Self-adaptive physical data hybrid-driven vehicle transverse dynamics modeling and state estimation method

Abstract

The invention provides a self-adaptive physical data hybrid-driven vehicle transverse dynamics modeling and state estimation method, which can improve the modeling precision under limiting conditions, enhance the self-adaptive capability of an unstructured environment and improve the real-time calculation efficiency, and comprises the following steps of: S1, constructing a nominal physical model of vehicle transverse dynamics, obtaining prediction output of the nominal physical model; s2, determining a total model residual error based on the predicted output of the nominal physical model and the state of the real system of the vehicle at the next moment; explicitly decomposing the total model residual error into a static structure residual error representing time-invariant system deviation and a dynamic random residual error representing time-varying random deviation; and S3, fusing prediction output of the nominal physical model, a static structure residual error estimation value output by the deep neural network model and a dynamic random residual error estimation value output by the sparse Gaussian process model to obtain a vehicle state estimation value.

Description

Technical Field

[0001] This invention belongs to the field of intelligent vehicle dynamics control and state estimation, specifically involving a vehicle lateral dynamics modeling and state estimation method based on a decoupled hybrid residual framework that integrates offline correction and online adaptation. Background Technology

[0002] High-precision vehicle dynamics models are the cornerstone of high-performance motion planning and control for autonomous vehicles. Under high-speed maneuvering or extreme handling conditions, the lateral dynamics of vehicles exhibit highly nonlinear and strongly coupled characteristics, posing significant challenges to prediction accuracy and real-time computational performance.

[0003] Traditional modeling methods are primarily based on first-principles calculations, such as linear two-degree-of-freedom (2DOF) models or nonlinear multibody dynamics models. While mechanistic models offer clear physical interpretability, they suffer from two inherent limitations under extreme conditions: first, simplified structural constraints struggle to accurately characterize complex nonlinear effects (such as tire saturation); second, key dynamic parameters exhibit time-varying uncertainties due to load fluctuations and environmental changes. Therefore, structural residuals inevitably exist between the physical model and the actual vehicle system.

[0004] To mitigate these limitations, purely data-driven methods based on deep neural networks (DNNs) have emerged. While DNNs can capture nonlinear dynamic characteristics, they typically require large-scale datasets covering all operating conditions. Once the test scenario deviates from the training data distribution, the model's generalization ability drops sharply. Physically Information Neural Networks (PINNs) combine the advantages of physical priors and data-driven approaches by embedding physical equations into the loss function, but their effectiveness depends on the fidelity of the physical priors. If the underlying physical model has severe structural biases, PINNs may introduce erroneous inductive biases.

[0005] Existing residual learning methods typically treat the error as a whole, failing to distinguish between static structural residuals arising from model simplification and dynamic stochastic residuals arising from environmental perturbations. This confusion hinders the model's ability to rapidly adapt to local time-varying perturbations while maintaining global steady-state fidelity. Summary of the Invention

[0006] This invention addresses the following shortcomings of existing vehicle dynamics modeling methods: simple mechanistic models suffer from decreased prediction accuracy under extreme conditions due to structural simplification and parameter uncertainties; purely data-driven models lack physical constraints and exhibit poor generalization ability under unknown conditions such as sudden changes in road adhesion coefficients; and existing hybrid models fail to effectively distinguish between static structural errors and dynamic environmental disturbances, making it difficult for the model to balance global steady-state accuracy and local dynamic adaptability. Therefore, this invention provides an adaptive physical-data hybrid-driven method for vehicle lateral dynamics modeling and state estimation, which improves the modeling accuracy under extreme conditions, enhances adaptability to unstructured environments, and increases real-time computational efficiency.

[0007] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0008] An adaptive physics data hybrid-driven method for vehicle lateral dynamics modeling and state estimation includes the following steps:

[0009] Step 1: Construct a nonlinear vehicle dynamics nominal model considering dynamic load transfer: Establish a two-degree-of-freedom dual-track model that includes lateral and yaw motions, introduce a dynamic transfer mechanism for vertical loads caused by vehicle roll, and use a nonlinear tire model to describe tire forces as the physical reference of the system.

[0010] Step 2: Construct a decoupled hybrid residual framework (DHRM): Define the total residual between the actual vehicle state and the nominal physical model output, and explicitly decompose this total residual into static structural residuals. and dynamic random residuals Construct a hybrid model architecture that includes a nominal physical model, an offline static compensation channel, and an online dynamic adaptive channel;

[0011] Step 3, Fusion Output: The output of the nominal physical model, the correction value of the offline network, and the compensation value of the online algorithm are linearly superimposed to obtain the final vehicle state estimate.

