Dynamic adaptive unmanned aerial vehicle path planning method based on RRT*

Abstract

The invention relates to a dynamic self-adaptive unmanned aerial vehicle path planning method based on RRT *. The technical problems that an existing unmanned aerial vehicle path planning method based on an RRT * algorithm is low in convergence speed, a generated path is high in tortuosity degree and poor in smoothness, and efficiency needs to be improved are solved. Sampling points are generated through self-adaptive Gaussian sampling according to self-adaptive target offset probability selection, different step lengths are used in different exploration periods by adopting an intelligent variable step size mechanism, and Pareto evaluation on path tortuosity degree is introduced to further obtain an optimal path. The path planned by the method is high in convergence speed, and the generated path is low in tortuosity and good in smoothness.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path planning technology, and more specifically, to a dynamic adaptive UAV path planning method based on RRT*. Background Technology

[0002] With the development of the low-altitude economy, drones are being used in more and more industries, such as pesticide spraying, crop pollination, power line inspection, and disaster search and rescue.

[0003] Unmanned aerial vehicle (UAV) path planning refers to the process of finding the optimal path from the starting point to the target point for a UAV under specific environmental and task constraints. Currently, the main UAV path planning algorithms include: A* algorithm, RRT algorithm, artificial potential field method, D* algorithm, genetic algorithm, and particle swarm optimization algorithm.

[0004] The RRT algorithm, through random sampling and tree structure expansion, can quickly find a feasible path from the starting point to the target point. Patent application CN112987799A discloses a UAV path planning method based on an improved RRT algorithm. To improve the performance of the RRT algorithm, the RRT* algorithm emerged. The RRT* algorithm adds a path reconnection mechanism to the RRT algorithm, enabling asymptotic convergence to the optimal path and exhibiting asymptotic optimality. However, the RRT* algorithm has a slow convergence speed, especially in environments with small target areas or narrow passages. The generated paths are highly tortuous, lack smoothness, and typically contain many inflection points, which is detrimental to actual UAV execution. The algorithm's efficiency and accuracy also need improvement when handling three-dimensional space and complex obstacles. Furthermore, due to its long sampling time, the algorithm performs poorly during autonomous UAV flight. Summary of the Invention

[0005] This invention aims to address the technical problems of existing UAV path planning methods based on the RRT* algorithm, such as slow convergence speed, high path tortuosity and poor smoothness, and low efficiency. It provides a dynamic adaptive UAV path planning method based on RRT*.

[0006] This invention is an improvement on the conventional RRT* algorithm in the prior art.

[0007] This invention provides a dynamic adaptive UAV path planning method based on RRT*, comprising the following steps: Step S1: Create a global map containing obstacles; Step S2: Determine the starting point and ending point of the drone; Step S3: Starting from the origin, initialize a tree structure; Step S4, calculate the adaptive target bias probability using the following formula (1). : (1); In formula (1), t is the progress of the exploration iteration. , It is the current iteration number. Maximum number of iterations; Step S5: Call the random number generation function to generate a random number r between [0,1]. If r is less than the adaptive target bias probability... Proceed to step S6 if the condition is met; otherwise proceed to step S7. Step S6: Generate sampling points using a biased target sampling method. Randomly generate sampling points at a certain step size in the direction from the new node to the endpoint vector in the current tree structure. After completion, proceed to step S8. Step S7: Generate sampling points using an adaptive Gaussian sampling method; Step S8: Find the node closest to the sampling point in the current tree. ; Step S9: Determine the step size through an intelligent variable step size mechanism; Step S10: Expand the tree to obtain new nodes. ; Step S11: Determine the new node's position using collision detection. The nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S12; if it does not collide, proceed to step S18. Step S12: Generate sampling points using an adaptive Gaussian sampling method; Step S13: Expand the tree to obtain new nodes. ; Step S14: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S15; if it does not collide, proceed to step S18. Step S15: Determine the step size through an intelligent variable step size mechanism; Step S16: Expand the tree to obtain new nodes. ; Step S17: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S15; if it does not collide, proceed to step S18. Step S18: Add the new node to the tree structure; Step S19: Determine the search radius; Step S20: Within the circular region centered on the new node and determined by the search radius, select the node with the minimum path cost as the parent node of the new node. Step S21: Reconnect and update the tree structure; Step S24: Determine if the new node has reached the endpoint. If yes, proceed to step S25; otherwise, proceed to step S4 and continue iterating. Step S25: Record the path.

