A robot trajectory prediction method based on time-frequency wavelet transform and graph network

Abstract

The application belongs to the technical field of trajectory prediction, and discloses a robot trajectory prediction method based on time-frequency wavelet transform and graph network, which comprises the following steps: 1, collecting body perception data; 2, obtaining high-quality multi-dimensional historical trajectory data; 3, mapping the multi-dimensional historical trajectory data into a feature information matrix and generating a graph structure; 4, obtaining potential spatio-temporal evolution characteristics; 5, the decoder converts the potential spatio-temporal evolution characteristics into wavelet coefficients; 6, the wavelet coefficients are transmitted to learn the local discriminative transition mode in the spatio-temporal dimension, and the reconstructed trajectory signal and the prediction target value are obtained respectively. The application can fully exploit the spatio-temporal dependence involved in the robot motion in an open environment to cope with the challenges brought by complex data relationships, and introduces a wavelet attention module on the basis of the asymmetric encoder-decoder architecture, which helps to supplement the supervision information and significantly improves the model prediction performance.

Description

Technical Field

[0001] This invention belongs to the field of trajectory prediction technology, specifically relating to a robot trajectory prediction method based on time-frequency wavelet transform and graph networks. Background Technology

[0002] With the rapid development of embodied intelligence technology, robots have been widely applied in various fields, such as industrial manufacturing, geographical exploration, traffic control, agricultural production, and medical and health care, to replace or assist humans in completing tasks with higher difficulty and safety requirements. In order to optimize scheduling strategies and improve decision-making efficiency, robot trajectory prediction has been studied in depth to fully support back-end tasks such as path planning and motion control.

[0003] The main goal of trajectory prediction is to predictively describe the attributes of discrete trajectory points of a robot, such as position, velocity, and attitude, by comprehensively considering the semantic information of the environment and the intent information of the target. This can be divided into short-term prediction and long-term prediction. Specifically, short-term prediction predicts the trajectory within the next two seconds based on the current target state information; long-term prediction has a broader coverage by combining intent recognition to generate a probability distribution of the trajectory. Although many powerful trajectory prediction methods based on physical models, statistics, and planning have been developed, designing practical and effective predictors for robots remains challenging for researchers due to complex coupled dynamics and uncertain external disturbances.

[0004] Chinese patent application CN120489100A discloses a method and system for localization and trajectory prediction of a swimming pool robot that integrates sonar and vision. This application can effectively improve the real-time performance and accuracy of trajectory prediction, providing strong support for subsequent tracking, control, and maintenance of the robot. However, this application fails to capture the spatial topology involved in robot motion in open environments. In practice, the robot's motion states are rich and varied, supported by multiple sensors such as LiDAR, cameras, GPS, and IMU. The relationship between the robot and the dynamic interactive environment is not linear, but involves complex nonlinear transitions and coupling connections. Without feature processing of the spatial topology, the model cannot adapt to this heterogeneous correlation and obtains biased trajectory prediction results. The solutions in this regard in this application are not yet clear, which may affect the stability of backend tasks such as path planning and motion control.

[0005] Chinese patent application CN120561884A discloses a model training method and trajectory prediction method based on multi-dimensional feature fusion. This application effectively overcomes the misjudgment of complex scenes caused by predictions relying solely on temporal and spatial feature sets in related technologies. However, it fails to model the trajectory in the frequency domain, losing more entangled local details. In fact, the robot's motion trajectory involves frequency information. Specifically, driven by motion intentions such as climbing, turning, and obstacle avoidance, the robot's position, speed, and posture react, producing non-stationary jitters that lead to changes in local details. These changes are usually unobservable in the time domain. Without using frequency domain analysis techniques to effectively decompose historical trajectories, the model may be unable to deeply infer key information from multi-dimensional sensor signals, significantly reducing the accuracy and reliability of trajectory predictions.

[0006] In summary, existing methods still suffer from two key problems that urgently need to be addressed. Firstly, current methods focus on temporal trajectory modeling, neglecting the analysis of more complex local frequency details. Secondly, they ignore the spatial topology involved in robot motion in open environments. These issues may prevent the model from learning the potential maneuvering patterns of the trajectory, thereby interfering with prediction performance and hindering the robot from making more accurate and efficient scheduling and decisions. Summary of the Invention

[0007] To address the aforementioned technical issues, this application provides a robot trajectory prediction method based on time-frequency wavelet transform and graph networks. It involves an asymmetric encoder-decoder architecture that integrates graph networks. This architecture combines high efficiency and scalability, and can fully exploit the spatiotemporal dependencies involved in robot motion in open environments to address the challenges posed by complex data relationships. Furthermore, a wavelet attention module is introduced on the basis of the asymmetric encoder-decoder architecture, which helps to supplement supervision information and significantly improves the model's prediction performance.

