A method for UAV path planning in mountainous environments

Abstract

This invention discloses a path planning method for unmanned aerial vehicles (UAVs) in mountainous environments. First, the mountainous environment is modeled, including the planning area, terrain, and visible obstacle threats. During UAV flight, constraints such as flight length, flight cost, and obstacle avoidance are met. The optimal path for the UAV is found by minimizing the objective function. The dung beetle algorithm is improved by employing a composite chaotic mapping method to enhance the initialization of the random population and using a nonlinear convergence method to adjust the oviposition boundary of breeding dung beetles and the foraging boundary of young dung beetles. A gradient descent population adjustment method is introduced to dynamically adjust the proportion of each dung beetle species in the population during iteration. Based on the improved dung beetle algorithm, the objective function for the optimal UAV path is solved to obtain the path planning result. This invention enables UAVs to plan shorter paths, improve flight safety, and reduce flight costs in mountainous environments, effectively improving the efficiency of UAVs in mountainous flight.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path planning, and more specifically to a method for UAV path navigation in mountainous environments. Background Technology

[0002] In recent years, unmanned aerial vehicles (UAVs), as small autonomous aircraft that do not require direct piloting, have been able to perform tasks such as battlefield reconnaissance and intelligence gathering when necessary. Compared to manned operations, they offer lower reconnaissance costs and higher security, thus possessing broad application prospects. In modern warfare, information warfare and intelligence warfare are undoubtedly more crucial. Due to their small size, portability, ease of operation, and low cost, UAVs play a vital role in early warning, jamming, countermeasures, and communication in small-scale airspace reconnaissance battlefields.

[0003] In the aforementioned application scenarios, the UAV is required to select a flight path that is safe, cost-effective, and highly feasible, based on constraints such as mission requirements, the distribution and size of known obstacles, UAV spatial accessibility, and maximum flight distance. In the UAV path planning problem in mountainous environments, the main considerations are flight distance, minimum flight altitude (i.e., flight safety), and path smoothness. Flight distance is represented by the path length. Reducing the path length can improve the efficiency of the UAV in completing the mission, thereby reducing the probability of being detected by detection equipment; it can also reduce energy consumption, thus lowering costs. Flight safety cost is represented by the minimum flyable altitude. To ensure the safety of the UAV's flight and avoid collisions with static obstacles along the flight path, the UAV must fly in a relatively safe space. Path smoothness cost is determined based on the steep and undulating terrain characteristics of mountainous environments. In this environment, the UAV's flight path must meet its own flight angle capabilities, enabling the UAV to reach the designated mission location as safely, efficiently, and quickly as possible.

[0004] For the UAV path planning problem facing complex mountainous environments with various obstacles and constraints, swarm intelligence optimization algorithms are widely used in UAV path planning due to their strong robustness, simple structure, and efficient integration with other algorithms. This patent mainly uses an improved dung beetle optimization algorithm for UAV path planning. Currently, many swarm intelligence algorithms have been applied to UAV path planning, among which typical intelligent optimization algorithms include Particle Swarm Optimization (PSO), Grey Wolf Algorithm (GWO), and Hippo Algorithm (HO). These algorithms are easy to implement, have low overhead, and fast optimization speed, and can achieve high-quality path planning solutions for UAVs under many constraints in many situations. Xing Na et al. addressed the issues of long search time and poor optimal solution accuracy in ant colony optimization by designing a novel dynamic search inducer. This increases the diversity of the initial population and improves the convergence speed in later stages, but the convergence accuracy is not significantly improved. Niu Qinyu et al., addressing the low efficiency and poor convergence of traditional genetic algorithms in 3D path planning, proposed an optimized genetic algorithm integrating artificial potential field and simulated annealing. This results in shorter planned paths and improved convergence, but the search efficiency decreases when obstacles and target points are close. The gray wolf optimization algorithm is a novel swarm intelligence biomimetic algorithm based on simulating the hierarchical mechanism and hunting behavior of gray wolves in nature. It features simple principles, parallelism, low parameter adjustment requirements, and no need to obtain gradient information, possessing strong global search capabilities. However, almost all swarm intelligence algorithms share a common problem: when solving complex engineering optimization problems, it is difficult to find a suitable balance between local optima and global search. Too high a balance leads to poor search capability, while too low a balance results in premature stagnation in local optima. Therefore, while the above algorithms have certain advantages in solving UAV path planning problems, they are inefficient in planning feasible paths when facing complex obstacle avoidance, and are prone to getting trapped in local optima too early, thus failing to obtain effective feasible flight path solutions. Based on this, researching how to quickly obtain effective optimal paths for UAVs in complex three-dimensional flight spaces such as mountainous terrain, and reducing UAV flight costs, is of great value. Summary of the Invention

[0005] Purpose of the invention: This invention provides a method for UAV path planning in mountainous environments, which solves the problem of optimizing UAV path planning in mountainous environments.

