Robust estimation of maximum tire-road friction coefficient considering road surface irregularity

An accurate estimation of the maximum tire-road friction coefficient may provide higher performance in a vehicle active safety control system. Unfortunately, real-time tire-road friction coefficient estimation is costly and necessitates additional sensors that must be installed and maintained at all times. This paper proposes an advanced longitudinal tire-road friction coefficient estimation method that is capable of considering irregular road surfaces. The proposed algorithm uses a stiffness based estimation method, however, unlike previous studies, improvements were made by suggesting a third order model to solve problems related to nonlinear mu-slip curve. To attain the tire-road friction coefficient, real-time normalized force is obtained from the force estimator as exerted from the tire in the low slip region using the recursive least squares method. The decisive aspect of using the suggested algorithm lies in its low cost and versatility. It can be used under irregular road conditions due to its capability of easily obtaining wheel speed and acceleration values from production cars. The newly improved algorithm has been verified to computer simulations as well as compact size cars on dry asphalt conditions.     

基于四轮轮边驱动电动车的路面附着系数估算方法

路面附着系数是影响车辆行驶安全性的重要因素,利用轮边驱动电动汽车驱动力矩可以对路面利用附着系数进行观测。当观测到μ-λ曲线接近于峰值点时,将该时刻的轮胎利用附着系数作为路面峰值附着系数,并根据识别的路面峰值附着系数进行驱动防滑控制。该方法能够有效防止轮胎滑转,提高车辆行驶稳定性。     

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.     

On the experimental analysis of single input single output control of yaw rate and sideslip angle

Electric vehicles with individually controlled drivetrains allow torque-vectoring, which improves vehicle safety and drivability. This paper investigates a new approach to the concurrent control of yaw rate and sideslip angle. The proposed controller is a simple single input single output (SISO) yaw rate controller, in which the reference yaw rate depends on the vehicle handling requirements, and the actual sideslip angle. The sideslip contribution enhances safety, as it provides a corrective action in critical situations, e.g., in case of oversteer during extreme cornering on a low friction surface. The proposed controller is experimentally assessed on an electric vehicle demonstrator along two maneuvers on surfaces with significantly varying tire-road friction coefficient. Different longitudinal locations of the sideslip angle used as control variable are compared during the experiments. Results show that: i) the proposed SISO approach provides significant improvements with respect to the vehicle without torque-vectoring, and the controlled vehicle with a reference yaw rate solely based on the handling requirements for high-friction maneuvering; and ii) the control of the rear axle sideslip angle provides better performance than the control of the sideslip angle at the center of gravity.     

Estimation of Tire-Road Friction Using Observer Based Identifiers

This paper presents methods for identifying the tire-road friction coefficient. The proposed methods are: an observer-based least square method and an observer/filtered-regressor-based method. These methods were designed assuming that some of the states are not available since physical parameter identification methods developed assuming that the system states are available are not attractive from a practical point of view. The observer is used to estimate signals which are difficult or expensive to measure. Using the estimated states of the system and the filtered-regressor, the parameter estimates are obtained. The proposed methods are evaluated on an eight state nonlinear vehicle/transmission simulation model with a Bakker-Pacejka's formula tire model. Vehicle tests have been performed on dry and wet roads to verify the performance of the methods. It has been shown through simulations and vehicle tests how the RPM sensors can be used with observer based identification methods to estimate the tire-road friction from measurements of engine rpm, transmission output speed and wheel speed. The proposed methods will be useful in the implementation and adaptation of vehicle collision warning/avoidance algorithm since the tire-road friction can be estimated only using the RPM sensors which are currently being used in production vehicles.     

