Self-adaptive RRT-Connect ship path planning method based on quadtree
The adaptive RRT-Connect method based on quadtrees solves the problem of low path planning efficiency in complex sea areas, realizes adaptive path planning, and improves the success rate and efficiency of path planning.
Patent Information
- Application Number
- CN202511432140.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-09
- Publication Date
- 2026-01-09
AI Technical Summary
Existing ship path planning methods are inefficient and have low success rates in complex marine environments. Traditional algorithms suffer from data redundancy and low search efficiency in unstructured sea areas, while the RRT algorithm is ineffective in areas with dense obstacles and expands slowly.
An adaptive RRT-Connect method based on quadtrees is adopted. By rasterizing and dilating the electronic nautical chart, the quadtree is reconstructed, the leaf nodes of the navigation area are selected, and the normalized sampling probability is calculated based on the node area. The expansion step size is dynamically adjusted to achieve adaptive path planning.
It improves the efficiency and success rate of path planning, significantly enhances search efficiency and path planning accuracy in complex sea areas, and is more adaptable.
Smart Images
Figure CN121297849A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of ship routing technology, specifically relating to an adaptive RRT-Connect ship routing method based on quadtrees. Background Technology
[0002] With the booming development of the marine economy and intelligent shipping, ships frequently need to traverse unstructured sea areas containing complex islands, reefs, and shoals when performing long-distance transportation, marine resource exploration, and environmental monitoring missions. Path planning in such marine environments faces two severe challenges: the complex shapes and highly irregular spatial distribution of obstacles, and the stringent real-time requirements of planning algorithms in large-scale marine scenarios.
[0003] Traditional path planning algorithms, such as Both Dijkstra's algorithm and the fixed grid modeling algorithm have significant limitations when dealing with unstructured environments. Their reliance on fixed grid modeling often leads to data redundancy and low search efficiency, and they are prone to data explosion in large sea areas. While the RRT series of algorithms has the advantage of probabilistic completeness, their uniform random sampling strategy in obstacle-dense areas is prone to ineffective exploration, resulting in a low success rate of path planning. In open and sparse areas, their expansion is slow due to the fixed step size, making it difficult to effectively meet the needs of ships for efficient path planning in large and complex sea areas.
[0004] In summary, existing ship path planning methods still suffer from low efficiency and low success rate in large-scale and complex marine environments. Therefore, it is an urgent need to propose an environmentally adaptable path planning algorithm to solve the problems of low efficiency and low success rate of traditional methods. Summary of the Invention
[0005] The purpose of this invention is to solve the problems of low efficiency and low success rate of existing ship routing methods, and to propose an adaptive RRT-Connect ship routing method based on quadtree.
[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: an adaptive RRT-Connect ship routing method based on quadtrees, the method specifically including the following steps:
[0007] Step 1: After processing the data on the electronic chart, the electronic chart is then rasterized to obtain a rasterized electronic chart; and the rasterized electronic chart is then dilated to obtain a dilated rasterized electronic chart.
[0008] Step 2: Reconstruct the expanded grid electronic chart using a quadtree to obtain the spatial regions corresponding to each leaf node of the quadtree.
[0009] Step 3: Select the leaf nodes corresponding to the allowed navigation areas in the quadtree, and plan the ship path based on the spatial areas corresponding to the selected leaf nodes.
[0010] Furthermore, the specific process of step one is as follows:
[0011] Step 1: Extract the data of sea surface obstacles from the downloaded electronic nautical chart to obtain an electronic nautical chart containing only the location information of sea surface obstacles;
[0012] Step 12: Rasterize the electronic nautical chart obtained in Step 11 to obtain a rasterized electronic nautical chart.
[0013] Step 13: Process the rasterized electronic nautical chart obtained in Step 12 to obtain the expanded rasterized electronic nautical chart.
[0014] Furthermore, the specific process of step two is as follows:
[0015] Step 21: Use the entire expanded grid electronic chart as the spatial region corresponding to the root node of the quadtree;
[0016] Step 22: Initialize the number of node layers ;
[0017] Steps two and three, for the first For any node in the layer, determine whether the spatial region corresponding to that node contains both permitted navigation areas and prohibited navigation areas;
[0018] If the permitted navigation area and the prohibited navigation area are mixed, the spatial area corresponding to the node is further divided into four equal parts, that is, the node has 4 child nodes and the spatial area corresponding to the 4 child nodes.
