Multi-strategy fusion improved arithmetic optimization algorithm for UAV three-dimensional path obstacle avoidance method

Abstract

This invention discloses a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm, which relates to the field of unmanned aerial vehicle trajectory planning technology. The method includes the following steps: modeling the flight terrain environment and planning the trajectory to the destination; hybrid improved arithmetic optimization algorithm HIAOA algorithm: the population initialization method is selected based on the Circle chaotic mapping, and the initial population individual positions are generated by combining the Circle chaotic mapping value, and the MOA update method is improved. The three-dimensional trajectory is planned by using the improved algorithm HIAOA.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) trajectory planning technology, specifically a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm. Background Technology

[0002] Unmanned Aerial Vehicles (UAVs) have been widely used in military and civilian fields such as power, agriculture, geological exploration, logistics, and detection due to their advantages of small size, ease of control, high speed, and flexibility. Three-dimensional trajectory planning for UAVs is key to their intelligence and a research hotspot in intelligent decision-making. Essentially, it involves comprehensively considering complex environmental factors such as terrain, radar detection, and adverse weather conditions, while simultaneously meeting hardware limitations, to generate the safest, collision-free shortest flight path. Current research indicates that trajectory planning for UAVs in complex spaces can primarily utilize traditional path search algorithms and heuristic optimization algorithms with swarm intelligence. Traditional algorithms include Dijkstra's method, A*, artificial potential fields, and random spanning trees. However, traditional algorithms exhibit performance shortcomings in practical applications: for example, the A* algorithm has significant track redundancy, and its computational efficiency is greatly affected by changes in scene scale, failing to guarantee search efficiency; the artificial potential field method is prone to rapid convergence and stagnation, especially under conditions of complex and diverse threat types in the scene, making it difficult to obtain the globally optimal path; the random tree algorithm lacks smoothness in track planning, easily generating many inflection points and invalid paths, reducing the algorithm's effectiveness. It is evident that these traditional algorithms all demonstrate various shortcomings in solving complex optimization problems, failing to balance search efficiency and search accuracy. In contrast, swarm intelligence heuristic optimization algorithms, without a global model, can solve nonlinear and nonconvex complex search problems through heuristic random search.

[0003] Arithmetic Optimization Algorithm (AOA) is a novel swarm intelligence optimization algorithm whose basic principle comes from the four arithmetic operations in mathematics. AOA has a simple basic principle, requiring only a few initial parameters, and its global optimization capability surpasses several traditional intelligent algorithms. It has already been effectively applied in fields such as optimization design of engineering problems, prediction models of neural networks, constrained multi-objective optimization, and PID parameter tuning and control. However, directly applying the AOA algorithm to solve the high-dimensional and complex trajectory planning problem of unmanned aerial vehicles in three dimensions still easily leads to poor global search accuracy and a tendency to obtain local optima. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm. A hybrid improved AOA algorithm HIAOA is designed and applied to UAV three-dimensional trajectory planning, and the optimal trajectory is searched through a group iterative mechanism.

[0005] The objective of this invention is achieved through the following technical solution: a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm, comprising the following steps:

[0006] S1. Model the flight terrain environment and plan the flight path to the destination.

[0007] S2. Hybrid Improved Arithmetic Optimization Algorithm (AOA) - HIAOA Algorithm: Population initialization method is selected based on Circle chaotic mapping. Combining Circle chaotic mapping values, the initial population individual positions are generated, and the MOA update method is improved as follows:

[0008] MOA ( t ) = ( MOA max - MOA min ) ×sin( ) + MOA min

[0009] The HIAOA algorithm introduces an unscented transformation.

[0010] S3. Calculate the 3D trajectory using the HIAOA algorithm: Step 1: Set the population size n and the maximum number of iterations T. max ; Start and end points; Height restrictions [h] min ,h max ], punishment factor a1, a2 Weights w1, w2, w3, w4; Number of track points m; Step 2: Construct the model's constraints and objective function, setting obstacle locations, threat source ranges, and altitudes; Step 3: Generate n initial track schemes using Circle chaotic mapping; Step 4: Calculate the initial track fitness based on the track cost function; Step 5: Update the parameter MOA; Step 6: Handle out-of-bounds individuals using boundary values; Step 7: Perform a trackless transformation on the global optimal solution and selectively retain the optimal track solution; Step 8: Update the iteration count t = t + 1; Step 9: If t <T max If yes, return to step 4; otherwise, output the optimal solution.

[0011] In step S1, the baseline terrain for flight terrain environment modeling is:

[0012] z 1( x , y ) = sin( y + a ) + b sin x +

[0013] In the formula, x and y are the horizontal and vertical coordinates projected onto the plane, and a, b, c, d, e, f, and g are constant factors that control the surface features of the terrain's undulations.

