A model predictive control trajectory tracking method based on physical information neural network

Abstract

The present invention is applicable to the field of autonomous vehicle control technology and provides a model predictive control trajectory tracking method based on a physical information neural network, including: deeply combining a neural network with a physics-based dynamic model; using the physical information neural network dynamic model as a prediction model, establishing a cost function and constraints based on the vehicle state and reference trajectory, forming an optimal control problem and solving it to obtain the desired control quantity; performing wheel speed control and steering system control, and using a feedforward plus feedback control concept to adjust the drive system and steering system to achieve the desired control quantity. The present invention not only optimizes model performance, reduces the risk of overfitting, and improves computational efficiency, but also enhances the interpretability and physical assurance of the model; by constructing a cost function and constraints, and using a feedforward plus feedback control concept to adjust the actuator, accurate trajectory tracking of the autonomous vehicle is achieved, effectively improving the performance and reliability of the autonomous driving system.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous driving vehicle control, and in particular relates to a model predictive control trajectory tracking method based on physical information neural network. Background Art

[0002] With the development of modern society, traffic congestion and travel safety are becoming increasingly serious. Autonomous driving technology has great potential to alleviate traffic congestion and improve travel safety. In autonomous driving systems, a modular architecture is widely used, which divides the driving task into different layers: perception, planning, and control. The control layer (also known as the trajectory tracking layer) is responsible for generating actuator commands, including steering angle and drive / brake torque, to stably track the reference path and state (including speed, sideslip angle, and yaw rate).

[0003] Currently, a variety of control methods have been used to achieve trajectory tracking, including sliding mode control, active disturbance rejection control, linear quadratic regulation, and model predictive control. Although model predictive control algorithms are computationally expensive when solving constrained optimization problems online, they optimize the current control law over the entire range. Their architecture can handle multi-input and multi-output systems, systematically consider constraints on state, input, and output variables, achieve smooth control actions, and demonstrate versatility and robustness across different driving styles. These characteristics have led to the widespread application of model predictive control in autonomous driving trajectory tracking.

[0004] However, model fidelity directly impacts the performance of model predictive control (MPC). Therefore, the vehicle system must be accurately modeled. Due to the presence of nonlinear behavior in vehicle systems, nonlinear system modeling is required in the real world. Currently, there are two main modeling approaches: physics-based models and data-driven approaches. Neural networks are a common solution due to their universal approximation properties within the limits. Interpretability is often a prerequisite for a model to be practical. While neural networks have a significant ability to infer complex relationships between variables and can better capture the dynamic characteristics of a vehicle, they have significant drawbacks. Their black-box nature makes them lack physical laws and interpretability, and they lack physics-based guarantees. While real-time vehicle control requires reliable and physically insightful extrapolation from the model, the complexity of neural networks must be balanced against issues of overfitting and computational efficiency.

[0005] In response to the above problems existing in the prior art, the present invention proposes a model predictive control trajectory tracking method based on physical information neural network. Summary of the Invention

[0006] The purpose of the present invention is to provide a model predictive control trajectory tracking method based on physical information neural network, aiming to solve the problems raised in the above background technology.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A model predictive control trajectory tracking method based on physical information neural network includes the following steps:

[0009] Step S1: physical information neural network dynamics modeling;

[0010] Deeply integrate neural networks with physics-based dynamic models to improve model fidelity and ensure the physical properties of the model;

[0011] Step S2: Establishing a model predictive control trajectory tracking method;

[0012] The physical information neural network dynamics model is used as a prediction model. According to the vehicle state and reference trajectory, the cost function and constraints are established to form an optimal control problem and solve it to obtain the desired control quantity.

[0013] Step S3: actuator adjustment;

[0014] Including wheel speed control and steering system control, using the control idea of ​​feedforward plus feedback to adjust the drive system and steering system to achieve the desired control amount to track the reference trajectory.

[0015] Furthermore, the specific steps of step S1 are as follows:

[0016] Step S11: establishing a physics-based dynamic model;

[0017] A three-degree-of-freedom dynamic model is used to describe changes in vehicle state, including speed, sideslip angle, and yaw rate. The Fiala tire model is also used to describe the longitudinal and lateral force coupling characteristics of the tire.

