Unmanned aerial vehicle flight path planning method based on fusion grey wolf optimization algorithm

Abstract

The invention belongs to the technical field of unmanned aerial vehicle path planning, and particularly discloses an unmanned aerial vehicle path planning method based on a multi-strategy fusion information acquisition optimization algorithm, and the method comprises the steps: obtaining the digital elevation model map data of a target region, and constructing a three-dimensional environment space model based on a task environment; constructing a path cost function and initializing an optimization algorithm population, wherein the initialization adopts three strategy fusion mechanisms of hypercube initialization, chaos initialization and random initialization to enhance the diversity of the population; a crisscross strategy is introduced, the adaptability and stability of the algorithm in the dynamic search process are enhanced, and a sine disturbance mechanism is adopted, so that the global optimization capacity and local development precision of the algorithm are enhanced; the flight path of the unmanned aerial vehicle is constructed by optimizing the path point sequence, and the path is smoothed by introducing B spline interpolation, so that the path is ensured to have continuity and feasibility, the flight requirement of the unmanned aerial vehicle is met, and the robustness and environmental adaptability of path generation are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle path planning, and particularly relates to an unmanned aerial vehicle flight path planning method based on a fusion grey wolf optimization algorithm. BACKGROUND

[0002] Modern unmanned aerial vehicles were first developed as a war tool for military action, and are used to perform dangerous military tasks such as armed attacks, pinpoint bombings, enemy reconnaissance, and regional patrols. In recent years, with the continuous development of science and technology and economy, the manufacturing cost of unmanned aerial vehicles has also been greatly reduced, which has enabled unmanned aerial vehicles to be widely promoted in civilian fields such as traffic monitoring and management, forest fire prevention and extinguishing, power inspection, geographic monitoring, agricultural and forestry plant protection, photography and aerial photography, scientific data collection, disaster assessment and rescue, and the like. Flight path planning is a key foundation for autonomous navigation of unmanned aerial vehicles. Unmanned aerial vehicle flight path planning is an NP-hard problem, which is a high-dimensional, multi-constrained and strongly coupled complex constrained optimization problem. First, an unmanned aerial vehicle task environment model in a three-dimensional complex environment is constructed, then constraint conditions and target costs are modeled using mathematical formulas, and then an efficient and stable intelligent algorithm is used to solve the problem, and the generated flight path is smoothed to ensure that the unmanned aerial vehicle body performance requirements are met.

[0003] The grey wolf optimization algorithm (GWO) is a swarm intelligence optimization algorithm based on the hunting behavior of grey wolves, and its core idea is derived from the social hierarchy and hunting strategies of grey wolves in nature. The algorithm realizes the search process of the optimal solution by simulating the leadership hierarchy (alpha wolf, beta wolf, delta wolf and omega wolf) and cooperative hunting mechanism of grey wolves. In the search process, the alpha wolf is the current optimal solution, the beta wolf and the delta wolf are the suboptimal solutions, and the other individuals are updated around the positions of the three, thereby realizing global exploration and local development of the target function. The update of the grey wolf position is jointly driven by the estimation of the prey position, the surrounding behavior and the pursuit mechanism, and has the characteristics of simple structure, easy implementation and superior convergence performance, and is suitable for solving continuous or discrete optimization problems.

[0004] The Sine Cosine Algorithm (SCA) is a heuristic optimization algorithm based on mathematical functions, and its basic idea is to use sine and cosine functions to control the position update of search individuals, thereby realizing dynamic search and convergence in the solution space. The algorithm adjusts the direction and distance of the search individual through the sine and cosine mechanism, so that the search process realizes adaptive balance between global optimization and local development. The SCA algorithm has a simple structure, few parameters, and good global exploration ability, and is particularly suitable for solving high-dimensional and complex optimization problems. By adjusting the parameters, the oscillation amplitude and convergence speed of the search trajectory can be effectively controlled, and the stability and robustness of the algorithm can be improved.

[0005] However, neither GWO nor SCA alone can solve complex 3D path planning problems without sufficient local accuracy or the ability to get trapped in local optima. Therefore, integrating the advantages of GWO and SCA, and combining them with chaotic mechanisms, nonlinear adjustment factors, and adaptive control strategies to construct a more robust and efficient 3D path optimization method has become an important research direction. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention aims to provide a UAV trajectory planning method based on the fusion of the gray wolf optimization algorithm. This method can effectively solve the problem that existing technologies cannot solve the problem of finding the shortest path in path planning, and has better robustness and adaptability.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for UAV trajectory planning based on a fusion gray wolf optimization algorithm, characterized by the following steps:

[0009] S1. 3D simulation environment construction: Establish a 3D simulation scene that includes terrain features and obstacles, define the initial coordinates and target coordinates of the UAV, and set environmental boundary constraints;

[0010] S2. Multi-constraint trajectory modeling: Based on the mission requirements of UAVs, a trajectory planning model is established that includes dual threats and multi-dimensional constraints such as static obstacles and no-fly zones; by weighted fusion of threat costs and constraint violation penalties, a comprehensive optimization objective function is constructed.

[0011] S3. Continuous Track Generation: The discrete waypoints are smoothed using cubic spline interpolation. The UAV's track consists of several discrete points, and a smooth path point is generated using cubic spline interpolation.

[0012] S4. Intelligent optimization algorithm solution: Initialize HGWOSCA algorithm parameters, use Tent chaotic mapping to generate a diverse initial population, retain high-quality individuals to form the initial solution set; introduce a nonlinear oscillation factor to dynamically adjust the search step size, and in the GWO and SCA fusion framework, realize the adaptive switching of the search stage through a piecewise sine strategy, taking into account both global exploration and local development.

[0013] S5. Iterative Search and Optimal Solution Update: During the algorithm execution, the positions of all individuals in the population are updated generation by generation, and the fitness value is calculated based on the objective function; the current global optimal solution is continuously updated by comparing the fitness of individuals, and after each iteration, it is determined whether the preset maximum number of iterations has been reached; if the termination condition is met, the current optimal path point sequence and its corresponding fitness value are output; otherwise, iterative updates continue until the termination criterion is met.

