Vehicle path tracking control method based on bayesian neural network substitute model

Abstract

This invention discloses a vehicle path tracking control method based on a Bayesian neural network substitution model, belonging to the field of vehicle path tracking control technology. The method includes: constructing a vehicle dynamics model; acquiring pseudo-random front wheel steering angle and accelerator / brake pedal signals, inputting them into the vehicle dynamics model for processing to obtain vehicle motion data; establishing a Bayesian long short-term memory network model based on the vehicle motion data; training a Bayesian neural network substitution model based on the input and output data of the Bayesian long short-term memory network model; constructing a model predictive control framework based on the Bayesian neural network substitution model, and transforming the optimal control problem into a mixed-integer linear programming problem; solving the problem to achieve predictive control of vehicle path tracking. Under complex path conditions, this invention exhibits superior robustness, effectively coping with interference factors such as parameter changes and measurement noise, ensuring the stability and reliability of vehicle path tracking.

Description

Technical Field

[0001] This invention belongs to the field of path tracking control technology for autonomous vehicles, and particularly relates to a vehicle path tracking control method based on a Bayesian neural network substitution model. Background Technology

[0002] With the rapid development of the automotive industry, autonomous driving technology has become an important direction for improving traffic efficiency, reducing driving burden, and enhancing driving safety. Path tracking control, as one of the core functions of autonomous driving systems, aims to enable vehicles to travel accurately and stably along the desired trajectory, and is widely used in various scenarios such as highways, urban roads, and closed parks.

[0003] Currently, path tracking control methods mainly include classic algorithms such as pure tracking, PID, and Stanley, as well as advanced strategies based on model predictive control (MPC). Classical methods are simple in structure and easy to implement, but they neglect vehicle dynamics or nonlinear constraints, making them difficult to handle complex conditions such as high speed, low adhesion, or sudden curvature changes. To address this, researchers have introduced the MPC framework, leveraging its ability to handle multiple constraints and its advantage in predicting future states to significantly improve tracking accuracy and robustness. However, traditional MPC heavily relies on accurate vehicle mechanism models, while in actual driving, tire lateral stiffness, load variations, and environmental disturbances introduce significant parameter uncertainties and measurement noise, leading to model mismatch and decreased control performance.

[0004] To reduce reliance on precise mechanistic models, data-driven approaches are gaining increasing attention. Neural networks and Gaussian processes are used to build vehicle dynamic prediction models and are combined with MPC to form a learning-based control architecture. Among these, Gaussian processes can provide uncertainty estimation, but the computational cost of calculating the inverse covariance matrix online is high, making it difficult to meet real-time requirements. Standard neural networks, while possessing nonlinear fitting capabilities, cannot quantify model uncertainties and suffer from heavy computational burden and poor stability when solving non-convex optimization problems.

[0005] In summary, existing technologies still present significant contradictions in terms of model accuracy, uncertainty quantification, and real-time performance, and there is an urgent need for a path tracking control scheme that can accurately capture parameter uncertainties while meeting the requirements for rapid online solutions. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a vehicle path tracking control method based on a Bayesian neural network substitution model, comprising the following steps: A vehicle dynamics model is constructed based on the single-track dynamics equations and the description of tire lateral stiffness uncertainty. The pseudo-random front wheel steering angle and accelerator / brake pedal signals of the vehicle are acquired and input into the vehicle dynamics model for processing to obtain vehicle motion data. Based on vehicle motion data, a Bayesian long short-term memory network model is established to quantify the uncertainty of vehicle parameters; Based on the input and output data of the Bayesian long short-term memory network model, a Bayesian neural network alternative model is trained. Based on the Bayesian neural network alternative model, a model predictive control framework is constructed, and the optimal control problem is transformed into a mixed-integer linear programming problem. The mixed-integer linear programming problem is solved to achieve path tracking predictive control of vehicles.

[0007] Optionally, the process of building a Bayesian long short-term memory network model based on vehicle motion data includes: The vehicle takes the front wheel steering angle, accelerator / brake pedal, global coordinate position, yaw angle, longitudinal velocity, lateral velocity and yaw rate of the previous moment as input, and takes the global coordinate position, yaw angle, longitudinal velocity, lateral velocity and yaw rate of the current moment as output. Treating network weights and biases as random variables, we first set a prior distribution and then approximate the posterior distribution through variational inference. Using the sum of mean squared error and KL divergence as the loss function, a Bayesian long short-term memory network model that can simultaneously output the mean and variance of state variables is obtained after reparameterization training.

[0008] Optionally, the process of training a Bayesian neural network alternative model based on the input and output data of the Bayesian long short-term memory network model includes: The mean and standard deviation of the state variables generated by the Bayesian long short-term memory network model under the same input sequence are used as the training targets. A single-layer recurrent neural network structure is adopted, with the hidden layer using a symmetric saturated linear transfer function as the activation function and the output layer using a linear function as the activation function; The Levenberg-Marquardt algorithm is used to iteratively optimize the network weights until the error between the predicted output and the mean and standard deviation converges, thus obtaining a Bayesian neural network alternative model that can simultaneously output the mean and standard deviation of the state variables.

[0009] Optionally, the process of constructing the model prediction control framework based on the Bayesian neural network alternative model includes: The mean and variance of the state variables given by the Bayesian neural network replacement model are used as the basis for prediction, and the prediction time domain and control time domain are preset. The objective function is constructed based on the deviation of the vehicle position, yaw angle and the reference path, and a probabilistic safety constraint is added to ensure that the variance of the prediction error multiplied by the confidence coefficient does not exceed the allowable deviation limit. The physical limits of the front wheel steering angle and the accelerator / brake pedal are used as control constraints to form a complete model predictive control framework.

[0010] Optionally, the process of transforming the optimal control problem into a mixed-integer linear programming problem includes: Based on the aforementioned model predictive control framework, an auxiliary continuous variable is introduced to transform the absolute value error term in the objective function into a linear inequality. The symmetric saturated linear function used in the hidden layer of the Bayesian neural network alternative model is piecewise linearized. Continuous variables and corresponding binary variables are introduced into each line segment, and the input-output relationship is described by linear equations and inequalities. The linearized objective function, activation function constraints, and original system constraints are unified and organized into a system of linear equations and inequalities, forming a standard mixed-integer linear programming problem.

[0011] Optionally, the process of solving the mixed-integer linear programming problem to achieve path tracking predictive control of the vehicle includes: At each sampling time, with the current state of the vehicle as the initial condition, the mixed integer linear programming solver is called to solve the transformed mixed integer linear programming problem, and the optimal front wheel steering angle and accelerator / brake pedal sequence in the prediction time domain are obtained. Apply the first control variable in the sequence to the vehicle to drive the vehicle to update its state; The state is re-acquired at the next sampling time and the above solution and control process is repeated to achieve continuous path tracking predictive control.