[0006] Technical solution: The present invention provides a method for unmanned aerial vehicle (UAV) path navigation in mountainous environments, comprising the following steps:

[0007] (1) Construct an environment model, including a mountain model and a static obstacle model, to simulate the obstacle threat posed by the complex mountain environment and three-dimensional obstacles to the UAV in the real environment;

[0008] (2) Construct multi-dimensional resource constraints for the UAV platform, including UAV flight path length constraints, flight space safety constraints, and path smoothness constraints;

[0009] (3) Under the condition of multi-dimensional resource constraints of UAV, with the goal of minimizing flight cost, construct the UAV optimal path objective function; the objective function is composed of three weighted parts: path length cost function, path smoothness cost function, and path flight safety cost function, plus a collision cost penalty function.

[0010] (4) Improve the dung beetle algorithm: improve the initialization of the random population by using a composite chaotic mapping method, adjust the oviposition boundary of the breeding dung beetle and the foraging boundary of the dung beetle by using a nonlinear convergence method, introduce the gradient descent population adjustment method to dynamically adjust the proportion of each dung beetle species in the population during the iteration process, and solve the objective function of the UAV's optimal path based on the improved dung beetle algorithm to obtain the path planning result;

[0011] (5) The flight trajectory is processed using a cubic spline interpolation smoothing method. The flight path includes the starting point p. s (x s y s , z s ), endpoint p z (x z y z , z z ) and passing through point p o (x o y o , z o ), to obtain the UAV trajectory plan, where p o (x o y o , z o () is the optimal solution The corresponding three-dimensional coordinate values.

[0012] Furthermore, the mountain model described in step (1) is as follows:

[0013] Terrain data is read to generate a mountain model. The minimum flight altitude of the drone is ≥1km, and the maximum flight altitude is ≤3km. The mountain environment model is simulated using scatter fitting and two-dimensional interpolation, as shown in the following formula:

[0014]

[0015] Among them, F ij (x i,y j )=z ij The z-direction value is given in the data table; coefficient a ijkl Solve using the following system of equations:

[0016] F ij (x i ,y j )=z ij and F ij (x i+1 ,y j )=z (i+1)j Obtain the value at the endpoint in the x-direction;

[0017] F ij (x i ,y j+1 )=z i(j+1) and F ij (x i+1 ,y j+1 )=z (i+1)(j+1) Obtain the value at the endpoint in the y-direction;

[0018] In summary, the interpolated coordinates in the z-direction are obtained, thus yielding the mountain model.

[0019] Further, the static obstacle model described in step (1) is:

[0020] The threat environment posed by static obstacles to UAVs is simulated using an n×3 matrix, as shown in the following formula:

[0021]

[0022] In the formula, a i b i R represents the coordinate information of the i-th static obstacle in space. i This represents the radius of the i-th static obstacle.

[0023] Furthermore, the constraints of the UAV platform described in step (2) are as follows:

[0024]

[0025] Among them, l o γ represents the length of the o-th segment of the flight path, L represents the flight distance of the UAV, and the total flight path of the UAV consists of n navigation points; o , The yaw and pitch angles during the drone's flight; (x o ,y o ,z o) represents the current position coordinates of the UAV; d represents the vertical distance between the center of the static obstacle and the two nearest adjacent nodes; R represents the obstacle radius; and M represents the UAV flight safety threshold.

[0026] Furthermore, the objective function for the optimal path of the UAV in step (3) is:

[0027] F C =ω1*f L +ω2*f E +ω3*f S +ω4f V

[0028] In the formula, ω1, ω2, ω3, and ω4 represent f respectively. L f E f S f V The weighting coefficients are ω1+ω2+ω3+ω4=1;

[0029] Track length cost function:

[0030]

[0031] In the formula, l o This corresponds to the length of the o-th track segment;

[0032] Path smoothing cost function:

[0033]

[0034] Where, φ o , These are the yaw and pitch angles during the drone's flight.

[0035] Flight safety cost function:

[0036]

[0037] Among them, f o d represents the safety cost function between two adjacent navigation points. o R represents the straight-line distance between this flight path and the center of its nearest obstacle, M is the set safety threshold constant, and R i Represents the radius of a static obstacle;

[0038] Collision penalty cost function:

[0039] f V =V×P f

[0040] Where V∈(0,1) is a constant, representing the penalty value; P fCharacterizes the penalty coefficient.

[0041] Furthermore, the process of improving the initialization of the random population by using a composite chaotic mapping in step (4) is as follows:

[0042] Logistic-Sine-Cosine mapping is used to improve the coordinate distribution of the random x-axis and y-axis; Tent mapping is used to improve the coordinate distribution of the z-axis.

[0043] X LSC =cos(π*4rx*(1-x)+(1-r)*sin(πx)-0.5))

[0044] Y LSC =cos(π*4rx*(1-x)+(1-r)*sin(πx)-0.5)), r∈(0,1)

[0045] Tent mapping:

[0046]

[0047] Furthermore, the process of adjusting the oviposition boundary of the breeding dung beetle and the foraging boundary of the dung beetle using the nonlinear convergence method in step (4) is as follows:

[0048] Calculate the objective function value for each dung beetle in the initial population based on the planned drone path objective function, and denote the optimal or minimum value as Pop. * And record the corresponding three-dimensional coordinates at this time.

