UAV three-dimensional path obstacle avoidance method based on multi-strategy fusion improved arithmetic optimization algorithm

Abstract

The invention discloses a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm, and relates to the technical field of unmanned aerial vehicle flight path planning, and the method comprises the following steps: modeling a flight terrain environment, and planning a flight path to a destination; a population initialization method selects a population initialization method based on Circle chaotic mapping, initial population individual positions are generated in combination with Circle chaotic mapping values, an MOA updating mode is improved, and the improved algorithm HIAOA is utilized to calculate a three-dimensional track plan.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) trajectory planning, and in particular to a UAV three-dimensional path obstacle avoidance method using a multi-strategy fusion improved arithmetic optimization algorithm. Background Art

[0002] Unmanned aerial vehicles (UAVs) have been widely used in military and civilian fields such as electricity, agriculture, geological exploration, logistics, and detection due to their small size, ease of control, high speed, and flexibility. Three-dimensional trajectory planning for UAVs is key to their intelligence and a research hotspot for intelligent decision-making. Essentially, it involves generating the shortest, safe, collision-free flight path while simultaneously meeting hardware limitations while taking into account complex environmental factors such as topography, radar detection, and inclement weather. Current research indicates that traditional path-finding algorithms and heuristic optimization algorithms with swarm intelligence can be used for trajectory planning in complex spaces. Traditional algorithms include Dijkstra's method, A*, artificial potential fields, and random spanning trees. However, traditional algorithms exhibit performance deficiencies in specific applications. For example, the A-star algorithm produces relatively redundant search paths, and its computational efficiency is significantly affected by changes in the scene scale, making it difficult to guarantee search efficiency. The artificial potential field method is prone to rapid convergence and stagnation, making it difficult to obtain a globally optimal path, especially when the threat types in the scene are complex and diverse. The random tree algorithm lacks smoothness in planned paths, easily generating many inflection points and invalid paths, reducing the algorithm's effectiveness. These traditional algorithms exhibit various deficiencies in solving complex optimization problems, failing to balance search efficiency and accuracy. However, heuristic optimization algorithms based on swarm intelligence can solve complex nonlinear and nonconvex search problems through heuristic random search, without the need for a global model.

[0003] The Arithmetic Optimization Algorithm (AOA) is a new type of swarm intelligence optimization algorithm, based on the four basic mathematical operations. AOA's fundamental principle is simple, requiring only minimal initial parameters. Its global optimization capabilities surpass those of several traditional intelligent algorithms, and it has been effectively applied in areas such as engineering optimization design, neural network prediction models, constrained multi-objective optimization, and PID parameter tuning and control. However, directly applying the AOA algorithm to solve the high-dimensional and complex three-dimensional trajectory planning problem for unmanned aerial vehicles still suffers from poor global search accuracy and the tendency to obtain local optimal solutions. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the existing technology, provide a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm, design a hybrid improved AOA algorithm HIAOA, and apply it to UAV three-dimensional trajectory planning, and search for the optimal trajectory through a swarm iteration mechanism.

[0005] The object of the present invention is achieved through the following technical solution: a UAV three-dimensional path obstacle avoidance method using a multi-strategy fusion improved arithmetic optimization algorithm, comprising the following steps: S1. Model the flight terrain environment and plan the flight path to the destination.

[0006] S2. HIAOA algorithm of hybrid improved arithmetic optimization algorithm AOA: The population initialization method selects the population initialization method based on Circle chaos map, combines the Circle chaos map value to generate the initial population individual position, and improves the MOA update method to: MOA ( t ) = ( MOA max - MOA min ) × sin( ) + MOA min The HIAOA algorithm introduces random traceless Sigma point mutation.

