CN113320542A - Tracking control method for automatic driving vehicle - Google Patents

Abstract

A tracking control method of an automatic driving vehicle is provided, which is characterized in that a vehicle dynamic model considering road inclination and curvature is pre-established, and the method also comprises the following steps: 1) constructing a dynamic prediction process at the current moment based on a vehicle dynamics model, and designing an extended model prediction controller considering driving path information; 2) acquiring the state information of the vehicle at the current moment, and establishing a constraint envelope according to the state information; 3) solving by utilizing a differential evolution algorithm according to a dynamic prediction process and a constraint envelope to obtain an optimal control steering angle at the current moment, and controlling the vehicle to autonomously track an optimal smooth path in a drivable road area according to the optimal control steering angle; 4) and returning to the step 1) to calculate the optimal control steering angle of the next control period until the vehicle reaches the end point of the path. The invention can process the dynamic interactive information between the vehicle and the road surface in the process of path tracking, fully utilizes the maneuverability of the automatic driving vehicle and realizes the stable and smooth path tracking control in the travelable road area.

Description

Tracking control method for automatic driving vehicle

Technical Field

The invention relates to the field of automatic driving vehicle motion control, in particular to a tracking control method of an automatic driving vehicle.

Background

The automatic driving vehicle has the advantages of being capable of predicting driving behaviors, reducing traffic accidents, relieving traffic pressure and the like, and has wide application prospects in future intelligent traffic systems and military fields. After decades of research and experiments, the automatic driving technology is continuously improved from auxiliary driving to full-automatic driving. The full-automatic driving vehicle needs to construct key technologies such as map positioning, environment perception and decision, motion control and the like from top to bottom. Path tracking is the key functional part of implementing the motion control layer and directly determines the overall performance of the autonomous vehicle. The path tracking control is used for researching how to control the action of a steering actuator to drive along an ideal lane path on the premise of considering driving safety and riding comfort according to motion planning and vehicle driving state feedback information. In the path tracking control, the tracking precision and the driving stability are difficult to be simultaneously ensured, and the path tracking performance of the automatic driving vehicle under different driving conditions can be effectively improved by considering the further integrated interaction between the vehicle and the road dynamic information.

The highly dynamic nonlinear characteristics and coupling of the vehicle itself and the susceptibility to external disturbances make it challenging to implement accurate path tracking control of an autonomous vehicle. At present, many classical control methods have been widely applied to path tracking, and can be mainly classified into the following categories: 1) geometric motion control, mainly pure trajectory tracking, Stanley control and the like; 2) model-free control, mainly PID control, fuzzy control, neural network control and the like; 3) the state feedback control mainly comprises LQG control, sliding mode control and H_∞Robust control, etc.; the above method doesThe constraints of the vehicle and the road can be effectively considered, and the actuator can be saturated and even the dynamics can be unstable. 4) And (3) model prediction control, wherein the model prediction control method can predict the multi-step output behavior of the future nonlinear system, and the following error of the system is controlled and corrected by solving the constrained optimal target problem in a rolling manner. Model predictive control has been widely used for path tracking in autonomous vehicles, since it explicitly solves the multi-constraint problem of multiple-input multiple-output systems in complex dynamic environments.

In the existing path tracking problem, the central line of a road is strictly tracked by minimizing lateral error and heading error, or path planning and tracking problems are respectively solved by two independent controllers. However, a reference path obtained from a road center line or path planning is usually not smooth enough and even conflicts with the vehicle motion characteristics, the above method generally lacks consideration of the interaction between the vehicle and the road dynamic information, and the direct following of the reference path easily causes unstable phenomena such as response overshoot, oscillation and the like.

Disclosure of Invention

The invention mainly aims to overcome the defects in the path tracking problem and provide a tracking control method of an automatic driving vehicle.

The invention adopts the following technical scheme:

a tracking control method for an autonomous vehicle is characterized in that a vehicle dynamic model considering road inclination and curvature is established in advance, and the control method comprises the following steps:

1) constructing a dynamic prediction process at the current moment based on a vehicle dynamics model, and designing an extended model prediction controller considering driving path information;

2) acquiring state information of a vehicle at the current moment through a vehicle dynamics model, and establishing a constraint envelope according to the state information, wherein the constraint envelope comprises anti-slip constraint, anti-rollover constraint, drivable road region constraint and extended model predictive controller constraint;

3) solving by using a differential evolution algorithm according to a dynamic prediction process and a constraint envelope to obtain an optimal control steering angle at the current moment, and controlling the vehicle to autonomously track an optimal smooth path in a travelable road area by the extended model prediction controller according to the optimal control steering angle;

4) and returning to the step 1) to calculate the optimal control steering angle of the next control period until the vehicle reaches the end point of the path.

