Tire-road Friction Coefficient Estimation Research Articles

Enhanced Vehicle Dynamics and Safety through Tire–Road Friction Estimation for Predictive ELSD Control under Various Conditions of General Racing Tracks

This study focuses on the tire–road friction estimation for the predictive control strategy of electronically limited slip differential (ELSD) to improve the handling and acceleration performance of front-wheel drive cars, which typically suffer from excessive understeer and inner drive wheel spin during acceleration while turning due to reduced vertical load on the wheel. To mitigate this, we propose a control logic for ELSD that enhances course followability and acceleration by pre-transferring the driving torque from the inside to the outside wheel, considering the estimated traction potential for rapid response. It is essential to improve the control accuracy of wheel spin prediction by predicting the friction coefficient of the road surface. Furthermore, this study extends to the analysis of vehicle dynamics during lane-change maneuvers on low-friction surfaces, emphasizing the role of accurate tire–road friction estimation in vehicle safety. A CarSim 2023-based simulation study was conducted to investigate the vehicle response on snowy roads with low friction coefficients (μ = 0.2) and low temperatures (−5 °C). The results demonstrated that even minimal steering input could result in significant side-slip angles, highlighting the nonlinear vehicle behavior and the critical need for robust traction estimation in such challenging conditions of general racing tracks. The proposed friction-estimation method was evaluated through vehicle testing and has been substantiated by patents for its originality in control and friction-estimation approaches. The outcomes of these combined methodologies underline the critical importance of tire–road friction coefficient estimation in both the effectiveness of the ELSD system and the broader context of active safety systems.

Tire Road Friction Coefficient Estimation for Individual Wheel based on two Robust PMI Observers and a Multilayer Perceptron

Tire Road Friction Coefficient Estimation for Individual Wheel based on two Robust PMI Observers and a Multilayer Perceptron

A phase plane H∞ controller for distributed drive electric vehicles with stability enhancement based on 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%.

Tire-Road Friction Coefficient Estimation for Distributed Drive Electric Vehicles Using PMSM Sensorless Control

Many tire-road friction coefficient estimation methods require the wheel angular speed sensor to provide a signal. In this paper, a tire-road friction coefficient estimation algorithm for distributed drive electric vehicles using permanent magnet synchronous motors(PMSM) sensorless control is proposed to reduce the use of wheel angular speed sensors. The wheel angular speed signal is replaced by the rotor speed signal obtained from PMSM sensorless control. First, the three degrees of freedom vehicle dynamics model and the PMSM mathematical model are established, and a strong tracking cubature Kalman filtering algorithm based on orthogonal transformation (T-STCKF) is derived to overcome the problem that the STCKF algorithm is prone to nonlocal sampling when dealing with high dimensional systems. Second, a PMSM sensorless control system based on the adaptive exponent reaching law of sliding mode control and the T-STCKF algorithm is established, and confirmed its validity. Finally, the feasibility of the proposed algorithm is demonstrated through multicase simulation and experiment and the results shows that the T-STCKF algorithm is more accurate than the STCKF algorithm.

Tire-road friction coefficient estimation for automatic guided vehicle under multiple road conditions

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.

Pavement Friction Evaluation Based on Vehicle Dynamics and Vision Data Using a Multi-Feature Fusion Network

The tire–road friction coefficient is a critical evaluation index of the service performance of roads: it governs the stopping distance, traction control, and stability of vehicles. Moreover, friction information is also needed in many function units of modern vehicles. This paper proposes a novel data-driven approach for inference of the maximum tire–road friction coefficient using a combination of vehicle dynamics signal and machine vision data. The approach is aimed at robust road condition perception that can provide frequent measurements over large areas across all weather conditions. Two different neural network architectures were adopted to extract in-depth features behind vehicle dynamics signals and road surface images. Features from these two types of data were then fused in two different levels, namely feature level and decision level, forming a multi-feature fusion neural network. The proposed network performs better than models based only on dynamic signals or vision data. The method proposed was applied to real data obtained from an electric car in a highway driving scenario. For classification of the maximum tire–road friction coefficient, the proposed network can yield F1-score increments of 0.09 and 0.18 from dynamics-based and vision-based sub-models, respectively. For the maximum tire–road friction coefficient value regression, the proposed model also achieves the highest R-square score of 0.71. Of these two types of data collected under highway driving scenarios, the vision data contribute more to the overall performance of the proposed model. Nevertheless, the dynamics data possess excellent potential in poor lighting conditions. With these fused features, the proposed multi-feature fusion network can not only improve the accuracy of maximum tire–road friction coefficient estimation but also is deemed workable for a broader range of scenarios.

