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.     

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.     

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.     

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.     

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.     

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.     

Influence of tyre–road contact model on vehicle vibration response

The influence of the tyre–road contact model on the simulated vertical vibration response was analysed. Three contact models were compared: tyre–road point contact model, moving averaged profile and tyre-enveloping model. In total, 1600 real asphalt concrete and Portland cement concrete longitudinal road profiles were processed. The linear planar model of automobile with 12 degrees of freedom (DOF) was used. Five vibration responses as the measures of ride comfort, ride safety and dynamic load of cargo were investigated. The results were calculated as a function of vibration response, vehicle velocity, road quality and road surface type. The marked differences in the dynamic tyre forces and the negligible differences in the ride comfort quantities were observed among the tyre–road contact models. The seat acceleration response for three contact models and 331 DOF multibody model of the truck semi-trailer was compared with the measured response for a known profile of test section.     

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

In this paper, a vehicle's lateral dynamic model is developed based on the pure and the combined-slip LuGre tyre models. Conventional vehicle's lateral dynamic methods derive handling models utilising linear tyres and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviours of the tyre into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tyre–vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method.     

Model-Based Road Friction Estimation

The tire/road friction coefficient, μ, has a significant role in vehicle longitudinal and lateral control, and there has been associated efforts to measure or estimate the road surface condition to provide additional information for stability augmentation systems of automobiles. In this paper, a model based road friction estimation algorithm is proposed from easily measured signals such as yaw rate and wheel speed. For the development of the estimator, a low order vehicle model incorporated with simple but effective tire model. Field tests of the estimator using actual vehicle measurements show promising results.     

Slip-Angle Estimation for Vehicle Stability Control

Recently, some direct yaw-moment control systems have been in development. Obviously, such systems need accurate slip-angle information. This paper describes a strategy of vehicle slip angle estimation. The difficulty in slip angle estimation is due to nonlinear characteristics of tyres and influence of relative slant of the road surface. To solve this difficulty, a combined method of model observer and direct integration method is proposed. In this method, two kinds of values of the side forces of the wheels are provided, i.e., direct detected values by the G-sensor and values from a tyre model. Then those values are combined appropriately which results in the combination of model observer and direct integration. A feedback algorithm, redesigned to suppress the influence of tyre model error, is applied in the observer. Considering interference of road surface and its avoidance, road slant angle is estimated and consequently vehicle model is corrected. The estimated value of the road friction coefficient is given by the acceleration, and an adequate bias, depending on yaw-deviation, is added. The calculation method of reference yaw-velocity is improved, in order to avoid interference of road slant and variation of dynamic characteristic of vehicle.     

Slip-Angle Estimation for Vehicle Stability Control

Recently, some direct yaw-moment control systems have been in development. Obviously, such systems need accurate slip-angle information. This paper describes a strategy of vehicle slip angle estimation. The difficulty in slip angle estimation is due to nonlinear characteristics of tyres and influence of relative slant of the road surface. To solve this difficulty, a combined method of model observer and direct integration method is proposed. In this method, two kinds of values of the side forces of the wheels are provided, i.e., direct detected values by the G-sensor and values from a tyre model. Then those values are combined appropriately which results in the combination of model observer and direct integration. A feedback algorithm, redesigned to suppress the influence of tyre model error, is applied in the observer. Considering interference of road surface and its avoidance, road slant angle is estimated and consequently vehicle model is corrected. The estimated value of the road friction coefficient is given by the acceleration, and an adequate bias, depending on yaw-deviation, is added. The calculation method of reference yaw-velocity is improved, in order to avoid interference of road slant and variation of dynamic characteristic of vehicle.     

Customer loads of two-wheeled vehicles

Customer usage profiles are the most unknown influences in vehicle design targets and they play an important role in durability analysis. This publication presents a customer load acquisition system for two-wheeled vehicles that utilises the vehicle's onboard signals. A road slope estimator was developed to reveal the unknown slope resistance force with the help of a linear Kalman filter. Furthermore, an automated mass estimator was developed to consider the correct vehicle loading. The mass estimation is performed by an extended Kalman filter. Finally, a model-based wheel force calculation was derived, which is based on the superposition of forces calculated from measured onboard signals. The calculated wheel forces were validated by measurements with wheel–load transducers through the comparison of rainflow matrices. The calculated wheel forces correspond with the measured wheel forces in terms of both quality and quantity. The proposed methods can be used to gather field data for improved vehicle design loads.     

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.     

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.     

基于交互多模型的车辆质量与道路坡度估计（双语出版）

车辆结构参数和道路环境信息的实时准确获取是提高智能汽车运动控制性能的重要因素之一，而车辆质量与道路坡度信息是多种汽车控制系统的必要信息，因此质量与坡度在线估计的研究一直受到关注。针对车辆质量与道路坡度的联合估计问题，提出了一种基于交互多模型的质量与坡度融合估计方法。首先，设定了适宜进行质量精确估计的工况条件，据此提出了基于模糊规则的质量估计置信度因子计算算法，进而设计了基于置信度因子的递推最小二乘车辆质量估计算法，以实现质量的在线估计。然后，以车辆纵向动力学模型为基础，建立了运动学和动力学2种坡度估计模型，并设计了基于运动学模型的线性卡尔曼滤波坡度观测器，基于电子稳定性程序ESP的纵向加速度信息实现坡度估计，设计了基于动力学模型的无迹卡尔曼滤波坡度观测器，基于ESP和发动机管理系统EMS的力信息实现坡度估计。运动学模型未考虑车辆姿态信息，坡度估算结果与实际值有偏差；动力学模型对模型精度要求高，算法稳定性差，为充分发挥2种方法优势实现坡度的精确估计，采用交互多模型算法实现了2种坡度估计方法的加权融合。最后，对所设计的算法进行了实车试验验证。结果表明：所设计的质量与坡度估算算法具有较好的实时性和准确性，适合智能汽车运动控制的应用需求。     

Development of a slip control anti-lock braking system model

This paper describes the initial phase of work carried out as part of an on going study investigating the interaction between the tyre, suspension system and an antilock braking system (ABS). The modelling, analysis simulations and integration of results have been performed using an industry standard Multibody Systems Analysis (MBS) program. A quarter vehicle model has been used together with an individual front suspension system represented by interconnected rigid bodies. The tyre model used can be integrated into vehicle handling simulations but only the theory associated with the generation of longitudinal braking forces is described here. An ABS model based on slip control has been used to formulate the braking forces described in this paper. The simulations, which have been performed braking on wet and dry road surfaces, compare the performance of two different tyres.     

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.     

Dual extended Kalman filter for vehicle state and parameter estimation

The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus 'splitting' the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.