[0007] S3. Use the HIAOA algorithm to calculate the three-dimensional trajectory plan: Step 1: Set the population size n and the number of iterations T max ; Starting and ending positions; Height limit [h min ,h max ], penalty factor 、a1、a2、 ; Weights w1, w2, w3, w4; Number of track points m; Step 2: Construct the constraints and objective function of the model, set the obstacle position, threat source range and height; Step 3: Generate n initial track solutions using Circle chaos mapping; Step 4: Calculate the initial track fitness according to the track cost function; Step 5: Update the parameter MOA; Step 6: Treat the out-of-bounds individuals with the boundary value; Step 7: Perform random untraceable Sigma mutation on the global optimal solution and retain the optimal track solution; Step 8: Update the number of iterations t=t+1; Step 9: If t <T max , return to step 4; otherwise, output the optimal solution.

[0008] In step S1, the reference terrain for flight terrain environment modeling is: z 1( x , y ) = sin( y + a ) + b sin x +

[0009] Where 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 characteristics of the terrain.

[0010] Based on the baseline terrain, the following function is used to define the natural mountains that may be encountered:

[0011] In the formula, (x i ,y i ) is the center coordinate of mountain i, n is the number of mountains, h i is the mountain height, x si 、y si They correspond to the attenuation of mountain i in x and y respectively.

[0012] To plan the trajectory to the destination, it is necessary to calculate the trajectory length, threat cost, altitude and turning cost, and calculate the overall cost function of the trajectory planning.

[0013] Let P i,j =(x i,j ,y i,j , z i,j ) is the track point P i,j 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 starting point and the end point, the other elements are the coordinates of m track points. Let | P i,j , P i,j+1 | is the track point P i,j 、 P i,j+1 The track length is:

[0014]

[0015] The threat cost is:

[0016]

[0017] in, K is the set of threat areas, φ c is the penalty factor; make P i,j 、 P i,j+1 、 P i,j+2 are adjacent track points, z i,j for P i,j The sea level is high, h i,j for P i,j The base is high, P i,j The height function is:

[0018] in, is the penalty factor, and the track height cost is:

[0019] 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 angle, β i,j+1 is the pitch angle, then:

[0020]

[0021]

[0022] make a 1. a 2 is the penalty factor for the horizontal angle and pitch angle exceeding the constraint. The track angle cost is:

[0023] Taking into account the track length, threat cost, altitude and turning angle cost, the overall cost function of track planning is defined as: 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 )

[0024] in, w 1. w 2. w 3. w 4 correspond to weights of different costs.

[0025] In step S2, the Circle chaos mapping formula is: z ( t +1) = mod( z ( t ) + a - sin(2 × z ( t )),1); Among them, a and b are two chaotic factors.

[0026] Combined with the Circle chaos map value, the initial population individual positions are generated by the following formula: y ( t +1) = lb + ( ub - lb ) × z ( t ); Among them, lb and ub are the lower and upper bounds of the individual position, and z(t) is the Circle chaos value.

[0027] Symmetric traceless Sigma points are generated by the following formula: ; Where κ = ɑ 2 (d+λ)-d, ɑ is the minimum value, d is the dimension, λ=3-d, x avg is the mean of x, SD x is the covariance matrix of x, () i (d+κ)SD x The square root matrix of column i, Sigma point is used Propagation generates 2d+1 y values, then the mean of y is y avg and variance SD y for:

[0028]

[0029] Where, () T is the transpose operator.

[0030] The idea of ​​random traceless Sigma point mutation is: take X best (t) The position is random and untraceable, and the X best (t) Perform Sigma point mutation to generate 2d+1 mutant individuals. The mutant individuals are:

[0031]

[0032] In the formula, SD X is the covariance matrix of the current population, and r6 is the scale factor. HIAOA finally uses greedy selection to retain the optimal solution from the generated mutant individuals, namely:

[0033] S3. Use the improved HIAOA algorithm to calculate the three-dimensional trajectory planning.

