Tire-road Friction Research Articles

A review on estimation of vehicle tyre-road friction

A review on estimation of vehicle tyre-road friction

Real-time estimation of longitudinal tire stiffness considering dynamic characteristics of tire

To enhance the effectiveness of active safety control, the tire–road friction coefficient (TRFC) must be precisely estimated, and the longitudinal tire stiffness coefficient is an important vehicle dynamic parameter to estimate TRFC. In this research, we present an observer that improves the performance of longitudinal tire stiffness coefficient estimation by applying tire dynamics that were previously applied in the lateral direction to the longitudinal direction. To begin, we model longitudinal tire dynamics using the relaxation length concept and validate the model using vehicle braking tests. We develop an observer that estimates the longitudinal tire stiffness coefficient by integrating the proposed tire dynamics and vehicle dynamics. The observer, which is based on an extended Kalman filter, can be applied to nonlinear systems and successfully removes noise from wheel speed measurement. The observer’s estimation performance is verified using CarSim simulation and vehicle tests, and the results are compared to existing approaches that do not account for longitudinal tire dynamics. Even in the transient section when the vehicle begins accelerating, the difference between the estimate and the reference value is about 0.3% using the proposed method, but if tire dynamics are not taken into account, the estimate is 6.5% lower than the reference value.

Joint vehicle state and parameters estimation via twin-in-the-loop observers

Vehicular control systems are required to be both extremely reliable and robust to different environmental conditions, e.g. load or tyre–road friction. In this paper, we extend a new paradigm for state estimation, called Twin-in-the-Loop filtering (TiL-F), to the estimation of the unknown parameters describing the vehicle operating conditions. In such an approach, a digital-twin of the vehicle (usually already available to the car manufacturer) is employed on-board as a plant replica within a closed-loop scheme, and the observer gains are tuned purely from experimental data. The proposed approach is validated against experimental data, showing to significantly outperform the state-of-the-art solutions.

Dynamic Characteristics of Three-Body Braking System Considering Tire-Road Friction

Abstract With the significant increase in vehicle ownership in our country, urban traffic conditions have become increasingly congested. Low-speed driving has become more prevalent, leading to more frequent instances of starting and braking. Consequently, the issue of low-speed braking flutter has become increasingly prominent. While the brake is in an open environment, the dust and particles in the air and the debris generated by the brake itself will have an impact on the braking behavior. In addition, according to the theory of modal coupling, the braking stability of the vehicle is also affected by other components. In this paper, different dynamic torsional models of braking system are established according to different braking conditions. Through numerical calculation, the influence of tire parameters, road conditions, and particles on the friction dynamics characteristics of braking system pairs is explored. The results show that the instability of the brake pair system often occurs at low speed. Different tire slip ratios, tire offset factors, and road conditions will lead to different relative motions of the braking system, but the existence of particles in the brake lining-disk interface can enhance the motion stability of the system.

An Enabling Tire-Road Friction Estimation Method for Four-in-Wheel-Motor-Drive Electric Vehicles

In this paper, a particle filter (PF)-based tire-road friction estimation method is proposed for four-in-wheel-motor-drive electric vehicles by synthetically using the Dual Global Positioning System (DGPS) and three low-cost Inertia Measurement Units (IMUs). In the scheme, two independent PF-based road friction estimators are developed for straight driving and cornering conditions. For straight driving conditions, the longitudinal tire forces are first estimated using the output torque and rotational speed of motor, based on which a tire-road friction estimator is put forward by using a particle filter and the nonlinear relationship between longitudinal tire force and tire-road friction. For cornering conditions, the lateral tire forces and vehicle sideslip angle are estimated by using three IMUs and the DGPS. A PF-based tire-road friction estimator is established based on the nonlinear lateral tire characteristics. An estimation mode decision scheme is developed to determine which of the two PF-based estimators is used to update the tire-road friction estimate by considering both tire dynamics states and tire force characteristics. The accuracy and reliability of the proposed tire-road friction estimation scheme is verified under various maneuvers and road friction conditions through hardware-in-the-loop tests. The results show that the proposed method exhibits high estimation accuracy, robustness, and computational efficiency.