[0008] Preferably, step S7 is as follows: Step S701: Calculate the mean of the Gaussian distribution. There are two situations: In the first scenario, initially the tree structure only has a starting point, and the ending point is used as the mean. , ; The second scenario involves a new node in the tree structure, where a feasible path already exists. (2); In formula (2), This is a new node in the current tree structure. As the endpoint, These are the weighting coefficients. t represents the exploration iteration progress; Step S702, calculate the dynamic covariance matrix: (3); In formula (3), Standard deviation It is the identity matrix. Scaling factor t represents the exploration iteration progress; Step S703, further obtaining the three-dimensional Gaussian distribution as follows: : (4); In formula (4), Spatial dimension; Step S704, based on and Generate 3 sampling points, namely x1, x2, and x3; First, generate 4 sets of uniformly distributed random numbers: Secondly, three sets of standard normal random numbers z are generated from four sets of uniformly distributed random numbers using the Box-Muller transformation: Group 1: Group 2: Group 3: Then, Cholesky decomposition is performed on the dynamic covariance matrix Σ, which is decomposed into a lower triangular matrix. : ; Then, three sampling points x1, x2, and x3 are generated. The first sampling point x1 is: ; Expand into component form: ; The second sampling point x2 is: ; Expand into component form: ; The third sampling point x3 is: ; Expand into component form: ; Finally, the three sampling points and the new nodes in the current tree structure were compared respectively. Obstacle collision detection is performed on the line segments between them. If there is no collision, the requirements are met, and the corresponding sampling points without collisions are added to the array. If none of the three sampling points meet the requirements, they are regenerated. If the sampling points saved in the array are not unique, the sampling point saved first in the array is selected as the final sampling point; if the sampling point saved in the array is unique, that point is selected as the final sampling point.

[0009] Preferably, the process of determining the step size through the intelligent variable step size mechanism in step S9 is as follows: Step S901, calculate the large step size factor using the following formula (5). : (5); In formula (5), h is the exploration space parameter, α is the step size constant, and t is the exploration iteration progress; The small step size factor is calculated using the following formula (6). : (6); In formula (6), h is the exploration space parameter and α is the step size constant; Step S902, calculate the step distance using the following formula (7): (7); In formula (7), the random direction component is: ; in, For the generated sampling points, The node in the current tree that is closest to the sampling point; The target direction component is: ; in, The endpoint; The composite vector is: ; The process of determining the step size through the intelligent variable step size mechanism in step S12 is as follows: the distance of the step size is calculated using the following formula (8): (8); In formula (8), the random direction component is: ; in, For the generated sampling points, The node in the current tree that is closest to the sampling point; The target direction component is: ; in, The endpoint; The composite vector is: ; Step S15 involves determining the step size using an intelligent variable step size mechanism. The step distance is calculated using the following formula (9): (9); Simplified to: (10); In formula (10), the random direction component is: ; in, For the generated sampling points, It is the node in the current tree that is closest to the sampling point.

[0010] Preferably, after step S21 and before step S24, steps S22 and S23 are added; in step S22, it is determined whether a certain number of iterations have been performed. If so, proceed to step S23; otherwise, proceed to step S24. Step S23, attempt a direct connection: First, determine whether the Euclidean distance dist from the new node to the endpoint is less than or equal to the threshold dis. If dist≤dis, then perform collision detection. Through collision detection, determine whether the line segment between the new node and the endpoint collides with an obstacle. If there is a collision, proceed to step S24. If there is no collision, then form the final path segment by connecting the new node and the endpoint with the straight line. At this time, the completed path from the starting point to the endpoint is formed, and proceed to step S24. If dist > dis, proceed to step S24.

[0011] This invention also provides a dynamic adaptive UAV path planning method based on RRT*, which involves repeating any of the above path planning methods several times to obtain n paths, and then performing Pareto evaluation on the n paths, as follows: Step 1): Select the path with a dominance count of 0 from the n paths to obtain the Pareto front. : ; In the formula, For path dominance count; For paths with a path dominance count of 0; If there is a unique path in the Pareto front, then that path is the optimal path, and the optimized path is generated; if there are multiple paths in the Pareto front, then the congestion degree is calculated subsequently. Step 2) Sort the multiple paths in the Pareto front in ascending order of path length. Let the sorted paths be: ; for The formula for calculating the congestion distance in the path length dimension is: ; In the formula, The congestion level is the path length. This is the path length; , which is the longest path length; This represents the shortest path length. for and ,set up ; Step 3) Sort the multiple paths in the Pareto front in ascending order of tortuosity. The sorted paths are as follows: ; for The formula for calculating the congestion distance in terms of tortuosity is as follows: ; In the formula, The congestion distance is a measure of the degree of path tortuosity. The degree of path twists and turns; , which represents the maximum degree of path tortuosity; , which represents the minimum degree of path tortuosity; for and ,set up ; Step 4), Calculate the path Total congestion distance: ; In the formula, For path The corresponding path length, congestion level, and distance. For path The corresponding path curvature, congestion level, and distance; Step 5) Select the path with the highest total congestion as the optimal path, which generates the optimized path.