[0014] S6. Optimal Track Generation and Verification: After completing the optimization iteration, the final global optimal solution path is output, and the performance of the generated track is evaluated by combining indicators such as path length, smoothness, and obstacle avoidance effectiveness. The effectiveness and feasibility of the algorithm in a multi-constraint environment are verified by drawing convergence curves, path images, etc., and finally the optimal flight track of the 3D UAV that meets the mission requirements and engineering application conditions is obtained.

[0015] Furthermore, step S2 specifically includes the following:

[0016] S2-1. Obstacle Constraints:

[0017] The distance between the drone and the obstacle is a key factor in whether the obstacle can be detected, and its mathematical expression is as follows:

[0018]

[0019] In the formula, F o d is the threat cost of the obstacle area, k is the threat weight of the obstacle area, and d is the threat cost of the obstacle area. r R is the distance from the UAV to the center of the threat in the obstacle area, and R is the maximum detection radius of the obstacle area. i ,y i ,z i (x) represents the current position coordinates of the drone. R ,y R ,z R ) represents the coordinates of the obstacle center.

[0020] S2-2. No-fly zone constraints:

[0021] No-fly zones include high-risk areas and areas of unknown danger. The constraints of no-fly zones are defined as follows:

[0022]

[0023] In the formula, F N This indicates the cost of the threat posed by a no-fly zone; and These represent the lower and upper limits of the no-fly zone in the X-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the Y-coordinate, respectively;

[0024] S2-3. Track length constraint:

[0025] The track length constraint is the length of the UAV's flight track, and the corresponding function is defined as follows:

[0026]

[0027] In the formula, F L It is the sum of the path lengths of each discrete point of the UAV, where N represents the total number of discrete points generated by the control point, l i It is the distance from one waypoint to the next, (x s ,y s ,z s (x) represents the coordinates of the drone's starting point. g ,y g ,z g ) represents the coordinates of the UAV target point, L EC The starting point S(x) s ,y s ,z s ) to target point G(x) g ,y g ,z g The Euclidean distance of )

[0028] S2-4. Turning angle constraint:

[0029] Suppose the flight path consists of a series of three-dimensional control points, with the following positions:

[0030] P i =(x i ,y i ,z i (6);

[0031] The direction vector between adjacent waypoints is defined as:

[0032]

[0033] Define the cosine of the angle between two adjacent flight paths as:

[0034]

[0035] In the formula, P i+1 These are the coordinates of the next-generation waypoints, x i+1 y i+1 and z i+1 θ represents the coordinates of the next adjacent point. i Let be the turning angle of the trajectory at the i-th control point. and These represent the current vector and the next-generation neighboring vector, respectively. and Let represent the Euclidean norms of the current vector and its neighboring next-generation vector, respectively.

[0036] The smoothness of the turning angle is incorporated into the optimization objective, and the following evaluation function is constructed:

[0037]

[0038] In the formula, M represents the total number of discrete points in the track, and φ is the reference angle under ideal conditions, usually set as φ = 90° turn as the reference; this evaluation function reflects the degree of deviation of the turning change between track segments, and the smaller the value, the smoother the track;

[0039] S2-5. Height Constraints:

[0040] Suppose the track consists of M discrete points, and the altitude of the i-th point on the track is Z. i Then the average altitude of the flight path is:

[0041]

[0042] The vertical fluctuation of the flight path is represented by calculating the degree of deviation between each altitude point and the average altitude, which is expressed as:

[0043]

[0044] This value reflects the degree of deviation between each altitude point in the track and the overall average altitude. The smaller the value, the more stable the vertical direction of the track.

[0045] S2-6. Comprehensive Constraints on Unmanned Aerial Vehicles:

[0046] The UAV trajectory planning uses a linear weighted sum method to handle constraints, and its cost function can be expressed as:

[0047]

[0048] In the formula, F Whole It contains 5 objective functions, including obstacle threat, no-fly zone threat, track length constraint, yaw angle constraint and altitude constraint; m1, m2, m3 and m4 are the weight factors of the corresponding cost functions.

[0049] Furthermore, step S3 specifically includes the following:

[0050] Due to the physical constraints of drones, their flight paths may not meet flight conditions. Therefore, cubic spline interpolation is introduced, and its mathematical expression is as follows:

[0051] S i (t)=a i +b i (ssi )+c i (ss i ) 2 +d i (ss i ) 3 (13);

[0052] In the formula, S i (t) is the interpolation function for the i-th interval, representing the trajectory expression of the UAV in that interval, where s represents the current time; s i This represents the i-th time node, i.e., the interpolation point; a i Indicates the starting value of the interpolation interval; b i The coefficient of the first derivative determines the slope of the curve, i.e., the velocity; c i The second derivative coefficient determines the acceleration trend of the curve; d i The third derivative coefficients determine the curvature of the curve, i.e., the change in curvature.

[0053] Every two adjacent nodes (P) i ,P i+1 Construct a cubic function; let the sequence of control points be {P0, ..., P}. i+1 Construct a three-dimensional trajectory:

[0054]

[0055] in, The trajectory of a point in three-dimensional space at any time t, including spatial coordinates in the X, Y, and Z directions;

[0056]

[0057] In the formula, X(t)=S x Y(t) is a curve function controlling the position in the x-direction as a function of t, and the x-coordinates of the control points are fitted using cubic splines; y (t) controls the positional change in the y-direction, and the y-coordinates of the control points are fitted to a cubic spline curve; Z(t) = S z (t) controls the change in the z-direction (height), representing the smooth path of the UAV in the vertical direction.

[0058] This method constructs a piecewise cubic polynomial between the starting point, the ending point, and several intermediate control points, so that the generated track maintains continuity in function values, first derivatives, and second derivatives.

[0059] Furthermore, step S4 specifically includes the following steps:

[0060] S4-1. Construct the basic gray wolf optimization algorithm;

[0061] S4-2. Constructing a basic sine and cosine optimization algorithm;

[0062] S4-3. Tent chaotic initialization, nonlinear control parameter update strategy and piecewise sine selection strategy are introduced into the fusion algorithm.

[0063] Furthermore, step S4-1 specifically includes:

[0064] S4-1. Construction of the Grey Wolf Optimization Algorithm:

[0065] The GWO algorithm simulates the group hunting process of gray wolves to optimize operations, mainly including surrounding and attacking prey. The specific process is as follows:

[0066] S4-1-1. Encircle the prey:

[0067] The behavior of gray wolves surrounding their prey is shown below.