A model-based method of tire-road friction estimation for articulated steering vehicles

Articulated steering vehicles (ASV) are widely used in many industries for their high efficiency and excellent maneuverability. The autonomous driving and intelligent control of ASV are extremely critical owing to the operation characteristics. As a very important parameter, the tire-road friction coefficient (TRFC) determines the extreme tire force directly in the process of intelligent control. However, it cannot be obtained with the existing methods for the harsh environment and special structure of ASV. This paper proposed a two-layer model-based method of tire-road friction coefficient estimation for ASV. The dynamic models of ASV in the XY plane, including the longitudinal and lateral models of frames, tire forces, and steering system models, are established first. The dynamic models are embedded into the upper layer with a Kalman filter (KF) to estimate the tire forces in longitudinal and lateral directions. During the process, some self-contained sensors, including the state sensors of frames and steering system, are used to provide the observation data. In the lower layer, a recursive least square (RLS) method with a forgetting factor is used to obtain the TRFC and tire stiffness parameters with the aid of the tire model. The simulation and field test are carried out to validate the method under comprehensive conditions, in which different steering commands, velocities, and roads are included. The simulation and field test results show that the forgetting factor has a significant influence on the convergence and robustness of the proposed method. The forgetting factor τ = 0.95 is used in the field test, the estimation result of dry concrete road friction coefficient is around 0.83. The results indicated that the proposed method can obtain the TRFC and tire parameters dynamically for ASVs.

Tire-Road Friction Coefficient Estimation Based on Fusion of Model- and Data-Based Methods

Abstract The tire-road interaction generates vehicle driving forces, which affect vehicle performance such as maximum acceleration and stability. Sequential extended Kalman filter (S-EKF) integrated with a slope method has been used for tire-road friction coefficient estimation with its own limitations, along with several “cause-based” and “effect-based” methods. This research proposes a new stochastic-based evaluation criterion using existing vehicle sensor signals with the help of the data-driven Kriging model. The proposed estimation method is validated by both CarSim™ simulation and experimental studies, respectively, under different road conditions. The results show that the proposed novel criterion has a strong correlation with the road friction coefficient and provide an improved tire-road friction coefficient estimation. A signal fusion estimation scheme based on both S-EKF and proposed evaluations is developed to improve estimation robustness.

Tire-road friction coefficient estimation method design for intelligent tires equipped with PVDF piezoelectric film sensors

Intelligent tires, as an emerging technology, have great potential in real-time monitoring of tire-road contact information and new automotive active safety design. In this paper, a tire-road friction coefficient estimation method is proposed based on intelligent tire technology. First, an intelligent tire finite element model with the use of five PVDF piezoelectric film sensors attached to the inner liner of the tire is built using ABAQUS software, and the validity of the finite element model is verified by a piezoelectric intelligent tire test platform. Then, through the finite element analysis method and control variable method, the influence of sideslip angle on the voltage signal of each piezoelectric film under the rolling state of tire is analyzed, and when the sideslip angle is 4°, the influence of load, tire pressure, vehicle speed and slip ratio on the voltage signal of each piezoelectric film under the rolling state of tire is analyzed. Finally, based on the signal response analysis of the piezoelectric film sensors, the response mechanism of the predicted object and the linear correlation analysis, the input eigenvalues of each prediction model are extracted. The longitudinal contact patch length estimation model based on the numerical method and the sideslip angle, vertical force, lateral force and aligning moment estimation model based on the neural network algorithm are built, and the predicted parameters are input into the brush tire model to solve the tire-road friction coefficient. The result shows that the estimation error percentage of the friction coefficient estimation method without genetic algorithm optimization is 16.98%, and the estimation error percentage of the friction coefficient estimation method with genetic algorithm optimization is 5.14%, indicating that the genetic algorithm optimization effect is ideal, and the friction coefficient estimation method is practical. ● Developing an intelligent tire finite element model equipped with PVDF sensors ● Real vehicle test verifies the validity of the intelligent tire finite element model ● Analyzing the signal response of PVDF sensors under different working conditions ● Estimating the tire-road friction coefficient using intelligent tire system and brush tire model