[0014] Based on the baseline terrain, the following functions are used to define the possible natural mountains encountered:

[0015]

[0016] In the formula, (x i y i Let ) represent the center coordinates of mountain i, n represent the number of mountains, and h represent the coordinates of the center of mountain i. i x represents the height of the mountain. si y si These correspond to the attenuation of mountain i in the x and y directions, respectively.

[0017] Planning a flight path to the destination requires calculating the path length, threat cost, altitude and turning cost, as well as the overall cost function for path planning.

[0018] Let P i,j =(x i,j y i,j , z i,j ) is the waypoint P i,j The coordinates, and the complete trajectory planning solution can be expressed as: X i = { P i,0 , P i,1 , P i,2 ,..., P i,n , P i,n+1}, P i,0 , P i,n+1 Corresponding to the start and end points, the other elements are the coordinates of m track points, let | P i,j , P i,j+1 |For waypointsP i,j , P i,j+1 If the distance is such that the track length is:

[0019]

[0020]

[0021] The cost of the threat is:

[0022]

[0023]

[0024] in, K A collection of threat areas. φ c As a penalty factor;

[0025] make P i,j , P i,j+1 , P i,j+2 For adjacent waypoints, z i,j for P i,j Sea level is high. h i,j for P i,j The base is high, P i,j The height function is:

[0026]

[0027] in, As a penalty factor, the cost of track altitude is:

[0028]

[0029] Let k be the unit vector in the positive direction of the axis. α i,j+1 for P i,j , P i,j+1 , P i,j+2 Between | P i,j , P i,j+1 |Turn| P i,j+1 , P i,j+2 | Horizontal corner,β i,j+1 Let be the pitch angle, then we have:

[0030]

[0031]

[0032]

[0033] make a 1. a 2 is the penalty factor for exceeding the constraints in horizontal and pitch angles. The cost of track turning is:

[0034]

[0035] Taking into account track length, threat cost, altitude, and turning angle cost, the overall cost function for track planning is defined as follows:

[0036] F ( X i ) = w 1 F 1( X i ) + w 2 F 2( X i )+ w 3 F 3( X i ) + w 4 F 4( X i )

[0037]

[0038] in, w 1. w 2. w 3. w 4 corresponds to the weights of different costs.

[0039] In step S2, the Circle chaotic mapping formula is:

[0040] z ( t +1) = mod( z ( t ) + a - sin(2 × z ( t ),1);

[0041] Here, a and b are two chaotic factors.

[0042] Combining the Circle chaotic mapping value, the initial population individual positions are generated using the following formula:

[0043] y ( t +1) = lb + ( ub - lb ) × z ( t );

[0044] Where lb and ub are the lower and upper bounds of the individual position, and z(t) is the Circle chaotic mapping value.

[0045] Symmetric unscented Sigma points are generated by the following formula:

[0046] ;

[0047] Where κ=ɑ 2 (d+λ)-d, where α is the minimum value, d is the dimension, λ=3-d, and x avg Let x be the mean, and SD be the mean. x Let x be the covariance matrix, () i (d+κ)SD x Given the square root matrix in column i, and Sigma point propagation generating 2d+1 y values, then the mean of y is yi. avg and variance SD y for:

[0048]

[0049]

[0050] In the formula, () T This is the transpose operator.

[0051] The idea behind the unscented transformation is: using X best (t) The position is a random, unscented transformation of the mean, for X best (t) Perform Sigma point mutation to generate 2d+1 mutated individuals. The mutated individuals are:

[0052]

[0053]

[0054] In the formula, SD XLet r be the covariance matrix of the current population, and r6 be the scale factor. HIAOA ultimately uses greedy selection to retain the optimal solution from the generated mutant individuals, i.e.:

[0055]

[0056] S3. The improved algorithm HIAOA is used to calculate the planning of the three-dimensional trajectory.

[0057] To address the shortcomings of UAV trajectory planning in complex 3D environments, such as search stagnation and convergence to local optima, a hybrid improved arithmetic optimization algorithm, HIAOA, is proposed. The optimization capability of the standard AOA algorithm is improved by designing a Circle chaotic mapping population initialization method to generate the individual distribution of the initial population, increasing its diversity. A sine function is used to nonlinearly improve the mathematical optimizer, balancing the global search and local exploitation capabilities for the optimal trajectory. Simultaneously, an unscented transformation is introduced to avoid the algorithm getting trapped in local optima, thus improving the overall convergence accuracy. The convergence of the HIAOA algorithm is analyzed, and numerical simulations are performed using a benchmark function to verify that the algorithm can improve search accuracy and convergence speed. The HIAOA algorithm is used to solve the 3D trajectory planning of the UAV. A trajectory planning model is constructed by combining the 3D terrain map of the flight environment, and a multi-constraint trajectory cost function is designed to iteratively solve the 3D trajectory planning scheme for the UAV. Results show that the improved algorithm solves a shorter trajectory with lower cost compared to the comparative algorithm, and achieves higher search accuracy for the optimal solution. Attached Figure Description

