Estimation of Road Friction Coefficient in Different Road Conditions Based on Vehicle Braking Dynamics
- You-Qun Zhao^{1},
- Hai-Qing Li^{1},
- Fen Lin^{1}Email author,
- Jian Wang^{2} and
- Xue-Wu Ji^{3}
https://doi.org/10.1007/s10033-017-0143-z
© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2017
Received: 12 October 2015
Accepted: 20 April 2017
Published: 3 May 2017
The Erratum to this article has been published in Chinese Journal of Mechanical Engineering 2017 30:178
Abstract
The accurate estimation of road friction coefficient in the active safety control system has become increasingly prominent. Most previous studies on road friction estimation have only used vehicle longitudinal or lateral dynamics and often ignored the load transfer, which tends to cause inaccurate of the actual road friction coefficient. A novel method considering load transfer of front and rear axles is proposed to estimate road friction coefficient based on braking dynamic model of two-wheeled vehicle. Sliding mode control technique is used to build the ideal braking torque controller, which control target is to control the actual wheel slip ratio of front and rear wheels tracking the ideal wheel slip ratio. In order to eliminate the chattering problem of the sliding mode controller, integral switching surface is used to design the sliding mode surface. A second order linear extended state observer is designed to observe road friction coefficient based on wheel speed and braking torque of front and rear wheels. The proposed road friction coefficient estimation schemes are evaluated by simulation in ADAMS/Car. The results show that the estimated values can well agree with the actual values in different road conditions. The observer can estimate road friction coefficient exactly in real-time and resist external disturbance. The proposed research provides a novel method to estimate road friction coefficient with strong robustness and more accurate.
Keywords
1 Introduction
It is a powerful means to improve vehicle driving safety and stability performances via active safety system such as emergency collision avoidance (ECA), active front steering (AFS), anti-lock braking system (ABS), direct yaw moment control (DYC) and traction control system (TCS) [1–6]. They work well only with the tire forces within the friction limit, which means knowledge of the road friction coefficient may improve the performance of the systems. For example, during a steering process, the lateral tire force is limited by the road friction coefficient. The vehicle would drift out if the vehicle steers severely at a relatively high speed because of limitation of the lateral tire force. If the active control system could estimate the friction limitation at the time driver begins to steer and initiatives to reduce the speed, the lateral dynamics of the vehicle would be improved [4]. Wheel braking under the different road condition, we usually can’t get the real-time value of road friction coefficient, which leads the instability of the whole control process [7, 8]. So road friction coefficient has an important significance in the vehicle chassis electronic control system design. The accurate estimation of the road friction coefficient can facilitate the improvement of the active safety system and attain a better performance in operating vehicle safety systems. Active safety system can automatically adjust the control strategy according to changing of road surfaces with respect to the friction properties, and which can maximize the function of the control system.
In recent years, to obtain road friction coefficient, many scholars have proposed various estimation methods [8–21]. Among them, domestic scholars especially Liang LI and their teams used signal fusion method [8, 9], double cubature kalman filter method [10], and observer [11] to estimate the road friction coefficient. Generally speaking, they are mainly classified into two groups of special-sensor-based [12–14] methods and vehicle-dynamics-based methods, also known as Cause-based and Effect-based [15]. Method of Cause-based was used by optical sensors to measure light absorption and scattering of road according to the road surface shapes and physical properties. This method looks simple and direct, but has practical issue of cost, which limits its use in production vehicle. Effect- based method was presented by measuring the related response of vehicle dynamics model and applies extended kalman filtering or other algorithm to obtain its value. The vehicle dynamics model included both longitudinal and/or lateral dynamics [16, 17]. The main features of these methods could make full use of the on-board sensors and reduce costs, which has been widely used.
