1. A track tracking control method and a performance evaluation method for realizing road surface self-adaption based on model predictive control by an automatic driving vehicle running under all working conditions are characterized by comprising the following steps:

step 1) establishing a prediction model of a model prediction control method by combining a three-degree-of-freedom nonlinear dynamics model of a vehicle;

step 2) formulating an objective function and constraint conditions of the model predictive control method, and performing road surface self-adaptive vehicle speed range matching according to the road adhesion coefficient detected by the sensor, so as to improve the driving safety under the extreme working condition;

step 3) providing an evaluation system consisting of path tracking error, lateral acceleration, a centroid slip angle, a maximum value of a front wheel slip angle and a standard deviation, and comprehensively and accurately evaluating the track tracking precision and the driving safety under all working conditions;

and 4) dividing the vehicle all-working-condition track tracking stable area/unstable area to provide reference for the control method.

2. The automatic driving full-condition road surface self-adaptive MPC trajectory tracking control method and the performance evaluation method as claimed in claim 1, wherein in step 2), the objective function and the constraint condition of the model prediction control method are as follows:

s.t.ΔU_min≤ΔU≤ΔU_max (4-a)

U_min≤A·ΔU+U≤U_max (4-b)

y_hc,min≤y_hc≤y_hc,max (4-c)

y_sc,min-ε≤y_sc≤y_sc,max+ε (4-d)

ε＞0 (4-e)

-12 ° < β < 12 ° (good road) (4-f)

-2 ° < β < 2 ° (snow-ice road) (4-g)

-2.5°＜α_f＜2.5° (4-i)

In the formula: y is_hcIs a hard constraint output; y is_scIs the soft constrained output; y is_hc,minAnd y_hc,maxIs a hard constraint limit; y is_sc,minAnd y_sc,maxIs a soft constraint limit; a is a coefficient matrix; epsilon is a relaxation factor; rho and Q, R are both weight coefficients; beta is the centroid slip angle; a is_yIs the lateral acceleration; alpha is alpha_fIs a front wheel side slip angle; setting soft constraints to ensure that each control step is solved to obtain a feasible solution, and properly amplifying an output range;

among the above multiple constraint conditions, equations (4-f) and (4-g) constrain the centroid slip angle; the formula (4-h) constrains the lateral acceleration; the formula (4-i) restrains the side deflection angle of the front wheel, so that the running safety of the vehicle is ensured; equation (4-a) constrains the vehicle speed and the nose wheel angle increment;

in the vehicle speed range matching module based on road surface self-adaptation shown in fig. 3, a front road image detected by a vehicle-mounted camera is transmitted to a CPU, image processing is performed by combining with intelligent algorithms such as a deep learning neural network and the like, and a front road attachment coefficient is estimated; according to different road adhesion coefficients, self-adaptive matching of the vehicle speed is achieved, and vehicle speed increment delta v is obtained through calculation; and the vehicle speed increment is transmitted to the constraint condition of the model predictive controller to realize the optimal solution of the optimization model.

3. The automatic driving full-condition road surface self-adaptive MPC (MPC) trajectory tracking control method and the performance evaluation method as claimed in claim 1, wherein in the step 3), an automatic driving vehicle trajectory tracking evaluation index system is provided, and the trajectory tracking precision and the driving safety under the full condition are comprehensively and accurately evaluated by the path tracking error, the lateral acceleration, the centroid slip angle, the maximum value of the front wheel slip angle and the standard deviation; the path tracking error represents the track tracking precision, and the lateral acceleration, the centroid slip angle and the front wheel slip angle represent the driving safety; the maximum value of the index represents the limit conditions of the track tracking precision and the driving safety when the vehicle runs through a large-curvature road section, and the standard deviation represents the dispersion degree of the index relative to the average value and reflects the performance fluctuation condition of the vehicle in the whole track tracking process.

