A quick flexible all-pure embedded automatic driving lateral motion control method

Abstract

The application provides a kind of fast flexible full pure embedded automatic driving lateral motion control method, including establishing vehicle system dynamic model;Vehicle system dynamic model is carried out continuous time system discretization processing, and the discrete time system for model predictive controller is obtained;The cost function and constraint condition of model predictive controller are constructed;The optimal control decision of model predictive controller is calculated according to the cost function and constraint condition.The application can improve the calculation efficiency of automatic driving lateral control MPC to meet the needs of real-time control;The application solves MPC problem through three main steps of series expansion, rational approximation and piecewise continuation, and the calculation speed is faster and the calculation accuracy is higher in the same time, solves the deficiencies such as low calculation efficiency and slow convergence speed of existing method, meets the needs of automatic driving real-time control.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic driving, and in particular to a fast and flexible full-pure embedded automatic driving lateral motion control method. BACKGROUND

[0002] With the continuous development of the field of artificial intelligence, the field of automatic driving technology gradually forms an architecture with three major functional modules of perception positioning, decision planning and motion control. As a key component of automatic driving technology, automatic driving lateral control controls the vehicle steering angle through an automatic steering system to follow the given reference trajectory, so that the lateral deviation in the trajectory tracking process is as small as possible, which helps to improve road traffic efficiency and reduce traffic accident risk.

[0003] Model predictive control (MPC) is also known as rolling horizon control. It can predict the future output behavior of the control system based on the dynamic model and current state of the system, and obtain the optimal system control input by solving the optimal control problem with constraints. It also has the ability to handle multi-constraint optimization problems, and can consider safety constraints, actuator constraints, etc. while optimizing the control objective, and is widely used in the field of automatic driving lateral control.

[0004] However, the field of automatic driving technology has high real-time requirements. Real-time performance is directly related to driving safety, vehicle control, environmental perception and decision planning, and is a key factor in realizing and optimizing automatic driving technology. For MPC controllers, a complex constrained optimization problem needs to be solved in each control period, which can be converted into a linear complementarity problem (LCP) for solving. The computational efficiency of this problem directly affects the real-time performance of the system. However, the existing iterative method (such as the interior point method) for solving LCP has strict requirements for the initial point and is highly dependent on the iteration step size, and multiple calculations and adjustments are required to find the optimal solution, resulting in low computational efficiency and difficulty in meeting the real-time requirements of automatic driving lateral control.

[0005] Therefore, there is an urgent need for a fast and efficient method to improve the computational efficiency of LCP, thereby improving the real-time performance of the MPC controller to ensure the safety and stability of the automatic driving vehicle. SUMMARY

[0006] In view of the deficiencies of the prior art, the present application provides a fast and flexible full-pure embedded automatic driving lateral motion control method.

[0007] The technical solution of the present application is: a fast and flexible full-pure embedded automatic driving lateral motion control method, comprising the following steps:

[0008] S1), establishing a vehicle system dynamic model;

[0009] S2), discretizing the continuous-time system of the vehicle system dynamics model to obtain a discrete-time system for the model predictive controller;

[0010] S3), constructing a cost function and constraints of the model predictive controller;

[0011] S4), calculating the optimal control decision of the model predictive controller according to the cost function and constraints of step S3).

[0012] Preferably, in step S1), the vehicle system dynamics model comprises a vehicle steering system dynamics model and a path following vehicle tire dynamics model.

[0013] Preferably, in step S1), the vehicle steering system dynamics model has an expression as follows:

[0014]

[0015] wherein N s , N m are the motion ratios of the motor reducer and the steering system respectively; τ m is the steering motor torque; τ f is the friction torque; τ dis is the steering resistance torque; J eq and B eq are the equivalent inertia and equivalent damping of the steering system with respect to the kingpin respectively; sgn(·) is the sign function; δ is the steering wheel steering angle, is the steering wheel steering angle velocity, is the steering wheel steering angle acceleration.