The three-degree-of-freedom dynamic model of the vehicle dynamic model comprises the following specific steps:

wherein m and m_sVehicle mass and sprung mass, respectively; g is the acceleration of gravity; l_fAnd l_rThe distances from the center of mass of the vehicle to the front axle and the rear axle respectively; i is_xAnd I_zRoll and yaw moments of inertia, respectively;

and

respectively vehicle roll stiffness and damping coefficient; h is the distance from the center of mass of the vehicle to the center of roll; r is the vehicle yaw rate;

yaw acceleration of the vehicle; psi is the vehicle yaw angle; κ is a reference road curvature; v. of_xAnd v_yLongitudinal and lateral velocities, respectively;

is the lateral acceleration; f_yfAnd F_yrThe lateral force of the front wheel and the rear wheel is respectively;

and

respectively as a vehicle roll angle and a road roll angle;

and

roll velocity and roll acceleration of the vehicle, respectively; e.g. of the type_yAnd e_ψRespectively vehicle lateral deviation and course deviation;

and

respectively the change rates of the lateral deviation and the course deviation of the vehicle;

and

the lateral speed and the longitudinal speed of the vehicle in the global coordinate system are respectively.

The tire model is modeled linearly as:

F_yf＝-C_fα_f,F_yr＝-C_rα_r

wherein, C_fAnd C_rFront and rear wheel cornering stiffness, respectively; alpha is alpha_fAnd alpha_rFront and rear wheel side slip angles, respectively, are expressed under the assumption of a small angle as:

wherein, delta_fIs the corner of the front wheel.

For state variables, u is δ in the vehicle input state_fAs a control input, will

Setting an external disturbance input, selecting y ═ e in the vehicle output state_ye_ψ]^TAs the tracking error output, the state space system from which the vehicle dynamics model can be derived is:

wherein A is_c、B_ucAnd B_vcCoefficient matrixes of state variables, control inputs and interference inputs respectively; c_cA matrix of coefficients output for the tracking error.

The dynamic prediction process for constructing the current moment based on the vehicle dynamics model specifically comprises the following steps: using the sampling time T_sDiscretizing a state space system of the vehicle dynamics model to obtain a discrete state space model, and introducing an increment form to reduce a control error; controlling the sequence of increments DeltaU by the current state xi (k)_c(k) The dynamic prediction process capable of obtaining the future output behavior of the state space system by the external interference gamma (k) is as follows:

wherein the content of the first and second substances,

and

is a state coefficient matrix;

and

is a matrix of output coefficients; x_p(k) Predicting a sequence for the state at time k; y is_p(k) A sequence is predicted for the output at time k.

The design considers the expansion model prediction controller of the driving path information, optimizes indexes by referring to path planning, and obtains a target optimization function considering the shortest tracking path, the optimal path curvature and the path course following as follows:

wherein N is_pIs a prediction time domain; n is a radical of_cIs a control time domain; ρ (k + i) is the travel path curvature at time k; s (k + i) is the travel path length at time k; r_k、Г_s、Г_ψAnd r_uAre the corresponding weighting factors.

Given a Global vehicle attitude (x)₀,y₀,t_s) As a transient variable in a time step, resolving and solving the curvature and the length of a corresponding running path in a prediction step through a dynamic prediction process, and adding an intermediate variable between the prediction process and an objective function as follows:

wherein the content of the first and second substances,

and

respectively the lateral acceleration and the longitudinal acceleration of the vehicle under the global coordinate system; the delta x and the delta y are respectively the transverse displacement and the longitudinal displacement of two adjacent path control points under the global coordinate system; psi_refIs the heading angle of the tracked path.

The antiskid constraint is that the constraint conditions are applied to the tire side deflection angle through the following steps:

wherein alpha is_tIs the tire restraint angle; and setting the yaw rate constraint as:

the rollover prevention constraint transfers the lateral load to the rate LTR_dThe equivalent is expressed as:

wherein, T_rIs the wheel track; the anti-rollover constraint is then expressed as:

-LTR_dmax≤LTR_d≤LTR_dmax

wherein, LTR_dmaxIs the rollover threshold.

