CN116409327A - Road surface adhesion coefficient estimation method considering transient characteristics of tire under lateral working condition - Google Patents
Road surface adhesion coefficient estimation method considering transient characteristics of tire under lateral working condition Download PDFInfo
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Abstract
The invention provides a road surface adhesion coefficient estimation method considering transient characteristics of a tire under a lateral working condition, which comprises the following steps: step one: modeling vehicle dynamics; step two: estimating road adhesion coefficient based on unscented Kalman filtering; step three: UKF estimation error adjustment; step four: and (5) time delay estimation. The invention solves the problem of inaccurate road adhesion coefficient estimation caused by lateral response lag generated by the transient characteristic of the tire; meanwhile, the invention utilizes a time delay estimation method to carry out time sequence delay estimation on the estimated value and the actual measured value of the lateral acceleration of the vehicle, and corrects the lateral slip rate on the steady-state tire model, so that the time sequence between the estimated value and the actual measured value of the lateral acceleration is consistent, and the recognition precision of the road surface attachment coefficient is further improved.
Description
Technical Field
The invention relates to the technical field of vehicle dynamics model parameter estimation.
Background
The magnitude of the road attachment coefficient directly determines the limit boundary of motion of the vehicle, i.e., at low road attachment coefficients, the force that the ground can provide to the vehicle for motion is less and the vehicle tire force is more likely to saturate than at high road attachment coefficients. Thus, road adhesion coefficient is a key variable in vehicle chassis motion control systems. The existing road surface adhesion coefficient identification method is generally based on a Kalman filter estimator, and utilizes vehicle state variables and control variables to identify the current road surface adhesion coefficient. Because of the limitation of the continuous excitation condition, the methods have strict limitation on the identification working condition, for example, the road adhesion coefficient identification can be performed only when the linear acceleration driving is performed and the acceleration is larger than the threshold value. This limitation greatly restricts the accuracy and instantaneity of the road surface adhesion coefficient estimation method.
Compared with the recognition of the road surface adhesion coefficient based on the longitudinal working condition, the real-time estimation coefficient under the lateral working condition is more important to the chassis control system, and the yaw movement limit of the vehicle is calculated in real time according to the estimation coefficient, so that the vehicle is prevented from being unstable under the lateral movement working condition. However, the existing road surface adhesion coefficient estimation methods based on Kalman filter estimators all adopt steady-state tire models, neglect transient characteristics of tires when the tires perform lateral movement, and lead to phase lag between estimated values and actual measured values based on the steady-state models, so that the accuracy of road surface adhesion coefficient estimation is directly affected.
Disclosure of Invention
In order to ensure the estimation precision of the road surface adhesion coefficient when the vehicle moves laterally, the invention provides a road surface adhesion coefficient estimation method considering the transient characteristic of a tire under the lateral working condition.
The technical scheme of the invention is as follows:
the road adhesion coefficient estimation method considering the transient characteristics of the tire under the lateral working condition comprises the following steps:
step one: vehicle dynamics modeling
Aiming at the problem of estimating the road adhesion coefficient under the lateral working condition, a three-degree-of-freedom vehicle model is selected, wherein the three-degree-of-freedom vehicle model comprises three degrees of freedom, namely longitudinal movement, transverse movement and rotation around the z axis of a vehicle coordinate system;
step two: estimation of road adhesion coefficient based on unscented Kalman filtering
Based on the vehicle dynamics model established in the first step, the relation between the road adhesion coefficient and the observed variables (longitudinal acceleration, lateral acceleration and yaw rate) is obtained; the road adhesion coefficient is used as a state variable, and the observation variable is
The vehicle state variables (longitudinal speed, lateral speed, front and rear axle wheel speeds, steering wheel angles and the like) in the vehicle dynamics model are time-varying parameters, and the vehicle structural parameters (mass center to front axle distance, wheelbase, steering transmission ratio, tire effective radius and the like) are fixed parameters;
step three: UKF estimation error adjustment
When the slip rate is smaller, under different road surface attachment coefficients, the relationship between the tire force and the slip rate is consistent, the original value is maintained, and when the lateral acceleration estimation error is larger, the P covariance matrix is updated;
when a is detected y When the error between the estimated and measured values is greater than ε, then covariance matrix P is reset to P 0 ，
Wherein a is y For the actual measurement value of the sensor,
the UKF current estimated value is epsilon as the parameter to be calibrated
Step four: delay estimation
The time delay between the actual measurement value and the estimated value of the lateral acceleration is calculated through a time cross-correlation (cross-correlation) function, and the delay time is added to the estimated value of the lateral acceleration, so that time sequence calibration between the actual measurement value and the estimated value is realized.