[0012] As a further improvement to the present invention, step 2 specifically includes:

[0013] Step 2.1, Define the system feature vector: Define The vehicle state observation vector at time t is The control input vector is Construct a joint feature vector for residual prediction. ;

[0014] Step 2.2, Establish a residual decoupling mechanism: Record the actual vehicle system in... The state at time is The nominal physical model is The predicted output at time is Define the total model residuals. And mathematically, it is explicitly decomposed into static structural residuals and dynamic stochastic residuals:

[0015]

[0016] in, Characterizes the deviations of time-invariant systems caused by simplification of the physical model structure and parameter uncertainties. Characterizes time-varying random deviations caused by external environmental disturbances and sensor noise;

[0017] Step 2.3: Constructing the Hybrid Model Architecture: Based on the above decomposition, establish the prediction equations for the Decoupled Hybrid Residual Model (DHRM):

[0018] ,

[0019] in, For parameters Fixed offline static compensation network, For parameters A real-time updated online dynamic compensation network.

[0020] Step 2.4: Construct the KAN nonlinear feature extraction layer: Use the Kolmogorov-Arnold network (KAN) as the pre-feature extractor to extract the joint feature vector. Mapped to a high-dimensional latent feature space; for the input feature of the th... Each component Through learnable B-spline functions located on the network edges Perform a nonlinear transformation to calculate the first... Layer Output of each node :

[0021] ,

[0022] formula This describes the computational process of a neuron in a layer of a KAN network. This neuron receives all signals from the previous layer. Input vector It includes four physical quantities (lateral velocity, yaw rate, steering angle, and longitudinal velocity). Summation symbol This means that these four input components are processed through their respective nonlinear activation functions. Add them together after transformation.

[0023] Compared to traditional multilayer perceptrons, this layer utilizes the local approximation capability of spline functions to accurately capture highly nonlinear structural features such as tire force saturation regions.

[0024] Step 2.5: Construct the LSTM temporal dependency modeling layer: This involves processing the high-dimensional feature sequence output from the KAN layer. Input the data into a Long Short-Term Memory (LSTM) network and utilize its gating mechanism to update the internal cell state. and hidden layer state To capture the historical dependence and time-delay characteristics of vehicle dynamics:

[0025] ,

[0026] It is the scalar output of a single node in a certain layer of the KAN network; while It is a vector composed of the outputs of all nodes in the last layer (layer L) of the KAN network at time k. . It represents the number of nodes on layer L.

[0027] The estimated value of the static residual is then calculated through a fully connected output layer. ;

[0028] To output the weight matrix, it will contain the high-dimensional hidden states of the LSTM. (e.g., 64 dimensions) linearly mapped back to the dimensions of the physical residual (e.g., 2 dimensions). This is the output bias vector, used to correct the constant deviation of the system.

[0029] Step 2.6, Offline Supervised Training: Based on historical datasets covering typical working conditions (Includes vehicle status data under high-adhesion road surface conditions) Simulation data from CarSim high-fidelity simulation software, in The system utilizes open-loop control of the accelerator and steering wheel on the road surface, as well as vehicle state data collected by onboard sensors (IMU) and cameras running the VIO algorithm on dry asphalt surfaces. This data is used to train the model to learn the inherent structural characteristics of the vehicle and to construct the mean squared error (MSE) loss function.

[0030] ,

[0031] N represents the historical dataset. The total number of samples, i.e. the number of data points participating in the loss calculation.

[0032] Optimize network parameters using backpropagation algorithm Once the training converges, the set of parameters will be frozen in the subsequent online phase.

[0033] As a further improvement to the present invention, step 4 specifically includes:

[0034] Step 2.7, Sparse Induced Point Topology Initialization: In the offline phase, the K-Means clustering algorithm is used to initialize the sparse induced points from the feature space of the training data (the training data comes from the historical dataset, and the induced points are initialized through K-Means clustering). Extracted from the feature space of the (offline dataset) Cluster centers serve as the fixed induced point set for the sparse Gaussian process. Pre-calculate and store the kernel covariance matrix between induced points. Its inverse matrix, and the kernel function hyperparameters remain fixed after optimization at this stage;

[0035] Step 2.8, Sliding Window and Exponential Forgetting Mechanism: Establish a window with a capacity of... First-In-First-Out (FIFO) Sliding Window Buffer It is used to store the most recent observation residual samples; a forgetting factor is introduced. Construct a diagonal weight matrix , of which The weights of each sample are To give greater importance to recent data;

[0036] Step 2.9, Online weight update based on weighted ridge regression: using the induced point set and buffer data The weight vector of the Gaussian process is updated in real time through low-dimensional matrix operations. :

[0037]

[0038] in, The cross-kernel matrix of the induction point and buffer data. The observed values ​​of dynamic residuals after removing static residuals; Indicates the variance of observation noise;

[0039] Step 2.10, Dynamic Stochastic Residual Inference: Based on the Updated Weight Vector The input features at the current time are calculated through kernel interpolation. The corresponding dynamic random residual estimate:

[0040] , It represents a kernel vector containing elements Its physical meaning lies in measuring the current vehicle state. With each typical working condition induced point in the feature space The degree of similarity between them.

[0041] The beneficial effects of this invention are as follows:

[0042] This invention proposes an adaptive physical data hybrid-driven method for vehicle lateral dynamics modeling and state estimation. By constructing a decoupled hybrid residual framework, it explicitly separates and specifically compensates for static structural residuals and dynamic random residuals, thereby achieving high-precision state estimation and adaptive modeling of vehicles under complex and variable environments and extreme handling conditions, resulting in significant benefits in many aspects.