Novel electronic braking system design for EVS based on constrained nonlinear hierarchical control

Both environment protection and energy saving have attracted more and more attention in the electric vehicles (EVs) field. In fact, regarding control performance, electric motor has more advantages over conventional internal combustion engine. To decouple the interaction force between vehicle and various coordinating and integrating active control subsystems and estimate the real-time friction force for Advanced Emergency Braking System (AEBS), this paper’s primary intention is uniform distribution of longitudinal tire-road friction force and control strategy for a Novel Anti-lock Braking System (Nov- ABS) which is designed to estimate and track not only any tire-road friction force, but the maximum tire-road friction force, based on the Anti-Lock Braking System (ABS). The longitudinal tire-road friction force is computed through real-time measurement of breaking force and angular acceleration of wheels. The Magic Formula Tire Model can be expressed by the reference model. The evolution of the tire-road friction is described by the constrained active-set SQP algorithm with regard to wheel slip, and as a result, it is feasible to identify the key parameters of the Magic Formula Tire Model. Accordingly, Inverse Quadratic Interpolation method is a proper way to estimate the desired wheel slip in regards to the reference of tireroad friction force from the top layer. Then, this paper adapts the Nonlinear Sliding Mode Control method to construct proposed Nov-ABS. According to the simulation results, the objective control strategy turns out to be feasible and satisfactory.     

路面附着系数估算技术发展现状综述

对路面附着系数估算领域的研究状况进行了综合叙述,并对其缺陷和今后发展方向进行了讨论。     

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.     

车速和路面附着系数的滚动时域估计

基于Dugoff轮胎模型建立了车辆的非线性动力学方程,并给出了路面附着系数的约束条件.针对车速和路面附着系数约束的非线性估计,提出了一种基于滚动优化原理的滚动时域估计法(MHE),并给出了MHE法的具体步骤.在不同路面上对MHE法进行了多种工况的实验验证,并在同样条件下与扩展Kalman滤波法进行了比较.实验结果表明,MHE法的估计性能优于扩展Kalman滤波法.     

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.     

Sliding-mode-based parameter identification with application to tire pressure and tire-road friction

This paper presents a method of simultaneous estimation of tire pressure and tire-road friction. A sliding-mode scheme is designed to identify the system state and the parameter variation of a torsional tire system, which greatly depend on the change in tire pressure. Then, the recursive least-squares method with a forgetting facto is used to estimate the parameter variations of the tire system and the tire-road friction force without a friction model using the information retrieved from the equivalent input for sliding motion. A simulation study is performed to illustrate the effectiveness of the proposed method.     

Road profile input estimation in vehicle dynamics simulation

Vehicle motion simulation accuracy, such as in accident reconstruction or vehicle controllability analysis on real roads, can be obtained only if valid road profile and tire-road friction models are available. Regarding road profiles, a new method based on sliding mode observers has been developed and is compared with two inertial methods. Experimental results are shown and discussed to evaluate the robustness of our approach.     

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.     

Re-adhesion control for a railway single wheelset test rig based on the behaviour of the traction motor

A method for detecting wheel slip/slide and re-adhesion control of AC traction motors in railway applications is presented in this paper. This enables a better utilisation of available adhesion and could also reduce wheel wear by reducing high creep values. With this method, the wheel–rail (roller) creepage, creep force and friction coefficient can be indirectly detected and estimated by measuring the voltage, current and speed of the AC traction motor and using an extended Kalman filter. The re-adhesion controller is designed to regulate the motor torque command according to the maximum available adhesion based on the estimated results. Simulations under different friction coefficients are carried out to test the proposed method.     

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.     

Investigation on evaluation of yaw stability for medium commercial vehicles

This paper proposes test scenarios for evaluation of yaw stability for medium commercial vehicles. Maneuvering, speed, longitudinal tire force, tire-road friction coefficient, road slope, and load condition are considerable factors that have effect on the medium commercial vehicle yaw stability. After conducting an analysis on these six factors, effective test scenarios were developed. A sine with dwell test is well known as a test scenario for evaluation of performance of electronic stability control (ESC) on passenger vehicles and heavy commercial vehicles. The SWD test was modified considering medium commercial vehicle dynamics, and the ramp steer maneuver with maximum acceleration test was proposed. Simulation validation has been conducted using field test data. From simulation study, it was shown that the ESC system for medium commercial vehicle is effectively evaluated by the proposed test scenarios.     