[0068] D = |C·X P (t)-X(t)| (16)

[0069] X(t+1)=X P (t)+A·D (17);

[0070] In the formula, t is the current iteration number, D is the distance between the current gray wolf and the target prey, and X is the distance between the individual gray wolf and the target prey. P Let X be the position of the target prey, X be the position of the current gray wolf, X(t+1) be the position of the next generation of gray wolves, and A and C be coefficient vectors. The update formulas for vectors A and C are as follows:

[0071] A = 2a × r1 - a (18)

[0072]

[0073] C = 2 × r² (20);

[0074] In the formula, a is the convergence factor, whose value decreases linearly from 2 to 0 during the iteration process, and t max Represents the maximum number of iterations, and r1 and r2 are random numbers uniformly distributed on [0,1].

[0075] S4-1-2. Attack the prey:

[0076] To simulate the attack behavior of gray wolves, the GWO algorithm uses α, β, and δ wolves to represent the current optimal solution, and infers the prey's location based on this. The mathematical model for position updating is established as follows:

[0077] D a =|C1·X α -X|

[0078] Dβ =|C2·X β -X|

[0079] D δ =|C3·X δ -X| (21)

[0080] X1(t+1)=X α (t)-A1·D α

[0081] X2(t+1)=X β (t)-A2·D β

[0082] X3(t+1)=X δ (t)-A3·D δ (twenty two)

[0083]

[0084] In the formula, C1, C2, and C3 are the three component vectors of C; X α X β X δ Let X1(t+1), X2(t+1), and X3(t+1) represent the position vectors of α, β, and δ in the current population, respectively; X1(t+1), X2(t+1), and X3(t+1) represent the positions of the three best gray wolf individuals in the population, respectively; A1, A2, and A3 represent the strength and direction controlling the update of the current individual's reference α, β, and δ positions, respectively; and D... α D β D δ X(t+1) represents the distance between the candidate gray wolf and α, β, and δ wolves, and X(t+1) represents the optimal individual value of the output.

[0085] Furthermore, the construction of the S4-2.sine and cosine optimization algorithm includes:

[0086] The sine-cosine algorithm uses sine and cosine functions to guide the search entity to iteratively update the solution space, aiming to enhance the development and exploration capabilities in global optimization problems. It creates different initial randomized proxy solutions and uses a mathematical model based on sine and cosine functions to require them to fluctuate outwards or towards the best possible solution; specifically:

[0087]

[0088] In the formula, It is the position of the t-th iteration in the i-th dimension. It is the position of the (t+1)th iteration in the i-th dimension, P i t Let r1, r2, r3, and r4 represent the target guidance positions for an individual, where r1, r2, r3, and r4 are all random numbers in the range [0, 1]. Then:

[0089]

[0090] In the formula, r4 is used to alternate between the two in order to balance the exploration and development of the algorithm. It is the current optimal position output.

[0091] Furthermore, step S4-3, the multi-strategy fusion and improvement optimization process, specifically includes:

[0092] S4-3-1.Tent Chaotic Mapping:

[0093] To improve the population diversity and convergence stability of the Grey Wolf Optimization Algorithm during the global search phase, a Tent chaotic map is introduced to improve the initial population. The chaotic sequence generated by the Tent map is used to assign initial positions to the search individuals in the improved Grey Wolf Optimization algorithm, making them more evenly distributed in the solution space, thereby enhancing the coverage of the solution space in the early stages of the search. Its mathematical expression is as follows:

[0094]

[0095] In the formula, x n Let x represent the nth chaotic variable. n+1 The next generation of chaotic variables is represented by μ, which is a pre-defined constant. When μ = 2, the system is in a completely chaotic state, with the maximum information entropy and ergodicity.

[0096] S4-3-2. Tent Chaos Mapping:

[0097] To improve the search efficiency of the Grey Wolf Optimization Algorithm at different iteration stages, a novel nonlinear control parameter update strategy is designed and introduced, the expression of which is shown below:

[0098] a=cos(0.5π(t / t) max ) 4 (28);

[0099] This strategy assigns a large control parameter 'a' in the early stages of the algorithm to enhance global exploration capabilities; as iterations proceed, 'a' gradually decreases in a non-linear manner, guiding the search to focus on local development near high-quality solutions.

[0100] S4-3-3. Piecewise Sine Selection:

[0101] The update strategy is determined by probability C. r Confirmed, and C r The adjustment is dynamically made using a sine function, as shown in the following formula:

[0102] C r =0.5*(sin(2π*0.25*t+π)*t / tmax +1) (29);

[0103] C r The value fluctuated around 0.5 in both the early and late stages; C r The relatively small fluctuations in the early stages of iteration indicate that the GWO and SCA strategies are in equilibrium. Half of the new solutions are generated by the improved GWO, and the other half by SCA, which increases population diversity and enhances the global search. r When the value is small, the solution is mostly updated by SCA; C r When the value is large, the solution is mostly updated by improving GWO; this mechanism dynamically adjusts C. r Balance exploration and development, and optimize global search capabilities.

[0104] The beneficial effects of this invention are as follows:

[0105] This invention addresses the trajectory planning problem in complex obstacle environments by proposing an improved HGWOSCA algorithm. This algorithm incorporates several improvements: Tent chaotic initialization is introduced to enhance population diversity; the parameter 'a' is modified to a nonlinear perturbation to strengthen its global search capability; and finally, a piecewise sinusoidal selection strategy is combined with the SCA algorithm to enhance the algorithm's adaptability and robustness in complex scenarios. The improved algorithm enhances both global search capability and local search accuracy, and further optimizes its trajectory planning performance, providing strong support for its application in real-world complex scenarios and offering a theoretical basis for future research and optimization in dynamic environments. In complex obstacle environments, HGWOSCA demonstrates superior performance across multiple dimensions, including trajectory planning quality, convergence speed, and search stability. Attached Figure Description

[0106] Figure 1 This is a flowchart of the steps of the present invention;

[0107] Figure 2 (a) is a 3D diagram of the UAV planning path implemented by the present invention based on the fusion strategy gray wolf and sine and cosine algorithms;

[0108] Figure 2 (b) is a top view of the UAV planning path implemented by the present invention based on the fusion strategy gray wolf and sine and cosine algorithms;

[0109] Figure 3 (a) A 3D diagram of the UAV planning path implemented by the traditional Grey Wolf optimization algorithm;

[0110] Figure 3 (b) Top view of the UAV planning path implemented by the traditional gray wolf optimization algorithm;

[0111] Figure 4 (a) is a 3D diagram of the UAV planning path implemented by the traditional sine and cosine optimization algorithm;

[0112] Figure 4 (b) is a top view of the UAV planning path implemented by the traditional sine and cosine optimization algorithm. Detailed Implementation

[0113] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are for illustrative purposes only and are not intended to limit the scope of the invention.