[0016] Preferably, in step S1), according to the formula (1) and taking as the state vector, the expression of the state equation of the vehicle steering system dynamics model is obtained as follows:

[0017]

[0018] wherein:

[0019] C1 = [1 0];

[0020] y1 = δ;

[0021] The above formula gives the dynamic relationship between the steering motor torque τ m and the steering wheel steering angle δ, wherein the steering resistance torque τ dis and the friction torque τ f are external disturbances of the steering system.

[0022] As a preference, in step S1), the lateral dynamics in the path following process is analyzed by using a 2-DOF vehicle model, the present embodiment assumes that the δ angle is small, then cosδ≈1, sinδ≈δ, the longitudinal velocity v x is constant; therefore, the lateral acceleration and the yaw acceleration of the vehicle are expressed as:

[0023]

[0024] where m is the vehicle mass, I z is the vehicle moment of inertia, v x , v y are the vehicle longitudinal and lateral velocities, F yf , F yr are the lateral forces of the front and rear tires, α f , α r are the slip angles of the front and rear tires, a, b are the distances from the center of the front and rear tires to the main shaft; is the yaw angle, is the yaw angular velocity;

[0025] In order to simplify the nonlinear characteristics of the tires and reduce the calculation complexity, the nonlinear tire lateral force is approximated as a linearized function of Fiala tire model curve α f and α r around the working point, which is specifically expressed as:

[0026]

[0027] where F yf0 is the lateral force of the front wheel at the starting point, F yr0 is the lateral force of the rear wheel at the starting point, C f0 , C r0 are the slopes of the Fiala tire model at α f0 , α r0 .

[0028] As a preference, in step S1), the lateral position Y of the vehicle and the yaw angle of the vehicle measured on the fixed ground shaft are combined as a state vector Therefore, the expression of the tire dynamic model of the path tracking vehicle is:

[0029]

[0030] where:

[0031]

[0032]

[0033] Where, v x ,v y are the vehicle longitudinal speed and lateral speed respectively; is the lateral acceleration of the vehicle; is the yaw acceleration; F yf0 is the lateral force of the front wheel at the starting point, F yr0 is the lateral force of the rear wheel at the starting point, C f0 ,C r0 α f0 ,α r0 The slope of the Fiala tire model at α f0 ,α r0 are the sideslip angles of the front and rear tires at the starting point; a, b are the distances from the spindle to the center of the front and rear tires; m is the vehicle mass; I z is the vehicle's moment of inertia.

[0034] Preferably, in step S1), the state equation of the vehicle steering system dynamic model of formula (2) and the state equation of the vehicle tire dynamic model of path tracking of formula (5) are uniformly expressed as follows:

[0035]

[0036] in:

[0037]

[0038] C=[0 2×2 C2] T .

[0039] As a preference, in step S2), by discretizing the continuous-time system of formula (6), the sampling interval is T s , the expression of the discrete-time system for the model predictive controller is obtained as:

[0040] x(k+1)=A d x(k)+B d τ m (k)+N d ζ(k) , (7)

[0041] in; A d =T s A+I6,B d =T s B,N d =T s N;

[0042] x(k+1) and x(k) represent the variable values ​​at the k+1th time step and the kth time step respectively; τ m is the steering motor torque; I6 is the 6th-order unit matrix; k is the time step;

[0043] The desired path of the vehicle is tracked by adjusting the torque of the motor. The steering wheel angle δ is the state variable, and the variable ζ(k) is calculated according to the motion state of the vehicle.

[0044] Preferably, in step S3), the cost function J(k) and the constraint conditions of the model predictive controller are:

[0045]

[0046] Where k is the time step; N p is the prediction time domain, N c is the control time domain, Q is the state weight matrix, and R is the input weight matrix; Q ,‖·‖ R represents the weighted norm, ε is the relaxation factor, κ is the weight coefficient, is the ratio of the horizontal and vertical speeds; x(k+i|k) represents the output prediction value of k at time k+i in the prediction time domain; x ref (k+i|k) represents the output reference value of k at time k+i in the prediction domain;

[0047] τ m (k+i|k) represents the predicted value of the steering motor torque at time k+i by k in the control time domain; δ min ,β min , τ mmin For the constraints δ,β, τ m The minimum value of (k); δ max ,β max ,

[0048] τ mmax Constraints δ, β, τ m The maximum value of (k).