[0019] If there is no mixture of permitted and prohibited navigation areas, then there is no need to further divide the spatial area corresponding to the node, and the node is treated as a leaf node of the quadtree.
[0020] Traversing the first After each node of the layer, we obtain the quadtree of the th layer. All nodes of the layer;
[0021] Step 2.4: Determine the fourth position of the quadtree. Does the layer contain nodes?
[0022] If the quadtree's first... If a layer has nodes, then let Return to steps two and three;
[0023] If the quadtree's first... If no nodes exist in a layer, the quadtree reconstruction is complete, yielding all leaf nodes of the quadtree and the spatial regions corresponding to each leaf node.
[0024] Furthermore, the specific process of step three is as follows:
[0025] Step 3: 1. Determine whether the spatial region corresponding to each leaf node of the quadtree is a permitted navigation area. Filter out the leaf nodes corresponding to the permitted navigation areas to obtain a candidate leaf node set composed of the filtered leaf nodes.
[0026] Step 3.2: Calculate the area of the spatial region corresponding to each of the selected leaf nodes;
[0027] Step 3: Calculate the normalized sampling probability of the selected leaf nodes based on the area of the spatial region corresponding to the selected leaf nodes.
[0028] Steps 3 and 4: Perform ship path planning based on the normalized sampling probabilities of each selected leaf node.
[0029] Furthermore, the specific process of step three is as follows:
[0030] Step 331: Calculate the total area of the spatial regions corresponding to all the selected leaf nodes. :
[0031]
[0032] In the formula, The total number of leaf nodes selected. For the selected first The area of the spatial region corresponding to each leaf node;
[0033] Step 332, the selected first The normalized sampling probability of each leaf node is:
[0034]
[0035] In the formula, For the selected first Normalized sampling probability of leaf nodes.
[0036] Furthermore, the specific process of steps three and four is as follows:
[0037] Based on the normalized sampling probability of each selected leaf node, the search starts simultaneously from the ship's starting position and target position. The search tree obtained by searching from the ship's starting position is called the starting tree, and the search tree obtained by searching from the ship's target position is called the target tree.
[0038] The search stops when the starting tree and the target tree find the spatial region corresponding to the same leaf node in the candidate leaf node set. The starting tree and the target tree are then connected to obtain the path of the ship from the starting position to the target position.
[0039] Furthermore, the search process for the starting tree is as follows:
[0040] Step 1: Construct a cumulative probability table based on the normalized sampling probabilities of each selected leaf node;
[0041] Step 2: Initialize the number of iterations ;
[0042] Step 3, Generate Random numbers between According to random numbers Within the interval of the cumulative probability table, select a leaf node from the set of candidate leaf nodes, and randomly select a point A from the spatial region corresponding to the selected leaf node;
[0043] Step 4: Connect the latest position found on the starting tree to point A using a line segment, and select point B on the line segment whose distance from the latest position found on the starting tree is the expansion step size;
[0044] If the selected point B is located in the spatial region corresponding to the candidate leaf node, then the selected point B will be used as the next point found by the starting tree search, and then step 5 will be executed.
[0045] If the selected point B is not located in the spatial region corresponding to the candidate leaf node, then return to step 3.
[0046] Step 5, let Return to step 3.
[0047] Furthermore, the specific process of step 1 is as follows:
[0048] The selected leaf nodes are randomly sorted, and the normalized sampling probability corresponding to the first leaf node in the sorting result is denoted as . Then the first interval in the cumulative probability table is ;
[0049] Let the normalized sampling probability corresponding to the second leaf node in the sorting result be denoted as . Then the second interval in the cumulative probability table is ;
[0050] The first in the sorted results The normalized sampling probability corresponding to each leaf node is denoted as . Then the th in the cumulative probability table The intervals are ;
[0051] The first in the sorted results The normalized sampling probability corresponding to each leaf node is denoted as . Then the th in the cumulative probability table The intervals are .