4. The automatic driving full-working-condition road surface self-adaptive MPC trajectory tracking control method and the performance evaluation method as claimed in claim 1, wherein in step 4), in order to obtain good trajectory tracking accuracy and driving safety, the matching relationship between the vehicle speed and the road adhesion coefficient is considered, and the driving working condition of the vehicle is divided into two areas of a stable area and a destabilized area; when the vehicle runs in a stable area working condition, the vehicle has good track tracking precision and running safety; when the vehicle runs under the working condition of the unstable area, the track tracking precision and the running safety are rapidly deteriorated, and the vehicle speed needs to be adjusted in time according to the road information detected by the sensor, and the vehicle returns to the stable working condition area to run again.

Background

As the automatic driving technology continues to develop, the trajectory tracking control technology of the automatic driving vehicle becomes a research hotspot and difficulty. The accurate track tracking control method plays an important role in ensuring the driving safety of the vehicle during the driving under all working conditions. At present, the commonly used Control methods for trajectory tracking Control of an autonomous vehicle include a backstepping method, a sliding mode variable structure Control method, a fuzzy Control method, a Model Predictive Control (MPC) method, and the like. The model predictive control method is widely applied due to the advantages of multi-vehicle motion constraint, excellent control performance, good robustness and the like, and scholars at home and abroad obtain certain achievements in the field.

For example, Chinese patent "a vehicle track tracking control method based on linear model predictive control algorithm" (patent number: CN 112394734A) discloses a vehicle track tracking control method based on linear model predictive control algorithm, which comprises the steps of collecting vehicle state information, positioning information and reference track, filtering, calculating course angle error, establishing a linear vehicle dynamics model, obtaining vehicle steering wheel turning angle and vehicle steering wheel rotating speed, etc.; the vehicle track tracking function is realized, the vehicle dynamic characteristics and the sudden change of the control quantity are considered, the vehicle track tracking capability is improved, and the stability of the vehicle in high-speed running is ensured.

Chinese patent "a vehicle track-changing track tracking control method based on model prediction" (patent number: CN 112092815A) discloses a vehicle track-changing track tracking control method based on model prediction, which comprises the steps of establishing a track-changing expected track model, establishing a three-degree-of-freedom vehicle dynamics model, converting the three-degree-of-freedom vehicle dynamics model into a discrete linear prediction model, designing a target function and constraint conditions of a model prediction controller, calculating output quantity and control quantity and the like; the lane change expected track improves the comfort of a driver, meets the requirement of lateral lane change, ensures the vehicle speed control with higher precision, has stronger robustness and higher control precision, and reduces the lateral tracking error.

In summary, the track tracking control method and the performance evaluation method of the autonomous vehicle after the document retrieval, investigation and analysis have the following disadvantages:

(1) the method is only researched under the working conditions of certain specific vehicle speed and road adhesion coefficient, and the research result has no universality under all the working conditions and cannot represent the actual running condition of the vehicle under all the working conditions;

(2) the performance evaluation method is one-sided, and the track tracking precision and the driving safety of the vehicle under all working conditions cannot be accurately and comprehensively evaluated;

(3) and the self-adaptive control of the road surface is lacked, and the vehicle speed restriction range is not limited according to different road surfaces.

Disclosure of Invention

The invention mainly solves the technical problem of providing a track tracking control method and a performance evaluation method based on model predictive control, which realize road surface self-adaptation of an automatic driving vehicle under all working conditions, aiming at the defects in the prior art.

In order to solve the technical problems, the invention adopts the following technical scheme:

a method for automatically driving full-working-condition road surface self-adaptive MPC (MPC) trajectory tracking control and performance evaluation comprises the following steps:

step 1) establishing a prediction model of a model prediction control method by combining a three-degree-of-freedom nonlinear dynamics model of an automatic driving vehicle;

step 2) formulating an objective function and constraint conditions of the model predictive control method, and performing road surface self-adaptive vehicle speed range matching according to the road adhesion coefficient detected by the sensor, so as to improve the driving safety under the extreme working condition;

step 3) providing an evaluation system consisting of path tracking errors, lateral acceleration, a centroid slip angle, a maximum value of a front wheel slip angle and a standard deviation, and comprehensively and accurately evaluating the track tracking precision and the driving safety of the automatic driving vehicle in all working conditions;

and 4) dividing a track tracking stable area/instability area of the automatic driving vehicle running under all working conditions, and providing reference for an optimization control method.

