Comparative study of vehicle tyre–road friction coefficient estimation with a novel cost-effective method

This paper qualitatively and quantitatively reviews and compares three typical tyre–road friction coefficient estimation methods, which are the slip slope method, individual tyre force estimation method and extended Kalman filter method, and then presents a new cost-effective tyre–road friction coefficient estimation method. Based on the qualitative analysis and the numerical comparisons, it is found that all of the three typical methods can successfully estimate the tyre force and friction coefficient in most of the test conditions, but the estimation performance is compromised for some of the methods during different simulation scenarios. In addition, all of these three methods need global positioning system (GPS) to measure the absolute velocity of a vehicle. To overcome the above-mentioned problem, a novel cost-effective estimation method is proposed in this paper. This method requires only the inputs of wheel angular velocity, traction/brake torque and longitudinal acceleration, which are all easy to be measured using available sensors installed in passenger vehicles. By using this method, the vehicle absolute velocity and slip ratio can be estimated by an improved nonlinear observer without using GPS, and the friction force and tyre–road friction coefficient can be obtained from the estimated vehicle velocity and slip ratio. Simulations are used to validate the effectiveness of the proposed estimation method.     

Robust road friction estimation during vehicle steering

Automated vehicles require information on the current road condition, i.e. the tyre–road friction coefficient for trajectory planning, braking or steering interventions. In this work, we propose a framework to estimate the road friction coefficient with stability and robustness guarantee using total aligning torque in vehicle front axle during steering. We first adopt a novel strategy to estimate the front axle lateral force which performs better than the classical unknown input observer. Then, combined with an indirect measurement based on estimated total aligning torque and front axle lateral force, a non-linear adaptive observer is designed to estimate road friction coefficient with stability guarantee. To increase the robustness of the estimation result, criteria are proposed to decide when to update the estimated road conditions. Simulations and experiments under various road conditions validate the proposed framework and demonstrate its advantage in stability by comparing it with the method utilising the wide-spread Extended Kalman Filter.     

Effective assessment of tyre–road friction coefficient using a hybrid estimator

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.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

Tyre–road grip coefficient assessment – Part II: online estimation using instrumented vehicle,extended Kalman filter,and neural network

The main objective of this work is to determine the limit of safe driving conditions by identifying the maximal friction coefficient in a real vehicle. The study will focus on finding a method to determine this limit before reaching the skid, which is valuable information in the context of traffic safety. Since it is not possible to measure the friction coefficient directly, it will be estimated using the appropriate tools in order to get the most accurate information. A real vehicle is instrumented to collect information of general kinematics and steering tie-rod forces. A real-time algorithm is developed to estimate forces and aligning torque in the tyres using an extended Kalman filter and neural networks techniques. The methodology is based on determining the aligning torque; this variable allows evaluation of the behaviour of the tyre. It transmits interesting information from the tyre–road contact and can be used to predict the maximal tyre grip and safety margin. The maximal grip coefficient is estimated according to a knowledge base, extracted from computer simulation of a high detailed three-dimensional model, using Adams^® software. The proposed methodology is validated and applied to real driving conditions, in which maximal grip and safety margin are properly estimated.     

Design of tyre force excitation for tyre–road friction estimation

Knowledge 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.     

Analysis of wheel speed vibrations for road friction classification

ABSTRACT

With higher level of vehicle automation, it becomes increasingly important to know the maximum possible tyre forces during normal driving. An interesting method in this respect is estimating the tyre–road friction from the resonance peak in the wheel speed signal, excited by road roughness. A simulation environment using the MF-Swift tyre model is proposed, which gives insight in the correctness and functioning of this method. From implementing the estimation algorithm and considering the tyre torsional vibration system, it is concluded that frequencies and damping ratios can be estimated with reasonable accuracy and that the trends observed with changing road friction are consistent. Furthermore, the proposed simulation environment gives opportunity to investigate other issues like robustness of the estimation method to road roughness. Additionally, the tyre modelling aspect of the estimation method is analysed and improvements are proposed.     