[0012] The beneficial effects of this invention are: it not only accelerates path convergence speed but also effectively improves the smoothness of the planned path, making it more adaptable to the actual flight requirements of UAVs. Path generation efficiency is high. The accuracy of path planning is improved in complex, densely obstacle-filled three-dimensional spaces. It achieves efficient, smooth, and reliable path planning in complex 3D environments, resulting in a superior overall path planning effect, suitable for navigation scenarios of UAVs and other autonomous mobile devices.

[0013] The intelligent variable step size mechanism uses different step sizes at different stages of exploration, and can quickly explore when facing dense obstacles, thus improving exploration efficiency. In the early stages of exploration, the large step size factor affects the large-scale exploration. As the algorithm explores the space, the large step size factor also decreases, which is conducive to the fine-grained exploration in the later stages.

[0014] In the later stages of exploration, direct target connections were introduced, which reduced the inflection points in the tree structure and accelerated the exploration speed.

[0015] A dynamic balance between "global exploration and local focus" is achieved through adaptive Gaussian sampling and target bias strategies.

[0016] Further features and aspects of the present invention will be clearly described in the following detailed description with reference to the accompanying drawings. Attached Figure Description

[0017] Figure 1 This is a flowchart of steps S1 to S11 of the dynamic adaptive UAV path planning method based on RRT*.

[0018] Figure 2 This is a flowchart of steps S11 to S25 of the dynamic adaptive UAV path planning method based on RRT*.

[0019] Figure 3 This describes the effect of adaptive Gaussian sampling in tree structure expansion during the first iteration.

[0020] Figure 4 This shows the effect of adaptive Gaussian sampling in tree structure expansion after 10 iterations;

[0021] Figure 5 This shows the effect of adaptive Gaussian sampling on tree structure expansion after 20 iterations;

[0022] Figure 6 This is the effect of adaptive Gaussian sampling on tree structure expansion after 30 iterations;

[0023] Figure 7 This shows the effect of adaptive Gaussian sampling on tree structure expansion after 40 iterations;

[0024] Figure 8 It is an adaptive Gaussian sampling method that explores the distribution of sampling points in the initial stage;

[0025] Figure 9 It is an adaptive Gaussian sampling method that explores the distribution of sampling points in the middle stage;

[0026] Figure 10 It uses adaptive Gaussian sampling to explore the distribution of sampling points in the later stages;

[0027] Figure 11 This is the effect of adaptive Gaussian sampling on path planning in two-dimensional space during the first iteration;

[0028] Figure 12 This is the effect of adaptive Gaussian sampling on path planning in two-dimensional space after 5 iterations;

[0029] Figure 13 This is the effect of adaptive Gaussian sampling on path planning in two-dimensional space after 10 iterations;

[0030] Figure 14This is the effect of adaptive Gaussian sampling on path planning in two-dimensional space after 20 iterations;

[0031] Figure 15 This is the effect of adaptive Gaussian sampling on path planning in two-dimensional space after 30 iterations;

[0032] Figure 16 This is a schematic diagram of the Pareto front;

[0033] Figure 17 This is a diagram illustrating the congestion level;

[0034] Figure 18 These are the 10 planned routes;

[0035] Figure 19 Yes Figure 18 The middle path is evaluated for multi-objective optimization, and the Pareto optimal solution is selected.

[0036] Figure 20 This is a comparison chart of the optimal path obtained through Pareto evaluation and existing paths based on RRT*, GB-RRT*, and Informed-RRT* algorithms;

[0037] Figure 21 yes Figure 20 XY projection of the path in the middle. Detailed Implementation

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] like Figure 1 and Figure 2 As shown, the dynamic adaptive UAV path planning method based on RRT* mainly includes the following steps: Step S1: Create a global map that includes obstacles.

[0040] Step S2: Determine the starting point and ending point of the drone.