[0012] This invention also proposes a vehicle path tracking control system based on a Bayesian neural network substitution model for implementing the method, the system comprising: The dynamics model building module is used to generate vehicle dynamics models based on the single-track dynamics equations and the tire lateral stiffness uncertainty description. The motion data acquisition module is used to input pseudo-random front wheel steering angle and accelerator / brake pedal signals into the vehicle dynamics model, and obtain vehicle motion data through numerical integration. The Bayesian modeling substitution module is used to establish a Bayesian long short-term memory network model based on the vehicle motion data, and to train a Bayesian neural network substitution model based on the input and output data of the Bayesian long short-term memory network model. The control framework construction module is used to construct a model prediction control framework based on the Bayesian neural network replacement model and transform the optimal control problem into a mixed-integer linear programming problem. The path tracking prediction module is used to solve the mixed integer linear programming problem and apply the obtained control quantity to the vehicle to realize path tracking predictive control.

[0013] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0014] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0015] The present invention also proposes a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: This invention achieves high-precision, robust, and fast real-time control for vehicle path tracking based on Bayesian Long Short-Term Memory (LSTM) network models and recurrent neural network (RNN) substitution model construction techniques. The Bayesian LSTM network model accurately quantifies vehicle parameter uncertainties, such as the dynamic changes in tire lateral stiffness, thereby improving the vehicle model's adaptability and prediction accuracy under complex operating conditions. Furthermore, the use of the Bayesian neural network substitution model significantly reduces computational complexity, enabling model predictive control to be solved within milliseconds, meeting the requirements of real-time control. In addition, transforming the optimal control problem into a mixed-integer linear programming problem further improves solution efficiency and control accuracy. Under complex path conditions, this invention exhibits superior robustness, effectively coping with interference factors such as parameter changes and measurement noise, ensuring the stability and reliability of vehicle path tracking. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the vehicle dynamics model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a vehicle BLSTM model according to an embodiment of the present invention; Figure 4 This is a diagram of the vehicle BLNNSM model training framework according to an embodiment of the present invention; Figure 5 This is a schematic diagram of a continuous piecewise function according to an embodiment of the present invention; Figure 6 This is a design framework diagram of a vehicle path tracking system based on BLNNSM according to an embodiment of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] With the rapid advancement of technology and the booming development of the automotive industry, autonomous vehicle technology plays a significant role in improving traffic efficiency, reducing driver workload, and enhancing vehicle safety. Path tracking control, as a core component of autonomous driving technology, has become a research hotspot. Path tracking control strategies are typically implemented based on constrained nonlinear system optimization problems and are widely used in the field of autonomous driving. However, existing path tracking control algorithms face challenges in balancing model accuracy and real-time performance in practical applications. Furthermore, vehicles are often affected by parameter variations and measurement noise during actual driving, which severely impacts the accuracy of path tracking and poses a threat to the safety of the vehicle and its occupants. Therefore, improving the accuracy of vehicle models and enhancing the real-time performance of control algorithms have become important research directions for both academic and industrial communities both domestically and internationally.

[0021] Vehicle path tracking control has received widespread attention over the past few decades. Simple path tracking control methods include pure tracking control, proportional-integral-derivative (PID) control, and Stanley control. Zhang's team proposed a path tracking algorithm for four-wheel steering (4WS) agricultural machinery based on a fuzzy control pure tracking model. This algorithm employs a pure tracking model and a fuzzy controller. Simulation and experimental results show that the algorithm has good tracking accuracy and convergence in both straight and turning path tracking. However, this method neglects the influence of vehicle dynamics in path tracking. Kang et al. used a fractional-order PID controller for path tracking, and simulation results show that this method can accurately control vehicle heading deviation. However, PID controllers still face difficulties in dealing with system nonlinear characteristics and multi-constraint coupling problems. Seiffer et al. proposed an enhanced Stanley path tracking controller by using the curvature of the path as a feedforward. This controller selects a point further along the path as the reference point for the feedforward input to compensate for delays in signal processing and steering angle control. Simulation results show that this method effectively improves path tracking accuracy. However, this method is mainly optimized for low-to-medium speed, low-dynamic autonomous driving applications, and may not perform well when the path curvature changes drastically.

[0022] To improve path tracking performance, Pan et al. proposed a model-free adaptive dynamic programming method to solve the path tracking problem of autonomous vehicles caused by actuator failure. This method eliminates the impact of actuator failure, modeling errors, and curvature disturbances on the vehicle system by designing an adaptive regulator. Although model-free control methods have simple controller structures, stability analysis of the control system is relatively difficult. Ni et al. proposed an improved linear quadratic regulator (LQR) lateral motion control method. This method uses the Lagrangian function method to construct a kinematic model of the robot's tracking error and designs an LQR feedforward controller for a tracked mobile robot, improving the controller's adaptability, control accuracy, and system dynamic performance. However, the performance of the LQR controller is highly dependent on the accuracy of the system model. In practical applications, due to modeling errors, parameter uncertainties, and other factors, the system model may deviate from the actual situation. This model mismatch may lead to a decrease in LQR controller performance and cause system instability. Zhang et al. designed a novel adaptive sliding mode control method. This method addresses the path tracking problem of automated ground vehicles under complex conditions. It derives the conditions ensuring the admissibility of the vehicle system using Lyapunov functions and Jensen's inequality, and simulations verify the controller's superior tracking accuracy and anti-interference capabilities. However, this method is highly dependent on the accuracy of vehicle parameters, and the inherent chattering problem of sliding mode control is not fully addressed. Furthermore, the singular matrices and observer design involved in the control algorithm increase computational complexity, potentially hindering real-time online applications.

[0023] The aforementioned methods have certain limitations in handling nonlinear systems and model errors and disturbances, resulting in less than ideal control accuracy. Since Model Prediction Control (MPC) algorithms have the ability to predict the future state of a system and also have the advantage of handling multiple constraints, researchers have begun to use MPC for vehicle path tracking. Zhou et al. proposed an autonomous vehicle path tracking control method based on MPC, combining the Particle Swarm Optimization (PSO) algorithm and the Adaptive Neural Fuzzy Inference System (ANFIS). Simulation results show that this method improves path tracking accuracy and real-time performance. Liu et al. designed a VMPC controller combining zero-order hold (ZOH) and first-order hold (FOH) strategies. ZOH discretization is used in the first part of the prediction interval to improve prediction accuracy; FOH discretization is used in the latter part of the prediction interval to reduce computational burden. Experimental results show that this method improves path tracking accuracy and shortens the average solution time compared to traditional MPC controllers. However, the above-mentioned MPC methods based on vehicle mechanism models require accurate vehicle models, but this information is difficult to obtain accurately in practical applications.