The method solves the problem of inaccurate road adhesion coefficient estimation caused by lateral response lag generated by transient characteristics of the tire; and carrying out time sequence delay estimation on the estimated value and the actually measured value of the lateral acceleration of the vehicle by using a time delay estimation method, and correcting the lateral slip rate on a steady-state tire model so that the time sequence between the estimated value and the actually measured value of the lateral acceleration is consistent, thereby improving the recognition precision of the road surface adhesion coefficient.
Drawings
FIG. 1 is a block diagram of a method for estimating road adhesion coefficient taking into account transient characteristics of a tire under lateral conditions;
FIG. 2 is a relationship between slip ratio and nominal tire force;
FIG. 3 shows the road adhesion coefficient recognition result;
FIG. 4 is a graph showing the change of the estimated value and the actual value of the lateral acceleration;
FIG. 5 is a schematic diagram of a vehicle model;
FIG. 6 is a simulation comparison chart of road adhesion coefficients;
FIG. 7 is a simulated comparison of lateral acceleration;
FIG. 8 is a graph of front wheel angle change during simulation;
fig. 9 is a graph of the change in vehicle speed during simulation.
Detailed Description
The technical solutions provided in the present application will be further described below with reference to specific embodiments and accompanying drawings. The advantages and features of the present application will become more apparent in conjunction with the following description.
The invention provides a road surface adhesion coefficient identification method integrating time delay estimation by considering the transient characteristics of a tire, and simulation verification is carried out in known dynamics simulation software Carsim. Simulation results under the standard double-lane-change working condition show that compared with a comparison method, the method provided by the invention has great improvement in multiple aspects of convergence time, recognition precision, static error and the like.
The structural block diagram of the road surface adhesion coefficient estimation method taking the transient characteristic of the tire into consideration under the lateral working condition is shown in fig. 1, and the process is as follows:
step one: vehicle dynamics modeling
Aiming at the problem of estimating the road adhesion coefficient under the lateral working condition, the invention selects the three-degree-of-freedom vehicle model. The three degree of freedom vehicle model includes three degrees of freedom, longitudinal motion, lateral motion, and rotation about the z-axis of the vehicle coordinate system. The interaction between the road surface and the tires directly determines the vehicle motion characteristics, so that the selection of a proper tire model is the key for constructing a vehicle dynamics model. Since the Burckhardt tire model can describe the tire force coupling characteristics in a simple structure, the model represents the tire force in an exponential form with a simple structure, which is suitable for a large number of calculations of the present invention. If a more accurate tire model is used here, the effect will be consistent with our analysis, but the tire model parameters involved are more, the expression is more complex, and a more accurate high complexity tire model will greatly increase the difficulty in identifying road adhesion coefficients.
Step two: estimation of road adhesion coefficient based on unscented Kalman filtering
Based on the vehicle dynamics model established in the step one, the relation between the road adhesion coefficient and the observed variables (longitudinal acceleration, lateral acceleration and yaw rate) is obtained. Considering that the vehicle dynamics model is a nonlinear model, a basic method for identifying road adhesion coefficient is constructed by using an unscented Kalman filtering method. The road adhesion coefficient is used as a state variable, and the observation variable is
The vehicle state variables (longitudinal speed, lateral speed, front and rear axle wheel speeds, steering wheel angles and the like) in the vehicle dynamics model are time-varying parameters, and the vehicle structural parameters (mass center to front axle distance, wheelbase, steering transmission ratio, tire effective radius and the like) are fixed parameters.
