)| contributes to the cognitive process of the search process, B|x best (t)-x i (t)| contributes a social component, combining the best of the individual and the best of the group during the search process, providing dung beetles with an efficient and promising direction when encountering obstacles.

[0201] (3) Combining the strategy of Lévy flight and Brownian motion

[0202] Levy flight is a special random walk process, and the probability distribution of its step length conforms to the characteristics of heavy-tailed probability distribution. The introduction of Levy flight will produce random movements with longer jumps and multiple mutation directions, which can improve the global search ability of the algorithm and help the algorithm jump out of the local optimum. The step length formula of Levy distribution is as follows:

[0203]

[0204] 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:

[0205]

[0206] Where: Γ is the standard gamma function.

[0207] Brownian motion is a random motion with shorter steps, and is a random process that follows a Gaussian distribution. When targets are sparse and the search range is wide, Levy flight can cover a larger search area due to its long-distance "jumps", explore unknown or changing environments, and avoid over-concentration on a small area. When targets are densely distributed, the random small steps of Brownian motion help to explore local areas in detail. Studies have shown that in some cases, a search strategy that combines Levy flight and Brownian motion may be more effective than a single strategy.

[17] Therefore, Lévy flight and Brownian motion are introduced into the position update of the stealing dung beetle, and the improved mathematical expression of formula (20) is as follows:

[0208] x i (t+1)=ω×levy×X b +Bl×S×g×(xi (t)-X * |+|x i (t)-X b |)

[0209] Where: Levy is Levy flight, Bl is Brownian motion.

[0210] The stealing behavior is the competition for food in the best foraging area by thieves. By introducing the nonlinear adjustment parameter ω, the searcher's dependence on its position can be effectively changed, thereby enhancing the efficiency of the global search. The expression is:

[0211]

[0212] (4) Simplex method

[0213] The simplex method (SM) is an unconstrained direct optimization algorithm, also known as the variable polyhedron search method. It has strong local search capabilities and seeks the optimal solution to the problem through geometric transformations such as reflection, expansion, and contraction. Each operation will replace the current worst solution with a better solution. Assume x c is the optimal point x g and the suboptimal value x b The center of x s It's the worst point.

[0214] Reflection operation: x r =x c +α(x c -x s ), x r It is the reflection point, and the reflection coefficient α is usually 1.

[0215] Expansion operation: x e =x c +γ(x r -x c ), x e is the expansion point, and the expansion coefficient γ is usually 2.

[0216] External contraction operation: x t =x c +β(x s -x c ), x t It is the external contraction point, and the external contraction coefficient β is 0.5.

[0217] Inner contraction operation: x w =x c -β(x s -x c ), x w It is the internal contraction point, and the internal contraction coefficient β is 0.5.

[0218] The basic steps of the simplex method are:

[0219] Step 1: Calculate the midpoint: Find the worst position x s , calculate the current optimal position x g and the second best position x b The midpoint x c , this midpoint is used for subsequent reflection and extension operations.

[0220] Step 2: Reflection operation: Calculate the reflection point x using the reflection formula r , if the response of the reflection point is better than the current optimal solution, an expansion operation is performed.

[0221] Step 3: Extension operation: If the fitness of the reflection point is better than the current optimal solution, calculate the extension point x e If the fitness of the extension point is better, then choose x e as the new position, otherwise select the reflection point x r .

[0222] Step 4: External contraction operation: If the fitness of the reflection point is not better than the current optimal solution, calculate the external contraction point x t If the fitness of the external contraction point is better than the worst position x s , then select x t As new location.

[0223] Step 5: Internal contraction operation: If the fitness of the reflection point is between the current optimal solution and the worst solution, calculate the internal contraction point x w If the fitness of the internal contraction point is better than the worst position x s , then select x w as the new position, otherwise choose the external contraction point x t .

[0224] Therefore, the reflection operation can expand the scope and make the worst point explore the new solution space position; the expansion operation is used to further expand the scope, especially when the reflection point shows improved fitness, it can make the current optimal value point jump out of the local extreme point and find a better solution; and the contraction operation is used to refine the search, especially when the reflection point or the expansion point does not show improvement, the contraction operation can pull the worse point back to a better position, improving the local search ability and optimization ability of the algorithm. The present invention adopts the simplex method to update the optimal position, the suboptimal position and the worst position, helping the algorithm to improve the worst position and jump out of the local optimal solution.