Development of an Autonomous Measurement System for Estimation of Snow Profile on Road Surfaces

This paper presents the development of a novel prototype system to measure the profile of snow and detect ice on road surfaces. While researchers have previously developed methods to estimate the tire-road friction coefficient, methods to create a high resolution map of snow cover and ice on roads have not been developed. The prototype and data processing methods presented in this study provide a potential solution that would greatly benefit winter road maintenance teams. Having a device capable of creating a detailed map of snow and ice cover on roads would allow for more efficient plowing and salt deployment, better informing of the public about current road conditions, as well as better analysis of current plowing techniques to improve winter road maintenance operations. The measurement of the snow profile is based on the use of two types of inexpensive ranging sensors mounted on a rotationally controlled stepper motor platform. The technical challenges addressed in the development include analysis of the scan path over which the system scans the road, differentiation between asphalt, concrete, and snow surfaces using reflection amplitudes, accurate transformation of raw distance measurements to inertial coordinates, and identification of the Euler angles of the sensors using parameters associated with the scanned surface profile. Extensive experimental results and test data are presented, which show that the system is capable of measuring the snow profile on a road with an accuracy of ±1 cm when a reasonable portion of bare road is visible, and ±2 cm when only small portions of bare road are visible.

Weather-aware fuzzy adaptive cruise control: Dynamic reference signal design

This paper presents a novel Adaptive Cruise Control (ACC) system, as part of Advanced Driver Assistance Systems (ADAS), in which weather conditions are included in the ACC operations adapting to different weather conditions and road-tire friction. A controller in the main loop of the ACC generates, in real-time, a dynamic reference signal to adjust the safe distance and velocity of the vehicle, based on different weather conditions using innovative polynomial, Sine, or Gaussian functions. A slave loop minimizes the velocity error and ensures collision prevention and passenger comfort. The system considers the nonlinear behavior of the vehicles’ actuators and dynamics. Simulations with various driving scenarios, such as hard stops and frequent stop-and-go maneuvers, show that the system can achieve high safety and comfort performance in icy, snowy, rainy, or dry weather. On average, the relative distance and velocity error are less than 0.6% and 0.5%, respectively.

On the Benefits of Active Aerodynamics on Energy Recuperation in Hybrid and Fully Electric Vehicles

In track-oriented road cars with electric powertrains, the ability to recuperate energy during track driving is significantly affected by the frequent interventions of the antilock braking system (ABS), which usually severely limits the regenerative torque level because of functional safety considerations. In high-performance vehicles, when controlling an active rear wing to maximize brake regeneration, it is unclear whether it is preferable to maximize drag by positioning the wing into its stall position, to maximize downforce, or to impose an intermediate aerodynamic setup. To maximize energy recuperation during braking from high speeds, this paper presents a novel integrated open-loop strategy to control: (i) the orientation of an active rear wing; (ii) the front-to-total brake force distribution; and (iii) the blending between regenerative and friction braking. For the case study wing and vehicle setup, the results show that the optimal wing positions for maximum regeneration and maximum deceleration coincide for most of the vehicle operating envelope. In fact, the wing position that maximizes drag by causing stall brings up to 37% increased energy recuperation over a passive wing during a braking maneuver from 300 km/h to 50 km/h by preventing the ABS intervention, despite achieving higher deceleration and a 2% shorter stopping distance. Furthermore, the maximum drag position also reduces the longitudinal tire slip power losses, which, for example, results in a 0.4% recuperated energy increase when braking from 300 km/h to 50 km/h in high tire–road friction conditions at a deceleration close to the limit of the vehicle with passive aerodynamics, i.e., without ABS interventions.

Design and Verification of Offline Robust Model Predictive Controller for Wheel Slip Control in ABS Brakes

Wheel slip control is a critical aspect of vehicle safety systems, notably the antilock braking system (ABS). Designing a robust controller for the ABS faces the challenge of accommodating its strong nonlinear behavior across varying road conditions and parameters. To ensure optimal performance during braking and prevent skidding or lock-up, the ideal wheel slip value can be determined from the peak of the tire–road friction curve and maintained throughout the braking process. Among various control approaches, model predictive control (MPC) demonstrates superior performance and robustness. However, online MPC implementation encounters significant computational burdens and real-time limitations, particularly when dealing with larger problem sizes. To address these issues, this study introduces an offline robust model predictive control (RMPC) methodology. The proposed approach is based on the robust asymptotically stable invariant ellipsoid methodology, which employs linear matrix inequalities (LMIs) to calculate a collection of invariant state feedback laws associated with a sequence of nested invariant stable ellipsoids. Simulation results indicate a significant reduction in computational burden with the offline RMPC approach compared to online implementation, while effectively tracking the desired wheel slip reference values and system constraints. Moreover, the offline RMPC design aligns well with the online MPC design and verifies its effectiveness in practice.