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.     

基于车路系统的事故现场轮胎印迹强度参数化研究

为明确事故现场可视轮胎印迹强度与车辆动力学特性、轮胎橡胶磨损特征及道路表面灰度之间的关联特性,提出基于车路耦合的事故现场轮胎印迹强度参数化研究方法。通过结合动态滑动摩擦因数模型及轮胎非线性模型,建立车辆路面9 DOF非线性系统动力学模型,运用VBOX惯性测量技术验证模型的有效性。运用胎面磨损能量模型,从车路系统角度确定车辆、轮胎和路面特性对轮胎全局摩擦力及胎面磨损特性的影响。结合印迹强度特征模型提出轮胎印迹强度参数研究方法,选取不同制动、转向角工况及3组路面、胎面特性对轮胎路面接地力学特性、胎面橡胶磨损量、可视轮胎印迹特征进行仿真分析。结果表明：印迹强度仅与全局摩擦力大小有关,与轮胎路面滑移方向无关;滑移工况下胎面橡胶磨损量随着全局摩擦力和滑移速度的增大而增大,而印迹强度变化不明显;制动力矩和道路表面灰度对产生可视轮胎印迹起决定作用,转向角主要影响不规则可视轮胎印迹的产生;前轮轮胎最先出现可视印迹,且可视印迹长度和强度均高于后轮轮胎;采取可视印迹起点作为事故车辆速度判定具有一定的误差,应根据具体情况进行具体分析;研究成果能够为基于可视轮胎印迹的交通事故重建提供理论基础。     

The stability mechanism and its application to heavy-haul couplers with arc surface contact

To investigate the stability mechanism of a type of heavy-haul coupler with arc surface contact, the force states of coupler were analysed at different yaw angles according to the friction circle theory and the structural characteristics of this coupler were summarised. A multi-body dynamics model with four heavy-haul locomotives and three detailed couplers was established to simulate the process of emergency braking. In addition, the coupler yaw instability was tested in order to investigate the effect of relevant parameters on the coupler stability. The results show that this coupler exhibits the self-stabilisation and less lateral force at a small yaw angle. The yaw angle of force line is less than the actual coupler yaw angle which reduces the lateral force and the critical instability. An increase in the friction coefficient of the arc contact surfaces can improve the stability of couplers. The friction coefficient needs to be increased with the increase in the maximum coupler longitudinal compressive force. The stability of couplers is significantly enhanced by increasing the secondary suspension stiffness and reducing the clearance of the lateral stopper of the locomotives. When the maximum coupler compressive force reaches 2500 kN, the required friction coefficient reduces from 0.6 to 0.35, which notably lowers the derailment risk caused by the coupler. The critical instability angle of the coupler mainly depends on the arc contact friction coefficient. When the friction coefficient is 0.3, the critical instability angle was 4–4.5°. The simulation results are consistent with the locomotive line tests. These studies establish meaningful improvements for the stability of couplers and match the heavy-haul locomotive with its suspension parameters.     

Effect of arc surfaces friction coefficient on coupler stability in heavy haul locomotives: simulation and experiment

The heavy haul coupler/buffer system equipped with arc surfaces on the coupler tail and the follower is widely applied to connect the locomotives and wagons. As one of the most important parameters, arc surfaces friction coefficient plays a key role in coupler instability, which threatens the safety of trains. To investigate the effect of arc surfaces friction coefficient on coupler stability, a simulation model adopting the latest modelling methods is established and field tests employing the locomotives equipped with different friction coefficients are conducted. The results show that the friction coefficient of arc surfaces can affect the coupler yaw angle remarkably. Increasing the friction coefficient can improve the coupler stability. However, under severe compressive force condition, the increased friction coefficient can be reduced quickly, which calls for further attention.