[0058] Figure 1 A schematic diagram of the obstacle threat area;

[0059] Figure 2 A schematic diagram illustrating flight altitude constraints;

[0060] Figure 3 This is a schematic diagram of flight angle constraints;

[0061] Figure 4 The distributions are random distributions and Circle chaotic mapping distributions, where (a) is the random distribution graph and (b) is the Circle chaotic mapping distribution graph;

[0062] Figure 5 The result of trajectory planning in a simple scenario;

[0063] Figure 6 The algorithm's convergence curve in a simple scenario;

[0064] Figure 7 For trajectory planning results in complex scenarios;

[0065] Figure 8The convergence curve of the algorithm in complex scenarios;

[0066] Figure 9 This refers to the iterative solution process for the trajectory.

[0067] Figure 10 This represents the ratio of global search to local development. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0069] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0070] In one embodiment of this application:

[0071] like Figures 1 to 10 As shown, a UAV 3D path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm includes the following steps:

[0072] S1. Model the flight terrain environment and plan the flight path to the destination; to construct a more realistic unmanned aerial vehicle application environment, outdoor terrain factors and obstacle factors are considered simultaneously in the environmental modeling. The baseline terrain is:

[0073] z 1( x , y ) = sin( y + a ) + b sin x +

[0074] In the formula, x and y are the horizontal and vertical coordinates projected onto the plane, and a, b, c, d, e, f, and g are constant factors that control the surface features of the terrain's undulations.

[0075] Based on the baseline terrain, the following functions are used to define the possible natural mountains encountered:

[0076]

[0077] In the formula, (x i y i Let ) represent the center coordinates of mountain i, n represent the number of mountains, and h represent the coordinates of the center of mountain i. i x represents the height of the mountain. si y si Let P represent the attenuation of mountain i in the x and y directions, respectively. i,j =(x i,j y i,j , z i,j ) is the waypoint P i,j The coordinates, the trajectory planning solution can be expressed as X i = { P i,0 , P i,1 , P i,2 ,..., P i,n , P i,n+1}, P i,0 , P i,n+1 Corresponding to the start and end points, the other elements are the coordinates of m track points, let | P i,j , P i,j+1 |For waypoints P i,j , P i,j+1 If the distance is such that the track length is:

[0078]

[0079]

[0080] Using a cylinder to represent the range of obstacles in three-dimensional space, let C k Let R be the position of the center point of cylinder k. k Where is the actual threat radius, and D is the outer threat area of ​​the obstacle. Figure 1 Top view of the obstacle threat.

[0081] Threat cost and trackpoint spacing Distance d to the center point k Inversely proportional, the cost of the threat is:

[0082]

[0083]

[0084] in, K A collection of threat areas. φ c This is a penalty factor.

[0085] Unmanned aerial vehicles should satisfy the given interval [h] min ,h max Maintain high stability under the premise of […]. P i,j , P i,j+1 , P i,j+2 For adjacent waypoints, z i,j for P i,j Sea level is high. h i,j for P i,j The base shape is high, such as Figure 2 , P i,j The height function is:

[0086]

[0087] in, As a penalty factor, the cost of track altitude is:

[0088]

[0089] Unmanned aerial vehicles (UAVs) should minimize track deviation and altitude changes to achieve a smooth and stable trajectory. For example... Figure 3 As shown, flight turning angles are divided into horizontal turning angles and vertical pitch angles. If... P i,j , P i,j+1 , P i,j+2 For adjacent waypoints, | P i,j , P i,j+1 |、| P i,j+1 , P i,j+2 |for P i,j , P i,j+1 and P i,j+1 , P i,j+2 The spacing, , They are respectively | P i,j ,P i,j+1 |、| P i,j+1 , P i,j+2 Projected onto a two-dimensional plane.

[0090] Let k be the unit vector in the positive direction of the axis. α i,j+1 for P i,j , P i,j+1 , P i,j+2 Between | P i,j , P i,j+1 |Turn| P i,j+1 , P i,j+2 | Horizontal corner, β i,j+1 Let be the pitch angle, then we have:

[0091]

[0092]

[0093]

[0094] make a 1. a 2 is the penalty factor for exceeding the constraints in horizontal and pitch angles. The cost of track turning is:

[0095]

[0096] Taking into account track length, threat cost, altitude, and turning angle cost, the overall cost function for track planning is defined as follows:

[0097] F ( X i ) = w 1 F 1( X i ) + w 2 F 2( X i )+ w 3 F 3( X i ) + w 4 F 4( X i )

[0098]

[0099] in, w 1. w 2. w 3. w 4 corresponds to the weights of different costs.