[0034] To address the problem of search stagnation and convergence to local optima in unmanned aerial vehicle (UAV) trajectory planning in complex three-dimensional environments, a hybrid improved arithmetic optimization algorithm (HIAOA) strategy for UAV trajectory planning is proposed. To improve the optimization capability of the standard AOA algorithm, a Circle chaos map population initialization method is designed to generate the individual distribution of the initial population, thereby increasing the initial population diversity. A nonlinear improvement of the mathematical optimizer is made using a sine function to balance the global search for the optimal trajectory with the local exploitation capability. Random untraceable Sigma point mutation is simultaneously introduced to prevent the algorithm from being stuck in local optima, thereby improving overall convergence accuracy. The convergence of the HIAOA algorithm is analyzed, and numerical simulations of the algorithm's optimization performance using benchmark functions confirm that the algorithm improves search accuracy and convergence speed. The HIAOA algorithm is used to solve the three-dimensional trajectory planning of the UAV. A trajectory planning model is constructed based on a three-dimensional terrain map of the flight environment. A multi-constrained trajectory cost function is designed, and the three-dimensional trajectory planning solution of the UAV is iteratively solved. Results show that the improved algorithm produces smaller paths and shorter costs than the comparative algorithm, while achieving higher accuracy in finding the optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the obstacle threat area; Figure 2 Schematic diagram of flight altitude constraint; Figure 3 This is a schematic diagram of the flight angle constraint; Figure 4 Random distribution and Circle chaotic mapping distribution, where (a) is the random distribution diagram and (b) is the Circle chaotic mapping distribution diagram; Figure 5 Results of trajectory planning for a simple scenario; Figure 6 This is the optimization convergence curve of the algorithm in a simple scenario; Figure 7 The trajectory planning results in complex scenarios; Figure 8 It is the optimization convergence curve of the algorithm in complex scenarios; Figure 9 It is the iterative solution process of the track; Figure 10 The ratio of global search to local development. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0038] In one embodiment of the present application: like Figures 1 to 10 As shown, a UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm includes the following steps: S1. Model the flight terrain environment and plan the flight path to the destination. To build a more realistic UAV application environment, consider outdoor terrain factors and obstacle factors for environmental modeling. The baseline terrain is: z 1( x , y ) = sin( y + a ) + b sin x +

[0039] Where 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 characteristics of the terrain.

[0040] Based on the baseline terrain, the following function is used to define the natural mountains that may be encountered:

[0041] In the formula, (x i ,y i ) is the center coordinate of mountain i, n is the number of mountains, h i is the mountain height, x si 、y si They correspond to the attenuation of mountain i in x and y respectively. Let P i,j =(x i,j ,y i,j , z i,j ) is the track point P i,jThe coordinates of 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 starting point and the end point, the other elements are the coordinates of m track points. Let | P i,j , P i,j+1 | is the track point P i,j 、 P i,j+1 The track length is:

[0042]

[0043] Use a cylinder to represent the obstacle threat range in three-dimensional space, let C k is the center point position of cylinder k, R k is the actual threat radius, D is the outer threat area of ​​the obstacle, Figure 1 This is a bird's-eye view of obstacle threats.

[0044] Threat cost and track point spacing Distance to center point d k Inversely proportional, the threat cost is:

[0045]

[0046] in, K is the set of threat areas, φ c is the penalty factor.

[0047] The UAV should meet the given interval [h min ,h max ] under the premise of maintaining high stability. P i,j 、 P i,j+1 、 P i,j+2 are adjacent track points, zi,j for P i,j The 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:

[0048] in, is the penalty factor, and the track height cost is:

[0049] UAVs should minimize track deviation and altitude switching to achieve a smooth and stable trajectory. Figure 3 As shown in the figure, the flight angle is divided into the horizontal turning angle and the vertical pitch angle. P i,j 、 P i,j+1 、 P i,j+2 are adjacent track points, | 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, 、 Respectively | P i,j , P i,j+1 |、| P i,j+1 , P i,j+2 |Projection on a two-dimensional plane.

[0050] 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 angle, β i,j+1 is the pitch angle, then:

[0051]

[0052]

[0053] make a 1. a 2 is the penalty factor for the horizontal angle and pitch angle exceeding the constraint. The track angle cost is:

[0054] Taking into account the track length, threat cost, altitude and turning angle cost, the overall cost function of track planning is defined as: 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 )

[0055] in, w 1. w 2. w 3. w 4 correspond to weights of different costs.