[0225] (5) Adaptive reverse learning

[0226] Opposition-Based Learning (OBL) is an effective method to enhance the optimization ability of various optimization algorithms. The core idea is to simultaneously calculate candidate solutions and their reverse solutions to increase the probability of finding the global optimal solution, thereby accelerating the convergence speed of the optimization algorithm. Extending reverse learning to D-dimensional space, for a solution x=(x 1 ,x 2 ,…,x D ), its reverse point is defined as:

[0227]

[0228] Where: i∈[1,2,…D], a i and b i are the lower and upper bounds of the i-th dimension respectively.

[0229] Quasi-Opposition-Based Learning (QOBL) is a variant of OBL. Studies have shown that quasi-opposition-based learning is more effective than reverse solution in finding the global optimal solution. The quasi-reverse solution is defined as:

[0230]

[0231] Quasi-reflection learning proposes a new quasi-reflection learning mechanism (Quasi-Reflection-Based Learning, QRBL) based on OBL and QOBL. The quasi-reflection solution is obtained based on the quasi-reflection solution. The quasi-reflection solution is defined as follows.

[0232]

[0233] However, when the optimal solution x best When approaching the solution x, the optimization algorithm is in the interval The search efficiency is better when the optimal solution is close to the reverse solution. When the optimization algorithm is in the interval Therefore, the present invention uses an adaptive reverse learning (AdaptiveOpposition-Based Learning, AOBL)

[20] It uses the prior information of the optimal solution to adaptively adjust the reverse search interval, improving the algorithm's global search capability and convergence speed. The definition is as follows:

[0234]

[0235] Where: d(x 1 -x 2)=|x 1 -x 2 | is the distance calculation function.

[0236] In the present invention, an adaptive reverse learning strategy is used to reversely perturb the top 20% of the dung beetle population individuals in terms of fitness, stimulating the dung beetle individuals to achieve global search in a wider range and have the ability to jump out of the local optimum. The dung beetles before and after the update are compared, and if the individual is better, the previous individual is replaced.

[0237] Example 2

[0238] 1. Modeling the UAV flight environment

[0239] To study the path planning of UAV, it is necessary to convert its actual flight environment into a three-dimensional space model. Good terrain environment modeling can provide key information for UAV, so that it can effectively avoid obstacles, respond to threats and ensure flight safety when performing tasks. The path planning environment modeling of the present invention includes two main parts: baseline terrain modeling and radar threat area modeling.

[0240] 2. Establish constraints

[0241] In the path planning of UAV, the key to ensure safe and efficient navigation is to set constraints reasonably. Considering the performance limitations of UAV and the challenges of terrain environment, the present invention proposes detailed constraints from three aspects: turning angle constraint, maximum climbing angle constraint and altitude constraint to ensure that the UAV can fly stably in complex environment.

[0242] 3. Establish the objective function

[0243] The objective function is a key tool for evaluating and optimizing flight paths, and usually involves multiple dimensions of evaluation to ensure that the drone's path is both efficient and safe. The present invention comprehensively considers the range cost, altitude cost, and threat area cost, which are all key factors in ensuring the flight performance and safety of the drone.

[0244] 1. Use the improved dung beetle optimization algorithm for UAV global path planning.

[0245] The present invention constructs two sets of terrain environments to simulate the flight scenarios of UAVs. The radar is used as a threat to the UAV. The mission space size is 200×200×25, the starting point is (0, 0, 10), and the target point is (200, 200, 20). When the algorithm is run independently 30 times, the generated range cost, average range, and algorithm running time are compared, as shown in Table 1.

[0246] Figure 3 and Figure 4The following are the simulation results of the drone path planning under two sets of terrain. As can be seen from the figure, the paths planned by the DBO algorithm and the HDBO algorithm can bypass the mountains and radar detection areas, allowing the drone to successfully complete the mission and reach the set target point. However, compared with the DBO algorithm, the route planned by the HDBO algorithm is shorter, which can save the drone time to complete the mission and reduce energy consumption. At the same time, the path planned by the HDBO algorithm has relatively small height changes, and the twists and turns are smaller and smoother, which makes the path quality better.