[0043] First, regarding modeling accuracy under extreme conditions, this invention introduces a hybrid architecture that integrates Kolmogorov-Arnold networks (KAN) and Long Short-Term Memory networks (LSTM) to deeply mine and effectively compensate for the nonlinear dynamic characteristics lost by the nominal physical model due to simplification assumptions (such as small angle assumptions and stiffness linearization). This strategy enables the model to effectively eliminate steady-state errors under extreme conditions such as when the tire enters the nonlinear saturation region, significantly improving the vehicle dynamics model's ability to represent complex nonlinear characteristics and its prediction accuracy, thus overcoming the inherent defects of traditional mechanistic models.

[0044] Secondly, this method exhibits strong robustness in environmental adaptability. Through a lightweight adaptive mechanism constructed using an online sparse Gaussian process (SGP) module, this invention can rapidly capture dynamic stochastic residuals generated by changes in the external environment, such as abrupt changes in road surface adhesion coefficient and crosswind interference. This mechanism endows the model with "instant learning" capabilities in unstructured environments, effectively solving the problem of poor generalization ability of traditional offline trained models when facing unknown test conditions, and ensuring the stability and reliability of vehicle state estimation in dynamic environments.

[0045] Furthermore, the method of this invention achieves a perfect balance between high computational efficiency and real-time performance. By utilizing sparse induced point technology and a weighted ridge regression online update strategy, the computational complexity of online learning is significantly reduced from the cubic level of the sample size to the linear level related to the number of induced points. This breakthrough successfully solves the computational bottleneck that makes it difficult for traditional Gaussian processes to run in real time on resource-constrained automotive embedded platforms, meeting the stringent requirements of autonomous driving control systems for millisecond-level latency.

[0046] In summary, the modeling and state estimation method implemented in this invention has achieved significant benefits in improving the modeling accuracy of extreme working conditions, enhancing the adaptability of unstructured environments, and optimizing real-time computing efficiency, providing strong technical support for the accurate perception, autonomous navigation, and safe control of intelligent vehicles in complex dynamic scenarios. Attached Figure Description

[0047] Figure 1 This is a diagram of a dual-track dynamic model;

[0048] Figure 2 It is a network architecture diagram;

[0049] Figure 3 The comparison shows the vehicle state prediction results under offline conditions. Figure (a) shows the lateral velocity prediction results, and Figure (b) shows the yaw rate prediction results.

[0050] Figure 4 The figures are magnified views of the offline prediction errors. Figure (a) shows the lateral velocity prediction results of the pure physical model and DHRM, Figure (b) shows the yaw rate prediction results of the pure physical model and DHRM, Figure (c) shows the lateral velocity prediction results of KAN-LSTM and PINN, and Figure (d) shows the yaw rate prediction results of KAN-LSTM and PINN.

[0051] Figure 5 The figures are box plots of prediction errors under offline conditions. Figure (a) shows the lateral velocity prediction error of the pure physical model and DHRM, Figure (b) shows the yaw rate prediction error of the pure physical model and DHRM, Figure (c) shows the lateral velocity prediction error of KAN-LSTM and PINN, and Figure (d) shows the yaw rate prediction error of KAN-LSTM and PINN.

[0052] Figure 6 The comparison shows the trajectory tracking prediction results under sudden environmental changes. Figure (a) shows the lateral velocity prediction results, and Figure (b) shows the yaw rate prediction results.

[0053] Figure 7 The figures are box plots of prediction errors under sudden environmental changes. Figure (a) shows the lateral velocity prediction error of the pure physical model, DHRM, and Online SGP; Figure (b) shows the yaw rate prediction error of the pure physical model, DHRM, and Online SGP; Figure (c) shows the lateral velocity prediction error of KAN-LSTM and PINN; and Figure (d) shows the yaw rate prediction error of KAN-LSTM and PINN.

[0054] Figure 8 The figures are magnified views of the local conditions under sudden environmental changes. Figure (a) shows the lateral velocity prediction results of the pure physical model, DHRM, and OnlineSGP; Figure (b) shows the yaw rate prediction results of the pure physical model, DHRM, and OnlineSGP; Figure (c) shows the lateral velocity prediction results of KAN-LSTM and PINN; and Figure (d) shows the yaw rate prediction results of KAN-LSTM and PINN.

[0055] Figure 9 This is a schematic diagram of the hardware architecture of the miniature intelligent vehicle experimental platform;

[0056] Figure 10 Comparison of state prediction results in real vehicle experiment, where (a) is the lateral velocity prediction result and (b) is the yaw rate prediction result.

[0057] Figure 11 shows a magnified view of the prediction error of the actual vehicle. (a) shows the lateral velocity prediction results of the pure physical model, DHRM, and OnlineSGP; (b) shows the yaw rate prediction results of the pure physical model, DHRM, and OnlineSGP; (c) shows the lateral velocity prediction results of KAN-LSTM and PINN; and (d) shows the yaw rate prediction results of KAN-LSTM and PINN.

