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.     

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.     

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.     

Estimation of maximum road friction coefficient based on Lyapunov method

With the real time and accurate information of motor torque and rotation speed of the four-in-wheel-motordrive electric vehicles, a slip based algorithm for estimating maximum road friction coefficient is designed using Lyapunov stability theory. Modified Burckhardt tire model is used to describe longitudinal slip property of the tire. By introducing a new state variable, a nonlinear estimator is proposed to estimate the longitudinal tire force and the maximum road friction coefficient simultaneously. With the appropriate selection of estimation gain, the convergence of the estimation error of the tire longitudinal force and maximum road friction coefficient is proved through Lyapunov stability analysis. In addition, the error is exponentially stable near the origin. Finally the method is validated with Carsim-Simulink co-simulation and real vehicle tests under multi working conditions in acceleration situation which demonstrate high computational efficiency and accuracy of this method.     

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 vehicle sideslip angle and tire-road friction coefficient based on magnetometer with GPS

This paper presents a method that estimates the vehicle sideslip angle and a tire-road friction coefficient by combining measurements of a magnetometer, a global positioning system (GPS), and an inertial measurement unit (IMU). The estimation algorithm is based on a cascade structure consisting of a sensor fusing framework based on Kalman filters. Several signal conditioning techniques are used to mitigate issues related to different signal characteristics, such as latency and disturbances. The estimated sideslip angle information and a brush tire model are fused in a Kalman filter framework to estimate the tire-road friction coefficient. The performance and practical feasibility of the proposed approach were evaluated through several tests.     

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.     

轮胎／路面附着系数估算方法

为提高汽车主动安全系统自适应控制性能,需要对轮胎／路面附着系数进行精确的识别或估算。鉴于附着系数估计的复杂性,文章综述了目前路面附着系数估算中的汽车动力学建模和轮胎／路面摩擦模型建模,重点讨论了轮胎／路面附着系数识别算法中传感器的直接检测估计法,以及基于车辆动力学、回正力矩和状态观测器等动力学模型的估计算法,并对各估算方法存在的问题与发展趋势等进行了分析。对开发汽车主动安全电控系统和提高汽车产业核心竞争力具有重要意义。     

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.     

Real-Time Longitudinal Location Estimation of Vehicle Center of Gravity

The longitudinal location of a vehicle’s center of gravity (CG) is used as an important parameter for vehicle safety control systems, and can change considerably according to various driving conditions. Accordingly, for the better performance of vehicle safety control systems, it is essential to obtain the accurate CG location. However, it is generally difficult to acquire the value of this parameter directly through sensors due to cost reasons. In this study, a practical algorithm for estimating vehicle’s longitudinal CG location in real time is proposed. This algorithm is derived based only on longitudinal motion of the vehicle, excluding excessive lateral, yaw and roll movements of the vehicle. Moreover, the proposed algorithm has main differences from previous studies in that it does not require information such as vehicle mass, vehicle moments of inertia, road grade or tire-road surface friction, which are difficult to acquire. In the proposed algorithm, the relationship between the ratio of rear-to-front tire longitudinal force and the corresponding wheel slips are used to determine the CG location. To demonstrate a practical use of the proposed algorithm, the ideal brake force distribution is tested. The proposed CG estimation algorithm and its practical use are verified via simulations and experiments using a test vehicle equipped with electro-mechanical brakes in the rear wheels. It is shown that the estimated CG locations are close to the actual ones, and that the deceleration can be maximized by the ideal brake force distribution.     

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。     

Vehicle velocity estimation using effective inertia for an in-wheel electric vehicle

In this study, a vehicle velocity estimation algorithm for an in-wheel electric vehicle is proposed. This algorithm estimates the vehicle velocity using the concept of effective inertia, which is based on the motor torque, the angular velocity of each wheel and vehicle acceleration. Effective inertia is a virtual mass that changes according to the state of a vehicle, such as acceleration, deceleration, turning or driving on a low friction road. The performance of the proposed vehicle velocity estimation algorithm was verified in various conditions that included straight driving, circle driving and low friction road driving using the in-wheel electric vehicle that was equipped with an in-wheel system in each of its rear wheels.     

路面附着系数的自适应衰减卡尔曼滤波估计

为了获得实时、准确的路面附着系数，进一步提高观测路面附着系数算法的精度和收敛速度，结合非线性车辆动力学模型和轮胎力修正模型，搭建分布式驱动电动汽车联合仿真平台，提出一种基于自适应衰减无迹卡尔曼滤波的路面附着系数观测算法。该算法设计与各轮对应的路面附着系数观测器，应用协方差匹配判据对观测器发散趋势进行判别，设计自适应加权系数修正预测协方差，以增强新近观测数据的利用率；同时采用次优Sage-Husa噪声估计器对未知的系统过程噪声进行估计，抑制观测器的记忆存储长度，调整过程噪声和测量噪声的均值与协方差，提高观测器的跟踪能力。利用分布式驱动电动汽车分别进行高、低附着路面和对开路面直线制动试验，并将自适应衰减无迹卡尔曼滤波路面附着系数观测器的观测结果与无迹卡尔曼滤波观测值、参考路面附着系数进行比较和分析。结果表明：高附着路面条件下，所设计的算法估计误差可控制在0.64%以内；低附着路面条件下，所设计的算法估计误差可控制在1.03%以内；对开路面条件下估计误差可控制在1.26%以内；自适应衰减无迹卡尔曼滤波算法相比无迹卡尔曼滤波算法响应速率更快，具有更高的估计精度和较强的自适应能力，估计结果整体上维持稳定，能够适应各种不同路面的估计。     

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.     

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.     

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.     

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。     

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.     

Co-operative control for regenerative braking and friction braking to increase energy recovery without wheel lock

This paper presents a regenerative braking co-operative control algorithm to increase energy recovery without wheel lock. Considering the magnitude of the braking force available between the tire and road surface, the control algorithm was designed for the regenerative braking force at the front wheel and friction braking force at the rear wheel to be increased following the friction coefficient line. The performance of the proposed regenerative braking co-operative control algorithm was evaluated by the hardware in the loop simulation (HILS) with an electronic wedge brake on its front wheels and an electronic mechanical brake on its rear wheels. The HILS results showed that a proper braking force on the front and rear wheels on a low μ road prevented the lock of the front wheels that was connected to the motor, and maintained the regenerative braking and increased energy recovery.