Robot path planning method and system based on deep learning and deformable scanning
Through a combination of deep learning and deformable scanning, a path probability distribution map is generated to guide non-uniform sampling of RRT, solving the problems of low sampling efficiency and insufficient real-time performance in robot path planning, and achieving efficient and real-time path planning in complex environments.
Patent Information
- Application Number
- CN202510568898.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-30
- Publication Date
- 2025-07-29
AI Technical Summary
The existing robot path planning algorithms have low sampling efficiency and slow convergence speed in complex environments, and the generalization ability of traditional manual rule design is limited. Deep learning auxiliary methods are difficult to model long-distance path dependencies, and lack real-time performance.
Using a method based on deep learning and deformable scanning, a path probability distribution map is generated through a deformable scanning encoder, directing the non-uniform sampling of RRT, replacing traditional manual rule design, combining dynamic programming and residual connection output feature maps, improving the algorithm's generalization ability to complex environments and ensuring real-time performance.
It realizes efficient and real-time path planning in complex environments, improves the generalization ability and path optimization of the algorithm, and solves the sampling blindness problem in traditional methods.
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Figure CN120385361A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field related to robot path planning, and particularly relates to a robot path planning method and system based on deep learning and deformable scanning. Background Technique
[0002] The statements in this part only provide background technical information related to the present invention, and do not necessarily constitute prior art.
[0003] Robot path planning is the core problem of autonomous navigation, and its goal is to generate safe and efficient motion trajectories in an environment with obstacles. Sampling-based path planning algorithms such as RRT* are mainstream in such problems. By randomly sampling to construct a search tree, although they have probabilistic completeness and asymptotic optimality, there are problems of low sampling efficiency and slow convergence speed in complex environments. Existing improvement methods are mainly divided into two categories. Among them, heuristic sampling such as goal-biased sampling and obstacle-repulsion sampling relies on manually designed rules, and the generalization ability is limited; most deep learning assistance uses convolutional neural network CNN to predict the sampling distribution, but the local receptive field of CNN is difficult to model long-distance path dependencies, and the number of parameters is large, resulting in insufficient real-time performance. Summary of the Invention
[0004] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a robot path planning method and system based on deep learning and deformable scanning. By generating a path probability distribution map through a deformable scanning encoder to guide the non-uniform sampling of RRT, it solves the problem of blind sampling in traditional methods, replaces traditional manual rule design, improves the generalization ability of the algorithm for complex environments, and at the same time ensures the real-time performance and path optimality of the algorithm.
[0005] To achieve the above purpose, the present invention adopts the following technical solutions: In the first aspect, the present invention provides a robot path planning method based on deep learning and deformable scanning, including: An encoder based on the deformable scanning mechanism generates a minimum spanning tree from a two-dimensional grid map, predicts the offset and scaling of vertices in the minimum spanning tree, dynamically adjusts the coverage area of vertices, performs bidirectional dynamic programming along the tree topology, and combines dynamic programming and residual connection to output a final feature map; An encoder based on the deformable scanning mechanism generates a minimum spanning tree from a two-dimensional grid map, predicts the offset and scaling of vertices in the minimum spanning tree, dynamically adjusts the coverage area of vertices, performs bidirectional dynamic programming along the tree topology, and combines dynamic programming and residual connection to output a final feature map; Generating a path probability distribution map reflecting the probability of generating path nodes at different positions in the map through the decoder and the gated attention mechanism for the final feature map; Use the generated path probability distribution map to guide the RRT* algorithm for dynamic non-uniform sampling to obtain the path planning result of the robot.
[0006] In a second aspect, the present invention provides a robot path planning system based on deep learning and deformable scanning, including: An encoding module, which is configured to: based on an encoder of a deformable scanning mechanism, generate a minimum spanning tree from a two-dimensional grid map, predict the offset and scaling of vertices in the minimum spanning tree, dynamically adjust the coverage area of the vertices, perform bidirectional dynamic programming along the tree topology, and combine dynamic programming with residual connection to output a final feature map; based on an encoder of a deformable scanning mechanism, generate a minimum spanning tree from a two-dimensional grid map, predict the offset and scaling of vertices in the minimum spanning tree, dynamically adjust the coverage area of the vertices, perform bidirectional dynamic programming along the tree topology, and combine dynamic programming with residual connection to output a final feature map; A path probability distribution map generation module, which is configured to: generate a path probability distribution map reflecting the probability of generating path nodes at different positions in the map from the final feature map through a decoder and a gated attention mechanism; A path planning module, which is configured to: use the generated path probability distribution map to guide the RRT* algorithm for dynamic non-uniform sampling to obtain the path planning result of the robot.