In conjunction with the lateral and longitudinal envelope range of the vehicle, the drivable road region constraint is expressed as:

Env_min≤e_y ^k≤Env_max

wherein the content of the first and second substances,

e_y ^kas a lateral deviation at the current time k；e_yl ^kAnd e_yr ^kThe left boundary and the right boundary of the road at the current moment k are respectively, and beta is the vehicle mass center slip angle.

The extended model predictive controller constraints represent the various constraint regimes of control input, control delta and predicted output within each step as:

△u_min(k+i)≤△u(k+i)≤△u_max(k+i)

i＝0,1,…,N_c-1

u_min(k+i)≤u(k+i)≤u_max(k+i)

i＝0,1,…,N_c-1

y_min(k+i)≤y(k+i)≤y_max(k+i)

i＝1,2,…,N_p

wherein, Δ u_min(k + i) and Δ u_max(k + i) are the upper and lower limits of the control increment, respectively; u. of_min(k + i) and u_max(k + i) are the upper and lower limits of the control input, respectively; y is_min(k + i) and y_maxAnd (k + i) are respectively the upper limit and the lower limit of the state space system output.

The step 3) specifically comprises the following steps:

3.1) setting the front wheel steering angle control increment as an optimization variable, and randomly generating an initial population of the control increment within a constraint range;

3.2) calculating the curvature, length and course error of the driving path in the prediction time domain by obtaining the initial population in the control time domain, and considering a multi-constraint target optimization function J_eSetting as a main fitness function, and recording a target fitness function value corresponding to each updated population;

3.3) generating a differential variable by subtracting two different random target control inputs, and generating a new experimental individual by updating the variation and the cross operation of the differential variable in a search space;

3.4) selecting operation is carried out by evaluating the fitness value of the updated population; when the updated test population fitness value is smaller than the fitness value of the previous generation target population, selecting the test population as the next generation population; the evolutionary process is finished when repeated fixed iterative optimization is carried out or given precision convergence is achieved in the searching process, and the optimal control steering angle sequence solving optimization problem is obtained.

As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:

(1) in order to better consider road dynamic information, the invention takes the road inclination angle and the curvature as external interference input in the path tracking process, establishes a vehicle dynamic model containing the lateral degree, the yaw degree and the roll degree of freedom of the vehicle, improves the prediction accuracy of the vehicle future state and further improves the control precision of the path tracking.

(2) The method designs an extended model predictive control method considering the information of the driving path by combining the dynamic information of the vehicle and the road, simultaneously deduces and applies the constraints of rollover prevention, the envelope of the driving road and the like, solves the path tracking optimization problem of the process of introducing the extended variables by a differential evolution algorithm, and effectively combines path planning and tracking control to obtain an ideal tracking path.

(3) The method can fully utilize the maneuverability of the automatic driving vehicle, realize the optimal smooth path tracking in the travelable road area, improve the path tracking quality in the turning process, and is beneficial to improving the driving comfort of the vehicle and the road utilization rate.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is a first schematic diagram of a vehicle dynamics model of the present invention considering road inclination.

FIG. 3 is a schematic diagram of a vehicle dynamics model of the present invention with consideration of road inclination.

FIG. 4 is a schematic diagram of a differential evolution algorithm solving process of the path tracking optimization problem of the present invention.

FIG. 5 is a schematic diagram comparing the tracking effect of the invention on the path of an autonomous vehicle.

The invention is described in further detail below with reference to the figures and specific examples.

Detailed Description

The invention is further described below by means of specific embodiments.

In order to improve the reliability of an automatically driven vehicle running on a high-speed and complex road, the lateral and roll dynamics characteristics need to be further accurately described in a vehicle model, so that more accurate system future state prediction and constraint performance design are realized, and therefore, a vehicle dynamics model considering the road inclination angle and the curvature is established in advance. The invention considers the interference of the inclination angle and the curvature of the running road of the vehicle, increases the roll degree of freedom of the vehicle, and establishes a three-degree-of-freedom vehicle dynamic model, as shown in fig. 2 and 3, which is specifically as follows:

wherein m and m_sVehicle mass and sprung mass, respectively; g is the acceleration of gravity; l_fAnd l_rThe distances from the center of mass of the vehicle to the front axle and the rear axle respectively; i is_xAnd I_zRoll and yaw moments of inertia, respectively;

and

respectively vehicle roll stiffness and damping coefficient; h is the distance from the center of mass of the vehicle to the center of roll; r is the vehicle yaw rate;

yaw acceleration of the vehicle; psi is the vehicle yaw angle; κ is a reference road curvature; v. of_xAnd v_yLongitudinal and lateral velocities, respectively;

is the lateral acceleration; f_yfAnd F_yrThe lateral force of the front wheel and the rear wheel is respectively;

and

respectively as a vehicle roll angle and a road roll angle;

and

roll velocity and roll acceleration of the vehicle, respectively; e.g. of the type_yAnd e_ψRespectively vehicle lateral deviation and course deviation;

and

respectively the change rates of the lateral deviation and the course deviation of the vehicle;

and

the lateral speed and the longitudinal speed of the vehicle in the global coordinate system are respectively.