[0018] The three-degree-of-freedom dynamic model formula is as follows:

[0019] ;

[0020] Where, are the rates of change of vehicle speed, sideslip angle and yaw rate respectively; is the front wheel longitudinal force, is the front wheel lateral force, is the rear wheel longitudinal force, is the rear wheel lateral force; is the front wheel turning angle; is the sideslip angle of the center of mass; is the vehicle mass; is the vehicle speed; is the yaw angular velocity; is the vehicle’s moment of inertia; and The distance from the vehicle's center of mass to the front and rear axles, respectively, and the wheelbase ;

[0021] Step S12: training the physical information neural network dynamics model;

[0022] A physical information neural network is used to model vehicle dynamics, integrating the advantages of data-driven and physics-driven modeling. The neural network is used to encode and estimate the vehicle's dynamic parameters, and the rationality of the neural network output is ensured through physical constraints. The vehicle state is then obtained by decoding through a physics-based dynamic model.

[0023] Furthermore, the specific process of step S12 is as follows:

[0024] Collect vehicle data under double lane change and steady-state circular conditions, including vehicle speed, center of mass sideslip angle, yaw rate, front wheel angle and wheel speed. As a state quantity, As a control quantity, a data set is formed , input to the physical information neural network for training;

[0025] The physical information neural network takes the state and control variables of three sampling times as input, and adopts four hidden layers with 16 neurons, including two fully connected layers and two gated recurrent unit layers. The output layer adopts Sigmoid activation function and the maximum value of the parameter is obtained. and minimum value To implement physical constraints and limit the output of the physical neural network, the formula is as follows:

[0026] ;

[0027] Where, are the outputs of two fully connected layers respectively; are the outputs of two gated recurrent unit layers respectively; is the output of the output layer; is a fully connected layer; is a gated recurrent unit; is the activation function; is the input of the network; and is in hidden state; is the weight of the network; is the bias of the network; is the kinetic parameter.

[0028] Furthermore, the specific steps of step S2 are as follows:

[0029] Step S21: establishing a prediction model;

[0030] The physical information neural network dynamics model trained in step S12 is used to represent the dynamic state of the vehicle, including the vehicle speed. , center of mass side slip angle and yaw rate ,use The coordinate system locates the position of the vehicle relative to the reference trajectory. The model has a total of 5 state quantities and 3 control quantities , the prediction model formula is as follows:

[0031] ;

[0032] ;

[0033] Where, is the differential of the lateral deviation; is the heading angle deviation between the vehicle velocity vector and the path; is the differential of the heading angle deviation; is the rate of change of the heading angle between the vehicle velocity vector and the path; is the rate of change of heading angle of the reference trajectory;

[0034] Step S22: establishing a cost function;

[0035] Cost function It is constructed by minimizing the deviation between the state quantity and the control quantity and the reference value. The formula is as follows:

[0036] ;

[0037] Where, is the prediction time domain; is the time step; and are the state and control quantities predicted for each time step respectively; and are the reference state quantity and control quantity respectively; and is an adjustable weight matrix; To control the amount; For inversion;

[0038] Step S23: establishing constraints;

[0039] Including initial state constraints, model constraints and actuator constraints;

[0040] The initial state constraint is the vehicle predicted state after 100ms. As the initial state :

[0041] ;

[0042] The model constraints use a predictive model discretization method to force the system state and control input to conform to the dynamic relationship:

[0043] ;

[0044] Where, represents the prediction model; and are the state quantity and control quantity predicted for the next time step respectively;

[0045] Actuator constraints limit the maximum and minimum values ​​of the steering angle and wheel speed:

[0046] ;

[0047] Where, and are the front wheel angle, front wheel speed and rear wheel speed at the current time step; and are the minimum and maximum front wheel turning angles of the vehicle; and are the minimum and maximum wheel speeds of the vehicle’s front wheels, respectively; and are the minimum and maximum wheel speeds of the vehicle’s rear wheels, respectively;

[0048] Step S24: solving the optimal control problem;

[0049] According to the cost function and constraints, the optimal control problem is constructed. The following finite domain optimal control problem is solved at each time step to obtain the desired turning angle: and wheel speed ;

[0050] .