[0008] To achieve the above objectives, this application employs the following technical solution:

[0009] This application discloses a robot trajectory prediction method based on time-frequency wavelet transform and graph networks. The robot trajectory prediction method is implemented through a prediction system, and specifically includes the following steps:

[0010] Step 1: Collect embodied perception data: Collect embodied perception data by moving the robot in the physical world and dynamically interacting with the open environment. The embodied perception data includes data from LiDAR, camera, GPS, and IMU.

[0011] Step 2: Perform noise reduction, filtering, and feature extraction on the embodied perception data obtained in Step 1 to achieve normalized dimensions, avoid abnormally large or small outliers, and remove interference information, so as to obtain high-quality multi-dimensional historical trajectory data.

[0012] Step 3: Use the one-dimensional CNN of the prediction system to map the multi-dimensional historical trajectory data obtained in Step 2 into a feature information matrix, and design a graph builder to generate a graph structure oriented towards the feature information matrix.

[0013] Step 4: Input the graph structure and feature information matrix generated in Step 3 into the graph attention (GAT) layer of the prediction system to capture the corresponding spatial coupling relationship, and use the multi-layer gated recurrent unit (GRU) of the prediction system to extract the temporal dimension information to obtain the potential spatiotemporal evolution features.

[0014] Step 5: Decoder of the prediction system The latent spatiotemporal evolution features obtained in step 4 are converted into wavelet coefficients with multi-scale resolution to capture non-stationary jitter.

[0015] Step 6: Use the inverse wavelet transform module of the prediction system to pass the wavelet coefficients with multi-scale resolution to learn the local discriminative transition mode in the spatiotemporal dimension, and obtain the reconstructed trajectory signal and the predicted target value respectively.

[0016] A further improvement of this application is that step 3 specifically includes the following steps:

[0017] Step 3.1: A one-dimensional CNN integrates multi-dimensional historical trajectory data. Project the model into the embedding space (a continuous, low-dimensional vector space) and compute the corresponding feature information matrix. Extracting the unique characteristics of embodied perception data:

[0018]

[0019] in, Indicates an S-shaped growth curve. This represents a one-dimensional CNN operation with a kernel size of 1. Represents the weight matrix. Indicates deviation, An index representing a timestamp. This helps the model understand the robot's position, posture, velocity, and other motion states, as well as open environmental elements such as obstacles and weather.

[0020] Step 3.2: Use a graph builder to process multi-dimensional historical trajectory data. View it as a graph structure ,in Represents a set of nodes, nodes It is a continuous vector based on trajectory attributes. Represents the set of edges, with any node. and nodes There must be mutual connections between them (implicit interactions exist between trajectory attributes). Therefore, the adjacency matrix of the complete graph is set. The connection weights are , Representing the node index, adjacency matrix It is diagonal, and the nodes have the maximum connectivity.

[0021] A further improvement in this application is that step 4 specifically includes the following steps:

[0022] Step 4.1: Calculate the graph structure generated in Step 3. and feature information matrix The input is fed into the Graph Attention (GAT) layer, which allows each node to aggregate messages from its neighbors and calculate the attention score of its neighbors.

[0023]

[0024] in, Represents a linear rectified function with leakage; Represents the learnable weight matrix; This indicates a splicing operation. Indicates the transpose symbol. Represents the index of a node in the set of neighboring nodes. , and Both represent nodes. Represents a node The set of neighboring nodes;

[0025] No. The output representation of each node is formalized as follows:

[0026]

[0027] Feature information matrix Transformed into an output representation with spatial correlation The Graph Attention (GAT) layer does not change the dimensionality of the graph structure;

[0028] Step 4.2, considering the encoder The task is to extract autoregressive properties with dynamic attributes, connect multi-layer gated recurrent units (GRUs) to graph attention (GAT) layers, and process them sequentially over time. Mapping is performed to obtain potential spatiotemporal evolution features. .

[0029] A further improvement of this application is that step 5 specifically includes the following steps:

[0030] Step 5.1: Use the decoder Generating wavelet coefficients Each sub-decoder Generate hierarchical wavelet coefficients :

[0031]

[0032] in, Indicates the index of the graded wavelet coefficients. Indicates the total number of sub-decoders;

[0033] Step 5.2: Apply wavelet attention module to latent spatiotemporal evolution features Weighted summation is performed to obtain the enhanced spatiotemporal features. :

[0034]

[0035]

[0036]

[0037] in, , , and Both represent weighted matrices. Indicates the spatiotemporal characteristics of transition. Represents the linear rectified function. Returns a matrix with the input elements as its diagonal. The attention score is used to determine the importance of historical trajectory variables relative to the current variable (including spatial information), and the weighting process is performed by the jump connection.

