Model predictive control trajectory tracking method based on physical information neural network

Abstract

The invention is applicable to the technical field of automatic driving vehicle control, and provides a model predictive control trajectory tracking method based on a physical information neural network, which comprises the following steps of: deeply combining a neural network with a physics-based dynamic model; taking the physical information neural network dynamics model as a prediction model, establishing a cost function and constraint according to the vehicle state and the reference trajectory, forming and solving an optimal control problem, and obtaining an expected control quantity; and wheel speed control and steering system control are carried out, and a driving system and a steering system are adjusted by applying a feedforward and feedback control thought, so that expected control quantity is realized. According to the method, the model performance is optimized, the over-fitting risk is reduced, the calculation efficiency is improved, and the interpretability and the physical guarantee of the model are enhanced; by constructing a cost function and a constraint condition and using a feedforward and feedback control thought to adjust an actuator, accurate trajectory tracking of an automatic driving vehicle is realized, and the performance and reliability of an automatic driving system are effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous vehicle control, and particularly relates to a model predictive control trajectory tracking method based on a physics-informed neural network. Background Art

[0002] With the development of modern society, traffic congestion and travel safety problems have become increasingly severe. Autonomous driving technology has great potential in improving traffic congestion and enhancing travel safety. In an autonomous driving system, a modular architecture is widely used, which divides driving tasks into different levels such as perception, planning, and control. Among them, the control layer (also called the trajectory tracking layer) is responsible for generating actuator commands, including steering angle and drive / brake torque, to stably track the reference path and states (including speed, centroid side slip 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 regulator, and model predictive control, etc. Although the model predictive control algorithm has a relatively high computational cost when solving the constrained optimization problem online, model predictive control optimizes the current control law over the entire range. Its structure can handle multi-input multi-output systems, and can systematically consider the constraints on state, input, and output variables to achieve smooth control actions, showing versatility and robustness in different driving styles. These characteristics make model predictive control more widely applied in autonomous driving trajectory tracking.

[0004] However, the fidelity of the model directly affects the performance of model predictive control. Therefore, it is necessary to accurately model the vehicle system. Since there are nonlinear behaviors in the vehicle system, nonlinear system modeling is required in the real world. Currently, there are mainly two modeling methods. One is to use a physics-based model, and the other is a data-driven method. Among them, neural networks have become a common solution due to their universal approximation characteristics within a limited range. Interpretability is often a necessary condition for a model to have practical value. Although neural networks have great capabilities in inferring complex relationships between variables and can better capture the dynamic characteristics of vehicles, neural networks have obvious defects. Their black-box nature makes them lack physical laws and interpretability, and there is no physical guarantee. When real-time vehicle control requires the model to perform reliable and physically insightful extrapolation, the complexity of neural networks also needs to be balanced with overfitting and computational efficiency problems.

[0005] Aiming at the problems existing in the above-mentioned prior art, the present invention proposes a model predictive control trajectory tracking method based on a physics-informed neural network. Summary of the Invention

[0006] The object of the present invention is to provide a model predictive control trajectory tracking method based on a physics-informed neural network, aiming to solve the problems presented in the above background art.

[0007] The object of the present invention is achieved through the following technical solutions: A model predictive control trajectory tracking method based on a physics-informed neural network, comprising the following steps: Step S1: Physics-informed neural network dynamics modeling; Deeply combine the neural network with the physics-based dynamics model to improve the model fidelity and ensure the physical characteristics of the model. Step S2: Establish a model predictive control trajectory tracking method; Take the physics-informed neural network dynamics model as the prediction model, establish a cost function and constraints based on the vehicle state and the reference trajectory, 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, apply the control idea of feedforward plus feedback to adjust the drive system and the steering system to achieve the desired control quantity to track the reference trajectory.

