Vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraint

Abstract

The invention discloses a vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraint, which comprises an upper-layer controller and a lower-layer controller, and is characterized in that the upper-layer controller comprises a tire lateral force estimator and a trajectory tracking controller based on model predictive control; the tire lateral force estimator is used for calculating tire lateral force, the tire lateral force, the vehicle state and the reference trajectory are input into the trajectory tracking controller to calculate the expected front wheel steering angle and the expected longitudinal acceleration, and the lower-layer controller achieves output of the upper-layer controller through the steering system and the driving device. After the MPC is used in trajectory tracking control, the trajectory tracking precision is greatly improved, and the peak value of a transverse tracking error is reduced by 70%; the tire lateral force estimated based on the RBF neural network can meet the requirements of actual driving conditions; after the vehicle uses slippage constraint, the slippage phenomenon can be effectively reduced, and the operation stability of the vehicle is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned vehicle control, and in particular to an automatic control system taking vehicle slip into consideration. Background Art

[0002] With the increase in the number of cars and the number of car users, the rate of car traffic accidents is also increasing year by year. Car traffic accidents seriously endanger social security, personal and family life and property safety. Unmanned vehicles have great potential in improving traffic flow and reducing car traffic accident rates and safety performance. The current vehicle automatic control system or algorithm has the following technical defects:

[0003] First, for trajectory tracking control, currently, many studies are devoted to selecting appropriate control algorithms. Most of the studies cannot consider multiple constraints at the same time while achieving the control objectives.

[0004] Secondly, ignoring aerodynamics and gravity, all forces affecting vehicle handling are generated by the tires, and an accurate tire model can further improve the vehicle's handling performance. However, existing literature mainly regards these parameters as known, which will affect the controller effect to a certain extent. Therefore, the uncertainty of vehicle state parameters is also very important;

[0005] Finally, when a vehicle is traveling on a low-adhesion road or at a high speed, the vehicle is very likely to slip, which will seriously affect the vehicle's handling stability. The existing technical solutions mainly use the yaw rate-lateral velocity phase plane method to determine whether the vehicle is unstable, but the phase plane method only limits the yaw rate and lateral velocity to a stable area, ignoring the fact that the tire lateral force and slip constraints change all the time during the vehicle's driving. Summary of the invention

[0006] The technical problem to be solved by the present invention is: for the trajectory tracking control problem of the existing automatic control system, a trajectory tracking control algorithm taking into account parameter uncertainty and tire dynamics constraints is provided.

[0007] The technical solution of the present invention is:

[0008] A trajectory tracking control system based on numerical uncertainty and tire dynamics constraints includes an upper controller and a lower controller, and is characterized in that: a trajectory tracking model with parameter uncertainty is designed, the upper controller is a trajectory tracking controller based on model predictive control, the trajectory tracking controller is used to calculate the expected front wheel steering angle and the expected longitudinal acceleration, and the lower controller realizes the output of the upper controller through a steering system and a drive device.

[0009] The upper controller also includes a RBF neural network estimator to estimate the tire lateral force.

[0010] The reference trajectory is generated by a quintic polynomial. The parameters of the reference trajectory include: road curvature C R , road heading angle Reference speed v r , the lateral coordinate y of the reference trajectory r , the longitudinal coordinate x of the reference trajectory r .

[0011] The dynamic differential equations of the vehicle trajectory tracking model are:

[0012]

[0013] In the formula, m represents the vehicle mass, l f and l r are the front and rear wheelbases of the vehicle, v x and v y represents the velocity components of the velocity V at the center of mass of the vehicle along the X-axis and Y-axis, respectively, x is the longitudinal acceleration of the vehicle; is the vehicle's yaw angle; is the vehicle's yaw rate; β is the center of mass sideslip angle, which indicates the angle of the center of mass's current velocity relative to the longitudinal axis of the vehicle; δ f is the front wheel steering angle; F yf and F yr Represent the lateral forces of the front and rear tires respectively; I z is the moment of inertia of the vehicle around the Z axis;

[0014] Tire lateral force F yf and F yr The RBF neural network estimator is used to obtain the neural network, which consists of three layers. The first layer is the input layer, which consists of three input quantities: vertical load F z , road friction coefficient μ, side slip angle α. The second layer is the hidden layer, and the activation function used in the hidden layer is the Gaussian function:

[0015]

[0016] where β j is the center width of the hidden layer. X is the input vector; C j is the central unit of the jth radial basis function, which has the same dimension as the input vector X. The third layer is the output layer, and the output is the tire lateral force F y , which is solved as follows:

[0017]

[0018] Among them, w i is the weight.

