Unmanned vehicle tracking control method considering input time delay and speed time variation

Abstract

The application provides a self-driving vehicle tracking control method considering input time delay and speed time variation, relates to the field of self-driving vehicle tracking control, and utilizes a look-ahead distance on a kinematic model, introduces look-ahead error and curvature, considers speed time variation on the basis, establishes a linear parameter variation vehicle lateral dynamics model. In order to model the input time delay problem, the model is expanded on the basis of the lateral dynamics model, the system state is increased by the control input quantity of the time delay period number, and the influence of the input time delay is compensated; a path tracking controller based on robust model prediction control is designed, the controller is obtained by the Lyapunov asymptotic stability principle and solving an optimization problem based on a linear matrix inequality, and the controller can guarantee vehicle stability and improve tracking precision under the conditions of input time delay and speed time variation.

Description

Technical Field

[0001] This invention relates to the field of autonomous vehicle tracking control, and in particular to an autonomous vehicle tracking control method that takes into account input delay and speed time variation. Background Technology

[0002] With the rapid development of computer technology, chip manufacturing, and communication technology, autonomous vehicles are widely used in port logistics, unmanned mining areas, and urban roads. Among these, urban roads, due to their complexity, large pedestrian traffic, and congestion, have become one of the most challenging scenarios for the application of autonomous driving technology. Autonomous driving technology mainly includes three technical areas: environmental perception, decision-making and planning, and tracking control. Tracking control, which outputs smooth control signals to ensure passenger comfort and tracking accuracy, is one of the fundamental problems of autonomous driving technology. Furthermore, vehicle speed is often time-varying during operation, requiring consideration of the impact of time-varying speed. In practical vehicle systems, the process of algorithm calculations and signal transmission between the upper-level controller and actuators takes time. This necessitates that autonomous vehicles simultaneously ensure tracking accuracy and passenger comfort while also handling the impact of system input latency. Therefore, designing effective tracking control strategies for autonomous vehicles that can reduce the impact of input latency and time-varying speed has significant research value and practical significance.

[0003] Model predictive control (MDC) is widely used in autonomous driving, robotics, chemical engineering, and power grid control due to its ability to explicitly handle constraints. MDC is based on a predictive model and performs rolling optimization, typically applying the first term of the optimized control sequence to the controlled system. Therefore, the accuracy of the model significantly impacts the control performance of MDC. For complex nonlinear systems, simple linearization modeling, such as Taylor series expansion, struggles to accurately predict the system state; iterative optimization using nonlinear models is time-consuming, hindering real-time control and potentially leading to unsolvable problems. Furthermore, in practical vehicle dynamics systems, time-varying parameters and external disturbances affect the stability of the control system, posing challenges to controller design. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an unmanned vehicle tracking control method that takes into account input delay and speed time variation, which can ensure vehicle stability and improve tracking accuracy under the conditions of input delay and speed time variation.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a tracking control method for unmanned vehicles that considers input delay and time-varying speed, comprising the following steps:

[0006] Step S1: Establish a lateral dynamics model of the vehicle. Based on this, establish a kinematic model that includes both look-ahead distance and curvature. The tracking error of the look-ahead point can be calculated using the look-ahead distance, and the state space expression is given.

[0007] Step S2: Considering the time-varying speed of the autonomous vehicle, the longitudinal speed of the vehicle is taken as a time-varying parameter, and the lateral dynamics model of the vehicle is improved based on the linear parameter variation method.

[0008] Step S3: Model the input delay problem. Based on the linear parameter change transverse dynamics model, expand the model dimension and add a control input with a delay period to the system state to compensate for the impact of input delay.

[0009] Step S4: Design a path tracking controller based on robust model predictive control. The state feedback controller is obtained by solving an optimization problem based on linear matrix inequalities, which satisfies the requirements of ensuring vehicle stability and improving tracking accuracy under conditions of time-varying speed and input delay.