[0041] Step S3: Starting from the origin, initialize a tree structure.

[0042] Step S4, calculate the adaptive target bias probability using the following formula (1). : (1); In formula (1), t is the exploration iteration progress (ranging from 0 to 1). , It is the current iteration number. Maximum number of iterations. It's manually set. For example, if the maximum number of iterations is set to 100, initially the tree structure only has a starting point, and the current iteration count is 1, then t = 1 / 100 = 0.01, meaning t ≈ 0, and the target bias probability is 0.1, which is a low probability. Target bias probability The maximum value is 0.5. When 0 ≤ t < 0.3, it is the early stage of iteration. When 0.3 ≤ t < 0.8, it is the middle stage of iteration. When 0.8 ≤ t ≤ 1, it is the late stage of iteration.

[0043] Step S5: Call the random number generation function (rand()) to generate a random number r between [0,1]. If r is less than the adaptive target bias probability... If yes, proceed to step S6; otherwise, proceed to step S7.

[0044] Step S6: Generate sampling points using a biased target sampling method. Randomly generate sampling points at a certain step size along the vector direction from the new node to the endpoint in the current tree structure. This certain step size is... : In the above formula, h is the exploration space parameter, α is the step size constant, and t is the exploration iteration progress. The new node in the current tree structure refers to the new node generated in the previous iteration. After completion, proceed to step S8.

[0045] Step S7: Generate sampling points using an adaptive Gaussian sampling method.

[0046] Step S701: Calculate the mean of the Gaussian distribution. There are two situations: In the first scenario, initially the tree structure only has a starting point, and the ending point is used as the mean. , This allows for priority exploration towards the destination, avoiding random scattering of sampling points in the initial stage. The second scenario involves a new node in the tree structure and an existing feasible path. (2) In formula (2), This refers to the new node in the current tree structure (the new node generated in the previous iteration). As the endpoint, These are the weighting coefficients. t represents the exploration iteration progress. Mean Used to control the sampling center, prioritize exploration in the target direction, and avoid random dispersion of sampling points in the initial stage; Step S702, calculate the dynamic covariance matrix: (3) In formula (3), Standard deviation It is an identity matrix (a three-dimensional diagonal matrix). Scaling factor t represents the exploration iteration progress; Step S703, further obtaining the three-dimensional Gaussian distribution as follows: , (4) In formula (4), Spatial dimension; Step S704: Generate sampling points. Based on and Generate 3 sampling points, namely x1, x2, and x3; each sampling point is a 3×1 vector; First, generate 4 sets of uniformly distributed random numbers: U(0,1) represents a uniform distribution in the interval (0,1); Secondly, three sets of standard normal random numbers z are generated from four sets of uniformly distributed random numbers using the Box-Muller transformation: Group 1 (corresponding to z of the first sampling point x1): Group 2 (corresponding to z of the second sampling point x2): Group 3 (corresponding to z of the 3rd sampling point x3): Then, Cholesky decomposition is performed on the dynamic covariance matrix Σ, which is decomposed into a lower triangular matrix. : There are a total of 8 standard normal random numbers; Then, three sampling points x1, x2, and x3 are generated. The first sampling point x1 is: Expand into component form: The second sampling point x2 is: Expand into component form: ; The third sampling point x3 is: Expand into component form: Finally, the three sampling points and the new nodes in the current tree structure were compared respectively. Obstacle collision detection is performed on the line segments between them. If there is no collision, the requirements are met, and the corresponding sampling points without collisions are added to the array. If none of the three sampling points meet the requirements, they are regenerated. If the sampling points saved in the array are not unique, the sampling point saved first in the array is selected as the final sampling point, and the final sampling point participates in subsequent processing. If the sampling points saved in the array are unique, that point is selected as the final sampling point.

[0047] Step S8: Find the node closest to the sampling point in the current tree. .

[0048] Step S9: Determine the step size through an intelligent variable step size mechanism.

[0049] Step S901, calculate the large step size factor using the following formula (5). : (5) In formula (5), h is the exploration space parameter, α is the step size constant, and t is the exploration iteration progress. The small step size factor is calculated using the following formula (6). : (6) In formula (6), h is the exploration space parameter and α is the step size constant.

[0050] Step S902, calculate the step distance using the following formula (7): (7) In formula (7), the random direction component is: in, For the generated sampling points, The node in the current tree that is closest to the sampling point; The target direction component is: in, The endpoint; The composite vector is:

[0051] Step S10: Expand the tree to obtain new nodes. , .