[0056] Arithmetic Optimization Algorithm AOA: 1) Initialization. AOA randomly generates a set of candidate solutions X for the target problem:

[0057] Where n and d correspond to the size of the population and the search dimension of the solution space, respectively. is the position of particle i in dimension j, i=1,2,...,n, j=1,2,...,j.

[0058] 2) Global search. The multiplication operator M and the division operator D in AOA are used to widely implement global search. The mathematical model is:

[0059]

[0060] Where: is a random quantity between [0,1], To update the location, is the optimal solution, ε is the minimum factor, 、 is the search boundary, u is the control factor, and MOP is the iteration coefficient:

[0061] Where: Sensitive factors, usually .

[0062] 3) Local development. The addition operator A and the subtraction operator S in AOA are used to achieve local development. The mathematical model is:

[0063] Where, It is a random quantity between [0,1] that determines the execution probability of the operator.

[0064] The AOA algorithm uses the mathematical optimizer acceleration function MOA to calculate the search and development ratio, which is defined as:

[0065] Where: 、 Its minimum and maximum values.

[0066] S2. HIAOA algorithm of the hybrid improved arithmetic optimization algorithm AOA: The initialization position of the population determines the distribution of the initial population individuals in the solution space. Since the AOA algorithm has no prior knowledge of the target position, in order to realize the random search of the solution space, the population is initialized in a pseudo-random manner. The random distribution of individuals generated by this method has obvious uncertainties and poor uniformity, which will reduce the search efficiency of the algorithm. Taking into account the randomness, ergodicity and regularity characteristics of the chaotic system, the improved algorithm HIAOA designs a population initialization method based on Circle chaos mapping, which enhances the ergodicity and uniformity of the initial distribution of the population to the solution space, and uses Circle chaotic variables to replace the original random variables to improve the population diversity and the search efficiency of the algorithm. The Circle chaos mapping formula is: z ( t +1) = mod( z ( t ) + a - sin(2 × z ( t )),1); Where a and b are two chaotic factors, usually a=0.2 and b=0.5. Combined with the Circle chaotic map value, the initial population individual positions can be generated by the following formula: y ( t +1) = lb + ( ub - lb ) × z ( t ); Where lb and ub are the lower and upper bounds of individual positions, and z(t) is the Circle chaos value. Taking dimension 30 as an example, let a = 0.2 and b = 0.5, and search boundaries in each dimension to [0, 1]. Individual distributions were generated using both random initialization and Circle chaos initialization, as shown in Figure 4. As can be seen, the uniformity of the randomly initialized individual distribution is significantly worse than that of the Circle chaos map, resulting in a higher population diversity.

[0067] The mathematical optimization acceleration function (MOA) is the switching factor between the AOA algorithm's global search and local development. MOA increases linearly with the number of iterations. For the AOA algorithm, a larger MOA indicates a relatively stronger local development capability, while a smaller MOA indicates a stronger global search capability. However, the AOA's selection of four operators is not completely linear; in other words, switching between different operators within the actual search space cannot be strictly linear. Therefore, HIAOA improves the MOA update method to: MOA ( t ) = ( MOA max - MOA min ) × sin( ) + MOA min in, MOA min 、 MOA max are the minimum and maximum values ​​of the acceleration function. The sine function was chosen for nonlinear adjustment because its curve oscillates in a wave-like manner and is relatively smooth overall, facilitating gradual scaling of the search step size and adapting to the search characteristics of different iteration stages. While the exponential function can also achieve nonlinear adjustment, it has the characteristic of a unilateral steep rise and slow fall. Testing has shown that the sine function slightly outperforms the exponential function in adjusting MOA.

[0068] When AOA is optimizing, the individuals in the population have a tendency to move towards X when the algorithm reaches the late stage of iteration. best As the area approaches the trend, the diversity of individuals gradually decreases, and the probability of generating a local optimum increases. HIAOA introduces random untraceable Sigma point mutation to solve this problem. Untraceable Sigma point transformation uses the mean of random variables x 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 traceless Sigma points are generated by the following formula:

[0069] Where κ = ɑ 2 (d+λ) - d, ɑ is the minimum value, d is the dimension, λ=3-d, x avg is the mean of x, SD x is the covariance matrix of x, () i (d+κ)SD x The square root matrix of column i. Sigma point is used Propagation generates 2d+1 y values. Then the mean of y is y avg and variance SD y for:

[0070]

[0071] Where, () T is the transposition operator. The unscented transformation ensures that the mean and variance of the random variable function to be estimated have at least second-order accuracy.