A real-time approach to robust identification of tyre–road friction characteristics on mixed-μ roads

ABSTRACT

The interaction between the tyre and the road is crucial for understanding the dynamic behaviour of a vehicle. The road–tyre friction characteristics play a key role in the design of braking, traction and stability control systems. Thus, in order to have a good performance of vehicle dynamic stability control, real-time estimation of the tyre–road friction coefficient is required. This paper presents a new development of an on-line tyre–road friction parameters estimation methodology and its implementation using both LuGre and Burckhardt tyre–road friction models. The proposed method provides the capability to observe the tyre–road friction coefficient directly using measurable signals in real-time. In the first step of our approach, the recursive least squares is employed to identify the linear parameterisation form of the Burckhardt model. The identified parameters provide, through a T–S fuzzy system, the initial values for the LuGre model. Then, a new LuGre model-based nonlinear least squares parameter estimation algorithm using the proposed static form of the LuGre to obtain the parameters of LuGre model based on recursive nonlinear optimisation of the curve fitting errors is presented. The effectiveness and performance of the algorithm are demonstrated through the real-time model simulations with different longitudinal speeds and different kinds of tyres on various road surface conditions in both Matlab/Carsim environments as well as collected data from real experiments on a commercial trailer.     

An ABS control logic based on wheel force measurement

The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre–road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force.

The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficient.     

Contents Index Volume 35 and 36

Active safety systems would benefit from tyre force and friction potential information. Different sensor concepts, including, among others, the EU–funded Apollo–project developed tyre sensor based on optical position detection, are being studied. The sensor can measure tyre carcass deflections with respect to the rim. The carcass deflections can be used to calculate tyre forces and they may be exploited in the estimation of friction potential. The waveforms of the sensor signal are illustrated. The vertical and lateral force estimations are presented with unavoidable compensation parts. The tyre sensor measurements were compared to the measurement–vehicle results and good correlations achieved. Continuing activities are concerned with the estimation of friction potential and the detection of aquaplaning.     

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation.     

Tyre–road grip coefficient assessment. Part 1: off-line methodology using multibody dynamic simulation and genetic algorithms

A key factor to understand the vehicle dynamic behaviour is to know as accurately as possible the interaction that occurs between the tyre and the road, since it depends on many factors that influence the dynamic response of the vehicle. This paper aims to develop a methodology in order to characterise the tyre–road behaviour, applying it to obtain the tyre–road grip coefficient. This methodology is based on the use of dynamic simulation of a virtual model, integrated into a genetic algorithm that identifies the tyre–road friction coefficient in order to adjust the response obtained by simulation to real data. The numerical model was developed in collaboration with SEAT Technical Centre and it was implemented in multibody dynamic simulation software Adams®, from MSC®.     

Sideslip angle estimation based on input–output linearisation with tire–road friction adaptation

An adaptive sideslip angle observer considering tire–road friction adaptation is proposed in this paper. The single-track vehicle model with nonlinear tire characteristics is adopted. The tire parameters can be easily obtained through road test data without using special test rigs. Afterwards, this model is reconstructed and a high-gain observer (HGO) based on input–output linearisation is derived. The observer stability is analysed. Experimental results have confirmed that the HGO has a better computational efficiency with the same accuracy when compared with the extended Kalman filter and the Luenberger observer. Finally, a road friction adaptive algorithm based on vehicle lateral dynamics is proposed and validated through driving simulator data. As long as the tires work in the nonlinear region, the maximal friction coefficient could be estimated. This algorithm has excellent portability and is also suitable for other observers.     

Investigation of Features of Tyre Rolling at Non-Small Velocities on the Basis of a Simple Tyre Model with Distributed Mass Periphery

SUMMARY

On the basis of the brush-type tyre model the paper considers the interaction between steady-state rolling deformable wheel and flat road surface as well as corresponding force and moment characteristics of the wheel.

At least two zones of sliding, anisotropic dry friction, sliding friction coefficient speed-dependent and instantaneous leap of the friction coefficient when transition from sliding to adhesion zone occurs, have been taken into account, as well as distributed peripheral mass of tyre, elasticity, pseudo-dry friction and damping properties in radial, tangential and lateral directions of the elements at the wheel periphery, including a visco-elastic belt. Vertical force distribution in the contact area is not supposed to be known in advance and follows from the calculation. As a result, sliding zone lengths, distributed forces in contact area, six components of generalized road reaction reduced to the wheel center, and rolling resistance moment are found as functions of vertical load, movement velocity, longitudinal and side slip, friction in contact area with road, stiffnesses, dry friction and damping in the tyre model elements and of distributed peripheral mass.