[0052] Step S11: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S12; if it does not collide, proceed to step S18.

[0053] Step S12, calculate the step distance using the following formula (8): (8) In formula (8), the random direction component is: in, For the generated sampling points, The node in the current tree that is closest to the sampling point; The target direction component is: in, The endpoint is; the composite vector is:

[0054] Step S13: Expand the tree to obtain new nodes. , .

[0055] Step S14: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S15; otherwise, proceed to step S18.

[0056] Step S15: Using only the pure random direction component and canceling the target direction component, calculate the distance of the step size using the following formula (9): (9) Simplified to: (10) In formula (10), the random direction component is: in, For the generated sampling points, It is the node in the current tree that is closest to the sampling point.

[0057] Step S16: Expand the tree to obtain new nodes. , .

[0058] Step S17: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S15; otherwise, proceed to step S18.

[0059] Step S18: Add the new node to the tree structure.

[0060] Step S19: Determine the search radius.

[0061] The search radius can be determined using the method employed in the standard RRT* algorithm. Alternatively, twice the maximum step size can be used as the search radius. Typically, as the tree structure expands, the nodes for pathfinding need to become increasingly refined, and the search radius changes continuously with the exploration progress. The dynamic radius formula is: (11) In formula (11), It is a spatial dimension (a path in three-dimensional space). =3), n is the number of spatial nodes, and γ is an environment-related constant, usually taken as: (12) In formula (12), yes The volume of a unit sphere in three-dimensional space. , where free-spacevolume is the volume of free space.

[0062] Step S20: Within the circular region centered on the new node and determined by the search radius, select the node with the minimum path cost as the parent node of the new node.

[0063] Step S21: Reconnect and update the tree structure.

[0064] Step S22: Has it been iterated 50 times? If so, proceed to step S23; otherwise, proceed to step S24.

[0065] Step S23: Attempt a direct connection. First, determine if the Euclidean distance *dist* from the new node to the endpoint is less than or equal to the threshold *dis*, which is set to 1.15 times the Euclidean distance between the start and end points. If *dist* ≤ *dis*, perform collision detection to determine if the line segment between the new node and the endpoint collides with an obstacle. If a collision occurs, a direct connection cannot be made in one step, and proceed to step S24. If no collision occurs, the line segment connecting the new node and the endpoint forms the final path segment, thus completing the path from the start to the endpoint, and proceed to step S24. If *dist* > *dis*, it means the distance is too far to connect in one step, and proceed to step S24.

[0066] As can be seen, introducing a direct connection mechanism, periodically attempting to connect the current new node with the target point (e.g., attempting a direct connection on the 50th iteration and another on the 100th iteration), can reduce path detours caused by tree structure expansion, significantly reduce path costs, make the path locally optimal between the current new node and the destination, avoid redundant iterations near the destination, and achieve rapid convergence to the destination.

[0067] Step S24: Determine whether the new node has reached the endpoint. If yes, proceed to step S25; otherwise, proceed to step S4 and continue iterating. The method for determining whether the new node has reached the endpoint can be the same as that used in conventional RRT* algorithms in existing technologies.

[0068] Step S25: Record the path.

[0069] As can be seen, the aforementioned UAV path planning method, on the one hand, in the sampling point generation stage, biases towards the endpoint with a certain probability and samples within the adaptive Gaussian space with a certain probability, realizing a sampling strategy of "ensuring exploration in the early stage of iteration and promoting convergence in the later stage." In the early stage of exploration, a lower target bias probability allows the algorithm to prioritize exploring the entire space; in the middle stage of exploration, a moderate target bias probability can balance global space exploration and target-oriented exploration; in the later stage of exploration, large-scale space exploration is no longer the focus, and fine exploration is carried out near the endpoint. On the other hand, an intelligent variable step size mechanism is adopted to use different step sizes at different stages of exploration, ensuring effective exploration in different environments (open areas, obstacle areas, and obstacle-dense areas), and rapid exploration when facing dense obstacles, effectively guaranteeing exploration efficiency. Furthermore, in the iteration process, a direct target connection mechanism is introduced to achieve rapid convergence to the endpoint.

