Literature review and fundamental approaches for vehicle and tire state estimation*

ABSTRACT

Most modern day automotive chassis control systems employ a feedback control structure. Therefore, real-time estimates of the vehicle dynamic states and tire-road contact parameters are invaluable for enhancing the performance of vehicle control systems, such as anti-lock brake system (ABS) and electronic stability program (ESP). Today's production vehicles are equipped with onboard sensors (e.g. a 3-axis accelerometer, 3-axis gyroscope, steering wheel angle sensor, and wheel speed sensors), which when used in conjunction with certain model-based or kinematics-based observers can be used to identify relevant tire and vehicle states for optimal control of comfort, stability and handling. Vehicle state estimation is becoming ever more relevant with the increased sophistication of chassis control systems. This paper presents a comprehensive overview of the state-of-the-art in the field of vehicle and tire state estimation. It is expected to serve as a resource for researchers interested in developing vehicle state estimation algorithms for usage in advanced vehicle control and safety systems.     

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.     

基于横摆力矩的汽车稳定性控制策略

为提高车辆的横向稳定性,获得良好的操纵性能,利用ADAMS/car和MATLAB/simulink建立了以横摆角速度和质心侧偏角为控制变量的多级PID仿真模型,分别采用了单个车轮制动和单侧车轮制动产生附加横摆力矩的方式.通过蛇形试验验证了ESP控制器的有效性和对比了2种制动方式的控制效果.仿真试验表明：采用该ESP控制器可以很好地保持车辆的稳定性,采用单侧车轮制动产生附加横摆力矩的方式具有更快的控制速度和更好的控制效果.     

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。     

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.     

Vehicle stability control system for enhancing steerabilty,lateral stability,and roll stability

The Vehicle stability control system is an active safety system designed to prevent accidents from occurring and to stabilize dynamic maneuvers of a vehicle by generating an artificial yaw moment using differential brakes. In this paper, in order to enhance vehicle steerability, lateral stability, and roll stability, each reference yaw rate is designed and combined into a target yaw rate depending on the driving situation. A yaw rate controller is designed to track the target yaw rate based on sliding mode control theory. To generate the total yaw moment required from the proposed yaw rate controller, each brake pressure is properly distributed with effective control wheel decision. Estimators are developed to identify the roll angle and body sideslip angle of a vehicle based on the simplified roll dynamics model and parameter adaptation approach. The performance of the proposed vehicle stability control system and estimation algorithms is verified with simulation results and experimental results.     

大型客车横向稳定性仿真分析

为了给营运客车横向稳定状态监测提供理论依据,针对极限工况下状态参数的临界值仿真结果,进行了营运客车稳定区域边界条件的研究。基于非线性三自由度车辆模型建立了基于扩展卡尔曼滤波（EKF）的状态参数估计器,对营运客车的质心侧偏角和横摆角速度进行实时估计,并利用Trucksim验证估计值具有较好的一致性和状态跟随能力。基于MATLAB/Simulink建立非线性七自由度车辆模型,分析不同行驶状态参数对质心侧偏角-质心侧偏角速度（β-β）相平面稳定区域边界的影响,基于仿真数据确定了以车速、前轮转角和路面附着系数为变量的稳定区域边界条件,结合状态估计模型获得以β-β决定的控制变量。在Trucksim中进行连续正弦方向盘转角输入标准稳定性试验,通过分析营运客车行驶过程中控制变量的曲线变化趋势是否超出稳定区域边界确定车辆的运行状态。结果表明：营运客车以60 km·h^-1车速、小方向盘转角行驶在低附着系数（μ=0.3）路面和高附着系数（μ=0.85）路面时,横摆角速度对驾驶人的意图（方形盘转角曲线趋势）有很好的跟随能力,具有较小的延迟响应,车辆处于稳定状态,此时控制变量曲线一直处于稳定区域内;当相同工况下以大方向盘转角输入时,横摆角速度已经不能很好地跟随驾驶人意图,且低附着系数路面下,在3.5 s左右时方向盘转角已经回正,但横摆角速度仍位于最大值,具有较大的延迟,营运客车发生急转侧滑;高附着系数路面下第2.5 s和第6.2 s左右车辆发生严重偏移,车辆处于失稳状态,而对应时刻的控制变量曲线部分超出稳定边界,验证了营运客车横向稳定状态判据的准确性。     

基于MPC的独立驱动电动汽车稳定性集成控制

针对独立驱动电动汽车在高附着系数路面高速急转时易发生侧翻事故,在低附着系数路面急转易发生侧滑失稳事故,且单一控制器在不同附着系数路面适应性较差等问题,根据独立驱动电动汽车特点设计了基于分层式结构的稳定性集成控制器。建立了整车动力学模型,并进行了车辆状态参数估计;设计了稳定性集成控制器的控制策略,对车辆的侧倾、横向稳定性状态判定条件和协调策略的制定进行了研究,分别设计了侧倾稳定性控制器和横向稳定性控制器;设置了路面附着系数0.9到0.2的对接路面仿真工况,并在此工况下对所设计的控制器的控制性能进行了仿真测试。结果表明,所设计的稳定性集成控制器相比于单一控制器具有更好的适应性,可有效降低车辆高速行驶过程中的横向载荷转移系数、质心侧偏角等状态量,提高车辆行驶的稳定性和安全性。     

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.     