[0010] A further improvement to the technical solution of the present invention is that the specific process of establishing the vehicle lateral dynamics model in step S1 is as follows:

[0011] A two-degree-of-freedom lateral dynamics model of the vehicle is constructed in the local coordinate system;

[0012]

[0013] Among them, v x (t) and v y (t) represents the longitudinal and lateral velocities of the vehicle, respectively, ω(t) represents the yaw rate of the vehicle, and F xf (t) and F xr (t) represents the resultant longitudinal forces of the front and rear axles of the vehicle, F. yf (t) and F yr (t) represent the resultant lateral forces on the front and rear axles of the vehicle, respectively. f and l r Here, δ(t) represents the distances from the center of the front axle and the center of the rear axle to the vehicle's center of gravity, respectively; δ(t) is the front wheel deflection angle. In vehicle lateral control, the resultant longitudinal force F of the front axle is ignored. xf With the effect of (t), cosδ(t)≈1, the lateral dynamics model of the vehicle can be expressed as:

[0014]

[0015] The method for calculating tire lateral force is as follows:

[0016]

[0017] Among them, Cf and C r Let α be the tire lateral stiffness of the front and rear axles of the vehicle, respectively, and be a constant; f and α r Let be the tire slip angles of the front and rear axles of the vehicle, respectively, which can be approximated by the following equation:

[0018]

[0019] A further improvement to the technical solution of this invention lies in the following: In step S1, a kinematic model is established that simultaneously includes look-ahead distance and curvature. The tracking error of the look-ahead point can be calculated using the look-ahead distance. The specific process of giving the state-space expression is as follows: The vehicle kinematics is analyzed, y... e (t) represents the vehicle's lateral tracking error, defined as the distance between the vehicle's center of mass and the reference point P1, and its derivative can be calculated using the following equation:

[0020]

[0021] Where, θ e (t) represents the vehicle yaw angle error, defined as the deviation between the vehicle yaw angle and the yaw angle of the reference trajectory point, let sinθ e ≈θ e Therefore, the derivative of the lateral tracking error can be converted to:

[0022]

[0023] Use KV x (t) represents the reference angular velocity, and the derivative of the yaw angle error can be expressed as:

[0024]

[0025] l e (t) represents the look-ahead error, and its derivative can be obtained from the following equation:

[0026]

[0027] Based on the above vehicle kinematics and dynamics model, the state-space expression of the vehicle system is given as follows:

[0028]

[0029] Wherein, the system state vector is Let the product of path curvature and longitudinal velocity be the system disturbance w(t) = kv x System matrix A, control matrix B u And coefficient matrix B w They are represented as follows:

[0030]

[0031] A further improvement to the technical solution of this invention lies in the following: the specific process of step S2 is as follows: the vehicle's longitudinal velocity is set to be time-varying, thereby providing a vehicle lateral dynamics model considering time-varying parameters, and the time-varying longitudinal velocity v is modeled using a linear parameter variation modeling method. x To perform the modeling, two time-varying parameters are selected as follows:

[0032]

[0033] The range of time-varying parameters can be expressed as:

[0034] π1∈[π 1,min ,π 1,max ],π2∈[π 2,min ,π 2,max ],

[0035] π i,min and π i,max (i = 1, 2) represent the minimum and maximum vehicle speeds, respectively. Therefore, the system matrix A is represented as:

[0036]

[0037] The time-varying parameter vector is represented as π = [π1 π2] T Take the maximum and minimum values ​​of π1 and π2 respectively;

[0038]

[0039] Ω1=[π 1,max π 2,min ],Ω2=[π 1,min π 2,max ]

[0040] Therefore, the state-space expression of the system is:

[0041]

[0042] The two weighting coefficients of the linear parameter variation model are obtained from the following expressions:

[0043] θ1=σ(1-λ), θ2=(1-σ)λ

[0044] in,

[0045] A further improvement to the technical solution of the present invention is that the specific steps of step S3 are as follows:

[0046] Step S3.1: To consider the impact of input delay on the system, we first model the input delay system:

[0047]

[0048] Where p is the input delay, and the delay time is measurable;

[0049] S3.2. To compensate for the impact of input delay, the system is represented in discrete form, and the system state is extended in dimension, as follows:

[0050]

[0051] Where N is the number of delay periods, δ(t) k-i ) for t k-i The control input signal at any given time is represented in the augmented system form of the system state space:

[0052]

[0053] in,

[0054]

[0055] make And satisfy Where β is a positive definite constant.