[0247] Table 1 Algorithm test results comparison

[0248] 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

[0249] As can be seen from Table 3, the average path length planned by the HDBO algorithm is shortened by about 7.48% compared with the DBO algorithm, the shortest path is shorter, and the average flight cost is also lower, which is reduced by about 1.46%. Figure 5 and Figure 6 It is the iterative convergence diagram under two sets of environments. It can be seen that the HDBO algorithm can obtain a lower fitness value in the early stage and converge quickly. It is easier to find the global optimum in the later stage, and the planned path is more stable and of high quality.

[0250] 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 path planning method for unmanned aerial vehicles based on an improved dung beetle algorithm, characterized in that: Here are the steps: S1. Modeling the UAV flight environment; S2. Establish constraints; S3, establish the objective function; S4. Use the improved dung beetle optimization algorithm to perform global path planning for the UAV.

2. The method for three-dimensional path planning of a UAV using an improved dung beetle algorithm as claimed in claim 1, characterized in that: The environmental modeling in step S1 includes: S1.

1. Benchmark terrain modeling: The peak function is used, and the mathematical expression is as follows: Where: z(x,y) is the terrain height at (x,y), h i is the height of the ith peak, (x i ,y i ) is the center coordinate of the i-th peak, x ni and ni are the attenuation of the i-th peak in the x-direction and the y-direction respectively; S1.

2. Radar threat area modeling: The model uses a hemispherical model, and the mathematical expression is as follows: Where: W j (x,y,z) is the jth radar threat area, (x j ,y j ,z j ) is the center coordinate of the jth radar threat area, R wj is the radius of the jth radar threat area.

3. The method for three-dimensional path planning of unmanned aerial vehicle using the improved dung beetle algorithm as claimed in claim 1, characterized in that: In step S2, detailed constraints are proposed for the UAV path planning to ensure that the UAV can fly stably in complex environments, including S2.

1. Turning Angle Constraint Limit the maximum turning angle μ of the drone during flight max and the minimum turning angle μ min , turning angle μ i satisfy: Where: a i =[x i -x i-1 ,y i -y i-1 ] T is the vector of the i-th path, (x i ,y i ,z i ) and (x i+1 ,y i+1 ,z i+1 ) represent the coordinates of the i-th path node and the i+1-th path node respectively; S2.2, Maximum climb angle constraint Set the maximum climb angle β max , turning angle β i satisfy: S2.

3. Height Constraint Set the minimum ground clearance to H min , the flight altitude of the drone is z i satisfy: z i >H min #。 4. The method for three-dimensional path planning of unmanned aerial vehicle using the improved dung beetle algorithm as claimed in claim 1, characterized in that: In step S3, the range cost, altitude cost and threat area cost are comprehensively considered: S3.

1. Flight cost: Considering the flight distance required by the drone from the starting point to the end point, the mathematical expression is: S3.2, Altitude cost: Ensure that the UAV maintains a stable flight trajectory and reduce frequent adjustments to the flight altitude. The mathematical expression is: S3.3, Threat area cost: Prevent the drone from colliding with the mountain and entering the enemy's radar detection area; by keeping a safe distance from the mountain and radar, the drone can ensure smooth flight, effectively reduce the probability of being discovered and attacked, and ensure the successful completion of the mission; Based on the above analysis, the overall objective function of the UAV is: f=min{ω1L+ω2H+ω3T} Where: v1, ω2, ω3 are the weight coefficients of each cost function, and satisfy ω1+ω2+ω3=1.

5. The method for three-dimensional path planning of unmanned aerial vehicle using improved dung beetle algorithm as claimed in claim 1, characterized in that: In step S4, the dung beetle algorithm includes: (1) Ball-rolling 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; The tangent function is used to simulate 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; (2) Breeding dung beetles Spawning areas are simulated using a boundary selection strategy, which is 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 position update of the breeding 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; (3) Small dung beetle 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, xx(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); (4) Stealing Dung Beetles X b is the optimal food source, X in the algorithm b Nearby represents the best place to compete for food. The position update of the thief dung beetle is shown below: 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.