[0072] The specific mutation idea of ​​random traceless Sigma point is: best (t) The position is random and untraceable, and the X best (t) Perform Sigma point mutation to generate 2d+1 mutant individuals. The mutant individuals are:

[0073]

[0074] In the formula, SD X is the covariance matrix of the current population, and r6 is the scale factor. HIAOA finally uses a greedy strategy to retain the optimal solution from the generated mutant individuals, namely:

[0075] HIAOA convergence analysis: Let x i,j (t) is the position of individual i in dimension j, i=1,2,...,n, j=1,2,...,d, n is the population size, d is the dimension, is the fitness function. Then the global optimal solution set can be expressed as:

[0076] Definition 1: Let θ(t) be a random sequence, t=1,2,...,n, if there exists θ such that: holds; or for any θ>0, we have:

[0077] Then it can be proved that the random sequence {θ(t)} converges to θ.

[0078] Lemma 1: (Borel-Cantelli Assumption) Let E n is a sequence of n independent events, p(E i ) is the probability of event i occurring, then:

[0079]

[0080] Theorem 1: The solution set of HIAOA algorithm {x i,j (t), t≥0} is a homogeneous Markov chain in a finite state space.

[0081] Proof: The HIAOA algorithm updates individual positions (i.e., target solutions) based on a finite state space. The Circle Chaos Map, MOA adaptive update, and Sigma mutation strategies involved in population updates all satisfy the random conditions of mutual independence. The algorithm updates the individuals in the population in an iterative manner, i.e., the impact of the population state only occurs between two adjacent population generations, and the population state at iteration t only affects the population state at iteration t+1. In summary, the solution set {x i,j (t), t≥0} is a finite state space homogeneous Markov chain.

[0082] Lemma 2: For the finite state space of HIAOA, there must exist u∈(0,1) such that p i,j <u,p i,j is the probability of state i transitioning to state j.

[0083] Theorem 2: The probability that HIAOA converges to the global optimum is 1.

[0084] Proof: According to Theorem 1, the HIAOA solution set is a homogeneous Markov chain in a finite state space. For a given search accuracy and dimension d, >0, the algorithm's sequence state space can be divided into:

[0085] When the population iterates from generation t-1 to generation t, the predetermined search accuracy is not achieved. The probability of is p2, and from Lemma 2 we can get:

[0086] At the same time, according to Lemma 1, we can get:

[0087] According to Definition 1, the probability that HIAOA converges to the global optimal solution is 1.

[0088] S3. Use HIAOA algorithm to calculate the three-dimensional trajectory plan: Step 1: Set the population size n and the number of iterations T max ; Starting and ending positions; Height limit [h min ,h max ], penalty factor 、a1、a2、 ; Weights w1, w2, w3, w4; Number of track points m; Step 2: Construct the constraint conditions and objective function of the model, and set the positions of obstacles, the ranges and heights of threat sources; Step 3: Use the Circle chaotic mapping to generate n initial track plans; Step 4: Calculate the fitness of the initial tracks according to the track 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, use 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 random unscented Sigma mutation on the global optimal solution and preferentially retain the optimal track 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.

[0089] Algorithm complexity analysis. Set the population size of HIAOA to n, the number of iterations to T max , and the dimension to d. The track 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 unscented Sigma mutation 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 the same as the time complexity of the original AOA, indicating that the track planning process based on HIAOA does not increase the computational cost on the basis of the original algorithm while improving the performance.