[0008] Further, the specific steps of the said Step S1 are as follows: Step S11: Establish a physics-based dynamics model; Use a three-degree-of-freedom dynamics model to describe the change of vehicle state, including speed, center-of-mass sideslip angle and yaw rate, and at the same time use the Fiala tire model to describe the longitudinal and lateral force coupling characteristics of the tire. The formula of the three-degree-of-freedom dynamics model is as follows: ; In the formula, are the change rates of vehicle speed, center-of-mass sideslip angle and yaw rate respectively; is the longitudinal force of the front wheel, is the lateral force of the front wheel, is the longitudinal force of the rear wheel, is the lateral force of the rear wheel; is the front wheel steering angle; is the center-of-mass sideslip angle; is the vehicle mass; is the vehicle speed; is the yaw rate; is the moment of inertia of the vehicle; and are the distances from the vehicle center of mass to the front axle and the rear axle respectively, and the wheelbase ; Step S12: Train the physics-informed neural network dynamics model; Model the vehicle dynamics using a physics-informed neural network, integrating the modeling advantages of data-driven and physics-driven approaches. Use a neural network for encoding to estimate the vehicle's dynamic parameters, and ensure the rationality of the neural network output through physical constraints. Then, decode through a physics-based dynamic model to obtain the vehicle state.

[0009] Further, the specific process of step S12 is as follows: Collect vehicle data under double lane change and steady-state circular driving conditions, including vehicle speed, center of mass side slip angle, yaw rate, front wheel steering angle, and wheel speed. Take as the state variables, as the control variables, and form a data set , which is input to the physics-informed neural network for training; The physics-informed neural network takes the state variables and control variables at three sampling times as inputs, and uses four hidden layers with 16 neurons each, namely two fully connected layers and two gated recurrent unit layers. The output layer uses a Sigmoid activation function, and realizes physical constraints through the maximum value and minimum value of the parameters to limit the output of the physical neural network. The formula is as follows: ; In the formula, are the outputs of the two fully connected layers respectively; are the outputs of the two gated recurrent unit layers respectively; is the output of the output layer; is the fully connected layer; is the gated recurrent unit; is the activation function; is the input of the network; and are the hidden states; is the weight of the network; is the bias of the network; is the dynamic parameter.

[0010] Further, the specific steps of step S2 are as follows: Step S21: Establish a prediction model; Use the physics-informed neural network dynamics model trained in step S12 to represent the vehicle's dynamic state, including vehicle speed , center of mass side slip angle , and yaw rate . Use coordinate system to locate the vehicle's position relative to the reference trajectory. The model has a total of 5 state variables and 3 control variables . The prediction model formula is as follows: ; ; In the formula, is the differential of the lateral deviation; is the heading angle deviation between the vehicle speed vector and the path; is the differential of the heading angle deviation; is the rate of change of the heading angle between the vehicle speed vector and the path; is the rate of change of the heading angle of the reference trajectory; Step S22: Establish a cost function; Cost function is constructed by minimizing the deviation between the state variables and control variables and the reference values, and the formula is as follows: ; In the formula, is the prediction horizon; is the time step; and are the predicted state variables and control variables at each time step respectively; and are the reference state variables and control variables respectively; and are adjustable weight matrices; is the control variable; is the inversion; Step S23: Establish constraints; including initial state constraints, model constraints, and actuator constraints; The initial state constraint uses the predicted state of the vehicle 100 ms later as the initial state : ; The model constraint adopts the discrete form of the prediction model to force the system state and control input to conform to the dynamic relationship: ; In the formula, represents the prediction model; and are the predicted state variables and control variables at the next time step respectively; The actuator constraint limits the maximum and minimum values of the steering angle and wheel speed: ; In the formula, and are the front wheel steering angle, front wheel speed, and rear wheel speed at the current time step; and are the minimum and maximum front wheel angles of the vehicle; and are the minimum and maximum wheel speeds of the front wheels of the vehicle, respectively; and are the minimum and maximum wheel speeds of the rear wheels of the vehicle, respectively; Step S24: Solve the optimal control problem; Construct an optimal control problem based on the cost function and constraints, and solve the following finite-domain optimal control problem at each time step to obtain the desired steering angle and wheel speed ; .

