Estimation of Road Friction Coefficient via the Data Enforced Unscented Kalman Filter

Tire-road friction coefficient (TRFC) estimation is significant to ADAS and high-level autonomous driving. This paper presents a dynamics-based method of real-time TRFC estimation. 2D-LuGre model and unscented Kalman Filtering have been utilized to achieve real time TRFC estimation during both straight driving and steering condition. Observability of the established system based on LuGre model is proved. The observable condition is compatible with reality and simulation result, which can be considered as the theoretical effective boundary of all dynamics-based methods. The performance of our method has been verified by simulation experiment, and results show that our method can achieve high accuracy, convergence speed and robustness.

The traditional unscented Kalman filter (UKF) will have the problem of reduced accuracy or even divergence in the estimation process due to state model perturbation, unknown noise of the system, and other factors, which in turn affect the estimation results of the tire-road friction coefficient. By this problem, the paper investigates the tire-road friction coefficient estimation by taking an automatic guided vehicle (AGV) as the research object and proposes an adaptive singular value decomposition unscented Kalman filter (ASVD-UKF) with a noise estimator. Singular value decomposition (SVD) is introduced into the unscented Kalman filter (UKF) for Sigma sampling to suppress the negative definiteness of the state covariance matrix in UFK. The paper considered estimation schemes for joint road, μ-split road, and μ-different road and constructed corresponding ASVD-UKF observers to reduce the dimension of the road estimation model and real-time observation of four tire-road friction coefficients. Results show that the average absolute error of the μ-split road, joint road, and μ-different road proposed in this paper is significantly smaller than that of UFK, and the estimation accuracy is improved by 13.39%, 6.74%, and 5.71%, respectively. A Distributed Drive AGV prototype was developed for a real vehicle verification experiment, with only a 1.14% error between simulation and experiment. It is further proved that the designed observers are practical. The research can provide a theoretical basis and experimental foundation for the tire-road friction coefficient estimation.

An H∞ control strategy based on the phase plane method (phase plane H∞ controller) tracking two degrees of freedom (DOF) ideal vehicle trajectory scheme is designed for distributed drive electric vehicles with stability enhancement. Firstly, an Extended Kalman Filter (EKF) tire road friction coefficient estimation method based on Keras neural network is presented to accurately and efficiently identify the tire road friction coefficient, taking into account the huge influence of the tire road friction coefficient on vehicle equilibrium point and stability region. Secondly, the phase plane method is applied to provide a dynamic stability boundary for the switching control strategy of direct yaw moment for different tire road friction coefficients; Furthermore, based on the dynamic stability boundary, the weighted phase stability is applied to achieve more realistic stability evaluation criteria, and the fuzzy control strategy is adopted to carry out the feedback regulator of the target side slip angle and yaw rate on the purpose of limiting its maximum value max ( β) and max ( ωr). Then the torque of the four-wheel was optimized by the quadratic programming method. Finally, the presented method is verified and the results indicate that: (1) the phase plane H∞ control has the advantage in terms of stability and maneuvering performance. More importantly, under a low tire road friction coefficient, the amplitude of the side slip angle is decreased by 26.52% over the H∞; (2) the designed EKF based on Keras neural network parameter correction has a quick and accurate performance in identifying the tire road friction coefficient, and the steady-state error does not exceed 3.25%.

A tire-road friction coefficient estimation approach is proposed which makes use of the uncoupled lateral deflection profile of the tire carcass measured from inside the tire through the entire contact patch. The unique design of the developed wireless piezoelectric sensor enables the decoupling of the lateral carcass deformations from the radial and tangential deformations. The estimation of the tire-road friction coefficient depends on the estimation of slip angle, lateral tire force, aligning moment, and the use of a brush model. The tire slip angle is estimated as the slope of the lateral deflection curve at the leading edge of the contact patch. The portion of the deflection profile measured in the contact patch is assumed to be a superposition of three types of lateral carcass deformations, namely, shift, yaw, and bend. The force and moment acting on the tire are obtained by using the coefficients of a parabolic function which approximates the deflection profile inside the contact patch and whose terms represent each type of deformation. The estimated force, moment, and slip angle variables are then plugged into the brush model to estimate the tire-road friction coefficient. A specially constructed tire test rig is used to experimentally evaluate the performance of the developed estimation approach and the tire sensor. Experimental results show that the developed sensor can provide good estimation of both slip angle and tire-road friction coefficient.