[0007] In a third aspect, the present invention provides an electronic device, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the method described in the first aspect is completed.
[0008] In a fourth aspect, the present invention provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the method described in the first aspect is completed.
[0009] In a fifth aspect, the present invention provides a computer program product, including a computer program. When the computer program is executed by a processor, the method described in the first aspect is implemented.
[0010] The above one or more technical solutions have the following beneficial effects: In the present invention, a path probability distribution map is generated through a deformable scanning encoder to guide the non-uniform sampling of RRT, solve the problem of blind sampling in traditional methods, replace traditional manual rule design, improve the generalization ability of the algorithm for complex environments, and at the same time ensure the real-time performance and path optimality of the algorithm.
[0011] In the present invention, deep learning and deformable scanning are combined, and the deformable scanning encoder can adapt to path planning work in different scenarios through large-scale data understanding.
[0012] Advantages of additional aspects of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The accompanying drawings forming a part of this specification are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention.
[0014] Figure 1 It is the overall block diagram of the robot path planning method based on deep learning and deformable scanning in the first embodiment of the present invention; Figure 2 It is a partial visualization diagram of the robot path planning result in the first embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0015] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.
[0016] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention.
[0017] In the case of no conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.
[0018] TERMINOLOGY EXPLANATION: RRT path planning algorithm: A path planning algorithm based on random sampling, which explores the state space by incrementally constructing a search tree. Its basic process is: starting from the starting point, randomly sampling points in the free space, selecting the nearest node on the tree to extend towards the sampling point, avoiding obstacles to generate new nodes, and gradually expanding the tree structure until reaching the target area. RRT has probabilistic completeness. When a feasible solution exists, the solution will definitely be found when the number of samplings approaches infinity, but there is no guarantee of optimality.
[0019] State space model: The mathematical representation of a continuous linear time-invariant system, which describes the dynamic response of the state vector to the input through differential equations and realizes the linear complexity calculation of sequence modeling.
[0020] TERMINOLOGY EXPLANATION: RRT Path Planning Algorithm: A path planning algorithm based on random sampling that explores the state space by incrementally constructing a search tree. Its basic process is as follows: Starting from the starting point, randomly sample points in the free space, select the nearest node on the tree and extend it towards the sampled point, generate new nodes while avoiding obstacles, and gradually expand the tree structure until the target area is reached. RRT has probabilistic completeness (when a feasible solution exists, it is certain to find the solution as the number of samplings approaches infinity), but lacks an optimality guarantee.
[0021] State Space Model: The mathematical representation of a continuous linear time-invariant system that describes the dynamic response of the state vector to inputs through differential equations, achieving linear complexity calculations for sequence modeling.
[0022] Example 1 This example discloses a robot path planning method based on deep learning and deformable scanning, including: An encoder based on a deformable scanning mechanism generates a minimum spanning tree from a two-dimensional grid map, predicts the offset and scaling of vertices in the minimum spanning tree, dynamically adjusts the coverage area of vertices, performs bidirectional dynamic programming along the tree topology, and combines dynamic programming with residual connections to output the final feature map; Pass the final feature map through a decoder and a gated attention mechanism to generate a path probability distribution map reflecting the probabilities of generating path nodes at different positions in the map; Use the generated path probability distribution map to guide the RRT* algorithm for dynamic non-uniform sampling to obtain the robot's path planning result.
[0023] This example uses an encoder-decoder architecture based on the Vision Mamba model, namely DTMamba, to replace the traditional CNN architecture, and inputs a two-dimensional grid map as the Ground Truth, where 0 represents the free space, 1 represents the obstacle, the starting point , the end point . The original two-dimensional grid map is encoded to obtain a feature map . The feature map is input to the decoder to obtain a feature map of a regular size, and then a path probability distribution map is generated through gated attention . Finally, based on the path probability distribution map guide the RRT for dynamic non-uniform sampling.
[0024] In this example, an improved Mamba model is used as each block of the decoder, and the Mamba model is used as each block of the decoder. The improved Mamba model is specifically: replacing the TSA module in the existing Mamba model with a deformable scanning module, namely DTSA.
[0025] In this embodiment, a deformable scanning module is designed to predict the offset of tokens in a two-dimensional grid map and generate a dynamic graph through a tree topology , and then input the state space layer updated by parameter training for feature extraction to obtain a feature map .