[0114] like Figure 1 As shown, this invention proposes a UAV trajectory planning method based on the fusion gray wolf optimization algorithm, which specifically includes the following steps:

[0115] S1. Construction of 3D Simulation Environment:

[0116] Establish a 3D simulation scene that includes terrain features and obstacles, and define the initial coordinates of the UAV.

[0117] P start (x0, y0, z0) and target coordinates P end (x n ,y n ,z n ), and set environmental boundary constraints.

[0118] In the modeling and analysis of real-world geographic scenes, remote sensing imagery and Digital Elevation Model (DEM) data are typically relied upon to obtain accurate topographic elevation information for the target area. As a crucial representation of topographic spatial features, DEMs provide a continuous distribution of surface elevation, laying the foundation for subsequent image conversion and visualization analysis. Based on the acquired elevation data, grayscale mapping techniques are employed to convert different elevation values ​​into grayscale images of corresponding brightness levels, allowing the topographic undulations to be visually presented through variations in image brightness. This method effectively visualizes abstract spatial elevation information, enabling researchers to intuitively identify and analyze the spatial distribution characteristics of the terrain through images at different grayscale levels, thus providing strong support for geomorphological analysis, environmental monitoring, and related applications.

[0119] S2. Multi-constraint trajectory modeling:

[0120] In real-world environments, drone flights face numerous threats and constraints that can affect mission progress or even lead to serious incidents such as crashes.

[0121] This invention, based on the mission requirements of unmanned aerial vehicles (UAVs), establishes a trajectory planning model incorporating dual threats and multi-dimensional constraints, including static obstacles and no-fly zones. By weighted fusion of threat costs and constraint violation penalties, a comprehensive optimization objective function is constructed. Specifically, it includes:

[0122] S2-1. Obstacle Constraints:

[0123] The distance between the drone and the obstacle is a key factor in whether the obstacle can be detected, and its mathematical expression is as follows:

[0124]

[0125] In the formula, F o d is the threat cost of the obstacle area, k is the threat weight of the obstacle area, and d is the threat cost of the obstacle area. r R is the distance from the UAV to the center of the threat in the obstacle area, and R is the maximum detection radius of the obstacle area. i ,y i ,z i (x) represents the current position coordinates of the drone. R ,y R ,z R ) represents the coordinates of the obstacle center.

[0126] S2-2. No-fly zone constraints:

[0127] No-fly zones are generally high-risk areas or areas of unknown danger. The constraints of no-fly zones are defined as follows:

[0128]

[0129] In the formula, F N This indicates the cost of the threat posed by a no-fly zone; and These represent the lower and upper limits of the no-fly zone in the X-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the Y-coordinate, respectively;

[0130] S2-3. Track length constraint:

[0131] The path length constraint is the length of the UAV's flight path. Since UAVs have limited electrical energy, a shorter optimal path is preferred. Shorter paths typically result in lower fuel consumption and reduce the probability of encountering unexpected threats. The corresponding function is defined as follows:

[0132]

[0133] In the formula, F L It is the sum of the path lengths of each discrete point of the UAV, where N represents the total number of discrete points generated by the control point, l i It is the distance from one waypoint to the next, (x s ,y s ,z s (x) represents the coordinates of the drone's starting point. g ,y g ,z g) represents the coordinates of the UAV target point, L EC The starting point S(x) s ,y s ,z s ) to target point G(x) g ,y g ,z g The Euclidean distance of )

[0134] S2-4. Turning angle constraint:

[0135] Suppose the flight path consists of a series of three-dimensional control points, with the following positions:

[0136] P i =(x i ,y i ,z i (6);

[0137] The direction vector between adjacent waypoints is defined as:

[0138]

[0139] Define the cosine of the angle between two adjacent flight paths as:

[0140]

[0141] In the formula, P i+1 These are the coordinates of the next-generation waypoints, x i+1 y i+1 and z i+1 θ represents the coordinates of the next adjacent point. i Let be the turning angle of the trajectory at the i-th control point. and These represent the current vector and the next-generation neighboring vector, respectively. and Let represent the Euclidean norms of the current vector and its neighboring next-generation vector, respectively.

[0142] The smoothness of the turning angle is incorporated into the optimization objective, and the following evaluation function is constructed:

[0143]

[0144] In the formula, M represents the total number of discrete points in the track, and φ is the reference angle under ideal conditions, usually set as φ = 90° turn as the reference; this evaluation function reflects the degree of deviation of the turning change between track segments, and the smaller the value, the smoother the track;

[0145] S2-5. Height Constraints:

[0146] Suppose the track consists of M discrete points, and the altitude of the i-th point on the track is Z. iThen the average altitude of the flight path is:

[0147]

[0148] The vertical fluctuation of the flight path is represented by calculating the degree of deviation between each altitude point and the average altitude. This invention uses the following form to represent it:

[0149]

[0150] This value reflects the degree of deviation between each altitude point in the track and the overall average altitude. The smaller the value, the more stable the vertical direction of the track.