[0038] Step 5.3: The wavelet attention module uses convolution operations to extract enhanced spatiotemporal features. Context embedding :

[0039]

[0040] Among them, high-pass filter and low-pass filter Embedding context Decomposed into multi-scale features, the first High-pass filter of layer and low-pass filter The output is represented as and ;

[0041] Step 5.4: As the filter approaches the edge of the finite signal, the convolution operation needs to supplement the values ​​exceeding the boundary using signal expansion techniques. Therefore, the context embedding is determined based on the properties of the wavelet attention module and the multi-dimensional historical trajectory data. The length of the context embedding is generally used. Symmetric extensions are typically used to guarantee context embedding. Continuity at the boundary:

[0042]

[0043] in, Indicates the first Layer context embedding Length, , , This represents half the length of the high-pass filter. This indicates a round-down operation;

[0044] Step 5.5: Model context embedding using a single-layer gated recurrent unit (GRU). , to obtain wavelet embedding Embedding wavelets The data is fed into a fully connected network to generate wavelet coefficients for the decoder. :

[0045]

[0046] in, express layer; This indicates a fully connected network.

[0047] A further improvement in this application is that step 6 specifically includes the following steps:

[0048] Step 6.1: Directly reconstruct the wavelet coefficients to enable the decoder to... Learn time-frequency representations at different scales and compute the encoder. Generated wavelet coefficients Compared with the true wavelet coefficients The mean square error between them, and the wavelet loss function is:

[0049]

[0050]

[0051] in, It is the first The output of the first sub-decoder The first variable The estimated value of each element, It is the first [data source] obtained directly from multi-dimensional historical trajectory data through wavelet transform analysis. The first variable The fundamental truth value of each element. Represents the generated wavelet coefficients Compared with the true wavelet coefficients The sum of the total mean square errors between them Indicates the first The mean square error of each decomposition. Indicates the index of the sub-decoder. This indicates the total number of sub-decoders. Dimensions representing historical trajectory data Indicates the first Layer context embedding Length;

[0052] Step 6.2: The inverse wavelet transform module processes the wavelet coefficients of each sensor variable. Performing an inverse transform to reconstruct the trajectory signal helps supplement supervisory information and improve model performance. Therefore, the wavelet coefficient matrix set... Converted to The trajectory sequence;

[0053] Step 6.3: The reconstruction filter iteratively combines low-frequency and high-frequency coefficient pairs until a series of trajectory signals are recovered in the time domain.

[0054]

[0055] in, This represents the inverse wavelet transform operation. Used to trim redundant segments caused by signal spread. , and All represent wavelet coefficients. The reconstructed multi-dimensional trajectory data is the reconstructed signal;

[0056] Step 6.4: Calculate the reconstructed signal With real signals Differences between :

[0057]

[0058] Step 6.5: Reuse the inverse wavelet transform module to convert the wavelet coefficient matrix set... Convert to The key attribute variables, i.e., to obtain the corresponding predicted values. The prediction loss function is calculated as follows:

[0059]

[0060] in, The dimension representing the trajectory prediction value. Represents the actual trajectory value;

[0061] Step 6.6, Joint , , The loss function for end-to-end training of the one-dimensional CNN, graph attention layer, and decoder is:

[0062]

[0063] in, and Each represents a trade-off factor used to balance the importance of different losses. The model weights are updated after each training epoch.

[0064] A further improvement of this application is that the prediction system includes an encoder. decoder And the inverse wavelet transform module,

[0065] The encoder Composed of a one-dimensional CNN, a graph constructor, a graph attention layer, and multiple gated recurrent units, the one-dimensional CNN processes multi-dimensional historical trajectory data. Mapped into feature information matrix The graph builder generates a graph structure oriented towards the feature information matrix, and the graph attention layer extracts multidimensional historical trajectory data. The spatial coupling relationship, the multi-layer GRU extracts multi-dimensional historical trajectory data. The temporal dimension information, after being processed by a graph attention layer and multiple GRU layers, is then processed by the encoder. Capturing multidimensional historical trajectory data Potential spatiotemporal evolution characteristics ;

[0066] The decoder Composed of multiple sub-decoders Stacked sequentially, each sub-decoder Each decoder includes a wavelet attention module, a single-layer gated recurrent unit, and a fully connected network. Used to generate hierarchical wavelet coefficients By combining multi-level wavelet coefficients Find the final wavelet coefficients. ;

[0067] The wavelet attention module will incorporate latent spatiotemporal evolution features. Converted into initial wavelet coefficients with multi-scale resolution;

[0068] A single-layer gated cyclic unit (GRU) models the initial wavelet coefficients to capture their context dependencies, resulting in the wavelet embedding. ;