[0052] Preferably, the expansion step size is:
[0053]
[0054] Where ratio is the adjustment coefficient. This represents the maximum side length of the spatial region corresponding to the leaf node where the latest position found in the initial tree is located. To extend the step size.
[0055] The beneficial effects of this invention are:
[0056] This invention proposes an adaptive RRT-Connect ship path planning method based on quadtrees. After reconstructing an inflated raster map using quadtrees, the map resolution can be adaptively adjusted according to the distribution density of marine obstacles based on the spatial hierarchical data structure of the quadtrees. This enables intelligent environmental representation by simplifying the modeling of sparse obstacle areas and finely depicting dense obstacle areas. Furthermore, an adaptive step size mechanism is proposed to dynamically adjust the expansion step size based on environmental complexity, improving the adaptability to the environment during path planning, significantly enhancing the search efficiency of the RRT-Connect algorithm in complex nautical chart environments, and greatly increasing the success rate of path planning. Attached Figure Description
[0057] Figure 1 This is a flowchart of an adaptive RRT-Connect ship routing method based on a quadtree according to the present invention;
[0058] Figure 2 This is a schematic diagram of an electronic nautical chart after rasterization.
[0059] Figure 3 This is a schematic diagram of the rasterization result after dilation.
[0060] Figure 4 This is a schematic diagram of quadtree reconstruction of a small area of a raster map;
[0061] Figure 5 This is a schematic diagram of the tree structure of a quadtree map;
[0062] Figure 6 This is a path planning result diagram obtained using the method of the present invention. Detailed Implementation
[0063] To make the method of the present invention clearer and easier to understand, the method of the present invention will be further described in detail below with reference to the accompanying drawings.
[0064] Specific implementation method one: Combining Figure 1 This embodiment describes an adaptive RRT-Connect ship routing method based on a quadtree, which specifically includes the following steps:
[0065] Step 1: After processing the data on the electronic nautical chart, the electronic nautical chart is then rasterized to obtain a rasterized electronic nautical chart; and the rasterized electronic nautical chart is then dilated to obtain a dilated rasterized electronic nautical chart.
[0066] The specific details of step one are explained in detail below with reference to the accompanying drawings:
[0067] Step 1: Download the electronic nautical chart file in 000 format, and extract the data of sea surface obstacles from the downloaded electronic nautical chart. That is, remove all data other than sea surface obstacles from the downloaded electronic nautical chart to obtain an electronic nautical chart containing only the location information of sea surface obstacles.
[0068] Step 12: Rasterize the electronic nautical chart obtained in Step 11 to obtain a rasterized electronic nautical chart.
[0069] For example, the range of the downloaded electronic nautical chart is... , The rasterization resolution of electronic nautical charts is The grid size is If the number of rows or columns in the raster is odd, then copy the last row or column to make the number of rows and columns in the rasterized result even. The result of rasterizing an electronic nautical chart is as follows: Figure 2 As shown.
[0070] Step 13: Guided by the requirements of safe navigation for ships, the obstacle boundaries on the electronic chart need to be expanded by approximately 1 kilometer to allow for a safe obstacle avoidance buffer distance for ships. Therefore, the rasterized electronic chart obtained in Step 12 is processed to obtain the expanded rasterized electronic chart.
[0071] It should be noted that after obtaining the rasterized electronic nautical chart, for each grid cell containing an obstacle, the distance between the center of the obstacle's grid cell and the center of each surrounding grid cell can be calculated. Grid cells surrounding obstacles with distances less than 1 kilometer are also marked as obstacles. By traversing each obstacle grid cell in the rasterized electronic nautical chart obtained in steps one and two, the following can be obtained: Figure 3 The expanded grid electronic chart shown.
[0072] Step 2: Reconstruct the expanded grid electronic chart using a quadtree to obtain the spatial regions corresponding to each leaf node of the quadtree.
[0073] The specific details of step two are explained in detail below with reference to the accompanying drawings:
[0074] Step 21: Use the entire expanded grid electronic chart as the spatial region corresponding to the root node of the quadtree;
[0075] Step 22: Initialize the number of node layers In this invention, the root node of the quadtree is taken as the first-level node of the quadtree.