[0019] Based on the lateral path controller of model predictive control (MPC), the optimal control performance evaluation function J of the linear quadratic regulator is established, as shown in the following formula:

[0020]

[0021]

[0022] Where Y r (k) is the state variable of the system; Δu(k) is the control increment of the system; Q and R are weight matrices respectively; x(k): the vehicle state variable at discrete time k, including lateral velocity, yaw rate, lateral error, yaw error and longitudinal velocity error (Note: In model predictive control, the state equation of the system is usually: [x(k+1)=Ax(k)+Bu(k)])

[0023] ΔU(k): input vector of the system at time (k)

[0024] Y(k): predict future system status

[0025] Np: prediction time domain

[0026] Nc: Control time domain

[0027] B u , B d , A d : Indicates the parameters to be requested

[0028] ρ(k): disturbance, including parameters such as road curvature and expected longitudinal velocity change rate

[0029] H sh : Matrix, which maps the state and control inputs of the system to outputs

[0030] G sh (k): Upper limit value, indicating the maximum allowable value of the system output (or state).

[0031] The stability of the vehicle is determined by the vehicle's state lateral velocity v y The tire cornering force under different driving conditions is estimated by the RBF neural network, and the threshold of the slip angle α under different driving conditions is calculated according to the tire model using the cornering force estimated by the RBF neural network. In addition, the lateral speed (v y )’s limit:

[0032]

[0033] The maximum tire cornering force is estimated by the RBF neural network estimator:

[0034]

[0035] A hardware-in-the-loop test platform was developed and a V-shaped technical route was designed. We first verified the effectiveness of the trajectory tracking control system through CarSim and Simulink. On this basis, we compiled the trajectory tracking control system into the Raspberry Pi by generating C++ code through Matlab to further verify the effectiveness of the algorithm. To verify the application of the trajectory tracking control algorithm in engineering, IMU was used to obtain the vehicle's lateral and longitudinal speed, yaw angle and yaw angular velocity, RTK was used to obtain the vehicle's position information, and the ROS car was used to verify the trajectory tracking control algorithm.

[0036] The beneficial effects of the present invention are:

[0037] 1. After using the MPC controller in trajectory tracking control, the trajectory tracking accuracy is greatly improved, and the peak value of the lateral tracking error is reduced by 70%;

[0038] 2. The tire lateral force estimated based on the RBF neural network can meet the needs of actual driving conditions; when the vehicle uses slip constraint, it can effectively reduce the slip phenomenon and improve the vehicle's handling stability.

[0039] 3. The developed hardware-in-the-loop test platform can greatly shorten the development cycle and reduce the development cycle of automatic control technology. In the absence of a real vehicle verification platform, the use of this technical route can effectively reduce the development cost and have good results. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a system framework diagram of the present invention;

[0041] Figure 2 A schematic diagram of a vehicle trajectory tracking model of the present invention;

[0042] Figure 3 It is a schematic diagram of the principle of RBF neural network estimator;

[0043] Figure 4 Schematic diagram of sliding constraint.

[0044] Figure 5 Schematic diagram of the technical route DETAILED DESCRIPTION

[0045] The overall research framework of the present invention is as follows Figure 1As shown in the figure. A hierarchical control structure is proposed to construct the controller of the model predictive trajectory tracking control system. The overall goal of the control strategy is to calculate the expected front wheel steering angle and expected longitudinal acceleration based on the MPC trajectory tracking control algorithm, and to achieve this control goal through the vehicle upper steering angle and driving brake actuators to achieve the desired trajectory. The control system consists of two sub-controllers, namely the upper controller and the lower controller. The upper controller is the MPC trajectory tracking controller, which is used to collect the vehicle state, the tire lateral force estimated by the RBF neural network and the trajectory information given by the trajectory planning, and then calculate the expected front wheel steering angle and expected longitudinal acceleration of the vehicle. The functional implementation of the MPC trajectory tracking controller is divided into two parts, namely the vehicle trajectory tracking model and the control rate. The trajectory tracking model is used to describe the positional relationship between the vehicle's dynamic characteristics and the desired trajectory. The control rate includes the control objectives of minimizing the lateral error, yaw angle error and longitudinal velocity error of the vehicle and the design of the vehicle's handling stability considering the slip constraint. The lower controller implements the output of the upper controller based on the steering and driving brake devices and tracks the desired trajectory.