[0011] Furthermore, the specific steps of step S3 are as follows: Step S31: Wheel speed control; Consider the influence of vehicle load transfer on the wheel speed control of both sides of the front and rear axles, and ignore the influence of longitudinal load transfer during vehicle acceleration and deceleration; According to the geometric relationship of the vehicle, the formula for calculating the desired wheel speed of each wheel of the vehicle is as follows: ; In the formula, is the desired 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 left and right wheels of the vehicle; is the wheel radius; In the wheel speed control of each wheel, the actual input control quantity is the torque of each wheel, and a PID method is used to design a wheel speed closed-loop controller to achieve the control of the desired wheel speed. The formula is as follows: ; In the formula, is the wheel torque; is an adjustable wheel speed control parameter; is the wheel speed of each wheel; Step S32: Steering system control; Obtain the final front wheel angle by using the feedforward plus feedback method: ; In the formula, is the front wheel angle output by the controller; is the desired front wheel angle; is an adjustable steering system control parameter; is the front wheel angle.

[0012] Compared with the prior art, the beneficial effects of the present invention are: Improving the Model Predictive Control Performance: The present invention deeply integrates a neural network with a physics-based dynamics model to construct a physics-informed neural network dynamics model. On the one hand, this model accurately describes the vehicle dynamics characteristics using the physics-based model, and on the other hand, it estimates the dynamics parameters with the powerful learning ability of the neural network, significantly improving the model fidelity. In the model predictive control algorithm, the high-fidelity model can more precisely simulate the vehicle motion state, laying a solid and reliable foundation for subsequent trajectory tracking control, and thus significantly enhancing the trajectory tracking performance of autonomous vehicles.

[0013] Enhancing Model Interpretability and Physical Assurance: Aiming at the lack of physical laws and interpretability caused by the black-box characteristics of traditional neural networks, the present invention introduces physical constraints during the model training process. By restricting the neural network output to conform to physical reality and endowing the model with physical meaning, the interpretability is enhanced. This enables the model to perform reliable extrapolation based on physical insights during the real-time control of autonomous vehicles, providing a more persuasive basis for control decisions and ensuring the reliability and stability of the model in practical applications.

[0014] Optimizing the Neural Network Performance: In dealing with the problems of overfitting and computational efficiency brought about by the complexity of neural networks, the present invention reasonably selects data acquisition working conditions, optimizes the network structure and parameter settings, and combines physical constraints for model training. These measures effectively balance the complexity of the neural network, improve the computational efficiency, and reduce the risk of overfitting, enabling the neural network to play a more efficient and accurate role in the autonomous driving trajectory tracking task.

[0015] Precisely Achieving Trajectory Tracking Control: The model predictive control trajectory tracking method established by the present invention constructs a cost function and constraint conditions by combining the vehicle state and the reference trajectory, and obtains the desired control quantity by solving the optimal control problem. In the actuator adjustment link, the feedforward plus feedback control idea is used to precisely adjust the wheel speed and the steering system. This series of operations ensures that the autonomous vehicle can stably and precisely track the reference trajectory, improving the safety and reliability of the autonomous driving system. Brief Description of the Drawings

[0016] Figure 1 is the flowchart of the method of the present invention.

[0017] Figure 2 is the method framework diagram of the present invention.

[0018] Figure 3 is the reference path.

[0019] Figure 4 is the path tracking performance. Detailed Embodiments

[0020] For a clearer understanding of the technical features, objectives, and beneficial effects of the present invention, the following provides a detailed description of the technical solution of the present invention, but it should not be construed as a limitation on the scope of implementation of the present invention.

[0021] To meet the physical guarantees and interpretability of the model, physics-informed machine learning is an effective solution. This method integrates physics-based knowledge into the neural network model of the system, which can improve data efficiency and model generalization ability. This characteristic gives it significant advantages in the field of autonomous driving research. In autonomous driving, using physical insights to learn the dynamic model from data and applying it to the model predictive control algorithm helps 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 a physics-informed neural network, and its flowchart and framework diagram are respectively as Figure 1 and Figure 2 shown. The method specifically includes the following steps: Step S1: Physics-informed neural network dynamic modeling; In this step, by deeply integrating the neural network with the physics-based dynamic model, while improving the model fidelity, the physical characteristics of the model are ensured.