[0069] The fully connected network fits wavelet embeddings And adjust the wavelet embedding The dimension is determined to generate wavelet coefficients for each sub-decoder. Only generate hierarchical wavelet coefficients By cascading all the hierarchical wavelet coefficients The final wavelet coefficients are obtained. , computational encoder Generated wavelet coefficients Compared with the true wavelet coefficients The mean square error between and ;

[0070] The inverse wavelet transform module passes wavelet coefficients, and the inverse wavelet transform module passes wavelet coefficients with multi-scale resolution, respectively, to obtain reconstructed multi-dimensional historical trajectory data. and trajectory prediction value Calculate real, multi-dimensional historical trajectory data With reconstructed multi-dimensional historical trajectory data The loss function value between Calculate the actual trajectory value and the predicted trajectory value The loss function value between

[0071] Cascade the above , and The overall loss function value is obtained. ,in, and It is a trade-off factor used to balance the importance of each loss.

[0072] The beneficial effects of this application are:

[0073] This application utilizes graph networks to design an asymmetric encoder-decoder architecture that can effectively learn the complex nonlinear transitions and coupling relationships of data from various sensors such as LiDAR, cameras, GPS, and IMU. This provides the model with spatiotemporal evolution characteristics related to the robot's motion state and open environment elements, thereby enhancing autoregressive properties and heterogeneous correlation, significantly improving trajectory prediction performance, and providing strong support for backend tasks such as path planning and motion control.

[0074] The wavelet attention module designed in this application can fully integrate the semantic information of the environment and the intention information of the target, and directly transmit and reconstruct the trajectory signal in the frequency-space to provide local discrimination transition modes related to robot motion attributes such as position, attitude, and velocity. This helps to supplement the model's supervision information, better adapt to changes in trajectory data, and reduce prediction bias caused by external interference or motion intention. Attached Figure Description

[0075] Figure 1 This is the overall framework diagram of the prediction system in this application.

[0076] Figure 2 This is a flowchart of the prediction method in this application.

[0077] Figure 3 This is a schematic diagram of the wavelet attention module in this application. Detailed Implementation

[0078] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not essential.

[0079] like Figure 1 As shown, this application discloses a robot trajectory prediction system based on time-frequency wavelet transform and graph networks. The prediction system includes an encoder. decoder And the inverse wavelet transform module.

[0080] The encoder Composed of a one-dimensional CNN, a graph constructor, a graph attention layer, and multiple gated recurrent units, the one-dimensional CNN processes multi-dimensional historical trajectory data. Mapped into feature information matrix The graph builder generates a graph structure oriented towards the feature information matrix, and the graph attention layer extracts multidimensional historical trajectory data. The spatial coupling relationship, the multi-layer GRU extracts multi-dimensional historical trajectory data. The temporal dimension information, after being processed by a graph attention layer and multiple GRU layers, is then processed by the encoder. Capturing multidimensional historical trajectory data Potential spatiotemporal evolution characteristics .

[0081] The decoder Composed of multiple sub-decoders Stacked sequentially, each sub-decoder Each decoder includes a wavelet attention module, a single-layer gated recurrent unit, and a fully connected network. Used to generate hierarchical wavelet coefficients By combining multi-level wavelet coefficients Find the final wavelet coefficients. .

[0082] The wavelet attention module will incorporate latent spatiotemporal evolution features. Converted into initial wavelet coefficients with multi-scale resolution;

[0083] A single-layer gated cyclic unit (GRU) models the initial wavelet coefficients to capture their context dependencies, resulting in the wavelet embedding. .

[0084] The fully connected network fits wavelet embeddings And adjust the wavelet embedding The dimension is determined to generate wavelet coefficients for each sub-decoder. Only generate hierarchical wavelet coefficients By cascading all the hierarchical wavelet coefficients The final wavelet coefficients are obtained. , computational encoder Generated wavelet coefficients Compared with the true wavelet coefficients The mean square error between and .

[0085] The inverse wavelet transform module transmits wavelet coefficients, specifically wavelet coefficients with multi-scale resolution (due to the hierarchical extraction of wavelet coefficients by the sub-encoder), thereby obtaining reconstructed multi-dimensional historical trajectory data. and trajectory prediction value Calculate real, multi-dimensional historical trajectory data With reconstructed multi-dimensional historical trajectory data The loss function value between Calculate the actual trajectory value and the predicted trajectory value The loss function value between

[0086] Cascade the above , and The overall loss function value is obtained. ,in, and It is a trade-off factor used to balance the importance of each loss.

[0087] This application was trained on a server equipped with an Intel i7-12700KF CPU and a GeForce RTX 4090 GPU.

[0088] The following section uses the example of autonomous vehicle trajectory prediction in a weaving area of ​​a highway in China to illustrate this application in detail.