[0049] Preferably, in step S4), calculating the optimal control decision of the model predictive controller specifically includes the following steps:

[0050] S41) Order:

[0051]

[0052] in:

[0053] X ref(k) = [x ref (k+1)x ref (k+2)…x ref (k+N p )] T is the desired path;

[0054]

[0055] S42), let:

[0056]

[0057] wherein:

[0058]

[0059]

[0060] wherein the symbol diag{·} denotes a diagonal matrix;

[0061] S43), let:

[0062]

[0063] wherein:

[0064]

[0065] wherein the symbol denotes a Kronecker product;

[0066] S44), let the Lagrange multiplier vector be w and the nonnegative slack vector be z, then the first-order optimality conditions of the optimization problem can be expressed as a linear complementarity problem, i.e. to calculate w, z≥0 such that:

[0067] z = Mw + q, w T z = 0; (11)

[0068] wherein,

[0069] S45), after calculating the solution of the linear complementarity problem, the optimal control decision at the current time can be obtained by back substitution.

[0070] As preferred, in step S44), the fast flexible holomorphic embedding method is used to calculate the linear complementarity problem, i.e.

[0071] For calculating w, z≥0 such that z = Mw + q, w T z = 0 is equivalent to calculating:

[0072]

[0073] Where n is the number of unknowns;

[0074] In addition, in order to solve the above problem, this embodiment introduces an extension parameter h∈[h0,h1], where the extension starting point h0=0; the extension end point h1=1;

[0075] For any satisfying w (0) ,z (0) Initial point w ≥ 0 (0) ,z (0) ; Design the following embedded system:

[0076]

[0077] in:

[0078]

[0079] At any point h # At , expand w(h),z(h) into a power series form:

[0080]

[0081] Where p is the order of the power series, ξ i,p ,η i,p w i (h),z i (h) corresponds to (hh # ) p The coefficient of the term;

[0082] Substitute equation (14) into equation (13) and compare the left and right sides of the equation (hh # ) p The coefficient of the term determines the power series coefficient ξ i,p ,η i,p the system of linear equations satisfied;

[0083] Solving the above linear equations can yield w i (h),z i (h) is expanded into a power series, and then a rational approximation function is constructed based on the obtained power series coefficients to expand the convergence region;

[0084] Next, find the parameter value in the solution path that satisfies the error of the embedded system less than the given allowable error and is as close to h1 as possible. Will As a new starting point, Repeat the above steps until h # ≥h1-∈; where ∈ is the allowable error.

[0085] As preferred, in step S45), the solution w of the linear complementarity problem is obtained by * Substitution obtains the optimal control decision U of the current moment * (k), namely:

[0086]

[0087] and returns U * (k) to the vehicle system (7) for path tracking.

[0088] The beneficial effects of the present application are:

[0089] 1. The present application can improve the calculation efficiency of automatic driving lateral control MPC problem, thereby improving the real-time performance of MPC controller, meeting the real-time demand of automatic driving lateral control, and ensuring the safety and stability of automatic driving vehicles.

[0090] 2. The present application solves the problems of low calculation efficiency and slow convergence speed of the existing method by solving the MPC problem through three main steps of series expansion, rational approximation and piecewise continuation, and has faster calculation speed and higher calculation accuracy in the same time, which meets the needs of automatic driving real-time control. BRIEF DESCRIPTION OF DRAWINGS

[0091] Figure 1 The flow framework diagram of the lateral motion control method of the present application;

[0092] Figure 2 The flowchart of the present application using fast flexible holomorphic embedding method to calculate linear complementarity problem. DETAILED DESCRIPTION

[0093] The specific embodiments of the present application will be further described below in conjunction with the accompanying drawings:

[0094] As Figure 1 shown, the present embodiment provides a fast flexible holomorphic embedded automatic driving lateral motion control method, which comprises the following steps:

[0095] S1), a vehicle system dynamic model is established; wherein the vehicle system dynamic model includes a vehicle steering system dynamic model and a path tracking vehicle tire dynamic model.