In the step 1), in order to track the reference track safely, accurately and efficiently, the vehicle model is a three-degree-of-freedom nonlinear dynamics model, and only three degrees of freedom of longitudinal, transverse and transverse motions are provided in a plane.

The three-degree-of-freedom nonlinear motion differential equation of the automatic driving vehicle is analyzed by Newton's second motion law and momentum moment theorem

Combining small angle hypothesis and tire model linearization process based on magic formula, wherein the nonlinear dynamic model of the vehicle is represented by formula (1)

In the formula: m is the whole vehicle preparation mass; a is the distance from the center of mass to the center of the front axle; b is the distance from the center of mass to the center of the rear axle; i is_zIs moment of inertia about the z-axis;is the longitudinal velocity;is the lateral velocity;the yaw angular velocity;is the longitudinal acceleration;is the lateral acceleration;yaw angular acceleration; c_cfIs the cornering stiffness of the front wheel; c_crIs the cornering stiffness of the rear wheel; c_lfIs the longitudinal stiffness of the front wheel; c_lrLongitudinal stiffness of the rear wheel; s_fIs the front wheel slip ratio; s_rIs the rear wheel slip ratio; f_lf,rLongitudinal force applied to the front and rear wheels; f_cf,rThe transverse force applied to the front wheel and the rear wheel; f_xf,rThe force along the x-axis direction received by the front wheel and the rear wheel; f_yf,rThe force along the y-axis direction received by the front wheel and the rear wheel; delta_fIs the corner of the front wheel.

The state quantity of the system isThe control quantity of the system is u_dyn＝δ_f. In the trajectory tracking controller, the established vehicle dynamics model is used as a prediction model.

Based on a discrete linear time-varying model, an output equation of the system is iteratively deduced to be

Y＝Ψξ(k)+ΘΔU (3)

In the formula: Ψ and Θ are both coefficient matrices; y is the output vector, Y ═ η (k +1), η (k +2),. -, η (k + N)_p)]^T(ii) a Δ U is a control increment vector, Δ U ═ Δ U (k), andk+1),...,Δu(k+N_c-1)]。

as can be seen from equation (3), if the state quantity ξ (k) and the control time domain N at the current time are known_cThe control increment delta U can predict the future prediction time domain N_pSince the internal output Y is obtained, the equation (3) is used as a prediction model of the control system.

In the step 2), a drive-by-wire chassis is selected as an executing system of the track tracking control, the drive-by-wire steering subsystem realizes the front wheel steering control, and the drive-by-wire braking subsystem and the drive-by-wire subsystem realize the vehicle speed control. As shown in fig. 2, the controlled system (autonomous vehicle drive-by-wire chassis), the model predictive controller and the state estimator constitute a complete model predictive control system. The model predictive controller is designed by combining constraint conditions, a prediction model and an objective function on the basis of three basic elements of the prediction model, rolling optimization and feedback correction of a predictive control theory. The controller continuously solves the objective function by combining constraint conditions, and a control variable sequence u is obtained through calculation^*After (t), the first value is applied to the system under control, and the system performs control. And the state estimator calculates the state quantity of the system and feeds the state quantity back to the controller, and the prediction model is continuously updated.

The optimization problem solved by the trajectory tracking controller in each control cycle is summarized as

s.t.