[0089] like Figure 2 The present application describes a robot trajectory prediction method based on time-frequency wavelet transform and graph networks, comprising the following steps:

[0090] Step 1: Collect lane environment and autonomous vehicle sensor data: The weaving zone consists of six main roads and two auxiliary roads. Its characteristic is that each vehicle needs to change lanes at least once to complete the weaving operation. Based on this, the trajectory data features include autonomous vehicle motion state data such as position coordinates, instantaneous speed, instantaneous acceleration, and heading, as well as lane environment data collected by multiple source sensors such as LiDAR, camera, GPS, and IMU.

[0091] Step 2: Preprocessing of Autonomous Vehicle Trajectory Data: By applying visualization technology, discontinuities in the trajectory can be observed. For these discontinuous trajectories, null value imputation is used, and centroid coordinates and bounding box coordinates are obtained through linear interpolation. In addition, techniques such as Z-Score scaling, smoothing and denoising, and optical transformation are used to normalize, clean, and enhance the lane environment and autonomous vehicle sensor data.

[0092] Step 3, Expected Encoder To efficiently capture the topological coupling of multi-source data, a graph builder was designed to generate trajectory feature graph structures for autonomous vehicles. The specific steps include:

[0093] Step 3.1: A one-dimensional CNN integrates multi-dimensional historical trajectory data. Projected into the embedding space (a continuous, low-dimensional vector space), a feature information matrix containing the autonomous vehicle's position, speed, heading, and other motion states, as well as the lane environment, is extracted. Extracting the unique characteristics of embodied perception data:

[0094]

[0095] in, Indicates an S-shaped growth curve. This represents a one-dimensional CNN operation with a kernel size of 1. Represents the weight matrix. Indicates deviation, An index representing a timestamp; this helps the model understand the robot's position, posture, speed, and other motion states, as well as open environmental elements such as obstacles and weather.

[0096] Step 3.2: Use a graph builder to process multi-dimensional historical trajectory data. View it as a graph structure ,in Represents a set of nodes, nodes It is a continuous vector based on trajectory attributes. Represents the set of edges, with any node. and nodes There must be mutual connections between them (implicit interactions exist between trajectory attributes). Therefore, the adjacency matrix of the complete graph is set. The connection weights are , Representing the node index, adjacency matrix It is diagonal, and the nodes have the maximum connectivity.

[0097] Step 4: Input the graph structure and feature information matrix generated in Step 3 into the graph attention (GAT) layer of the prediction system to capture the corresponding spatial coupling relationships. Then, use the multi-layer gated recurrent unit (GRU) of the prediction system to extract the temporal dimension information, obtain the potential spatiotemporal evolution features, and further transmit and reconstruct the trajectory signal with the help of the decoder. Step 4 specifically includes the following steps:

[0098] Step 4.1: Calculate the graph structure generated in Step 3. and feature information matrix The input is fed into the Graph Attention (GAT) layer, which allows each node to aggregate messages from its neighbors and calculate the attention score of its neighbors.

[0099]

[0100] in, Represents a linear rectified function with leakage; Represents the learnable weight matrix; This indicates a splicing operation. Indicates the transpose symbol. Represents the index of a node in the set of neighboring nodes. , and Both represent nodes. Represents a node The set of neighboring nodes;

[0101] No. The output representation of each node is formalized as follows:

[0102]

[0103] Feature information matrix Transformed into an output representation with spatial correlation The Graph Attention (GAT) layer does not change the dimensionality of the graph structure;

[0104] Step 4.2, considering the encoder The task is to extract autoregressive properties with dynamic attributes, connect multi-layer gated recurrent units (GRUs) to graph attention (GAT) layers, and process them sequentially over time. Mapping is performed to obtain potential spatiotemporal evolution features. .

[0105] Step 5: The decoder of the prediction system, which consists of multiple wavelet attention modules, multi-layer gated recurrent units (GRUs), and fully connected networks stacked together. The latent spatiotemporal evolution features obtained in step 4 are converted into wavelet coefficients with multi-scale resolution to capture non-stationary jitter. Specifically, this includes the following steps:

[0106] Step 5.1: Use the decoder Generating wavelet coefficients Each sub-decoder Generate hierarchical wavelet coefficients :

[0107]

[0108] in, Indicates the index of the graded wavelet coefficients. Indicates the total number of sub-decoders;

[0109] Step 5.2: Apply wavelet attention module to latent spatiotemporal evolution features Weighted summation is performed to obtain the enhanced spatiotemporal features. :

[0110]

[0111]

[0112]

[0113] in, , , and Both represent weighted matrices. Indicates the spatiotemporal characteristics of transition. Represents the linear rectified function. Returns a matrix with the input elements as its diagonal. The attention score represents the importance of historical trajectory variables relative to the current variable (including spatial information). The weighting process is performed by the jump connection;

[0114] Step 5.3: The wavelet attention module uses convolution operations to extract enhanced spatiotemporal features. Context embedding :