Step three: UKF estimation error adjustment
For a time-varying system, the traditional unscented Kalman filtering can achieve higher estimation accuracy, but as the unscented Kalman filtering process is carried out, the covariance matrix is iterated continuously, the influence of the accumulation of old data on the covariance matrix P is gradually increased, so that the covariance matrix P is gradually reduced, the estimation process is stabilized, and the unscented Kalman filtering cannot track parameter changes rapidly and accurately. The road adhesion coefficient is determined by the tire and the road type together, is greatly influenced by the driving road type, and when the road type is suddenly changed, such as from asphalt road to snow road, the road adhesion coefficient is suddenly changed along with the road type, and new data can more respond to the parameter change condition than old data at the moment.
Nominal tire force f(s) under different road conditions i ) The change relation with the above is shown in fig. 2.
It can be found from fig. 2 that when the slip ratio is smaller, that is, the four-wheel tire force is smaller, the relationship between the tire force and the slip ratio is almost identical under different road surface adhesion coefficients, and therefore, the slip ratio and the tire force of the tire under different road surface adhesion coefficients are almost identical under the conditions of uniform running and small acceleration of the vehicle. At this time, the recognition of the road adhesion coefficient cannot be realized only based on the vehicle chassis information, so we choose to maintain the original value, and update the P covariance matrix when the lateral acceleration estimation error is large, so as to quickly recognize the road adhesion coefficient value.
Thus when a is detected y When the error between the estimated and measured values is greater than epsilon, the covariance matrix P will be reset.
Wherein a is y For the actual measurement value of the sensor,
the UKF current estimated value is epsilon as the parameter to be calibrated
Step four: delay estimation
From the third step, it can be found that the judgment condition for resetting the covariance matrix is the difference between the measured value of the lateral acceleration and the estimated value of the model. The change process of the lateral acceleration is similar to a sinusoidal signal, the positive and negative values are alternated, and the change range of the acceleration derivative is larger. When the acceleration derivative is large, the tire lateral movement delay will cause a large error and further cause the covariance matrix to be triggered by mistake. When the acceleration is larger, the tire slip angle is positioned near 0 value at the positive-negative conversion point of the lateral acceleration, the excitation condition for identifying the road adhesion coefficient is not met, if the covariance matrix is reset at the moment, the road adhesion coefficient is caused to oscillate violently, as shown in figure 3, the estimated value of the road adhesion coefficient oscillates when the lateral acceleration alternates positive and negative, and the steady state value of the road adhesion coefficient has a great phase difference with the true value.
The invention calculates the time delay between the actual measurement value and the estimated value of the lateral acceleration through a time cross-correlation (cross-correlation) function, and adds the delay time to the estimated value of the lateral acceleration, thereby realizing the time sequence calibration between the actual measurement value and the estimated value.
Step five: software in-loop simulation verification
According to the method proposed above, verification is performed in a carsim-simulink joint simulation environment.
The above steps are described in detail as follows:
step one: vehicle model modeling
Aiming at the recognition problem of road adhesion coefficient under lateral working condition, the invention selects the three-degree-of-freedom model of the vehicle as shown below
ma x ＝F xr -F yf sinδ+F xf cosδ
ma y ＝E yr +F yf cosδ+F xf sinδ
A schematic diagram of the vehicle dynamics model is shown in fig. 5, where m is the vehicle mass; f (F) xf ，F xr The longitudinal force of the front axle and the longitudinal force of the rear axle of the vehicle respectively; f (F) yf ，F yr The lateral force of the front axle and the lateral force of the rear axle of the vehicle respectively; a, a x ，a y 
Longitudinal acceleration, lateral acceleration and yaw rate of the vehicle, respectively; i z Is the rotational inertia of the vehicle about the Z axis; a, b are the centroid to front axis distance and the centroid to rear axis distance, respectively; delta is the front wheel angle of the vehicle.
Then, a formula of longitudinal and lateral forces of a front shaft and a rear shaft in the vehicle three-degree-of-freedom model is established, and the formula is shown as follows by adopting a Burckhardt model:
wherein s is xi I= { f, r } which is the longitudinal slip ratio of the front and rear shafts; r is (r) dyn Is the effective radius of the tire; w (w) wi Wheel speed of the front and rear axles; v x Is the longitudinal speed at the centroid of the vehicle; v y Lateral velocity at the vehicle centroid;
yaw rate at the vehicle centroid; s is(s) i The comprehensive slip rate of the vehicle; f(s) i ) Is the nominal tire force; s is(s) yf The lateral slip rate of the front axle is the lateral slip rate of the front axle; s is(s) yr The lateral slip rate of the rear axle is obtained; f (F) zi For vertical loads c in front of and behind the vehicle 1 ，c 2 Parameters in the tire model, which are determined by the tire characteristics; mu is the road adhesion coefficient and is determined by the running environment of the vehicle.