[0046] The working principle is as follows:

[0047] 1. First, generate a reference trajectory through a quintic polynomial. The parameters of the reference trajectory include: The parameters of the reference trajectory include: Road curvature C R , road heading angle Reference speed v r , the lateral coordinate y of the reference trajectory r , the longitudinal coordinate of the reference trajectory.

[0048] 2. Secondly, the planned trajectory information is transmitted to the upper controller, which is a trajectory tracking controller based on model predictive control. The RBF neural network estimator is used as an auxiliary module to obtain the tire lateral force parameters required by the controller. The following is an explanation of the principle of the trajectory tracking controller:

[0049] 2.1 Trajectory tracking model establishment

[0050] An effective vehicle model can improve the vehicle's smoothness during driving and the vehicle's handling stability during actual control. This paper uses a trajectory tracking model to describe the state of the vehicle. The dynamic model is as follows Figure 2 shown.

[0051] To describe the positional relationship between the vehicle and the road, we assume that the road position x r / y r , the angle between the tangent of the road centerline and the X-axis of the inertial coordinate system Road curvature C R and the expected speed v r Given, the yaw angle deviation and longitudinal velocity error can be described as:

[0052]

[0053] in, represents the deviation of the yaw angle from the desired trajectory direction, e v Represents the error between the current speed and the expected speed, v r is the expected speed, is the yaw angle of the target trajectory.

[0054] When the road curvature is known:

[0055]

[0056] C R is the road curvature.

[0057] According to the above formula, we can get:

[0058]

[0059] in, is the expected longitudinal velocity change rate, and r is the yaw angular velocity.

[0060] Assuming a small angle for the yaw angle error, the vehicle lateral error change rate It can be defined as:

[0061]

[0062] Under inertia, the vehicle yaw dynamics model can be expressed as:

[0063]

[0064] Where a x is the generalized longitudinal acceleration of the vehicle, F xf is the front wheel longitudinal force, F xr is the rear wheel longitudinal force, δ f is the front wheel turning angle, the front and rear lateral forces F yf and F yr .

[0065] The dynamic differential equation of the vehicle trajectory tracking model is summarized as follows:

[0066]

[0067] In the formula, m represents the vehicle mass, l f and l r are the front and rear wheelbases of the vehicle, v x and v y represents the velocity components of the velocity V at the center of mass of the vehicle along the X-axis and Y-axis, respectively, xis the longitudinal acceleration of the vehicle; is the vehicle's yaw angle; is the vehicle's yaw rate; β is the center of mass sideslip angle, which indicates the angle of the center of mass's current velocity relative to the longitudinal axis of the vehicle; δ f is the front wheel steering angle; F yf and F yr Represent the lateral forces of the front and rear tires respectively; I z is the moment of inertia of the vehicle around the Z axis;

[0068] Finally, the linear time-varying model of the trajectory tracking controller is obtained:

[0069]

[0070] The state function is The control input is u(t)=[a x δ f ] T , the output variable is Define ρ(t) as the disturbance,

[0071]

[0072] 2.2 RBF neural network estimator design

[0073] According to the tire characteristics, the factors that affect the tire lateral force F y There are three main factors: vertical load F z , road adhesion coefficient μ, tire slip angle α, this is a complex nonlinear time-varying function with 3 inputs and 1 output. It is difficult to establish a more accurate mathematical model using traditional methods. Therefore, this paper uses the characteristics of RBF neural network to approximate nonlinear functions to establish the RBF neural network model of tire lateral force. The principle diagram is as follows Figure 3 As shown, the neural network consists of three layers. The first layer is the input layer, which consists of three input quantities: F z , μ, α. The second layer is the hidden layer, and the activation function used in the hidden layer is the Gaussian function:

[0074]

[0075] where β j is the center width of the hidden layer. X is the input vector; C j is the central unit of the jth radial basis function, which has the same dimension as the input vector X. The third layer is the output layer, and the output is the tire lateral force F y , which is solved as follows:

[0076]

[0077] Among them, w i is the weight.