[0100] Arithmetic Optimization Algorithm (AOA):

[0101] 1) Initialization. AOA randomly generates a set of candidate solutions X for the target problem:

[0102]

[0103] In the formula: n and d correspond to the population size and the search dimension of the solution space, respectively. Let i be the position of particle i in dimension j, where i = 1, 2, ..., n and j = 1, 2, ..., j.

[0104] 2) Global Search. The multiplication operator M and division operator D in AOA are used to widely implement global search. The mathematical model is:

[0105]

[0106] In the formula: It is a random variable in the range [0,1]. To update the location, This is the optimal solution, where ε is the minimum factor. , The search boundary is defined by u, which is a control factor. MOP is the iteration coefficient.

[0107]

[0108] In the formula: As a sensitive factor, usually .

[0109] 3) Localized development. The addition operator A and subtraction operator S in AOA are used to implement localized development. The mathematical model is:

[0110] In the formula, It is a random variable in the range [0,1], which determines the execution probability of the operator.

[0111] The AOA algorithm uses the mathematical optimizer to accelerate the calculation of the search-to-exploitation ratio, defined as:

[0112] In the formula: , It is its minimum and maximum values.

[0113] S2. The HIAOA algorithm, a hybrid improved arithmetic optimization algorithm (AOA): The initial position of the population determines the distribution of individuals in the solution space. However, since the AOA algorithm lacks prior knowledge of the target position, it initializes the population in a pseudo-random manner to achieve random search of the solution space. This method, through randomly generated individual distributions, suffers from significant uncertainty and poor uniformity, reducing the algorithm's search efficiency. Considering the randomness, ergodicity, and regularity of chaotic systems, the improved HIAOA algorithm designs a population initialization method based on Circle chaotic mapping. This enhances the ergodicity and uniformity of the initial population distribution across the solution space, using Circle chaotic variables to replace the original random variables, thereby improving population diversity and the algorithm's search efficiency. The Circle chaotic mapping formula is:

[0114] z ( t +1) = mod( z ( t ) + a - sin(2 × z ( t ),1);

[0115] Here, a and b are two chaos factors, typically a = 0.2 and b = 0.5. Combining the Circle chaos mapping values, the initial population individual positions can be generated using the following formula:

[0116] y ( t +1) = lb + ( ub - lb ) × z ( t );

[0117] Where lb and ub are the lower and upper bounds of the individual position, and z(t) is the Circle chaotic mapping value. Taking dimension 30 as an example, let a=0.2, b=0.5, and the search boundary for each dimension be [0,1]. Individual distributions are generated using random initialization and Circle chaotic initialization, and the results are shown in Figure 4. It can be seen that the uniformity of the randomly initialized individual distribution is significantly worse than that of the individual distribution initialized by the Circle chaotic mapping, resulting in better population diversity.

[0118] The Mathematical Optimization Acceleration Function (MOA) is the switching factor for the AOA algorithm between global search and local exploitation. MOA increases linearly only with the number of iterations. For the AOA algorithm, a larger MOA results in stronger local exploitation capabilities, while a smaller MOA provides stronger global search capabilities. However, AOA's selection of the four operators is not entirely linear; that is, the switching between different operators within the actual search space cannot be strictly linear. Therefore, HIAOA improves the MOA update method as follows:

[0119] MOA ( t ) = ( MOA max - MOA min ) ×sin( ) + MOA min

[0120] in, MOA min , MOA max The minimum and maximum values ​​of the acceleration function are represented by the sine function. The reason for choosing the sine function for nonlinear adjustment is that its curve exhibits a wave-like oscillation, with a relatively smooth overall curve, which facilitates gradual scaling of the search step size and adapts to the search characteristics at different iteration stages. While the exponential function can also achieve nonlinear adjustment, it has a characteristic of steep rises followed by gradual falls. Testing showed that the sine function's performance in adjusting the MOA is slightly better than that of the exponential function.

[0121] During AOA optimization, in the later stages of the algorithm, all individuals in the population tend to move towards X. best As the local area approaches the same level, individual diversity gradually decreases, and the probability of generating a local optimum increases. HIAOA introduces an unscented transformation to address this problem. The unscented transformation uses the mean x of the random variable... avg and variance SD x Generate 2d+1 random points to evaluate the mean and variance of the random variable function y=g(x). The Sigma points of the unscented transformation are generated by the following formula:

[0122]

[0123] Where κ=ɑ 2 (d+λ) - d, where α is the minimum value, d is the dimension, and λ=3-d, x avg Let x be the mean, and SD be the mean. x Let x be the covariance matrix, () i (d+κ)SD xThe square root of the matrix is ​​in the i-th column. Sigma point propagation generates 2d+1 y values. Then the mean of y is yij. avg and variance SD y for:

[0124]

[0125]

[0126] In the formula, () T This is the transpose operator. Unscented transformations guarantee that the mean and variance of the function of the random variable to be estimated have at least second-order accuracy.