[0051] Furthermore, the specific steps of step S3 are as follows:

[0052] Step S31: wheel speed control;

[0053] Consider the impact of vehicle load transfer on the wheel speed control of the wheels on both sides of the front and rear axles, and ignore the impact of longitudinal load transfer during vehicle acceleration and deceleration;

[0054] According to the geometric relationship of the vehicle, the expected wheel speed of each wheel of the vehicle is calculated as follows:

[0055] ;

[0056] Where, is the expected wheel speed of each wheel, is the desired wheel speed of the front and rear axles, Represents the front and rear wheels, Represents the left and right wheels; is the wheelbase of the vehicle's left and right wheels; is the wheel radius;

[0057] In the wheel speed control of each wheel, the actual input control variable is the torque of each wheel. The PID method is used to design a wheel speed closed-loop controller to achieve the desired wheel speed control. The formula is as follows:

[0058] ;

[0059] Where, is the wheel torque; is an adjustable wheel speed control parameter; is the wheel speed of each wheel;

[0060] Step S32: steering system control;

[0061] The final front wheel angle is obtained by using the feedforward plus feedback method:

[0062] ;

[0063] Where, The front wheel angle output by the controller; is the desired front wheel turning angle; It is an adjustable steering system control parameter; is the front wheel turning angle.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] Improving Model Predictive Control Performance: This invention deeply integrates neural networks with physics-based dynamic models to construct a physical information neural network dynamics model. This model uses a physics-based model to accurately describe vehicle dynamics while leveraging the powerful learning capabilities of neural networks to estimate dynamic parameters, significantly improving model fidelity. Within the model predictive control algorithm, high-fidelity models can more accurately simulate vehicle motion, laying a solid and reliable foundation for subsequent trajectory tracking control, significantly improving the trajectory tracking performance of autonomous vehicles.

[0066] Enhanced model interpretability and physical assurance: To address the lack of physical laws and interpretability caused by the black-box nature of traditional neural networks, this paper introduces physical constraints during model training. By constraining neural network outputs to align with physical reality, the model is given physical meaning and enhanced interpretability. This enables the model to reliably extrapolate based on physical insights during real-time control of autonomous vehicles, providing a more convincing basis for control decisions and ensuring the model's reliability and stability in practical applications.

[0067] Optimizing Neural Network Performance: To address the overfitting and computational efficiency issues associated with neural network complexity, this paper addresses this issue by rationally selecting data acquisition conditions, optimizing network structure and parameter settings, and incorporating physical constraints into model training. These measures effectively balance neural network complexity, improve computational efficiency, and reduce the risk of overfitting, enabling neural networks to function more efficiently and accurately in autonomous driving trajectory tracking tasks.

[0068] Precise trajectory tracking control: The model predictive control trajectory tracking method developed in this paper combines the vehicle state and reference trajectory to construct a cost function and constraints, and obtains the desired control variable by solving the optimal control problem. In the actuator adjustment process, a feedforward plus feedback control principle is applied to precisely adjust the wheel speed and steering system. This series of operations ensures that the autonomous vehicle can stably and accurately track the reference trajectory, improving the safety and reliability of the autonomous driving system. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Flow chart of the method of the present invention.

[0070] Figure 2 This is a framework diagram of the method of the present invention.

[0071] Figure 3 is the reference path.

[0072] Figure 4 Path tracing performance. DETAILED DESCRIPTION

[0073] In order to have a clearer understanding of the technical features, objectives and beneficial effects of the present invention, the technical solution of the present invention is now described in detail below, but it should not be understood as limiting the scope of implementation of the present invention.

[0074] In order to meet the physical guarantee and interpretability of the model, physical information machine learning is an effective solution. This method integrates physics-based knowledge into the system's neural network model, which can improve data efficiency and model generalization ability. This feature gives it a significant advantage in the field of autonomous driving research. In autonomous driving, using physical insights to learn dynamic models from data and applying them to model predictive control algorithms can help improve the trajectory tracking control accuracy of autonomous vehicles. Based on this, the present invention provides a model predictive control trajectory tracking method based on physical information neural network, and its flow chart and framework diagram are shown as follows: Figure 1 and Figure 2 The method specifically comprises the following steps:

[0075] Step S1: physical information neural network dynamics modeling;

[0076] This step improves model fidelity while maintaining the physical properties of the model by deeply combining neural networks with physics-based dynamic models.