[0058] Figure 12 shows the box plot statistics of prediction errors in real vehicle experiments. Figure (a) shows the lateral velocity prediction error of the pure physical model, DHRM, and Online SGP; Figure (b) shows the yaw rate prediction error of the pure physical model, DHRM, and Online SGP; Figure (c) shows the lateral velocity prediction error of KAN-LSTM and PINN; and Figure (d) shows the yaw rate prediction error of KAN-LSTM and PINN. Detailed Implementation

[0059] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and mathematical formulas. The core of the adaptive physical data hybrid-driven vehicle lateral dynamics modeling and state estimation method proposed in this invention lies in constructing a decoupled hybrid residual framework of "physical model baseline + offline static correction + online dynamic compensation". For example... Figure 2 The network architecture diagram shown illustrates that this method mainly includes the following five steps:

[0060] Step 1: Construct a nonlinear vehicle dynamics nominal model considering dynamic load transfer. This embodiment first establishes a nominal model incorporating physical priors as the benchmark for the entire system. For example... Figure 1 The diagram shown illustrates a dual-track dynamics model that describes the vehicle's motion characteristics in a plane.

[0061] Step 1.1: Define system variables. Vehicle state vector at time:

[0062]

[0063] in, The lateral speed of the vehicle. ω represents the yaw rate.

[0064] Define the control input vector:

[0065]

[0066] in, This refers to the steering angle of the front wheels.

[0067] Step 1.2: Establish the dynamic differential equations. Based on the Newton-Euler equations, establish a two-degree-of-freedom dual-track vehicle dynamic model:

[0068]

[0069] in, For the overall vehicle quality, For vehicles to bypass Moment of inertia of the shaft and These are the horizontal distances from the center of gravity to the front and rear axles, respectively. This refers to the longitudinal speed of the vehicle. to These represent the lateral forces of the four wheels: front left, front right, rear left, and rear right. This represents the velocity component of the vehicle's center of gravity along the Y-axis of the vehicle coordinate system, i.e., the lateral vehicle speed. This represents the yaw rate, which is the angular velocity of the vehicle rotating around the Z-axis. It is the yaw rate at time k.

[0070] Step 1.3: Introducing a Nonlinear Tire and Load Transfer Model. To overcome the failure problem of traditional linear models under extreme conditions, this embodiment adopts a quadratic nonlinear tire model that considers the vertical load coupling effect:

[0071]

[0072] in, The fitting coefficient for tire lateral stiffness is... This refers to the slip angle of each tire. Crucially, this step introduces dynamic load transfer calculations caused by vehicle roll, updating the vertical load on each wheel in real time. :

[0073]

[0074] in, For the sprung mass, For the height of the center of mass, It is half the wheel track. This represents lateral acceleration. Based on the above calculations, the predicted output of the nominal physical model is obtained: .

[0075] Step 2: Construct a decoupled hybrid residual framework. To address the structural biases and external environmental interference issues present in the physical model, this invention establishes the following... Figure 2 The decoupling framework shown.

[0076] Step 2.1: Define the total residual and the next time-instance state of the decoupled vehicle system as... Define the total model residuals. And it is explicitly decomposed into two parts:

[0077]

[0078] in, This is the joint feature vector at the current time. The static structural residuals originate from the simplification of the physical model (such as ignoring suspension flexibility) and parameter uncertainties. They are time invariant and are learned by an offline network. The residuals are dynamic random residuals, which originate from sudden changes in road surface adhesion coefficients and environmental disturbances such as crosswinds. They are highly time-varying and are learned by online algorithms.

[0079] Step 2.2: Construct the final prediction equation using a hybrid model architecture:

[0080]

[0081] Step 2.3: Design and train an offline static residual compensation network (KAN-LSTM)

[0082] This step utilizes historically collected high-adhesion road surface data to offline train a deep neural network to fit the data. .

[0083] Step 2.4, KAN Feature Extraction Layer

[0084] Constructing a KAN nonlinear feature extraction layer: A Kolmogorov-Arnold network (KAN) is used as the pre-feature extractor to extract joint feature vectors. Mapped to a high-dimensional latent feature space; for the input feature of the th... Each component Through learnable B-spline functions located on the network edges Perform a nonlinear transformation to calculate the first... Layer Output of each node :

[0085] ,

[0086] formula This describes the computational process of a neuron in a layer of a KAN network. This neuron receives all signals from the previous layer. Input vector It includes four physical quantities (lateral velocity, yaw rate, steering angle, and longitudinal velocity). Summation symbol This means that these four input components are processed through their respective nonlinear activation functions. Add them together after transformation.

[0087] Compared to traditional multilayer perceptrons, this layer utilizes the local approximation capability of spline functions to accurately capture highly nonlinear structural features such as the tire force saturation region.

[0088] Step 2.5: LSTM Timing Modeling Layer

[0089] The feature sequences extracted by KAN are input into a Long Short-Term Memory (LSTM) network to handle the time delay characteristics of the dynamic system.

