On the Stability of a Flexible Vehicle Controlled by a Human Pilot

SUMMARY

This paper presents a stability analysis of a vehicle flexible in the plane of yawing and being controlled by a human pilot. The vehicle is represented by a two degrees-of-freedom model and the pilot is assumed to respond to the lateral displacement and to the lateral velocity with a time delay. It is shown that in order for the pilot model to exhibit a realistic human operator behavior, driver's gain must be linearly proportional to vehicle velocity and also inversely related to frontal visibility. Moreover, application of the Hurwitz criterion indicated that flexibility of the vehicle frame has a destabilising effect on the lateral stability and reduces the stable domain of operation.     

Characterization of Dynamic Vehicle Stability Using Two Models of the Human Pilot Behaviour

This article deals with a study of the stability of the vehicle/pilot system for two different models of human operator behaviour. These models, are the outcome of various.approximations of the precision model for single loop compensatory situations. The vehicle is represented with two degrees of freedom and the pilot is assumed to respond to the lateral displacement and to the lateral velocity with a time delay. The properties of these resulting systems are presented and it is observed that, for any given forward visibility, a critical velocity defines a domain of controllability from a domain of uncontrollability. Furthermore this critical velocity is shown independant of the vehicle/ pilot parameters and may be considered as a possible vehicle safety criterion.     

Finite Disturbance Directional Stability of Vehicles with Human Pilot Considering Nonlinear Cornering Behavior

The driver of a vehicle has a significant influence on handling and stability of the vehicle. Due to the complex behavior of a human pilot, a driver model is usually neglected when dealing with the problem of vehicle stability. This work focuses on the interaction between the vehicle and the human pilot. A model characterizing human operator behavior in a regulation task is employed to study directional stability. Linear stability is analyzed by the application of the Routh-Hurwitz criterion and stability boundaries separating the stable domain of operation of the driver from the unstable one are constructed.

The linear analysis predicts that the only possible instability in a driver/vehicle system is an oscillatory instability with increasing amplitude. It is shown that the addition of kinematic as well as slip angle nonlinearities in the vehicle model can have a stabilizing effect on these oscillations of the combined driver/vehicle system. They may also be responsible for the opposite, namely a linearly stable motion may become unstable to finite size disturbances. These nonlinear motions are predicted by a bifurcation analysis and are verified by direct numerical simulation.     

半挂汽车列车直线行驶横向摆振研究

建立了双质心单轨半挂汽车列车数学模型,对某重型半挂汽车列车进行仿真,探讨了不同车速、不同装载条件及挂车轴距的变化对其直线行驶横向稳定性的影响。根据相似准则求得了某重型汽车列车模型,并对其进行了台架试验。试验结果与理论结果的对比分析表明,两误差较小,具有较好的一致性。     

基于ADAMS/Car弹性运动学对整车分析的影响

ADAMS软件提供了柔性体模块,可真实地模拟物体的运动,文章以某轿车为研究对象,利用ADAMS仿真软件建立了带有弹性下控制臂悬架的整车模型。选择开环转向事件里的转向阶跃输入进行仿真分析,在后处理中对横摆角速度、车速、侧向加速度和纵向加速度进行分析。结果表明,柔性体悬架模型比多刚体悬架模型对车身的横摆角速度、侧向加速度、纵向加速度以及速度等具有更好的抑制作用,有利于提高汽车操纵稳定性。     

变路面车辆稳定性控制策略研究

建立了某四轮汽车9自由度车辆模型和轮胎动力模型,并提出了一种基于侧向力利用系数的差动制动、主动转向切换控制策略。模拟了汽车以车速24.5m/s行驶时的一个紧急避让情况,研究了无控制模式、差动制动控制模式、联合控制模式下的车辆横摆角速度、质心侧偏角、质心侧向位移的变化。结果表明,所提出的差动制动联合主动转向技术的控制策略可以满足变路面下车辆稳定性控制要求。     

Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents

For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.     