The nonlinear dynamic characteristics of the vehicle mainly derive from the lateral force of the tire, and the tire model is subjected to linear modeling to obtain the following characteristics:

F_yf＝-C_fα_f,F_yr＝-C_rα_r

wherein, C_fAnd C_rFront and rear wheel cornering stiffness, respectively; alpha is alpha_fAnd alpha_rFront and rear wheel side slip angles, respectively, are expressed under the assumption of a small angle as:

wherein, delta_fIs the corner of the front wheel.

To be provided with

For state variables, u is δ in the vehicle input state_fAs a control input, will

Setting an external disturbance input, selecting y ═ e in the vehicle output state_ye_ψ]^TAs the tracking error output, the state space system from which the vehicle dynamics model can be derived is:

wherein A is_c、B_ucAnd B_vcCoefficient matrixes of state variables, control inputs and interference inputs respectively; c_cA matrix of coefficients output for the tracking error.

Therefore, a vehicle dynamic system model considering lateral and roll dynamics is established, and the influence of road roll change on the system is mainly considered.

Referring to fig. 1, the control method of the present invention includes the steps of:

1) and constructing a dynamic prediction process at the current moment based on a vehicle dynamics model, and designing an extended model prediction controller considering driving path information.

The method specifically comprises the following steps: to predict the output of the system over a future period of time, a sampling time T is used_sDiscretizing a state space system of the vehicle dynamics model:

obtaining a discrete state space model:

x(k+1)＝A_dx(k)+B_udu(k)+B_vdγ(k)

y(k)＝C_dx(k)

wherein, C_d＝C_c。

In order to improve the accurate execution and constraint of the control input, an incremental form Δ u is introduced to reduce the control error, so as to obtain:

ξ(k+1)＝Aξ(k)+B_u△u(k)+B_vγ(k)

y(k)＝Cξ(k)

wherein the state vector is augmented

C＝[C_d 0]；△u(k)＝u(k)-u(k-1)。

Defining the prediction time domain as N_pControl time domain as N_c(N_c<N_p) The current vehicle state is dynamically acquired by measuring or estimating the state variable ξ (k). At time k, from k +1 to k + N, based on the current vehicle state_pThe future vehicle state at the time may be predicted as:

ξ(k+1)＝Aξ(k)+B_u△u(k)+B_vγ(k)

ξ(k+2)＝A²ξ(k)+AB_u△u(k)+B_u△u(k+1)+AB_vγ(k)+B_vγ(k)

when the control range exceeds N_cAfter the time domain step size, the control input will remain unchanged. By using successive substitutions of Δ u (k + N)_c)＝Δu(k+N_c+1)＝…＝Δu(k+N_p-1) ═ 0, such that u (k + N)_c-1)＝u(k+N_c)＝…＝u(k+N_p-1). K +1 to k + N are obtained by the calculation of the formula_pThe future vehicle outputs at that time are:

y(k+1)＝CAξ(k)+CB_u△u(k)+CB_vγ(k)

y(k+2)＝CA²ξ(k)+CAB_u△u(k)+CB_u△u(k+1)+CAB_vγ(k)+CB_vγ(k)

in the prediction time domain N_pAnd the control time domain is N_cThe predicted sequence within is represented as:

wherein, X_p(k) Predicting a sequence for the state at time k; y is_p(k) Predicting a sequence for the output at time k; delta U_c(k) Is the control sequence at time k.

Thus, the sequence of increments Δ U is controlled by the current state ξ (k)_c(k) The dynamic prediction process capable of obtaining the future output behavior of the state space system by the external interference gamma (k) is as follows:

wherein the content of the first and second substances,

and

is a state coefficient matrix;

and

is a matrix of output coefficients; x_p(k) Predicting a sequence for the state at time k; y is_p(k) A sequence is predicted for the output at time k.