[0026] Use PyCharm to build a Pytorch deep learning framework, use a single RTX3090 graphics card for training, set Epoch to 100, and the corresponding network training set parameters are shown in Table 1.
[0027] Table 1: Network training parameters
[0028] The deformable scanning module optimizes the feature propagation path by constructing a dynamic minimum spanning tree (MST). Defining edge weights using feature similarity, generating a tree topology in combination with the Contractive Boruvka algorithm, and adjusting the node coverage area through dynamic offset / scale to achieve long-distance path dependence modeling and efficient aggregation of features.
[0029] The deformable scanning module (DTSA) is based on state space models (SSMs). State space models are generally considered continuous linear time-invariant systems, and map the input to the output signal through the state vector , where , and represent the time step, the number of the signal, and the state size respectively. The state space model can be represented by the following linear ordinary differential equation:
[0030] where is the hidden state at time t, , representing the system matrix, control matrix, output matrix, and connection matrix respectively ; the parameter update of the state space model is essentially a process in which the hidden state h(t) is updated with the input x(t) .
[0031] Use the zero-order hold rule to discretize the continuous system described by the equation. Convert the continuous variables A, B, C, D to the corresponding discrete parameters at the specified sampling scale :
[0032] Mamba introduces a dynamic mechanism to selectively filter the input into sequential states. Use linear projection to calculate the parameters , and , to improve context awareness, and then use these inputs to adaptively discretize parameters, and obtain path graph features through training and parameter update , and the specific calculation method is as follows:
[0033] As Figure 1 shown, the deformable scanning module, i.e., DTSA, specifically includes the following steps: Step 21: Construct a dynamic topology graph : Given an input two-dimensional grid map , regard it as a graph structure , where each token is a vertex. In particular, the tokens where the path start point and end point are located are determined as fixed vertices, and no offset and scaling are performed subsequently. The edges adopt a four-neighborhood graph, and each vertex is connected to the four neighborhoods of up, down, left, and right.
[0034] Define the edge weights through feature similarity:
[0035] where is the feature vector of adjacent vertices.
[0036] Adopt the Contractive Boruvka algorithm to gradually merge the minimum-weight edges and generate a minimum spanning tree MST.
[0037] Step 22: Dynamic offset and scaling: Based on the feature extraction layer, dynamically predict the offset and scaling :
[0038] where is the feature extraction layer, such as the Linear projection Linear layer; Tanh and ReLU are activation functions, and are dynamic weight coefficients, is the initial bias.
[0039] For each vertex , dynamically adjust its coverage area:
[0040] where is the initial center coordinate of each token before moving.
[0041] Step 23: Tree State Propagation: Dynamic programming acceleration: Perform bidirectional dynamic programming along the tree topology, aggregate child node states from bottom to top (Leaf→Root), and update parent node to child node states from top to bottom (Root→Leaf):
[0042] in, The intermediate state calculated for the Leaf to Root or Root to Leaf stage, For the parent node The hidden state of is a collection of child nodes, 、 is the discretized form of the system matrix.
[0043] Combine dynamic programming with residual connection to output the final features:
[0044] Among them, D is the connectivity matrix, which describes how the input directly affects the system output; X is the input matrix, which represents the entire image; H is the hidden state matrix, and C is the output matrix.
[0045] The loss function during the training of the deformable scanning module is: Task cross entropy loss :
[0046] Among them, G is the ground truth node distribution map. is the predicted path probability distribution map, H and W represent the height and width of the grid map respectively.
[0047] Apply L2 regularization to the bias and scale parameters:
[0048] The total loss function of the deformable scanning module is defined as :
[0049] The basic steps of the deep learning-guided non-uniform sampling RRT* algorithm are: input path starting point , target area collection , map Map, sampling space S, constraint C, first initialize the node set , edge set ,Tree , and load the results obtained from the DTMamba deep learning model Subsequently, perform cyclic iteration (N attempts) to expand nodes and generate paths. The solution to the corresponding path planning problem is as follows: Step 31: Let the state space be , the obstacle space and the free space . The path planning problem can be formulated as:
[0050] where is the total path time (or step size), is the time variable, represents the planned path, represents the path at time represents the optimal path, is the starting point of the path, is the set of target regions, indicating that the end point of the path needs to fall within the target region centered at , is the path cost function, is the set of all feasible paths.
[0051] Step 32: Cost function design: The cost functions for the obstacle space and the free space are defined as:
[0052] where is the weight parameter, is the linear velocity component at is the path point to the path point vector.