[0090] Algorithm optimization numerical simulation: Experimental configuration: To verify the performance of HIAOA, six benchmark functions are selected for optimization testing, and the function descriptions are shown in Table 1. Among them, ~ are unimodal functions, which are used to test the optimization accuracy, ~ It is a multi-peak function, which is used to test the judgment and escape ability of local extreme points in the optimization process of the algorithm, thereby opening up a new search space. The search dimensions of the above two types of functions are both 30 dimensions. ~ It is a complex multi-modal function of fixed dimension, used to test the algorithm's ability to solve complex mixed functions. Particle swarm optimization algorithm PSO, sparrow search algorithm SSA and standard arithmetic optimization algorithm AOA are introduced for comparative experiments. The population size n=30, the maximum number of iterations T max =300, MOA min =0.2, MOA max =1.

[0091] Table 1. Benchmark functions

[0092] Experimental analysis: Table 2 shows the optimal value, average value and standard deviation of the algorithm on the benchmark function. 、 and The optimal solution can be obtained on the function, although Although the optimal solution was not found, its search accuracy was higher than that of the comparison algorithms. Furthermore, HIAOA achieved the smallest standard deviation, demonstrating that HIAOA maintains stable search performance for both unimodal and multimodal functions with varying morphological characteristics. Even with varying peak distributions in the target function, it can still find or approach the optimal solution. In addition to the comparison of search accuracy.

[0093] Table 2. Optimization results

[0094] Algorithmic trajectory planning simulation: A 3D terrain map with a size of 50×50×2 (unit: km) was built to conduct a simulation experiment on trajectory planning. The population size was 30, and the maximum number of iterations was 500. The starting coordinates were (1, 50, 10), the end coordinates were (50, 0, 20), and the number of track points was 6. The altitude interval [h min ,h max ]=[5,100], the rotation angle is constrained to 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 then introduce the particle swarm optimization algorithm (PSO), the sparrow search algorithm (SSA), and the standard arithmetic optimization algorithm (AOA) for comparative experiments. To enhance the persuasiveness, we also introduce two recent improvements to the AOA algorithm: the enhanced improved arithmetic optimization algorithm (IAOA) and the sine-cosine improved arithmetic optimization algorithm (SCAAOA) for comparison, verifying the advantages of the improved strategies introduced in this paper.

[0095] 1. Experimental analysis of scenario 1 First, a simple terrain scenario is created in a 3D terrain map, including four mountains and three threat sources. The algorithm for this scenario is relatively easy to find a feasible solution for the trajectory.

[0096] Figure 5 The following are the trajectory planning results in a simple scenario. It can be seen that all five algorithms can effectively avoid all mountains and threat sources and reach the destination, but they differ slightly in the route selection, altitude, and distance from mountains and threat sources. PSO, SSA, and AOA all have a certain degree of detour, and the flight altitude fluctuates greatly. They do not search for a more direct path to the destination, and the trajectory cost is higher. Although SCAAOA, IAOA, and HIAOA also choose a path between the threat source and the mountain in the direction of the direct path, the flight altitudes of SCAAOA and IAOA in the middle and second half of the flight are significantly higher than that of HIAOA, resulting in a longer track length, indicating that it is not the optimal solution. HIAOA has a greater advantage in the balance of track length, altitude, and turning angle. Figure 6 This is the convergence curve of the algorithm in a simple scenario. PSO and AOA converge the fastest, but their track costs are the highest and not optimal. AOA's track cost is significantly lower than PSO. Although SSA converges slower than PSO, its track cost is lower. HIAOA and IAOA converge at roughly the same time, but HIAOA's track cost is lower. Combined with the track planning diagram, HIAOA's track length is shorter and its altitude is more stable.

[0097] 2. Experimental analysis of scenario 2 Let's create a more complex flight scenario, including six mountainous terrain and five threat sources. For trajectory planning, the greater the number of mountainous terrain and threat areas, the more compressed the search space will be, resulting in fewer feasible paths and a greater test of the algorithm's robustness.

