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.     

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.     

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.     

Shear forces in the contact patch of a braked-racing tyre

This article identifies tyre modelling features that are fundamental to the accurate simulation of the shear forces in the contact patch of a steady-rolling, slipping and cambered racing tyre. The features investigated include contact patch shape, contact pressure distribution, carcass flexibility, rolling radius (RR) variations and friction coefficient. Using a previously described physical tyre model of modular nature, validated for static conditions, the influence of each feature on the shear forces generated is examined under different running conditions, including normal loads of 1500, 3000 and 4500 N, camber angles of 0° and?3°, and longitudinal slip ratios from 0 to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest in terms of its connection with the limit-handling feel. The results of the simulations reveal that true representations of the contact patch shape, carcass flexibility and lateral RR variation are essential for an accurate prediction of the distribution and the magnitude of the shear forces generated at the tread–road interface of the cambered tyre. Independent of the camber angle, the contact pressure distribution primarily influences the shear force distribution and the slip characteristics around the peak longitudinal force. At low brake-slip ratios, the friction coefficient affects the shear forces in terms of their distribution, while, at medium to high-slip ratios, the force magnitude is significantly affected. On the one hand, these findings help in the creation of efficient yet accurate tyre models. On the other hand, the research results allow improved understanding of how individual tyre components affect the generation of shear forces in the contact patch of a rolling and slipping tyre.     

Tyre friction behaviour under abrupt wheel torque transients on slippery road surfaces: experimental analysis and modelling

The paper shows that, during abrupt wheel torque transients for ice surface and low vehicle speeds, the tyre can develop significantly larger longitudinal force than the peak value of the tyre static curve. This so-called dynamic tyre friction potential (DTFP) effect has many influencing factors such as the rate of change of the wheel torque, the vehicle speed, and the tyre dwell time. The paper presents a detailed analysis of the DTFP behaviour based on the experimental data collected by using an in-wheel motor-based tyre test vehicle. The analysis results and an insight into the brush structure of a tyre model lead to the hypothesis that the different influencing factors may be predominantly explained by the bristle dwell time (BDT) effect. Following this hypothesis, the LuGre model of the tyre friction dynamics is extended with a physical BDT sub-model. The experimental validation results show that the proposed model can accurately capture the low-speed tyre–ice friction behaviour during abrupt wheel torque transients.     

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.     

Geometric-based tyre vertical force estimation and stiffness parameterisation for automotive and unmanned vehicle applications

Advanced empirical, and physical-based tyre models have proven to be accurate for simulating tyre dynamics; however, these tyre models typically require expensive and intensive tyre parameterisation. Recent research into wheeled unmanned ground vehicles requiring vertical force analysis has shown good results using a simple linear spring model for the tyre which demonstrate the continued use for simple tyre models; however, parameterisation of the tyre still remains a challenge when load test equipment is not available. This paper presents a cost-effective tyre vertical stiffness parameterisation procedure using only measured tyre geometry and air pressure for applications where high-fidelity tyre models are unnecessary. Vertical forces calculated through an air volume optimisation approach are used to estimate tyre vertical stiffness. Nine tyres from the literature are compared to evaluate the performance of the vertical force estimation and stiffness parameterisation algorithms. Experimental results on a pair of ATV tyres are also presented.     

An optimal pole-matching observer design for estimating tyre–road friction force

In this paper, considering the dynamical model of tyre–road contacts, we design a nonlinear observer for the on-line estimation of tyre–road friction force using the average lumped LuGre model without any simplification. The design is the extension of a previously offered observer to allow a muchmore realistic estimation by considering the effect of the rolling resistance and a term related to the relative velocity in the observer. Our aim is not to introduce a new friction model, but to present a more accurate nonlinear observer for the assumed model. We derive linear matrix equality conditions to obtain an observer gain with minimum pole mismatch for the desired observer error dynamic system. We prove the convergence of the observer for the non-simplified model. Finally, we compare the performance of the proposed observer with that of the previously mentioned nonlinear observer, which shows significant improvement in the accuracy of estimation.     

A tyre slip-based integrated chassis control of front/rear traction distribution and four-wheel independent brake from moderate driving to limit handling

This paper presents a tyre slip-based integrated chassis control of front/rear traction distribution and four-wheel braking for enhanced performance from moderate driving to limit handling. The proposed algorithm adopted hierarchical structure: supervisor – desired motion tracking controller – optimisation-based control allocation. In the supervisor, by considering transient cornering characteristics, desired vehicle motion is calculated. In the desired motion tracking controller, in order to track desired vehicle motion, virtual control input is determined in the manner of sliding mode control. In the control allocation, virtual control input is allocated to minimise cost function. The cost function consists of two major parts. First part is a slip-based tyre friction utilisation quantification, which does not need a tyre force estimation. Second part is an allocation guideline, which guides optimally allocated inputs to predefined solution. The proposed algorithm has been investigated via simulation from moderate driving to limit handling scenario. Compared to Base and direct yaw moment control system, the proposed algorithm can effectively reduce tyre dissipation energy in the moderate driving situation. Moreover, the proposed algorithm enhances limit handling performance compared to Base and direct yaw moment control system. In addition to comparison with Base and direct yaw moment control, comparison the proposed algorithm with the control algorithm based on the known tyre force information has been conducted. The results show that the performance of the proposed algorithm is similar with that of the control algorithm with the known tyre force information.     