Wherein the content of the first and second substances,

in order to realize smooth tracking of the optimal running path of the automatic driving vehicle in the travelable road area and further improve the stability and comfort of path tracking, the invention optimizes the following indexes by referring to path planning: (1) the shortest tracking path, namely the length of the driving path is shortened as much as possible, so that the purposes of reducing the driving time and the oil consumption are achieved; (2) the optimal path curvature, namely the curvature of the driving path is minimized to obtain smooth path tracking performance, and meanwhile, the vehicle sideslip or rollover caused by the large-curvature turning is avoided; (3) the course of the path is followed, even if the course of the tracked path is basically consistent with the center line of the road, thereby ensuring the accurate course of the path. Therefore, an extended model predictive controller considering driving path information is designed, indexes are optimized by referring to path planning, and a target optimization function considering the shortest tracking path, the optimal path curvature and the path course following is obtained as follows:

wherein N is_pIs a prediction time domain; n is a radical of_cIs a control time domain; ρ (k + i) is the travel path curvature at time k; s (k + i) is the travel path length at time k; r_k、Г_s、Г_ψAnd r_uAre the corresponding weighting factors.

Given a Global vehicle attitude (x)₀,y₀,t_s) As transient variables in the time step, the corresponding curvature and length of the driving path in the prediction step can be solved by analysis through a dynamic prediction process, and an intermediate variable is added between the prediction process and an objective function:

wherein the content of the first and second substances,

and

respectively the lateral acceleration and the longitudinal acceleration of the vehicle under the global coordinate system; the delta x and the delta y are respectively the transverse displacement and the longitudinal displacement of two adjacent path control points under the global coordinate system; psi_refIs the heading angle of the tracked path.

2) The method comprises the steps of obtaining state information of a vehicle at the current moment through a vehicle dynamics model, and establishing a constraint envelope according to the state information, wherein the constraint envelope comprises anti-slip constraint, anti-rollover constraint, drivable road area constraint and extended model predictive controller constraint. Wherein the state information comprises an input state and an output state, the input state comprising a control input u ═ δ_fInput with external interference

The output state includes the tracking error output y ═ e_ye_ψ]^T。

The anti-slip constraint is as follows:

and the side slip angle of the tire is limited to avoid the sideslip of the vehicle, and the effectiveness of a linearized tire model is ensured. Vehicle slip can be generally characterized by envelope curves of lateral velocity and yaw rate, and lateral velocity can be constrained by applying to the tire sidewall slip angle:

wherein alpha is_tIs the tire restraint angle; further constraining the yaw rate can provide the maximum steady state condition of the system model, and setting the yaw rate constraint as follows:

to incorporate the constraint problem into the predictive model coupling, the constraint form can be rewritten as:

|E₁ξ(k)+F₁γ(k)|≤M₁

wherein the content of the first and second substances,

the rollover prevention constraint is as follows:

the high-speed emergency obstacle avoidance and the turning are easy to generate larger lateral acceleration to cause the vehicle to turn over. In order to take the rollover stability of the vehicle into account, active rollover prevention safety control based on the lateral load transfer rate is generally employed in motion control. However, when the vehicle is about to roll over, the driver often has no time to take emergency control measures and even performs an inappropriate operation. Therefore, in consideration of the critical unstable dynamic characteristics of the high-speed vehicle, the invention further reduces the rollover risk of the vehicle by adopting rollover constraint, and limits the rollover threshold value within a reasonable range to prevent the tires from driving off the ground. Because the transverse load transfer rate on the road surface with the complex inclination angle is difficult to accurately obtain, the transverse load transfer rate LTR is converted based on the roll state and the vehicle parameters_dThe equivalent is expressed as:

wherein, T_rIs the wheel track; the rollover prevention constraint is expressed as:

-LTR_dmax≤LTR_d≤LTR_dmax

wherein, LTR_dmaxIs the rollover threshold. The rollover constraint matrix is represented by a state space model as:

wherein the content of the first and second substances,

M₂＝LTR_dmax。

and considering the obstacles and the road boundary, ensuring that the collision-free optimal track is tracked in the given travelable area. The lateral road environment constraint on the vehicle travel path can be expressed as a lateral deviation threshold combination at the current time k according to the envelope dimensions of the vehicle and the travelable road region in the path tracking problem.

Wherein e is_ylAnd e_yrRespectively a left boundary and a right boundary of the road; w is the vehicle width; d_sThe minimum safe distance of the vehicle to an obstacle or road boundary.

Considering further the allowable vehicle length range of the longitudinal travelable road area, the lateral positions of the front and rear axles are expressed as:

y_F＝y₀+l_f(ψ+β)

y_R＝y₀-l_r(ψ+β)

wherein, y_FAnd y_RThe lateral positions of the front shaft and the rear shaft are respectively; beta is the vehicle centroid slip angle.