[0151] S2-6. Comprehensive Constraints on Unmanned Aerial Vehicles:

[0152] The UAV trajectory planning employs a linear weighted sum method to handle constraints, a method widely used in optimization algorithms for solving real-world problems. Its cost function can be expressed as:

[0153]

[0154] In the formula, F Whole It contains 5 objective functions, including obstacle threat, no-fly zone threat, track length constraint, yaw angle constraint, and altitude constraint; m1, m2, m3, and m4 are the weighting factors of the corresponding cost functions;

[0155] S3. Continuous Track Generation:

[0156] Discrete waypoints are smoothed using cubic spline interpolation. The UAV's trajectory consists of several discrete points, and a smooth path (including the starting and target points) is generated using cubic spline interpolation. Specifically, this includes:

[0157] In UAV trajectory planning, the UAV's flight path consists of N waypoints. Due to the physical constraints of the UAV, the trajectory may not meet the flight conditions. Therefore, the cubic spline interpolation method is introduced. This method is widely used in path smoothing problems. Its mathematical expression is:

[0158] S i (t)=a i +b i (ss i )+c i (ss i ) 2 +d i (ss i ) 3 (13);

[0159] In the formula, S i (t) is the interpolation function for the i-th interval, representing the trajectory expression of the UAV in that interval, where s represents the current time; s i This represents the i-th time node (i.e., the interpolation point); a i Indicates the starting value of the interpolation interval; b i The coefficient of the first derivative determines the slope (i.e., velocity) of the curve; c i The second derivative coefficient determines the acceleration trend of the curve; d i The third derivative coefficients determine the curvature of the curve (i.e., the change in curvature).

[0160] Every two adjacent nodes (P) i ,P i+1 Construct a cubic function; let the sequence of control points be {P0, ..., P}. i+1 Construct a three-dimensional trajectory:

[0161]

[0162] in, It represents the trajectory point in three-dimensional space at any time t, including the spatial coordinates in the three directions of X, Y, and Z.

[0163]

[0164] In the formula, X(t)=S x Y(t) is a curve function controlling the position in the x-direction as a function of t, and the x-coordinates of the control points are fitted using cubic splines; y (t) controls the positional change in the y-direction, and the y-coordinates of the control points are fitted to a cubic spline curve; Z(t) = S z (t) controls the change in the z-direction (height), representing the smooth path of the UAV in the vertical direction.

[0165] This method constructs a piecewise cubic polynomial between the starting point, the ending point, and several intermediate control points, so that the generated track maintains continuity in function values, first derivatives, and second derivatives.

[0166] S4. Solving using intelligent optimization algorithm:

[0167] The HGWOSCA algorithm parameters are initialized, and a diverse initial population is generated using the Tent chaotic mapping, retaining high-quality individuals to form the initial solution set. A nonlinear oscillation factor is introduced to dynamically adjust the search step size, and within the GWO and SCA fusion framework, a piecewise sine strategy is used to achieve adaptive switching of the search phase, balancing global exploration and local development. Specifically, the following steps are included:

[0168] S4-1. Construct the basic gray wolf optimization algorithm;

[0169] S4-1. Construction of the Grey Wolf Optimization Algorithm:

[0170] The Gray Wolf Algorithm is an optimization algorithm that simulates the hunting behavior of wolf packs in nature. This algorithm guides and converges the search space by simulating the social hierarchy and cooperative hunting mechanisms within a wolf pack. A clear hierarchy exists within a wolf pack, similar to a pyramid structure.

[0171] The GWO algorithm simulates the group hunting process of gray wolves to optimize operations, mainly including surrounding and attacking prey. The specific process is as follows:

[0172] S4-1-1. Encircle the prey:

[0173] The behavior of gray wolves surrounding their prey is shown below.

[0174] D = |C·X P (t)-X(t)| (16)

[0175] X(t+1)=X P (t)+A·D (17);

[0176] In the formula, t is the current iteration number, D is the distance between the current gray wolf and the target prey, and X is the distance between the individual gray wolf and the target prey. P Let X be the position of the target prey, X be the position of the current gray wolf, X(t+1) be the position of the next generation of gray wolves, and A and C be coefficient vectors. The update formulas for vectors A and C are as follows:

[0177] A = 2a × r1 - a (18)

[0178]

[0179] C = 2 × r² (20);

[0180] In the formula, a is the convergence factor, whose value decreases linearly from 2 to 0 during the iteration process, and t max Represents the maximum number of iterations, and r1 and r2 are random numbers uniformly distributed on [0,1].

[0181] S4-1-2. Attack the prey:

[0182] To simulate the attack behavior of gray wolves, the GWO algorithm uses α, β, and δ wolves to represent the current optimal solution, and infers the prey's location based on this. The mathematical model for position updating is established as follows:

[0183] D a =|C1·X α -X|

[0184] D β =|C2·X β -X|

[0185] D δ =|C3·X δ -X| (21)

[0186] X1(t+1)=X α (t)-A1·D α

[0187] X2(t+1)=X β (t)-A2·D β

[0188] X3(t+1)=X δ (t)-A3·D δ (twenty two)

[0189]

[0190] In the formula, C1, C2, and C3 are the three component vectors of C; X α X β X δ Let X1(t+1), X2(t+1), and X3(t+1) represent the position vectors of α, β, and δ in the current population, respectively; X1(t+1), X2(t+1), and X3(t+1) represent the positions of the three best gray wolf individuals in the population, respectively; A1, A2, and A3 represent the strength and direction controlling the update of the current individual's reference α, β, and δ positions, respectively; and D... α D β D δ X(t+1) represents the distance between the candidate gray wolf and α, β, and δ wolves, and X(t+1) represents the best individual value output.

[0191] S4-2. Constructing a basic sine and cosine optimization algorithm;

[0192] S4-2. Construction of Sine and Cosine Optimization Algorithm:

[0193] Sine Cosine Algorithm (SCA)

[14] is a novel intelligent optimization method that uses sine and cosine functions to guide the search entity to iteratively update the solution space, aiming to enhance the development and exploration capabilities in global optimization problems. SCA creates different initial random agent solutions and uses a mathematical model based on sine and cosine functions to require them to fluctuate outward or toward the best possible solution; specifically expressed as:

[0194]

[0195] In the formula, It is the position of the t-th iteration in the i-th dimension. It is the position of the (t+1)th iteration in the i-th dimension, P it Let r1, r2, r3, and r4 represent the target guidance position of an individual (generally the optimal solution), where r1, r2, r3, and r4 are all random numbers in the range [0, 1]. Then:

[0196]

[0197] In the formula, r4 is used to alternate between the two in order to balance the exploration and development of the algorithm. It is the current optimal position output.

[0198] S4-3. Tent chaotic initialization, nonlinear control parameter update strategy and piecewise sine selection strategy are introduced into the fusion algorithm.

