Quick and flexible full-pure embedded automatic driving transverse motion control method

Abstract

The invention provides a rapid and flexible full-pure embedded automatic driving transverse motion control method. The method comprises the following steps: establishing a vehicle system power model; performing continuous time system discretization processing on the vehicle system dynamic model to obtain a discrete time system for a model prediction controller; constructing a cost function and a constraint condition of the model prediction controller; and calculating an optimal control decision of the model prediction controller according to the cost function and the constraint condition. According to the method, the calculation efficiency of automatic driving transverse control MPC can be improved, so that the requirement of real-time control is met; the MPC problem is solved through the three main steps of series expansion, rational approximation and segmented continuation, the calculation speed is higher under the same precision, the calculation precision is higher within the same time, the defects that an existing method is low in calculation efficiency, low in convergence speed and the like are overcome, and the requirement for automatic driving real-time control is met.

Description

Technical Field

[0001] The present invention relates to the field of autonomous driving technology, and in particular to a fast, flexible, fully embedded autonomous driving lateral motion control method. Background Art

[0002] With the continuous development of artificial intelligence, the field of autonomous driving technology has gradually formed an architecture with three major functional modules: perception and positioning, decision-making and planning, and motion control. As a key component of autonomous driving technology, autonomous driving lateral control controls the vehicle's steering angle through the automatic steering system to drive along a given reference trajectory, making the lateral deviation of the trajectory tracking process as small as possible, which helps to improve road traffic efficiency and reduce the risk of traffic accidents.

[0003] Model Predictive Control (MPC), also known as rolling horizon control, can predict the future output behavior of the system based on the dynamic model and current state of the control 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 control objectives. It is widely used in the field of lateral control of autonomous driving.

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

[0005] Therefore, there is an urgent need to quickly and effectively improve the computational efficiency of LCP, thereby improving the real-time performance of the MPC controller to ensure the safety and stability of autonomous driving vehicles. Summary of the invention

[0006] In view of the deficiencies in the prior art, the present invention provides a fast, flexible and fully embedded autonomous driving lateral motion control method.

[0007] The technical solution of the present invention is: a fast, flexible, fully embedded automatic driving lateral motion control method, comprising the following steps:

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

[0009] S2), performing continuous-time system discretization processing on the vehicle system dynamic model to obtain a discrete-time system for a model predictive controller;

[0010] S3), constructing the 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 constraint conditions of step S3).

[0012] Preferably, in step S1), the vehicle system dynamic model includes a vehicle steering system dynamic model and a path tracking vehicle tire dynamic model.

[0013] Preferably, in step S1), the expression of the vehicle steering system dynamic model is:

[0014]

[0015] In the formula, 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 relative to the kingpin, respectively; sgn(·) is the sign function; δ is the steering wheel angle, is the steering wheel angular velocity, is the steering wheel angular acceleration.

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

[0017]

[0018] in:

[0019] C 1 = [1 0];

[0020] y 1 =δ;

[0021] 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 τ fExternal disturbance to the steering system.

[0022] Preferably, in step S1), a 2-DOF vehicle model is used to analyze the lateral dynamics during the path following process. In this embodiment, it is assumed that the angle δ is small, then cosδ≈1, sinδ≈δ, and the longitudinal velocity v x constant; therefore, the lateral acceleration of the vehicle and yaw acceleration It is expressed as:

[0023]

[0024] Where m is the vehicle mass, I z is the vehicle 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;

[0025] 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:

[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 They are α f0 ,α r0 The slope of the Fiala tire model at .

[0028] Preferably, in step S1), the lateral position Y of the vehicle and the yaw angle of the vehicle measured on the fixed earth axis are Combined into a state vector Therefore, the expression of the vehicle tire dynamic model of the path tracking is:

[0029]

[0030] in:

[0031]

[0032]

[0033] In the formula, v x ,v y are the longitudinal speed and lateral speed of the vehicle 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 They are 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:

[0035]

[0036] in:

[0037]

[0038] C=[0 2×2 C 2 ] T .

[0039] Preferably, in step S2), the continuous time system of equation (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:

[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+I 6 ,B d =T s B,N d =Ts 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; I 6 is a 6-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 vehicle's motion state.

