On Inverse Equations for Vehicle Dynamics

Abstract

Instead of writing equations which when solved yield the response of a vehicle to an input such as the front wheel steer angle, one can often invert the equations so that a response quantity is specified as an input and a new set of equations is solved yielding the steer angle required as an output. Using these equations one can discover the input steer angle a driver would need to impose in order to accomplish a specific maneuver for various vehicles.

It is shown that there are many possible inverse equation sets and that the eigenvalues of the inverse equations are hard to interpret since they may have little to do with the vehicle parameters. The linear single-input single-output case is studied first to fix ideas using a simple example. For the bicycle model vehicle, it is shown that any vehicle may have unstable inverse equations depending upon the response quantity used. Extensions to nonlinear and multiple-input multiple output systems are discussed.     

Impact of Dynamic Fluid Slosh Loads on the Directional Response of Tank Vehicles

SUMMARY

A comprehensive directional dynamics model of a tractor-tank trailer is developed by integrating a non-linear dynamic fluid slosh model to the three-dimensional vehicle dynamics model. The nonlinear fluid slosh equations are solved in an Eulerian mesh to determine dynamic fluid slosh loads caused by the dynamic motion of the vehicle. The dynamic fluid slosh forces and moments are coupled with the vehicle dynamics model to study the directional response characteristics of tank vehicles. The directional response characteristics of partially filled tank vehicles employing dynamic slosh model are compared to those employing quasi-dynamic vehicle model, for steady as well as transient directional maneuvers. Simulation results reveal that during a steady steer maneuver, the dynamic fluid slosh loads introduce oscillatory directional response about a steady-state value calculated from the quasi-dynamic vehicle model. The directional response characteristics obtained using the quasi-dynamic and dynamic fluid slosh models during transient steer inputs show good correlation. Based on this study, it can be concluded that the quasi-dynamic model can predict the directional response characteristics of tank vehicles quite close to that evaluated using the comprehensive fluid slosh model.     

Implementation and validation of a three degrees of freedom steering-system model in a full vehicle model

This paper describes the coupling between a three degrees of freedom steering-system model and a multi-body truck model. The steering-system model includes the king-pin geometry to provide the correct feedback torque from the road to the steering-system. The steering-system model is combined with a validated tractor semi-trailer model. An instrumented tractor semi-trailer has been tested on a proving ground and the steering-wheel torque, pitman-arm angle, king-pin angles and drag-link force have been measured during steady-state cornering, a step steer input and a sinusoidal steering input. It is shown that the steering-system model is able to accurately predict the steering-wheel torque for all tests and the vehicle model is accurate for vehicle motions up to a frequency where the lateral acceleration gain is minimum. Even though the vehicle response is not accurate above this frequency, the steering-wheel torque is still represented accurately.     

An Emergency Obstacle Avoidance Control Strategy for Automated Highway Vehicles

Summary This paper presents an emergency obstacle avoidance control strategy that may be used in automated highway vehicles. In the proposed control strategy, an inverse vehicle dynamics problem is solved on the selected emergency lane-change path to find out the nominal feedforward control inputs such as the steering wheel angle and the braking force. Then the overall vehicle lateral and yaw motion is controlled additionally in the feedback path by an active yaw moment for stability augmentation as well as a corrective steering angle that is added to the nominal steering angle in order to compensate for uncertainties involved in the nominal control input computation. The proposed control strategy has been tested by an ABS Hardware-In-the-Loop Simulation (HILS) system for rapid and safe control prototyping in a lab. Simulation results with a sample emergency avoidance distance (45 m) show that the proposed control strategy may be used as a feasible obstacle avoidance strategy for automated highway vehicles.     

An Emergency Obstacle Avoidance Control Strategy for Automated Highway Vehicles

Summary This paper presents an emergency obstacle avoidance control strategy that may be used in automated highway vehicles. In the proposed control strategy, an inverse vehicle dynamics problem is solved on the selected emergency lane-change path to find out the nominal feedforward control inputs such as the steering wheel angle and the braking force. Then the overall vehicle lateral and yaw motion is controlled additionally in the feedback path by an active yaw moment for stability augmentation as well as a corrective steering angle that is added to the nominal steering angle in order to compensate for uncertainties involved in the nominal control input computation. The proposed control strategy has been tested by an ABS Hardware-In-the-Loop Simulation (HILS) system for rapid and safe control prototyping in a lab. Simulation results with a sample emergency avoidance distance (45 m) show that the proposed control strategy may be used as a feasible obstacle avoidance strategy for automated highway vehicles.     