[0024] Given the difficulty in obtaining accurate vehicle mechanistic models in practical applications and the computational complexity of such models, researchers have begun to utilize data-driven methods to build vehicle predictive models during control design. Currently, the main data-driven models used for MPC design include Neural Network (NN) models and Gaussian Process (GP) models, which can effectively learn vehicle dynamic characteristics. Rokonuzzaman et al. used a neural network to learn vehicle dynamic characteristics, utilizing the large amount of data provided by modern vehicle systems to train the NN, and then integrated this neural network model into the MPC. Experimental results show that this method can accurately simulate vehicle behavior and exhibit excellent control performance in real-world road conditions. Spielberg et al. proposed a method based on Neural Network Model Predictive Control (NNMPC). This method constructs a neural network model suitable for the model predictive control framework by fusing the state and control input from historical vehicle operating data. Experimental results show that the NNMPC controller can adapt to different road conditions and friction conditions and effectively track the vehicle path. However, the highly nonlinear nature of neural network models leads to computational burden and stability issues when seeking optimal solutions. In contrast, Gaussian process models have a significant advantage in providing estimates of predictive uncertainty. Wang et al. designed an MPC controller by combining a Gaussian process model and a nominal kinematic model, which significantly reduced tracking errors and improved computational efficiency. However, the designed nonlinear MPC is not easy to solve with high quality, and it still faces the challenge of capturing uncertainties in complex environments. Han et al. integrated an error correction model based on Gaussian process regression into the MPC framework, constructing the LB-MPC (Learning-Based MPC) control strategy. Experiments showed that its longitudinal and lateral vehicle speed errors were reduced by more than 80% compared with the traditional model, and the tracking accuracy was significantly improved. However, the Gaussian process requires the calculation of the inverse of the covariance matrix, which has the problem of online computational complexity, making it difficult to achieve real-time control. Yufei et al. proposed a risk-aware vehicle motion planning method based on Bayesian neural networks (BNN) and MPC. This method quantifies the uncertainties in the vehicle path planning process through the BNN model, thereby improving the ability to handle dynamic obstacles and uncertain environmental factors. However, although this method shows good performance in simulations, the computational complexity of BNN is a potential challenge in practical applications.

[0025] Furthermore, reinforcement learning, with its powerful nonlinear mapping capabilities, offers a novel solution for vehicle control under complex operating conditions. Zhang et al. proposed a path tracking control algorithm based on deep reinforcement learning, which combines path curvature to construct a deep Q-network based on a five-layer backpropagation neural network. Experimental results show that the proposed path tracking control algorithm exhibits excellent adaptability and stability. However, while vehicle path tracking control based on reinforcement learning methods has high accuracy and robustness, it is highly dependent on data, and the computational load for training and debugging is large and time-consuming.

[0026] In summary, traditional neural network models lack the ability to quantify uncertainty. Although the combined model of Gaussian process and nominal model and Bayesian neural network model have the ability to represent uncertainty, their computational complexity is high, which makes it difficult to solve predictive controllers and meet the requirements of real-time control.

[0027] Example 1 To address the problems in existing technologies, this embodiment provides a vehicle path tracking control method based on a Bayesian neural network substitution model, such as... Figure 1 As shown, it includes the following steps: A vehicle dynamics model is constructed based on the single-track dynamics equations and the description of tire lateral stiffness uncertainty. The pseudo-random front wheel steering angle and accelerator / brake pedal signals of the vehicle are acquired and input into the vehicle dynamics model for processing to obtain vehicle motion data. Based on vehicle motion data, a Bayesian long short-term memory network model is established to quantify the uncertainty of vehicle parameters; Based on the input and output data of the Bayesian long short-term memory network model, a Bayesian neural network alternative model is trained. Based on the Bayesian neural network alternative model, a model predictive control framework is constructed, and the optimal control problem is transformed into a mixed-integer linear programming problem. The mixed-integer linear programming problem is solved to achieve path tracking predictive control of vehicles.

[0028] In this embodiment, the aim is to alleviate the daunting computational burden of existing probabilistically constrained MPC control frameworks and improve the quality of control solutions, thereby enhancing path tracking performance, by proposing a predictive control framework based on a Bayesian neural network alternative model. A Bayesian Long Short Term Memory Network (BLSTM) is used to establish a vehicle dynamic model, capturing the nonlinear dynamic characteristics under uncertain vehicle parameters, using only pseudo-experimental input and output data of the vehicle motion. To address the high computational burden of the Monte Carlo sampling process in the BLSTM model, a recurrent neural network model containing the output standard deviation is trained based on the input and output data of the established BLSTM model as an alternative model, reducing the computational load of the vehicle model. Based on this data-driven alternative vehicle model, an MPC controller is designed for vehicle path tracking control. The constructed MPC optimal control problem is transformed into a mixed-integer linear programming problem, which is efficiently solved in each control time step, improving path tracking accuracy under uncertain tire lateral stiffness. The proposed control method is compared with MPC based on traditional LSTM and MPC based on the BLSTM model; simulation results demonstrate its advantages and effectiveness.

[0029] Feasible vehicle system modeling is the foundation of vehicle dynamics simulation. In this embodiment, the mechanistic model of the vehicle and the description of the uncertainty of the tire lateral stiffness parameter are first introduced. Then, utilizing the temporal modeling capability of the LSTM model, a vehicle Bayesian LSTM model is established by integrating Bayesian inference theory to capture the dynamic characteristics of the vehicle under parameter uncertainty. Finally, to address the problem of low computational efficiency of the vehicle Bayesian LSTM model, an alternative model of the vehicle Bayesian LSTM is designed to reduce the computational burden.

[0030] Feasible vehicle dynamics model: Vehicles are affected by a variety of factors during operation, including longitudinal and lateral kinematic characteristics and the complex interaction between the tires and the ground. Therefore, constructing a reasonably simplified vehicle dynamics model is of great significance for effectively balancing computational efficiency and realistic dynamic characteristics.

[0031] Furthermore, the vehicle monorail model: This embodiment constructs a vehicle dynamics model based on the monorail dynamics assumption, as follows: Figure 2 As shown, this model, by constraining degrees of freedom, focuses on characterizing the vehicle's kinematics in the longitudinal and lateral directions, while neglecting the dynamic effects of pitch and roll. This simplified approach, while ensuring real-time computational performance, still effectively reflects the vehicle's core dynamic behavior. It is an inertial coordinate system. Using the vehicle body coordinate system, assume the vehicle has a global position coordinate system. and yaw angle The point mass.

[0032] Based on Newton's second law, the state variables of the vehicle are defined as follows: The control quantity is The equations for the vehicle dynamics model are as follows: MERGEFORMAT (1) in and These represent longitudinal velocity and lateral velocity, respectively. Indicates the yaw angle. Indicates yaw rate. For the front wheel steering angle, For vehicle quality, For the yaw moment of inertia, and These are the distances between the vehicle's center of gravity and the front and rear wheels, respectively. , , and These are the longitudinal front wheel force, the lateral front wheel force, the longitudinal rear wheel force, and the lateral rear wheel force, respectively.

[0033] Longitudinal wheel force and Related to accelerator / brake pedals and torque distribution: MERGEFORMAT (2) MERGEFORMAT (3) in To work together, and These are acceleration force and braking force, respectively. This is the input for the accelerator / brake pedal. When the accelerator pedal is depressed, i.e. When the brake pedal is depressed, the vehicle's speed increases; when the brake pedal is depressed, the speed increases. At that time, the vehicle's speed decreased. For torque distribution, For symbolic functions, it is defined as: MERGEFORMAT (4) The lateral force of a tire is described using Pacejka's magic formula, which has the following general form: MERGEFORMAT (5) The input variable is , Indicates the vehicle's slip angle. This indicates that the wheel curve is drifting horizontally. For wheel stiffness factor, Indicates the peak factor of the wheel curve. The shape factor representing the wheel curve. This represents the curvature factor of the wheel curve and the vertical drift of the wheel curve. The specific expressions are as follows: MERGEFORMAT (6) in This indicates the vertical load on the wheel. This indicates the camber angle of the wheel, which is usually set to zero. These represent the calculation coefficients of the tire model.