[0090]

[0091] in, In cellular state, This is the hidden layer state.

[0092] Step 2.6: Offline Training and Performance Verification

[0093] Construct a mean squared error (MSE) loss function and optimize the parameters using the backpropagation algorithm. After training, The freeze will remain in effect during the subsequent online phase. Figure 3 The comparison of vehicle state prediction results under offline operating conditions is shown. Figure 4 This is a magnified view of a portion of the image. Figure 5 The figure shows the prediction error box plot statistics. As can be seen from the figure, compared with the simple physical model, after introducing KAN-LSTM static correction, the steady-state error of the model under normal operating conditions is greatly eliminated, and it can closely follow the true value.

[0094] Step 2.7: Offline sparse induced point extraction

[0095] To overcome the drawback of the standard Gaussian process where computational complexity increases cubically with sample size during inference, this step employs a sparse approximation strategy. This strategy aims to extract the most representative feature points from massive historical data to fix the model's topology. Specifically, the algorithm uses the K-Means clustering algorithm to analyze the offline-collected historical vehicle state feature space, setting the number of cluster centers to M. After iterative convergence, the extracted cluster centers constitute a fixed set of induction points, denoted as […]. .

[0096] Each element Let d represent the feature vector of the m-th induced point, and let its dimension d be the same as the vehicle's real-time input state vector. The dimensions are completely consistent. The size of parameter M directly determines the upper limit of the matrix dimension in subsequent online computations, because... (Much smaller than the actual amount of sampled data), this strategy effectively ensures the controllability of the computational load.

[0097] Step 2.8: Kernel function hyperparameter optimization and freezing

[0098] After establishing the location of the sparse induced points, to further reduce the computational burden on the online dataset and improve the model's generalization ability, the system needs to pre-determine the geometric properties of the Gaussian process based on an offline dataset. The algorithm employs the method of maximizing the log-marginal likelihood for the hyperparameter set of the kernel function. Perform offline optimization. The optimization objective function is defined as:

[0099] ,

[0100] Where log is the natural logarithm. Let be the probability density function. This is the observation vector, which represents the true state output values ​​seen in the training data, used for label training, and its dimension is... ,in It represents the number of training samples. This is a condition symbol, indicating "under the condition of...". The input data matrix contains features from all training samples, and its dimensionality is typically... ,in It is the dimension of the feature. This is a set of hyperparameters, which are the parameters that need to be optimized. It includes the length scale of the kernel function. Signal variance .

[0101] Overall meaning: Given input data and a set of hyperparameters In the case of observing the current output The logarithm of the probability.

[0102] This term is called the data fit term, and it measures how well the model fits the data. The covariance matrix, calculated using the kernel function, describes the similarity between training data points. Its elements... Dimension is . Let be the noise variance, representing the level of inherent random noise in the observed data. Let I be the identity matrix, with dimension . . This means adding independent noise to each data point. This is the noisy covariance matrix, which is the core description of the data distribution by the model. The data fitting term is actually calculating the Mahalanobis distance. If If the distribution deviates from the center defined by the covariance matrix, this term will become smaller (because the term is preceded by a negative sign), and the probability will decrease.

[0103] This term is a complexity penalty term, which prevents the model from overfitting. Among them, The determinant of the covariance matrix geometrically represents the degree of dispersion. When the kernel function's length scale is short, the model is very flexible, and the determinant of the covariance matrix will be large, resulting in a smaller complexity penalty term (because this term is preceded by a negative sign), thus penalizing overfitting. When the length scale is long, the model is smooth, and the determinant is small.

[0104] This term is a normalization constant, where n is the number of training samples (number of data points). This constant exists solely to ensure that the integral of the probability density function equals 1. It is not included in the hyperparameter optimization derivative. This term is usually eliminated by differentiation and has no direct impact on finding the optimal solution, but it must be included when calculating the specific likelihood value.

[0105] Based on the optimized parameters, the autocovariance matrix between the induced points is pre-calculated and stored. and its inverse matrix The matrix is A matrix whose elements The similarity between different induced points was quantified. This study uses the squared exponential kernel function to quantify the similarity between induced points.

[0106]

[0107] in, This is the signal variance, which controls the vertical amplitude of the function. If... A large value indicates a wide range of fluctuations in the function's value. As a length scale, it controls the rate of horizontal fluctuation of the function (the rate of decay of the correlation). The larger the value, the smoother the function, and points that are far apart still have a high correlation. The smaller the value, the more drastic the function fluctuations, and the correlation decays rapidly with distance. The square of the Euclidean distance between the two induced points in the feature space.

[0108] Induced point autocovariance matrix It is a set of induced points The determined matrix describes the interrelationships within the induced points. It is The symmetric positive definite matrix (where M is the number of induced points) has elements in its i-th row and j-th column that are the kernel function values ​​mentioned above.

[0109]

[0110] In the subsequent online operation phase, to ensure real-time performance, the system will freeze the hyperparameters and the induced point set, and will no longer perform iterative optimization, focusing only on updating the weight vector.