ΔU_min≤ΔU≤ΔU_max (4-a)

U_min≤A·ΔU+U≤U_max (4-b)

y_hc,min≤y_hc≤y_hc,max (4-c)

y_sc,min-ε≤y_sc≤y_sc,max+ε (4-d)

ε＞0 (4-e)

-12 ° < β < 12 ° (good road) (4-f)

-2 ° < β < 2 ° (snow-ice road) (4-g)

-2.5°＜α_f＜2.5° (4-i)

In the formula: y is_hcIs a hard constraint output; y is_scIs the soft constrained output; y is_hc,minAnd y_hc,maxIs a hard constraint limit; y is_sc,minAnd y_sc,maxIs a soft constraint limit; a is a coefficient matrix; epsilon is a relaxation factor; rho and Q, R are both weight coefficients; beta is the centroid slip angle; a is_yIs the lateral acceleration; alpha is alpha_fIs a front wheel side slip angle. And setting soft constraints to ensure that a feasible solution is obtained in the process of solving in each control step, and properly amplifying the output quantity range.

In the above multi-constraint conditions, equations (4-f) and (4-g) constrain the centroid slip angle; the formula (4-h) constrains the lateral acceleration; and (4-i) restrains the side deflection angle of the front wheel to ensure the running safety of the vehicle. Equation (4-a) constrains the vehicle speed and the nose wheel angle increment.

In the vehicle speed range matching module based on road surface self-adaptation, the image of the front road detected by the vehicle-mounted camera is transmitted to the CPU, and the image processing is carried out by combining intelligent algorithms such as a neural network and the like, so that the attachment coefficient of the front road is estimated. According to different road adhesion coefficients, vehicle speed self-adaptive matching is achieved, and vehicle speed increment delta v is obtained through calculation. And the vehicle speed increment is transmitted to a constraint condition of a model predictive controller to participate in optimization solution of the optimization model.

In the step 3), the target track is a double-moving-line track widely used in a vehicle running stability test experiment. And selecting a vehicle speed value every 5m/s from 10m/s to 30m/s, and selecting a road adhesion coefficient from mu-0.1 to mu-0.9, and researching the track tracking condition and the stability of the vehicle under the full-speed working condition and the full-road adhesion coefficient working condition, wherein the research results are shown in fig. 5 to fig. 16.

In the adopted evaluation indexes, the path tracking error represents the track tracking precision, and the lateral acceleration, the centroid slip angle and the front wheel slip angle represent the driving safety. The maximum value of the indexes represents the limit conditions of the track tracking precision and the driving safety when the vehicle runs through a large-curvature road section, and the standard deviation represents the dispersion degree of the indexes relative to the average value and reflects the performance fluctuation condition of the vehicle in the whole track tracking process.

For example, as can be seen from fig. 5 and 6, when the vehicle travels on a good road surface with a high road adhesion coefficient at a low speed, the path tracking error is low and the track tracking effect is the best. The lower the vehicle speed, the more adaptable the vehicle can be to a road surface with a low road adhesion coefficient, that is, the vehicle can track a target trajectory at a low speed on a wet road surface with a low road adhesion coefficient. The maximum value of the path tracking error is already reduced to less than 1m when the vehicle runs on a road surface with a road adhesion coefficient of 0.2 at a speed of 10m/s, and is reduced to less than 1m when the vehicle runs on a road surface with a road adhesion coefficient of 0.7 at a speed of 20 m/s. When the vehicle tracks the target track at the high speed of 25m/s, 30m/s and the like, even if the vehicle runs on a good road surface with the road adhesion coefficient of 0.7 or 0.8, the maximum value of the path tracking error is still larger and is close to 3m, which shows that the track tracking effect of the vehicle at the turning position is poor, and the lateral acceleration is larger and is close to 9m/s at the moment²The lateral force is large, the vehicle operation stability is poor, and therefore the high-speed running is avoided in the track tracking process.

As can be seen from fig. 7, when the vehicle runs on a road surface with a high road adhesion coefficient at a low speed, the standard deviation of the path tracking error is relatively small, which indicates that the path tracking error has a smaller dispersion degree from the average value thereof, the path tracking error has a small change, and the tracking effect is relatively good.

As can be seen from fig. 16, when the vehicle travels on a road surface with a high road adhesion coefficient at a low speed, the standard deviation of the front wheel slip angle is relatively small, which indicates that the degree of dispersion of the front wheel slip angle from the average value of the front wheel slip angle is smaller and the vehicle travel stability does not change much during the trajectory tracking process of the vehicle. In order to ensure that the vehicle not only ensures the tracking effect but also maintains the driving stability and safety in the track tracking process, a vehicle stability system is necessary to be installed.