[0077] The specific steps of step S1 are as follows:

[0078] Step S11: establishing a physics-based dynamic model;

[0079] A three-degree-of-freedom dynamic model is used to describe changes in vehicle state (speed, sideslip angle, and yaw rate). In this model, the front and rear tires are grouped as a single tire on each axle, and the vehicle motion is considered to be planar motion. The model formula is as follows:

[0080] ;

[0081] Where, are the rates of change of vehicle speed, sideslip angle and yaw rate respectively; is the front wheel longitudinal force, is the front wheel lateral force, is the rear wheel longitudinal force, is the rear wheel lateral force; is the front wheel turning angle; is the sideslip angle of the center of mass; is the vehicle mass; is the vehicle speed; is the yaw angular velocity; is the vehicle’s moment of inertia; and The distance from the vehicle's center of mass to the front and rear axles, respectively, and the wheelbase .

[0082] During high-slip maneuvers, it is important to capture the impact of wheel speed dynamics on the longitudinal and lateral force distribution. To better describe the longitudinal and lateral force coupling characteristics of the tire, the Fiala tire model is used. The total tire force is calculated as follows:

[0083] ;

[0084] Where, Represents the front and rear wheels; is the total force on the tire; is the total slip of the tire; The saturation value of the total slip of the tire. If this value is exceeded, the tire will enter a state of complete slip. is the total stiffness of the tire; is the road adhesion coefficient (assuming the road adhesion coefficient is isotropic and the road adhesion coefficients of the front and rear tires are the same); Vertical force on the tire; is the tire's slip angle; is the longitudinal slip of the tire.

[0085] The distribution of longitudinal and lateral tire forces is determined by the ratio of their respective slip to the total slip, as follows:

[0086] ;

[0087] Where, Represents the front and rear wheels; is the longitudinal force of the tire; is the lateral force of the tire; the sideslip angle of the front wheel , front wheel longitudinal slip , rear wheel slip angle and rear wheel longitudinal slip The calculation formula is as follows:

[0088] ;

[0089] Where, is the wheel radius; is the front wheel speed; is the rear wheel speed.

[0090] Step S12: training the physical information neural network dynamics model;

[0091] The physics-based dynamic model proposed in step S11 can better describe the dynamic characteristics of the vehicle and can be applied to model predictive control to achieve the vehicle's extreme trajectory tracking control, but the vehicle's dynamic parameters (in The accuracy of the front and rear tire stiffnesses (respectively) significantly impacts model fidelity, and these parameters vary with vehicle state; for example, tire stiffness changes with load transfer. While data-driven models can build highly accurate models without requiring prior knowledge of physical parameters, they suffer from limited interpretability.

[0092] The present invention adopts physical information neural network to model vehicle dynamics, integrating the advantages of data-driven and physical-driven modeling, using neural network to encode and estimate the vehicle's dynamic parameters, and ensuring the rationality of the neural network output through physical constraints, and then decoding through a physics-based dynamic model to obtain the vehicle state.

[0093] Collect vehicle data under double lane change and steady-state circular conditions, including vehicle speed, center of mass sideslip angle, yaw rate, front wheel angle and wheel speed. As a state quantity, As a control quantity, a data set is formed , input into the physical information neural network for training.

[0094] The physical information neural network takes the state and control variables of three sampling times as input, and uses four hidden layers with 16 neurons, two fully connected layers and two gated recurrent unit layers. The output layer uses the Sigmoid activation function. and minimum value To implement physical constraints and limit the output of the physical neural network, the formula is as follows:

[0095] ;

[0096] Where, are the outputs of two fully connected layers respectively; are the outputs of two gated recurrent unit layers respectively; is the output of the output layer; is a fully connected layer; is a gated recurrent unit; is the activation function; is the input of the network; and is in hidden state; is the weight of the network; is the bias of the network; is the kinetic parameter.

[0097] Step S2: Establishing a model predictive control trajectory tracking method;

[0098] The physical information neural network dynamics model is used as a prediction model. The cost function and constraints are established according to the vehicle state and reference trajectory. The optimal control problem is formed and solved to obtain the desired control quantity.