非满载液罐半挂汽车列车侧向耦合动力学模型

为方便液罐半挂汽车列车（Tractor Semi-trailer Tank Vehicle,TSTTV）罐-车整体的优化设计匹配,综合提高整车的侧倾稳定性、侧向动力学稳定性及操纵特性,基于Lagrange方法和椭圆规摆等效机械液体晃动模型建立TSTTV的整车侧向耦合动力学模型,其典型特征是实现罐内液体侧向晃动与车辆横摆运动、侧向运动、悬挂质量的侧倾运动及非线性侧向轮胎力的集成一体化建模,贯通液体晃动动力学与车辆侧向动力学稳定性之间的联系。通过开环正弦停滞转向输入操作响应对所建立的模型进行分析评价,考察车辆横摆角速度、质心侧偏角、侧倾角、侧向载荷转移率及液体晃动角等状态量在2种充液比（F_L=40%,80%）及2种罐体椭圆率（Δ=1.0,1.3）下的响应。研究结果表明：所建立的TSTTV模型可以实现液体侧向晃动作用下的车辆侧向耦合动力学仿真分析,能够反映充液比、罐体截面椭圆率等运输条件和罐体几何参数对整车侧倾稳定性、侧向动力学稳定性及操纵特性的影响;基于该模型可以针对液体介质、充液比及道路环境等运输条件因素的影响,研究以提高整车侧向动力学稳定性为目标的TSTTV灌-车整体的优化设计匹配问题,这对提升液罐车的设计性能、提高行驶的安全性和运输效率具有重要意义。     

Analysis of bifurcation and stability for a tractor semi-trailer in planar motion

This paper is intended for bifurcation analysis of a nonlinear tractor semi-trailer vehicle model in planar motion and for investigating its stability under constant running conditions. Bifurcation analysis shows that bifurcation diagrams of a tractor semi-trailer are quite different from those of a single-unit vehicle. Some instability phenomena of the vehicle system such as jackknifing, sideslip, and spinning are explained by correlating them with the behaviour in the neighbourhood of unstable fixed points based on analysis of eigenvectors, phase trajectories, and status of lateral tyre force saturation. It is also found that yaw planar instability of a tractor semi-trailer is caused by lateral tyre force saturation of the tractor's rear axles and/or the trailer's axles. Moreover, the stability region in the state space is demarcated, and a stability index for evaluating size of the stability region in a feasible domain is proposed. Yaw stability under constant driving conditions is analysed by using the proposed stability index.     

Dynamic Estimation of Road Bank Angle

Road bank angles have a direct influence on vehicle dynamics and lateral acceleration measurement. A vehicle stability control system that knows road bank angle has an advantageous capability in achieving desired control sensitivities for maneuvers on ice and snow, among all surfaces, while avoiding false/nuisance activation on a banked road. Since neither lateral velocity nor road bank angle are directly measurable in current vehicle systems due to economical reasons, the major challenge is to differentiate the bias induced by road bank disturbances from actual effect of vehicle lateral dynamics in current measurements. This paper proposes a method of road bank estimation and provides theoretical background for the decoupling effort of lateral dynamics and road disturbances involved in bank estimation.     

Dynamic Estimation of Road Bank Angle

Road bank angles have a direct influence on vehicle dynamics and lateral acceleration measurement. A vehicle stability control system that knows road bank angle has an advantageous capability in achieving desired control sensitivities for maneuvers on ice and snow, among all surfaces, while avoiding false/nuisance activation on a banked road. Since neither lateral velocity nor road bank angle are directly measurable in current vehicle systems due to economical reasons, the major challenge is to differentiate the bias induced by road bank disturbances from actual effect of vehicle lateral dynamics in current measurements. This paper proposes a method of road bank estimation and provides theoretical background for the decoupling effort of lateral dynamics and road disturbances involved in bank estimation.     

Pivot point-based control for active rear-wheel steering in passenger vehicles

This paper presents a new application of active rear-wheel steering control to improve the lateral vehicle behaviour. In the state of the art, yaw or lateral velocity is used as control variable that means one degree of freedom being not directly controlled. A worse subjective impressions due to movements in the rear end of the vehicle during strong counter-steering are a consequence. To avoid this effect in urban surroundings, an innovative structure to control the pivot point distance of the vehicle is proposed. In this case the coupled elementary states yaw and lateral velocity can be influenced based on a higher level criteria. Analysis show that pivot point fixing provides a comprehensible reference behaviour. Solving the issue of singularity during disappearing yaw movement is the basis to design a performant modified feedforward input–output linearisation. An analytic stability analysis of the internal dynamics shows system immanent limitations which do not influence the target of improving the lateral vehicle dynamics in urban manoeuvres. Finally, the advantages of pivot-based control are highlighted by a comparison with state of the art rear axle control.     