Time-optimal control of the race car: influence of a thermodynamic tyre model

The robustness of an existing numerical method for the time-optimal control of the race car is demonstrated through its application to a model of a Formula 1 car equipped with a simplified thermodynamic tyre model. The tyre model includes a temperature- and frequency-dependent model of road/tyre friction. A lumped parameter approach is used to model the thermodynamics of the various parts of the tyre such as the tread, carcass and inflation gas. The influence of tyre, track surface and ambient temperatures on time-optimal manoeuvring is presented.     

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.     

Analysis of lateral tyre friction dynamics1

The tyre friction model is a key part of the overall multi-body tyre dynamics model. The LuGre dynamic tyre friction model is analytically linearised for pure cornering conditions. The linearised model parameters are conveniently expressed as functions of static curve slope parameters. The linearised lateral force and self-aligning torque submodels are described by equivalent mechanical systems. The linearised model and equivalent system parameters are analysed for different slip angle and wheel centre speed operating points. An example of the application of linearised tyre friction model to tyre vibration analysis is presented as well.     

Friction coefficient measurement for autonomous winter road maintenance

Real-time measurement of tyre–road friction coefficient is extremely valuable for winter road maintenance operations, since knowledge of tyre–road friction coefficient can be used to optimise application of deicing chemicals to the roadway. In this paper, a wheel-based tyre–road friction coefficient measurement system is developed for snowploughs. Unlike a traditional Norse meter, this system is based on measurement of lateral tyre forces, has minimal moving parts and does not use a brake actuator. Hence, it is reliable and inexpensive. A key challenge is quickly detecting changes in the estimated tyre–road friction coefficient while rejecting the high levels of vibratory noise in the measured force signal. Novel filtering and signal processing algorithms are developed to address this challenge, including a biased quadratic mean filter and an accelerometer-based vibration removal filter. Detailed experimental results are presented on the performance of the friction estimation system on different types of road surfaces. It is also shown that disturbances due to lateral and longitudinal vehicle manoeuvres on the estimated friction coefficient can be removed by using accelerometer-based filtering.     

Experimental analysis of tyre-enveloping characteristics at low speed

In this study, experiments are conducted to investigate tyre-enveloping characteristics. Four different types of tyres are tested. Parameters such as different tyre inflation pressures, vertical loads and types of obstacles (cleats) are considered. In addition to vertical stiffnesses of all tyres, vertical and horizontal force variations while traversing different obstacles at low speed are studied. The effects of inflation pressure and vertical load on variations of force and moment are investigated. Static test results showed that after a certain vertical displacement, all curves in force–deflection diagrams plotted with and without cleat intersect regardless of cleat and tyre types, depending on the inflation pressure of the tyre, which can be called typical static tyre-enveloping characteristics. Test results at low speed show that there is a considerable influence of the vertical load on vertical and lateral force responses of a tyre.     

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.     

Normal and shear forces in the contact patch of a braked racing tyre. Part 1: results from a finite-element model

In this first part of a two-part article, a previously described and validated finite-element model of a racing-car tyre is developed further to yield detailed information on carcass deflections and contact pressure and shear stress distributions for a steady rolling, slipping, and cambered tyre. Variations in running conditions simulated include loads of 1500, 3000 and 4500 N, camber angles of 0° and ?3°, and longitudinal slips from 0% to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest. Results generated are in broad agreement with limited experimental results from the literature and they provide considerable insight into how the tyre deforms and how the contact stresses are distributed as functions of the running conditions. Generally, each rib of the tyre behaves differently from the others, especially when the wheel is cambered. The results form a basis for the development of a simpler physical tyre model, the purpose of which is to retain accuracy over the full operating range while demanding much less computational resource. The physical tyre model is the topic of the second part of the article.     

Velocity and normal tyre force estimation for heavy trucks based on vehicle dynamic simulation considering the road slope angle

A precise estimation of vehicle velocities can be valuable for improving the performance of the vehicle dynamics control (VDC) system and this estimation relies heavily upon the accuracy of longitudinal and lateral tyre force calculation governed by the prediction of normal tyre forces. This paper presents a computational method based on the unscented Kalman filter (UKF) method to estimate both longitudinal and lateral velocities and develops a novel quasi-stationary method to predict normal tyre forces of heavy trucks on a sloping road. The vehicle dynamic model is constructed with a planar dynamic model combined with the Pacejka tyre model. The novel quasi-stationary method for predicting normal tyre forces is able to characterise the typical chassis configuration of the heavy trucks. The validation is conducted through comparing the predicted results with those simulated by the TruckSim and it has a good agreement between these results without compromising the convergence speed and stability.     

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.     

Dynamic emulation of road/tyre longitudinal interaction for developing electric vehicle control systems

Current research on electric vehicles (EVs) is focusing on the environment and energy aspects. However, electric motors also have much better control performance than conventional internal combustion engines. EVs could not only be ‘cleaner’ and ‘more energy efficient’, but also become ‘safer’ with ‘better driving performance’. In this paper, a discrete elasto-plastic friction model is proposed for a dynamic emulation of road/tyre friction in order to validate the control design of EV control systems in laboratory facilities. Experimental results show the dynamic emulation is able to capture the transient behaviour of the road/tyre friction force during braking and acceleration, therefore enabling a more reliable validation of various EV control methods. And the computation of inverse dynamics, which usually needs to be considered in conventional emulation approaches, can be avoided using the proposed dynamic friction model.