[0076] Steps two and three, for the first For any node in the layer, determine whether the spatial region corresponding to that node contains both permitted navigation areas and prohibited navigation areas;
[0077] If the permitted navigation area and the prohibited navigation area are mixed, the spatial area corresponding to the node is further divided into four equal parts, that is, the node has 4 child nodes and the spatial area corresponding to the 4 child nodes.
[0078] If there is no mixture of permitted and prohibited navigation areas (i.e., the spatial area corresponding to the node only includes permitted or prohibited navigation areas), then there is no need to further divide the spatial area corresponding to the node, and the node is treated as a leaf node of the quadtree.
[0079] Traversing the first After each node of the layer, we obtain the quadtree of the th layer. All nodes of the layer;
[0080] Step 2.4: Determine the fourth position of the quadtree. Does the layer contain nodes?
[0081] If the quadtree's first... If a layer has nodes, then let Return to steps two and three;
[0082] If the quadtree's first... If no nodes exist in a layer, the quadtree reconstruction is complete, yielding all leaf nodes of the quadtree and the spatial regions corresponding to each leaf node.
[0083] Figure 4 This is a schematic diagram illustrating the quadtree reconstruction of a small area of a raster map. Figure 5This is the tree structure of the quadtree map, where the green nodes are the leaf nodes. The quadtree is only subdivided at the densely and unevenly distributed boundaries between navigable and restricted areas in the grid map. This allows for large jumps in sparse obstacle areas and fine exploration in dense obstacle areas during path planning, ensuring search accuracy while improving planning efficiency.
[0084] Step 3: Select the leaf nodes corresponding to the allowed navigation areas in the quadtree, and perform ship path planning based on the spatial areas corresponding to the selected leaf nodes;
[0085] The specific details of step three are explained in detail below with reference to the accompanying diagram:
[0086] Step 3: 1. Determine whether the spatial region corresponding to each leaf node of the quadtree is a permitted navigation area. Filter out the leaf nodes corresponding to the permitted navigation areas to obtain a candidate leaf node set composed of the filtered leaf nodes.
[0087] Step 3.2: Calculate the area of the spatial region corresponding to each of the selected leaf nodes;
[0088] Step 3: Calculate the normalized sampling probability of the selected leaf nodes based on the area of the corresponding spatial regions; specifically:
[0089] Step 331: Calculate the total area of the spatial regions corresponding to all the selected leaf nodes. That is, summing the areas of the spatial regions corresponding to all feasible leaf nodes:
[0090]
[0091] In the formula, The total number of leaf nodes selected. For the selected first The area of the spatial region corresponding to each leaf node;
[0092] Then, assign a sampling probability to all feasible leaf nodes in the quadtree according to the area of the spatial region they represent. The sampling probability of each leaf node should be proportional to the area of its corresponding spatial region.
[0093] Step 332, the selected first The normalized sampling probability of each leaf node is:
[0094]
[0095] In the formula, For the selected first Normalized sampling probability of each leaf node;
[0096] Step 33 allows for automatic adjustment of the sampling distribution based on different map environments.
[0097] Steps three and four: Ship path planning is performed based on the normalized sampling probabilities of each selected leaf node. The path planning is based on the step-size adaptive RRT-Connect algorithm, and the specific planning process is as follows:
[0098] Based on the normalized sampling probability of each selected leaf node, the search starts simultaneously from the ship's starting position and target position. The search tree obtained by searching from the ship's starting position is called the starting tree, and the search tree obtained by searching from the ship's target position is called the target tree.
[0099] The search stops when the starting tree and the target tree find the spatial region corresponding to the same leaf node in the candidate leaf node set. The starting tree and the target tree are then connected to obtain the path of the ship from the starting position to the target position.