[0049] Let the initial iteration count t = 1, and set the size of the random number r1;

[0050] Determine the value of r1. If r1 < 0.9, the dung beetle updates its position based on the rolling ball search behavior and sets a natural random number α1, which is a random value between 0 and 1. If α1 > 0.1, set α = 1; otherwise, set α = -1.

[0051] Generate a random number r2 between 0 and 0.2, and a random number r3 between 0 and 1;

[0052] The search is performed using the following search equation:

[0053]

[0054] in, This represents the position of the i-th dung beetle in the (t+1)-th iteration; This represents the position of the i-th dung beetle in the t-th iteration; Δx represents the position of the i-th dung beetle in the (t-1)-th iteration; Δx is used to simulate natural factors such as light intensity. Indicates the worst-case position globally;

[0055] If r1 > 0.9, the dung beetle determines its search strategy by simulating dancing. It sets a random number r4 to a random integer between 0 and 180. If r4 = 0||90||180, it searches for the location according to the above search equation; otherwise, it searches using the following search equation:

[0056]

[0057] Where tan(aa) is the positional offset of the dung beetle when it encounters an obstacle;

[0058] Breeding dung beetles update their location through reproductive behavior; the boundaries of their breeding zones are set in the following ways:

[0059]

[0060] Among them, Lb * Ub represents the lower boundary of the breeding area. * Indicates the upper boundary of the breeding area. Here, f1 represents the location information corresponding to the current local optimal solution, and f1 is the boundary convergence factor of the breeding region. A nonlinear convergence boundary method is used, where f1 is the boundary convergence factor. k is Lb * and Ub * Any integer between;

[0061] Breeding dung beetles have arrived at the production area to incubate their eggs. Their locations have been updated as follows:

[0062]

[0063] in, This represents the position of the i-th hatching egg in the (t+1)-th iteration. This represents the position of the i-th hatching egg in the t-th iteration. and Each of the above represents a 1×3 dimensional independent random vector.

[0064] After the eggs hatch, dung beetles emerge and update their location through foraging behavior; the optimal foraging area is determined using the following methods:

[0065]

[0066] In the formula, Ub ** and Lb ** Let f1 and f2 represent the upper and lower boundaries of the optimal foraging region, respectively, and f2 represent the boundary convergence factor of the foraging region. Also using the nonlinear convergence boundary method, let f2 = f2 + ...

[0067] The dung beetle reaches the foraging area to forage for food, updating its location based on its foraging behavior:

[0068] Set a random number r5, which follows a normal distribution; generate a random vector ranging from 0 to 1.

[0069]

[0070] in, Let be the position of the i-th dung beetle in the (t+1)-th iteration. Let be the position of the i-th dung beetle in the t-th iteration; another group of dung beetles will engage in theft, and their positions will be updated based on the theft behavior.

[0071] Randomly generate a random vector of size 1×3 that follows a normal distribution. Generate a fixed constant r8;

[0072] The dung beetle steals and updates its location based on the act of theft.

[0073]

[0074] Calculate the objective function value of each dung beetle in the newly generated population Pop(i+1), and denote the minimum value as Pop. fit Comparing Pop fit and The size, and Update to the smaller value between the two.

[0075] Furthermore, the process of dynamically adjusting the proportion of each dung beetle species in the population during the iteration process using the gradient descent population adjustment method described in step (4) is as follows:

[0076] After each iteration, the best individual in the population is selected and replaced with the best individual in the current population; after every quarter of the total number of iterations, the proportion of rolling dung beetles is reduced, while the proportions of breeding dung beetles and small dung beetles are increased respectively.

[0077]

[0078] In the formula, r Percent When initializing the population, the proportion of the dung beetle in the population, v1, v2, and v3 are weight constants related to the number of iterations; when the number of iterations t equals MAX it Will As the optimal solution.

[0079] The beneficial effects are as follows: Compared with the prior art, the present invention has the following advantages: The present invention uses flight path length, flight path smoothness angle, flight altitude, and flight safety as performance indicators, and has established a three-dimensional improved optimization model under the constraints of mountainous environment and static obstacles; by constructing a weighted cost function and setting weight coefficients, an optimization model with a single performance indicator is obtained; in order to find the optimal solution in such a widely applicable three-dimensional problem model, based on the fact that the swarm intelligence optimization algorithms proposed in recent years have low search efficiency and are prone to getting trapped in local optima when solving three-dimensional and higher-dimensional problems, an improved dung beetle algorithm with better balance, convergence, and optimization ability is proposed; thus solving the optimal problem of UAV path planning in mountainous environment. Attached Figure Description

[0080] Figure 1 This is a flowchart of the present invention;

[0081] Figure 2 This is the flowchart of the UAV path planning method based on the improved dung beetle search algorithm in this invention;

[0082] Figure 3 An environmental model will be adopted for the implementation of this invention;

[0083] Figure 4 The convergence curve f1 is the convergence factor of the breeding region;

[0084] Figure 5 The convergence curve f2 represents the convergence factor of the foraging area.