[0111] To avoid time-consuming matrix inversion operations during the online phase, this step utilizes Cholesky decomposition to pre-calculate the matrix that satisfies... The inverse matrix is ​​stored in memory. During the subsequent online run phase, the system will freeze the hyperparameters and the induced point set, utilizing only the pre-stored... It directly participates in matrix multiplication operations for weight updates, thereby breaking through the computing power bottleneck and ensuring millisecond-level real-time response capability.

[0112] Step 2.9, Sliding Window and Forgetting Mechanism

[0113] Given the significant time-varying characteristics of vehicle operating environments, such as transitioning from a dry asphalt road with a high adhesion coefficient to a wet road with low adhesion coefficient, the model must possess the ability to quickly adapt to new environments. Therefore, the system establishes a fixed capacity... First-in, first-out buffer It is specifically designed to store the dynamic residual samples observed at the most recent time. To differentiate the degree of influence of data from different time points on the current model, an exponential forgetting factor is introduced. (The range of values ​​is) Construct a weight diagonal matrix The importance weight of the sample Its calculation formula is .

[0114] In this formula, Indicates the number of... The weights of each sample; The system timestamp at the current moment; This is the historical timestamp when the sample was collected. (Exponential term) Physically, this represents the age of the sample; the older the data, the larger this term becomes, leading to a higher weight. The index approaches zero exponentially, thus automatically removing old environmental data. This is achieved through adjustment. This can balance the model's memory length and sensitivity. The smaller the value, the faster the model forgets old data and the more sensitive it is to changes in new operating conditions.

[0115] Step 2.10: Online Weight Quick Update

[0116] This step is the core of achieving online adaptation. To meet the stringent requirements of vehicle control systems for millisecond-level real-time computation, this method abandons traditional variational inference or gradient descent optimization. Instead, it utilizes the fixed induced point structure determined in step 2.7 to transform the posterior inference of the Gaussian process into a weighted ridge regression form in kernel space, directly obtaining the analytical solution of the weight vector through low-dimensional matrix operations. Online weight vector The update formula is:

[0117] ,

[0118] in, It is the Gaussian process weight vector to be updated, which determines the shape of the prediction function in the feature space; It is a cross kernel matrix, whose elements The m-th induction point and the j-th real-time data in the buffer were calculated. The similarity between them; It is the diagonal weight matrix calculated in step 2.9, used to reduce the influence of old data; It is the vector of true dynamic residual observations stored in the buffer, that is, the residual after subtracting the physical model and static compensation from the sensor observations. The buffer... It stores Data from historical moments, indexed as follows .

[0119] For the i-th sample in the buffer, its corresponding scalar residual value The calculation formula is:

[0120] ,

[0121] (True observation): This is the actual vehicle state measured by the onboard sensors at time i+1, and it is the true value. (Physical Model Baseline): This is the result predicted by the nominal physical model (dual-track model) based on the state i at the previous moment. It represents the most basic dynamic behavior of the vehicle. (Static Residual Compensation): This is the compensation value output by the offline trained KAN-LSTM network. It corrects the systematic, time-invariant errors caused by model simplification (such as the linear tire assumption) or inaccurate parameters.

[0122] Represents the variance of observation noise; It contains tiny positive numbers The regularization term is used to ensure numerical stability during matrix inversion. The computational complexity of this algorithm mainly depends on the regularization term. The matrix inversion operation, since the number of induced points M is a fixed constant, has a constant computational load that does not increase with running time, thus strictly meeting the real-time requirements.

[0123] Step 2.11, Dynamic Residual Output

[0124] Using the updated weight vector from step 2.10 The algorithm calculates the current time using kernel interpolation. The dynamic compensation value is predicted by the following formula:

[0125] ,

[0126] It is the final output of the dynamic stochastic residual prediction value, which will be directly added to the output of the physical model to correct the state estimate; It is the current state feature input vector of the vehicle; For a fixed set of induced points; It is a kernel vector containing elements Its physical meaning lies in measuring the current vehicle state. With each typical working condition induced point in the feature space The similarity between them. Essentially, this calculation process is a weighted summation process: if the current vehicle state is very similar to a certain guidance point (i.e., the kernel function value is large), the weight corresponding to that guidance point will dominate the current prediction result, thereby achieving accurate inference and compensation for unseen working conditions.

[0127] Figure 6 This demonstrates that under abrupt environmental changes (a sudden decrease in road surface adhesion coefficient), only the physical model and the offline model exhibit prediction divergence. However, as... Figure 7 Error box plot and Figure 8 As shown in the magnified view, after adding SGP online compensation, the model can quickly capture the dynamic residuals caused by environmental changes and converge to the true state rapidly.

[0128] Step 3: Fusion Output and Real Vehicle Verification. The calculation results from the above three parts are linearly superimposed to obtain the final vehicle state estimate:

[0129]

[0130] To verify the effectiveness of this method, a system was built as follows: Figure 9 The 1:10 scale miniature intelligent vehicle experimental platform shown. Figure 10 The comparison of state prediction results in real vehicle experiments is shown. Figure 11 and Figure 12Do not include magnified views and box plot statistics of the actual vehicle test. Experimental results show that in real complex noise environments, the DHRM framework proposed in this invention has higher prediction accuracy and robustness compared to a single model. Through the above steps, when the vehicle is driving on a regular road, Provide basic constraints, Correcting structural errors to ensure high accuracy; when a vehicle enters a low-adhesion road surface causing model mismatch. It will quickly capture residual mutations and perform reverse compensation to ensure that the state estimate does not diverge.