[0100] The search process for the starting tree and the target tree is the same. The following is a detailed explanation of the search process for the starting tree, using the starting tree as an example and with reference to the attached diagram:
[0101] Step 1: Construct a cumulative probability table based on the normalized sampling probabilities of each selected leaf node; specifically:
[0102] The selected leaf nodes are randomly sorted, and the normalized sampling probability corresponding to the first leaf node in the sorting result is denoted as . Then the first interval in the cumulative probability table is ;
[0103] Let the normalized sampling probability corresponding to the second leaf node in the sorting result be denoted as . Then the second interval in the cumulative probability table is ;
[0104] The first in the sorted results The normalized sampling probability corresponding to each leaf node is denoted as . Then the th in the cumulative probability table The intervals are ;
[0105] The first in the sorted results The normalized sampling probability corresponding to each leaf node is denoted as . Then the th in the cumulative probability table The intervals are ;
[0106] Step 2: Initialize the number of iterations ;
[0107] Step 3, Generate Random numbers between According to random numbers Within the interval of the cumulative probability table, select a leaf node from the set of candidate leaf nodes (i.e., when the random number...). When the cumulative probability table is in the 5th interval, the selected leaf node is the 5th leaf node in the random sorting result, and a point A is randomly selected from the spatial region corresponding to the selected leaf node;
[0108] Step 4: Connect the latest position found on the starting tree to point A using a line segment, and select point B on the line segment whose distance from the latest position found on the starting tree is the expansion step size;
[0109] If the selected point B is located in the spatial region corresponding to the candidate leaf node, then the selected point B will be used as the next point found by the starting tree search, and then step 5 will be executed.
[0110] If the selected point B is not located in the spatial region corresponding to the candidate leaf node, then return to step 3.
[0111] Step 5, let Return to step 3.
[0112] It should be noted that the methods for setting the expansion step size in this invention include, but are not limited to, the following:
[0113]
[0114] Where ratio is the adjustment coefficient. The maximum side length of the spatial region corresponding to the leaf node where the latest position found in the starting tree is located (when the spatial region is a square). Let be the side length of the square; when the spatial region is rectangular, (The length of the rectangle). To extend the step size.
[0115] This invention adjusts the fixed expansion step size of the traditional RRT-Connect algorithm to an adaptive expansion step size based on the side length of the leaf nodes in a quadtree. This allows for faster expansion in sparse obstacle regions by increasing the step size, and for maintaining passability in dense obstacle regions by decreasing the step size. An adjustable coefficient `ratio` is set during the acquisition of the adaptive expansion step size. This coefficient is used to adjust the ratio of the adaptive expansion step size to the maximum side length of the current leaf node until the starting tree and the target tree satisfy the connection condition. This invention sets the adjustable coefficient `ratio` to 0.8, when the starting point is... The target point is At that time, the path planning results obtained are as follows Figure 6 As shown.
[0116] The experimental part of this invention performed 5000 path planning operations. The average path planning time of the traditional RRT-Connect algorithm was 0.77s, while the average path planning time of the method of this invention was 0.72s. The success rate of the traditional RRT-Connect algorithm in path planning was 75%, while the success rate of the method of this invention was 92.5%. It can be seen that the method of this invention greatly improves the adaptability to the environment. In a large-scale complex nautical chart environment, the method of this invention can effectively improve the efficiency and success rate of path planning, and the searched paths are improved in terms of the number of nodes and path curvature.
[0117] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. An adaptive RRT-Connect ship routing method based on quadtrees, characterized in that, The method specifically includes the following steps: Step 1: After processing the data on the electronic chart, the electronic chart is then rasterized to obtain a rasterized electronic chart; and the rasterized electronic chart is then dilated to obtain a dilated rasterized electronic chart. Step 2: Reconstruct the expanded grid electronic chart using a quadtree to obtain the spatial regions corresponding to each leaf node of the quadtree. Step 3: Select the leaf nodes corresponding to the allowed navigation areas in the quadtree, and plan the ship path based on the spatial areas corresponding to the selected leaf nodes.
2. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 1, characterized in that, The specific process of step one is as follows: Step 1: Extract the data of sea surface obstacles from the downloaded electronic nautical chart to obtain an electronic nautical chart containing only the location information of sea surface obstacles; Step 12: Rasterize the electronic nautical chart obtained in Step 11 to obtain a rasterized electronic nautical chart. Step 13: Process the rasterized electronic nautical chart obtained in Step 12 to obtain the expanded rasterized electronic nautical chart.
3. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 1, characterized in that, The specific process of step two is as follows: Step 21: Use the entire expanded grid electronic chart as the spatial region corresponding to the root node of the quadtree; Step 22: Initialize the number of node layers ; Steps two and three, for the first For any node in the layer, determine whether the spatial region corresponding to that node contains both permitted navigation areas and prohibited navigation areas; If the permitted navigation area and the prohibited navigation area are mixed, the spatial area corresponding to the node is further divided into four equal parts, that is, the node has 4 child nodes and the spatial area corresponding to the 4 child nodes. If there is no mixture of permitted and prohibited navigation areas, then there is no need to further divide the spatial area corresponding to the node, and the node is treated as a leaf node of the quadtree. Traversing the first After each node of the layer, we obtain the quadtree of the th layer. All nodes of the layer; Step 2.4: Determine the fourth position of the quadtree. Does the layer contain nodes? If the quadtree's first... If a layer has nodes, then let Return to steps two and three; If the quadtree's first... If no nodes exist in a layer, the quadtree reconstruction is complete, yielding all leaf nodes of the quadtree and the spatial regions corresponding to each leaf node.
4. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 3, characterized in that, The specific process of step three is as follows: Step 3:
1. Determine whether the spatial region corresponding to each leaf node of the quadtree is a permitted navigation area. Filter out the leaf nodes corresponding to the permitted navigation areas to obtain a candidate leaf node set composed of the filtered leaf nodes. Step 3.2: Calculate the area of the spatial region corresponding to each of the selected leaf nodes; Step 3: Calculate the normalized sampling probability of the selected leaf nodes based on the area of the spatial region corresponding to the selected leaf nodes. Steps 3 and 4: Perform ship path planning based on the normalized sampling probabilities of each selected leaf node.
5. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 4, characterized in that, The specific process of step 33 is as follows: Step 331: Calculate the total area of the spatial regions corresponding to all the selected leaf nodes. : In the formula, The total number of leaf nodes selected. For the selected first The area of the spatial region corresponding to each leaf node; Step 332, the selected first The normalized sampling probability of each leaf node is: In the formula, For the selected first Normalized sampling probability of leaf nodes.
6. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 5, characterized in that, The specific process of steps three and four is as follows: Based on the normalized sampling probability of each selected leaf node, the search starts simultaneously from the ship's starting position and target position. The search tree obtained by searching from the ship's starting position is called the starting tree, and the search tree obtained by searching from the ship's target position is called the target tree. The search stops when the starting tree and the target tree find the spatial region corresponding to the same leaf node in the candidate leaf node set. The starting tree and the target tree are then connected to obtain the path of the ship from the starting position to the target position.
7. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 6, characterized in that, The search process for the starting tree is as follows: Step 1: Construct a cumulative probability table based on the normalized sampling probabilities of each selected leaf node; Step 2: Initialize the number of iterations ; Step 3, Generate Random numbers between According to random numbers Within the interval of the cumulative probability table, select a leaf node from the set of candidate leaf nodes, and randomly select a point A from the spatial region corresponding to the selected leaf node; Step 4: Connect the latest position found on the starting tree to point A using a line segment, and select point B on the line segment whose distance from the latest position found on the starting tree is the expansion step size; If the selected point B is located in the spatial region corresponding to the candidate leaf node, then the selected point B will be used as the next point found by the starting tree search, and then step 5 will be executed. If the selected point B is not located in the spatial region corresponding to the candidate leaf node, then return to step 3. Step 5, let Return to step 3.
8. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 7, characterized in that, The specific process of step 1 is as follows: The selected leaf nodes are randomly sorted, and the normalized sampling probability corresponding to the first leaf node in the sorting result is denoted as . Then the first interval in the cumulative probability table is ; Let the normalized sampling probability corresponding to the second leaf node in the sorting result be denoted as . Then the second interval in the cumulative probability table is ; The first in the sorted results The normalized sampling probability corresponding to each leaf node is denoted as . Then the th in the cumulative probability table The intervals are ; The first in the sorted results The normalized sampling probability corresponding to each leaf node is denoted as . Then the th in the cumulative probability table The intervals are .
9. The adaptive RRT-Connect ship routing method based on a quadtree according to claim 8, characterized in that, The expansion step size is: Where ratio is the adjustment coefficient. This represents the maximum side length of the spatial region corresponding to the leaf node where the latest position found in the initial tree is located. To extend the step size.