An Integrated Scheme for Coefficient Estimation of Tire–Road Friction With Mass Parameter Mismatch Under Complex Driving Scenarios

The accurate knowledge of tire–road friction coefficient (TRFC) contributes to the optimization of driver maneuvers for further improving the safety of intelligent vehicles. The performance of the existing estimation methods would decline when a vehicle performs complex driving maneuvers. In addition, the mass parameter mismatch also deteriorates the estimation accuracy of TRFC. To address these problems, in this article, an integrated scheme for TRFC estimation is proposed by combining a strong tracking unscented Kalman filter and an interactive multiple model unscented Kalman filter. Real-time experiments are implemented on a mass-produced vehicle to demonstrate the feasibility and effectiveness of the proposed method. The results show that the proposed approach has better estimation accuracy than the existing ones under various driving scenarios.

A comparative study of the recursive least squares and fuzzy logic estimation methods for the measurement of road adhesion coefficient

ABSTRACT Vehicle active safety system is the hotspot of current research and development, and the road adhesion coefficient is one of the essential parameters in the development of automobile active safety system, which plays a pivotal role in automobile safety. To improve the real-time performance and accuracy of the road adhesion coefficient, this paper proposes different control methods and compares and analyzes them. To accurately estimate the road adhesion coefficient in real-time, an eight-degree-of-freedom vehicle model was adopted in this paper. According to the tire torque and wheel speed, the adhesion coefficient was estimated based on the second-order nonlinear extended state observer. The experimental data, such as slip rate, using the improved tire model, is based on the recursive least squares method with forgetting factor and fuzzy logic algorithm real-time of tire-road friction coefficient estimation. The results show that the observer can effectively observe utilisation adhesion coefficient, and both control algorithms can estimate the road adhesion coefficient in real-time, effectively and quickly. On different roads, the use of the recursive least squares algorithm resulted in higher estimation accuracy, better robustness, and better control effect than using a fuzzy logic algorithm.

Tire–road friction coefficient estimation based on designed braking pressure pulse

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.

Estimation of tire–road friction for road vehicles: a time delay neural network approach

The performance of vehicle active safety systems is dependent on 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 different vehicle control systems. This paper deals with the tire–road friction coefficient estimation problem through the knowledge of lateral tire force. A time delay neural network (TDNN) is adopted for the proposed estimation design. The TDNN aims at detecting road friction coefficient under lateral force excitations avoiding the use of standard mathematical tire models, which may provide a more efficient method with robust results. Moreover, the approach is able to estimate the road friction at each wheel independently, instead of using lumped axle models simplifications. Simulations based on a realistic vehicle model are carried out on different road surfaces and driving maneuvers to verify the effectiveness of the proposed estimation method. The results are compared with a classical approach, a model-based method modeled as a nonlinear regression.

Observer-based estimation of velocity and tire-road friction coefficient for vehicle control systems

A novel nonlinear observer for the estimation of vehicle velocity together with the tire-road friction coefficient is presented in this paper. The modular observer is designed based on a longitudinal tire force estimation approach and a lateral tire friction model. Compared to the state-of-art methods, the proposed observer design provides accurate estimation of the longitudinal velocity, lateral velocity, and the tire-road friction coefficient simultaneously. Particularly, the longitudinal tire forces are first estimated based on a filter observer. Then, according to the calculation of lateral tire forces, the nonlinear observer is proposed to estimate vehicle velocity and the tire-road friction coefficient. Moreover, the stability property of the observer is analyzed using a Lyapunov-based method. Simulation results validate the effectiveness of the proposed method.