[0131] The outputs corresponding to Pure Physics, KAN-LSTM, Online SGP, and DHRM listed in the attached figures are as follows:

[0132] Pure Physics: Corresponding output: This is the state at the next moment calculated solely by the nominal physical model using the Euler method, without any residual compensation.

[0133] KAN-LSTM (Offline Static Residual Network): Corresponding output: This is the residual prediction value output by the offline trained neural network, which is specifically responsible for compensating for static structural errors caused by model simplification (such as ignoring suspension stiffness and errors caused by linear assumptions).

[0134] Online SGP (Online Gaussian Process): Corresponding output: This is the dynamic residual prediction value output by the online sparse Gaussian process, which is specifically designed to capture time-varying random errors caused by sudden environmental changes (such as slippery roads and crosswinds) that cannot be predicted by physical models and offline networks.

[0135] DHRM (the complete framework proposed in this paper): Corresponding output: This is the final prediction result, which includes the sum of three parts: physical baseline, offline static compensation, and online dynamic compensation.

[0136] Furthermore, the method of this invention achieves a perfect balance between high computational efficiency and real-time performance. By utilizing sparse induced point technology and a weighted ridge regression online update strategy, the computational complexity of online learning is significantly reduced from the cubic level of the sample size to the linear level related to the number of induced points. This breakthrough successfully solves the computational bottleneck that makes it difficult for traditional Gaussian processes to run in real time on resource-constrained automotive embedded platforms, meeting the stringent requirements of autonomous driving control systems for millisecond-level latency.

[0137] In summary, the modeling and state estimation method implemented in this invention has achieved significant benefits in improving the modeling accuracy of extreme working conditions, enhancing the adaptability of unstructured environments, and optimizing real-time computing efficiency, providing strong technical support for the accurate perception, autonomous navigation, and safe control of intelligent vehicles in complex dynamic scenarios.

[0138] The scope of protection of this invention includes, but is not limited to, the above embodiments. The scope of protection of this invention is defined by the claims. Any substitutions, modifications, or improvements to this technology that are easily conceived by those skilled in the art fall within the scope of protection of this invention.

Claims

1. A method for adaptive physical data hybrid-driven vehicle lateral dynamics modeling and state estimation, characterized in that, Includes the following steps: S1: Construct a nominal physical model of the vehicle's lateral dynamics, and obtain the predicted output of the nominal physical model based on the vehicle state observation vector and the vehicle control input vector at the current moment. S2: Based on the predicted output of the nominal physical model and the next moment state of the actual vehicle system, determine the total model residual; explicitly decompose the total model residual into static structural residual and dynamic random residual; The static structural residual characterization is a time-invariant system deviation caused by the structural simplification and parameter uncertainty of the nominal physical model, which is fitted and compensated by an offline-trained deep neural network model. The dynamic random residual characterizes the time-varying random deviation caused by external environmental disturbances and sensor noise, and is compensated in real time by an online-updated sparse Gaussian process model. S3: The predicted output of the nominal physical model, the static structural residual estimate output of the deep neural network model, and the dynamic stochastic residual estimate output of the sparse Gaussian process model are fused to obtain the final vehicle state estimate.

2. The vehicle lateral dynamics modeling and state estimation method according to claim 1, characterized in that, The nominal physical model is a two-degree-of-freedom, dual-track nonlinear vehicle dynamics model that considers the dynamic transfer of vertical loads caused by vehicle roll. ； in, For the overall vehicle quality, For vehicles to bypass Moment of inertia of the shaft and These are the horizontal distances from the center of gravity to the front and rear axles, respectively. This refers to the longitudinal speed of the vehicle. to These represent the lateral forces of the four wheels: front left, front right, rear left, and rear right, respectively. The lateral speed is the speed of the vehicle. This refers to the yaw rate; ； The fitting coefficient for tire lateral stiffness is... For each tire's slip angle; Vertical loads for each wheel: in, For the sprung mass, For the height of the center of mass, It is half the wheel track. It is lateral acceleration; Vehicle state vector at time: in, Let k be the lateral velocity of the vehicle at time k. Let k be the yaw rate at time k; Vehicle control input vector: in, The steering angle of the front wheels; The predicted output of the nominal physics model: .

3. The vehicle lateral dynamics modeling and state estimation method according to claim 1, characterized in that, In step S2, the total model residual is explicitly decomposed into static structural residual and dynamic random residual, specifically as follows: ， in, The total model residual at time k is... Let be the vehicle state vector at time k+1. Let be the joint feature vector formed by the vehicle state observation vector and the control input vector at time k. , For static structural residuals, It represents dynamic random residuals.