Wherein L is the distance between the front axle and the rear axle of the vehicle; g is gravity acceleration; h is the height of the centroid from the ground.
Step two: estimation of road adhesion coefficient based on unscented Kalman filtering
Based on the vehicle dynamics model established in the step one, the relationship between the road adhesion coefficient and the observed variables (longitudinal acceleration, lateral acceleration and yaw rate) is obtained. Considering that the vehicle dynamics model is a nonlinear model, a basic method for identifying road adhesion coefficients is constructed by using an unscented Kalman filtering method. The road adhesion coefficient is used as a state variable, and the observation variable is
The vehicle state variables (longitudinal speed, lateral speed, four-wheel speed, steering wheel angle and the like) in the vehicle dynamics model are time-varying parameters, and the vehicle structural parameters (mass center to front axle distance, wheel base, steering transmission ratio, tire effective radius and the like) are fixed parameters.
The standard UKF process is the prior art, and is not described in the specification of the invention, and in the Unscented Kalman Filtering (UKF) process, the state quantity and the covariance P are continuously updated, so that the estimation of the road adhesion coefficient is realized.
Step three: UKF estimation error adjustment
For a time-varying system, the traditional unscented Kalman filtering can realize higher estimation accuracy, but as the unscented Kalman filtering process is carried out, the covariance matrix is iterated continuously, the influence of the accumulation of old data on the covariance matrix P is gradually increased, so that the covariance matrix P is gradually reduced, the estimation process tends to be stable, and the unscented Kalman filtering cannot quickly and accurately track parameter changes.
And when the lateral acceleration estimation error is larger, updating the P covariance matrix, and further rapidly identifying the road adhesion coefficient value.
Thus when an estimate of lateral acceleration is detected
And the measured value a y When the error is greater than ε, then covariance matrix P will be reset to P 0 ＝1×10 -5 。
Wherein a is y For the actual measurement value of the sensor,
the UKF current estimated value is epsilon as the parameter to be calibrated
Step four: delay estimation
From the third step, it can be found that the judgment condition for resetting the covariance matrix is the difference between the measured value of the lateral acceleration and the estimated value of the model. The change process of the lateral acceleration is similar to a sinusoidal signal, the positive and negative values are alternated, and the change range of the acceleration derivative is larger. When the acceleration derivative is large, the tire lateral movement delay will cause a large error and further cause the covariance matrix to be triggered by mistake. When the acceleration is larger, the tire slip angle is positioned near 0 value at the positive-negative conversion point of the lateral acceleration, the excitation condition for identifying the road adhesion coefficient is not met, if the covariance matrix is reset at the moment, the road adhesion coefficient is caused to oscillate violently, as shown in figure 3, the estimated value of the road adhesion coefficient oscillates when the lateral acceleration alternates positive and negative, and the steady state value of the road adhesion coefficient has a great phase difference with the true value. The invention calculates the lateral acceleration a measured by the sensor by using the time cross-correlation function y Lateral acceleration estimated with UKF
The time delay between the two steps is as follows:
first, a cross-correlation function between the measured lateral acceleration value and the estimate is defined:
wherein R (τ) is the cross-correlation function of the two signals; t is the current moment; n is the length of time window of two signals, and the maximum value of the final cross-correlation function is the delay time tau estimated by the sequences of the two signals est 。
Since the delay in the lateral acceleration response is due to tire cornering, the lateral acceleration estimate calculated based on the steady state model will lead τ est And the measured value. Therefore, the delay time τ needs to be added when the lateral slip rate is calculated in the standard UKF est This ensures that the measured value of the lateral acceleration is at the same time as the estimated value of the lateral acceleration, thus adding a delay time τ to the lateral slip rate in step one est The method comprises the following steps:
wherein s is yfτ For the front axle side slip rate after time delay s yrτ For the delayed lateral slip rate of the rear axle, the two slip rates are integrated into a Burckhardt model (vehicle three-degree-of-freedom model), so that the compensation of the transient characteristic of the tire is realized, the estimated lateral acceleration and the actual measurement value of the lateral acceleration are guaranteed to have the same time sequence, and the estimation precision of the road adhesion coefficient is improved. The specific effect is improved and please see step five simulation verification.