[0115]

[0116] Among them, high-pass filter and low-pass filter Embedding context Decomposed into multi-scale features, the first High-pass filter of layer and low-pass filter The output is represented as and ;

[0117] Step 5.4: As the filter approaches the edge of the finite signal, the convolution operation needs to expand the signal to obtain values ​​beyond the signal boundary. Therefore, the context embedding is determined based on the properties of the wavelet attention module and the multi-dimensional historical trajectory data. The length of the context embedding is generally used. Symmetric extensions are typically used to guarantee context embedding. Continuity at the boundary:

[0118]

[0119] in, Indicates the first Layer context embedding Length, , , This represents half the length of the high-pass filter. This indicates a round-down operation;

[0120] Step 5.5: Model context embedding using a single-layer gated recurrent unit (GRU). , to obtain wavelet embedding Embedding wavelets The data is fed into a fully connected network to generate wavelet coefficients for the decoder. :

[0121]

[0122] in, express layer; This indicates a fully connected network.

[0123] Step 6: Use the inverse wavelet transform module of the prediction system to pass the wavelet coefficients with multi-scale resolution to learn the local discriminative transition modes in the spatiotemporal dimensions, thereby obtaining the reconstructed trajectory signal and the predicted target value. This specifically includes the following steps:

[0124] Step 6.1: Directly reconstruct the wavelet coefficients to enable the decoder to... Learn time-frequency representations at different scales and compute the encoder. Generated wavelet coefficients Compared with the true wavelet coefficients The mean square error between them, and the wavelet loss function is:

[0125]

[0126]

[0127] in, It is the first The output of the first sub-decoder The first variable The estimated value of each element, It is the first [data source] obtained directly from multi-dimensional historical trajectory data through wavelet transform analysis. The first variable The fundamental truth value of each element. Represents the generated wavelet coefficients Compared with the true wavelet coefficients The sum of the total mean square errors between them Indicates the first The mean square error of each decomposition. Indicates the index of the sub-decoder. This indicates the total number of sub-decoders. Dimensions representing historical trajectory data Indicates the first Layer context embedding Length;

[0128] Step 6.2: The inverse wavelet transform module processes the wavelet coefficients of each sensor variable. Performing an inverse transform to reconstruct the trajectory signal helps supplement supervisory information and improve model performance. Therefore, the wavelet coefficient matrix set... Converted to The trajectory sequence;

[0129] Step 6.3: The reconstruction filter iteratively combines low-frequency and high-frequency coefficient pairs until a series of trajectory signals are recovered in the time domain.

[0130]

[0131] in, This represents the inverse wavelet transform operation. Used to trim redundant segments caused by signal spread. , and All represent wavelet coefficients. The reconstructed multi-dimensional trajectory data is the reconstructed signal;

[0132] Step 6.4: Calculate the reconstructed signal With real signals Differences between :

[0133]

[0134] Step 6.5: Reuse the inverse wavelet transform module to convert the wavelet coefficient matrix set... Convert to The key attribute variables, i.e., to obtain the corresponding predicted values. The prediction loss function is calculated as follows:

[0135]

[0136] in, The dimension representing the trajectory prediction value. Represents the actual trajectory value;

[0137] Step 6.6, Joint , , The loss function for end-to-end training of the one-dimensional CNN, graph attention layer, and decoder is:

[0138]

[0139] in, and Each represents a trade-off factor used to balance the importance of different losses. The model weights are updated after each training epoch.

[0140] Step 7: Adjust network parameters: Use the grid search algorithm to find the optimal parameters. If the model performance cannot meet the threshold requirements, modify the parameters and continue training.

[0141] Step 8, Model Deployment: Deploy the trained model onto the autonomous vehicle.

[0142] Step 9: Predict the trajectory. When the current target state information of the autonomous vehicle is received, the trajectory value of the next time slot is immediately predicted and compared with the actual value.

[0143] Through the above implementation steps, users can build a trajectory prediction model to predict the movement of autonomous vehicles in highway weaving zones. This will help users understand road conditions, dynamically optimize scheduling strategies, and improve decision-making efficiency, fully supporting backend tasks such as path planning and motion control to ensure driving safety. It is important to note that the implementation process requires flexible adjustments based on specific circumstances to ensure the model can adapt to different downstream tasks.

[0144] Effect demonstration:

[0145] This application utilizes three publicly available trajectory datasets to validate the effectiveness of the proposed method. These datasets are: 1) the CitySim dataset collected and released in 2022 by Dr. Mohamed Abdel-Aty's team at the University of Florida; 2) the AIS dataset provided by the Danish Maritime Authority; and 3) the Motion dataset released by Waymo. The AIS dataset selected 500 trajectories under different seasons and climatic conditions, and divided them into training, testing, and validation sets in a 7:2:1 ratio. The time interval between adjacent points on each track in the dataset is 1 minute. The Motion dataset consists of 103,354 segments, each containing 20 seconds of object trajectory with a sampling rate of 10 Hz. These segments are further divided into 9-second time windows.