4. The vehicle lateral dynamics modeling and state estimation method according to claim 1, characterized in that, The deep neural network model is a KAN-LSTM hybrid network, including: The KAN feature extraction layer is used to receive the joint feature vector and perform nonlinear transformation using learnable spline basis functions located on the network edges to extract high-dimensional nonlinear features. The LSTM temporal modeling layer receives the feature sequence output by the KAN feature extraction layer, captures the historical dependence and time delay characteristics of vehicle dynamics through its gating mechanism, and outputs the estimated value of the static structural residual.

5. The vehicle lateral dynamics modeling and state estimation method according to claim 4, characterized in that, In the KAN feature extraction layer, the joint feature vectors are... Mapped to a high-dimensional latent feature space; for the input feature of the th... Each component Through learnable B-spline functions located on the network edges Perform a nonlinear transformation to calculate the first... Layer Output of each node : ,in, ; In the LSTM temporal modeling layer, the high-dimensional feature sequence output by the KAN layer is... Input the data into a Long Short-Term Memory (LSTM) network and use its gating mechanism to update the internal cell state. and hidden layer state To capture the historical dependence and time-delay characteristics of vehicle dynamics: ， It is the scalar output of a single node in a certain layer of the KAN network; It is a vector composed of the outputs of all nodes in the last layer of the KAN network at time k. ; The estimated value of the static residual is then calculated through a fully connected output layer. ; To output the weight matrix, it will contain the high-dimensional hidden states of the LSTM. Linear mapping back to the dimension of the physical residual. This is the output bias vector, used to correct the constant deviation of the system; Based on historical datasets covering typical working conditions Construct the mean squared error (MSE) loss function: ， N represents the historical dataset. The total number of samples in the sample, Optimize network parameters using backpropagation algorithm After training converges, the parameters are frozen.

6. The vehicle lateral dynamics modeling and state estimation method according to claim 1, characterized in that, The online update process of the sparse Gaussian process model includes: Step 2.7, Offline Sparse Induced Point Extraction: In the offline stage, the K-Means clustering algorithm is used to extract sparse induced points from the historical vehicle state feature space. Cluster centers serve as the fixed induced point set for the sparse Gaussian process. ; Step 2.8, Kernel Function Hyperparameter Optimization and Freezing: The method of maximizing the logarithmic marginal likelihood is used to optimize and freeze the set of hyperparameters of the kernel function. Perform offline optimization; the objective function for optimization is: ， Where log is the natural logarithm; It is the probability density function; The observation vector represents the true output values ​​in the training data, used for label training, and its dimension is [dimensional value]. ,in It is the number of training samples; The input data matrix contains features from all training samples, and its dimension is [dimension number missing]. ,in It is the dimension of the feature; The hyperparameter set consists of parameters that need to be optimized, including the length scale of the kernel function. Signal variance ; The covariance matrix is ​​a matrix calculated using a kernel function, describing the similarity between training data points. Its elements... Dimension is ; Let be the noise variance, representing the level of inherent random noise in the observed data; I is the identity matrix, with dimension . ; The kernel function hyperparameters remain fixed after offline optimization; Based on the optimized parameters, the autocovariance matrix between the induced points is pre-calculated and stored. and its inverse matrix , Step 2.9, Sliding Window and Exponential Forgetting Mechanism: Establish a window with a capacity of... First-in, first-out buffer It is used to store the dynamic residual samples observed at the most recent time; a forgetting factor is introduced. Construct a diagonal weight matrix , of which The weights of each sample are To give greater importance to recent data; The system timestamp at the current moment; This is the historical timestamp when the sample was collected; Step 2.10, Online weight update based on weighted ridge regression: using the induced point set and buffer data The weight vector of the Gaussian process is updated in real time through low-dimensional matrix operations. : in, It is a cross kernel matrix, whose elements The m-th induction point and the j-th real-time data in the buffer were calculated. The similarity between them; It is the vector of true dynamic residual observations stored in the buffer, that is, the residual after subtracting the physical model and static compensation from the sensor observations. The buffer... It stores Data from historical moments, indexed as follows ; For the i-th sample in the buffer, its corresponding scalar residual value The calculation formula is: ， It is the actual vehicle state measured by the onboard sensors at time i+1; it is the true observation value. It is the result predicted by the nominal physical model based on the state i at the previous moment, and it represents the most basic dynamic behavior of the vehicle. It is the compensation value output by the offline trained KAN-LSTM network, which corrects the systematic, time-invariant errors caused by model simplification or inaccurate parameters; Represents the variance of observation noise; It contains tiny positive numbers The regularization term is used to ensure the numerical stability of matrix inversion. Step 2.11, Dynamic Residual Output: Based on the updated weight vector The current time is calculated through kernel interpolation. The dynamic compensation value is predicted by the following formula: ， It is the final output of the dynamic random residual prediction value; It is the current state feature input vector of the vehicle; For a fixed set of induced points; It is a kernel vector that contains elements .

7. The vehicle lateral dynamics modeling and state estimation method as described in claim 6, characterized in that: Final vehicle condition estimate: 。

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