In the step 4), in order to obtain good track tracking accuracy and driving safety, the vehicle driving condition is divided into a stable area and a unstable area as shown in fig. 17 by considering the matching relationship between the vehicle speed and the road adhesion coefficient. When the vehicle runs in a stable area working condition, the vehicle has good track tracking precision and running safety; when the vehicle runs under the working condition of the unstable area, the track tracking precision and the running safety are rapidly deteriorated, and the vehicle speed needs to be adjusted in time according to the road surface information detected by the sensor, and the vehicle returns to the stable working condition area to run again.

Compared with the prior art, the invention has the following advantages:

(1) when a speed constraint condition of the automatic driving vehicle is formulated, road self-adaptive speed range matching is carried out according to a road adhesion coefficient detected by a sensor, and the driving safety under the limit working condition is improved;

(2) an evaluation system consisting of path tracking errors, lateral acceleration, a centroid slip angle, a maximum value of a front wheel slip angle and a standard deviation is provided, and the track tracking accuracy and the driving safety of the automatic driving vehicle under all working conditions are comprehensively and accurately evaluated;

(3) dividing a track tracking stable area/instability area of the automatic driving vehicle under all working conditions, and providing reference for a control method;

(4) the vehicle speed is adjusted in real time according to the matching relation of the vehicle running conditions, so that the automatic driving vehicle always runs in a stable working condition area, and the self-adaptive control of the vehicle speed is realized according to the change of the road surface.

Drawings

FIG. 1 is a flow chart of an automatic driving full condition road surface adaptive MPC trajectory tracking control and evaluation method;

FIG. 2 is a three degree of freedom non-linear dynamical model of an autonomous vehicle;

FIG. 3 is a schematic diagram of a model predictive control-based vehicle trajectory tracking principle for an autonomous vehicle under all operating conditions;

FIG. 4 is a model predictive control-based autonomous vehicle trajectory tracking joint simulation model;

FIG. 5 is a graph of the maximum path tracking error of an autonomous vehicle as a function of road adhesion coefficients at various speeds;

FIG. 6 is a three-dimensional graph of path tracking error fluctuations of an autonomous vehicle under full operating conditions;

FIG. 7 is a graph of the standard deviation of path tracking error of an autonomous vehicle at various speeds as a function of road adhesion coefficient;

FIG. 8 is a graph of the lateral acceleration maximum as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds;

FIG. 9 is a three-dimensional plot of lateral acceleration maximum fluctuations of an autonomous vehicle under full operating conditions;

FIG. 10 is a plot of lateral acceleration standard deviation as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds;

FIG. 11 is a graph of the centroid slip angle maximum as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds;

FIG. 12 is a three-dimensional graph of the centroid slip angle maximum fluctuation of an autonomous vehicle under all operating conditions;

FIG. 13 is a graph of centroid side deviation angle standard deviation as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds;

FIG. 14 is a graph of the maximum front wheel side slip angle as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds;

FIG. 15 is a three-dimensional graph of the maximum fluctuation of the front wheel side slip angle of the autonomous vehicle under all operating conditions;

FIG. 16 is a graph of front wheel cornering power standard deviation versus road adhesion coefficient for an autonomous vehicle at various vehicle speeds;

FIG. 17 is a stable region/unstable region partition for full condition trajectory tracking of an autonomous vehicle;

Detailed Description

The following further describes preferred embodiments of the present invention in conjunction with the accompanying drawings so that the advantages and features of the present invention can be more readily understood by those skilled in the art, and the scope of the present invention is more clearly and clearly defined.