[0056] A further improvement to the technical solution of the present invention is that the specific steps of step S4 are as follows:

[0057] S4.1, Here is an optimization problem in the infinite time domain:

[0058]

[0059]

[0060]

[0061] Where z(t) k+i |t k ) and u(t) k+i |t k ) are respectively at t k t calculated at time t k+i The state prediction and optimal control variables at time points, W z and W u W represents the weight coefficient matrix corresponding to the system state variables and control input variables, respectively, and is positive definite and symmetric. z In addition to the error state quantity [y] e θ e l e ] T The weight coefficients for all states other than u are zero. maxTo optimize the maximum value of the control variable, it is given based on the vehicle's steering capability. During the optimization problem solution process, the magnitude of the output control variable is guaranteed not to exceed u. max ;

[0062] S4.2 Design a path tracking controller based on the robust model predictive control method:

[0063] u(t k+i |t k )=Kz(t k+i |t k ),

[0064] Where K is the feedback gain obtained considering the system model and ensuring the asymptotic stability of the closed-loop system, it can be expressed as K = YQ -1 If there exists γ > 0 and λ > 0, and the state feedback controller u(t) exists... k+i |t k )=Kz(t k+i |t k The system satisfies the stability condition, where Y and Q are both symmetric positive definite matrices, and Q = γP. -1 Then K is obtained by solving the following optimization problem of linear matrix inequalities:

[0065]

[0066] st

[0067]

[0068]

[0069]

[0070]

[0071] Where * denotes a symmetric term in the matrix, tr(Φ) denotes the trace of matrix Φ, and I n Let diag(t1,t2,...,t) represent an identity matrix of dimension n. n ) indicates that it contains t i The diagonal matrix of the term is obtained by solving an optimization problem based on linear matrix inequalities to obtain Y and Q, thereby obtaining the state feedback gain K = YQ. -1 Based on the LPV method, a state feedback controller is proposed:

[0072]

[0073] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0074] 1. This invention utilizes look-ahead distance in the kinematic model, introducing look-ahead error and curvature. The look-ahead error changes significantly according to the curvature of the path in front of the vehicle. The error can be significantly reduced by using a state feedback controller.

[0075] 2. This invention considers time-varying speed and establishes a vehicle lateral dynamics model with linear parameter variation (LPV). In order to model the input delay problem, the model is expanded in dimension based on the lateral dynamics model, and the control input with a delay period is added to the system state to compensate for the impact of input delay.

[0076] 3. This invention designs a path tracking controller based on robust model predictive control. This controller is obtained by the Lyapunov asymptotic stability principle and solving an optimization problem based on linear matrix inequalities (LMI). It can ensure vehicle stability and improve tracking accuracy under the conditions of input delay and time-varying speed. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the unmanned vehicle path tracking of the present invention;

[0078] Figure 2 A flowchart of the autonomous vehicle tracking control method considering input delay and speed time variation according to the present invention;

[0079] Figure 3 This is a curve diagram showing the curvature change reference path tracking in an embodiment of the present invention;

[0080] Figure 4 This is a lateral error tracking curve diagram of an embodiment of the present invention;

[0081] Figure 5 This is a diagram showing the heading angle error tracking error curve of an embodiment of the present invention;

[0082] Figure 6 This is a curve of the control quantity δ of an unmanned vehicle according to an embodiment of the present invention. Detailed Implementation

[0083] The present invention will be further described in detail below with reference to embodiments:

[0084] The purpose of this invention is to provide a vehicle path tracking control method that considers time-varying control speed and input delay. This method amplifies the impact of changes in the forward path on vehicle tracking accuracy and control performance by introducing look-ahead distance. Simultaneously, considering the time-varying effect of vehicle speed, a linear parameter variation method is used to treat the vehicle's longitudinal speed as a time-varying parameter of the lateral dynamics model. To model the input delay problem, the above model is extended in dimension, and the system state is increased by a control input with a delay period to compensate for the impact of input delay. A path tracking controller based on robust model predictive control is designed. This controller is derived from the Lyapunov asymptotic stability principle and solving an optimization problem based on linear matrix inequalities (LMI), which can ensure vehicle stability and improve tracking accuracy under conditions of input delay and time-varying speed.