[0146] To ensure fairness in the experiment, three methods were selected for comparison: LSTM, 1D-CNN, and Transformer, all of which are related to trajectory prediction. The average results of the comparison are shown in Table 1.

[0147] Table 1

[0148]

[0149] Observations show that the MAE and RMSE values ​​of the model proposed in this application are significantly lower than those of the comparative methods. Specifically, the MAE values ​​in the three datasets reach 3.0185×10^-1, 3.5342×10^-3, and 3.5052×10^-1, respectively, while the RMSE values ​​reach 4.2261×10^-1, 4.8178×10^-3, and 4.1512×10^-1, respectively. This fully demonstrates the superiority and effectiveness of this application.

[0150] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A robot trajectory prediction method based on time-frequency wavelet transform and graph networks, characterized in that: The robot trajectory prediction method is implemented through a prediction system, and specifically includes the following steps: Step 1: Collect embodied perception data: Collect embodied perception data by moving the robot in the physical world and dynamically interacting with the open environment. The embodied perception data includes data from LiDAR, camera, GPS, and IMU. Step 2: Preprocess the embodied perception data obtained in Step 1 to obtain high-quality multi-dimensional historical trajectory data; Step 3: Use the one-dimensional CNN of the prediction system to map the multi-dimensional historical trajectory data obtained in Step 2 into a feature information matrix, and design a graph builder to generate a graph structure oriented towards the feature information matrix. Step 4: Input the graph structure and feature information matrix generated in Step 3 into the graph attention layer of the prediction system to capture spatial coupling relationships, and use the multi-layer gated recurrent unit of the prediction system to extract temporal dimension information to obtain potential spatiotemporal evolution features. Step 5: The decoder of the prediction system converts the latent spatiotemporal evolution features obtained in Step 4 into wavelet coefficients with multi-scale resolution to capture non-stationary jitter. This specifically includes the following steps: Step 5.1: Use the decoder Generating wavelet coefficients Each sub-decoder Generate hierarchical wavelet coefficients : ， in, Indicates the index of the graded wavelet coefficients. Indicates the total number of sub-decoders; Step 5.2: Apply wavelet attention module to latent spatiotemporal evolution features Weighted summation is performed to obtain the enhanced spatiotemporal features. : ， ， ， in, , , and Both represent weighted matrices. Indicates the spatiotemporal characteristics of transition. Represents the linear rectified function. Returns a matrix with the input elements as its diagonal. The attention score is represented by a weighting process performed by the skip connections; Step 5.3: The wavelet attention module uses convolution operations to extract enhanced spatiotemporal features. Context embedding : ， Among them, high-pass filter and low-pass filter Embedding context Decomposed into multi-scale features, the first High-pass filter of layer and low-pass filter The output is and ; Step 5.4: Determine the context embedding based on the attributes of the wavelet attention module and the multi-dimensional historical trajectory data. The length is determined using symmetric extension to ensure context embedding. Continuity at the boundary: ， in, Indicates the first Layer context embedding Length, , , This represents half the length of the high-pass filter. This indicates a round-down operation; Step 5.5: Model context embedding through single-layer gated loop units. , to obtain wavelet embedding Embedding wavelets Feeding to a fully connected network to generate a decoder Generated wavelet coefficients : ， in, express layer; Indicates a fully connected network; Step 6: Use the inverse wavelet transform module of the prediction system to pass the wavelet coefficients with multi-scale resolution to learn the local discriminative transition mode in the spatiotemporal dimension, and obtain the reconstructed trajectory signal and the predicted target value, which specifically includes the following steps: Step 6.1: Directly reconstruct the wavelet coefficients to enable the decoder to... Learn time-frequency representations at different scales and compute the encoder. Generated wavelet coefficients Compared with the true wavelet coefficients The mean square error between them, and the wavelet loss function is: ， ， in, It is the first The output of the first sub-decoder The first variable The estimated value of each element, It is the first [data source] obtained directly from multi-dimensional historical trajectory data through wavelet transform analysis. The first variable The fundamental truth value of each element. Represents the generated wavelet coefficients Compared with the true wavelet coefficients The sum of the total mean square errors between them Indicates the first The mean square error of each decomposition. Indicates the index of the sub-decoder. This indicates the total number of sub-decoders. Dimensions representing historical trajectory data Indicates the first Layer context embedding Length; Step 6.2: The inverse wavelet transform module processes the wavelet coefficients. Perform an inverse transform to reconstruct the trajectory signal, resulting in the wavelet coefficient matrix set. Converted to The trajectory sequence; Step 6.3: The reconstruction filter iteratively combines low-frequency and high-frequency coefficient pairs until the trajectory signal is recovered in the time domain. ， in, This represents the inverse wavelet transform operation. Used to trim redundant segments caused by signal spread. , and All represent wavelet coefficients. The reconstructed multi-dimensional trajectory data is the reconstructed signal; Step 6.4: Calculate the reconstructed signal With real signals Differences between : ， Step 6.5: Reuse the inverse wavelet transform module to convert the wavelet coefficient matrix set... Convert to The key attribute variables, i.e., to obtain the corresponding predicted values. The prediction loss function is calculated as follows: ， in, The dimension representing the trajectory prediction value. Represents the actual trajectory value; Step 6.6, Joint , , The loss function for end-to-end training of the one-dimensional CNN, graph attention layer, and decoder is: ， in, and Each represents a trade-off factor, and the model weights are updated after each training round.