[0034] Under pure sideslip conditions, the lateral wheel force increases with the sideslip angle until it reaches its maximum value. When the sideslip angle is small, the lateral force has a linear relationship with the sideslip angle; when the sideslip angle is large, the lateral force tends to stabilize.

[0035] To simplify calculations, the lateral wheel force is approximated linearly within a small sideslip angle range: MERGEFORMAT (7) in and These represent the lateral stiffness of the front and rear wheels, respectively. and These represent the slip angles of the front and rear vehicles, respectively. It's important to note that the vehicle slip angle is defined as the angle between the tire direction and the vehicle speed, and its specific calculation formula is: MERGEFORMAT (8) Further, vehicle mechanism model verification: To systematically and comprehensively verify the adaptability of the vehicle mechanism model under different operating conditions and ensure its high accuracy and reliability in complex and ever-changing real-world driving scenarios, this embodiment constructs a co-simulation framework based on the CarSim-Simulink platform. This framework cleverly integrates multiphysics coupling analysis technology and high-dimensional data benchmarking methods to achieve a scientific and accurate evaluation of the model's credibility.

[0036] In the simulation experiment, the initial state is set as follows: The specific settings of the basic parameters of the vehicle dynamics model are shown in Table 1. Based on the model's validation requirements, the time-domain characteristics of the designed control inputs are characterized by the changes in longitudinal vehicle speed and front wheel steering angle over time. Table 1 This embodiment uses a hatchback sedan in the CarSim simulation platform as the research object. The vehicle is equipped with a front / rear independent suspension structure and uses radial tires with a specification of 205 / 55R16. Details of the settings for key parameters such as mass distribution and powertrain characteristics during the simulation modeling process are shown in Table 2.

[0037] Table 2 The validation results of the dynamic model show that under low-speed conditions (0-15 m / s), the model's output is consistent with CarSim's output, and under high-speed conditions (15-25 m / s), the model's output also matches CarSim's output well. At turns, the maximum deviation of the vehicle's X-coordinate position is less than 1.6 m, the maximum deviation of the vehicle's Y-coordinate position is less than 1 m, and the maximum deviation of the vehicle's yaw angle is less than 0.09 rad. These comparative results validate the effectiveness of the established vehicle mechanism model.

[0038] Further, the uncertainty of vehicle tire lateral stiffness is described as follows: Tire lateral stiffness is a key parameter in vehicle dynamics models, significantly impacting vehicle handling and stability. However, in practical applications, tire lateral stiffness is often accompanied by considerable uncertainty. First, changes in ambient temperature and humidity significantly affect tire stiffness parameters. Studies show that temperature fluctuations lead to substantial changes in the storage modulus of the tread rubber, especially under high or low temperature conditions, where tread rubber stiffness can change significantly by ±15%. This change directly affects the tire's contact characteristics with the road, thus impacting vehicle handling and stability. Second, factors such as the road surface's coefficient of friction, road unevenness, and degree of wetness and slipperiness also significantly influence tire lateral stiffness. Particularly in complex road environments, such as wet, muddy, or snow-covered roads, the frictional force between the tire and the road changes drastically, making tire stiffness characteristics even more unpredictable. Under these environmental conditions, tire lateral stiffness may deviate significantly from normal levels, thus affecting vehicle handling precision.

[0039] Furthermore, tire lateral stiffness is also affected by load. Under different load conditions, tire lateral stiffness exhibits different characteristics. The uncertainty in the lateral stiffness of the front and rear wheels can be described by the following formula: MERGEFORMAT (9) in This represents the lateral stiffness coefficient of the front wheel under normal load, while This represents the lateral stiffness coefficient of the rear wheel under normal load; This represents the maximum deviation of the front wheel lateral stiffness under normal conditions, while This represents the maximum deviation of the rear wheel lateral stiffness under normal conditions. This represents the time-varying coefficient of the front wheels, while Constrained by the dynamic characteristics of the sideslip angle and satisfying: MERGEFORMAT (10) The feasible process of building a Bayesian long short-term memory network model based on vehicle motion data includes: The system takes the vehicle's previous front wheel steering angle, accelerator / brake pedal position, global coordinate position, yaw angle, longitudinal velocity, lateral velocity, and yaw rate as inputs, and the current global coordinate position, yaw angle, longitudinal velocity, lateral velocity, and yaw rate as outputs. The network weights and biases are treated as random variables. A prior distribution is first set, and then the posterior distribution is approximated through variational inference. The sum of mean squared error and KL divergence is used as the loss function. After reparameterized training, a Bayesian long short-term memory network model that can simultaneously output the mean and variance of the state variables is obtained.

[0040] As a feasible implementation method, the vehicle Bayesian LSTM model: The complexity and uncertainty of vehicle systems make traditional vehicle mechanistic modeling extremely difficult and labor-intensive. In particular, the uncertainty of key parameters such as tire lateral stiffness makes it difficult to describe the vehicle's dynamic behavior with accurate mechanistic models. To address this issue, this embodiment proposes a data-driven BLSTM model to capture the nonlinear dynamic characteristics of vehicle motion. The introduction of the BLSTM model not only captures the long-term dependencies of time-series data but also quantifies the uncertainty of the model output through Bayesian inference. This feature enables the BLSTM model to provide more robust predictive performance in predictive control.

[0041] Furthermore, the vehicle Bayesian LSTM model framework: Bayesian Long Short Term Memory Network (BLSTM) introduces Bayesian inference into the traditional LSTM to achieve dynamic modeling under vehicle parameter uncertainty. Unlike conventional LSTM, BLSTM treats the weights and biases in the network as random variables, first defining their prior distribution, and then approximating their posterior distribution through variational inference. This approach quantifies the uncertainty of the output, provides probabilistic predictions of future states, and enables the model to express the dynamic characteristics of the system under parameter uncertainty, thereby improving the robustness of the model output.

[0042] To simplify the derivation of the posterior distribution, the variational distribution is usually assumed to be a Gaussian distribution, and the variational parameters are expressed as follows: ,in It is the mean vector. This is the standard deviation vector. To ensure the stability of numerical calculations, the standard deviation parameter needs to be guaranteed. The value is always non-negative, therefore it is necessary to... Reparameterize, and its reparameterized standard deviation The specific expression is as follows: MERGEFORMAT (11) In traditional Monte Carlo sampling, the randomness of the operation causes the gradient of the weights to be non-differentiable, therefore, the weights need to be modified. It also needs to be reparameterized, and its reparameterization form is as follows: . It follows a unit Gaussian distribution, i.e. Therefore, the sampling of the posterior distribution of the weights and biases can be expressed as: MERGEFORMAT (12) MERGEFORMAT (13) in , They represent the model number 1, 2, 3, 4, 5, 6, 7, 8, 9 Layer weights and biases in the first layer Secondary sample value.