[0085] To achieve the above objectives, the present invention adopts the following technical solution: a tracking and control method for unmanned vehicles that considers input delay and time-varying speed, such as... Figures 1 to 2 As shown, it includes the following steps:

[0086] S1. Establish a lateral dynamics model of the vehicle. Based on this, establish a kinematic model that includes both look-ahead distance and curvature. The tracking error of the look-ahead point can be calculated using the look-ahead distance, and the state-space expression is given. The specific steps are as follows:

[0087] S1.1 Construct a two-degree-of-freedom vehicle lateral dynamics model in the local coordinate system;

[0088]

[0089] Where v x (t) and v y (t) represents the longitudinal and lateral velocities of the vehicle, respectively, ω(t) represents the yaw rate of the vehicle, and F xf (t) and F xr (t) represents the resultant longitudinal forces of the front and rear axles of the vehicle, F. yf (t) and F yr (t) represent the resultant lateral forces on the front and rear axles of the vehicle, respectively. f and l r Here, δ(t) represents the distances from the front and rear wheels to the vehicle's center of gravity, respectively, and the front wheel deflection angle is δ(t). In vehicle lateral control, the resultant longitudinal force F of the front axle is usually neglected. xf The effect of (t) is that the front wheel deflection angle is assumed to be a small angle, satisfying cosδ(t)≈1. Therefore, the lateral dynamics model of the vehicle can be expressed as:

[0090]

[0091] When a vehicle is moving with relatively small lateral acceleration, the tire can be approximated using a linear model. The tire lateral force can be calculated by employing an equivalent tire lateral stiffness C. f and C r To simplify controller design, the lateral stiffness is considered constant, and the tire lateral force is calculated as follows:

[0092]

[0093] Where, α f and α r Let be the slip angles of the front and rear axles of the vehicle, respectively. They can be approximated by the following equation:

[0094]

[0095] S1.2, Analyze the vehicle's kinematics, y e (t) represents the vehicle's lateral tracking error, defined as the distance between the vehicle's center of mass and the reference point P1, and its derivative can be calculated using the following equation:

[0096]

[0097] Where θ e (t) represents the vehicle yaw angle error, defined as the deviation between the vehicle's yaw angle and the yaw angle of the reference trajectory point. Since the yaw angle error is typically assumed to be a small angle in vehicle lateral control, sinθ... e ≈θ e Therefore, the derivative of the lateral tracking error can be converted to:

[0098]

[0099] Use KV x (t) represents the reference angular velocity, and the derivative of the yaw angle error can be expressed as:

[0100]

[0101] l e (t) represents the look-ahead error, and its derivative can be obtained from the following equation:

[0102]

[0103] Based on the above vehicle kinematics and dynamics model, the state-space expression of the vehicle system is given as follows:

[0104]

[0105] Wherein, the system state vector is Let the product of path curvature and longitudinal velocity be the system disturbance w(t) = kvx System matrix A, control matrix B u And coefficient matrix B w They are represented as follows:

[0106]

[0107] S2. Considering the time-varying speed of the autonomous vehicle, the longitudinal speed of the vehicle is taken as a time-varying parameter. The lateral dynamics model of the vehicle is improved based on the linear parameter variation (LPV) method. The specific steps are as follows:

[0108] S2.1 The vehicle's longitudinal velocity is set to be time-varying, thus providing a vehicle model considering time-varying parameters. The LPV modeling method is used to model the time-varying longitudinal velocity v. x To perform the modeling, two time-varying parameters are selected as follows:

[0109] π1=v x ,

[0110] The range of time-varying parameters can be expressed as:

[0111] π1∈[π 1,min ,π 1,max ],π2∈[π 2,min ,π 2,max ]

[0112] π i,min and π i,max (i = 1, 2) represent the minimum and maximum vehicle speeds, respectively. Therefore, the system matrix A can be represented as:

[0113]

[0114] The time-varying parameter vector can be represented as π = [π1 π2] T We can take the maximum and minimum values ​​of these two parameters respectively, resulting in a total of 4 combinations. However, the extreme values ​​of the two parameters are contradictory, so there are two possible combinations: Ω1 and Ω2.

