Numerical estimation of tire–road friction coefficient based on tire grip margin

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. Hence, today’s vehicle control systems are limited by the lack of knowledge of critical tire-road states (i.e. the kinematic conditions of the tire to its dynamic properties). From aforementioned discussion, it is clear that some method of estimating tire-road contact parameters would be greatly desirable. 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 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 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.

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.

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 tire-road friction coefficient is critical information for conventional vehicle safety control systems. Most previous studies on tire-road friction estimation have only considered either longitudinal or lateral vehicle dynamics, which tends to cause significant underestimation of the actual tire-road friction coefficient. In this paper, the parameters, including the tire-road friction coefficient, of the combined longitudinal and lateral brushed tire model are identified by linearized recursive least squares (LRLS) methods, which efficiently utilize measurements related to both vehicle lateral and longitudinal dynamics in real time. The simulation study indicates that by using the estimated vehicle states and the tire forces of the four wheels, the suggested algorithm not only quickly identifies the tire-road friction coefficient with great accuracy and robustness before tires reach their frictional limits but successfully estimates the two different tire-road friction coefficients of the two sides of a vehicle on a split- μ surface as well. The developed algorithm was verified through vehicle dynamics software Carsim and MATLAB/Simulink.

Traction control, which can be performed by different types of chassis control system, plays an important role in vehicle motion control. Since the propulsive force is actually produced by the friction between the tyre and road, information on the tyre–road friction is crucial for traction control. In this paper, a robust and effective tyre–road friction coefficient identification algorithm for straight acceleration is proposed, and a coordinative traction control method is designed by integrated usage of gear shifting control, engine control and braking control. For different driving conditions, the tyre forces were observed by a sliding-mode observer or calculated from the states of the vehicle directly, and the tyre–road friction coefficients were estimated by the recursive least-squares method or calculated from the linear characteristics between the friction coefficient and the slip ratio consequently. Based on the estimated tyre–road information, a practical and systematic coordinative traction control algorithm was designed to integrate shifting control, engine torque control and braking pressure control. Finally, the proposed methods are verified by both simulations and road tests. The results show that the estimation algorithms can identify the variation in the road conditions with considerable accuracy and response speed, and the controller successfully adjusted the slip ratios of the driving wheels in the stable region with good performances on different types of road.

Tire–road friction is a fundamental factor in vehicle safety, energy efficiency, and environmental sustainability. This narrative review synthesizes current knowledge on the tire–road friction coefficient (TRFC), emphasizing its dynamic nature and the interplay of factors such as tire composition, tread design, road surface texture, temperature, load, and inflation pressure. Friction mechanisms, adhesion, and hysteresis are analyzed alongside their dependence on environmental and operational conditions. The study highlights the challenges posed by emerging mobility paradigms, including electric and autonomous vehicles, which demand specialized tires to manage higher loads, torque, and dynamic behaviors. The review identifies persistent research gaps, such as real-time TRFC estimation methods and the modeling of combined environmental effects. It explores tire–road interaction models and finite element approaches, while proposing future directions integrating artificial intelligence and machine learning for enhanced accuracy. The implications of the Euro 7 regulations, which limit tire wear particle emissions, are discussed, highlighting the need for sustainable tire materials and green manufacturing processes. By linking bibliometric trends, experimental findings, and technological innovations, this review underscores the importance of balancing grip, durability, and rolling resistance to meet safety, efficiency, and environmental goals. It concludes that optimizing friction coefficients is essential for advancing intelligent, sustainable, and regulation-compliant mobility systems, paving the way for safer and greener transportation solutions.

Vehicle stability and active safety control depend heavily on tyre forces available on each wheel of a vehicle. Since tyre forces are strongly affected by the tyre–road friction coefficient, it is crucial to optimise the use of the adhesion limits of the tyres. This study presents a hybrid method to identify the road friction limitation; it contributes significantly to active vehicle safety. A hybrid estimator is developed based on the three degrees-of-freedom vehicle model, which considers longitudinal, lateral and yaw motions. The proposed hybrid estimator includes two sub-estimators: one is the vehicle state information estimator using the unscented Kalman filter and another is the integrated road friction estimator. By connecting two sub-estimators simultaneously, the proposed algorithm can effectively estimate the road friction coefficient. The performance of the proposed estimation algorithm is validated in CarSim/Matlab co-simulation environment under three different road conditions (high-μ, low-μ and mixed-μ). Simulation results show that the proposed estimator can assess vehicle states and road friction coefficient with good accuracy.

The contact between the tire and the road is the key enabler of vehicle acceleration, deceleration and steering. However, due to changes to the road conditions, the driver's ability to maintain a stable vehicle may be 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 an 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 brush model-based nonlinear least squares (NLLS) parameter estimation approach is proposed. Hence an integrated approach using the 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 the ABS control systems. In order to achieve the aforementioned objectives, the design and implementation of a fuzzy/sliding mode/proportional integral (fuzzy-SMC-PI (FSP)) control methodology is proposed. The results show significant improvements in the stopping distance of a vehicle equipped with an intelligent tire based FSP controller as compared to a vehicle equipped with a standard ABS.