The effect of vehicle active safety systems is subject to the friction force arising from the contact of tires and the road surface. Therefore, an adequate knowledge of the tire-road friction coefficient is of great importance to achieve a good performance of these control systems. This paper presents a tire-road friction coefficient estimation method for an advanced vehicle configuration, four-motorized-wheel electric vehicles, in which the longitudinal tire force is easily obtained. A hierarchical structure is adopted for the proposed estimation design. An upper estimator is developed based on unscented Kalman filter to estimate vehicle state information, while a hybrid estimation method is applied as the lower estimator to identify the tire-road friction coefficient using general regression neural network (GRNN) and Bayes' theorem. GRNN aims at detecting road friction coefficient under small excitations, which are the most common situations in daily driving. GRNN is able to accurately create a mapping from input parameters to the friction coefficient, avoiding storing an entire complex tire model. As for large excitations, the estimation algorithm is based on Bayes' theorem and a simplified “magic formula” tire model. The integrated estimation method is established by the combination of the above-mentioned estimators. Finally, the simulations based on a high-fidelity CarSim vehicle model are carried out on different road surfaces and driving maneuvers to verify the effectiveness of the proposed estimation method.

In the case of modern day vehicle control systems employing a feedback control structure, a real-time estimate of the tire-road contact parameters is invaluable for enhancing the performance of the chassis control systems such as anti-lock braking systems (ABS) and electronic stability control (ESC) systems. However, at present, the commercially available tire monitoring systems are not equipped to sense and transmit high speed dynamic variables used for real-time active safety control systems. Consequently, under the circumstances of sudden changes to the road conditions, the driver's ability to maintain control of the vehicle maybe at risk. In many cases, this requires intervention from the chassis control systems onboard the vehicle. Although these systems perform well in a variety of situations, their performance can be improved if a real-time estimate of the tire-road friction coefficient is available. Existing tire-road friction estimation approaches often require certain levels of vehicle longitudinal and/or lateral motion to satisfy the persistence of excitation condition for reliable estimations. Such excitations may undesirably interfere with vehicle motion controls. This paper presents a novel development and implementation of a real-time tire-road contact parameter estimation methodology using acceleration signals from a smart/intelligent tire. The proposed method characterizes the terrain using the measured frequency response of the tire vibrations and provides the capability to estimate the tire road friction coefficient under extremely lower levels of force utilization. Under higher levels of force excitation (high slip conditions), the increased vibration levels due to the stick/slip phenomenon linked to the tread block vibration modes make the proposed tire vibrations based method unsuitable. Therefore for high slip conditions, a tire-road friction model-based parameter estimation approach is proposed. Hence an integrated approach using the smart/intelligent tire based friction estimator and the model based estimator gives us the capability to reliably estimate friction for a wider range of excitations. Considering the strong interdependence between the operating road surface condition and the instantaneous forces and moments generated; this real time estimate of the tire-road friction coefficient is expected to play a pivotal role in improving the performance of a number of vehicle control systems. In particular, this paper focuses on the possibility of enhancing the performance of collision mitigation braking systems. Language: en

The rapid development of autonomous driving technologies places higher demands on the accurate estimation of tire-road friction coefficient (TRFC) in vehicle motion and vehicle dynamics control. A tire model must be built to accurately describe the friction conditions between the tire and road surface. The Unitire model not only holds the advantage of highly accurate representation of tire properties under various complex situations, but it also takes complete account of the relationship between TRFC and road conditions, tire load, and slip speed through dynamic friction characteristics. Therefore, a method based on the Unitire model for TRFC estimation is proposed in this paper. A normalized force calculation method for the Unitire model is proposed subsequently. The simulation experiment results show that the proposed method performs better than the general tire model, which indicates the great potential of the Unitire model for TRFC estimation.

Accurately understanding the Tire-Road Friction Coefficient (TRFC) interaction is crucial for enhancing overall vehicle control performance. However, existing estimation methods heavily rely on the accuracy of tire modeling, which may not predict TRFC effectively under poor modeling accuracy or changing operating conditions. This paper proposes an interacting multiple-model TRFC estimation method using tire force observation. Firstly, taking advantage of the observation capabilities of distributed drive electric vehicles, a longitudinal force estimator with unknown inputs is designed. Simultaneously, a lateral force observer based on adaptive sliding mode observer (ASMO) is developed, fully utilizing the onboard sensor data of the vehicle. A TRFC estimator with square root cubature Kalman filter, incorporating square root filtering, is proposed to reduce algorithm complexity while ensuring accuracy. Finally, an interacting multiple-model mechanism is specifically developed for both pure longitudinal dynamics and combined conditions. Through Carsim-Matlab co-simulation and high TRFC test conditions of a real vehicle equipped with a 6-axis wheel transducer, it is shown that the algorithm proposed in this article can accurately estimate tire force and TRFC under various maneuvering conditions and different TRFC conditions. Based on the comparison with traditional algorithms, it shows that our proposed algorithm has higher estimation accuracy and robustness.