The characteristic velocity stability indicator for passenger cars

Driver assistance systems have received increased attention as market demands have pushed for improved automotive safety. These systems are designed to aid the driver by preventing any unstable or unpredictable vehicle behaviour. One global indicator for stability and driving conditions could help to manage the control algorithms and driver warning subroutines. Another problem which could be solved by a precise driving situation indicator is evaluating new vehicles during test drives. After a short introduction to a linear lateral vehicle model, an analytical approach for an online calculation of different driving conditions (i.e., stability, understeering, oversteering, and neutralsteering) is given. A characteristic velocity stability indicator is defined, which allows online computation of the present driving condition. Results are then checked against real measurements of a test vehicle.     

Design of a rollover index-based vehicle stability control scheme

This paper presents a rollover index (RI)-based vehicle stability control (VSC) scheme. A rollover index, which indicates an impending rollover, is developed by a roll dynamics phase plane analysis. A model-based roll estimator is designed to estimate the roll angle and roll rate of the vehicle body with lateral acceleration, yaw rate, steering angle and vehicle velocity measurements. The rollover index is computed using an estimated roll angle, estimated roll rate, measured lateral acceleration and time-to-wheel lift. A differential braking control law is designed using a direct yaw control method. The VSC threshold is determined from the rollover index. The effectiveness of the RI, the performance of the estimator and the control scheme are investigated via simulations using a validated vehicle simulator. It is shown that the proposed RI can be a good measure of the danger of rollover and the proposed RI-based VSC scheme can reduce the risk of a rollover.     

Dynamic stability of forklift trucks in cornering situations: parametrical analysis using a driving simulator

This paper describes the examination of the vehicle dynamics and stability of four-wheeled forklift trucks (FLTs) in cornering situations. Cornering at excessive speed is one major reason for fatal accidents with forklifts caused by lateral tipover. In order to increase the lateral stability of this kind of working machinery, the influence of certain important design properties has been studied using an appropriate vehicle simulation model and a driving simulator. The simulation model is based on a multi-body system approach and includes submodels for the propulsion system and the tyres. The driving behaviour of the operator has not been modelled. Instead, a driving simulator has been built up and a real human driver was employed for ensuring adequate and realistic model input. As there have not been any suitable standardised test manoeuvres available for FLTs, a new driving test has been developed to assess the lateral stability. This test resembles the well-known J turn/Fishhook turn, but includes a more dynamic counter-steering action. Furthermore, the dimensions of the test track are defined. Therefore, the test is better adapted to the driving dynamics of forklifts and reflects the real driver behaviour more closely. Finally, a parametrical study has been performed, examining the influence of certain important technical properties of the truck such as the maximum speed, the position of centre of gravity, rear axle design features and tyre properties. The results of this study may lead to a better understanding of the vehicle dynamics of forklifts and facilitate goal-oriented design improvements.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

The characteristic velocity stability indicator for passenger cars

Driver assistance systems have received increased attention as market demands have pushed for improved automotive safety. These systems are designed to aid the driver by preventing any unstable or unpredictable vehicle behaviour. One global indicator for stability and driving conditions could help to manage the control algorithms and driver warning subroutines. Another problem which could be solved by a precise driving situation indicator is evaluating new vehicles during test drives. After a short introduction to a linear lateral vehicle model, an analytical approach for an online calculation of different driving conditions (i.e., stability, understeering, oversteering, and neutralsteering) is given. A characteristic velocity stability indicator is defined, which allows online computation of the present driving condition. Results are then checked against real measurements of a test vehicle.     

Optimal preview game theory approach to vehicle stability controller design

Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.     

Stability Analysis of the Human Controlled Vehicle Moving Along a Curved Path

A method to study handling characteristics of a vehicle moving along a curved path is presented. A simple bicycle model and a feedback controller with proportional gain are used to simulate the vehicle and the driver. The lateral stability of the vehicle/driver system is analyzed by using the root locus method and numerical integration in the time domain. The effect of the curvature on the system stability is discussed in detail. A new suggestion is made for the look ahead distance to calculate the preview lateral error of the vehicle with respect to the center of the road. Interesting results are shown for some important parameters such as the gain factor, the vehicle speed and the curvature of the path. Possible extensions of the method to more general cases and other applications are discussed.