[0115]

[0116] Ω1=[π 1,max π 2,min ],Ω2=[π 1,min π 2,max ]

[0117] Therefore, the state-space expression of the system is:

[0118]

[0119] The two weight coefficients of the LPV model can be obtained from the following expressions:

[0120] θ1=σ(1-λ), θ2=(1-σ)λ

[0121] in,

[0122] S3. Model the input delay problem. Based on the LPV-based transverse dynamics model, extend the model's dimension by adding control inputs with delay cycles to the system state to compensate for the impact of input delay. The specific steps are as follows:

[0123] S3.1 To consider the impact of input delay on the system, we first model the input delay system:

[0124]

[0125] Where p is the input delay, and the delay time is measurable.

[0126] S3.2 In order to compensate for the impact of input delay, the system needs to be represented in discrete form, and the system state needs to be expanded in dimension, as follows:

[0127]

[0128] Where N is the number of delay periods, δ(t) k-i ) for t k-i The control input signal at each moment. The system state space is represented in the augmented system form:

[0129]

[0130] in,

[0131]

[0132] make And satisfy Where β is a positive definite constant.

[0133] S4. Design a path tracking controller based on robust model predictive control, which can be obtained by solving an optimization problem based on linear matrix inequalities (LMI). It can ensure vehicle stability and improve tracking accuracy under conditions of time-varying speed and input delay. The specific steps are as follows:

[0134] S4.1. An optimization problem in the infinite time domain is given;

[0135]

[0136]

[0137]

[0138] Where z(t) k+i |t k ) and u(t) k+i |t k ) are respectively at t k t calculated at time t k+i The state prediction and optimal control variables at each time step. W z and W u These are the weighting coefficient matrices corresponding to the system state variables and control input variables, respectively, and are positive definite and symmetric. It is important to note that W... z In addition to the error state quantity [y] e θ e l e ] T The weight coefficients for all states other than u are zero. max To optimize the maximum value of the control variable, it is given based on the vehicle's steering capability. During the optimization problem solution process, the magnitude of the output control variable is guaranteed not to exceed u. max .

[0139] S4.2 Design a path tracking controller based on the robust model predictive control method;

[0140] u(t k+i |t k )=Kz(t k+i |t k )

[0141] Where K is the feedback gain obtained considering the system model and ensuring the asymptotic stability of the closed-loop system, it can be expressed as K = YQ -1 If there exists γ > 0 and λ > 0, and the state feedback controller u(t) exists... k+i |t k )=Kz(t k+i |t k The system satisfies the stability condition, where Y and Q are both symmetric positive definite matrices, and Q = γP. -1 Then K is obtained by solving the following LMI optimization problem:

[0142]

[0143] st

[0144]

[0145]

[0146]

[0147]

[0148] Where * denotes a symmetric term in the matrix, tr(Φ) denotes the trace of matrix Φ, and I n Let diag(t1,t2,...,t) represent an identity matrix of dimension n. n ) indicates that it contains t i The diagonal matrix of the terms. Y and Q can be obtained by solving the LMI-based optimization problem, and thus the state feedback gain K = YQ can be calculated. -1 Based on the LPV method, a state feedback controller is proposed:

[0149]

[0150] Furthermore, the derivation of the above matrix inequality results is given. The magnitude input constraint must be satisfied during the solution process of the robust model predictive controller:

[0151]

[0152] Convert it to matrix inequality form:

[0153]

[0154] Right now:

[0155]

[0156] V(z(t k )) is the cost function J ∞ The upper bound of (k) can be minimized by solving the following optimization problem:

[0157]

[0158] st

[0159] f T (k)P0f(k)≤γ(k)

[0160] in P0 = diag{P, I n Based on Schuler's complement theorem, the inequality f T (k)P0f(k)≤γ(k) can be transformed into:

[0161]

[0162] Multiply by diag(I) on both sides n From P0, we can obtain:

[0163]

[0164] Let ΔV(z(t) k ))=V(z(t k+1 ))-V(z(t k Expanding it, we can express it as:

[0165]

[0166] in make Then the inequality W0(z)≤0 can be expanded as follows:

[0167]

[0168] in, Π=[A c I n ].

[0169] Based on the disturbance amplitude condition The following matrix inequalities can be obtained:

[0170]

[0171] Where, Ψ2=diag{-β 2 I n ,I n Based on Lemma 1, if W0(z) - λW1(z) ≤ 0, then W0(z) ≤ 0, from which we can obtain the inequality f. T (t k )(Ψ1+П T PΠ)f(t k )+λf T (t k )Ψ2f(t k )≤0, that is

[0172] Ψ1+Π T PΠ-λΨ2≤0

[0173] Expanding it into matrix inequality form using Schul complement theorem:

[0174]

[0175] in,

[0176]

[0177] Example

[0178] To verify the effectiveness of the proposed path tracking control method for autonomous vehicles that considers time-varying speed and input delay, simulation results are presented as verification, demonstrating that the autonomous vehicle can stably and accurately track the reference trajectory even in the presence of system input delay and time-varying speed. The specific implementation steps of the simulation are as follows:

[0179] Step S1.1: The reference path is a spliced ​​path of an arc and a straight line, obtained by collecting GPS and IMU data on actual roads. The radius of the arc is 50m. Cubic spline interpolation is used to interpolate the path data, and the path curvature is extracted as a new reference path.

[0180] Step S2.1: Provide the simulation vehicle parameters:

[0181]

[0182] Step S3.1: Select the controller parameter matrix W x W u They are respectively:

[0183] Q = diag(0,0,20,15,25), W x =diag(Q,0,...,0),W u =200

[0184] Step S4.1: The speed is set to be time-varying, with a variation range of 5m / s-10m / s and a control period of 50ms. Tracking control is performed under conditions of no time delay and a time delay period of four control periods.

[0185] Figure 3 The path tracking trajectory is shown in blue and red dashed lines. These represent the tracking paths under no-delay and delayed-delay conditions, respectively. The black solid line is the reference path. The initial state is x(t0) = [0 0 -59 355 1.52].

[0186] Figure 4 , Figure 5 These are the lateral tracking error and the heading angle error, respectively. The tracking error converges under both time delay and no time delay conditions.

[0187] Figure 6 The front wheel deflection angle obtained by the state feedback controller is within the amplitude constraint range.