[0127] The idea behind the unscented transformation is: using X best (t) The position is a random, unscented transformation of the mean, for X best (t) Perform Sigma point mutation to generate 2d+1 mutated individuals. The mutated individuals are:

[0128]

[0129]

[0130] In the formula, SD X Let r be the covariance matrix of the current population, and r6 be the scale factor. HIAOA ultimately uses a greedy strategy to retain the optimal solution from the generated mutant individuals, i.e.:

[0131]

[0132] HIAOA convergence analysis: Let x i,j (t) represents the position of individual i at dimension j, where i = 1, 2, ..., n, j = 1, 2, ..., d, n is the population size, and d is the dimension. Let be the fitness function. Then the global optimal solution set can be expressed as:

[0133]

[0134] Definition 1: Let θ(t) be a random sequence, t=1,2,...,n. If there exists θ such that:

[0135] It holds true; or for any θ>0, we have:

[0136]

[0137] It can then be proved that the random sequence {θ(t)} converges to θ.

[0138] Lemma 1: (Borrell-Cantelli hypothesis) Let E n Given n independent event sequences, p(E)i Let be the probability of event i occurring, then:

[0139]

[0140]

[0141] Theorem 1: The solution set of the HIAOA algorithm {x} i,j The chain {(t), t≥0} is a homogeneous Markov chain in a finite state space.

[0142] Proof: The HIAOA algorithm updates the individual positions (i.e., the target solution) based on a finite state space. The Circle chaotic mapping, MOA adaptive update, and unscented transformation strategies involved in population updates are all stochastic conditions that satisfy mutual independence. The algorithm updates the population individuals iteratively, meaning that the influence of the population state only occurs between two adjacent population generations, and the population state in iteration t only affects the population state in iteration t+1. In summary, the solution set of HIAOA {x} i,j The chain {(t), t≥0} is a homogeneous Markov chain in a finite state space.

[0143] Lemma 2: For the finite state space of HIAOA, there must exist u∈(0,1) such that p i,j <u,p i,j Let be the probability of transitioning from state i to state j.

[0144] Theorem 2: The probability that HIAOA converges to the global optimum is 1.

[0145] Proof: By Theorem 1, the solution set of HIAOA is a homogeneous Markov chain in a finite state space. For a given search precision... and dimension d, If the value is greater than 0, then the sequence state space of the algorithm can be partitioned as follows:

[0146]

[0147] When the population iterates from generation t-1 to generation t, the predetermined search accuracy is not achieved. The probability is p2, and by Lemma 2 we have:

[0148]

[0149] At the same time, according to Lemma 1, we can obtain:

[0150]

[0151] According to Definition 1, the probability that HIAOA converges to the global optimum is 1.

[0152] S3. Calculate the three-dimensional flight path planning using the HIAOA algorithm: Step 1: Set the population size n, the maximum number of iterations T max ; the starting and ending positions; the altitude limit [h min , h max , the penalty factor , a1, a2, ; the weights w1, w2, w3, w4; the number of flight path points m; Step 2: Construct the constraint conditions and objective function of the model, and set the obstacle positions, threat source ranges and altitudes; Step 3: Use the Circle chaotic mapping to generate n initial flight path solutions; Step 4: Calculate the fitness of the initial flight paths according to the flight path cost function and determine the global optimal solution; Step 5: Update the parameters MOA and MOP; Step 6: If r1≥MOA and r2≤0.5, update the position according to formula 1 in ; if r1≥MOA and r2>0.5, update the position according to formula 2; Step 7: If r1<MOA and r3≤0.5, update the position according to formula 1 in ; if r1<MOA and r3>0.5, update the position according to formula 2; Step 8: Process the out-of-bounds individuals with boundary values; Step 9: Perform an unscented transformation on the global optimal solution and preferentially retain the optimal flight path solution; Step 10: Update the iteration number t=t + 1; Step 11: If t<T max , return to Step 4; otherwise, output the optimal solution.

[0153] Algorithm complexity analysis. Set the HIAOA population size as n and the number of iterations as T max , and the dimension as d. The flight path planning is carried out in four stages. First, the time complexity of using the Circle chaotic mapping to generate the initial population is O(n×d). At the same time, it is necessary to traverse n individuals to calculate the fitness, and the time complexity is O(n×d×T max ). Second, the algorithm enters the global search, and the time complexity of updating the positions of all individuals is O(n×d×T max ). Then, in the local development stage, the time complexity of updating the individual positions is O(n×d×T max ). Finally, in each iteration, it is necessary to perform an unscented transformation on the optimal solution, and the worst time complexity of this stage is also O(n×d×T max ). It can be seen that the overall time complexity of HIAOA is still O(n×d×T max ). This is consistent with the time complexity of the original AOA, indicating that the flight path planning process based on HIAOA does not increase the computational cost on the basis of the original algorithm while improving the performance.

