Development and Verification of the Tire/Road Friction Estimation Algorithm for Antilock Braking System

Road friction coefficient is a key factor for the stability control of the vehicle dynamics in the critical conditions. Obviously the vehicle dynamics stability control systems,including the anti-lock brake system(ABS),the traction control system(TCS),and the active yaw control(AYC) system,need the accurate tire and road friction information. However,the simplified method based on the linear tire and vehicle model could not obtain the accurate road friction coefficient for the complicated maneuver of the vehicle. Because the active braking control mode of AYC is different from that of ABS,the road friction coefficient cannot be estimated only with the dynamics states of the tire. With the related dynamics states measured by the sensors of AYC,a comprehensive strategy of the road friction estimation for the active yaw control is brought forward with the sensor fusion technique. Firstly,the variations of the dynamics characteristics of vehicle and tire,and the stability control mode in the steering process are considered,and then the proper road friction estimation methods are brought forward according to the vehicle maneuver process. In the steering maneuver without braking,the comprehensive road friction from the four wheels may be estimated based on the multi-sensor signal fusion method. The estimated values of the road friction reflect the road friction characteristic. When the active brake involved,the road friction coefficient of the braked wheel may be estimated based on the brake pressure and tire forces,the estimated values reflect the road friction between the braked wheel and the road. So the optimal control of the wheel slip rate may be obtained according to the road friction coefficient. The methods proposed in the paper are integrated into the real time controller of AYC,which is matched onto the test vehicle. The ground tests validate the accuracy of the proposed method under the complicated maneuver conditions.

Measurement of road friction coefficient using strain on tire sidewall

<div class="section abstract"><div class="htmlview paragraph">Accurate road friction coefficient is crucial for the proper functioning of active chassis control systems. However, road friction coefficient is difficult to be measured directly. Using the available onboard sensors, a model-based Extended Kalman filter (EKF) algorithm is proposed in this paper to estimate road friction coefficient. In the development of estimation algorithm, vehicle motion states such as sideslip angle, yaw rate and vehicle speed are first estimated. Then, road friction coefficient estimator is designed using nonlinear vehicle model together with the pre-estimated vehicle motion states. The proposed estimation algorithm is validated by both simulations and tests on a scaled model vehicle.</div></div>

Reeds–Shepp (RS) curves are widely employed for path smoothing in path planning algorithms such as Hybrid A* and Rapidly-Exploring Random Trees (RRT). To ensure the stability of autonomous vehicles when traversing RS-curve paths, this paper proposes a velocity prediction and planning algorithm based on vehicle lateral dynamics. Specifically, given the path curvature and initial velocity, the yaw rate and side-slip angle of the vehicle during steady-state steering are derived using the lateral dynamics model. Considering load transfer effects, the lateral tire force is calculated from the rate of change of vertical loads, and the safe driving velocity is predicted through gradient descent with the tire force saturation coefficient as the optimization objective. Subsequently, a velocity planning method that integrates the Gaussian pseudospectral method (GPM) with sequential quadratic programming (SQP) is developed. The problem is formulated as a nonlinear programming model, in which the predicted safe velocity serves as the upper velocity constraint. Joint simulations in MATLAB/Simulink and CarSim are then conducted to evaluate the proposed framework. The results show that the prediction accuracy of the lateral tire force exceeds 94% under different road friction coefficients, confirming the reliability of the proposed prediction model. Furthermore, comparative experiments demonstrate that the velocity planning method can effectively reduce vehicle velocity from unsafe to safe levels, thereby ensuring driving stability and safety when negotiating curves.

Vehicle states and the road friction coefficient in active safety control systems have become increasingly prominent. However, a low‐cost, high‐precision system in real‐time has yet to be achieved. The use of complex models has led to poor real‐time estimation, while variations in the road friction coefficient have often been neglected. This paper adopts information fusion technology by using DEKF theory for rapid simulation and estimation of these parameters. Using a vehicle dynamic model based on three degrees of freedom (3‐DOF) and the Highway Safety Research Institute tire model, DEKF recursive estimation models are established and verified. In the DEKF, two recursive state and parameter estimation models exist in parallel. The models are dependent upon each other and have real‐time interaction correction in order to forecast information, which quickly yields true value estimation in simulation. Experimental brake test results show that the DEKF estimator not only accurately estimates the vehicle state parameters, but also estimates the road friction coefficient in real‐time. This can reduce the cost of the vehicle sensor, and can estimate the status parameter, which is difficult to measure. The validity and feasibility of this algorithm have been verified by an HIL driving simulator, offering the possibility of future application in real cars.

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.

Real-time knowledge of maximum road friction coefficient and road slope is crucial for active vehicle control systems. Most recent researches mainly assume that the road slope is constant and the influence on the identification of the maximum road friction coefficient is not considered. In this paper, the IMM Kalman filter method for the identification of road longitudinal slope is developed. Considering the axle load transfer caused by the road slope, the current road type is recognised by comparing the samples of the estimated instantaneous road friction coefficient with each standard road, then the maximum road friction coefficient can be easily determined by an online lookup table. Finally, experimental tests on the braking system hardware-in-the-loop test rig driven by the driving simulator are conducted. The results demonstrate that the identification approach can identify the current road slope and maximum road friction coefficient with good adaptability to various vehicle conditions.