[0099] The specific steps of step S2 are as follows:

[0100] Step S21: establishing a prediction model;

[0101] The physical information neural network dynamics model trained in step S12 is used to represent the dynamic state of the vehicle, including the vehicle speed. , center of mass side slip angle and yaw rate To locate the vehicle relative to the reference trajectory, use Coordinate system, with lateral deviation of the vehicle from the path and the heading angle deviation between the vehicle velocity vector and the path To express.

[0102] The model has a total of 5 state variables and 3 control quantities , the prediction model formula is as follows:

[0103] ;

[0104] ;

[0105] Where, is the differential of the lateral deviation; is the heading angle deviation between the vehicle velocity vector and the path; is the differential of the heading angle deviation; are the rates of change of vehicle speed, sideslip angle and yaw rate respectively; is the vehicle speed; is the rate of change of the heading angle between the vehicle velocity vector and the path; is the rate of change of heading angle of the reference trajectory; is the front wheel longitudinal force; is the lateral force of the front wheel; is the rear wheel longitudinal force, is the rear wheel lateral force; is the front wheel turning angle; is the sideslip angle of the center of mass; is the vehicle mass; is the yaw angular velocity; is the vehicle’s moment of inertia; and are the distances from the vehicle's center of mass to the front and rear axles, respectively. and The calculation formula is as follows:

[0106] ;

[0107] Where, is the curvature of the reference trajectory.

[0108] Step S22: establishing a cost function;

[0109] The cost function is used to quantify the performance indicators of the control system. The goal of model predictive control is to minimize this function by optimizing the input variables, thereby achieving optimal control of the system.

[0110] Cost function It is constructed by minimizing the deviation between the state quantity and the control quantity and the reference value. The formula is as follows:

[0111] ;

[0112] Where, is the prediction time domain; is the time step; and are the state and control quantities predicted for each time step respectively; and are the reference state quantity and control quantity respectively; and is an adjustable weight matrix; To control the amount; Inverted.

[0113] Step S23: establishing constraints;

[0114] Constraints are used to describe the physical, operational, and safety limitations of the system to ensure the feasibility of the control strategy in practical applications. They include initial state constraints, model constraints, and actuator constraints, enabling the vehicle to track the trajectory more stably.

[0115] The initial state constraint is the vehicle predicted state after 100ms. As the initial state , for delay compensation:

[0116] ;

[0117] The model constraints use a predictive model discretization method to force the system state and control input to conform to the dynamic relationship:

[0118] ;

[0119] Where, represents the prediction model; is the time step; and are the state and control quantities predicted for each time step respectively; and are the state and control variables predicted for the next time step respectively.

[0120] Actuator constraints limit the maximum and minimum values ​​of the steering angle and wheel speed to ensure that the control amount is within a reasonable range:

[0121] ;

[0122] Where, and are the front wheel angle, front wheel speed and rear wheel speed at the current time step; and are the minimum and maximum front wheel turning angles of the vehicle; and are the minimum and maximum wheel speeds of the vehicle’s front wheels, respectively; and are the minimum and maximum wheel speeds of the vehicle's rear wheels, respectively.

[0123] Step S24: solving the optimal control problem;

[0124] According to the cost function and constraints, the optimal control problem is constructed. The following finite domain optimal control problem is solved at each time step to obtain the desired turning angle: and wheel speed ;

[0125] .

[0126] Step S3: actuator adjustment;

[0127] Including wheel speed control and steering system control, using the feedforward plus feedback control idea to adjust the drive system and steering system to achieve the desired control amount, thereby tracking the reference trajectory.

[0128] The specific steps of step S3 are as follows:

[0129] Step S31: wheel speed control;

[0130] The vehicle will roll when turning, so the impact of vehicle load transfer on the wheel speed control of the wheels on both sides of the front and rear axles is considered, and the impact of longitudinal load transfer during vehicle acceleration and deceleration is ignored.

[0131] According to the geometric relationship of the vehicle, the expected wheel speed of each wheel of the vehicle is calculated as follows:

[0132] ;

[0133] Where, is the expected wheel speed of each wheel, is the desired wheel speed of the front and rear axles, Represents the front and rear wheels, Represents the left and right wheels; is the wheelbase of the vehicle's left and right wheels; is the yaw angular velocity; is the wheel radius.