[0085] Figure 6 The simulation results of this invention are shown in the figure, where (a) is a three-dimensional path diagram of the UAV; (b) is a top view of the UAV path; and (c) is a path function convergence curve. Detailed Implementation

[0086] The present invention will now be described in further detail with reference to the accompanying drawings.

[0087] like Figure 1 The present invention proposes a method for UAV path planning in mountainous environments, which solves the problem of optimizing UAV path planning in mountainous environments. The specific implementation process is as follows:

[0088] Step 1: Build an environment model, including a mountain model and a static obstacle model, to simulate the obstacle threat posed by the complex mountain environment and three-dimensional obstacles to the drone in the real environment.

[0089] Terrain data is read to generate a mountain model. The minimum flight altitude of the drone is ≥1km, and the maximum flight altitude is ≤3km. The mountain environment model is simulated using scatter fitting and two-dimensional interpolation, as shown in the following formula:

[0090]

[0091] Among them, F ij (x i ,y j )=z ij For the z-direction values ​​in the given data table, the coefficient a is... ijkl Solve using the following system of equations:

[0092] F ij (x i ,y j )=z ij and F ij (x i+1 ,y j )=z (i+1)j Obtain the value at the endpoint in the x-direction; F ij (x i ,y j+1 )=z i(j+1) and F ij (x i+1 ,y j+1 )=z (i+1)(j+1) The values ​​at the endpoints in the y-direction are obtained; that is, the interpolated coordinates in the z-direction are obtained, thus deriving the mountain model.

[0093] The threat environment posed by static obstacles to UAVs is simulated using an n×3 matrix, as shown in the following formula:

[0094]

[0095] In the formula, a i b i R represents the coordinate information of the i-th static obstacle in space. i This represents the radius of the i-th static obstacle.

[0096] Step 2: Construct multi-dimensional resource constraints for the UAV platform, including constraints on the length of the UAV flight path, the safety constraints of the flight space, and the constraints on the smoothness of the path.

[0097] Because drones possess high maneuverability, their position in space is constantly changing, and their flight altitude is not unlimited. Therefore, the maximum flight altitude of a drone is set to H. C The flyspace C is represented as: (x,y,z)∈{(x,y)|X min ≤x≤X max ,Y min ≤y≤Y max H min ≤z≤H C};X min X maxY min Y max H represents the flight space range of the drone. min H D The minimum and maximum safe flight altitudes for the UAV are given by the following values: The total length of the UVA's flight path is... Due to limitations in its own weight and the amount of energy it can carry, the distance L is not infinite; L < L< max In the formula L max This is the maximum length of a drone flying in a straight line when unloaded. Among them, (x o y o , z o ) represents the current coordinates of the drone; v o This indicates the deflection angle during the drone's flight. This refers to the pitch angle during drone flight. Drones need to maintain their maximum climb angle during flight, especially in mountainous terrain with steep slopes and overlapping peaks. If the pitch angle is too large, the drone may exceed its maximum climb speed, causing it to lose control and collide with obstacles in mountainous environments. Conversely, an excessive yaw angle can lead to excessive unilateral force and load, causing imbalance and posing significant safety hazards and risks to the flight control module. Therefore, both pitch and yaw angles should be below their maximum values.

[0098] Step 3: Under the multiple constraints of the UAV, construct the objective function for the optimal UAV path by taking the shortest flight time as the objective and combining the UAV's path length:

[0099] F C =ω1*f L +ω2*f E +ω3*f S +ω4f V

[0100] The objective function is the flight path length cost function f. L Flight path smoothness cost function f E Flight safety cost function f S and collision cost penalty function f V The components are defined by ω1, ω2, ω3, and ω4, which represent the weight coefficients of each component. In this invention, different tasks can use different weight coefficients, but the sum of the weight coefficients must be 1. Furthermore, it is worth noting that there can be multiple objective functions set for different UAV path planning problems.

[0101] In UAV trajectory planning, a shorter trajectory length results in shorter flight time and less energy consumption. The flight path length cost of the entire trajectory segment is the sum of the path length costs of each sub-segment. Calculating the length of the o-th trajectory segment requires calculating the Euclidean distance along the o-th trajectory segment. To reduce computational complexity, this invention sets n navigation points to calculate the path length cost of the entire trajectory segment. The specific formula for calculating the flight path length cost function is as follows:

[0102]

[0103] In the formula, l o This represents the length of the corresponding o-th track segment.

[0104] The smoothness of the flight path is crucial for the stability of a drone, especially in environments with significant terrain undulations and steep slopes. Generally, maintaining a relatively suitable flight angle is necessary to ensure the stability of the drone during mission execution. Turning and yaw angles during drone flight can disrupt its stability and maneuverability. Instantaneous turning angles in drone trajectory planning include the pitch angle in the vertical direction. and horizontal yaw angle φ o Furthermore, these two parameters satisfy the angle constraints during use. The path smoothness cost function can be described by the following formula:

[0105]

[0106] During flight in mountainous environments, drones also need to avoid collisions with obstacles such as trees and rocks. Therefore, a flight safety cost function is constructed based on the distance *d* from the center point of each flight path to the center of the obstacle, the obstacle radius *R*, and the safety threshold *M*. The flight safety cost function is shown in the following equation:

[0107]

[0108] Among them, f o d represents the safety cost function between two adjacent navigation points. o R represents the straight-line distance between this flight path and the center of its nearest obstacle, M is the set safety threshold constant, and R i This represents the radius of a static obstacle.