[0078] 2.3 Design of model-based prediction trajectory tracking controller

[0079] Design an MPC-based trajectory tracking controller.

[0080] The trajectory tracking model established in Section 2.1 is a continuous state equation, but the continuous state equation is difficult to use to predict the future state of the vehicle. Therefore, in real-time control applications, the trajectory tracking model is usually discretized. The zero-order hold (ZOH) method is used to transform the continuous state equation into:

[0081]

[0082] Where k represents the kth th Sampling time, A d , B u , B d and C can be expressed as:

[0083]

[0084] Where T s is the sampling time (T s =50ms), C is the weight matrix, y∈R 5 The state quantity of the trajectory tracking system.

[0085] To facilitate the design of the controller, the state vector x(k) and the incremental input Δu(k) are usually coupled in an augmented matrix, which can be expressed as Rewrite the above equation:

[0086]

[0087] In the formula, N x is the state dimension, N u is the control quantity dimension. The change of control input is Δu(k)=u(k)-u(k-1). Within the time step k, the change of the predicted performance vector Y(k) and the control input sequence ΔU(k) ​​of the trajectory tracking system is calculated as follows:

[0088]

[0089] Where N p is the prediction time domain, N c To control the time domain, For prediction performance, Δu(k), Δu(k+1),…, Δu(k+N c -1) is the change of control sequence.

[0090] The MPC controller can predict the state at the next moment based on the state at the current moment, and write this process in the form of an equation, so the prediction equation can be expressed as:

[0091]

[0092] In order to facilitate the design of the controller, the above formula is arranged in matrix form, and the matrix form of the predicted output vector of the system is obtained as follows:

[0093]

[0094] In the formula

[0095]

[0096] In order to obtain the desired control increment, the trajectory tracking problem can be converted into a quadratic optimal solution problem as follows:

[0097]

[0098]

[0099] In the formula, Q and E are weight matrices, ε is the relaxation coefficient,

[0100] x(k): vehicle state variables at discrete time k, including lateral velocity, yaw rate, lateral error, yaw error, and longitudinal velocity error (Note: In model predictive control, the state equation of the system is usually: [x(k+1)=Ax(k)+Bu(k)])

[0101] ΔU(k): input vector of the system at time (k)

[0102] Y(k): predict future system status

[0103] Np: prediction time domain

[0104] Nc: Control time domain

[0105] B u , B d , A d : indicates the parameters to be requested.

[0106] ρ(k): disturbance, including parameters such as road curvature and expected longitudinal velocity change rate

[0107] H sh : Matrix, which maps the state and control inputs of the system to outputs

[0108] G sh (k): Upper limit, indicating the maximum allowable value of the system output (or state). Definition E(k) = -Yr (k)+θ t Δu(k)+τ t φ(k), then combined with the constraints, the objective function can be transformed into a quadratic optimization problem:

[0109]

[0110] In the formula, G k =2E T Qθ t .

[0111] And by transforming the slip constraint into a control increment

[0112]

[0113] Among them, H ssh =diag(H sh ,H sh ,…H sh ) Np×Np ,

[0114] 2.4 Design of Slip Constraint

[0115] First, we need to design a yaw stability criterion to determine whether the vehicle has lost stability. We use the yaw rate-lateral velocity phase plane method to determine whether the vehicle has lost stability.

[0116] The stability of the vehicle is determined by the vehicle's state lateral velocity v y and yaw rate r. We estimate the tire cornering force under different driving conditions through the RBF neural network, and use the cornering force estimated by the RBF neural network to calculate the threshold of the slip angle α under different driving conditions according to the tire model. In addition, the lateral speed (v y ) is defined by limiting the rear tire slip angle:

[0117]

[0118] The maximum tire cornering force is estimated by the RBF neural network estimator:

[0119]

[0120] The above formula forms a closed envelope, such as Figure 4 The first equation defines the yaw rate control boundary, and the second equation defines the lateral velocity control boundary. When the vehicle state is within the envelope, the vehicle stability can be guaranteed.