[0134] In the wheel speed control of each wheel, the actual input control variable is the torque of each wheel. The PID method is used to design a wheel speed closed-loop controller to achieve the desired wheel speed control. The formula is as follows:

[0135] ;

[0136] Where, is the wheel torque; is an adjustable wheel speed control parameter; is the wheel speed of each wheel.

[0137] Step S32: steering system control;

[0138] The final front wheel angle is obtained by using the feedforward plus feedback method to give full play to the performance of the steering system:

[0139] ;

[0140] Where, The front wheel angle output by the controller; is the desired front wheel turning angle; It is an adjustable steering system control parameter; is the front wheel turning angle.

[0141] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0142] Example 1: This example is based on the method of the present invention to carry out experiments, and a reference path with variable curvature is set in the test scene (such as Figure 3 As shown in Figure 2), the road adhesion coefficient is 0.85. During the test, the vehicle tracks the trajectory from the starting point under the control method.

[0143] To directly demonstrate the performance advantages of the method of the present invention, this experiment is defined as "Experiment 1", and the traditional model predictive control trajectory tracking experiment based on physical models is selected as a control, named "Experiment 2". Lateral deviation and heading angle deviation are two key indicators to measure the path tracking performance of the control method. By comparing and analyzing the data performance of the two in the experiment, it is found that (such as Figure 4As shown): In terms of the lateral error curve, the lateral deviation with the maximum absolute value in Test 1 was -0.38m, while the lateral deviation with the maximum absolute value in Test 2 appeared around 10s, reaching -0.46m; in terms of heading angle deviation, the heading error with the maximum absolute value in Test 1 was 0.17rad, which was 0.04rad less than that in Test 2. The root mean square values ​​of the lateral error and heading angle deviation in the entire experiment were further calculated. The root mean square value of the lateral error in Test 1 was 0.12m, and that in Test 2 was 0.16m; the root mean square value of the heading angle deviation in Test 1 was 0.046rad, and that in Test 2 was 0.054rad. The data results clearly show that, whether in terms of the absolute maximum deviation or the root mean square value indicators, Test 1 performed better than Test 2 in both lateral deviation and heading angle deviation, fully verifying that the method of the present invention has significant advantages in path tracking control.

[0144] The above are only preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention. These should also be regarded as the scope of protection of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent.

Claims

1. A model predictive control trajectory tracking method based on physical information neural network, characterized in that: The following steps are involved: Step S1: physical information neural network dynamics modeling; Deeply integrate neural networks with physics-based dynamic models to improve model fidelity and ensure the physical properties of the model; Step S2: Establishing a model predictive control trajectory tracking method; The physical information neural network dynamics model is used as a prediction model. According to the vehicle state and reference trajectory, the cost function and constraints are established to form an optimal control problem and solve it to obtain the desired control quantity. Step S3: actuator adjustment; Including wheel speed control and steering system control, using the control concept of feedforward plus feedback to adjust the drive system and steering system to achieve the desired control amount to track the reference trajectory; The specific steps of step S1 are as follows: Step S11: establishing a physics-based dynamic model; A three-degree-of-freedom dynamic model is used to describe changes in vehicle state, including speed, sideslip angle, and yaw rate. The Fiala tire model is also used to describe the longitudinal and lateral force coupling characteristics of the tire. The three-degree-of-freedom dynamic model formula is as follows: ； Where, are the rates of change of vehicle speed, sideslip angle and yaw rate respectively; is the front wheel longitudinal force, is the front wheel lateral force, is the rear wheel longitudinal force, is the rear wheel lateral force; is the front wheel turning angle; is the sideslip angle of the center of mass; is the vehicle mass; is the vehicle speed; is the yaw angular velocity; is the vehicle’s moment of inertia; and The distance from the vehicle's center of mass to the front and rear axles, respectively, and the wheelbase ; Step S12: training the physical information neural network dynamics model; A physical information neural network is used to model vehicle dynamics, integrating the advantages of data-driven and physics-driven modeling. The neural network is used to encode and estimate the vehicle's dynamic parameters, and the rationality of the neural network output is ensured by physical constraints. The vehicle state is then decoded through a physics-based dynamic model. The specific process of step S12 is as follows: Collect vehicle data under double lane change and steady-state circular conditions, including vehicle speed, center of mass sideslip angle, yaw rate, front wheel angle and wheel speed. As a state quantity, As a control quantity, a data set is formed , input to the physical information neural network for training; The physical information neural network takes the state and control variables of three sampling times as input, and adopts four hidden layers with 16 neurons, two fully connected layers and two gated recurrent unit layers. The output layer uses the Sigmoid activation function and the maximum value of the parameter is obtained. and minimum value To implement physical constraints and limit the output of the physical neural network, the formula is as follows: ； Where, are the outputs of two fully connected layers respectively; are the outputs of two gated recurrent unit layers respectively; is the output of the output layer; is a fully connected layer; is a gated recurrent unit; is the activation function; is the input of the network; and is in hidden state; is the weight of the network; is the bias of the network; is the kinetic parameter.