[0044] Preferably, in step S3), the cost function J(k) and 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 time 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 (k) minimum value; δ max ,β max ,

[0048] τ mmax The constraints are 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), command:

[0051]

[0052] in:

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

[0054]

[0055] S42), command:

[0056]

[0057] Where:

[0058]

[0059]

[0060] Where, the symbol diag{·} represents a diagonal matrix;

[0061] S43), command:

[0062]

[0063] in:

[0064]

[0065] In the formula, the symbol represents the Kronecker product;

[0066] 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:

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

[0068] in,

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

[0070] Preferably, in step S44), a fast and flexible holomorphic embedding method is used to calculate the linear complementarity problem, that is:

[0071] For calculation w,z≥0, z=Mw+q,w T z=0 is equivalent to the calculation:

[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∈[h 0 ,h 1 ], where the initial point h is extended 0 =0; extension end point h 1 =1;

[0075] For any satisfying w (0) ,z (0) The 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 They are 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 linear equations satisfied;

[0083] Solving the above linear equations gives 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 a solution path that satisfies the error of the embedded system less than the given allowable error and is as close to h as possible. 1 Parameter value Will As a new starting point, Repeat the above steps until h # ≥h 1 -∈; where ∈ is the allowable error.

[0085] As a preferred embodiment, 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:

[0086]

[0087] And U * (k) Return vehicle system (7) for path tracking.

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

[0089] 1. The present invention can improve the computational efficiency of the MPC problem of lateral control of autonomous driving, thereby improving the real-time performance of the MPC controller and meeting the real-time requirements of lateral control of autonomous driving, so as to ensure the safety and stability of the autonomous driving vehicle;

[0090] 2. The present invention solves the MPC problem through three main steps: series expansion, rational approximation and piecewise extension. It has a faster calculation speed and higher calculation accuracy at the same time under the same accuracy, which solves the shortcomings of the existing methods such as low calculation efficiency and slow convergence speed, and meets the needs of real-time control of autonomous driving. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 It is a flow chart of the lateral motion control method of the present invention;

[0092] Figure 2 The present invention is a flow chart of using a fast and flexible holomorphic embedding method to calculate linear complementarity problems. DETAILED DESCRIPTION

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

[0094] like Figure 1 As shown, this embodiment provides a fast, flexible, fully embedded automatic driving lateral motion control method, including the following steps:

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

[0096] S2), performing continuous-time system discretization processing on the vehicle system dynamic model to obtain a discrete-time system for a model predictive controller;

[0097] S3), constructing the cost function and constraints of the model predictive controller;

[0098] 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.

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

[0100]

[0101] In the formula, 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 relative to the kingpin, respectively; sgn(·) is the sign function; δ is the steering wheel angle, is the steering wheel angular velocity, is the steering wheel angular acceleration.

[0102] As a preferred embodiment of this invention, in step S1), according to formula (1) and with As the state vector, the state equation of the vehicle steering system dynamic model is obtained as follows:

[0103]

[0104] in:

[0105] C 1 = [1 0];

[0106] y 1 =δ;

[0107] 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 τ f External disturbance to the steering system.

[0108] As a preferred embodiment of the present invention, in step S1), a 2-DOF vehicle model is used to analyze the lateral dynamics during the path following process. In the present embodiment, it is assumed that the angle δ is small, then cosδ≈1, sinδ≈δ, and the longitudinal velocity v xconstant; therefore, the lateral acceleration of the vehicle and yaw acceleration It is expressed as:

[0109]

[0110] Where m is the vehicle mass, I z is the vehicle 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] 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 They are α f0 ,α r0 The slope of the Fiala tire model at .

[0114] To describe the actual 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] In the formula, v x ,v y are the longitudinal speed and lateral speed of the vehicle 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 They are 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 C 2 ] T .

[0125] As a preferred embodiment of this invention, in step S2), the continuous time system of equation (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+I 6 ,B d =T s B,N d =T s N;

[0128] x(k+1) and x(k) represent the variable values ​​at 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 a preferred embodiment of this embodiment, in step S3), the cost function J(k) and the constraint conditions of the model predictive controller are respectively shown in equations (8) and (9):

[0131]

[0132] Where k is the time step; N p is the prediction time domain, N c is the control time domain, τ 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 time domain;

[0133] 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 (k) minimum value; δ max ,β max ,

[0134] τ mmax The constraints are δ, β, τ m The maximum value of (k).

[0135] As a preferred embodiment of this invention, in step S4), calculating the optimal control decision of the model predictive controller specifically includes the following steps:

[0136] S41), command:

[0137]

[0138] in:

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

[0140]

[0141] S42), command:

[0142]

[0143] Where:

[0144]

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

[0146] S43), command:

[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), the optimal control decision at the current time can be obtained by substituting the solution of the linear complementarity problem obtained by calculation.