[0199] The multi-strategy fusion and improvement optimization process specifically includes:

[0200] S4-3-1.Tent Chaotic Mapping:

[0201] To improve the population diversity and convergence stability of the Grey Wolf Optimization Algorithm (GWO) during the global search phase, this invention introduces the Tent chaotic mapping to improve the initial population. Traditional GWO typically relies on a uniformly distributed random number generator during population initialization; however, this approach can easily lead to uneven distribution of individuals in high-dimensional spaces, thus affecting the algorithm's global exploration capability.

[0202] Based on this, this invention uses a chaotic sequence generated by the Tent mapping to assign values ​​to the initial positions of the search individuals in the improved gray wolf optimization, making them more evenly distributed in the solution space, thereby enhancing the coverage of the solution space in the early stages of the search. Its mathematical expression is as follows:

[0203]

[0204] In the formula, x n Let x represent the nth chaotic variable. n+1 The next generation of chaotic variables is represented by μ, which is a pre-defined constant. When μ = 2, the system is in a completely chaotic state, with the maximum information entropy and ergodicity.

[0205] S4-3-2. Tent Chaos Mapping:

[0206] To improve the search efficiency of the Grey Wolf Optimization (GWO) algorithm at different iteration stages, a novel nonlinear control parameter update strategy is designed and introduced, the expression of which is shown below:

[0207] a=cos(0.5π(t / t) max ) 4 (28);

[0208] In the formula, t represents the current iteration number. This strategy assigns a large control parameter a in the early stages of the algorithm to enhance the global exploration capability. As the iteration progresses, a gradually decreases in a non-linear manner, guiding the search to focus on local development near the high-quality solution.

[0209] By introducing a nonlinear function, the parameter change process is made smoother, effectively reducing the instability caused by sudden changes. This strategy exhibits a dynamic adjustment characteristic of "heavy on the beginning and light on the end," which helps to achieve an effective balance between global exploration and local development.

[0210] S4-3-3. Piecewise Sine Selection:

[0211] To better balance exploration and development, strong perturbation capabilities are needed. The update strategy is determined by probability C. r Confirmed, and C r The adjustment is dynamically made using a sine function, as shown in the following formula:

[0212] C r =0.5*(sin(2π*0.25*t+π)*t / t max +1) (29);

[0213] C r The value fluctuated around 0.5 in both the early and late stages; C r The relatively small fluctuations in the early stages of iteration indicate that the GWO and SCA strategies are in equilibrium. Half of the new solutions are generated by the improved GWO, and the other half by SCA, which increases population diversity and enhances the global search. r When the value is small, the solution is mostly updated by SCA; C r When the value is large, the solution is mostly updated by improving GWO; this mechanism dynamically adjusts C. r Balance exploration and development, and optimize global search capabilities.

[0214] S5. Iterative Search and Optimal Solution Update:

[0215] During the algorithm execution, the positions of all individuals in the population are updated generation by generation, and the fitness value is calculated based on the objective function. The current global optimal solution is continuously updated by comparing the fitness of individuals, and after each iteration, it is determined whether the preset maximum number of iterations T has been reached. If the termination condition is met, the current optimal path point sequence and its corresponding fitness value are output; otherwise, iterative updates continue until the termination criterion is met.

[0216] S6. Optimal Track Generation and Verification:

[0217] After completing the optimization iteration, the final global optimal solution path is output, and the performance of the generated trajectory is evaluated by combining indicators such as path length, smoothness, and obstacle avoidance effectiveness. The effectiveness and feasibility of the algorithm in a multi-constraint environment are verified by drawing convergence curves and path images, and finally the optimal flight trajectory of the three-dimensional UAV that meets the mission requirements and engineering application conditions is obtained.

[0218] Simulation experiment:

[0219] Compared with traditional gray wolf optimization algorithms (such as Figure 3 (as shown) and sine / cosine optimization algorithms (such as Figure 4 Compared to (as shown), the fusion strategy proposed in this invention (such as...) Figure 2 As shown, this algorithm demonstrates significant advantages in path planning results. Specifically, by introducing the Tent chaotic initialization mechanism, the diversity of the population distribution is effectively improved, preventing the algorithm from getting trapped in local optima. The algorithm integrates the search mechanisms of the gray wolf optimization and the sine and cosine algorithms, supplemented by a nonlinear oscillation adjustment factor and a piecewise sine strategy, enabling the algorithm to adaptively balance global exploration and local exploitation capabilities at different iteration stages, thus improving convergence accuracy and stability. Simulation results show that in complex terrain and multi-obstacle environments, the path generated by this fusion algorithm is smoother, more continuous, and exhibits better obstacle avoidance performance, significantly outperforming single algorithms in terms of path length, smoothness, and obstacle avoidance rationality. It possesses stronger robustness and environmental adaptability, effectively solving the technical problems of existing path planning algorithms easily getting trapped in local optima and exhibiting low path quality in complex environments.

[0220] In summary, this invention proposes an improved HGWOSCA algorithm for the trajectory planning problem in complex obstacle environments. This algorithm incorporates several improvements: it introduces Tent chaotic initialization to enhance population diversity; it modifies parameter 'a' to a nonlinear perturbation to strengthen its global search capability; and finally, it combines a piecewise sinusoidal selection strategy with the SCA algorithm to enhance the algorithm's adaptability and robustness in complex scenarios.

[0221] The improved algorithm of this invention enhances global search capability and local search accuracy, and further optimizes its trajectory planning performance. It provides strong support for applications in complex real-world scenarios and offers a theoretical basis for future research and optimization in dynamic environments. Through testing in complex obstacle environments, HGWOSCA demonstrates excellent performance across multiple dimensions, including trajectory planning quality, convergence speed, and search stability.

[0222] Obviously, the embodiments described above are only some embodiments of this application, not all embodiments. The accompanying drawings show preferred embodiments of this application, but do not limit the patent scope of this application. This application can be implemented in many different forms; rather, the purpose of providing these embodiments is to provide a more thorough and comprehensive understanding of the disclosure of this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this application's specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of patent protection of this application.