2. The model predictive control trajectory tracking method based on physical information neural network according to claim 1 is characterized in that: The specific steps of step S2 are as follows: Step S21: establishing a prediction model; The physical information neural network dynamics model trained in step S12 is used to represent the dynamic state of the vehicle, including the vehicle speed. , center of mass side slip angle and yaw rate ,use The coordinate system locates the position of the vehicle relative to the reference trajectory. The model has a total of 5 state quantities and 3 control quantities , the prediction model formula is as follows: ； ； Where, is the differential of the lateral deviation; is the heading angle deviation between the vehicle velocity vector and the path; is the differential of the heading angle deviation; is the rate of change of the heading angle between the vehicle velocity vector and the path; is the rate of change of heading angle of the reference trajectory; Step S22: establishing a cost function; Cost function It is constructed by minimizing the deviation between the state quantity and the control quantity and the reference value. The formula is as follows: ； Where, is the prediction time domain; is the time step; and are the state and control quantities predicted for each time step respectively; and are the reference state quantity and control quantity respectively; and is an adjustable weight matrix; To control the amount; For inversion; Step S23: establishing constraints; Including initial state constraints, model constraints and actuator constraints; The initial state constraint is the vehicle predicted state after 100ms. As the initial state : ； The model constraints use a predictive model discretization method to force the system state and control input to conform to the dynamic relationship: ； Where, represents the prediction model; and are the state quantity and control quantity predicted for the next time step respectively; Actuator constraints limit the maximum and minimum values ​​of the steering angle and wheel speed: ； Where, and are the front wheel angle, front wheel speed and rear wheel speed at the current time step; and are the minimum and maximum front wheel turning angles of the vehicle; and are the minimum and maximum wheel speeds of the vehicle’s front wheels, respectively; and are the minimum and maximum wheel speeds of the vehicle’s rear wheels, respectively; Step S24: solving the optimal control problem; According to the cost function and constraints, the optimal control problem is constructed. The following finite domain optimal control problem is solved at each time step to obtain the desired turning angle: and wheel speed ; 。 3. The model predictive control trajectory tracking method based on physical information neural network according to claim 1 is characterized in that: The specific steps of step S3 are as follows: Step S31: wheel speed control; Consider the impact of vehicle load transfer on the wheel speed control of the wheels on both sides of the front and rear axles, and ignore the impact of longitudinal load transfer during vehicle acceleration and deceleration; According to the geometric relationship of the vehicle, the expected wheel speed of each wheel of the vehicle is calculated as follows: ; Where, is the expected wheel speed of each wheel, is the desired wheel speed of the front and rear axles, Represents the front and rear wheels, Represents the left and right wheels; is the wheelbase of the vehicle's left and right wheels; is the wheel radius; In the wheel speed control of each wheel, the actual input control variable is the torque of each wheel. The PID method is used to design a wheel speed closed-loop controller to achieve the desired wheel speed control. The formula is as follows: ; Where, is the wheel torque; is an adjustable wheel speed control parameter; is the wheel speed of each wheel; Step S32: steering system control; The final front wheel angle is obtained by using the feedforward plus feedback method: ; Where, The front wheel angle output by the controller; is the desired front wheel turning angle; It is an adjustable steering system control parameter; is the front wheel turning angle.

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