[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, setting the order of the 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 # =h 0 = 0, extension end point h 1 =1;

[0157] S442), introduce the extension parameter h to construct the embedded system, that is:

[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 (hh # ) p ,z i (h)=∑ p≥0 η i,p (hh # ) p ,i=1,…,n;

[0161] S444) i (h),z i Substituting the power series expansion of (h) into the embedded system, we obtain the equation with the coefficients of the power series expansion as unknowns:

[0162]

[0163] Among them, 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 obtained by i (h # ),z i (h # ) directly obtained;

[0165] S446), when p=1, compare the left and right sides of the above equation (hh # ) 1 The coefficients of are:

[0166]

[0167] Among them, ξ i,0 ,η i,0 Knowing that ξ can be obtained i,1 ,η i,1 ;

[0168] S447), when p≥2, compare the left and right sides of the above equation (hh # ) p The coefficients of are:

[0169]

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

[0171] S448) Due to i,p ,η i,p (1≤p≤p max ) is a linear system of equations, which can be solved directly for ξ i,p ,η i,p (1≤p≤p max );

[0172] S449), through the power series expansion coefficient ξ i,p ,η i,p (1≤p≤p max ), construct a rational approximation function to expand the convergence domain;

[0173] S4410) Determine the following conditions in h∈[h # ,h # +ΔH] satisfies:

[0174]

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

[0176] If Δh>Δ min ,make Repeat S4410);

[0177] If Δh≤Δ min ; Exit the loop, calculation failed;

[0178] S4411), let h # ←h # +Δh, repeat steps S443)-S4410) until h # >h 1 -∈.

[0179] As a preferred method, in step S45), the rational approximation of the last series expansion is performed at h # =h 1 The solution w of the linear complementarity problem obtained at * Back-substitution to obtain the optimal control decision U at the current moment * (k), i.e.

[0180]

[0181] And U * (k) Return vehicle system (7) for path tracking.

[0182] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. A fast, flexible, fully embedded, autonomous driving lateral motion control method, characterized in that: The following steps are involved: S1), establishing a vehicle system dynamic model; 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. A fast, flexible, fully embedded, automatic driving lateral motion control method according to claim 1, characterized in that: In step S1), the vehicle system dynamic model includes a vehicle steering system dynamic model and a path tracking vehicle tire dynamic model.

3. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 2, characterized in that: The state equation of the vehicle steering system dynamic model is expressed as: in: In the formula, is the state vector; 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 relative to the kingpin, respectively; sgn(·) is the sign function; δ is the steering wheel angle, is the steering wheel angular velocity, is the steering wheel steering angle 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 τ f External disturbance to the steering system.

4. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 3, characterized in that: In step S1), the lateral dynamics of the path following process are analyzed using a 2-DOF vehicle model, and the lateral position Y of the vehicle and the yaw angle of the vehicle measured on the fixed axis are calculated. Combined into a state vector Therefore, the expression of the vehicle tire dynamic model of the path tracking is: in: In the formula, v x ,v y are the longitudinal speed and lateral speed of the vehicle 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 They are 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.

5. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 4, characterized in that: 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: in:

6. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 5, characterized in that: In step S2), the continuous time system of equation (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 vehicle's motion state.

7. A fast, flexible, fully embedded, automatic driving lateral motion control method according to claim 6, 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, 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 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 The constraints are δ, β, τ m The maximum value of (k).

8. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 7, characterized in that: In step S4), the optimal control decision of the model predictive controller is calculated, which specifically includes the following steps: S41), command: in: X ref (k) = [x ref (k+1)x ref (k+2)…x ref (k+N p )] T is the expected path; S42), command: Where: Where, the symbol diag{·} represents a diagonal matrix; S43), command: 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: with=Mw+q,w T z=0; (11) in, S45), after calculating the solution of the linear complementarity problem, back-substitution can be performed to obtain the optimal control decision at the current time.

9. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 8, 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 initial point h0=0; the extension end point h1=1; For any satisfying w (0) ,z (0) The 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 They are w i (h),z i (h) corresponds to (hh # ) \ 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 linear equations satisfied; Solving the above linear equations gives 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.

10. A fast, flexible, fully embedded automatic driving lateral motion control method according to claim 9, characterized in that: In step S45), the solution of the linear complementarity problem is * 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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