The active safety systems, such as Electronic Stability Program (ESP) and Traction Control System (TCS), have been used widely in the modern production auto-mobile. These safety control systems function well only when the vehicle motion information is known. To achieve this purpose, various sensors are equipped in the production cars in order to detect vehicle motion information like yaw, wheel velocities and accelerations. However some key variables of the vehicle dynamic and road conditions, such as the sideslip angle, the tire road forces and the tire road friction coefficient are difficult to measure directly for technology or economic reasons. A new observer which uses the unscented Kalman filter to estimate simultaneously the sideslip angle, lateral tire road forces and the tire road friction coefficient has been proposed in this paper. The advantage of this observer is that no additional sensors is needed when the ESP has been installed in the auto-mobile. The performance of the proposed observer is demonstrated through the Chicane test.

Comprehensive tire–road friction coefficient estimation based on signal fusion method under complex maneuvering operations

Knowledge of tire–road friction conditions is indispensable for many vehicle control systems. In particular, friction information can be used to enhance the performance of wheel slip control systems, for example, knowledge of the current maximum coefficient of friction would allow an anti-lock brake system (ABS) controller to start braking with the optimal brake pressure, meaning the early cycles of operation are more efficient, resulting in shorter stopping distances. Also, from a passive safety perspective, it may be useful to present the driver with friction information so they can adjust their driving style to the road conditions. Hence, it is highly desirable to estimate friction using existing onboard vehicle sensor information. Many approaches for estimating tire–road friction estimation have been proposed in the literature with different sensor requirements and relative excitation levels. This paper aims at estimating the tire–road friction coefficient by using a well-defined model of the tire behavior. The model adopted for this purpose is the physically based brush tire model. In its simplest formulation, the brush model describes the relationship between the tire force and the slip as a function of two parameters, namely, tire stiffness and the tire–road friction coefficient. Knowledge of the shape of the force–slip characteristics of the tire, possibly obtained through the estimation of both friction and tire stiffness using the brush model, provides information about the slip values at which maximum friction is obtained. This information could be used to generate a target slip set point value for controllers, such as an ABS or a traction control system. It is also important to realize that a model-based approach is inherently limited to providing road surface friction information when the tire is exposed to an excitation with high utilization levels (i.e. under high-slip conditions). To be of greatest use to active safety control systems, an estimation method needs to offer earlier knowledge of the limits. In order to achieve the aforementioned objective, an integrated approach using an intelligent tire-based friction estimator and the brush tire model-based estimator is presented. An integrated approach gives us the capability to reliably estimate friction for a wider range of excitations (both low-slip and high-slip conditions).

This paper presents experimental results of using extended Kalman-Bucy filtering (EKBF) and Bayesian model selection to extract tire force characteristics and road friction coefficient from measured motion of ground vehicles on smooth surfaces. The filter estimates wheel slip and slip angles, along with longitudinal and per axle lateral tire forces. Force estimates are based on vehicle-mounted sensors and are derived without knowing road conditions and without a tire force model. Force estimates are compared statistically with those that result from a nominal tire model to select the most likely friction coefficient from hypothesized values. This paper verifies tire force estimation and road friction identification using off-line processing of field test data. Results confirm applicability of the EKBF and Bayesian selection approaches.

A model-based estimator design and implementation is described in this paper to undertake combined estimation of vehicle states and tire-road friction coefficients. The estimator is designed based on a vehicle model with three degrees of freedom (3-DOF) and the dual extended Kalman filter (DEKF) technique is employed. Effectiveness of the estimation is examined and validated by comparing the outputs of the estimator with the responses of the vehicle model in CarSim in three typical road adhesion conditions (high-friction, low-friction, and joint-friction roads). Simulation results demonstrate that the DEKF estimator algorithm designed is able to obtain vehicle states (e.g., yaw rate and roll angle) as well as road friction coefficients with reasonable accuracy.

Road friction coefficient is a critical component in traffic safety. The estimation of tire–road friction coefficient at tires allows the control algorithm in vehicle activity system to adapt to external driving conditions. This paper develops a new tire–road friction coefficient estimation algorithm based on tire longitudinal force estimation and tire slip estimation. Vehicle tire longitudinal forces are estimated by sliding mode observer combined with Kalman filter. Based on the tire forces estimation, road friction coefficient is estimated by recursive least squares algorithm (RLS). The test conditions which contain different friction level road are established in ADAMS/Car. The conclusions validate the reliability and efficiency of the proposed method for estimating the friction coefficient in different adhesion level roads. The research also indicates the theory of slip slope can also be reappeared in virtual experiment based on ADAMS.

ABSTRACTKnowledge of the current tyre–road friction coefficient is essential for future autonomous vehicles. The environmental conditions, and the tyre–road friction in particular, determine both the braking distance and the maximum cornering velocity and thus set the boundaries for the vehicle. Tyre–road friction is difficult to estimate during normal driving due to low levels of tyre force excitation. This problem can be solved by using active tyre force excitation. A torque is added to one or several wheels in the purpose of estimating the tyre–road friction coefficient. Active tyre force excitation provides the opportunity to design the tyre force excitation freely. This study investigates how the tyre force should be applied to minimise the error of the tyre–road friction estimate. The performance of different excitation strategies was found to be dependent on both tyre model choice and noise level. Furthermore, the advantage with using tyre models with more parameters decreased when noise was added to the force and slip ratio.