[0096] S2), the vehicle system dynamic model is discretized into a discrete time system for model predictive controller;

[0097] S3), a cost function and constraint condition of the model predictive controller are constructed;

[0098] S4) calculating the optimal control decision of the model predictive controller according to the cost function and the constraints of step S3) and using the fast flexible holonomic embedding method.

[0099] As preferred in the present embodiment, in step S1), the expression of the vehicle steering system dynamic model is:

[0100]

[0101] wherein N s , N m are the motion ratios of the motor reducer and the steering system respectively; τ m is the steering motor torque; τ f is the friction torque; τ dis is the steering resistance torque; j eq and B eq are the equivalent inertia and equivalent damping of the steering system with respect to the kingpin respectively; sgn(·) is the sign function; δ is the steering wheel steering angle, is the steering wheel steering angle velocity, is the steering wheel steering angle acceleration.

[0102] As preferred in the present embodiment, in step S1), according to formula (1) and taking as the state vector, the expression of the state equation of the vehicle steering system dynamic model is obtained as:

[0103]

[0104] wherein:

[0105] C1 = [1 0];

[0106] y1 = δ;

[0107] The above formula gives the dynamic relationship between the steering motor torque τ m and the steering wheel steering angle δ, wherein the steering resistance torque τ dis and the friction torque τ f are the external disturbances of the steering system.

[0108] As preferred in the present embodiment, in step S1), the lateral dynamics in the path following process is analyzed using a 2-DOF vehicle model, and the present embodiment assumes that the δ angle is small, so cos δ ≈ 1 and sin δ ≈ δ, and the longitudinal velocity v x is considered constant; therefore, the lateral acceleration and the yaw acceleration of the vehicle are expressed as:

[0109]

[0110] Where m is the vehicle mass, I z is the vehicle's moment of inertia, v x ,v y are the longitudinal and lateral velocities of the vehicle, respectively, and F yf ,F yr is the lateral force of the front and rear tires, α f ,α r is the sideslip angle of the front and rear tires, a, b is the distance from the main axis to the center of the front and rear tires; is the yaw angle, is the yaw angular velocity;

[0111] In order to simplify the nonlinear characteristics of the tire and reduce the computational complexity, the nonlinear tire lateral force is approximated as the Fiala tire model curve α f and α r The linearization function near the working point is specifically expressed as:

[0112]

[0113] Among them F yf0 is the lateral force of the front wheel at the starting point, F yr0 is the lateral force of the rear wheel at the starting point, C f0 ,C r0 α f0 ,α r0 The slope of the Fiala tire model at .

[0114] In order to describe the real trajectory of the vehicle, the lateral position Y of the vehicle and the yaw angle of the vehicle measured on the fixed axis are Combined into a state vector Therefore, the expression of the vehicle tire dynamic model of the path tracking is:

[0115]

[0116] in:

[0117]

[0118]

[0119] Where, v x ,v y are the vehicle longitudinal speed and lateral speed respectively; is the lateral acceleration of the vehicle; is the yaw acceleration; F yf0 is the lateral force of the front wheel at the starting point, F yr0 is the lateral force of the rear wheel at the starting point, C f0 ,Cr0 α f0 ,α r0 The slope of the Fiala tire model at α f0 ,α r0 are the sideslip angles of the front and rear tires at the starting point; a, b are the distances from the spindle to the center of the front and rear tires; m is the vehicle mass; I z is the vehicle's moment of inertia.

[0120] As a preferred embodiment of this invention, in step S1), the state equation of the vehicle steering system dynamic model of formula (2) and the state equation of the vehicle tire dynamic model of path tracking of formula (5) are expressed as the following integrated system:

[0121]

[0122] in:

[0123] ζ=[ω τ ζ s ] T ;

[0124] C=[0 2×2 C2] T .