Claims

1. A UAV trajectory planning method based on a fusion gray wolf optimization algorithm, characterized in that: Specifically, the following steps are included: S1. 3D simulation environment construction: Establish a 3D simulation scene that includes terrain features and obstacles, define the initial coordinates and target coordinates of the UAV, and set environmental boundary constraints; S2. Multi-constraint trajectory modeling: Based on the mission requirements of UAVs, a trajectory planning model is established that includes dual threats and multi-dimensional constraints such as static obstacles and no-fly zones; by weighted fusion of threat costs and constraint violation penalties, a comprehensive optimization objective function is constructed. S3. Continuous Track Generation: The discrete waypoints are smoothed using cubic spline interpolation. The UAV's track consists of several discrete points, and a smooth path point is generated using cubic spline interpolation. S4. Intelligent optimization algorithm solution: Initialize HGWOSCA algorithm parameters, use Tent chaotic mapping to generate a diverse initial population, retain high-quality individuals to form the initial solution set; introduce a nonlinear oscillation factor to dynamically adjust the search step size, and in the GWO and SCA fusion framework, realize the adaptive switching of the search stage through a piecewise sine strategy, taking into account both global exploration and local development. S5. Iterative Search and Optimal Solution Update: During the algorithm execution, the position of all individuals in the population is updated generation by generation, and the fitness value is calculated based on the objective function; The current global optimal solution is continuously updated by comparing individual fitness, and it is determined after each iteration whether the preset maximum number of iterations has been reached. If the termination condition is met, output the current optimal path point sequence and its corresponding fitness value. Otherwise, continue iterative updates until the termination criteria are met; S6. Optimal Track Generation and Verification: After completing the optimization iteration, the final global optimal solution path is output, and the performance of the generated track is evaluated by combining indicators such as path length, smoothness, and obstacle avoidance effectiveness. The effectiveness and feasibility of the algorithm in a multi-constraint environment are verified by drawing convergence curves, path images, etc., and finally the optimal flight track of the 3D UAV that meets the mission requirements and engineering application conditions is obtained.

2. The UAV trajectory planning method based on the fusion gray wolf optimization algorithm according to claim 1, characterized in that: Step S2 specifically includes the following: S2-1. Obstacle Constraints: The distance between the drone and the obstacle is a key factor in whether the obstacle can be detected, and its mathematical expression is as follows: In the formula, F o d is the threat cost of the obstacle area, k is the threat weight of the obstacle area, and d is the threat cost of the obstacle area. r R is the distance from the UAV to the center of the threat in the obstacle area, and R is the maximum detection radius of the obstacle area. i ,y i ,z i (x) represents the current position coordinates of the drone. R ,y R ,z R () represents the coordinates of the obstacle center; S2-2. No-fly zone constraints: No-fly zones include high-risk areas and areas of unknown danger. The constraints of no-fly zones are defined as follows: In the formula, F N This indicates the cost of the threat posed by a no-fly zone; and These represent the lower and upper limits of the no-fly zone in the X-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the Y-coordinate, respectively; S2-3. Track length constraint: The track length constraint is the length of the UAV's flight track, and the corresponding function is defined as follows: In the formula, F L It is the sum of the path lengths of each discrete point of the UAV, where N represents the total number of discrete points generated by the control point, l i It is the distance from one waypoint to the next, (x s ,y s ,z s (x) represents the coordinates of the drone's starting point. g ,y g ,z g ) represents the coordinates of the UAV target point, L EC The starting point S(x) s ,y s ,z s ) to target point G(x) g ,y g ,z g The Euclidean distance of ) S2-4. Turning angle constraint: Suppose the flight path consists of a series of three-dimensional control points, with the following positions: P i =(x i ,y i ,z i ) (6); The direction vector between adjacent waypoints is defined as: Define the cosine of the angle between two adjacent flight paths as: In the formula, P i+1 These are the coordinates of the next-generation waypoints; x i+1 y i+1 and z i+1 θ represents the coordinates of the next adjacent point. i Let be the turning angle of the trajectory at the i-th control point. and These represent the current vector and the next-generation neighboring vector, respectively. and Let represent the Euclidean norms of the current vector and its neighboring next-generation vector, respectively. The smoothness of the turning angle is incorporated into the optimization objective, and the following evaluation function is constructed: In the formula, M represents the total number of discrete points in the track, and φ is the reference angle under ideal conditions, usually set as φ = 90° turn as the reference; this evaluation function reflects the degree of deviation of the turning change between track segments, and the smaller the value, the smoother the track; S2-5. Height Constraints: Suppose the track consists of M discrete points, and the altitude of the i-th point on the track is Z. i Then the average altitude of the flight path is: The vertical fluctuation of the flight path is represented by calculating the degree of deviation between each altitude point and the average altitude, which is expressed as: This value reflects the degree of deviation between each altitude point in the track and the overall average altitude. The smaller the value, the more stable the vertical direction of the track. S2-6. Comprehensive Constraints on Unmanned Aerial Vehicles: The UAV trajectory planning uses a linear weighted sum method to handle constraints, and its cost function can be expressed as: In the formula, F Whole It contains 5 objective functions, including obstacle threat, no-fly zone threat, track length constraint, yaw angle constraint and altitude constraint; m1, m2, m3 and m4 are the weight factors of the corresponding cost functions.

3. The UAV trajectory planning method based on the fusion gray wolf optimization algorithm according to claim 1, characterized in that: Step S3 details Includes the following: Due to the physical constraints of drones, their flight paths may not meet flight conditions. Therefore, cubic spline interpolation is introduced, and its mathematical expression is as follows: S i (t)=a i +b i (s-s i )+c i (s-s i ) 2 +d i (s-s i ) 3 (13); In the formula, S i (t) is the interpolation function for the i-th interval, representing the trajectory expression of the UAV in that interval; s represents the current time; s i This represents the i-th time node, i.e., the interpolation point; a i Indicates the starting value of the interpolation interval; b i The coefficient of the first derivative determines the slope of the curve, i.e., the velocity; c i The second derivative coefficient determines the acceleration trend of the curve; d i The third derivative coefficients determine the curvature of the curve, i.e., the change in curvature. Every two adjacent nodes (P) i ,P i+1 Construct a cubic function; let the sequence of control points be {P0, ..., P}. i+1 Construct a three-dimensional trajectory: in, The trajectory of a point in three-dimensional space at any time t, including spatial coordinates in the X, Y, and Z directions; In the formula, X(t)=S x Y(t) is a curve function controlling the position in the x-direction as a function of t, and the x-coordinates of the control points are fitted using cubic splines; y (t) controls the positional change in the y-direction, and the y-coordinates of the control points are fitted to a cubic spline curve; Z(t) = S z (t) controls the change in the z-direction (height), representing the smooth path of the UAV in the vertical direction; This method constructs a piecewise cubic polynomial between the starting point, the ending point, and several intermediate control points, so that the generated track maintains continuity in function values, first derivatives, and second derivatives.