[0109] When a drone is about to encounter an obstacle while flying in complex mountainous environments, it will automatically veer off course to avoid collisions with trees and rocks. A violation degree V and a penalty coefficient P are set. f .

[0110] Step 4: An improved dung beetle optimization search algorithm is used to solve for the objective function of the UAV's optimal path. This objective function is then used as the fitness function of the dung beetle optimization search algorithm. Iterative optimization is then employed to obtain the corresponding path planning results. Figure 2 As shown, it includes the following steps:

[0111] The dung beetle algorithm is inspired by the physiological behaviors of dung beetles in nature, including rolling balls, dancing, foraging, stealing, and reproducing. First, the rolling dung beetle navigates using celestial information (sun, moon), rapidly rolling its dung ball in a straight line. If the light is dim or completely dark, it will use dancing to choose its direction, quickly reaching a suitable area to nest and lay eggs. This behavior embodies the first inspiration for the algorithm. Several dung beetles are randomly distributed throughout the search space, each exploring it through continuous movement. After finding a suitable area, the reproducing dung beetle lays eggs within that area. Once the eggs hatch and mature, baby dung beetles emerge and forage for food in the surrounding environment. Additionally, some dung beetles engage in stealing to gain more food in the competition.

[0112] Initialize and define the population size N of the dung beetle population. Pop 、rolling ball dung beetle Num Dung beetle breeding Num Dung beetle x Num , dung beetle Num Number of iterations t, maximum number of iterations MAX it .

[0113]

[0114] Where POP(i) represents the position of the initial population. Let represent the coordinates of the i-th dung beetle (rolling, breeding, small, thieving) in three-dimensional space. This represents the position of the i-th dung beetle in the t-th iteration. These represent the upper and lower boundaries of the 3D flyable space, respectively. It is a 3-dimensional random vector between 0 and 1.

[0115] The initial population fly distribution is improved by using a composite chaotic mapping, and the random initial population position is improved by using the tent mapping and the Logistic-Sine-Cosine mapping, so that the 3D coordinates are generated uniformly in space.

[0116] Logistic-Sine-Cosine mapping:

[0117] X LSC=cos(π*4rx*(1-x)+(1-r)*sin(πx)-0.5)),

[0118] Y LSC =cos(π*4rx*(1-x)+(1-r)*sin(πx)-0.5)), r∈(0,1)

[0119] tent mapping:

[0120]

[0121] The composite chaotic mapping can effectively improve the problem of uneven initial population distribution. Compared with the single logistic chaotic mapping, this composite chaotic mapping has better ergodicity, randomness and distribution when solving 3-dimensional and higher-dimensional problems.

[0122] Calculate the objective function value for each dung beetle in the initial population based on the planned drone path objective function, and denote the optimal or minimum value as Pop. * And record the corresponding three-dimensional coordinates at this time.

[0123] Let the initial iteration number t = 1, and set the size of the random number r1.

[0124] Determine the value of r1. If r1 < 0.9, the rolling dung beetle updates its position by rolling the ball. Set a random number α1, which is a random value between 0 and 1. If α1 > 0.1, set the natural coefficient α = 1; otherwise, set α = -1. When α = 1, it means that the rolling dung beetle has not deviated from its direction. When α = -1, it means that the dung beetle's search direction has shifted.

[0125] The search behavior is conducted randomly within the entire defined search space to find the optimal breeding area. This is called the search or exploration phase. The algorithm can explore the surrounding area suitable for egg-laying at different step sizes, updating the position of the dung beetle by simulating light intensity. The specific steps of the search behavior are as follows:

[0126] Generate a random number r2 between 0 and 0.2, and a random number r3 between 0 and 1.

[0127] The search is performed using the following search equation:

[0128]

[0129] in, This represents the position of the i-th dung beetle in the (t+1)-th iteration; This represents the position of the i-th dung beetle in the t-th iteration; Δx represents the position of the i-th dung beetle in the (t-1)-th iteration; Δx is used to simulate natural factors such as light intensity. This indicates the worst position globally.

[0130] Since dung beetles are affected not only by light intensity but also by wind direction and uneven terrain, a probabilistic approach is adopted, setting a natural coefficient α. Similarly, a higher Δx value indicates weaker light intensity. r2 represents the deflection coefficient, and r3 represents a constant. The closer to the global worst-case position, the weaker the light, prompting the dung beetle to move away from that position. By setting Δx, the dung beetle can perform a global search of the entire space as much as possible in the early stages of the algorithm. On the other hand, it also enhances search performance, reduces the probability of entering local optima, and helps improve the efficiency of the dung beetle search algorithm for UAV path planning.

[0131] If r1 > 0.9, it means that the dung beetle encountered an obstacle while moving forward. Therefore, it can use dancing behavior to search for a new direction of movement. This behavior is to avoid static obstacles that occur during the drone's path planning process and prevent the algorithm from getting stuck in a local optimum.