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%.

Characterization of tire and road wear particles in urban river samples

Tire and road wear particles (TRWP) consist of tread rubber elastomers with pavement encrustations generated from tire-road friction. Our previous work utilized density separation and chemical mapping to characterize chemical and physical properties of individual TRWP. The current research extends the use of chemical mapping methods to urban river samples including sediment from the Seine River (France). TRWP were identified using a weight of evidence framework including density separation, optical imaging, scanning electron microscopy coupled with energy dispersive X-ray spectroscopy (SEM/EDX) mapping, and Fourier-transform infrared (FTIR) spectroscopy. River sediment collected immediately downstream of the Rouen urban area (with an average TRWP concentration of 930 mg TRWP/kg sediment; n = 3) subsequently density separated demonstrated an average TRWP size of 133 µm by number and 171 µm by volume. Sediment from a second location (190 mg TRWP/kg sediment; n = 1) was density separated and showed an overlap in features of tire tread and bitumen/asphalt in the FTIR signatures (operationally defined as weathered bitumen/TRWP). Average particle size for weathered bitumen/TRWP were 250 µm and 981 µm by number and volume, respectively. Pulverization pre-treatment of the second location sediment sample reduced larger particle agglomerates to an average weathered bitumen/TRWP particle size of 97 µm and 116 µm by number and volume, respectively. A quantitative TRWP or bitumen/TRWP size distribution in filtered suspended river solids (3300 mg TRWP/kg suspended solid) could not be determined due to lack of TRWP enrichment in pre- or post-density separation steps; however, average particle size for all collected river particles were 27 µm and 160 µm by number and volume, respectively. Additionally, TRWP were not identified in a river biota sample (bivalves) with or without chemical digestion and future research was discussed. Taken together, our single particle analysis methodologies were useful for the determination of particle size distribution (including bitumen and TRWP) in urban river sediment samples. These results are expected to help advance the methods for identification and characterization of TRWP and potentially other microplastics in various environmental matrices.

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.

Data-driven and uncertainty-aware robust airstrip surface estimation

The performances of aircraft braking control systems are strongly influenced by the tire friction force experienced during the braking phase. The availability of an accurate estimate of the current airstrip characteristics is a recognized issue for developing optimized braking control schemes. The study presented in this paper is focused on the robust online estimation of the airstrip characteristics from sensory data usually available on an aircraft. In order to capture the nonlinear dependency of the current best slip on sequential slip-friction measurements acquired during the braking maneuver, multilayer perceptron (MLP) approximators have been proposed. The MLP training is based on a synthetic data set derived from a widely used tire–road friction model. In order to achieve robust predictions, MLP architectures based on the drop-out mechanism have been applied not only in the offline training phase but also during the braking. This allowed to online compute a confidence interval measure for best friction estimate that has been exploited to refine the estimation via Kalman Filtering. Open loop and closed loop simulation studies in 15 representative airstrip scenarios (with multiple surface transitions) have been performed to evaluate the performance of the proposed robust estimation method in terms of estimation error, aircraft braking distance, and time, together with a quantitative comparison with a state-of-the-art benchmark approach.

Friction-adaptive stochastic nonlinear model predictive control for autonomous vehicles

This paper addresses the trajectory-tracking problem under uncertain road-surface conditions for autonomous vehicles. We propose a stochastic nonlinear model predictive controller (SNMPC) that learns a tyre–road friction model online using standard automotive-grade sensors. Learning the entire tyre–road friction model in real time requires driving in the nonlinear, potentially unstable regime of the vehicle dynamics, using a prediction model that may not have fully converged. To handle this, we formulate the tyre-friction model learning in a Bayesian framework and propose two estimators that learn different aspects of the tyre–road friction. The estimators output the estimate of the tyre-friction model as well as the uncertainty of the estimate, which expresses the confidence in the model for different driving regimes. The SNMPC exploits the uncertainty estimate in its prediction model to take proper action when the uncertainty is large. We validate the approach in an extensive Monte Carlo study using real vehicle parameters and in CarSim. The results when comparing to various MPC approaches indicate a substantial reduction in constraint violations, as well as a reduction in closed-loop cost. We also demonstrate the real-time feasibility in automotive-grade processors using a dSPACE MicroAutoBox-II rapid prototyping unit, showing a worst-case computation time of roughly 40 ms.