Step five: software in-loop simulation verification
According to the method proposed above, verification is performed in a carsim-simulink joint simulation environment.
Waiting for a calibration value E=0.6m/s 2
The test results are shown in fig. 6, 7, 8 and 9.
In fig. 6 and 7, the scheme one estimation represents the estimation of the standard UKF method; the second estimated value of the scheme shows that the judgment of the lateral acceleration estimation error is added on the standard UKF method, but the influence of the delay time is not considered by the lateral acceleration estimation error; the scheme III estimated value represents that the lateral acceleration estimation error judgment, the delay time estimation and the compensation are added based on UKF, namely the method is provided.
As can be seen from fig. 6, in the scheme two, the covariance matrix P is reset to enable the standard UKF algorithm to eliminate the influence of the historical data on the covariance matrix on the fast and accurate tracking of the estimated value of the road adhesion coefficient when the road adhesion coefficient is suddenly changed, but the estimated value oscillation degree of the scheme is greater than that of the scheme three (the method of the invention), the method can be found to fast track the true value of the road adhesion coefficient when the road adhesion coefficient is suddenly changed, and ensure smaller static error.
It can be seen from fig. 7 that there is a large error in the estimated lateral acceleration value of the scheme and the actual value of the lateral acceleration is advanced, the error between the estimated lateral acceleration value of the scheme two and the actual value is small, but there is a phase advance, the error between the estimated lateral acceleration value of the scheme three (the method of the present invention) and the actual value is small, and the phase can be kept consistent.
Fig. 8 and 9 are graphs of the front wheel rotation angle and the vehicle speed in the simulation process, respectively, and it can be known that the simulation working condition is a pure lateral working condition.
The above description is merely illustrative of the preferred embodiments of the present application and is not intended to limit the scope of the present application in any way. Any alterations or modifications of the above disclosed technology by those of ordinary skill in the art should be considered equivalent and valid embodiments, which fall within the scope of the present application.
Claims (4)
1. The road adhesion coefficient estimation method considering the transient characteristics of the tire under the lateral working condition comprises the following steps:
step one: vehicle dynamics modeling
Aiming at the problem of estimating the road adhesion coefficient under the lateral working condition, a three-degree-of-freedom vehicle model is selected, wherein the three-degree-of-freedom vehicle model comprises three degrees of freedom, namely longitudinal movement, transverse movement and rotation around the z axis of a vehicle coordinate system;
step two: estimation of road adhesion coefficient based on unscented Kalman filtering
Based on the vehicle dynamics model established in the first step, obtaining the relation between the road adhesion coefficient and the observed variable, wherein the observed variable comprises longitudinal acceleration, lateral acceleration and yaw rate; the road adhesion coefficient is used as a state variable, and the observation variable is
The vehicle state variables in the vehicle dynamics model are time-varying parameters, the vehicle structure parameters are fixed parameters, wherein the vehicle state variables comprise longitudinal speed, lateral speed, front and rear axle speeds and steering wheel corners, and the vehicle structure parameters comprise a centroid-to-front axle distance, an axle base, a wheel base, a steering transmission ratio and a tire effective radius;
step three: UKF estimation error adjustment
When the slip rate is smaller, under different road surface attachment coefficients, the relationship between the tire force and the slip rate is consistent, the original value is maintained, and when the lateral acceleration estimation error is larger, the P covariance matrix is updated;
when a is detected y When the error between the estimated and measured values is greater than ε, then covariance matrix P is reset to P 0 ，
Wherein a is y For the actual measurement value of the sensor,
the UKF current estimated value is used, and epsilon is a parameter to be calibrated;
step four: delay estimation
And calculating the time delay between the actual measurement value and the estimated value of the lateral acceleration through a time cross-correlation function, and adding the delay time to the estimated value of the lateral acceleration so as to realize time sequence calibration between the actual measurement value and the estimated value.