[0043] The BLSTM model addresses the uncertainty of model parameters by introducing a Bayesian approach. The loss function of this model is designed as follows: MERGEFORMAT (14) The first term of the loss function is the mean square error (MSE), which is used to evaluate the difference between the predicted value and the true value for each sample. The output of the neural network, Indicates the number of samples. An index representing the number of samples. Representing the The true value of each sample Representing the The mean of the neural network output corresponding to each input sample. The second term of the loss function is the KL divergence. For prior probability, For posterior probability, As a regulating factor, it is used to control the degree of influence of KL divergence in the loss function.

[0044] A smaller MSE value indicates higher model accuracy. The introduction of the squared term in the MSE ensures that the signs of errors do not cancel each other out, and larger errors have a more significant impact on the results, thus more effectively reflecting the error distribution characteristics of the model. KL divergence represents the difference between the prior distribution and the actual error distribution. With variational distribution The degree of deviation between them The specific expression is shown in equation (15): MERGEFORMAT (15) Given the first When there are 1 sample, the prior probability and posterior probability It can be calculated as follows: MERGEFORMAT (16) MERGEFORMAT (17) In the formula, the prior probability is , , For custom parameters, the posterior probability , The parameter is the first The value obtained by variational reasoning for each sample.

[0045] In the loss function, KL divergence can impose constraints on the probability distribution of the model, thus handling parameter uncertainty more effectively. By combining KL divergence and MSE, the accuracy of the model's output can be improved.

[0046] The vehicle BLSTM model framework constructed in this embodiment is as follows: Figure 3 As shown. After collecting vehicle data through a pseudo-experiment of vehicle motion, the BLSTM model was trained using variational inference to determine the weight distribution. The vehicle dynamics model has 5 inputs, 3 outputs, and 16 neurons in the hidden layer.

[0047] The mathematical expression of the vehicle BLSTM model is described as follows: MERGEFORMAT (18) In the formula, This indicates the number of neurons in the output layer. This represents the index of each neuron in the output layer. This indicates the number of neurons in the hidden layer. This represents the index of each neuron in the hidden layer. Indicates the index of Monte Carlo sampling. Index representing time, Indicates the number of Monte Carlo samples. It is an activation function and These are two common activation functions. This represents the time series data input at the current moment. Indicates the first The first sampling of the hidden layer The hidden state of each neuron in the previous time step. Furthermore, , , They represent the first time. The first sampling of the hidden layer The outputs of the forget gate, input gate, and output gate of each neuron; and They represent the first The first sampling of the hidden layer The weight matrix and bias parameters of each neuron; Indicates the first The first sampling of the hidden layer The memory unit learned from the current time data of each neuron. Indicates the first The first sampling of the hidden layer Each neuron synthesizes the memory unit from the previous moment. and the memory unit at the current moment The resulting integrated memory unit, Indicates the first The first sampling of the hidden layer The final output of the hidden layer is obtained by fully computing the current time data of each neuron using LSTM. Finally, and They represent the first time. The output layer in the sampling... The weight matrix and bias vector of each neuron. To map the hidden state to the output of the output layer, This is the output of the model at the current time step.

[0048] Further validation of the vehicle Bayesian LSTM model: During model validation, the baseline values ​​for the lateral stiffness coefficients of the front and rear wheels were set at 66,900 N / rad and 62,700 N / rad, respectively. The maximum deviation of the lateral stiffness between the front and rear wheels during vehicle operation was also assumed. and The value is set to 0.2 to reveal the uncertain variation characteristics of tire lateral stiffness. In this embodiment, the vehicle control variables are the front wheel steering angle and the accelerator / brake pedal, where the front wheel steering angle randomly varies between -0.44 rad and 0.44 rad, and the accelerator / brake pedal value randomly varies between -1 and 1. To fully capture the different dynamic characteristics of the vehicle and enhance data diversity, pseudo-random sampling input is used to improve the adaptability of the trained BLSTM model under different operating conditions. The data sampling time is 0.1 s.

[0049] The input to the BLSTM model is the vehicle control variables and state variables from the previous time step, and the output is the state variables for the current time step, as detailed in Tables 3 and 4.

[0050] Table 3 Table 4 The vehicle BLSTM model was trained using the PyTorch framework and Bayesian inference was performed using the blitz library. Equation (16) specifies the parameters of the prior probability. Set it to 0.1. Set it to 0.002. Let it be 1. The mean of the posterior probability in formula (17) Set to 1, standard deviation The learning rate was set to -8. During training, the learning rate was set to 0.01. The normalized loss value rapidly decreased from approximately 0.3 to near 0 in the initial stage, demonstrating the efficiency of the optimization method in the initial phase. Subsequently, the loss value gradually stabilized and eventually converged to an extremely low loss value of 0.00000389. This result shows that the designed BLSTM model has reasonable parameter configuration and stable and effective training, laying a solid foundation for subsequent analysis and applications.

[0051] Model validation was performed using collected test data. The mean output of the BLSTM model largely matched the uncertainty trend of the sampled data, and the 95% confidence interval covered the range of variation in the validation data. This indicates that the BLSTM model can effectively capture system uncertainty while learning vehicle dynamic characteristics. The model not only possesses high output accuracy but also reasonably estimates the uncertainty of state variables, laying the foundation for vehicle motion prediction.

[0052] The feasible process of training a Bayesian neural network alternative model based on the input-output data of the Bayesian long short-term memory network model includes: The mean and standard deviation of the state variables generated by the Bayesian Long Short-Term Memory network model under the same input sequence are used as training targets. A single-layer recurrent neural network structure is adopted, with the hidden layer using a symmetric saturated linear transfer function as the activation function and the output layer using a linear function as the activation function. The Levenberg-Marquardt algorithm is used to iteratively optimize the network weights until the error between the predicted output and the mean and standard deviation converges, thus obtaining a Bayesian neural network alternative model that can simultaneously output the mean and standard deviation of the state variables.

[0053] As a feasible implementation method, the vehicle Bayesian LSTM alternative model is: As can be seen from formula (18), the BLSTM model has a large computational load and low computational efficiency due to the need for multiple Monte Carlo samplings during computation. In real-time control systems, this computational delay may seriously affect the closed-loop control performance and its stability. Therefore, the model needs to be simplified to improve computational efficiency. To address this problem, this embodiment proposes a strategy based on an alternative model. The core idea of ​​this strategy is to use the input and output data of the trained BLSTM model to retrain an RNN model with output standard deviation as an alternative model to Bayesian LSTM (BLNNSM). This alternative model has 5 inputs, 6 outputs, and 16 neurons in its hidden layer. The specific structure of the above alternative model is as follows: Figure 4 As shown, the model's six outputs consist of three mean outputs and three standard deviation outputs. In the BLNNSM model, choosing a suitable activation function for the hidden layers is crucial for model performance and training effectiveness. Therefore, factors such as the activation function's nonlinearity, smoothness, activation range, and gradient vanishing problem are considered. In this embodiment, the Symmetric Saturating Linear Transfer Function (SSL) is selected as the activation function for the model's hidden layers.