Stability control of 4WS vehicles using robust IMC techniques

A robust nonparametric approach to vehicle stability control by means of a four-wheel steer by wire system is introduced. Both yaw rate and sideslip angle feedbacks are used in order to effectively take into account safety as well as handling performances. Reference courses for yaw rate and sideslip angle are computed on the basis of the vehicle speed and the handwheel angle imposed by the driver. An output multiplicative model set is used to describe the uncertainty arising from a wide range of vehicle operating situations. The effects of saturation of the control variables (i.e. front and rear steering angles) are taken into account by adopting enhanced internal model control methodologies in the design of the feedback controller. Actuator dynamics are considered in the controller design. Improvements on understeer characteristics, stability in demanding conditions such as turning on low friction surfaces, damping properties in impulsive manoeuvres, and improved handling in closed loop (i.e. with driver feedback) manoeuvres are shown through extensive simulation results performed on an accurate 14 degrees of freedom nonlinear model, which proved to give good modelling results as compared with collected experimental data.     

Steady-state steering of a tilting three-wheeled vehicle

The design of a narrow-track enclosed vehicle for urban transport was the subject of the CLEVER project. Due to its narrow track and requirement for car-like controls, an actively controlled tilting system was integrated into the chassis to allow for high lateral accelerations without rolling over. The cornering behaviour of this unique vehicle concept is investigated and compared with the ideal Ackermann response. The steer kinematics of this 1F1T (one front wheel, one wheel tilting) configuration are assessed through the use of a steady-state steering model, with attention focused on how steer parameters such as tilt axis height and inclination can be tuned to provide the required response. A prototype vehicle was designed and built and the results of experimental testing are presented to illustrate the real balancing performance of the combined steering and tilting approach used for the CLEVER vehicle. The experimental results follow the trends demonstrated in the model.     

Numerical Simulation of Vehicle Behavior during Straight Line Keeping on Undulating Road Surfaces

Numerical design of vehicles having optimal straight line stability on undulating road surfaces requires an accurate vehicle model based on knowledge of the relevant phenomena. Therefore, vehicle behavior on undulating straight roads has been analyzed and modeled. Measurements on a flat road surface have shown that the dedicated vehicle model yields accurate simulation results of the steering response to medium steering wheel angle inputs. In addition, the model has been validated by measuring two vehicle responses during normal driving on an undulating straight road: viz. the responses to the small steering wheel angle input and to the input by the global inclination of the road surface.     

Numerical Simulation of Vehicle Behavior during Straight Line Keeping on Undulating Road Surfaces

SUMMARY

Numerical design of vehicles having optimal straight line stability on undulating road surfaces requires an accurate vehicle model based on knowledge of the relevant phenomena. Therefore, vehicle behavior on undulating straight roads has been analyzed and modeled. Measurements on a flat road surface have shown that the dedicated vehicle model yields accurate simulation results of the steering response to medium steering wheel angle inputs. In addition, the model has been validated by measuring two vehicle responses during normal driving on an undulating straight road: viz. the responses to the small steering wheel angle input and to the input by the global inclination of the road surface.     

Development of yonden electric vehicle “PIVOT”

A project was carried out to develop an appealing new electric vehicle that features those dynamic capabilities, including such universal drive as point rotation and lateral drive, which cannot be achieved by conventional engine-powered vehicles. The new electric vehicle, called “PIVOT”, was realized through the development of special steering and suspension systems that can steer each wheel at an angle wider than 90 degrees either way, the development of a control unit that can separately control the traction force and steer angles for each wheel, and the use of drive unit with motor-in-the-wheel systems.     

Influence of Liquid Load Shift on the Dynamic Response of Articulated Tank Vehicles

The influence of the lateral load shift on the dynamic response characteristics of an articulated tank vehicle is investigated assuming inviscid fluid flow conditions. A quasi-dynamic roll plane model of a partially filled cleanbore tank of circular cross-section is developed and integrated to a three-dimensional model of the articulated vehicle, assuming constant forward speed. The destabilizing effects of liquid load shift are studied by comparing the directional dynamics of the partially filled tank vehicle to that of an equivalent rigid cargo vehicle subject to steady steer input. Dynamic response characteristics demonstrate that the stability of a partially filled tank vehicle is adversely affected by the Liquid load shift The distribution of cornering forces caused by the liquid load shift yield considerable deviation of the path followed by the liquid tank vehicle. The influence of the vehicle speed on the dynamics of the liquid tank vehicle is also investigated for variations in the fill levels and fluid density.     

三轴汽车前后轮角输入时的响应特性

本文详细推导了三轴汽车线性二自由度模型的运动微分方程，分析了汽车对前后轮角输入时的移居记响应特性。从汽车动力学的角度讨论了前后轮转应具备的比例关系。该方法同样适用于其它多轴汽车的建模分析。     

Lane-keeping benefits of practical rear axle steer

The classic two-degree-of-freedom yaw-plane or ‘bicycle’ vehicle model is augmented with two additional states to describe lane-keeping behaviour and further augmented with an additional control input to steer the rear axle. A simple driver model is hypothesised where the driver closes a loop on a projected lateral lane position. The driver can select the preview distance to compensate driver/vehicle dynamics, consistent with the ‘cross-over’ model found in the literature. A rear axle steer control law is found to be a function of the front axle steering input and vehicle speed that exhibits stability similar to a positive-real system, while at the same time improving the ability of the driver/vehicle system to track a complex curved lane and improving steady-state manoeuvrability. The theoretically derived control law bears similarity to practical embodiments allowing a deeper understanding of the functional value of steering a rear axle.     