[0053] Step 33: Hybrid sampling strategy: DTMamba-RRT* uses a hybrid probability density function for sampling:
[0054] where is a uniform distribution, is the sampling ratio, is the non-uniform distribution obtained by gated attention calculation on the feature map output by DTMamba. The calculation method is:
[0055] where sigmoid is the activation function, and are the weight matrix and bias of the gated attention network layer, The probability distribution graph of the path nodes output by DTMamba.
[0056] Step 34: Progressive optimality guarantee: RRT* inherits the progressive optimality condition of RRT. Let the search radius Satisfy:
[0057] Among them, Is the state space dimension, Is the Lebesgue measure, Is The volume of the n-dimensional unit sphere. Based on the progressive optimality condition, if the final predicted target point enters the target area, the loop is stopped and the final path planning result is obtained.
[0058] In robot path planning, the deep learning model can process inputs such as grid maps, start-end coordinates, etc., learn the complex relationship between obstacle distribution and path topology, generate a probability distribution graph for guiding sampling, replace traditional manual rule design, and improve the generalization ability of the algorithm for complex environments. Its core advantage lies in the end-to-end feature learning mechanism and the modeling ability for high-dimensional space non-linear relationships.
[0059] Deformable scanning optimizes the feature propagation path by constructing a dynamic minimum spanning tree (MST). The edge weights are defined using feature similarity, combined with the Contractive Boruvka algorithm to generate the tree topology, and the node coverage area is adjusted by dynamic offset / scale to achieve long-distance path dependence modeling and efficient aggregation of features Using the DTMamba-RRT* algorithm for path planning, partial results are visualized as Figure 2 Shown.
[0060] The DTMamba-RRT* algorithm has higher accuracy and better real-time performance. The time comparison with the mainstream RRT algorithm is shown in Table 2: Table 2 Algorithm performance comparison
[0061] This implementation plan gives full play to the global modeling ability and linear computational complexity of Mamba, generates a path probability distribution through the deformable scanning state space model, guides the non-uniform sampling of RRT, solves the problem of sampling blindness of traditional methods, and at the same time ensures the real-time performance and path optimality of the algorithm.
[0062] Example two The purpose of this embodiment is to provide a robot path planning system based on deep learning and deformable scanning, including: An encoding module, which is configured to: use a deformable scanning encoder to generate a minimum spanning tree from a two-dimensional grid map, predict the offset and scaling of vertices in the minimum spanning tree, dynamically adjust the coverage area of the vertices, perform bidirectional dynamic programming along the tree topology, and combine dynamic programming with residual connections to output the final features; A path probability distribution map generation module, which is configured to: fuse the final features and multi-scale features extracted from the two-dimensional grid map, and generate a path probability distribution map reflecting the probabilities of generating path nodes at different positions in the map by combining a gated attention mechanism; A path planning module, which is configured to: use the generated path probability distribution map to guide the RRT* algorithm for dynamic non-uniform sampling to obtain the path planning result of the robot.
[0063] In more embodiments, there is also provided: An electronic device, including a memory and a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the method described in Embodiment 1 is completed. For the sake of brevity, it will not be elaborated here.
[0064] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.
[0065] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.
[0066] A computer-readable storage medium for storing computer instructions, which when executed by the processor, completes the method described in Embodiment 1.
[0067] The method in Embodiment 1 can be directly embodied as being executed and completed by a hardware processor, or by a combination of hardware and software modules in the processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.
[0068] A computer program product includes a computer program which, when executed by a processor, implements the method described in Embodiment 1.
[0069] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which are executed in a device on a target real or virtual processor to perform the process / method described above. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functions of program modules can be combined or divided as needed. The machine-executable instructions for program modules can be executed within local or distributed devices. In a distributed device, program modules can be located in local and remote storage media.
[0070] The computer program code for implementing the method of the present invention can be written in one or more programming languages. This computer program code can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when the program code is executed by the computer or other programmable data processing device, the functions / operations specified in the flowchart and / or block diagram are implemented. The program code can be executed entirely on the computer, partially on the computer, as a stand-alone software package, partially on the computer and partially on a remote computer, or entirely on a remote computer or server.
[0071] In the context of the present invention, the computer program code or related data can be carried by any suitable carrier so that a device, apparatus, or processor can perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, etc. Examples of signals can include electrical, optical, radio, acoustic, or other forms of propagated signals, such as carrier waves, infrared signals, etc.
[0072] Those of ordinary skill in the art will realize that the units and algorithm steps of the examples described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. A professional technician can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of this application.