[0125] As a preferred embodiment of the present invention, in step S2), the continuous time system of formula (6) is discretized and the sampling interval is T s , the expression of the discrete-time system for the model predictive controller is obtained as:

[0126] x(k+1)=A d x(k)+B d τ m (k)+N d ζ(K), (7)

[0127] in; A d =T s A+I6,B d =T s B,N d =T s N;

[0128] x(k+1) and x(k) represent the variable values ​​of the k+1th time step and the kth time step respectively; I6 is the 6th-order unit matrix; τ m is the steering motor torque; k is the time step;

[0129] The desired path of the vehicle is tracked by adjusting the torque of the motor. The steering wheel angle δ is the state variable, and the variable ζ(K) is calculated according to the motion state of the vehicle.

[0130] As preferred in the embodiment, in step S3), the cost function J(k) and the constraint condition of the model predictive controller are respectively shown as formula (8) and formula (9):

[0131]

[0132] In the formula, k is a time step; N p is a prediction time domain, N c is a control time domain, τ is a state weight matrix, R is an input weight matrix; ‖·‖ Q ,‖·‖ R denotes a weighted norm, ε is a relaxation factor, κ is a weight coefficient, is a lateral-longitudinal velocity ratio; x(k+i|k) denotes an output prediction value at k to k+i in the prediction time domain; x ref (k+i|k) denotes an output reference value at k to k+i in the prediction time domain;

[0133] τ m (k+i|k) denotes a prediction value of the steering motor torque at k to k+i in the control time domain; δ min ,β min , τ mmin is a constraint of δ, β, τ m (k) is a minimum value; δ max ,β max ,

[0134] τ mmax is a maximum value of the constraint δ, β, τ m (k) respectively.

[0135] As preferred in the embodiment, in step S4), the optimal control decision of the model predictive controller is calculated, specifically including the following steps:

[0136] S41), let:

[0137]

[0138] Wherein:

[0139] X ref (k)=[x ref (k+1)x ref (k+2)…x ref (k+N p )] T is an expected path;

[0140]

[0141] S42), order:

[0142]

[0143] Where:

[0144]

[0145] Where, the symbol diag{·} represents a diagonal matrix;

[0146] S43) Order:

[0147]

[0148] in:

[0149]

[0150] In the formula, the symbol represents the Kronecker product;

[0151] S44) Let the Lagrange multiplier vector be w, the non-negative relaxation vector be z, and express the first-order optimality condition of the optimization problem as a linear complementarity problem, that is, calculate w, z ≥ 0 so that:

[0152] z=Mw+q,w T z=0; (11)

[0153] in,

[0154] S45) Substituting the calculated solution of the linear complementarity problem back into the optimal control decision at the current time.

[0155] As preferred in this embodiment, Figure 2 As shown, in step S44), a fast and flexible holomorphic embedding method is used to calculate the linear complementarity problem, which specifically includes the following steps:

[0156] S441), initialization, set the order of power series expansion to p max , allowable error is ∈>0, initial extension interval Δh int >0, minimum threshold of extension interval Δ min , reduction ratio Initial iteration point w (0) ,z (0) , extend the initial point h # =h0=0, the extension end point h1=1;

[0157] S442) Introduce the extension parameter h to construct the embedded system, namely:

[0158]

[0159] S443), let Δh = Δh int , at point h # w i (h), z i (h) is expressed as a power series expansion:

[0160] w i (h) = ∑ p≥0 ξ i,p (h - h # ) p , z i (h) = ∑ p≥0 η i,p (h - h # ) p , i = 1, …, n;

[0161] S444), the power series expansion of w i (h), z i (h) is substituted into the embedding system, to obtain equations with power series expansion coefficients as unknowns:

[0162]

[0163] where γ p = [ξ 1,p ξ 2,p … ξ n,p ] T ; p = 0, 1, …, p max ;

[0164] S445), when p = 0, ξ i,0 , η i,0 can be directly obtained from w i (h # ), z i (h # );

[0165] S446), when p = 1, compare the coefficients of (h - h # ) 1 on both sides of the above equation, we have:

[0166]

[0167] where ξ i,0 , η i,0 are known, and ξ i,1 , η i,1 can be solved;