Predictive control of a vehicle trajectory using a coupled vector with vehicle velocity and sideslip angle

In this paper, a predictive algorithm for vehicle trajectory control using the vehicle velocity and sideslip angle is proposed. Since the driving state of a vehicle generates nonholonomic constraint equations, it is difficult to control the trajectory with a conventional control algorithm. Furthermore, control vectors such as vehicle velocity and sideslip angle are coupled together; hence, a separate control for each variable is not suitable. In this study, a coupled control vector that combines the velocity and sideslip angle is proposed for the predictive control of vehicle trajectory. Since the coupled control vector is derived from the status of the vehicle’s motion, it is easy to generate a feedback control vector for the predictive controller. The coupled vector cannot be directly used as input to the vehicle systems; therefore, the vehicle input vector should be calculated from the control vector using a nonlinear function. Since nonlinear functions are not inserted in the control loop, they are calculated by the controller. Therefore, this method does not require a linearization process in the control logic, which enhances the stability and accuracy of the predictive controller.     

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.     

Distributed and self-adaptive vehicle speed estimation in the composite braking case for four-wheel drive hybrid electric car

Considering the controllability and observability of the braking torques of the hub motor, Integrated Starter Generator (ISG), and hydraulic brake for four-wheel drive (4WD) hybrid electric cars, a distributed and self-adaptive vehicle speed estimation algorithm for different braking situations has been proposed by fully utilising the Electronic Stability Program (ESP) sensor signals and multiple powersource signals. Firstly, the simulation platform of a 4WD hybrid electric car was established, which integrates an electronic-hydraulic composited braking system model and its control strategy, a nonlinear seven degrees-of-freedom vehicle dynamics model, and the Burckhardt tyre model. Secondly, combining the braking torque signals with the ESP signals, self-adaptive unscented Kalman sub-filter and main-filter adaptable to the observation noise were, respectively, designed. Thirdly, the fusion rules for the sub-filters and master filter were proposed herein, and the estimation results were compared with the simulated value of a real vehicle speed. Finally, based on the hardware in-the-loop platform and by picking up the regenerative motor torque signals and wheel cylinder pressure signals, the proposed speed estimation algorithm was tested under the case of moderate braking on the highly adhesive road, and the case of Antilock Braking System (ABS) action on the slippery road, as well as the case of ABS action on the icy road. Test results show that the presented vehicle speed estimation algorithm has not only a high precision but also a strong adaptability in the composite braking case.     

基于模糊逻辑的车辆侧偏角估计方法

提出了一种基于模糊逻辑的汽车侧偏角估计方法。它利用模糊逻辑和汽车运动学模型,将汽车转向盘转角、车轮转速、汽车加速度和横摆角速度信息相融合,进行车辆侧偏角估计。试验结果显示,该方法的鲁棒性和精确性较好,而且响应频率较高,可以满足ESP的控制需要。     

转向加速工况下汽车驱动防滑控制系统滑转率算法研究

汽车低速转弯加速时,用后轮轮速作为参考车速计算驱动轮滑转率会造成计算偏差,引起驱动防滑控制系统误干预,为此提出了驱动轮滑转率计算的修正算法.该修正算法不需要增加前轮转角传感器,而是采用两非驱动轮轮速估计车身横摆角速度和汽车前轮转角,进而计算出前轮参考轮速,并将前轮参考轮速代替车速对转弯工况的驱动轮滑转率计算进行修正.试验结果表明,该修正算法消除了滑转率计算误差,可防止汽车在高附着路面上转弯加速时驱动防滑控制系统的误干预.     

Full-slip kinematics based estimation of vehicle yaw rate from differential wheel speeds

Vehicle yaw rate is a key parameter required for various active stability control systems. Accurate yaw rate information may be obtained from the fusion of some on-vehicle sensors and GPS data. In this study, the closed-form expression of the yaw rate–written as a function of front wheel rolling speeds and steering angle–was derived via kinematic analysis of a planar four-wheel vehicle on the assumption of no longitudinal slip at the both front tires. The obtained analytical solution was primarily verified by computational simulation. In terms of implementation, the 1:10th scaled rear-wheel-drive vehicle was modified so that the front wheel rolling speeds and the steering angle could be measured. An inertial measurement unit was also installed to provide the directly measured yaw rate used for validation. Preliminary experiment was done on some extremely random sideslip maneuvers beneath the global positioning using four recording cameras. Comparing with the vision-based and the gyro-based references, the vehicle yaw rate could be well approximated at any slip condition without requiring integration or vehicle and tire models. The proposed cost-effective estimation strategy using only on-vehicle sensors could be used as an alternative way to enhance performance of the GPS-based yaw rate estimation system while the GPS signal is unavailable.     

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.     

Sideslip angle estimation considering short-duration longitudinal velocity variation

The accurate estimation of sideslip angle is necessary for many vehicle control systems. The detection of sliding and skidding is especially critical in emergency situations. In this paper, a sideslip angle estimation method is proposed that considers severe longitudinal velocity variation over the short period of time during which a vehicle may lose stability due to sliding or spinning. An extended Kalman filter (EKF) based on a kinematic model of a vehicle is used without initialization of the inertial measurement unit to estimate vehicle longitudinal velocity. A dynamic compensation method that compensates for the difference in the locations of the vehicle velocity sensor and the IMU in on-road vehicle tests is proposed. Evaluations with a CarSim™ 27-degree-of-freedom (DOF) model for various vehicle test scenarios and with on-road tests using a real vehicle show that the proposed sideslip angle estimation method can accurately predict sideslip angle, even when vehicle longitudinal velocity changes significantly.     

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.     

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.