Predictive Anti-Jerk and Traction Control for V2X Connected Electric Vehicles With Central Motor and Open Differential

V2X connectivity and powertrain electrification are emerging trends in the automotive sector, which enable the implementation of new control solutions. Most of the production electric vehicles have centralized powertrain architectures consisting of a single central on-board motor, a single-speed transmission, an open differential, half-shafts, and constant velocity joints. The torsional drivetrain dynamics and wheel dynamics are influenced by the open differential, especially in split- scenarios, i.e., with different tire-road friction coefficients on the two wheels of the same axle, and are attenuated by the so-called anti-jerk controllers. Although a rather extensive literature discusses traction control formulations for individual wheel slip control, there is a knowledge gap on: a) model based traction controllers for centralized powertrains; and b) traction controllers using the preview of the expected tire-road friction condition ahead, e.g., obtained through V2X, for enhancing the wheel slip tracking performance. This study presents nonlinear model predictive control formulations for traction control and anti-jerk control in electric powertrains with central motor and open differential, and benefitting from the preview of the tire-road friction level. The simulation results in straight line and cornering conditions, obtained with an experimentally validated vehicle model, as well as the proof-of-concept experiments on an electric quadricycle prototype, highlight the benefits of the novel controllers.

Boxes-Based Representation and Data Sharing of Road Surface Friction for CAVs

Vehicles can easily lose control unexpectedly when encountering unforeseen hazardous road friction conditions. With automation and connectivity increasingly available to assist drivers, vehicle performance can significantly benefit from a road friction preview map, particularly to identify where and how friction ahead of a vehicle may be suddenly decreasing. Although many techniques enable the vehicle to measure the local friction as driving upon a surface, these encounters limit the ability of a vehicle to slow down before a low-friction surface is already encountered. Using the connectivity of connected and autonomous vehicles (CAVs), a global road friction map can be created by aggregating information from vehicles. A challenge in the creation of these global friction maps is the very large quantity of data involved, and that the measurements populating the map are generated by vehicle trajectories that do not uniformly cover the grid. This paper presents a road friction map generation strategy that aggregates the measured road-tire friction coefficients along the individual trajectories of CAVs into a road surface grid. In addition, through clustering the friction grids further, an insight of this work is that the friction map can be represented compactly by rectangular boxes defined by a pair of corner coordinates in space, a friction value, and a confidence interval within the box. To demonstrate the method, a simulation is presented that integrates traffic simulations, vehicle dynamics and on-vehicle friction estimators, and a highway road surface, where friction is changing in space, particularly over a bridge segment. The experimental results indicate that the road friction distribution can be measured effectively by collecting and aggregating the friction data from CAVs.

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.

Estimation of Tire-road Friction Limit with Low Lateral Excitation Requirement Using Intelligent Tire

<div class="section abstract"><div class="htmlview paragraph">Tire-road friction condition is crucial to the safety of vehicle driving. The emergence of autonomous driving makes it more important to estimate the friction limit accurately and at the lowest possible excitation. In this paper, an early detection method of tire-road friction coefficient based on pneumatic trail under cornering conditions is proposed using an intelligent tire system. The previously developed intelligent tire system is based on a triaxial accelerometer mounted on the inner liner of the tire tread. The friction estimation scheme utilizes the highly sensitive nature of the pneumatic trail to the friction coefficient even in the linear region and its approximately linear relationship with the excitation level. An indicator referred as slip degree indicating the utilization of the road friction is proposed using the information of pneumatic trail, and it is used to decide whether the excitation is sufficient to adopt the friction coefficient estimate. The friction coefficient is estimated by the ratio of the normalized lateral force and the nonlinear adaptation of the slip degree. The tire forces and pneumatic trail are estimated by neural networks. The experimental validation demonstrates that the pneumatic trail has a good potential to precisely predict the friction coefficient at a low excitation under cornering conditions.</div></div>

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.