FIG. 1 is a flow chart of an automatic driving full condition road surface self-adaptive MPC trajectory tracking control and evaluation method. The automatic driving full-working-condition road surface self-adaptive MPC trajectory tracking control method and the performance evaluation method comprise the following steps:

step 1) establishing a prediction model of a model prediction control method by combining a three-degree-of-freedom nonlinear dynamics model of a vehicle;

step 2) formulating an objective function and constraint conditions of the model predictive control method, and performing road surface self-adaptive vehicle speed range matching according to the road adhesion coefficient detected by the sensor, so as to improve the driving safety under the extreme working condition;

step 3) providing an evaluation system consisting of path tracking errors, lateral acceleration, a centroid slip angle, a maximum value of a front wheel slip angle and a standard deviation, and comprehensively and accurately evaluating the track tracking precision and the driving safety under all working conditions;

and 4) dividing the vehicle all-working-condition track tracking stable area/unstable area to provide reference for the control method.

FIG. 2 is a three-degree-of-freedom non-linear dynamics model of an autonomous vehicle. The nonlinear dynamical model of the vehicle is

In the formula: m is the whole vehicle preparation mass; a is the distance from the center of mass to the center of the front axle; b is the distance from the center of mass to the center of the rear axle; i is_zIs moment of inertia about the z-axis;is the longitudinal velocity;is the lateral velocity;the yaw angular velocity;is the longitudinal acceleration;is the lateral acceleration;yaw angular acceleration; c_cfIs the cornering stiffness of the front wheel; c_crIs the cornering stiffness of the rear wheel; c_lfIs the longitudinal stiffness of the front wheel; c_lrLongitudinal stiffness of the rear wheel; s_fIs the front wheel slip ratio; s_rIs the rear wheel slip ratio; f_lf,rLongitudinal force applied to the front and rear wheels; f_cf,rThe transverse force applied to the front wheel and the rear wheel; f_xf,rThe force along the x-axis direction received by the front wheel and the rear wheel; f_yf,rThe force along the y-axis direction received by the front wheel and the rear wheel; delta_fIs the corner of the front wheel.

FIG. 3 illustrates a vehicle trajectory tracking principle of an autonomous vehicle under all operating conditions based on model predictive control. The controlled system (autonomous vehicle drive-by-wire chassis), the model predictive controller and the state estimator constitute a complete model predictive control system. The model predictive controller is designed by combining constraint conditions, a predictive model and an objective function on the basis of a predictive model, rolling optimization and feedback correction of a predictive control theory. The controller continuously solves the objective function by combining constraint conditions, and a control variable sequence u is obtained through calculation^*After (t), the first value is applied to the system under control, and the system performs control. And the state estimator calculates the system state quantity and feeds the system state quantity back to the controller, and the prediction model is continuously updated.

FIG. 4 is a model predictive control-based combined simulation model for trajectory tracking of an autonomous vehicle. Taking the full speed and the full road adhesion coefficient as examples, the track tracking precision and the driving safety of the automatic driving vehicle under the full working condition are researched, and CarSim and MATLAB software are fused for research.

FIG. 5 is a graph of path tracking error maximum versus road adhesion coefficient for an autonomous vehicle at various vehicle speeds.

FIG. 6 is a three-dimensional graph of path tracking error fluctuations of an autonomous vehicle under full operating conditions.

Fig. 5 and 6 show that, when the road adhesion coefficient approaches μ ═ 0.1, five kinds of road adhesion coefficientsThe maximum value of the path tracking error under the vehicle speed is larger and even approaches to 5 m. And as can be seen from fig. 8 and 9, when the road adhesion coefficient is close to μ ═ 0.1, the maximum values of the lateral acceleration at the five vehicle speeds are small, close to 0.1m/s²At the moment, the lateral adhesion force of the vehicle is small, the lateral stability is weak, so the steering capacity of the vehicle is greatly influenced, and the track tracking effect is poor. When the road adhesion coefficient gradually rises, the maximum value of the lateral acceleration is increased, the lateral adhesion force of the vehicle is gradually increased, the lateral stability is gradually enhanced, and the steering capacity of the vehicle is also improved, so that the maximum value of the path tracking error is also rapidly reduced along with the rise of the road adhesion coefficient, as can be seen from fig. 5, the minimum value is reduced to be close to 0.5m, and the track tracking effect is better.