In conjunction with the lateral and longitudinal envelope range of the vehicle, the drivable road region constraint is expressed as:

Env_min≤e_y ^k≤Env_max

wherein the content of the first and second substances,

and the expanded model predictive controller constraint considers various constraint conditions in the control input, the control increment and the predicted output in each step, and the various constraint conditions of the control input, the control increment and the predicted output in each step are expressed as follows:

△u_min(k+i)≤△u(k+i)≤△u_max(k+i)

i＝0,1,…,N_c-1

u_min(k+i)≤u(k+i)≤u_max(k+i)

i＝0,1,…,N_c-1

y_min(k+i)≤y(k+i)≤y_max(k+i)

i＝1,2,…,N_p

wherein, Δ u_min(k + i) and Δ u_min(k + i) are the upper and lower limits of the control increment, respectively; u. of_min(k + i) and u_max(k + i) are the upper and lower limits of the control input, respectively; y is_min(k + i) and y_maxAnd (k + i) are respectively the upper limit and the lower limit of the state space system output.

To this end, all constraint designs are incorporated into the solution process of the control objective function.

3) And solving by using a differential evolution algorithm according to the dynamic prediction process and the constraint envelope to obtain the optimal control steering angle at the current moment, and controlling the vehicle to autonomously track the optimal smooth path in the travelable road area by the extended model prediction controller according to the optimal control steering angle.

Interaction of the vehicle and road dynamic characteristics and multi-constraint behaviors enable the path tracking problem to be expanded, the analysis process of intermediate variables is increased, and the optimization problem is further enabled to be non-convex. In order to effectively implement the multi-constraint extended model prediction path tracking control method for the autonomous vehicle, the path tracking optimization problem is solved by adopting a differential evolution algorithm with strong robustness, and the algorithm iteratively searches a candidate solution of a large space for the constraint optimization problem through operations such as variation, intersection, selection and the like to obtain an optimal target control increment input sequence, as shown in fig. 4, the method specifically comprises the following steps:

3.1) setting the front wheel steering angle control increment as an optimization variable, and randomly generating an initial population of the control increment within a constraint range. In this operation, the population size, the mutation weight and the cross probability of the differential evolution algorithm are required to be configured. The initial population is randomly initialized to:

{W_i△δ_fij＝△δ_fmin+rand×(△δ_fmax-△δ_fmin)}i＝1,2,...,P,j＝1,2,...,D

wherein, W_iIs an initial population; delta delta_fijInitiating individuals for control increments; rand is one in [0,1 ]]Random numbers uniformly distributed are taken within the range; delta delta_fminAnd delta_fmaxRespectively an upper limit and a lower limit of the front wheel steering angle control increment; p is the size of the population; d is a target control input dimension and is used for generating a population in a corresponding control step length, namely D is equal to N_c。

3.2) calculating the curvature, length and course error of the driving path in the prediction time domain by obtaining the initial population in the control time domain, and considering a multi-constraint target optimization function J_eAnd setting as a main fitness function, and recording a target fitness function value corresponding to each updated population.

3.3) generating a differential variable by performing subtraction on two different random target control inputs, and generating new trial individuals by updating the variation and crossover operations of the differential variable in the search space. In the process, adaptive robust operation is considered, and the differential variation process of each target control input is represented as follows:

wherein, V_i ^G+1The G +1 generation variation control input; sequence number r₁、r₂And r₃Are generated randomly differently; eta is variation weight in the range of [0, 2%]Internal; eta_rIs a robust variation factor.

In order to increase the diversity of the population, crossover operations are performed between the original individuals and the variant individuals:

wherein u is_ijIs a new test individual; v. of_ijIs a variant individual; CR is the crossover probability, which ranges from [0,1 ]]Internal; rd is in [1,2, …, D ]]Randomly generated integers within the range.

3.4) selecting operation is carried out by evaluating the fitness value of the updated population; when the updated test population fitness value is smaller than the fitness value of the previous generation target population, selecting the test population as the next generation population; the evolutionary process is finished when repeated fixed iterative optimization is carried out or given precision convergence is achieved in the searching process, and the optimal control steering angle sequence solving optimization problem is obtained. The selection operation is described as follows:

wherein, U_i(ii) is a renewed test population; and f is a fitness function.

4) And returning to the step 1) to calculate the optimal control steering angle of the next control period until the vehicle reaches the end point of the path.