6. The method for three-dimensional path planning of a UAV using an improved dung beetle algorithm as claimed in claim 5, characterized in that: Optimizing the Dung Beetle Algorithm through Good Point Sets: G S is a unit cube of S-dimensional Euclidean space, that is, S∈G S ,X=(x1,x2,x3,…,x s ), where 0≤x i ≤1,i=1,2,…S,G S The point r in the s ), let r∈G S , in the form of P n (k)={(r1(k),…r s (k)),k=1,2,…n} satisfy Where C(r,ε) is a constant that is only related to r,ε(ε>0), then P n (k) is the set of good points, and r is a good point.

7. The method for three-dimensional path planning of a UAV using an improved dung beetle algorithm as claimed in claim 5, characterized in that: Optimizing the dung beetle algorithm using the sine algorithm: The information of the optimal position of individual i so far and the global optimal position is introduced. When encountering an obstacle in the rolling stage, the sine operation is used to guide the dung beetle to update its position. The mathematical expression is as follows: x i (t+1)=x i (t)+Asin(θ)|Bx i,best (t)-x i (t)|+C|x best (t)-x i (t)| Where a is a constant, B represents the weight, C is a uniformly distributed random number between 0 and 1, and x i,best (t) is the optimal position of individual i so far; x best (t) is the global optimal position; In the modified sine function, Asin(θ)|x i,best (t)-x i (t)|Contribution to the cognition in the search process becomes, B|x best (t)-x i (t)|Contribute social components, combining the best of individuals and the best of the group in the search process.

8. The method for three-dimensional path planning of a UAV using an improved dung beetle algorithm as claimed in claim 5, characterized in that: Combining Levy flight and Brownian motion strategy to optimize the dung beetle algorithm: 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; Introducing Lévy flight and Brownian motion in the position update of the stealing dung beetle, the improved mathematical expression is as follows: x i (t+1)=ω×Levy×X b +Bl×S×g×(x i (t)-X * |+|x i (t)-X b |) Where: Levy is Levy flight, Bl is Brownian motion; Introducing the nonlinear adjustment parameter ω, the expression is:

9. The method for three-dimensional path planning of a UAV using an improved dung beetle algorithm as claimed in claim 5, characterized in that: Optimizing the Dung Beetle Algorithm via the Simplex Method: Assume x c is the optimal point x g and the suboptimal value x b The center of x s It’s the worst point; Reflection operation: x r =x c +α(x c -x s ), x r is the reflection point, and the reflection coefficient α is 1; Expansion operation: x e =x c +γ(x r -x c ), x e is the expansion point, and the expansion coefficient γ is 2; External contraction operation: x t =x c +β(x s -x c ), x t It is the external contraction point, and the external contraction coefficient β is 0.5; Inner contraction operation: x w =x c -β(x s -x c ), x w is the internal contraction point, and the internal contraction coefficient β is 0.5; The basic steps of the simplex method are: Step 1: Calculate the midpoint: Find the worst position x s , calculate the current optimal position x g and the second best position x b The midpoint x c , this midpoint is used for the following reflection and extension operations; Step 2: Reflection operation: Calculate the reflection point x using the reflection formula r , if the fitness of the reflection point is better than the current optimal solution, then the expansion operation is performed; Step 3: Extension operation: If the fitness of the reflection point is better than the current optimal solution, calculate the extension point x e ; If the fitness of the extension point is better, choose x e as the new position, otherwise select the reflection point x r ; Step 4: External contraction operation: If the fitness of the reflection point is not better than the current optimal solution, calculate the external contraction point x t ; If the fitness of the external contraction point is better than the worst position x s , then select x t As a new location; Step 5: Internal contraction operation: If the fitness of the reflection point is between the current optimal solution and the worst solution, calculate the internal contraction point x w ; If the fitness of the internal contraction point is better than the worst position x s , then select x w as the new position, otherwise choose the external contraction point x t .

10. The method for three-dimensional path planning of unmanned aerial vehicle using improved dung beetle algorithm as claimed in claim 5, characterized in that: Optimizing the Dung Beetle Algorithm via Adaptive Backward Learning: For a solution x=(x1,x2,…,x D ), its reverse point is defined as: Where: i∈[1,2,…D], a i and b i are the lower and upper bounds of the i-th dimension respectively; The quasi-reverse solution is defined as: The quasi-reflective solution is defined as follows: Adaptive reversal point The definition is as follows: Wherein: d(x1-x2)=|x1-x2| is the distance calculation function.

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