[0070] To observe the effect of adaptive Gaussian sampling in tree structure expansion, the overall morphological evolution of adaptive Gaussian sampling was constructed in three-dimensional space, with a starting point (1, 2, 3) and an ending point (8, 8, 8). The effect is as follows. Figures 3-7 As shown. In Figures 3-7In the upper left 3D probability distribution plot, the probability density of each point in 3D space is visualized by the varying shades of color of the scatter points, intuitively showing the "probability cloud" shape of the Gaussian distribution. In the lower right covariance ellipsoid, the geometric shape of the covariance matrix is ​​visualized through the 3D ellipsoid, directly showing the spatial expansion characteristics of the distribution. In the lower left probability density evolution plot, the horizontal axis value (axis value) represents the position where the mean is the same on the X, Y, and Z axes in 3D space, and the vertical axis represents the probability density value at that position. The curves for different iteration numbers are distinguished by color mapping, clearly reflecting the iteration progress. In the lower right contour plot, the spatial distribution of probability density is shown through 3D isosurfaces (with equal Z values), highlighting the "shape outline" of the distribution. The initial state surface is large and irregular in shape, shrinking into a compact surface that is close to a sphere as the number of iterations increases (because the target covariance is a diagonal matrix).

[0071] The role of the dynamic covariance matrix in the algorithm, and its sampling characteristics in the early iteration stage (global exploration phase): the standard deviation Σ is close to the initial value, the Gaussian distribution has a wide coverage, and the sampling points form a "loose probability cloud" near the target, such as... Figure 8 As shown. Sampling characteristics during the mid-iteration phase (β linear decay, transition stage): β gradually decreases from 1, the variance of the Gaussian distribution shrinks, sampling points "focus" towards the target direction, randomness decreases, and determinism increases, as shown. Figure 9 As shown. In the later stages of iteration (β close to 0.3, local development phase), sampling characteristics include: the standard deviation shrinks to 30% of the initial value, sampling points are highly concentrated in the target neighborhood, almost degenerating into "target-oriented" deterministic sampling, as... Figure 10 As shown.

[0072] Adaptive Gaussian sampling performs as follows in two-dimensional path planning: Figures 11-15 As shown, the red dot represents the starting point, the green dot represents the target point, and the pink triangle represents the mean. Location: The pink circle represents the dynamic sampling area. Figure 11 It is one iteration. Figure 12 It is 5 iterations. Figure 13 It is 10 iterations. Figure 14 It is 20 iterations. Figure 15 It is 30 iterations.

[0073] To further optimize, steps S3 to S25 are repeated ten times to obtain 10 paths. Pareto evaluation is performed on these 10 paths, and the Pareto-optimal path is selected as the optimized path. The evaluation uses two metrics: path length and tortuosity. Tortuosity is defined as the angle between the vector between two nodes and the vector of the next adjacent node (a commonly used definition in existing technologies). If a path has a lower cost in both path length and tortuosity than other paths in these two aspects, that path is selected as the optimized path. The specific process is as follows: Step 1): Select the path with a dominance count of 0 from the n paths (e.g., 10 paths) to obtain the Pareto front. : In the formula, For path dominance count; For paths with a path dominance count of 0; such as Figure 16 As shown; If there is a unique path to the Pareto front, then that path is the optimal path, and the optimized path is generated. If there are multiple paths to the Pareto front, then subsequent congestion calculations are performed. Step 2) Sort the multiple paths in the Pareto front in ascending order of path length. Let the sorted paths be: ; for The formula for calculating the congestion distance in the path length dimension is: ; In the formula, The congestion level is the path length. This is the path length; , which is the longest path length; This represents the shortest path length. for and ,set up ; Step 3) Sort the multiple paths in the Pareto front in ascending order of tortuosity. The sorted paths are as follows: ; for The formula for calculating the congestion distance in terms of tortuosity is as follows: ; In the formula, The congestion distance is a measure of the degree of path tortuosity. The degree of path twists and turns; , which represents the maximum degree of path tortuosity; , which represents the minimum degree of path tortuosity; for and ,set up ; Step 4), Calculate the path Total congestion distance: ; In the formula, For path The corresponding path length, congestion level, and distance. For path The corresponding path tortuosity, congestion level, and distance; congestion level as follows: Figure 17 As shown; Step 5) Select the path with the highest total congestion as the optimal path, which generates the optimized path.