Tire-Road Friction Coefficient Estimation under Constant Vehicle Speed Control

Abstract Tire-road friction coefficient (TRFC) is of critical importance for advanced vehicle control systems and autonomous vehicle applications. This paper presents a sequential tire longitudinal stiffness and TRFC estimation method for road vehicles by separate control of the front and rear wheels, for which only standard Kalman filter (KF) and recursive least squares (RLS) techniques are required. While braking torque is actively applied to rear wheels, the proportional-integral-derivative (PID) speed controller dictates the corresponding driving torque to front wheels to compensate the decrease of the vehicle longitudinal speed. Tire force of rear tires are estimated based on the KF, both longitudinal stiffness and TRFC of rear tires are identified using RLS technique. The proposed method has simple structure and the potential of estimating the parameters without severely affecting the vehicle’s desired longitudinal speed. Simulation results from vehicle dynamics software CarSim and Matlab/Simulink validate the effectiveness of the proposed method.

A hierarchical estimator development for estimation of 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.

Slip Control of Electric Vehicle Based on Tire-Road Friction Coefficient Estimation

The real-time change of tire-road friction coefficient is one of the important factors that influence vehicle safety performance. Besides, the vehicle wheels’ locking up has become an important issue. In order to solve these problems, this paper comes up with a novel slip control of electric vehicle (EV) based on tire-road friction coefficient estimation. First and foremost, a novel method is proposed to estimate the tire-road friction coefficient, and then the reference slip ratio is determined based on the estimation results. Finally, with the reference slip ratio, a slip control based on model predictive control (MPC) is designed to prevent the vehicle wheels from locking up. In this regard, the proposed controller guarantees the optimal braking torque on each wheel by individually controlling the slip ratio of each tire within the stable zone. Theoretical analyses and simulation show that the proposed controller is effective for better braking performance.

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

Tire-road friction coefficient is an important parameter for vehicle stability and active safety systems. However, precise measurement of tire-road friction coefficient is hard to achieve without expensive equipment. Considering easy availability and good economy, this paper proposes a method which first combines auxiliary particle filter and the iterated extended kalman filter (APF-IEKF), and then processes the results of the first step using iteration algorithm. APF-IEKF is used to estimate the slip angle of the front tires with strong nonlinearity and non-Gaussian noise, in which APF filters non-Gaussian noise and reach a preliminary estimation of sideslip angle, then IEKF is used to optimize the result, making the estimation of the sideslip angle more accurate. The iteration algorithm is used to estimate the tire-road friction coefficient based on self-aligning torque, which is more sensitive to tire slip angle and provides faster estimation. In this way, this method can estimate tire road friction coefficient more accurately and in real time. Both numerical simulation in Carsim/Simulink and actual off-vehicle tests in winter are provided to demonstrate the efficiency of the proposed algorithm.

Estimation of tire-road friction coefficient based on frequency domain data fusion

Due to the noise of sensing equipment, the tire states, such as the sideslip angle and the slip ratio, cannot be accurately observed under the conditions with small acceleration, which results in the inapplicability of the time domain data based tire-road friction coefficient (TRFC) estimation method. In order to overcome this shortcoming, frequency domain data fusion is proposed to estimate the TRFC based on the natural frequencies of the steering system and the in-wheel motor driving system. Firstly, a relationship between TRFC and the steering system natural frequency is deduced by investigating its frequency response function (FRF). Then the lateral TRFC is determined by the steering natural frequency which is only identified using the information of the assist motor current and the steering speed of the column. With spectral comparison between the steering and driving systems, the data fusion is carried out to get a comprehensive TRFC result, using the different frequency information of the longitudinal and lateral value. Finally, simulations and experiments on different road surfaces validated the correctness of the steering system FRF and the effectiveness of the proposed approach.

Tire/wheel torsional dynamic behaviour and road friction coefficient estimation

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.