基于LabVIEW RT的硬件在环仿真

利用实时仿真环境LabVIEW RT,构建了包括整车转向盘转角、油门、制动物理信号的硬件在环仿真系统.采用实时车辆动力学软件CarSim RT建立了车辆模型,并利用所搭建的试验台架进行了HIL仿真.结果表明,利用LabVIEW RT和CarSim RT能快速搭建面向整车开发的HIL系统,所建系统性价比高,而且有很好的实时性和扩展性.     

On the objective assessment and quantification of the transient-handling response of a vehicle

This article suggests a new methodology for the objective assessment and quantification of the response of a vehicle subjected to transient-handling manoeuvres. For this purpose, a non-dimensional measure is defined, namely the normalized yaw impulse. This measure appears in two variations. In its general or dynamic form, it represents the difference between the yaw moment due to the front-tyre forces and the yaw moment due to the rear-tyre forces, divided by the sum of the aforementioned yaw moments. By employing a linear, two-degree-of-freedom bicycle model, it is shown that the general form of the normalized yaw impulse can be written as a function of the steer angle and the forward, lateral and yaw velocities of the vehicle. This form is referred to as the kinematic yaw impulse. It is demonstrated that the combined application of the dynamic and kinematic expressions of the yaw impulse not only facilitates the explicit assessment and quantification of the transient behaviour of a vehicle, but also reveals the influence of parameters such as the yaw moment of inertia, which traditionally leave the steady-state behaviour unaffected.     

On the objective assessment and quantification of the transient-handling response of a vehicle

This article suggests a new methodology for the objective assessment and quantification of the response of a vehicle subjected to transient-handling manoeuvres. For this purpose, a non-dimensional measure is defined, namely the normalized yaw impulse. This measure appears in two variations. In its general or dynamic form, it represents the difference between the yaw moment due to the front-tyre forces and the yaw moment due to the rear-tyre forces, divided by the sum of the aforementioned yaw moments. By employing a linear, two-degree-of-freedom bicycle model, it is shown that the general form of the normalized yaw impulse can be written as a function of the steer angle and the forward, lateral and yaw velocities of the vehicle. This form is referred to as the kinematic yaw impulse. It is demonstrated that the combined application of the dynamic and kinematic expressions of the yaw impulse not only facilitates the explicit assessment and quantification of the transient behaviour of a vehicle, but also reveals the influence of parameters such as the yaw moment of inertia, which traditionally leave the steady-state behaviour unaffected.     

Influence of Liquid Load Shift on the Dynamic Response of Articulated Tank Vehicles

SUMMARY

The influence of the lateral load shift on the dynamic response characteristics of an articulated tank vehicle is investigated assuming inviscid fluid flow conditions. A quasi-dynamic roll plane model of a partially filled cleanbore tank of circular cross-section is developed and integrated to a three-dimensional model of the articulated vehicle, assuming constant forward speed. The destabilizing effects of liquid load shift are studied by comparing the directional dynamics of the partially filled tank vehicle to that of an equivalent rigid cargo vehicle subject to steady steer input. Dynamic response characteristics demonstrate that the stability of a partially filled tank vehicle is adversely affected by the Liquid load shift The distribution of cornering forces caused by the liquid load shift yield considerable deviation of the path followed by the liquid tank vehicle. The influence of the vehicle speed on the dynamics of the liquid tank vehicle is also investigated for variations in the fill levels and fluid density.     

A methodology for vehicle sideslip angle identification: comparison with experimental data

Sideslip angle could provide important information concerning vehicle's stability. Unfortunately direct measurement of sideslip angle requires a complex and expensive experimental set-up, which is not suitable for implementation on ordinary passenger cars; thus, this quantity has to be estimated starting from the measurements of vehicle lateral/longitudinal acceleration, speed, yaw rate and steer angle. According to the proposed methodology, sideslip angle is estimated as a weighted mean of the results provided by a kinematic formulation and those obtained through a state observer based on vehicle single-track model. Kinematical formula is considered reliable for a transient manoeuvre, while the state observer is used in nearly quasi-state condition. The basic idea of the work is to make use of the information provided by the kinematic formulation during a transient manoeuvre to update the single-track model parameters (tires cornering stiffnesses). A fuzzy-logic procedure was implemented to identify steady state or transient conditions.