[0074] The above method was verified to a certain extent through simulation. The simulation experiment was conducted in the following environment: Windows 11 system, Intel(R) Core(TM) i5-13500HX processor with a main frequency of 2.50 GHz and 16GB of memory. A complex obstacle environment was built with the map size set to (1000, 1000, 1000), the starting point being (150, 150, 150), and the ending point being (950, 950, 800). Figure 18 These are the 10 planned routes. Figure 19 To Figure 18 The path is evaluated using multi-objective optimization to select the Pareto optimal solution. Figure 20 This is a comparison chart of the optimal path obtained through Pareto evaluation and existing paths based on RRT*, GB-RRT*, and Informed-RRT* algorithms. Figure 21 The XY projection of the path shows that the optimal path has significantly reduced tortuosity compared to the other three algorithms, with fewer bends and substantial improvements in both path length and tortuosity. For example... Figure 20 , Figure 21 As shown in the simulation experiment on the complex environment map, all four algorithms successfully completed path planning. After 30 repetitions of each experiment, in terms of path length, the present invention shortened the path planning time by 9.25%, 4.93%, and 10.61% compared to the existing technologies RRT*, GB-RRT*, and Informed-RRT*, respectively. Furthermore, in terms of planning time, the present invention reduced the time by 45.90%, 57.14%, and 80.00%, respectively. This extremely short path planning time ensures real-time path planning and can be used in scenarios with strict time requirements. Regarding path tortuosity, since the other three existing algorithms did not plan for path tortuosity, the tortuosity values ​​of the planned paths fluctuated greatly, sometimes being less tortuous and sometimes more tortuous with more bends. In contrast, the algorithm of the present invention reduced the path tortuosity by 65.89%, 52.55%, and 68.40%, respectively; and reduced the number of nodes by 92.60%, 92.67%, and 96.34%, respectively. The experimental results are shown in Table 1.

[0075] Table 1 Statistical Table of Experimental Results

[0076] The specific embodiments described above are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to these embodiments.

Claims

1. A dynamic adaptive UAV path planning method based on RRT*, characterized in that, Includes the following steps: Step S1: Create a global map containing obstacles; Step S2: Determine the starting point and ending point of the drone; Step S3: Starting from the origin, initialize a tree structure; Step S4, calculate the adaptive target bias probability using the following formula (1). : （1）； In formula (1), t is the progress of the exploration iteration. , It is the current iteration number. Maximum number of iterations; Step S5: Call the random number generation function to generate a random number r between [0,1]. If r is less than the adaptive target bias probability... Proceed to step S6 if the condition is met; otherwise proceed to step S7. Step S6: Generate sampling points in a biased target sampling manner. Randomly generate sampling points at a certain step size in the direction from the new node to the endpoint vector in the current tree structure. Proceed to step S8 after completion; Step S7: Generate sampling points using an adaptive Gaussian sampling method; Step S8: Find the node closest to the sampling point in the current tree. ; Step S9: Determine the step size through an intelligent variable step size mechanism; Step S10: Expand the tree to obtain new nodes. ; Step S11: Determine the new node's position using collision detection. The nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S12; if it does not collide, proceed to step S18. Step S12: Generate sampling points using an adaptive Gaussian sampling method; Step S13: Expand the tree to obtain new nodes. ; Step S14: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S15; if it does not collide, proceed to step S18. Step S15: Determine the step size through an intelligent variable step size mechanism; Step S16: Expand the tree to obtain new nodes. ; Step S17: Determine the new node through collision detection. With the nearest node Check whether the line segment between them collides with an obstacle. If it collides with an obstacle, proceed to step S15; if it does not collide, proceed to step S18. Step S18: Add the new node to the tree structure; Step S19: Determine the search radius; Step S20: Within the circular area centered on the new node and determined by the search radius, select the node with the minimum path cost as the parent node of the new node. Step S21: Reconnect and update the tree structure; Step S24: Determine if the new node has reached the endpoint. If yes, proceed to step S25; otherwise, proceed to step S4 and continue iterating. Step S25: Record the path.