[0098] Figure 7 This is the trajectory planning result for a complex scenario. As can be seen, the trajectory curve fluctuates significantly more after the number of obstacles increases. However, HIAOA still finds the optimal trajectory. Figure 8It can be seen from the convergence curve of complex scenarios that SSA has the highest track cost, which is higher than PSO, but the two algorithms also converge the fastest, and both obtain local optimal solutions. The difference in track cost between IAOA and AOA in the early stage of iteration is not large, but after 200 iterations, IAOA jumps away from the local optimal track of AOA, further reducing the track cost. HIAOA converges slightly slower than AOA, but after iteration, it can quickly reduce the track cost, search for a better track, and quickly approach the global optimal solution. The reason is that for the track planning search in three-dimensional space, the population gradually converges in the later stage of algorithm iteration, resulting in insufficient diversity of planned tracks, accumulation of approximate solutions, and convergence to the local optimum. Since the HIAOA algorithm introduces an untraceable mutation mechanism for the optimal solution, the algorithm can expand the search space through mutation in the later stage of iteration, effectively avoiding falling into the local optimal track.

[0099] To demonstrate the convergence of HIAOA, Figure 9 shows the trajectory planning results for the first 40 iterations of the algorithm in this scenario. As can be seen, with each iteration, the optimal trajectory found by the algorithm shows a clear trend of converging towards the optimal intermediate path. Furthermore, there are fewer trajectories located in non-optimal solution areas, while more tracks accumulate in the intermediate areas. This demonstrates that the algorithm can quickly identify individuals with better fitness, guiding the population towards the optimal trajectory solution, demonstrating the superiority of the improved mechanism.

[0100] An analysis of the algorithm's search capability balance in complex scenarios. Figure 10 shows the ratio of global search to local development processes for AOA and HIAOA trajectory planning solutions. Generally, in the early stages of algorithm iteration, the algorithm should focus on global search; in the later stages, the algorithm should conduct detailed development within the neighborhood of the optimal solution located in the early stages. Research has shown that a search-to-development ratio of approximately 1:9 achieves optimal performance. This shows that AOA clearly lacks development capabilities, while HIAOA clearly favors global search in the early stages of iteration, with a relatively small development ratio. However, in the later stages, the local development ratio increases rapidly, accelerating algorithm convergence. This suggests that HIAOA's improved strategy can generate higher-quality trajectory planning solutions, achieving an effective balance between global search and local development.

[0101] 3. Statistical experimental analysis Table 3 shows the trajectory cost statistics obtained by the five algorithms. HIAOA reduces the mean trajectory cost by 5.72%, 7.34%, 15.09%, 24.16%, and 35.46% compared to SCAAOA, IAOA, AOA, SSA, and PSO, respectively. HIAOA also has a smaller standard deviation, indicating greater algorithm stability and the ability to search for higher-quality trajectory planning solutions. Furthermore, HIAOA has a shorter runtime and higher execution efficiency, and the algorithm continues to operate more efficiently after introducing the improved strategy. In summary, HIAOA can stably converge to the optimal trajectory in both scenarios, and the hybrid improvement mechanism has a performance advantage in effectively improving the AOA algorithm's global optimization capability and convergence speed.

[0102] Table 3. Track cost statistics

[0103] A new trajectory planning algorithm, HIAOA, for unmanned aerial vehicles (UAVs) is proposed. Circle chaos map population initialization is designed to generate the individual distribution of the initial population, improving initial population diversity. A sine function is used to nonlinearly update the mathematical optimizer to effectively balance global search capability and local development accuracy. Untraceable Sigma point mutation is introduced to avoid generating local optimal trajectories, improving overall optimization accuracy. The HIAOA algorithm is used to solve three-dimensional trajectory planning for UAVs. Results show that HIAOA achieves higher search accuracy than the competing algorithms and reduces the overall trajectory cost.