[0022] The specific steps of step S1 are as follows: Step S11: Establish a physics-based dynamic model; A three-degree-of-freedom dynamic model is used to describe the changes in vehicle states (speed, center of mass side slip angle, and yaw rate). In this model, the front and rear tires are respectively concentrated into a single tire for each axle, and the vehicle motion is regarded as planar motion. The model formula is as follows: ; In the formula, are respectively the change rates of vehicle speed, center of mass side slip angle, and yaw rate; is the longitudinal force of the front wheel, is the lateral force of the front wheel, is the longitudinal force of the rear wheel, is the lateral force of the rear wheel; is the front wheel steering angle; is the center of mass side slip angle; is the vehicle mass; is the vehicle speed; is the yaw rate; is the moment of inertia of the vehicle; and are respectively the distances from the vehicle center of mass to the front axle and the rear axle, and the wheelbase .

[0023] During high lateral acceleration maneuvers, it is very important to capture the influence of wheel speed dynamics on the longitudinal and lateral force distributions. To better describe the longitudinal-lateral force coupling characteristics of the tire, the Fiala tire model is adopted. The total tire force calculation formula is as follows: ; In the formula, represents the front and rear wheels; is the total tire force; is the total tire slip; is the saturation value of the total tire slip. When exceeding this value, the tire will enter the full-slip state; is the total tire stiffness; is the road surface adhesion coefficient (assuming the road surface adhesion coefficient is isotropic and the front and rear tire road surface adhesion coefficients are the same); the vertical force of the tire; is the tire side slip angle; is the longitudinal slip of the tire.

[0024] The distributions of the longitudinal and lateral tire forces are determined by the ratios of their respective slips to the total slip, and the formula is as follows: ; In the formula, represents the front and rear wheels; is the longitudinal tire force; is the lateral tire force; the side slip angle of the front wheel 、the longitudinal slip of the front wheel 、the side slip angle of the rear wheel and the longitudinal slip of the rear wheel are calculated as follows: ; In the formula, is the wheel radius; is the front wheel speed; is the rear wheel speed.

[0025] Step S12: Train the physics-informed neural network dynamics model; The physics-based dynamics model proposed in Step S11 can better describe the vehicle's dynamics characteristics and can be applied to model predictive control to achieve the vehicle's limit trajectory tracking control. However, the accuracy of the vehicle's dynamic parameters (where are the front and rear tire stiffnesses respectively) has a great influence on the fidelity of the model, and these parameters will change with the vehicle state. For example, the tire stiffness will change with load transfer. Although the data-driven model can establish a high-precision model without prior knowledge such as physical parameters, its interpretability is weak.

[0026] The present invention uses a physics-informed neural network to model vehicle dynamics, integrating the modeling advantages of data-driven and physics-driven approaches. The neural network is used for encoding to estimate the vehicle's dynamic parameters, and physical constraints are used to ensure the rationality of the neural network output. Then, decoding is performed through a physics-based dynamic model to obtain the vehicle state.

[0027] Collect vehicle data under double lane change and steady-state circular driving conditions, including vehicle speed, center of mass side slip angle, yaw rate, front wheel steering angle, and wheel speed. Take them as state variables, take them as control variables, and form a data set , which is input to the physics-informed neural network for training.

[0028] The physics-informed neural network takes the state variables and control variables at three sampling times as inputs, and uses four hidden layers with 16 neurons each, namely two fully connected layers and two gated recurrent unit layers. The output layer uses a Sigmoid activation function. Physical constraints are implemented through the maximum value and minimum value of the parameters to limit the output of the physical neural network. The formula is as follows: ; In the formula, are the outputs of the two fully connected layers respectively; are the outputs of the two gated recurrent unit layers respectively; is the output of the output layer; is the fully connected layer; is the gated recurrent unit; is the activation function; is the input of the network; and are the hidden states; is the weight of the network; is the bias of the network; are the dynamic parameters.

[0029] Step S2: Establish a model predictive control trajectory tracking method; Take the physics-informed neural network dynamic model as the prediction model, establish a cost function and constraints based on the vehicle state and reference trajectory, form an optimal control problem and solve it to obtain the desired control variables.

[0030] The specific steps of step S2 are as follows: Step S21: Establish a prediction model; Use the physics-informed neural network dynamic model trained in step S12 to represent the dynamic state of the vehicle, including vehicle speed , center of mass side slip angle and yaw rate To locate the position of the vehicle relative to the reference trajectory, a coordinate system is used to represent the lateral deviation of the vehicle from the path and the heading angle deviation between the vehicle speed vector and the path.