2. The dynamic adaptive UAV path planning method based on RRT* according to claim 1, characterized in that, Step S7 is as follows: Step S701: Calculate the mean of the Gaussian distribution. There are two situations: In the first scenario, initially the tree structure only has a starting point, and the ending point is used as the mean. , ; The second scenario involves a new node in the tree structure, where a feasible path already exists. （2）； In formula (2), This is a new node in the current tree structure. As the endpoint, These are the weighting coefficients. t represents the exploration iteration progress; Step S702, calculate the dynamic covariance matrix: （3）； In formula (3), Standard deviation, It is the identity matrix. Scaling factor t represents the exploration iteration progress; Step S703, further obtaining the three-dimensional Gaussian distribution as follows: : （4）； In formula (4), Spatial dimension; Step S704, based on and Generate 3 sampling points, namely x1, x2, and x3; First, generate 4 sets of uniformly distributed random numbers: ； Secondly, three sets of standard normal random numbers z are generated from four sets of uniformly distributed random numbers using the Box-Muller transformation: Group 1: ； Group 2: ； Group 3: ； Then, Cholesky decomposition is performed on the dynamic covariance matrix Σ, which is decomposed into a lower triangular matrix. : ； Then, three sampling points x1, x2, and x3 are generated. The first sampling point x1 is: ； Expand into component form: ； The second sampling point x2 is: ； Expand into component form: ； The third sampling point x3 is: ； Expand into component form: ； Finally, the three sampling points and the new nodes in the current tree structure were compared respectively. Obstacle collision detection is performed on the line segments between them. If there is no collision, it meets the requirements. The corresponding sampling point without collision is selected and added to the array. If none of the three sampling points meet the requirements, they are regenerated. If the sampling points saved in the array are not unique, the sampling point saved first in the array is selected as the final sampling point. If the sampling point saved in the array is unique, that point is selected as the final sampling point.

3. The dynamic adaptive UAV path planning method based on RRT* according to claim 1 or 2, characterized in that, The process of determining the step size through the intelligent variable step size mechanism in step S9 is as follows: Step S901, calculate the large step size factor using the following formula (5). : （5）； In formula (5), h is the exploration space parameter, α is the step size constant, and t is the exploration iteration progress; The small step size factor is calculated using the following formula (6). : （6）； In formula (6), h is the exploration space parameter and α is the step size constant; Step S902, calculate the step distance using the following formula (7): （7）； In formula (7), the random direction component is: ； in, For the generated sampling points, The node in the current tree that is closest to the sampling point; The target direction component is: ； in, The endpoint; The composite vector is: ； The process of determining the step size through the intelligent variable step size mechanism in step S12 is as follows: the step size distance is calculated using the following formula (8): （8）； In formula (8), the random direction component is: ； The target direction component is: ； The composite vector is: ； The process of determining the step size through the intelligent variable step size mechanism in step S15 is as follows: The step distance is calculated using the following formula (9): （9）； Simplified to: （10）； In formula (10), the random direction component is: 。 4. The dynamic adaptive UAV path planning method based on RRT* according to claim 1, characterized in that, After step S21 and before step S24, add steps S22 and S23; in step S22, check if a certain number of iterations have been performed. If so, proceed to step S23; otherwise, proceed to step S24. Step S23, attempt a direct connection: First, determine whether the Euclidean distance dist from the new node to the endpoint is less than or equal to the threshold dis. If dist≤dis, then perform collision detection. Through collision detection, determine whether the line segment between the new node and the endpoint collides with an obstacle. If there is a collision, proceed to step S24. If there is no collision, then form the final path segment by connecting the new node and the endpoint with the straight line. At this time, the completed path from the starting point to the endpoint is formed, and proceed to step S24. If dist > dis, proceed to step S24.

5. A dynamic adaptive UAV path planning method based on RRT*, characterized in that, The path planning method described in claim 1 or 2 is repeated several times to obtain n paths. The Pareto evaluation of these n paths is then performed as follows: Step 1): Select the path with a dominance count of 0 from the n paths to obtain the Pareto front. : ； In the formula, For path dominance count; For paths with a path dominance count of 0; If there is a unique path in the Pareto front, then that path is the optimal path, and the optimized path is generated; if there are multiple paths in the Pareto front, then the congestion degree is calculated subsequently. Step 2) Sort the multiple paths in the Pareto front in ascending order of path length. Let the sorted paths be: ； for The formula for calculating the congestion distance in the path length dimension is: ； In the formula, The congestion level is the length of the path. This is the path length; , which is the longest path length; This represents the shortest path length. for and ,set up ; Step 3) Sort the multiple paths in the Pareto front in ascending order of tortuosity. The sorted paths are as follows: ； for The formula for calculating the congestion distance in terms of tortuosity is as follows: ； In the formula, The congestion distance is a measure of the degree of path tortuosity. The degree of path tortuosity; , represents the maximum degree of path tortuosity; , which represents the minimum degree of path tortuosity; for and ,set up ; Step 4), Calculate the path Total congestion distance: ； In the formula, For path The corresponding path length, congestion level, and distance. For path The corresponding path curvature, congestion level, and distance; Step 5) Select the path with the highest total congestion as the optimal path, which generates the optimized path.

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