Fig. 5 shows the comparison of the tracking effect of the automatic driving vehicle path, wherein in fig. 5, (a), (b), (c) and (d) are respectively the comparison of the track, the turning angle and the yaw rate of the automatic driving vehicle path tracking with the rollover threshold value. It can be seen that the conventional model predictive controller strictly tracks the road centerline, and since the road dynamic information is not considered, the dynamic response when the vehicle turns shows significant overshoot and oscillation, which will greatly reduce the comfort and stability during the path tracking process.

As can be seen from fig. 5 (a), in the extended model predictive control method considering the travel path information, the autonomous vehicle realizes the transient smooth steering during the turning, and continues to keep the heading travel when the turning is finished, so as to achieve the tracking effect of the optimal path planning, and improve the path tracking quality during the turning.

As can be seen from fig. 5 (b), the steering angle of the extended model predictive control method is more smoothly represented, and more conforms to the driving habits of a skilled driver. As can be seen from (c) and (d) of fig. 5, the extended model predicted path tracking has more stable yaw rate and rollover threshold, and better yaw stability and rollover prevention performance can be obtained. The result shows that the expanded model prediction path tracking method can fully utilize the maneuverability of the vehicle, so that the automatic driving vehicle can drive along the optimal route in the drivable road area, and the driving comfort and the road utilization rate of the vehicle are improved.

The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.

Claims (9)

1. A tracking control method for an autonomous vehicle is characterized in that a vehicle dynamic model considering road inclination and curvature is established in advance, and the control method comprises the following steps:

1) constructing a dynamic prediction process at the current moment based on a vehicle dynamics model, and designing an extended model prediction controller considering driving path information;

2) acquiring state information of a vehicle at the current moment through a vehicle dynamics model, and establishing a constraint envelope according to the state information, wherein the constraint envelope comprises anti-slip constraint, anti-rollover constraint, drivable road region constraint and extended model predictive controller constraint;

3) solving by using a differential evolution algorithm according to a dynamic prediction process and a constraint envelope to obtain an optimal control steering angle at the current moment, and controlling the vehicle to autonomously track an optimal smooth path in a travelable road area by the extended model prediction controller according to the optimal control steering angle;

4) and returning to the step 1) to calculate the optimal control steering angle of the next control period until the vehicle reaches the end point of the path.

2. The tracking control method for the autonomous vehicle as claimed in claim 1, wherein the three-degree-of-freedom dynamic model of the vehicle dynamic model is as follows:

wherein m and m_sVehicle mass and sprung mass, respectively; g is the acceleration of gravity; l_fAnd l_rThe distances from the center of mass of the vehicle to the front axle and the rear axle respectively; i is_xAnd I_zRoll and yaw moments of inertia, respectively;

and

respectively vehicle roll stiffness and damping coefficient; h is the distance from the center of mass of the vehicle to the center of roll; r is the vehicle yaw rate;

yaw acceleration of the vehicle; psi is the vehicle yaw angle; κ is a reference road curvature; v. of_xAnd v_yLongitudinal and lateral velocities, respectively;

is the lateral acceleration; f_yfAnd F_yrThe lateral force of the front wheel and the rear wheel is respectively;

and

respectively as a vehicle roll angle and a road roll angle;

and

respectively the roll velocity of the vehicleAnd roll acceleration; e.g. of the type_yAnd e_ψRespectively vehicle lateral deviation and course deviation;

and

respectively the change rates of the lateral deviation and the course deviation of the vehicle;

and

respectively the transverse speed and the longitudinal speed of the vehicle under the global coordinate system;

the tire model is modeled linearly as:

F_yf＝-C_fα_f,F_yr＝-C_rα_r

wherein, C_fAnd C_rFront and rear wheel cornering stiffness, respectively; alpha is alpha_fAnd alpha_rFront and rear wheel side slip angles, respectively, are expressed under the assumption of a small angle as:

wherein, delta_fIs a front wheel corner;

to be provided with

For state variables, u is δ in the vehicle input state_fAs a control input, will

Setting an external disturbance input, selecting y ═ e in the vehicle output state_ye_ψ]^TAs a tracking error output, can be obtainedThe state space system of the vehicle dynamic model is as follows:

wherein A is_c、B_ucAnd B_vcCoefficient matrixes of state variables, control inputs and interference inputs respectively; c_cA matrix of coefficients output for the tracking error.