[0154] Numerical Simulation for Algorithm Optimization: Experimental Configuration: To verify the performance of HIAOA, six benchmark functions were selected for optimization testing. Function descriptions are shown in Table 1. Among them, ~ It is a unimodal function, used to check the accuracy of the optimization. ~ These are multimodal functions used to test the algorithm's ability to identify and escape local extrema during the optimization process, thereby opening up new search spaces. The search dimension of both types of functions is 30. ~ This is a complex multimodal function with fixed dimensions, used to test the algorithm's ability to solve complex mixed functions. Comparative experiments are conducted using Particle Swarm Optimization (PSO), Sparrow Search Algorithm (SSA), and the standard Arithmetic Optimization Algorithm (AOA). The population size is n=30, and the maximum number of iterations is T. max =300, MOA min =0.2, MOA max =1.

[0155] Table 1. Benchmark Functions

[0156]

[0157] Experimental Analysis: Table 2 shows the optimal value, mean, and standard deviation of the algorithm on the benchmark function. HIAOA in , and The optimal solution can be found on the function, although While the optimal solution was not found, its search accuracy was higher than that of the comparison algorithms. Furthermore, HIAOA achieved the smallest standard deviation, indicating that it maintains stable search performance when handling unimodal and multimodal functions with different morphological characteristics, and can still find or approach the optimal solution even when the peak distribution of the objective function varies. (This is in addition to the comparison of search accuracy.)

[0158] Table 2. Optimization Results

[0159]

[0160] Algorithm trajectory planning simulation:

[0161] A simulation experiment of flight path planning was conducted using a 50×50×2 (km) 3D topographic map. The population size was 30, and the maximum number of iterations was 500. The starting coordinates were (1, 50, 10), the ending coordinates were (50, 0, 20), and the number of track points was 6. The altitude range [h] min ,h max [5, 100], with a rotation constraint of 45°. =0.5, =0.8, a1=a2=0.5, MOA min =0.2, MOA max =1, weights w1=w2=0.3, w3=w4=0.2. We continue by introducing the Particle Swarm Optimization (PSO) algorithm, the Sparrow Search (SSA) algorithm, and the standard Arithmetic Optimization (AOA) algorithm for comparative experiments. To enhance the persuasiveness, we further introduce two recent improvements to the AOA algorithm: the Enhanced Improved Arithmetic Optimization (IAOA) algorithm and the Sine-Cosine Improved Arithmetic Optimization (SCAAOA) algorithm, for comparison, verifying the advantages of the improvement strategies introduced in this paper.

[0162] 1. Scenario 1 Experiment Analysis

[0163] First, a simple terrain scenario is created on the 3D terrain map, including four mountains and three threat sources. The algorithm can easily find feasible solutions for the flight paths in this scenario.

[0164] Figure 5 The results show the trajectory planning in a simple scenario. It can be seen that all five algorithms can effectively avoid all mountains and threat sources to reach the destination, but they differ slightly in route selection, altitude, and distance from mountains and threat sources. PSO, SSA, and AOA all involve some degree of detour, with significant fluctuations in flight altitude, and they did not find a more direct path to the destination, resulting in higher trajectory costs. Although SCAAOA, IOA, and HIAOA all chose the path between the threat source and the mountain in the direct path direction, SCAAOA and IOA fly at significantly higher altitudes in the middle and latter half of the journey than HIAOA, resulting in longer trajectory lengths, indicating that they are not the optimal solution. HIAOA has a greater advantage in balancing trajectory length, altitude, and turning angle. Figure 6 These are the convergence curves of the algorithms in simple scenarios. PSO and AOA converge the fastest, but their track costs are the highest, making them not optimal tracks. AOA's track cost is significantly lower than PSO's. SSA converges slower than PSO, but its track cost is even lower. HIAOA and IAOA converge at roughly the same time, but HIAOA's track cost is lower. Combined with the track planning graph, it can be seen that HIAOA has a shorter track length and more stable altitude.

[0165] 2. Experimental Analysis in Scenario Two

[0166] Another relatively complex flight scenario is established, including six mountains and five threat sources. For trajectory planning, the more mountains and threat areas there are, the more the search space will be compressed in this scenario, and the fewer feasible paths there will be, which will further test the robustness of the algorithm.