[0073] Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications or deformations that can be made without creative efforts on the basis of the technical solutions of the present invention are still within the protection scope of the present invention.
Claims
1. A robot path planning method based on deep learning and deformable scanning, characterized in that Including: An encoder based on a deformable scanning mechanism that generates a minimum spanning tree from a two-dimensional grid map, predicts the offset and scaling of vertices in the minimum spanning tree, dynamically adjusts the coverage area of vertices, performs bidirectional dynamic programming along the tree topology, and combines dynamic programming with residual connections to output a final feature map; Pass the final feature map through a decoder and a gated attention mechanism to generate a path probability distribution map reflecting the probabilities of generating path nodes at different positions in the map; Use the generated path probability distribution map to guide the RRT* algorithm for dynamic non-uniform sampling to obtain the path planning result of the robot.
2. The robot path planning method based on deep learning and deformable scanning according to claim 1, wherein, The encoder of the deformable scanning mechanism uses an improved Mamba model, and the improved Mamba model replaces the TSA module in the Mamba model with a deformable scanning module, and the deformable scanning module obtains path map features based on a state space model.
3. The robot path planning method based on deep learning and deformable scanning according to claim 1 or 2, characterized in that, Generate a minimum spanning tree from a two-dimensional grid map, predict the offset and scaling of vertices in the minimum spanning tree, and dynamically adjust the coverage area of vertices, specifically: Regard the two-dimensional grid map as a graph structure; where each pixel or marker is used as a vertex, the edges use a four-neighborhood graph, and the edge weights are calculated through feature similarity; Use the Contractive Boruvka algorithm to gradually merge the minimum-weight edges to generate a minimum spanning tree; Based on the feature extraction layer, dynamically predict the offset and scaling of each vertex, and dynamically adjust the corresponding coverage area of each vertex.
4. The robot path planning method based on deep learning and deformable scanning according to claim 1 or 2, characterized in that, Perform bidirectional dynamic programming along the tree topology, combine dynamic programming with residual connections to output a final feature map, specifically: Perform bidirectional dynamic programming along the tree topology, aggregate the states of child nodes from bottom to top, and update the states from parent nodes to child nodes from top to bottom; Combine the dynamic programming result with the residual connection to output the final feature map.
5. The robot path planning method based on deep learning and deformable scanning according to claim 1, wherein During training, the deformable scanning module uses the task cross-entropy loss and the loss function obtained by applying L2 regularization to the offset and scaling parameters as the total loss function; where the task cross-entropy loss is: , Among them, H and W respectively represent the height and width of the grid map, and G is the distribution map of the true path nodes of the true path, The predicted path probability distribution map; Applying L2 regularization to the offset and scaling parameters is: , Among them, is the offset of each vertex, is the scaling of each vertex.
6. The robot path planning method based on deep learning and deformable scanning according to claim 1, wherein, Use the generated path probability distribution map to guide the non-uniform sampling of the RRT* algorithm through a hybrid sampling strategy, and the probability density function of the hybrid sampling strategy is a weighted combination of the uniform distribution of the free space and the predicted non-uniform distribution.
7. A robot path planning system based on deep learning and deformable scanning, characterized in that, Including: An encoding module configured to: based on an encoder of a deformable scanning mechanism, generate a minimum spanning tree from a two-dimensional grid map, predict the offset and scaling of vertices in the minimum spanning tree, dynamically adjust the coverage area of vertices, perform bidirectional dynamic programming along the tree topology, and combine dynamic programming with residual connections to output a final feature map; Based on an encoder of a deformable scanning mechanism, generate a minimum spanning tree from a two-dimensional grid map, predict the offset and scaling of vertices in the minimum spanning tree, dynamically adjust the coverage area of vertices, perform bidirectional dynamic programming along the tree topology, and combine dynamic programming with residual connections to output a final feature map; A path probability distribution map generation module configured to: pass the final feature map through a decoder and a gated attention mechanism to generate a path probability distribution map reflecting the probabilities of generating path nodes at different positions in the map; A path planning module, which is configured to: use the generated path probability distribution map to guide the RRT* algorithm for dynamic non-uniform sampling to obtain the path planning result of the robot.
8. An electronic device, characterized in that, It includes a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the method according to any one of claims 1-6 is completed.
9. A computer-readable storage medium, characterized in that, It is used to store computer instructions. When the computer instructions are executed by the processor, the method according to any one of claims 1-6 is completed.
10. A computer program product, characterized in that, It includes a computer program. When the computer program is executed by the processor, the method according to any one of claims 1-6 is implemented.
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