[0168] S447), when p≥2, compare the coefficients of (h-h # ) p

[0169]

[0170] At this time, ξ i,0 ,ξ i,1 ,…,ξ i,p-1 ;η i,0 ,η i,1 ,…,η i,p-1 are known;ξ i,p ,η i,p can be calculated;

[0171] S448), since the equations satisfied by ξ i,p ,η i,p (1≤p≤p max ) are linear equations,ξ i,p ,η i,p (1≤p≤p max ) can be directly solved;

[0172] S449), by the power series expansion coefficients ξ i,p ,η i,p (1≤p≤p max ) that have been solved, construct a rational approximation function to expand the convergence domain;

[0173] S4410), determine whether the following conditions are met when h∈[h # ,h # +ΔH]:

[0174]

[0175] If yes, go to S4411); if not, reduce the interval Δh; until the condition is met; the specific process is as follows:

[0176] If Δh>Δ min , let repeat S4410);

[0177] If Δh≤Δ min ; exit the loop, the calculation fails;

[0178] S4411), let h # ←h # +Δh, repeat steps S443)-S4410), until h # >h1-∈.

[0179] As a preferred, in step S45), the rational approximation of the last series expansion is h​# = h1- e the solution of the linear complementarity problem obtained at * Substitution gives the optimal control decision U * (k), i.e.

[0180]

[0181] and return U * (k) to the vehicle system (7) for path tracking.

[0182] The embodiments and examples described above are only illustrative of the principles and best modes of the application, and various changes and modifications can be made without departing from the spirit and scope of the application, which are defined in the claims.

Claims

1. A fast, flexible, fully embedded, autonomous driving lateral motion control method, characterized by: The following steps are involved: S1), establishing a vehicle system dynamic model; The vehicle system dynamic model includes a vehicle steering system dynamic model and a path tracking vehicle tire dynamic model; The state equation of the vehicle steering system dynamic model is expressed as: in: C1＝[1 0]； y1=δ; Where, is the state vector; N s 、N m are the motion ratios of the motor reducer and steering system respectively; τ m is the steering motor torque; τ f is the friction torque; τ dis is the steering resistance torque; J eq and B eq are the equivalent inertia and equivalent damping of the steering system relative to the kingpin; sgn(·) is the sign function; δ is the steering wheel angle, is the steering wheel angular velocity, is the steering wheel angular acceleration; The above formula gives the steering motor torque τ m The dynamic relationship between the steering wheel angle δ and the steering resistance torque τ dis and friction torque t f External disturbances to the steering system; The lateral dynamics during the path following process are analyzed using a 2-DOF vehicle model, where the vehicle's lateral position Y and the vehicle's yaw angle measured on a fixed earth axis are calculated. Combined into a state vector Therefore, the expression of the vehicle tire dynamic model of the path tracking is: in: Where, v x ,v y are the vehicle longitudinal speed and lateral speed respectively; is the lateral acceleration of the vehicle; is the yaw acceleration; F yf0 is the lateral force of the front wheel at the starting point, F yr0 is the lateral force of the rear wheel at the starting point, C f0 ,C r0 α f0 ,α r0 The slope of the Fiala tire model at α f0 ,α r0 are the sideslip angles of the front and rear tires at the starting point; a, b are the distances from the spindle to the center of the front and rear tires; m is the vehicle mass; I z is the vehicle's moment of inertia; The state equation of the vehicle steering system dynamic model of formula (2) and the state equation of the vehicle tire dynamic model of path tracking of formula (5) are unified as follows: in: ζ=[ω τ g s ] T ; C=[0 2×2 C2] T ; S2), performing continuous-time system discretization processing on the vehicle system dynamic model to obtain a discrete-time system for a model predictive controller; S3), constructing the cost function and constraints of the model predictive controller; S4), according to the cost function and constraints of step S3), a fast and flexible holomorphic embedding method is used to calculate the optimal control decision of the model predictive controller.