[0167] Figure 7 The results show the trajectory planning in complex scenarios. It can be seen that the trajectory curve fluctuates significantly more after the addition of obstacles. HIAOA can still find the optimal trajectory. Figure 8 The convergence curves in complex scenarios show that SSA has the highest path cost, higher than PSO, but both algorithms converge the fastest, obtaining local optima. IAOA and AOA have similar path costs in the early iterations, but after 200 iterations, IAOA escapes AOA's local optima, further reducing path costs. HIAOA converges slightly slower than AOA, but after iterations, it rapidly reduces path costs, finds better paths, and quickly approaches the global optimum. This is because, in 3D path planning and searching, the population tends to converge in the later iterations, leading to insufficient path diversity, accumulation of approximate solutions, and convergence to local optima. Since the HIAOA algorithm introduces a traceless mutation mechanism for the optimal solution, it can expand the search space through mutation in the later iterations, effectively avoiding getting trapped in local optima.

[0168] To demonstrate the convergence of HIAOA, Figure 9 shows the trajectory planning results of the algorithm in the first 40 iterations in this scenario. It can be seen that with each iteration, the optimal trajectories searched by the algorithm show a clear tendency to converge towards the intermediate optimal path. Furthermore, fewer trajectories are distributed in the non-optimal solution region, while more trajectories accumulate in the intermediate region. This indicates that the algorithm can quickly find individuals with better fitness, guiding the population to rapidly approach the optimal trajectory solution, demonstrating the superiority of the improvement mechanism.

[0169] Analysis of the balance of search capabilities of algorithms in complex scenarios. Figure 10 shows the ratio of global search to local development in AOA and HIAOA for solving trajectory planning. Generally, in the early stages of algorithm iteration, the focus should be on global search; in the later stages, the algorithm should refine the local development within the neighborhood of the previously located optimal solution. Research shows that a search-to-development ratio of approximately 1:9 yields the best performance. It is evident that AOA has insufficient development capability, while HIAOA clearly favors global search in the early stages of iteration, with a smaller development ratio, but the local development ratio increases rapidly in the later stages, thus accelerating algorithm convergence. Therefore, the improved strategy of HIAOA can generate higher-quality trajectory planning solutions, achieving an effective balance between global search and local development.

[0170] 3. Statistical Experimental Analysis

[0171] Table 3 shows the statistical results of the trajectory costs obtained by the five algorithms. In terms of the mean trajectory cost, HIAOA reduces the cost by 5.72%, 7.34%, 15.09%, 24.16%, and 35.46% compared to SCAAOA, IAOA, AOA, SSA, and PSO, respectively. Furthermore, HIAOA has a smaller standard deviation, indicating better algorithm stability and the ability to find higher-quality trajectory planning solutions. In addition, HIAOA has a shorter running time and higher execution efficiency; even after introducing the improvement strategy, the algorithm still runs more efficiently. In summary, HIAOA can stably converge to the optimal trajectory in both scenarios, and the hybrid improvement mechanism has performance advantages in effectively improving the global optimization capability and convergence speed of the AOA algorithm.

[0172] Table 3. Statistical Indicators of Track Cost

[0173]

[0174] A novel UAV trajectory planning algorithm, HIAOA, is proposed. A Circle chaotic mapping population initialization method is designed to generate the initial population's individual distribution, improving initial population diversity. A sine function is used for nonlinear updates of the mathematical optimizer, achieving an effective balance between global search capability and local optimization accuracy. An unscented transformation is introduced to avoid generating locally optimal trajectories, thus improving overall optimization accuracy. The HIAOA algorithm is then used to solve the UAV's 3D trajectory planning problem. Results show that HIAOA achieves higher search accuracy than comparative algorithms while incurring lower overall trajectory cost.

[0175] The above description is merely an embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm, characterized in that: Includes the following steps: S1. Flight terrain environment modeling: calculate the baseline terrain, and calculate the possible natural mountains encountered based on the baseline terrain. Plan the flight path to the destination, and calculate the overall cost function of the flight path planning by taking into account the flight path length, threat cost, altitude and turning cost. S2. The HIAOA algorithm of the hybrid improved arithmetic optimization algorithm AOA: The population initialization method is based on the Circle chaotic mapping. Combining the Circle chaotic mapping value, the initial population individual positions are generated, and the MOA update method in the AOA algorithm is improved as follows: MOA ( t ) = ( MOA max - MOA min ) ×sin( ) + MOA min MOA is the switching factor for the AOA algorithm to perform global search or local exploitation. MOA(t) is the value of MOA at the t-th iteration. MOA max The maximum value of MOA MOA min Let T be the minimum value of MOA, t be the number of iterations, and T be the minimum value of MOA. max To maximize the number of iterations, the HIAOA algorithm introduces an unscented transformation and uses greedy selection to retain the optimal solution from the generated mutant individuals. S3. Calculate the 3D trajectory using the HIAOA algorithm: Set the population size, number of iterations, start and end points, altitude limit, penalty factor, weights, and number of trajectory points; construct the model's constraints and objective function; set obstacle locations, threat source ranges, and altitudes; generate n initial trajectory schemes using Circle chaotic mapping; calculate the initial trajectory fitness based on the overall cost function of trajectory planning; update the MOA parameter; handle out-of-bounds individuals using boundary values; perform a traceless transformation on the global optimal solution and selectively retain the optimal trajectory solution; update the number of iterations; output the optimal solution.

2. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1, characterized in that: In step S1, the baseline terrain for flight terrain environment modeling is: z 1( x , y ) = sin( y + a ) + b its x + In the formula, x and y are the horizontal and vertical coordinates projected onto the plane, and a, b, c, d, e, f, and g are constant factors that control the surface features of the terrain's undulations.

3. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 2, characterized in that: Based on the baseline terrain, the following function is used to define a natural mountain: In the formula, (x i y i Let ) represent the center coordinates of mountain i, n represent the number of mountains, and h represent the coordinates of the center of mountain i. i x represents the height of the mountain. si y si These correspond to the attenuation of mountain i in the x and y directions, respectively.

4. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1, characterized in that: Let P i,j =(x i,j y i,j , z i,j ) is the waypoint P i,j The coordinates, the trajectory planning solution can be expressed as X i = { P i,0 , P i,1 , P i,2 ,..., P i,n , P i,n+1 }, P i,0 , P i,n+1 Corresponding to the start and end points, the other elements are the coordinates of m track points, let | P i,j , P i,j+1 |For waypoints P i,j , P i,j+1 If the distance is such that the track length is: The cost of the threat is: in, K A collection of threat areas. φ c D is the penalty factor, and D is the outer threat area of ​​the obstacle. T represents the actual threat radius. k For the k-th iteration, d k Spacing between track points Distance to the center point; make P i,j , P i,j+1 , P i,j+2 For adjacent waypoints, z i,j for P i,j Sea level is high. h i,j for P i,j The base is high, P i,j The height function is: in, As a penalty factor, h max h is the maximum height. min To achieve the minimum altitude, the altitude cost of the track is: Let k be the unit vector in the positive direction of the axis. α i,j+1 for P i,j , P i,j+1 , P i,j+2 Between | P i,j , P i,j+1 |Turn| P i,j+1 , P i,j+2 | Horizontal corner, β i,j+1 Let be the pitch angle, then we have: , They are respectively | P i,j , P i,j+1 |、| P i,j+1 , P i,j+2 Projecting onto a two-dimensional plane, let a 1. a 2 is the penalty factor for exceeding the constraints in horizontal and pitch angles. The cost of track turning is: 。 5. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 4, characterized in that: Taking into account track length, threat cost, altitude, and turning angle cost, the overall cost function for track planning is defined as follows: F ( X i ) = w 1 F 1( X i ) + w 2 F 2( X i )+ w 3 F 3( X i ) + w 4 F 4( X i ) in, w 1. w 2. w 3. w 4 corresponds to the weights of different costs.

6. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1, characterized in that: In step S2, the Circle chaotic mapping formula is: z ( t +1) = mod( z ( t ) + a - sin(2 × z ( t )),1); Where a and b are two chaotic factors, and z(t) is the Circle chaotic mapping value.

7. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1, characterized in that: In step S2, the initial population individual positions are generated by combining the Circle chaotic mapping value using the following formula: y ( t +1) = lb + ( ub - lb ) × z ( t )； Where lb and ub are the lower and upper bounds of the individual position, and z(t) is the Circle chaotic mapping value.

8. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1, characterized in that: The Sigma point of the unscented transformation is generated by the following formula: ； Where κ=ɑ 2 (d+λ)-d, where α is the minimum value, d is the dimension, λ=3-d, and x avg Let x be the mean, and SD be the mean. x Let x be the covariance matrix, () i (d+κ)SD x Given the square root matrix in column i, and Sigma point propagation generating 2d+1 y values, then the mean of y is yi. avg and variance SD y for: In the formula, () T This is the transpose operator.

9. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1, characterized in that: The idea behind the unscented transformation is: to use the globally optimal solution X best (t) The position is the mean, and a traceless transformation is performed on X. best (t) Perform Sigma point mutation to generate 2d+1 mutated individuals.

10. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 9, characterized in that: The mutated individuals are: In the formula, κ=ɑ 2 (d+λ)-d, where α is the minimum value, d is the dimension, λ=3-d, SD X Let be the covariance matrix of the current population, () i (d+κ) SD X The square root matrix has the i-th column as r6, which is the scaling factor. HIAOA ultimately uses a greedy strategy to retain the optimal solution from the generated mutant individuals, i.e.: , For the fitness function, The optimal path solution that is retained.

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