[0054] The activation function SSL restricts the input to the range [-1, 1] and performs saturation when the input exceeds this range. SSL is defined as: MERGEFORMAT (19) In the output layer of BLNNSM, the activation function of each neuron is a linear function, expressed as: MERGEFORMAT (20) At each time step, the neuron output of the BLNNSM hidden layer is obtained through a linear combination of the input, weights, and biases, plus a nonlinear transformation of the activation function, as follows: MERGEFORMAT (21) in For indexing time, For the index of each neuron in the input layer, The number of neurons in the input layer. This is the index of each neuron in the hidden layer. The number of neurons in the hidden layer. It was the previous moment. No. The output of each hidden layer neuron It is a moment No. The output of each hidden layer neuron It is the weight matrix from the input layer to the hidden layer. It is the weight matrix from hidden layer to hidden layer. It is the output of each neuron in the input layer. It is the bias vector of the hidden layer.

[0055] Then, by using the neuron outputs of the BLNNSM hidden layer as input, and applying a linear combination of weights and biases along with an activation function, the neuron outputs of the BLNNSM output layer are obtained, expressed as: MERGEFORMAT (22) in For each neuron in the output layer, The number of neurons in the output layer. It is a moment No. The output of each output layer neuron It is the first in the hidden layer The nth neuron and the nth neuron in the output layer The weight coefficients of each neuron, It is the bias vector of the output layer.

[0056] In the BLNNSM alternative model, only the activation function (SSL) of the hidden layers is nonlinear. Therefore, the entire BLNNSM model can be linearized by expressing this activation function as a mixed-integer linear function, thereby reducing the complexity of the model and improving computational efficiency. This is highly advantageous for optimization control design based on the BLNNSM model.

[0057] The mixed-integer linearization of the piecewise function SSL (19) can be achieved by introducing some auxiliary variables, including continuous and binary variables. A schematic diagram of the SSL function is shown below. Figure 5 As shown, it consists of three linear interval segments and four breakpoints ( , , , Composed of ) breakpoints. and These represent the inputs to neurons in the hidden layer, respectively. The lower and upper bounds are obtained through testing.

[0058] For any given value( , There are always specific and Make the following equation true: MERGEFORMAT (23) In the formula, For breakpoints Introducing a positive continuous variable.

[0059] Therefore, the piecewise function SSL in The value at that location is: MERGEFORMAT (24) To ensure that each The values ​​can all be matched with suitable continuous interval breakpoints and The following constraints have been added in connection with this: MERGEFORMAT (25) MERGEFORMAT (26) In the formula, To introduce a linear interval segment The corresponding binary variable.

[0060] In summary, when any given value( When ), the mixed-integer linear expression for SSL is: MERGEFORMAT (27) In the formula, .

[0061] This embodiment utilizes MATLAB's Neural Network Toolbox, calling the built-in function "layrecnet" to model and train the BLNNSM model. During BLNNSM model training, the neural network's input latency is set to 1:5, the hidden layer size to 16, and the learning rate to 0.01 to ensure stability and convergence speed. The training algorithm employs the Levenberg-Marquardt algorithm, which combines the characteristics of gradient descent and Gauss-Newton methods. By approximating the inverse of the Hessian matrix, it updates the model parameters more quickly and accurately, thereby minimizing the loss function.

[0062] The model validation results show that the output mean and standard deviation of the BLNNSM model are in high agreement with the output of the BLSTM model, indicating that the BLNNSM model is accurate and can be used as a replacement model for BLSTM.

[0063] The feasible process of constructing a model predictive control framework based on the Bayesian neural network alternative model includes: The mean and variance of the state variables given by the Bayesian neural network replacement model are used as the basis for prediction, and the prediction time domain and control time domain are preset. The objective function is constructed with the deviation of vehicle position, yaw angle and reference path, and probabilistic safety constraints are added to ensure that the standard deviation multiplied by the confidence coefficient does not exceed the allowable deviation limit. The physical limits of front wheel steering angle and accelerator / brake pedal are used as control variables to form a complete model predictive control framework.

[0064] A feasible process for transforming the optimal control problem into a mixed-integer linear programming problem includes: Based on the aforementioned model predictive control framework, auxiliary continuous variables are introduced to transform the absolute value error term in the objective function into a linear inequality. The symmetric saturated linear function used in the hidden layer of the Bayesian neural network replacement model is piecewise linearized, with continuous variables and corresponding binary variables introduced for each segment, and the input-output relationship is described using linear equations and inequalities. The linearized objective function, activation function constraints, and original system constraints are then unified into a system of linear equations and inequalities to form a standard mixed-integer linear programming problem.

[0065] The feasible process of solving the mixed-integer linear programming problem to achieve vehicle path tracking predictive control includes: At each sampling time, with the current state of the vehicle as the initial condition, the mixed-integer linear programming solver is invoked to solve the transformed mixed-integer linear programming problem, obtaining the optimal front wheel steering angle and accelerator / brake pedal sequence in the prediction time domain; the first control variable in the sequence is applied to the vehicle to drive the vehicle to update its state; at the next sampling time, the state is re-acquired and the above solution and control process is repeated to achieve continuous path tracking predictive control.

[0066] As a feasible implementation method, a robust model predictive controller is designed: In robust MPC, the BLNNSM model plays a crucial role by predicting the vehicle's dynamic characteristics over a future period, thereby deriving the optimal control strategy. Unlike traditional MPC methods, BLNNSM-based alternative model MPC not only outputs the mean of the system state during optimization but also provides the variance of the output state, offering the controller the ability to quantify uncertainty. Within the robust MPC framework, the controller's objective is to minimize the system state deviation under system constraints, achieving path tracking.

[0067] Furthermore, the objective function and constraints: The objective function of the MPC controller primarily measures and minimizes the deviation between the system and the desired path. Specifically, the objective function is expressed as follows: MERGEFORMAT(28) in For indexing time, To predict the time domain, , , For the first The predicted values ​​of the vehicle's X-coordinate position, Y-coordinate position, and yaw angle at each time point. , , The first Reference values ​​for the vehicle's X-coordinate position, Y-coordinate position, and yaw angle at any given time. , , In the prediction time domain The weighting coefficients of the error term in the internal objective function. To achieve adaptive weight changes, the weighting coefficients are specifically defined as follows: MERGEFORMAT (29) Considering the actual constraints of the vehicle, the constraints in the controller are as follows: (1) The maximum value of the front wheel steering angle of the vehicle It is 0.44 rad, the minimum value The value is -0.44 rad, and its constraint condition can be expressed as: MERGEFORMAT (30) In the formula To control the time domain.

[0068] (2) To ensure the vehicle operates within a safe speed range, the travel range of the accelerator / brake pedals needs to be limited. Therefore, the accelerator / brake pedals... The maximum travel value is set to 1, and the minimum travel value is set to 1. Set it to -1, as follows: MERGEFORMAT (31) (3) To avoid excessive tracking errors caused by parameter uncertainty, probabilistic safety constraints are introduced to ensure that the tracking error remains within an acceptable range. When the constraint is required to be feasible with a 95% probability, the constraint expression is: MERGEFORMAT (32) In the formula, , and They represent in The variance of the predicted global vehicle coordinates X, Y, and yaw angle at each moment, and... , , This indicates the maximum deviation between each state value and the reference value during vehicle path tracking.

[0069] Furthermore, the optimal control problem is solved: Using the vehicle BLNNSM model established in this embodiment as the prediction model, the MPC controller can be constructed by combining the objective function and constraints as follows: MERGEFORMAT (33) in The front wheel steering angle vector. For the accelerator / brake pedal vectors, the vehicle BLNNSM model is described as follows: MERGEFORMAT (34) Where k is the index of each neuron in the current layer. It is the output vector of the BLNNSM output layer.