4. The UAV trajectory planning method based on the fusion gray wolf optimization algorithm according to claim 1, characterized in that: Step S4 Specifically, the following steps are included: S4-1. Construct the basic gray wolf optimization algorithm; S4-2. Constructing a basic sine and cosine optimization algorithm; S4-3. Tent chaotic initialization, nonlinear control parameter update strategy and piecewise sine selection strategy are introduced into the fusion algorithm.

5. The UAV trajectory planning method based on the fusion gray wolf optimization algorithm according to claim 4, characterized in that: Step S4-1 specifically includes: S4-1. Construction of the Grey Wolf Optimization Algorithm: The GWO algorithm simulates the group hunting process of gray wolves to optimize operations, mainly including surrounding and attacking prey. The specific process is as follows: S4-1-1. Encircle the prey: The behavior of gray wolves surrounding their prey is shown below. D=|C·X P (t)-X(t)| (16) X(t+1)=X P (t)+A·D (17); In the formula, t is the current iteration number, D is the distance between the current gray wolf and the target prey, and X is the distance between the individual gray wolf and the target prey. P Let X be the position of the target prey, X be the position of the current gray wolf, X(t+1) be the position of the next generation of gray wolves, and A and C be coefficient vectors. The update formulas for vectors A and C are as follows: A = 2a × r1 - a (18) C＝2×r2 (20)； In the formula, a is the convergence factor that decreases linearly from 2 to 0 during the iteration process, and t max Represents the maximum number of iterations, and r1 and r2 are random numbers uniformly distributed on [0,1]. S4-1-2. Attack the prey: To simulate the attack behavior of gray wolves, the GWO algorithm uses α, β, and δ wolves to represent the current optimal solution, and infers the prey's location based on this. The mathematical model for position updating is established as follows: D a =|C1·X α -X| D β =|C2·X β -X| D δ =|C3·X δ -X| (21) X1(t+1)=X α (t)-A1·D α X2(t+1)=X β (t)-A2·D β X3(t+1)=X δ (t)-A3·D δ (22) In the formula, C1, C2, and C3 are the three component vectors of C; X α X β X δ Let X1(t+1), X2(t+1), and X3(t+1) represent the position vectors of α, β, and δ in the current population, respectively; X1(t+1), X2(t+1), and X3(t+1) represent the positions of the three best gray wolf individuals in the population, respectively; A1, A2, and A3 represent the strength and direction controlling the update of the current individual's reference α, β, and δ positions, respectively; and D... α D β D δ denoted by and representing the distances between the candidate gray wolf and α, β, and δ wolves respectively, and X(t+1) represents the optimal individual value output.

6. The UAV trajectory planning method based on the fusion gray wolf optimization algorithm according to claim 5, characterized in that: The construction of the sine and cosine optimization algorithm in step S4-2 specifically includes: The sine-cosine algorithm uses sine and cosine functions to guide the search entity to iteratively update the solution space, aiming to enhance the development and exploration capabilities in global optimization problems. It creates different initial randomized proxy solutions and uses a mathematical model based on sine and cosine functions to require them to fluctuate outwards or towards the best possible solution; specifically: In the formula, It is the position of the t-th iteration in the i-th dimension. It is the position of the (t+1)th iteration in the i-th dimension, P i t Let r1, r2, r3, and r4 represent the target guidance positions for an individual, where r1, r2, r3, and r4 are all random numbers in the range [0, 1]. Then: In the formula, r4 is used to alternate between the two in order to balance the exploration and development of the algorithm. It is the current optimal position output.

7. The UAV trajectory planning method based on the fusion gray wolf optimization algorithm according to claim 6, characterized in that: Step S4-3, the multi-strategy fusion and improvement optimization process, specifically includes: S4-3-1.Tent Chaotic Mapping: To improve the population diversity and convergence stability of the Grey Wolf Optimization Algorithm during the global search phase, a Tent chaotic map is introduced to improve the initial population. The chaotic sequence generated by the Tent map is used to assign initial positions to the search individuals in the improved Grey Wolf Optimization algorithm, making them more evenly distributed in the solution space, thereby enhancing the coverage of the solution space in the early stages of the search. Its mathematical expression is as follows: In the formula, x n Let x represent the nth chaotic variable. n+1 The next generation of chaotic variables is represented by μ, which is a pre-defined constant. When μ = 2, the system is in a completely chaotic state, with the maximum information entropy and ergodicity. S4-3-2. Tent Chaos Mapping: To improve the search efficiency of the Grey Wolf Optimization Algorithm at different iteration stages, a novel nonlinear control parameter update strategy is designed and introduced, the expression of which is shown below: a=cos(0.5π(t / t max ) 4 ) (28); This strategy assigns a large control parameter 'a' in the early stages of the algorithm to enhance global exploration capabilities; as iterations proceed, 'a' gradually decreases in a non-linear manner, guiding the search to focus on local development near high-quality solutions. S4-3-3. Piecewise Sine Selection: The update strategy is determined by probability C. r Confirmed, and C r The adjustment is dynamically made using a sine function, as shown in the following formula: C r =0.5*(sin(2π*0.25*t+π)*t / t max +1) (29); C r The value fluctuated around 0.5 in both the early and late stages; C r The relatively small fluctuations in the early stages of iteration indicate that the GWO and SCA strategies are in equilibrium. Half of the new solutions are generated by the improved GWO, and the other half by SCA, which increases population diversity and enhances the global search. r When the value is small, the solution is mostly updated by SCA; C r When the value is large, the solution is mostly updated by improving GWO; this mechanism dynamically adjusts C. r Balance exploration and development, and optimize global search capabilities.

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