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.     

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.     

On the handling performance of a vehicle with different front-to-rear wheel torque distributions

ABSTRACT

The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.     

Nonlinear adaptive sliding mode control for vehicle handling improvement via steer-by-wire

This paper proposes a nonlinear adaptive sliding mode control that aims to improve vehicle handling through a Steer-By-Wire system. The designed sliding mode control, which is insensitive to system uncertainties, offers an adaptive sliding gain to eliminate the precise determination of the bound of uncertainties. The sliding gain value is calculated using a simple adaptation algorithm that does not require extensive computational load. Achieving the improved handling characteristics requires both accurate state estimation and well-controlled steering inputs from the Steer-By-Wire system. A second order sliding mode observer provides accurate estimation of lateral and longitudinal velocities while the driver steering angle and yaw rate are available from the automotive sensors. A complete stability analysis based on Lyapunov theory has been presented to guarantee closed loop stability. The simulation results confirmed that the proposed adaptive robust controller not only improves vehicle handling performance but also reduces the chattering problem in the presence of uncertainties in tire cornering stiffness.     

基于扩展卡尔曼滤波的汽车质心侧偏角估计

基于二自由度汽车动力学模型和轮胎模型,运用扩展卡尔曼滤波方法建立了汽车质心侧偏角估计器.利用汽车动力学仿真平台,通过仿真对比了线性轮胎模型和非线性轮胎模型的质心侧偏角估计结果.仿真结果表明,轮胎模型对于质心侧偏角估计精度至关重要,而采用非线性轮胎模型能显著提高质心侧偏角估计精度,估计结果能满足ESC控制的要求.     

Tire Lateral Force Estimation Using Kalman Filter

As for the tire analysis, lateral tire force is a fundamental factor that describes the stability of vehicle handling. Attempts to analyze the vehicle stability have been made based on various objective test methods and some specific factors such as yaw, lateral acceleration and roll angle. However, the problem to identify which axle is lack of the tire grip at a certain situation still remains. Since indoor tire force measurement system cannot represent a real road and vehicle conditions, tire force measurement through a real vehicle test is inevitable. Due to the high price of the tire force measurement device, tire force estimator can be an alternative toward cost reduction and device failure. In this paper, nonlinear planar full car model combined with tire model is proposed. Then, using discrete-time extended Kalman-Bucy filter (EKBF), individual tire lateral force are estimated with modified relaxation length model.     

Analysis of handling performance based on simplified lateral vehicle dynamics

In this article, the analysis methods for vehicle handling performance are studied. Using simple models, dynamic characteristic parameters such as yaw, natural frequency, and the damping coefficient of a vehicle can be theoretically formulated. Here, the vehicle is simplified by a bicycle (single-track) model, and the tire is modeled by an equivalent cornering stiffness and first order lag. From the experimental road data, the tire model parameters (equivalent cornering stiffness and time lag constant) are extracted. These parameters are then inserted into the theoretically formulated equations of dynamic characteristic parameters. For the purpose of validating the efficiency of the suggested methods, experimental road tests (where the cars have different handling performances) are performed. The results show that vehicle handling performance can be sufficiently represented by the suggested dynamic characteristic parameters. So, it is concluded that the proposed method has practical use for the development of new cars or for the comparison of similar cars since the evaluations of the vehicle handling performance can be efficiently determined by the suggested dynamic characteristic parameters.     

轮胎动力学特性仿真分析研究

分析了各种常用轮胎模型的特点与应用范围,根据汽车操纵动力学研究的需求,在Matlab环境下运用魔术公式建立了轮胎动力学模型,并对汽车轮胎力与纵向滑移率,纵向力、侧向力及回正力矩与纵向滑移率、侧偏角、外倾角、垂直载荷的关系等轮胎特性进行了仿真分析,实验结果表明,魔术公式轮胎动力学模型可以较好地模拟轮胎的动力学特性,适用于车辆动力学研究领域。     

整车多体动力学模型的建立、验证及仿真分析

利用多体动力学方法建立了某轿车的整车非线性多体动力学模型,模型中考虑了前后悬架、转向系统的详细几何结构参数,以及连接处的橡胶衬套、阻尼器的非线性特性,轮胎采用M agic Formu la模型。对所建模型进行了多种试验验证,并分析了该样车的操纵稳定性等相关特性,仿真结果表明所建整车多体模型有较高的精度。     

Integrated fuzzy/optimal vehicle dynamic control

There are basically two methods to control yaw moment which is the most efficient way to improve vehicle stability and handling. The first method is indirect yaw moment control, which works based on control of the lateral tire force through steering angle control. It is mainly known as active steering control (ASC). Nowadays, the most practical approach to steering control is active front steering (AFS). The other method is direct yaw moment control (DYC), in which an unequal distribution of longitudinal tire forces (mainly braking forces) produces a compensating external yaw moment. It is well known that the AFS performance is limited in the non-linear vehicle handling region. On the other hand, in spite of a good performance of DYC in both the linear and non-linear vehicle handling regions, continued DYC activation could lead to uncomfortable driving conditions and an increase in the stopping distance in the case of emergency braking. It is recommended that DYC be used only in high-g critical maneuvers. In this paper, an integrated fuzzy/optimal AFS/DYC controller has been designed. The control system includes five individual optimal LQR control strategies; each one, has been designed for a specific driving condition. The strategies can cover low, medium, and high lateral acceleration maneuvers on high-μ or low-μ roads. A fuzzy blending logic also has been utilized to mange each LQR control strategy contribution level in the final control action. The simulation results show the advantages of the proposed control system over the individual AFS or DYC controllers.     