[0132] Set the random number r4 to a random integer between 0 and 180. If r4 = 0||90||180, then perform the position search according to the above search equation; otherwise, perform the search according to the following search equation:

[0133]

[0134] Wherein, tan(aa) is the positional offset of the rolling dung beetle when it encounters an obstacle, representing the new rolling direction.

[0135] In nature, dung beetles push their dung balls to a safe and suitable location and hide them, providing a safe environment for their unhatched offspring. Once a suitable egg-laying area is found, the breeding dung beetle begins to lay its eggs, and all the hatched eggs are laid in a restricted area.

[0136] The boundaries of the breeding area for dung beetles can be set in the following way:

[0137]

[0138] Among them, Lb * Ub represents the lower boundary of the breeding area. * Indicates the upper boundary of the breeding area. The location information corresponding to the current local optimum is given, and f1 is the boundary convergence condition of the breeding region. The convergence curve is shown in Figure 1. Figure 4 As shown.

[0139] Breeding dung beetles have arrived at the production area to incubate their eggs. Their locations have been updated as follows:

[0140]

[0141] in, This represents the position of the i-th hatching egg in the (t+1)-th iteration. This represents the position of the i-th hatching egg in the t-th iteration. and Each of the above are 1×3 dimensional independent random vectors.

[0142] In the dung beetle algorithm discussed in this invention, each breeding dung beetle produces only one hatching egg, corresponding to one baby dung beetle. After the hatching egg completes hatching, the baby dung beetle is produced. The baby dung beetle departs from the hatching area and travels to a suitable foraging area to forage for food. Its foraging area is also limited to a certain range. This behavior is intended to enhance the ability to find local optimizations and improve the convergence of the algorithm. The specific steps of the foraging behavior are as follows:

[0143] The optimal foraging area can be set using the following methods:

[0144]

[0145] In the formula, Ub ** and Lb ** f1 and f2 represent the upper and lower boundaries of the optimal foraging region, respectively, and f2 represents the boundary convergence condition of the foraging region. The convergence curve is shown in Figure 1. Figure 5 As shown.

[0146] The dung beetle reaches the foraging area to forage for food, updating its location based on its foraging behavior:

[0147] Set a random number r5, which follows a normal distribution; generate a random vector ranging from 0 to 1.

[0148]

[0149] in, Let be the position of the i-th dung beetle in the (t+1)-th iteration. Let be the position of the i-th dung beetle in the (t+1)-th iteration.

[0150] Other dung beetles will engage in theft, stealing dung balls from other dung beetles to compete for the best food source. This behavior aims to escape local optima and avoid the algorithm getting trapped in local optima. The specific steps of this theft behavior are as follows:

[0151] Randomly generate a random vector of size 1×3 that follows a normal distribution. Generate a fixed constant r8.

[0152] The dung beetle steals and updates its location based on the act of theft.

[0153]

[0154] Common population communication mechanisms include: 1) Selecting the best individual in the population after iterations and replacing the best individual in the historical population with the one that has the worst initial global position (i.e., the individual with the largest fitness value); however, if this strategy selects a locally optimal individual, it may cause all individuals in the population to get stuck in a local optimum. 2) Adjusting the proportion of different types of dung beetle individuals in the population after a certain number of iterations to optimize the global and local search capabilities of the algorithm; this strategy lacks stability, and if the individuals in the subpopulation are all poor individuals, the population quality will be low. 3) Collision penalty mechanism: To avoid the drone colliding with static obstacles such as trees and rocks in the mountainous environment during flight, a penalty function is set. When the drone is within the safety threshold, it will be considered that the drone will make obstacle avoidance choices and improve safety by detouring. Although this strategy will increase the path length function of the drone, it can reduce the flight safety cost function and ensure the safety of the drone. 4) Boundary convergence strategy. Restrictions are imposed on the breeding and foraging areas of breeding dung beetles and small dung beetles within the population. However, the linear convergence of traditional dung beetle algorithms may lead to incomplete global search in the early stages and excessively rapid convergence in later stages, resulting in local optima. To better balance the algorithm's global search capability and local optimization capability, the boundary convergence strategy is changed to a nonlinear convergence strategy. This strategy improves the balance between global and local search, enhancing the global search capability in the early stages while increasing the convergence speed in later stages and reducing the risk of getting trapped in local optima. Furthermore, by adjusting the proportion of different types of dung beetles during the iteration process, the gradient descent method is proposed to optimize the algorithm's convergence performance.

[0155] The nonlinear boundary convergence strategy and gradient descent method are as follows:

[0156] Convergence strategy for the breeding region boundary:

[0157]

[0158] Where k is Lb * and Ub * Any integer between the ranges.

[0159] Foraging area boundary convergence strategy:

[0160]

[0161] Gradient descent method:

[0162]

[0163] Where, rPercent When initializing the population, the proportion of the dung beetle in the population is given by v1, v2, and v3, which are weight constants related to the number of iterations.