[0121] In order to achieve high lateral tracking accuracy and handling stability, the physical characteristics of the vehicle's turning angle and driving and braking should also be considered in the vehicle trajectory tracking model. The following constraints are applied to the vehicle's variables:

[0122]

[0123] Where u(k) and Δu(k) are the control input and control input increment of the trajectory tracking system.

[0124] 2.5 Design of trajectory tracking control algorithm verification platform

[0125] In order to verify the effectiveness of the trajectory tracking algorithm, the present invention built a CarSim / Simulink joint simulation platform, a hardware-in-the-loop test platform, and a ROS car verification platform. The technical route flow chart is as follows Figure 5 As shown in the figure, the trajectory tracking control system is first analyzed functionally. Then, based on the CarSim / Simulink joint simulation to verify the effectiveness of the MPC trajectory tracking algorithm, the MPC trajectory tracking controller is compiled into the Raspberry Pi by generating C++ code from Matlab. The Raspberry Pi is used as a controller to control the virtual controlled vehicle in CarSim. CarSim is a simulation software for vehicle dynamics. It uses detailed vehicle characteristic parameters to simulate the dynamic behavior of the vehicle and is widely used in the development of modern automobile control systems. Finally, the verified trajectory tracking controller is configured in the ROS car, and the IMU is used to obtain the vehicle's lateral and longitudinal speeds, yaw angles, and yaw angular velocity. The RTK is used to obtain the vehicle's position information, and the effectiveness of the trajectory tracking algorithm is further verified in engineering applications.

[0126] Firstly, the vehicle-road model in CarSim software is combined with the controller proposed in Matlab / Simulink to perform joint simulation to achieve trajectory tracking. First, the tire lateral force is estimated using the RBF neural network estimator based on the front wheel steering angle, body mass, vehicle speed and yaw rate given by the vehicle sensor. Then, the expected longitudinal acceleration and expected front wheel steering angle are calculated by the MPC trajectory tracking algorithm based on the vehicle speed, yaw angle, yaw rate, vehicle position and road information. In addition, the tire lateral force estimated based on the RBF neural network is used to update the boundary conditions of the slip constraint. Finally, the longitudinal control module is used to convert the expected longitudinal acceleration into the brake master cylinder pressure and throttle opening, and the brake master cylinder pressure, throttle opening and front wheel steering angle are applied to the vehicle to control the vehicle to track the expected trajectory.

[0127] Then, a hardware-in-the-loop test platform is built. The hardware-in-the-loop test platform mainly consists of a Raspberry Pi and a host computer (desktop computer). The host computer (desktop computer) is equipped with software such as Matlab / Simulink and CarSim. Matlab / Simulink receives ROS topics containing control instructions from the Raspberry Pi and passes them to the vehicle model in CarSim. CarSim gives feedback on this information and passes it to the Raspberry Pi through Matlab / Simulink. The MPC controller is compiled in the Raspberry Pi. The corresponding control instructions are calculated by the MPC trajectory tracking controller and passed to CarSim through Matlab. The process is repeated.

[0128] Finally, the ROS car verification platform. The ROS car mainly consists of a controller (Raspberry Pi or industrial computer), MPU9250, RTK and STM32 car chassis. MPU9250 is used to obtain the vehicle's lateral and longitudinal speeds, yaw angle and yaw angular velocity, and RTK is used to obtain the vehicle's position information. The information obtained through the sensor is then used by a controller compiled with the MPC trajectory tracking control algorithm to calculate the longitudinal acceleration and front wheel angle, and then transmitted to the car chassis to control the car to track the desired trajectory.

[0129] It is necessary to point out here that the above embodiments are limited to further elaborating and understanding the technical solutions of the present invention, and cannot be understood as further limiting the technical solutions of the present invention. Inventions and creations with non-outstanding substantial features and significant progress made by those skilled in the art still fall within the protection scope of the present invention. In addition, it should be understood that although this specification is described according to the implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that those skilled in the art can understand.

Claims

1. A vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints, comprising an upper controller and a lower controller, characterized in that: The upper-level controller includes a tire lateral force estimator and a trajectory tracking controller based on model predictive control. The tire lateral force estimator is used to calculate the tire lateral force. The tire lateral force, vehicle status and reference trajectory are input into the trajectory tracking controller to calculate the expected front wheel turning angle and expected longitudinal acceleration. The lower-level controller realizes the output of the upper-level controller through the steering system and the drive device.