[0070] Since the activation function (19) and objective function (28) of BLNNSM are nonlinear, the optimal control problem (33) becomes a nonlinear programming problem. Although many algorithms exist for solving this nonlinear optimization problem, such as interior-point methods, particle swarm optimization (PSO), and sequential quadratic programming (SQP), none can guarantee obtaining the global optimal solution. In order to efficiently obtain a high-quality optimal solution and improve the computational efficiency of the controller, the optimal control problem of MPC is transformed into a MILP solution. Existing optimization solvers and algorithms can effectively handle discrete and binary variables in MILP, find the optimal control sequence, and achieve precise control of unmanned vehicles.

[0071] To transform the optimal control problem (33) into a mixed-integer linear programming problem, we first introduce new auxiliary variables and constraints to transform the nonlinear objective function into a linear objective, as shown below: MERGEFORMAT (35) In the formula, , and The three auxiliary variables introduced represent the absolute error term of the objective expression at each prediction time. Simultaneously, the following constraints must be satisfied: MERGEFORMAT (36) Then, according to the method shown in formula (27), the nonlinear activation function in the BLNNSM model (34) is linearized using mixed-integer methods. Finally, the MILP form of the optimal control problem (33) can be obtained: MERGEFORMAT (37) In the formula, , It is a vector of auxiliary variables for linearizing the objective function. It is the auxiliary variable vector used by the activation function for linearization. , , and The first One neuron in Four continuous variables at time points. It is used to determine the linear interval of the activation function SSL and constrain auxiliary variables. binary vector, , and The first One neuron in Three binary variables at time. For the hidden layer One neuron in Input at the specified time.

[0072] The design block diagram of the vehicle path tracking control system based on the BLNNSM model is as follows: Figure 6 As shown, firstly, the vehicle's current motion state and reference path are input into the MPC controller; then, the MPC controller calculates the error between the current predicted motion state and the reference state, and optimizes the obtained optimal control quantity to control the vehicle; finally, the newly generated motion state of the controlled vehicle is fed back into the MPC controller for control calculation at the next moment, thus continuously looping to achieve path tracking control of the vehicle.

[0073] Further analysis of path tracking results: To verify the effectiveness of the predictive control method based on the BLNNSM model, it was compared with control methods based on BLSTM and LSTM models. All three controllers used the "minimize" function from the "scipy.optimize" library in PyCharm to solve their nonlinear optimal control problem, and the "solve_ivp" function from the "scipy.integrate" library to solve the vehicle dynamics model to update the vehicle state. It is worth noting that, as Carsim is a commercial closed-source software, its core parameter interface for the tire model is not fully open, making it difficult to directly embed the stochastic distribution characteristics of tire lateral stiffness for dynamic modeling. Therefore, in the vehicle path tracking control experiment, this embodiment uses the vehicle dynamics model as the controlled object.

[0074] During the verification experiment, the vehicle's global coordinate position , Maximum tracking deviation and The maximum deviation for vehicle yaw rate tracking is set to 0.2 rad, and the sampling time is 0.1 s. See Table 5 for relevant control parameters.

[0075] Table 5 Comparative analysis of path tracking experiment results based on the PyCharm simulation platform revealed that, under relatively smooth conditions such as straight paths, the three controllers exhibited similar control performance in path tracking. This is because, under smooth conditions, the vehicle's sideslip angle is small, and the uncertain parameter of tire sideslip stiffness has little impact on the vehicle's dynamics. Under conditions with many curves, the BLNNSM-based MPC showed similar path tracking performance to the BLSTM-based MPC, with significantly smaller tracking errors. This is because the BLNNSM and BLSTM models are more accurate under uncertain tire sideslip stiffness, and the MPC designed based on them has better robustness. The LSTM-based MPC exhibited larger tracking deviations, primarily because the LSTM model cannot accurately represent the vehicle's dynamic characteristics under uncertain tire sideslip stiffness, leading to an inability to accurately predict the vehicle's state and reduced control accuracy.

[0076] Furthermore, to further quantify the control performance of each control method, the Integral Square Error (ISE) exponent was calculated as an objective evaluation index of control accuracy. Its specific mathematical expression is as follows: MERGEFORMAT (38) in For tracking and control at every moment The deviation.

[0077] Table 6 presents the ISE (Inverse Sequence) values ​​for the three control methods described above. As can be seen from the table, the ISE value of the MPC control result based on the BLNNSM substitution model is similar to that of the MPC control result based on the BLSTM model. Compared to the LSTM-based MPC, the predictive control method proposed in this embodiment shows a significant advantage in ISE performance. Specifically, the method proposed in this embodiment achieves better performance in terms of vehicle global coordinate position. , and vehicle yaw angle The proposed method improves the ISE (Indicators of Optimal Sequence) by 36.3%, 38.0%, and 66.8% respectively compared to the LSTM-based predictive control method. This demonstrates the effectiveness of the proposed BLNNSM-based alternative model.

[0078] Table 6 Vehicle global coordinate position during path tracking control , and vehicle yaw angle The path tracking results of the LSTM-based MPC model deviated significantly over time, while the MPC control results based on the BLNNSM alternative model tracked the reference path well, all within the confidence interval. Furthermore, the 95% confidence interval of the predicted output of the vehicle state variables by the proposed BLNNSM alternative model also covered the reference path, indicating that the designed BLNNSM alternative model is accurate and the controller solution is successful. Moreover, in areas of rapid state change, the confidence interval given by the BLNNSM alternative model when predicting the output values ​​of the state variables is correspondingly larger, demonstrating that the proposed BLNNSM alternative model can reasonably represent the uncertainties of vehicle dynamics and has good robustness.

[0079] Table 7 shows the maximum deviation of the three MPC control results. As can be seen from the table, the maximum deviation of the control result obtained by the proposed method in this embodiment is similar to the maximum deviation of the MPC control result based on the BLSTM model, and significantly smaller than the maximum deviation of the MPC control result based on the LSTM model. This indicates that the proposed MPC method has good road tracking control accuracy.

[0080] Table 7 Based on the solution times of each controller, it can be seen that the solution time of the MPC controller based on the BLNNSM alternative model is significantly shorter than that of the other two controllers. Furthermore, as shown in Table 8, the average solution time of the MPC controller based on the BLNNSM alternative model (0.0569s) is reduced by 83.9% and 53.3% compared to the average solution times of the MPC controller based on the BLSTM model (0.8501s) and the MPC controller based on the LSTM model (0.1219s), respectively. This indicates that the proposed MPC method has an advantage in solution time and is more suitable for application in practical vehicle control.

[0081] Table 8 In summary, when there is uncertainty in the tire lateral stiffness parameter of the vehicle, the proposed BLNNSM alternative model MPC method not only has high path tracking accuracy but also short control solution time, and has good control performance and robustness.