[0164] Calculate the objective function value of each dung beetle in the newly generated population POP(i+1), and denote the minimum value as POP. fit Comparing POP fit and And Update to the smaller of the two values.

[0165] Let t = t + 1, and determine whether the iteration number t is equal to t. max If not equal, repeat the steps above, setting the size of the random number r1 and then proceeding. Specifically, when t satisfies one-quarter, two-quarters, and three-quarters of the total number of iterations, perform gradient descent. If equal, then... As the optimal solution.

[0166] Step 5: The flight trajectory is smoothed using cubic spline interpolation. The flight path includes the starting point p. s (x s y s , z s ), endpoint p z (x z y z , z z ) and passing through point p o (x o y o , z o ), thus obtaining the drone's flight path plan. Where p o (x o y o , z o () is the optimal solution The corresponding three-dimensional coordinate trajectory smoothing uses the basis functions in the cubic B-spline curve equation as follows:

[0167]

[0168] in The factorial can be simplified to:

[0169]

[0170] Establish as Figure 3 The environment model shown contains six obstacle models. Figure 4 , Figure 5The modified boundary convergence curve is shown below. Compared to the original algorithm's convergence curve (linear straight line), the modified convergence curve f1 can perform a better global search in the early stages of the algorithm and can better avoid getting trapped in local optima in the later stages. The f2 curve improves the dung beetle's ability to find local optimizations in the later stages of the algorithm, making the path function value found smaller. Figure 6 The final simulation results are shown below. (a) is the 3D path diagram of the UAV; (b) is the top view of the UAV path; and (c) is the path function convergence curve. It can be seen that the path curve obtained by the improved algorithm has good smoothness, fast convergence speed, and high convergence accuracy.

[0171] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the path and trajectory of a UAV in a mountainous environment, characterized in that, Includes the following steps: (1) Construct an environment model, including a mountain model and a static obstacle model, to simulate the obstacle threat posed by the complex mountain environment and three-dimensional obstacles to the UAV in the real environment; (2) Construct multi-dimensional resource constraints for the UAV platform, including UAV flight path length constraints, flight space safety constraints, and path smoothness constraints; (3) Under the condition of multi-dimensional resource constraints of UAV, with the goal of minimizing flight cost, construct the UAV optimal path objective function; the objective function is composed of three weighted parts: path length cost function, path smoothness cost function, and path flight safety cost function, plus a collision cost penalty function. (4) Improve the dung beetle algorithm: improve the initialization of the random population by using a composite chaotic mapping method, adjust the oviposition boundary of the breeding dung beetle and the foraging boundary of the dung beetle by using a nonlinear convergence method, introduce the gradient descent population adjustment method to dynamically adjust the proportion of each dung beetle species in the population during the iteration process, and solve the objective function of the UAV's optimal path based on the improved dung beetle algorithm to obtain the path planning result; (5) The flight trajectory is processed using a cubic spline interpolation smoothing method. The flight path includes the starting point p. s (x s y s , z s ), endpoint p z (x z y z , z z ) and passing through point p o (x o y o , z o ), to obtain the UAV trajectory plan, where p o (x o y o , z o () is the optimal solution The corresponding three-dimensional coordinate values; The implementation process of improving the initialization of the random population using the composite chaotic mapping method in step (4) is as follows: Logistic-Sine-Cosine mapping is used to improve the coordinate distribution of the random x-axis and y-axis; Tent mapping is used to improve the coordinate distribution of the z-axis. X LSC =cos(π*4rx*(1-x)+(1-r)*sin(πx)-0.5)) Y LSC =cos(π*4rx*(1-x)+(1-r)*sin(πx)-0.5)),r∈(0,1) Tent mapping: The process of adjusting the oviposition boundary of the breeding dung beetle and the foraging boundary of the dung beetle using the nonlinear convergence method in step (4) is as follows: Calculate the objective function value for each dung beetle in the initial population based on the planned drone path objective function, and denote the optimal or minimum value as Pop. * And record the corresponding three-dimensional coordinates at this time. Let the initial iteration count t = 1, and set the size of the random number r1; Determine the value of r1. If r1 < 0.9, the dung beetle updates its position based on the rolling ball search behavior and sets a natural random number α1, which is a random value between 0 and 1. If α1 > 0.1, set α = 1; otherwise, set α = -1. Generate a random number r2 between 0 and 0.2, and a random number r3 between 0 and 1; The search is performed using the following search equation: in, This represents the position of the i-th dung beetle in the (t+1)-th iteration; This represents the position of the i-th dung beetle in the t-th iteration; Δx represents the position of the i-th dung beetle in the (t-1)-th iteration; Δx is used to simulate natural factors such as light intensity. Indicates the worst-case position globally; If r1 > 0.9, the dung beetle determines its search strategy by simulating dancing. It sets a random number r4 to a random integer between 0 and 180. If r4 = 0||90||180, it searches for the location according to the above search equation; otherwise, it searches using the following search equation: Where tan(aa) is the positional offset of the dung beetle when it encounters an obstacle; Breeding dung beetles update their location through reproductive behavior; the boundaries of their breeding zones are set in the following ways: Among them, Lb * Ub represents the lower boundary of the breeding area. * Indicates the upper boundary of the breeding area. Here, f1 represents the location information corresponding to the current local optimal solution, and f1 is the boundary convergence factor of the breeding region. A nonlinear convergence boundary method is used, where f1 is the boundary convergence factor. k is Lb * and Ub * Any integer between; Breeding dung beetles have arrived at the production area to incubate their eggs. Their locations have been updated as follows: in, This represents the position of the i-th hatching egg in the (t+1)-th iteration. This represents the position of the i-th hatching egg in the t-th iteration. and Each of the above represents a 1×3 dimensional independent random vector. After the eggs hatch, dung beetles emerge and update their location through foraging behavior; the optimal foraging area is determined using the following methods: In the formula, Ub ** and Lb ** Let f1 and f2 represent the upper and lower boundaries of the optimal foraging region, respectively, and f2 represent the boundary convergence factor of the foraging region. Also using the nonlinear convergence boundary method, let f2 = f2 + ... The dung beetle reaches the foraging area to forage for food, updating its location based on its foraging behavior: Set a random number r5, which follows a normal distribution; generate a random vector ranging from 0 to 1. in, Let be the position of the i-th dung beetle in the (t+1)-th iteration. Let be the position of the i-th dung beetle in the t-th iteration; another group of dung beetles will engage in theft, and their positions will be updated based on the theft behavior. Randomly generate a random vector of size 1×3 that follows a normal distribution. Generate a fixed constant r8; The dung beetle steals and updates its location based on the act of theft. Calculate the objective function value of each dung beetle in the newly generated population Pop(i+1), and denote the minimum value as Pop. fit Comparing Pop fit and The size, and Update to the smaller of the two; The process of dynamically adjusting the proportion of each dung beetle species in the population during the iteration process using the gradient descent population adjustment method described in step (4) is as follows: After each iteration, the best individual in the population is selected and replaced with the best individual in the current population; after every quarter of the total number of iterations, the proportion of rolling dung beetles is reduced, while the proportions of breeding dung beetles and small dung beetles are increased respectively. In the formula, r Percent When initializing the population, the proportion of the dung beetle in the population, v1, v2, and v3 are weight constants related to the number of iterations; when the number of iterations t equals MAX it Will As the optimal solution.