This paper proposes a novel hybrid framework for estimating longitudinal tire forces by combining a model-based observer and a Transformer neural network architecture. A key advantage of the proposed approach is its independence from wheel torque measurements, which are commonly used in vehicle force estimation methods. The proposed framework first employs a model-based observer using the Pacejka tire model to generate preliminary estimates of longitudinal tire forces. These estimates are then refined by a neural network featuring an encoder-only Transformer architecture augmented with dilated convolutions, which effectively captures long-term temporal dependencies in sensor data while compensating for model inaccuracies. Additionally, our hybrid approach is able to estimate the longitudinal velocity and road friction coefficient, which are crucial for observer's preliminary force estimate in extreme road and driving conditions. Experimental validation on an electric Equinox vehicle under diverse driving scenarios-including highslip maneuvers on dry, wet, and icy roads-demonstrates the framework's superior performance compared to model-based and neural network-only approaches. The proposed method achieves robust estimation accuracy even under sensor faults (e.g., biased acceleration signals) and harsh driving conditions, indicating its potential for enhancing vehicle safety systems such as traction and stability control.

This paper deals with the problem of static and dynamic (or kinetic) friction, namely the coefficients of friction for the two states. The coefficient of static friction is well known, and its theory and practice are commonly accepted by the academia and the industry. The coefficient of kinetic friction, however, has not fully been understood. The popular theory for the kinetic friction is that the coefficient of dynamic friction is smaller than the coefficient of static friction, by comparison of the forces applied in the two states. After studying the characteristics of the coefficient of friction, it is found that the comparison is not appropriate, because the inertial force was excluded. The new discovery in the paper is that coefficients of static friction and dynamic friction are identical. Wheel “locked” in wheel braking is further used to prove the conclusion. The key to cause confusions between the two coefficients of friction is the inertial force. In the measurement of the coefficient of static friction, the inertial force is initiated as soon as the testing object starts to move. Therefore, there are two forces acting against the movement of the object, the frictional force and the inertial force. But in the measurement of the coefficient of kinetic friction, no inertial force is involved because velocity must be kept constant.

The road friction coefficient is often estimated based on vehicle dynamics models, but the ideal mathematical model is difficult to describe the actual vehicle operation, which in turn leads to deviations between the estimated friction coefficient and the actual situation. In order to take full account of the actual vehicle driving conditions, back propagation (BP) neural network model is often applied to assess the friction coefficient. To further improve the generalization ability of the network model, this paper proposes a method to predict the friction coefficient using the whale optimized algorithm-BP (WOA-BP) neural network model. The whale algorithm improves the weights and thresholds of the BP neural network model to improve generalization ability and convergence speed. First, the vehicle dynamics analysis is utilized to determine the vehicle dynamics parameters as a function of the friction coefficient. Then, the WOA-BP is compared against the BP under various realistic operating scenarios. The results demonstrate that the WOA-BP estimator is accurate and efficient in estimating the friction coefficient, and the proposed method reduces the mean absolute error by 51.9% and the root mean squared error by 49.1% compared to the BP.

Estimation of Nonlinear Tire Forces and Road Friction for Modeling and Control

ABSTRACTThis paper proposes a linear predictive lateral control method to stabilise a highly automated vehicle (HAV) at the tire-road friction limits when tracking a (tight) desired path. Two approaches are adopted to linearise the vehicle model around the tire saturation region: (1) the lateral force of the front tire is selected as the control input instead of the steer angle and (2) the rear tire dynamics is locally linearised at the current operating point within the predictive horizon. The friction limits of both the front and rear tires are utilised to define an enveloped stable zone, which serves as the safety constraints for the predictive controller. Simulation results show that the proposed controller is able to stabilise a vehicle when tracking a tight desired path at a high speed even on a low-adhesion road. Moreover, the robustness of the proposed controller is also verified as it tolerates small estimation errors in the road friction coefficient.

<div>One of the most important factors affecting the performance of vehicle active chassis control systems is the tire-road friction coefficient. Accurate estimation of the friction coefficient can lead to better performance of these controllers. In this study, a new three-step friction estimation algorithm, based on intelligent tire concept, is proposed, which is a combination of experiment-based and vehicle dynamic based approaches. In the first step of the proposed algorithm, the normal load is estimated using a trained Artificial Neural Network (ANN). The network was trained using the experimental data collected using a portable tire testing trailer. In the second step of the algorithm, the tire forces and the wheel longitudinal velocity are estimated through a two-step Kalman filter. Then, in the last step, using the estimated tire normal load and longitudinal and lateral forces, the friction coefficient can be estimated. To evaluate the performance of the algorithm, experiments were performed using the trailer test setup and friction was calculated using the measured forces. Good agreement was observed between the estimated and actual friction coefficients.</div>

The towing device was designed to provide a rapid screening test that might be applied to measure the wear resistance of small quantities of experimental polymers. The reproducibility of the test has been found to depend to a large degree upon the care was taken to design measuring equipment that would provide a good estimate of this value. The nature of the road surface will produce a change in the rate of wear and, with certain polymers, excessive cutting has been encountered that affected the reproducibility of the measurement. This difficulty may be avoided by selecting a smoother road surface and longer test runs may be employed without increasing the duration of the test beyond 6 hours. A towing device has been developed that allows the wear resistance of a small quantity of polymer to be evaluated by towing a test wheel at a slight angle over the surface of a road at normal tire loads and speeds. Data from road wear tests of tires of various sizes showed that a log-log plot of the volume loss per unit width of tread of the experimental against the control vulcanizate gave a single correlation. The volume loss of the control vulcanizate may be taken as a measure of the severity of the test. Tests using the towing device at various angles of tow gave data that showed a correlation of wear values similar to that found in road tests. The towing device provides an adequate method for screening the wear qualities of small quantities of experimental polymer.

Lowering friction coefficient under low loads by minimizing effects of adhesion force and viscous resistance