A computer program developed in Fortran and results of calculations are of particular interest for qualitative analysis including steady rolling of studded tyre and also racing car and aircraft tyres which peripheral mass shows itself in a special way because of great movement velocities.     

Estimation of longitudinal speed robust to road conditions for ground vehicles

This article seeks to develop a longitudinal vehicle velocity estimator robust to road conditions by employing a tyre model at each corner. Combining the lumped LuGre tyre model and the vehicle kinematics, the tyres internal deflection state is used to gain an accurate estimation. Conventional kinematic-based velocity estimators use acceleration measurements, without correction with the tyre forces. However, this results in inaccurate velocity estimation because of sensor uncertainties which should be handled with another measurement such as tyre forces that depend on unknown road friction. The new Kalman-based observer in this paper addresses this issue by considering tyre nonlinearities with a minimum number of required tyre parameters and the road condition as uncertainty. Longitudinal forces obtained by the unscented Kalman filter on the wheel dynamics is employed as an observation for the Kalman-based velocity estimator at each corner. The stability of the proposed time-varying estimator is investigated and its performance is examined experimentally in several tests and on different road surface frictions. Road experiments and simulation results show the accuracy and robustness of the proposed approach in estimating longitudinal speed for ground vehicles.     

论轮胎与路面间的摩擦

对轮胎与路面间摩擦产生的机理和影响因素进行了分析。其中产生的机理可归纳为轮胎与路面间分子引力的作用、轮胎与路面间的粘着作用、胎面橡胶的弹性变形及路面上小尺寸微凸体的微切削作用四种；影响轮胎与路面间摩擦的主要因素有滑移率，轮胎类型，胎面花纹的类型、密度系数、深度，路面粗糙度，路面污染情况，路面水膜，气候及充气压力等。     

3D brush model to predict longitudinal tyre characteristics

A 3D tyre brush model, which aims to predict the longitudinal tyre characteristic under steady-state conditions by modelling the occurring physical effects in the tyre–road contact patch, is presented. The model includes an analytical method to describe the tyre footprint geometry, the pressure distribution, the slip due to the lateral tyre contour, the slip due to braking or traction and the longitudinal as well as the lateral shear stresses on a flattened tyre. The presented development tool offers a method to investigate different rubber friction data (caused by different tread compounds and/or surface textures) and to analyse its influence on longitudinal tyre characteristics. The tyre design is fixed (same casing, dimension and pattern). The results include the shear stresses as well as the different sliding velocities in the contact patch for different slip conditions. The model was developed for a standard summer pattern design and a standard tyre dimension (205/55R16). It can also be adapted to other tread designs and tyre dimensions. To offer a good comparability between model results and test bench measurements, the surface curvature of an internal test rig is considered.     

Adaptive Yaw Rate Feedback 4WS with Tire/Road Friction Coefficient Estimator

This paper proposes an adaptive yaw rate feedback control system for a four-wheel-steering (4WS) vehicle which involves a tire/road friction coefficient estimator. The adaptive 4WS system has been developed so that the vehicle possesses desirable lateral characteristics even on slippery roads and in critical driving situations. The friction coefficient is estimated on real time from the yaw rate response of the controlled vehicle with the least squares. The control system adopts a two degree of freedom structure which consists of a feedforward compensator and a feedback control subsystem. The feedforward compensator is determined with the estimated friction coefficient to minimize the steady-state and transient vehicle slip angle in spite of changes in tire/road conditions. The feedback subsystem adopts the Internal Model Control (IMC) structure in order to compensate for nonlinearities and to realize robustness against modelling and estimation errors.     

The Tyre as a Sensor to Estimate Friction

Continuously updated knowledge of the friction potential and the friction demand can help to improve manoeuvrability and thereby safety of vehicles under slippery road conditions. An on line friction estimation method is presented using a simple brush type tyre model. First the method is verified by outdoor experiments using a tyre test trailer. Then the setup of a low-cost measurement system in a vehicle is discussed and results from both simulations and outdoor experiments are presented. Neural networks have been used both for modelling and identification of friction potential and friction demand.