Two very similar studies [18, 19] used the kalman filter (KF) to estimate the longitudinal force of the vehicle first and then through the recursive least squares (RLS) method and the change of CUSUM estimated the road friction coefficient. Wenzel, et al. [20], reported another method of the dual extended kalman filter (DEKF) for road friction coefficient estimation. Comparing kalman filter algorithm and the extended kalman filtering algorithm, Ref. [21] design a extended state observer (ESO) by means of the dynamics model of 1/4 tire for braking to estimate road friction coefficient. This method can ensure high calculation accuracy and do not need to solve Jacobian trial.
This article, considering load transfer of front and rear axles, the braking dynamic model of two-wheeled vehicle was built. Sliding mode control method was used to build the ideal braking torque controller, which control objective is to control the actual wheel slip ratio of front and rear wheels tracking the ideal wheel slip ratio. In order to eliminate chattering problem of the sliding mode controller, integral switching surface was used to design the sliding mode surface. Road friction coefficient can be observed by second order linear extended state based on wheel speed and braking torque of front and rear wheels. Comparing with the article discussed, this method considered the effect of axle load transfer to the road friction coefficient estimation. It has both fewer parameters taking into account and higher computational efficiency.
2 Vehicle Braking Dynamics Model
2.1 Full-Vehicle Model
2.2 Full-Vehicle Model
Friction model parameters of different road
Road surface conditions | C _{1} | C _{2} | C _{3} |
---|---|---|---|
Dry asphalt | 1.2801 | 23.990 | 0.5200 |
Dry concrete | 1.1973 | 25.186 | 0.5373 |
Snow | 0.1946 | 94.129 | 0.0646 |
Ice | 0.0500 | 306.390 | 0.0000 |
As can be seen from the figure, Burckhardt tire model describes the nonlinear change law of road friction coefficient vs. wheel slip rate is good.
3 Braking Torque Controller Design
3.1 Braking Torque Design
3.2 Eliminate chattering
4 Road Friction Coefficient Observer Design
Linear extended state observer can expand the uncertainties and unknown perturbation controlled object model into new state observation and it is very suitable for road friction coefficient estimation problems which only have the measured output and control input [25, 26]. Using the linear extended state observer, road friction coefficient can be observed, where friction coefficient between tire and road as output of the second order linear extended state and angular speed and braking torque of front and rear wheels as the input.
If the estimation scheme of rear wheel is the same with front wheel, there is no need to show the estimation scheme of rear wheel.
5 Simulation Results
5.1 High Friction Coefficient Road Surface
5.2 Low Friction Coefficient Road Surface
It can be easily seen that the proposed linear extended state observer can estimate the road friction coefficient, with good accuracy in comparison with the measurements in vehicle braking on a single high or low friction coefficient road surface. Even in noise interference, it also can estimate road friction coefficient efficiently. However, the road friction coefficient estimation values of using the front wheels are better than rear wheels.
Next, simulations in uneven friction coefficient road conditions are discussed in detail.
5.3 Uneven Friction Coefficient Road
For road friction coefficient estimation in uneven friction road, the road surface with friction coefficients ranged from high to low and low to high are designed.
We can easily find that the estimated road friction coefficient in ideal condition (Fig. 12(a), (c)) or measurement with noise interference (Fig. 12(b), (d)) is close to the reference values and the estimated values are less influenced by noise interference.
Though the road coefficients change greatly, the simulation results show that the proposed estimate method can still estimate road friction coefficient exactly with strong robustness, which can resist external disturbance.
6 Conclusions
- (1)
According to the vehicle braking dynamics, the linear extended state observer to estimate the road friction coefficient is presented, which has a good accuracy when vehicle drive on the road of different friction coefficient.
- (2)
Using the method of saturation function and integral switching surface can eliminate chattering of sliding mode control.
- (3)
Simulation results using the front wheels of road friction coefficient estimation values are better than rear wheels.
- (4)
The proposed method has strong robustness in different road conditions, which can resist external disturbance.
Notes
Authors’ Affiliations
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