Claims

1. A tracking control method for unmanned vehicles that considers input delay and time-varying speed, characterized in that: Includes the following steps: Step S1: Establish a lateral dynamics model of the vehicle. Based on this, establish a kinematic model that simultaneously includes look-ahead distance and curvature. Calculate the tracking error of the look-ahead point using the look-ahead distance and give the state-space expression. The specific process involves analyzing the vehicle's kinematics. The lateral tracking error of the vehicle is defined as the distance from the vehicle's center of gravity to the reference point. The distance between them, its derivative is calculated by the following equation: ， in, and These are the vehicle's longitudinal and lateral speeds, respectively. The vehicle yaw angle error is defined as the deviation between the vehicle yaw angle and the yaw angle of the reference trajectory point, let... Therefore, the derivative of the lateral tracking error is transformed into: ， use Representing the reference angular velocity, the derivative of the yaw angle error is expressed as: ， in, The vehicle's yaw rate; The look-ahead error, its derivative is obtained from the following equation: ， Based on the above vehicle kinematics and dynamics model, the state-space expression of the vehicle system is given as follows: Wherein, the system state vector is The product of path curvature and longitudinal velocity is set as the system disturbance. System matrix Control matrix sum coefficient matrix They are represented as follows: ； in, and Here, are the tire lateral stiffnesses of the front and rear axles of the vehicle, respectively, and are constants. and These are the distances from the center of the front axle and the center of the rear axle to the vehicle's center of gravity, respectively. Step S2: Considering the time-varying speed of the autonomous vehicle, the longitudinal speed is taken as a time-varying parameter. The lateral dynamics model of the vehicle is improved based on the linear parameter variation method. Specifically, the longitudinal speed of the vehicle is set to be time-varying, thus giving a lateral dynamics model of the vehicle considering the time-varying parameter. The linear parameter variation modeling method is used to model the time-varying longitudinal speed. To perform the modeling, two time-varying parameters are selected as follows: ， The range of time-varying parameters is expressed as follows: ， and Let represent the minimum and maximum vehicle speeds, respectively. Then, the system matrix... Represented as: ， The time-varying parameter vector is represented as Take respectively and The maximum and minimum values; Therefore, the state-space expression of the system is: ， The two weighting coefficients of the linear parameter variation model are obtained from the following expressions: ， in, ; Step S3: Model the input delay problem. Based on the linear parameter variation transverse dynamics model, expand the model's dimension by adding a control input with a delay period to the system state to compensate for the impact of the input delay. The specific steps are as follows: Step S3.1: To consider the impact of input delay on the system, we first model the input delay system: ， in, Input delay; the delay time is measurable. S3.

2. To compensate for the impact of input delay, the system is represented in discrete form, and the system state is extended in dimension, as follows: ， in, The number of delay cycles. for The control input signal at any given time is represented in the augmented system form of the system state space: ， in, ， make And satisfy ,in It is a positive definite constant; Step S4: Design a path tracking controller based on robust model predictive control. The state feedback controller is obtained by solving an optimization problem based on linear matrix inequalities, which satisfies the requirements of ensuring vehicle stability and improving tracking accuracy under conditions of time-varying speed and input delay.

2. The unmanned vehicle tracking control method considering input delay and speed time variation according to claim 1, characterized in that: The specific process of establishing the vehicle's lateral dynamics model in step S1 is as follows: A two-degree-of-freedom lateral dynamics model of the vehicle is constructed in the local coordinate system; ， in, This is the resultant force of the longitudinal forces on the front axle of the vehicle. and These represent the resultant lateral forces on the front and rear axles of the vehicle, respectively. This refers to the front wheel deflection angle; in vehicle lateral control, the resultant longitudinal force of the front axle is ignored. The function, Therefore, the lateral dynamics model of the vehicle is expressed as: ， The method for calculating tire lateral force is as follows: ， in, and Let be the tire slip angles of the front and rear axles of the vehicle, respectively, which can be approximated by the following equation: 。 3. The unmanned vehicle tracking control method considering input delay and speed time variation according to claim 2, characterized in that: The specific steps of step S4 are as follows: S4.

1. An optimization problem in the infinite time domain is given; ， in, and They are respectively in Time-based calculations The state prediction and optimal control variables at each time step and These are the weight coefficient matrices corresponding to the system state variables and control input variables, respectively, and are positive definite and symmetric. Error state quantity The weight coefficients for all states other than those specified are zero. To optimize the maximum value of the control variable, it is given based on the vehicle's steering capability. During the optimization problem solution process, the output control variable is guaranteed to not exceed [a certain value]. ; S4.2 Design a path tracking controller based on the robust model predictive control method; ， in, The feedback gain, which can be obtained while considering the system model and ensuring the asymptotic stability of the closed-loop system, is expressed as: If it exists and and state feedback controller The stability condition is satisfied, where and All are symmetric positive definite matrices. ,So This is obtained by solving the following optimization problem based on linear matrix inequalities: ， in, To represent a symmetric term in a matrix, Representation matrix traces, The dimension is The identity matrix, Indicates inclusion The diagonal matrix of the terms is obtained by solving an optimization problem based on linear matrix inequalities. and Thus, the state feedback gain is obtained. Based on the LPV method, a state feedback controller is proposed: 。

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