[0031] The model has a total of 5 state variables and 3 control variables . The prediction model formula is as follows: ; ; In the formula, is the differential of the lateral deviation; is the heading angle deviation between the vehicle speed vector and the path; is the differential of the heading angle deviation; are the rates of change of vehicle speed, sideslip angle at the center of mass, and yaw rate respectively; is the vehicle speed; is the rate of change of the heading angle between the vehicle speed vector and the path; is the rate of change of the heading angle of the reference trajectory; is the longitudinal force of the front wheels; is the lateral force of the front wheels; is the longitudinal force of the rear wheels, is the lateral force of the rear wheels; is the steering angle of the front wheels; is the sideslip angle at the center of mass; is the vehicle mass; is the yaw rate; is the moment of inertia of the vehicle; and are the distances from the vehicle center of mass to the front and rear axles respectively. and The calculation formulas are as follows: ; In the formula, is the curvature of the reference trajectory.

[0032] Step S22: Establish a cost function; The cost function is used to quantify the performance index of the control system. The goal of model predictive control is to minimize this function by optimizing the input variables, thereby achieving the optimal control of the system.

[0033] The cost function is constructed by minimizing the deviation between the state variables and control variables and their reference values. The formula is as follows: ; In the formula,​ is the prediction horizon; is the time step; and are the predicted state variables and control variables at each time step respectively; and are the reference state variables and control variables respectively; and are adjustable weight matrices; is the control variable; is the inversion.

[0034] Step S23: Establish constraints; The constraints are used to describe the physical, operational, and safety limitations of the system, ensuring the feasibility of the control strategy in practical applications, including initial state constraints, model constraints, and actuator constraints, to achieve more stable tracking of the vehicle along the trajectory.

[0035] The initial state constraint uses the predicted state of the vehicle 100 ms later as the initial state for delay compensation: ; The model constraint adopts the discrete form of the prediction model to force the system state and control input to conform to the dynamic relationship: ; In the formula, represents the prediction model; is the time step; and are the predicted state variables and control variables at each time step respectively; and are the predicted state variables and control variables at the next time step respectively.

[0036] The actuator constraint limits the maximum and minimum values of the steering angle and wheel speed to ensure that the control variable is within a reasonable range: ; In the formula, and are the front wheel steering angle, front wheel speed, and rear wheel speed at the current time step; and are the minimum and maximum front wheel steering angles of the vehicle; and are the minimum and maximum front wheel speeds of the vehicle respectively; and are the minimum and maximum rear wheel speeds of the vehicle respectively.

[0037] Step S24: Solve the optimal control problem; Construct an optimal control problem based on the cost function and constraints, and solve the following finite-domain optimal control problem at each time step to obtain the desired steering angle and wheel speed ; 。

[0038] Step S3: Actuator adjustment; It includes wheel speed control and steering system control. Using the control idea of feedforward plus feedback, adjust the drive system and steering system to achieve the desired control quantity, so as to track the reference trajectory.

[0039] The specific steps of the said step S3 are as follows: Step S31: Wheel speed control; During the vehicle turning process, there will be a roll phenomenon. Therefore, consider the influence of vehicle load transfer on the wheel speed control of the wheels on both sides of the front and rear axles, and ignore the influence of longitudinal load transfer during vehicle acceleration and deceleration.

[0040] According to the geometric relationship of the vehicle, the calculation formula for the desired wheel speed of each wheel of the vehicle is as follows: ; In the formula, is the desired wheel speed of each wheel, is the desired wheel speed of the front and rear axles, represents the front wheel and the rear wheel, represents the left wheel and the right wheel; is the wheelbase of the left and right wheels of the vehicle; is the yaw angular velocity; is the wheel radius.

[0041] In the wheel speed control of each wheel, the actual input control quantity is the torque of each wheel. The wheel speed closed-loop controller is designed by the PID method to achieve the control of the desired wheel speed. The formula is as follows: ; In the formula, is the wheel torque; is the adjustable wheel speed control parameter; is the wheel speed of each wheel.