3. The tracking control method for the autonomous vehicle as claimed in claim 2, wherein the dynamic prediction process for constructing the current time based on the vehicle dynamics model is specifically: using the sampling time T_sDiscretizing a state space system of the vehicle dynamics model to obtain a discrete state space model, and introducing an increment form to reduce a control error; controlling the sequence of increments DeltaU by the current state xi (k)_c(k) The dynamic prediction process capable of obtaining the future output behavior of the state space system by the external interference gamma (k) is as follows:

wherein the content of the first and second substances,

and

is a state coefficient matrix;

and

is a matrix of output coefficients; x_p(k) Predicting a sequence for the state at time k; y is_p(k) A sequence is predicted for the output at time k.

4. The tracking control method of an autonomous vehicle as claimed in claim 2, wherein the extended model predictive controller designed taking into account driving path information optimizes the index by referring to the path plan to obtain an objective optimization function taking into account the shortest tracking path, the optimal path curvature and the path heading following as:

wherein N is_pIs a prediction time domain; n is a radical of_cIs a control time domain; ρ (k + i) is the travel path curvature at time k; s (k + i) is the travel path length at time k; r_k、Г_s、Г_ψAnd r_uIs the corresponding weight factor;

given a Global vehicle attitude (x)₀,y₀,t_s) As a transient variable in a time step, resolving and solving the curvature and the length of a corresponding running path in a prediction step through a dynamic prediction process, and adding an intermediate variable between the prediction process and an objective function as follows:

e_ψ(k+i)＝ψ(k+i)-ψ_ref(k+i)；

wherein the content of the first and second substances,

and

respectively the lateral acceleration and the longitudinal acceleration of the vehicle under the global coordinate system; the delta x and the delta y are respectively the transverse displacement and the longitudinal displacement of two adjacent path control points under the global coordinate system; psi_refIs the heading angle of the tracked path.

5. A tracking control method for autonomous vehicles as claimed in claim 2, characterized in that said anti-slip constraint is specified as follows:

the constraint condition applied to the tire side deflection angle is as follows:

wherein alpha is_tIs the tire restraint angle; and setting the yaw rate constraint as:

6. the tracking control method for the autonomous vehicle as claimed in claim 2, wherein the rollover prevention constraint is specified as follows:

transferring lateral load to the ratio LTR_dThe equivalent is expressed as:

wherein, T_rIs the wheel track; the rollover prevention constraint is expressed as:

-LTR_dmax≤LTR_d≤LTR_dmax

wherein, LTR_dmaxIs the rollover threshold.

7. A tracking control method for an autonomous vehicle as claimed in claim 2 wherein, in combination with the lateral and longitudinal envelope of the vehicle, the drivable road region constraint is expressed as:

Env_min≤e_y ^k≤Env_max

wherein the content of the first and second substances,

e_y ^kis the lateral deviation at the current time k;

and

the left boundary and the right boundary of the road at the current moment k are respectively, and beta is the vehicle mass center slip angle.

8. The tracking control method for an autonomous vehicle as claimed in claim 2, characterized in that the extended model prediction

The controller constraints are specifically: the various constraints on the control inputs, control increments, and predicted outputs for each step are expressed as:

△u_min(k+i)≤△u(k+i)≤△u_max(k+i)

i＝0,1,…,N_c-1

u_min(k+i)≤u(k+i)≤u_max(k+i)

i＝0,1,…,N_c-1

y_min(k+i)≤y(k+i)≤y_max(k+i)

i＝1,2,…,N_p

wherein, Δ u_min(k + i) and Δ u_max(k + i) are control increases, respectivelyUpper and lower limits of amount; u. of_min(k + i) and u_max(k + i) are the upper and lower limits of the control input, respectively; y is_min(k + i) and y_maxAnd (k + i) are respectively the upper limit and the lower limit of the state space system output.

9. The tracking control method of an autonomous vehicle as claimed in claim 1, wherein the step 3) comprises the following steps:

3.1) setting the front wheel steering angle control increment as an optimization variable, and randomly generating an initial population of the control increment within a constraint range;

3.2) calculating the curvature, length and course error of the driving path in the prediction time domain by obtaining the initial population in the control time domain, and considering a multi-constraint target optimization function J_eSetting as a main fitness function, and recording a target fitness function value corresponding to each updated population;

3.3) generating a differential variable by subtracting two different random target control inputs, and generating a new experimental individual by updating the variation and the cross operation of the differential variable in a search space;

3.4) selecting operation is carried out by evaluating the fitness value of the updated population; when the updated test population fitness value is smaller than the fitness value of the previous generation target population, selecting the test population as the next generation population; the evolutionary process is finished when repeated fixed iterative optimization is carried out or given precision convergence is achieved in the searching process, and the optimal control steering angle sequence solving optimization problem is obtained.

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