2. The method for unmanned aerial vehicle (UAV) path navigation in mountainous environments according to claim 1, characterized in that, The mountain model mentioned in step (1) is as follows: Terrain data is read to generate a mountain model. The minimum flight altitude of the drone is ≥1km, and the maximum flight altitude is ≤3km. The mountain environment model is simulated using scatter fitting and two-dimensional interpolation, as shown in the following formula: Among them, F ij (x i ,y j )=z ij The z-direction value is given in the data table; coefficient a ijkl Solve using the following system of equations: F ij (x i ,y j )=z ij and F ij (x i+1 ,y j )=z (i+1)j Obtain the value at the endpoint in the x-direction; F ij (x i ,y j+1 )=z i(j+1) and F ij (x i+1 ,y j+1 )=z (i+1)(j+1) Obtain the value at the endpoint in the y-direction; In summary, the interpolated coordinates in the z-direction are obtained, thus yielding the mountain model.

3. The method for unmanned aerial vehicle (UAV) path navigation in mountainous environments according to claim 1, characterized in that, The static obstacle model mentioned in step (1) is: The threat environment posed by static obstacles to UAVs is simulated using an n×3 matrix, as shown in the following formula: In the formula, a i b i R represents the coordinate information of the i-th static obstacle in space. i This represents the radius of the i-th static obstacle.

4. The method for unmanned aerial vehicle (UAV) path navigation in mountainous environments according to claim 1, characterized in that, The constraints of the UAV platform in step (2) are as follows: Among them, l o γ represents the length of the o-th segment of the flight path, L represents the flight distance of the UAV, and the total flight path of the UAV consists of n navigation points; o , The yaw and pitch angles during the drone's flight; (x o ,y o ,z o ) represents the current position coordinates of the UAV; d represents the vertical distance between the center of the static obstacle and the two nearest adjacent nodes; R represents the obstacle radius; and M represents the UAV flight safety threshold.

5. The method for unmanned aerial vehicle (UAV) path navigation in mountainous environments according to claim 1, characterized in that, The objective function for the optimal path of the UAV in step (3) is: F C =ω1*f L +ω2*f E +ω3*f S +ω4f V In the formula, ω1, ω2, ω3, and ω4 represent f respectively. L f E f S f V The weighting coefficients are ω1+ω2+ω3+ω4=1; Track length cost function: In the formula, l o This corresponds to the length of the o-th track segment; Path smoothing cost function: Where, φ o , These are the yaw and pitch angles during the drone's flight. Flight safety cost function: Among them, f o d represents the safety cost function between two adjacent navigation points. o R represents the straight-line distance between this flight path and the center of its nearest obstacle, M is the set safety threshold constant, and R i Represents the radius of a static obstacle; Collision penalty cost function: f V =V×P f Where V∈(0,1) is a constant, representing the penalty value; P f Characterizes the penalty coefficient.

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