2. The robot trajectory prediction method based on time-frequency wavelet transform and graph network according to claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1: A one-dimensional CNN integrates multi-dimensional historical trajectory data. Project the feature information matrix into the embedding space and compute the feature information matrix. Extracting the unique characteristics of embodied perception data: ， in, Indicates an S-shaped growth curve. This represents a one-dimensional CNN operation with a kernel size of 1. Represents the weight matrix. Indicates deviation, An index representing a timestamp; Step 3.2: Use a graph builder to process multi-dimensional historical trajectory data. View it as a graph structure ,in Represents a set of nodes, nodes It is a continuous vector based on trajectory attributes. Represents the set of edges, with any node. and nodes There are mutual connections between them; set the adjacency matrix of the complete graph. The connection weights are , Representing the node index, adjacency matrix It is diagonal, and the nodes have the maximum connectivity.

3. The robot trajectory prediction method based on time-frequency wavelet transform and graph network according to claim 1, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Calculate the graph structure generated in Step 3. and feature information matrix The input is fed into the graph attention layer, which allows each node to aggregate messages from its neighbors and calculate the attention score of its neighbors. ， in, Represents a linear rectified function with leakage; Represents the learnable weight matrix; This indicates a splicing operation. Indicates the transpose symbol. Represents the index of a node in the set of neighboring nodes. , and Both represent nodes. Represents a node The set of neighboring nodes; No. The output representation of each node is formalized as follows: ， Feature information matrix Transformed into an output representation with spatial correlation ; Step 4.2: Connect the multi-layer gated loop unit to the graph attention layer, and process them in chronological order. Mapping is performed to obtain potential spatiotemporal evolution features. .

4. The robot trajectory prediction method based on time-frequency wavelet transform and graph network according to claim 1, characterized in that: The prediction system includes an encoder. decoder And the inverse wavelet transform module, The encoder Composed of a one-dimensional CNN, a graph constructor, a graph attention layer, and multiple gated recurrent units, the one-dimensional CNN processes multi-dimensional historical trajectory data. Mapped into feature information matrix The graph builder generates a graph structure oriented towards the feature information matrix, and the graph attention layer extracts multidimensional historical trajectory data. The spatial coupling relationship is used to extract multidimensional historical trajectory data from the multi-layer gated loop unit. The time dimension information is processed by the graph attention layer and multiple gating loop units, and the encoder... Capturing multidimensional historical trajectory data Potential spatiotemporal evolution characteristics ; The decoder Composed of multiple sub-decoders Stacked sequentially, each sub-decoder Each decoder includes a wavelet attention module, a single-layer gated recurrent unit, and a fully connected network. Used to generate hierarchical wavelet coefficients By combining multi-level wavelet coefficients Find the final wavelet coefficients. ; The wavelet attention module will incorporate latent spatiotemporal evolution features. Converted into initial wavelet coefficients with multi-scale resolution; A single-layer gated cyclic unit (GRU) models the initial wavelet coefficients to obtain the wavelet embedding. ; The fully connected network fits wavelet embeddings And adjust the wavelet embedding The dimension is determined to generate wavelet coefficients for each sub-decoder. Only generate hierarchical wavelet coefficients By cascading all the hierarchical wavelet coefficients The final wavelet coefficients are obtained. , computational encoder Generated wavelet coefficients Compared with the true wavelet coefficients The mean square error between and ; The inverse wavelet transform module passes wavelet coefficients, and the inverse wavelet transform module passes wavelet coefficients with multi-scale resolution, respectively, to obtain reconstructed multi-dimensional historical trajectory data. and trajectory prediction value Calculate real, multi-dimensional historical trajectory data With reconstructed multi-dimensional historical trajectory data The loss function value between Calculate the actual trajectory value and the predicted trajectory value The loss function value between ; Cascade the above , and The overall loss function value is obtained. ,in, and It is a trade-off factor used to balance the importance of each loss.

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