2. The vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints according to claim 1, characterized in that: The tire lateral force estimator calculates the tire lateral force based on the RBF neural network. The calculated tire lateral force is used in the vehicle trajectory tracking model and updates the boundary conditions of the slip constraint.

3. The vehicle trajectory tracking control system based on considering tire dynamic constraints and parameter uncertainties according to claim 1, characterized in that: The reference trajectory is generated by a quintic polynomial. The parameters of the reference trajectory include: road curvature C R , road heading angle Reference speed v r , the lateral coordinate y of the reference trajectory r , the longitudinal coordinate x of the reference trajectory r .

4. The vehicle trajectory tracking control system considering tire dynamics constraints and parameter uncertainties according to claim 3, characterized in that: The dynamic differential equation of the vehicle trajectory tracking model is: In the formula, m represents the vehicle mass, l f and l r are the front and rear wheelbases of the vehicle, v x and v y represents the velocity components of the velocity V at the center of mass of the vehicle along the X-axis and Y-axis, respectively, x is the longitudinal acceleration of the vehicle; is the vehicle's yaw angle; is the vehicle's yaw rate; β is the center of mass sideslip angle, which indicates the angle of the center of mass's current velocity relative to the longitudinal axis of the vehicle; δ f is the front wheel steering angle; α f and α r Respectively represent the side slip angles of the front and rear tires; C af and C ar Respectively represent the cornering stiffness of the front tire and the rear tire; F yf and F yr Represent the lateral forces of the front and rear tires respectively; I z is the vehicle's moment of inertia about the Z axis.

5. The vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints according to claim 4, characterized in that: Tire lateral force F yf and F yr The RBF neural network estimator is used to obtain the neural network, which consists of three layers. The first layer is the input layer, which consists of three input quantities: vertical load F z , road friction coefficient μ, sideslip angle α; the second layer is the hidden layer, and the activation function used in the hidden layer is the Gaussian function: where β j is the center width of the hidden layer; X is the input vector; C j is the central unit of the jth radial basis function, which has the same dimension as the input vector X; the third layer is the output layer, and the output is the tire lateral force F y , which is solved as follows: Among them, w i is the weight.

6. The vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints according to claim 4, characterized in that: The trajectory tracking controller includes a lateral path controller based on model predictive control. The optimal control performance evaluation function J of the linear quadratic regulator is established as shown in the following formula: Where Y r (k) is the state variable of the system; Δu(k) is the control increment of the system; Q and R are weight matrices respectively; x(k): vehicle state variables at discrete time k, including lateral velocity, yaw rate, lateral error, yaw error, and longitudinal velocity error (Note: In model predictive control, the state equation of the system is usually: [x(k+1)=Ax(k)+Bu(k)]) ΔU(k): input vector of the system at time (k) Y(k): predict future system status Np: prediction time domain Nc: Control time domain B u , B d , A d : indicates the parameter to be calculated. The calculation method is given on page 11 of the document. ρ(k): disturbance, including parameters such as road curvature and expected longitudinal velocity change rate H sh : Matrix, which maps the state and control inputs of the system to outputs G sh (k): Upper limit value, indicating the maximum allowable value of the system output (or state).

7. The vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints according to any one of claims 1 to 6, characterized in that The stability of the vehicle is determined by the vehicle's state lateral velocity v y The tire cornering force under different driving conditions is estimated by RBF neural network, and the threshold of the slip angle α under different driving conditions is calculated according to the tire model using the cornering force estimated by RBF neural network.

8. The vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints according to claim 7, characterized in that: Lateral velocity (v y ) is defined by limiting the rear tire slip angle: The maximum tire cornering force is estimated by the RBF neural network estimator:

9. The vehicle trajectory tracking control system based on parameter uncertainty and tire dynamics constraints according to claim 7, characterized in that: Firstly, the effectiveness of the trajectory tracking control system is verified through CarSim and Simulink. On this basis, the trajectory tracking control system is compiled into the Raspberry Pi by generating C++ code through Matlab. The effectiveness of the algorithm is further verified. The IMU is used to obtain the vehicle's lateral and longitudinal speeds, yaw angle and yaw angular velocity. RTK is used to obtain the vehicle's position information. The trajectory tracking control algorithm is verified using the ROS car.

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