Tire wear estimation based on nonlinear lateral dynamic of multi-axle steering vehicle

This paper presents a novel nonlinear dynamic model of a multi-axle steering vehicle to estimate the lateral wear amount of tires. Firstly, a 3DOF nonlinear vehicle dynamic model is developed, including dynamic models of the hydropneumatic suspension, tire, steering system and toe angle. The tire lateral wear model is then built and integrated into the developed vehicle model. Based on the comparison of experimental and simulation results, the nonlinear model is proved to be better than a linear model for the tire wear calculation. In addition, the effects of different initial toe angles on tire wear are analyzed. As simulation results shown, the impact of the dynamic toe angle on the tire wear is significant. The tire wear amount will be much larger than that caused by normal wear if the initial toe angle increases to 1° - 1.5°. The results also suggest that the proposed nonlinear model is of great importance in the design and optimazation of vehicle parameters in order to reduce the tire wear.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development,Validation and Comparison

SUMMARY

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development, Validation and Comparison

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Lateral load transfer and normal forces estimation for vehicle safety: experimental test

Knowledge of vehicle dynamics data is important for vehicle control systems that aim to enhance vehicle handling and passenger safety. This study introduces observers that estimate lateral load transfer and wheel–ground contact normal forces, commonly known as vertical forces. The proposed method is based on the dynamic response of a vehicle instrumented with cheap and currently available standard sensors. The estimation process is separated into three blocks: the first block serves to identify the vehicle’s mass, the second block contains a linear observer whose main role is to estimate the roll angle and the one-side lateral transfer load, while in the third block we compare linear and nonlinear models for the estimation of four wheel vertical forces. The different observers are based on a prediction/estimation filter. The performance of this concept is tested and compared with real experimental data acquired using the INRETS-MA (Institut National de Recherche sur les Transports et leur Sécurité – Département Mécanismes d’Accidents) Laboratory car. Experimental results demonstrate the ability of this approach to provide accurate estimation, thus showing its potential as a practical low-cost solution for calculating normal forces.     

汽车加速过程动力学仿真模拟研究

对不同附着路面上汽车加速过程的模拟是驱动防滑控制模拟研究的基础。在建立两轮驱动汽车和四轮驱动汽车发动机模型、传动系模型、轮胎模型和车辆模型的基础上，采用MATLAB SIMULINK编制了适于加速过程模拟的动力学仿真模拟程序，并针对样车进行了各种附着路面的车辆加速过程的模拟。     

UniTire与Magic Formula稳态模型的对比研究

荷兰学者Pacejka提出的魔术公式Magic Formula和我国郭孔辉教授提出的统一轮胎模型UniTire在汽车操纵动力学研究中得到了广泛的应用。通过对这两种模型建模机理的对比表明,UniTire轮胎模型比MagicFor-mula模型具有更强的理论基础;通过试验数据辨识模型参数对比两种模型的全局辨识精度以及预测精度的结果表明,UniTire轮胎模型的全局辨识精度略高于Magic Formula模型,而且明显具有更高的预测能力。     

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.     

Advanced Chassis Control Systems for Vehicle Handling and Active Safety

In this paper chassis controls for vehicle handling and active safety have been reviewed. In particular, we have observed the effectiveness and limit of 4WS and DYC. It is pointed out that DYC is more effective in vehicle motion with larger side-slip and/or higher lateral acceleration and taking the nonlinearity of tire and vehicle dynamics into consideration is essential for introducing the control law for the chassis controls and their integration/coordination. We wish to emphasize that there is a need to further propose control laws based on deeper observation and understanding on the tire and vehicle dynamics.     

Measurement of vehicle attitude with RTK-GPS for analyzing the vehicle motion behavior

Elucidating the relation between the phenomena evaluated by the test driver subjectively and objective data is important in the development of the steering and handling performance of the vehicle. For this purpose, we have developed a system, which estimates the 6-DOF movement of a vehicle based on the vehicle angular velocities around its three axes and the positions through plural real-time-kinematic-GPS (RTK-GPS) on the vehicle. The rotation axis of the body is defined based on the results estimated by the system, and the difference is observed in the rotation axis corresponding to the difference of subjective evaluation.     

A Comparison between Four Computing Models of Different Complexity Describing the Steering Behavior of Two-axled Automobiles

SUMMARY

In this paper chassis controls for vehicle handling and active safety have been reviewed. In particular, we have observed the effectiveness and limit of 4WS and DYC. It is pointed out that DYC is more effective in vehicle motion with larger side-slip and/or higher lateral acceleration and taking the nonlinearity of tire and vehicle dynamics into consideration is essential for introducing the control law for the chassis controls and their integration/coordination. We wish to emphasize that there is a need to further propose control laws based on deeper observation and understanding on the tire and vehicle dynamics.