[0082] This embodiment considers the uncertainty of vehicle tire lateral stiffness and establishes a Bayesian neural network model based on an LSTM structure to accurately represent the nonlinear dynamics of the vehicle. To address the high computational cost caused by Monte Carlo sampling of weight coefficients in the Bayesian neural network model, a recurrent neural network model with standard deviation output is trained using the input and output data of the Bayesian neural network model as an alternative, and its accuracy is verified. Subsequently, an MPC controller with probabilistic constraints is designed based on this alternative model, and the optimal controller is transformed into a mixed integer linear programming (MILP) problem for fast solution. Finally, the effectiveness of the proposed method is verified on the PyCharm simulation platform, providing an effective and robust control scheme for path tracking control. The main steps are summarized as follows: (1) To address the uncertainty of the vehicle tire lateral stiffness, a Bayesian neural network vehicle model based on LSTM was constructed to capture the dynamic characteristics of the vehicle. (2) In order to solve the problem of high computational complexity of LSTM-based Bayesian neural network models, an alternative model strategy is proposed; (3) For the vehicle path tracking problem under parameter uncertainty, an MPC controller with probabilistic constraints was designed based on an alternative model, and the designed controller was compared with predictive controllers based on Bayesian LSTM models and ordinary LSTM models. The results show that the proposed method is superior in terms of path tracking accuracy and controller solution time.

[0083] Example 2 Based on the same general inventive concept, this invention also provides a vehicle path tracking control system based on a Bayesian neural network substitution model. The system provided by this invention is described below, and the system described below can be referred to in conjunction with the method described above. The system includes: The dynamics model building module is used to generate vehicle dynamics models based on the single-track dynamics equations and the tire lateral stiffness uncertainty description. The motion data acquisition module is used to input pseudo-random front wheel steering angle and accelerator / brake pedal signals into the vehicle dynamics model, and obtain vehicle motion data through numerical integration. The Bayesian modeling substitution module is used to establish a Bayesian long short-term memory network model based on the vehicle motion data, and to train a Bayesian neural network substitution model based on the input and output data of the Bayesian long short-term memory network model. The control framework construction module is used to construct a model prediction control framework based on the Bayesian neural network replacement model and transform the optimal control problem into a mixed-integer linear programming problem. The path tracking prediction module is used to solve the mixed integer linear programming problem and apply the obtained control quantity to the vehicle to realize path tracking predictive control.

[0084] Example 3 This embodiment also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in Embodiment 1.

[0085] Example 4 This embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0086] Example 5 This embodiment also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0087] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A vehicle path tracking control method based on a Bayesian neural network substitution model, characterized in that, Includes the following steps: A vehicle dynamics model is constructed based on the single-track dynamics equations and the description of tire lateral stiffness uncertainty. The pseudo-random front wheel steering angle and accelerator / brake pedal signals of the vehicle are acquired and input into the vehicle dynamics model for processing to obtain vehicle motion data. Based on vehicle motion data, a Bayesian long short-term memory network model is established to quantify the uncertainty of vehicle parameters; Based on the input and output data of the Bayesian long short-term memory network model, a Bayesian neural network alternative model is trained. Based on the Bayesian neural network alternative model, a model predictive control framework is constructed, and the optimal control problem is transformed into a mixed-integer linear programming problem. The mixed-integer linear programming problem is solved to achieve path tracking predictive control of vehicles.

2. The method according to claim 1, characterized in that, The process of building a Bayesian long short-term memory network model based on vehicle motion data includes: The vehicle takes the front wheel steering angle, accelerator / brake pedal, global coordinate position, yaw angle, longitudinal velocity, lateral velocity and yaw rate of the previous moment as input, and takes the global coordinate position, yaw angle, longitudinal velocity, lateral velocity and yaw rate of the current moment as output. Treating network weights and biases as random variables, we first set a prior distribution and then approximate the posterior distribution through variational inference. Using the sum of mean squared error and KL divergence as the loss function, a Bayesian long short-term memory network model that can simultaneously output the mean and variance of state variables is obtained after reparameterization training.

3. The method according to claim 1, characterized in that, The process of training a Bayesian neural network alternative model based on the input and output data of the Bayesian long short-term memory network model includes: The mean and standard deviation of the state variables generated by the Bayesian long short-term memory network model under the same input sequence are used as the training targets. A single-layer recurrent neural network structure is adopted, with the hidden layer using a symmetric saturated linear transfer function as the activation function and the output layer using a linear function as the activation function; The Levenberg-Marquardt algorithm is used to iteratively optimize the network weights until the error between the predicted output and the mean and standard deviation converges, thus obtaining a Bayesian neural network alternative model that can simultaneously output the mean and standard deviation of the state variables.

4. The method according to claim 1, characterized in that, The process of constructing the model prediction control framework based on the Bayesian neural network alternative model includes: The mean and variance of the state variables given by the Bayesian neural network replacement model are used as the basis for prediction, and the prediction time domain and control time domain are preset. The objective function is constructed based on the deviation of the vehicle position, yaw angle and the reference path, and a probabilistic safety constraint is added to ensure that the prediction standard deviation multiplied by the confidence coefficient does not exceed the allowable deviation limit. The physical limits of the front wheel steering angle and the accelerator / brake pedal are used as control constraints to form a complete model predictive control framework.

5. The method according to claim 1, characterized in that, The process of transforming the optimal control problem into a mixed-integer linear programming problem includes: Based on the aforementioned model predictive control framework, an auxiliary continuous variable is introduced to transform the absolute value error term in the objective function into a linear inequality. The symmetric saturated linear function used in the hidden layer of the Bayesian neural network alternative model is piecewise linearized. Continuous variables and corresponding binary variables are introduced into each line segment, and the input-output relationship is described by linear equations and inequalities. The linearized objective function, activation function constraints, and original system constraints are unified and organized into a system of linear equations and inequalities, forming a standard mixed-integer linear programming problem.

6. The method according to claim 5, characterized in that, Solving the mixed-integer linear programming problem to achieve path tracking predictive control of the vehicle includes: At each sampling time, with the current state of the vehicle as the initial condition, the mixed integer linear programming solver is called to solve the transformed mixed integer linear programming problem, and the optimal front wheel steering angle and accelerator / brake pedal sequence in the prediction time domain are obtained. Apply the first control variable in the sequence to the vehicle to drive the vehicle to update its state; The state is re-acquired at the next sampling time and the above solution and control process is repeated to achieve continuous path tracking predictive control.

7. A vehicle path tracking control system based on a Bayesian neural network substitution model, characterized in that, The system for implementing the method according to any one of claims 1-6 comprises: The dynamics model building module is used to generate vehicle dynamics models based on the single-track dynamics equations and the tire lateral stiffness uncertainty description. The motion data acquisition module is used to input pseudo-random front wheel steering angle and accelerator / brake pedal signals into the vehicle dynamics model, and obtain vehicle motion data through numerical integration. The Bayesian modeling substitution module is used to establish a Bayesian long short-term memory network model based on the vehicle motion data, and to train a Bayesian neural network substitution model based on the input and output data of the Bayesian long short-term memory network model. The control framework construction module is used to construct a model prediction control framework based on the Bayesian neural network replacement model and transform the optimal control problem into a mixed-integer linear programming problem. The path tracking prediction module is used to solve the mixed integer linear programming problem and apply the obtained control quantity to the vehicle to realize path tracking predictive control.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-6.

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