FIG. 7 is a graph of standard deviation of path tracking error as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds. When the vehicle runs on a good road surface with high road adhesion coefficient at low speed, the path tracking error is low, and the track tracking effect is best. When the road adhesion coefficient approaches μ equal to 0.1, the maximum value of the path tracking error is large at all five vehicle speeds, and can approach even 5 m. The lower the vehicle speed, the more adaptable the vehicle can be to a road surface with a low road adhesion coefficient, that is, the vehicle can track a target trajectory at a low speed on a wet road surface with a low road adhesion coefficient. The maximum value of the path tracking error is already reduced to less than 1m when the vehicle runs on a road surface with a road adhesion coefficient of 0.2 at a speed of 10m/s, and is reduced to less than 1m when the vehicle runs on a road surface with a road adhesion coefficient of 0.7 at a speed of 20 m/s. When the vehicle tracks the target track at the high speed of 25m/s, 30m/s and the like, even if the vehicle runs on a good road surface with the road adhesion coefficient of 0.7 or 0.8, the maximum value of the path tracking error is still larger and is close to 3m, which shows that the track tracking effect of the vehicle at the turning position is poor, and the lateral acceleration is larger and is close to 9m/s at the moment²The lateral force is large, the operation stability of the vehicle is poor, and therefore the high-speed running is avoided in the track tracking process.

When the vehicle runs on a road surface with a high road adhesion coefficient at a low speed, the standard deviation of the path tracking error is smaller, which shows that the dispersion degree of the path tracking error of the vehicle relative to the average value is smaller, the change of the path tracking error is small, and the tracking effect is better.

FIG. 8 is a graph of lateral acceleration maximum versus road adhesion coefficient for an autonomous vehicle at various vehicle speeds.

FIG. 9 is a three-dimensional plot of lateral acceleration maximum fluctuations under full operating conditions for an autonomous vehicle.

FIG. 10 is a graph of standard deviation of lateral acceleration of an autonomous vehicle as a function of road adhesion coefficient at various vehicle speeds.

As can be seen from fig. 8, 9 and 10, when the road adhesion coefficient is close to μ ═ 0.1, the maximum values of the lateral acceleration at the five vehicle speeds are small, close to 0.1m/s²At this time, the lateral adhesion force of the vehicle is relatively small, and the lateral stability is relatively weak, so that the steering capability of the vehicle is greatly influenced, and the track tracking effect is poor. When the road adhesion coefficient gradually rises, the maximum value of the lateral acceleration is increased along with the increase of the road adhesion coefficient, the lateral adhesion force of the vehicle is gradually increased, the lateral stability is gradually enhanced, and the steering capacity of the vehicle is improved along with the increase of the road adhesion coefficient, so that the maximum value of the path tracking error is also rapidly reduced to be close to 0.5m at least, and the track tracking effect is good.

FIG. 11 is a graph of centroid slip angle maximum as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds.

FIG. 12 is a three-dimensional graph of the maximum value fluctuation of the centroid slip angle of the autonomous vehicle under all operating conditions.

FIG. 13 is a graph of centroid side deviation angle standard deviation as a function of road adhesion coefficient for an autonomous vehicle at various vehicle speeds. When the road attachment coefficient is between 0.1 and 0.4, the vehicle mass center slip angle is limited within a constraint range of (-2 degrees, 2 degrees); when the road adhesion coefficient is between 0.5 and 0.9, the vehicle mass center slip angle is limited within the constraint range of (-12 degrees and 12 degrees), and the driving safety of the automobile is guaranteed.

As can be seen from fig. 11, 12 and 13, when the road attachment coefficient is between 0.1 and 0.4, the vehicle centroid slip angle is limited to the constraint range of (-2 °,2 °); when the road adhesion coefficient is between 0.5 and 0.9, the vehicle mass center slip angle is limited within the constraint range of (-12 degrees and 12 degrees), and the driving safety of the automobile is guaranteed.