[0042] Step S32: Steering system control; Use the method of feedforward plus feedback to obtain the final front wheel steering angle to give full play to the performance of the steering system: ; In the formula, is the front wheel steering angle output by the controller; is the desired front wheel steering angle; is the adjustable steering system control parameter; is the front wheel steering angle.

[0043] The following describes the specific implementation of the present invention in detail with reference to specific embodiments.

[0044] Embodiment 1: This embodiment conducts an experiment based on the method of the present invention. A reference path with variable curvature is set in the experimental scenario (as Figure 3 shown), and the road surface adhesion coefficient is 0.85. During the experiment, under the action of the control method, the vehicle starts from the starting point and tracks the trajectory.

[0045] To intuitively reflect the performance advantages of the method of the present invention, this experiment is defined as "Experiment 1", and a traditional model predictive control trajectory tracking experiment based on a physical model is selected as a control, named "Experiment 2". Lateral deviation and heading angle deviation are two key indicators for measuring the path tracking performance of the control method. Through comparative analysis of the data performance of the two in the experiment, it is found that (as Figure 4 shown): In terms of the lateral error curve, the maximum absolute lateral deviation in Experiment 1 is -0.38 m, while in Experiment 2, the maximum absolute lateral deviation appears near 10 s, reaching -0.46 m; in terms of the heading angle deviation, the maximum absolute heading error in Experiment 1 is 0.17 rad, which is 0.04 rad less than that in Experiment 2. Further calculating the root mean square values of the lateral error and heading angle deviation in the entire experiment, the root mean square value of the lateral error in Experiment 1 is 0.12 m, and that in Experiment 2 is 0.16 m; the root mean square value of the heading angle deviation in Experiment 1 is 0.046 rad, and that in Experiment 2 is 0.054 rad. The data results clearly show that in terms of both the maximum absolute deviation and the root mean square value index, the performance of Experiment 1 in lateral deviation and heading angle deviation is better than that of Experiment 2, fully verifying that the method of the present invention has significant advantages in path tracking control.

[0046] The above is only the preferred embodiment of the present invention. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several deformations and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicability 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, and the cost function and constraints are established according to the vehicle state and reference trajectory to form and solve the optimal control problem and obtain the desired control amount; Step S3: actuator adjustment; 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.

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 S1 are as follows: Step S11: establishing a physics-based dynamics model; A three-degree-of-freedom dynamics model is used to describe the changes in vehicle state, including speed, sideslip angle of center of mass, 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: ； In the formula, are the rates of change of vehicle speed, sideslip angle at center of mass, and yaw rate, respectively; 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 vehicle speed; is the yaw angular velocity; is the moment of inertia of the vehicle; and The distance from the center of mass of the vehicle to the front axle and the rear axle, respectively, and the wheelbase ; Step S12: training a physical information neural network dynamics model; The vehicle dynamics is modeled using a physical information neural network, 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.

3. The model predictive control trajectory tracking method based on physical information neural network according to claim 2 is characterized in that: 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 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 the maximum value of the parameter is used. and minimum value To implement physical constraints and limit the output of the physical neural network, the formula is as follows: ； In the formula, 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 a hidden state; is the weight of the network; is the bias of the network; is the kinetic parameter.

4. The model predictive control trajectory tracking method based on physical information neural network according to claim 3 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 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: ； ； In the formula, 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 heading angle between the vehicle velocity vector and the path; is the heading angle change rate 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: ； In the formula, For the prediction time domain; is the time step; and are the state quantity and control quantity predicted at 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; Includes initial state constraints, model constraints, and actuator constraints; The initial state constraint is the vehicle predicted state after 100ms. As initial state : ； The model constraints use the predictive model discretization method to force the system state and control input to conform to the dynamic relationship: ； In the formula, represents a 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: ； In the formula, 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 steering 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 ; 。 5. 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: ; In the formula, 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 left and right wheels of the vehicle; is the wheel radius; In the wheel speed control of each wheel, the actual input control quantity is the torque of each wheel. The PID method is used to design the wheel speed closed-loop controller to achieve the desired wheel speed control. The formula is as follows: ; In the formula, 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 steering angle is obtained by using the feedforward plus feedback method: ; In the formula, The front wheel steering 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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