Knowledge of tire–road friction coefficient (TRFC) is valuable for autonomous vehicle control and design of active safety systems. This paper investigates TRFC estimation on the basis of longitudinal vehicle dynamics. A two-stage TRFC estimation scheme is proposed that limits the disturbances to the vehicle motion. A sequence of braking pressure pulses is designed in the first stage to identify desired minimal pulse pressure for reliable estimation of TRFC with minimal interference with the vehicle motion. This stage also provides a qualitative estimate of TRFC. In the second stage, tire normal force and slip ratio are directly calculated from the measured signals, a modified force observer based on the wheel rotational dynamics is developed for estimating the tire braking force. A constrained unscented Kalman filter (CUKF) algorithm is subsequently proposed to identify the TRFC for achieving rapid convergence and enhanced estimation accuracy. The effectiveness of the proposed methodology is evaluated through CarSim™-MATLAB/Simulink™ co-simulations considering vehicle motions on high-, medium-, and low-friction roads at different speeds. The results suggest that the proposed two-stage methodology can yield an accurate estimation of the road friction with a relatively lower effect on the vehicle speed.

The aims of the research are to overview of the existing online tire-road friction estimation methods, available in the scientific literature, and investigate the possibilities of employing new methodologies to improve the estimation accuracy of this parameter. For this purpose a Matlab/Simulink vehicle dynamics based model was created to facilitate the study of different methods and is suitable also for new concept validation. Three methods were selected for deeper analysis, such as: Slip-Slope Method [2] which utilizes the relationship between normalized longitudinal tire force and slip ratio to determine the friction coefficient; Cornering Stiffness Method [3] which try to detect the maximum of the friction coefficient; Burckhardt Method [4] based on a special formula. All these methods was verified by simulations based on real measurement data recorded by a test car on a test track.

Lateral tire deflection enables the estimation of the tire-road friction coefficient. Vehicle steering, such as driving on a curved highway, can influence the friction coefficient estimation. This paper demonstrates an algorithm to estimate the tire-road friction coefficient when a vehicle is steering. The relationship between the friction coefficient and the vehicle steering is derived through a tire brush model. The change of lateral velocity inside the tire-road contact patch is used in the algorithm along with the lateral deflection. The models for the lateral deflection and the change of lateral velocity are derived with the tire brush model, a simple tire model, and a parabolic lateral deflection model. Approximated tire slip angles are fed to the estimation algorithm to capture the change of the steering angle. This algorithm is evaluated in experiments with the steering of a test vehicle.

In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a permanent magnet synchronous motor (PMSM). The algorithm replaces the wheel angular velocity signal with the rotor speed signal obtained from the sensorless control of the PMSM. Firstly, a seven-degree-of-freedom vehicle dynamics model and a mathematical model of the PMSM are established, and the maximum correntropy singular value decomposition generalized high-degree cubature Kalman filter algorithm (MCSVDGHCKF) is derived. Secondly, a sensorless control system of a PMSM based on the MCSVDGHCKF algorithm is established to estimate the rotor speed and position of the PMSM, and its effectiveness is verified. Finally, the feasibility of the algorithm for TRFC estimation in non-Gaussian noise is demonstrated through simulation experiments, the Root Mean Square Error (RMSE) of TRFC estimates for the right front wheel and the left rear wheel were reduced by at least 41.36% and 40.63%, respectively. The results show that the MCSVDGHCKF has a higher accuracy and stronger robustness compared to the maximum correntropy high-degree cubature Kalman filter (MCHCKF), singular value decomposition generalized high-degree cubature Kalman filter (SVDGHCKF), and high-degree cubature Kalman filter (HCKF).

Many surveys on vehicle traffic safety have shown that the tire road friction coefficient (TRFC) is correlated with the probability of an accident. The probability of road accidents increases sharply on slippery road surfaces. Therefore, accurate knowledge of TRFC contributes to the optimization of driver maneuvers for further improving the safety of intelligent vehicles. A large number of researchers have employed different tools and proposed different algorithms to obtain TRFC. This work investigates these different methods that have been widely utilized to estimate TRFC. These methods are divided into three main categories: off-board sensors-based, vehicle dynamics-based, and data-driven-based methods. This review provides a comparative analysis of these methods and describes their strengths and weaknesses. Moreover, some future research directions regarding TRFC estimation are presented.

The performance of vehicle active safety electric control system often depends on accurate estimation of the tire/road friction coefficient. The control target parameters should change along with the tire/road friction coefficient and implement different control strategy and control algorithm. Due to the interaction mechanism between tire and ground is very complex, so the multi-freedom rim-beam dynamic model with tire dynamic friction model is set up in this paper. And the key parameters influence characteristics was simulated analysis and the tire/road coefficient estimation model was established. The wheel speed signal conditioning circuit was designed and filtered out the noise by soft threshold wavelet. Finally, vehicle field tests of high, low and joint road were carried out, and the brake pressure (brake torque), vehicle velocity (wheel speed), slip ratio and wheel speed sensor sine wave time-frequency analysis and tire-road friction coefficient estimation were analyzed.

Estimation of tire-road friction coefficient based on combined APF-IEKF and iteration algorithm