[0104] The foregoing description is merely an embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments and can be modified within the scope of the concept described herein through the above teachings or techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. A UAV three-dimensional path obstacle avoidance method based on a multi-strategy fusion improved arithmetic optimization algorithm, characterized by: The following steps are involved: S1. Model the flight terrain environment, calculate the baseline terrain, and based on the baseline terrain, calculate the natural mountains that may be encountered, plan the trajectory to the destination, and calculate the overall cost function of the trajectory planning by integrating the trajectory length, threat cost, altitude and corner cost; S2. HIAOA algorithm of hybrid improved arithmetic optimization algorithm AOA: The population initialization method selects the population initialization method based on Circle chaos map, combines the Circle chaos map value to generate the initial population individual position, and improves the MOA update method to: MOA ( t ) = ( MOA max - MOA min ) ×sin( ) + MOA min MOA max is the maximum value of MOA, MOA min is the minimum value of MOA, T max For the number of iterations, the HIAOA algorithm introduces random untraceable Sigma point mutation and uses greedy selection to retain the optimal solution from the generated mutation individuals; S3. Use the HIAOA algorithm to calculate the three-dimensional trajectory plan: set the population size, number of iterations, starting and ending positions, altitude limit, penalty factor, weight, and number of track points, build the model's constraints and objective function, set the obstacle location, threat source range, and altitude; use Circle chaos mapping to generate n initial trajectory plans; calculate the initial trajectory fitness based on the overall trajectory planning cost function; update the parameter MOA; treat out-of-bounds individuals as boundary values; perform random untraceable Sigma mutation on the global optimal solution and retain the optimal trajectory solution; update the number of iterations; and 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 is characterized by: In step S1, the reference terrain for flight terrain environment modeling is: z 1( x , y ) = sin( y + a ) + b its x + Where 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 characteristics of the terrain.

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

4. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1 is characterized by: Let P i,j =(x i,j ,y i,j , z i,j ) is the track point P i,j The coordinates of 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 starting point and the end point, the other elements are the coordinates of m track points. Let | P i,j , P i,j+1 | is the track point P i,j 、 P i,j+1 The track length is: The threat cost is: in, K is the set of threat areas, φ c is the penalty factor, D is the outer threat area of ​​the obstacle, is the actual threat radius, T k is the kth iteration, d k Track point spacing Distance to the center point; make P i,j 、 P i,j+1 、 P i,j+2 are adjacent track points, z i,j for P i,j The sea level is high, h i,j for P i,j The base is high, P i,j The height function is: in, is the penalty factor, h max is the maximum height, h min is the minimum height, and the track height cost 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 angle, β i,j+1 is the pitch angle, then: 、 Respectively | P i,j , P i,j+1 |、| P i,j+1 , P i,j+2 |Projection on the two-dimensional plane, let a 1. a 2 is the penalty factor for the horizontal angle and pitch angle exceeding the constraint. The track angle cost is: 。 5. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 4 is characterized by: Taking into account the track length, threat cost, altitude and turning angle cost, the overall cost function of track planning is defined as: 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 correspond to 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 is characterized by: In step S2, the Circle chaos mapping formula is: z ( t +1) = mod( z ( t ) + a - sin(2 × z ( t )),1); Among them, a and b are two chaotic factors, and z(t) is the Circle chaos value.

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

8. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 1 is characterized by: The traceless Sigma point is generated by the following formula: ； Where κ = ɑ 2 (d+λ)-d, ɑ is the minimum value, d is the dimension, λ=3-d, x avg is the mean of x, SD x is the covariance matrix of x, () i (d+κ)SD x The square root matrix of column i, Sigma point is used Propagation generates 2d+1 y values, then the mean of y is y avg and variance SD y for: Where, () T 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 is characterized by: The idea of ​​random traceless Sigma point mutation is: take X best (t) The position is random and untraceable, and the X best (t) Perform Sigma point mutation to generate 2d+1 mutant individuals.

10. The UAV three-dimensional path obstacle avoidance method based on the multi-strategy fusion improved arithmetic optimization algorithm according to claim 9 is characterized by: The variant individuals are: Where κ = ɑ 2 (d+λ)-d, ɑ is the minimum value, d is the dimension, λ=3-d, SD X is the covariance matrix of the current population, () i (d+κ) SD X The i-th column of the square root matrix, r6 is the scale factor, and HIAOA finally uses a greedy strategy to retain the optimal solution from the generated mutant individuals, that is: 。

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