Fig. 14 is a graph showing the variation of the maximum value of the front wheel side slip angle with the road adhesion coefficient at various vehicle speeds of the autonomous vehicle.

FIG. 15 is a three-dimensional graph of the maximum front wheel side slip angle fluctuation of an autonomous vehicle under all operating conditions. When the vehicle runs on a road surface with a road adhesion coefficient larger than 0.3 at a speed of 10m/s, the maximum value of the front wheel side deviation angle is lower than 3 degrees, and the side deviation characteristic of the wheel is in a linear region; when the vehicle is driven on a road surface with a road adhesion coefficient of more than 0.5 at a vehicle speed of 15m/s, the maximum value of the front wheel slip angle is less than 3 degrees, and the slip characteristic of the wheels is in a linear region. When the vehicle speed is greater than 20m/s, the maximum value of the front wheel slip angle is higher than 3 degrees regardless of the change in the road adhesion coefficient, and the wheel slip characteristic is in a non-linear region. This means that when the vehicle travels through a sharp curve at 50m or 100m at a speed of more than 20m/s, the cornering characteristic of the wheel is in a nonlinear region, and the lateral force generated by the tire gradually becomes saturated, and the steering characteristic of the vehicle changes, thereby causing a risk of sideslip or the like. In addition, when the cornering characteristics of the wheels are in a non-linear region, it is difficult for a driver to accurately manipulate the steering wheel according to driving experience, and the driving direction of the vehicle is controlled, so that traffic accidents are likely to occur.

As can be seen from fig. 14 and 15, when the vehicle is running on a road surface having a road adhesion coefficient greater than 0.3 at a vehicle speed of 10m/s, the maximum value of the front wheel cornering angle is less than 3 °, and the wheel cornering characteristics are in the linear region; when the vehicle is driven on a road surface having a road adhesion coefficient of greater than 0.5 at a vehicle speed of 15m/s, the maximum value of the front wheel cornering angle is less than 3 °, and the wheel cornering characteristics are in a linear region. When the vehicle speed is greater than 20m/s, the maximum value of the front wheel cornering angle is higher than 3 ° regardless of the change in the road adhesion coefficient, and the wheel cornering characteristics are in a non-linear region. This means that when the vehicle travels through a sharp curve at 50m or 100m at a speed of more than 20m/s, the cornering characteristic of the wheel is in a nonlinear region, and the lateral force generated by the tire gradually becomes saturated, and the steering characteristic of the vehicle changes, causing a risk of sideslip or the like. In addition, when the wheel cornering characteristics are in a non-linear region, it is difficult to control the vehicle running direction, and traffic accidents are very likely to occur.

FIG. 16 is a graph of front wheel cornering power standard deviation versus road adhesion coefficient for an autonomous vehicle at various vehicle speeds. When the vehicle runs on a road surface with a high road adhesion coefficient at a low speed, the standard deviation of the front wheel side deflection angle is relatively small, which indicates that the dispersion degree of the front wheel side deflection angle relative to the average value of the front wheel side deflection angle is smaller in the track tracking process of the vehicle, and the running stability of the vehicle is not greatly changed. In order to ensure that the tracking effect of the vehicle is ensured and the driving stability and safety of the vehicle are maintained in the process of tracking the track, a vehicle stability system such as an ESP (electronic stability program) is required to be installed.

FIG. 17 is a chart of the autonomous vehicle full condition trajectory tracking stability/instability region partitioning. In order to obtain good track tracking accuracy and driving safety, the matching relation between the vehicle speed and the road adhesion coefficient is considered, and the driving condition of the vehicle is divided into two areas: a stable region and a destabilizing region. When the vehicle runs in a stable area working condition, the vehicle has good track tracking precision and running safety; when the vehicle runs under the working condition of the unstable area, the track tracking precision and the running safety are rapidly deteriorated, and at the moment, the vehicle speed needs to be timely adjusted according to the road information detected by the sensor, and the vehicle returns to the stable working condition area to run again.