2. The fast, flexible, fully embedded, autonomous driving lateral motion control method according to claim 1, characterized in that: In step S2), the continuous time system of formula (6) is discretized and the sampling interval is T s , the expression of the discrete-time system for the model predictive controller is obtained as: x(k+1)=A d x(k)+B d t m (k)+N d g(k);(7) in; A d =T s A+I6,B d =T s B,N d =T s N; x(k+1) and x(k) represent the variable values ​​at the k+1th time step and the kth time step, respectively; τ m is the steering motor torque; I6 is the 6th-order unit matrix; k is the time step; The desired path of the vehicle is tracked by adjusting the torque of the motor. The steering wheel angle δ is the state variable, and the variable ζ(k) is calculated according to the motion state of the vehicle.

3. The fast, flexible, fully embedded, autonomous driving lateral motion control method according to claim 2, characterized in that: In step S3), the cost function J(k) and constraints of the model predictive controller are: Where k is the time step; N p is the prediction time domain, N c is the control time domain, Q is the state weight matrix, and R is the input weight matrix; Q ,‖·‖ R represents the weighted norm, ε is the relaxation factor, k is the weight coefficient, is the ratio of the horizontal and vertical speeds; x(k+i|k) represents the output prediction value of k at time k+i in the prediction time domain; x ref (k+i|k) represents the output reference value of k at time k+i in the prediction time domain; τ m (k+i|k) represents the predicted value of the steering motor torque at time k+i by k in the control time domain; δ min ,β min , τ mmin For the constraints δ,β, τ m The minimum value of (k); δ max ,β max , τ mmax Constraints δ, β, τ m The maximum value of (k).

4. The fast, flexible, fully embedded, autonomous driving lateral motion control method according to claim 3, characterized in that: In step S4), the optimal control decision of the model predictive controller is calculated, which specifically includes the following steps: S41) Order: in: X ref (k) = [x ref (k+1)x ref (k+2)…x ref (k+N p )] t is the expected path; S42), order: Where: Where, the symbol diag{·} represents a diagonal matrix; S43) Order: in: In the formula, the symbol represents the Kronecker product; S44) Let the Lagrange multiplier vector be w and the non-negative relaxation vector be z. Then the first-order optimality condition of the optimization problem can be expressed as a linear complementarity problem, that is, calculate w, z ≥ 0 so that: z=Mw+q,w T z=0; (11) in, S45) Calculate the solution of the linear complementarity problem and then perform back substitution to obtain the optimal control decision at the current time.

5. The fast, flexible, fully embedded, autonomous driving lateral motion control method according to claim 4, characterized in that: In step S44), a fast and flexible holomorphic embedding method is used to calculate the linear complementarity problem, namely: For calculation w,z≥0, z=Mw+q,w T z=0, which is equivalent to the calculation: Where n is the number of unknowns; In addition, in order to solve the above problem, this embodiment introduces an extension parameter h∈[h0,h1], where the extension starting point h0=0; the extension end point h1=1; For any satisfying w (0) ,z (0) Initial point w ≥ 0 (0) ,z (0) ; Design the following embedded system: in: At any point h # At , expand w(h),z(h) into a power series form: Where p is the order of the power series, ξ i,p ,η i,p w i (h),z i (h) corresponds to (hh # ) p The coefficient of the term; Substitute equation (14) into equation (13) and compare the left and right sides of the equation (hh # ) p The coefficient of the term determines the power series coefficient ξ i,p ,η i,p the system of linear equations satisfied; Solving the above linear equations can yield w i (h),z i (h) is expanded into a power series, and then a rational approximation function is constructed based on the obtained power series coefficients to expand the convergence region; Next, find the parameter value in the solution path that satisfies the error of the embedded system less than the given allowable error and is as close to h1 as possible. Will As a new starting point, Repeat the above steps until h # ≥h1-∈; where ∈ is the allowable error.

6. The fast, flexible, fully embedded, autonomous driving lateral motion control method according to claim 5, characterized in that: In step S45), the solution of the linear complementarity problem w * Back-substitution to obtain the optimal control decision U at the current moment * (k), namely: And U * (k) Return vehicle system (7) for path tracking.

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