2. The method for estimating road adhesion coefficient taking into account transient characteristics of tire under lateral conditions as claimed in claim 1, wherein said step one, vehicle model modeling:
the three degrees of freedom model of the vehicle is as follows:
ma x ＝F xr -F yf sinδ+F xf cosδ
ma y ＝F yr +F yf cosδ+F xf sinδ
wherein m is the mass of the automobile; f (F) xf ，F xr The longitudinal force of the front axle and the longitudinal force of the rear axle of the vehicle respectively; f (F) yf ，F yr The lateral force of the front axle and the lateral force of the rear axle of the vehicle respectively; a, a x ，a y ，
Longitudinal acceleration, lateral acceleration and yaw rate of the vehicle, respectively; i z Is the rotational inertia of the vehicle about the Z axis; a, b are the centroid to front axis distance and the centroid to rear axis distance, respectively; delta is the front wheel corner of the vehicle;
then, a formula of longitudinal and lateral forces of a front shaft and a rear shaft in the vehicle three-degree-of-freedom model is established, and the formula is as follows:
wherein s is xi I= { f, r } which is the longitudinal slip ratio of the front and rear shafts; r is (r) dyn Is the effective radius of the tire; w (w) wi Wheel speed of the front and rear axles; upsilon (v) x Is the longitudinal speed at the centroid of the vehicle; upsilon (v) y Lateral velocity at the vehicle centroid;
yaw rate at the vehicle centroid; s is(s) i The comprehensive slip rate of the vehicle; f(s) i ) Is the nominal tire force; s is(s) yf The lateral slip rate of the front axle is the lateral slip rate of the front axle; s is(s) yr The lateral slip rate of the rear axle is obtained; f (F) zi Is the vertical load of the front and the rear of the vehicle; c 1 ，c 2 Parameters in the tire model, which are determined by the tire characteristics; mu is the road adhesion coefficient and is determined by the running environment of the vehicle.
Wherein L is the distance between the front axle and the rear axle of the vehicle; g is gravity acceleration; h is the height of the centroid from the ground.
3. The method for estimating road adhesion coefficient taking into account transient characteristics of tire under lateral working condition as claimed in claim 1, wherein said step three, UKF estimation error adjustment:
when an estimated value of lateral acceleration is detected
And the measured value a y When the error is greater than ε, then covariance matrix P will be reset to P 0 ＝1×10 -5 。
4. The method for estimating road adhesion coefficient taking into account transient characteristics of tire under lateral conditions as claimed in claim 1, wherein said step four: delay estimation
First, a cross-correlation function between the measured lateral acceleration value and the estimate is defined:
wherein R (τ) is the cross-correlation function of the two signals; t is the current moment; n is the length of time window of two signals, and the maximum value of the final cross-correlation function is the delay time tau estimated by the sequences of the two signals est ；
Then, adding a delay time tau to the lateral slip rate in the first step est The method comprises the following steps:
wherein s is yfτ For delayed lateral sliding of front axleRate s yrτ For the delayed rear axle lateral slip rate, the two slip rates are integrated into a vehicle three-degree-of-freedom model, so that the compensation of the transient characteristic of the tire is realized, and the estimated lateral acceleration and the lateral acceleration actual measurement value have the same time sequence.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310325902.1A CN116409327A (en) | 2023-03-29 | 2023-03-29 | Road surface adhesion coefficient estimation method considering transient characteristics of tire under lateral working condition |
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| CN117217015A (en) * | 2023-09-22 | 2023-12-12 | 重庆大学 | Road surface adhesion coefficient estimation method based on vehicle dynamics response |
| CN117217015B (en) * | 2023-09-22 | 2024-06-04 | 重庆大学 | Road surface adhesion coefficient estimation method based on vehicle dynamics response |
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| CN117217015A (en) * | 2023-09-22 | 2023-12-12 | 重庆大学 | Road surface adhesion coefficient estimation method based on vehicle dynamics response |
| CN117217015B (en) * | 2023-09-22 | 2024-06-04 | 重庆大学 | Road surface adhesion coefficient estimation method based on vehicle dynamics response |
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