An investigation on motor-driven power steering-based crosswind disturbance compensation for the reduction of driver steering effort

This paper describes a lateral disturbance compensation algorithm for an application to a motor-driven power steering (MDPS)-based driver assistant system. The lateral disturbance including wind force and lateral load transfer by bank angle reduces the driver's steering refinement and at the same time increases the possibility of an accident. A lateral disturbance compensation algorithm is designed to determine the motor overlay torque of an MDPS system for reducing the manoeuvreing effort of a human driver under lateral disturbance. Motor overlay torque for the compensation of driver's steering torque induced by the lateral disturbance consists of human torque feedback and feedforward torque. Vehicle–driver system dynamics have been investigated using a combined dynamic model which consists of a vehicle dynamic model, driver steering dynamic model and lateral disturbance model. The human torque feedback input has been designed via the investigation of the vehicle–driver system dynamics. Feedforward input torque is calculated to compensate additional tyre self-aligning torque from an estimated lateral disturbance. The proposed compensation algorithm has been implemented on a developed driver model which represents the driver's manoeuvreing characteristics under the lateral disturbance. The developed driver model has been validated with test data via a driving simulator in a crosswind condition. Human-in-the-loop simulations with a full-scale driving simulator on a virtual test track have been conducted to investigate the real-time performance of the proposed lateral disturbance compensation algorithm. It has been shown from simulation studies and human-in-the-loop simulation results that the driver's manoeuvreing effort and a lateral deviation of the vehicle under the lateral disturbance can be significantly reduced via the lateral disturbance compensation algorithm.     

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.     

Design of a feedback-feedforward steering controller for accurate path tracking and stability at the limits of handling

This paper presents a feedback-feedforward steering controller that simultaneously maintains vehicle stability at the limits of handling while minimising lateral path tracking deviation. The design begins by considering the performance of a baseline controller with a lookahead feedback scheme and a feedforward algorithm based on a nonlinear vehicle handling diagram. While this initial design exhibits desirable stability properties at the limits of handling, the steady-state path deviation increases significantly at highway speeds. Results from both linear and nonlinear analyses indicate that lateral path tracking deviations are minimised when vehicle sideslip is held tangent to the desired path at all times. Analytical results show that directly incorporating this sideslip tangency condition into the steering feedback dramatically improves lateral path tracking, but at the expense of poor closed-loop stability margins. However, incorporating the desired sideslip behaviour into the feedforward loop creates a robust steering controller capable of accurate path tracking and oversteer correction at the physical limits of tyre friction. Experimental data collected from an Audi TTS test vehicle driving at the handling limits on a full length race circuit demonstrates the improved performance of the final controller design.     

A theoretical model of speed-dependent steering torque for rolling tyres

ABSTRACT

It is well known that the tyre steering torque is highly dependent on the tyre rolling speed. In limited cases, i.e. parking manoeuvre, the steering torque approaches the maximum. With the increasing tyre speed, the steering torque decreased rapidly. Accurate modelling of the speed-dependent behaviour for the tyre steering torque is a key factor to calibrate the electric power steering (EPS) system and tune the handling performance of vehicles. However, no satisfactory theoretical model can be found in the existing literature to explain this phenomenon. This paper proposes a new theoretical framework to model this important tyre behaviour, which includes three key factors: (1) tyre three-dimensional transient rolling kinematics with turn-slip; (2) dynamical force and moment generation; and (3) the mixed Lagrange–Euler method for contact deformation solving. A nonlinear finite-element code has been developed to implement the proposed approach. It can be found that the main mechanism for the speed-dependent steering torque is due to turn-slip-related kinematics. This paper provides a theory to explain the complex mechanism of the tyre steering torque generation, which helps to understand the speed-dependent tyre steering torque, tyre road feeling and EPS calibration.     

Influencing driver chosen cornering speed by means of modified steering feel

This paper presents an investigation about influencing the driver's behaviour intuitively by means of modified steering feel. For a rollover indication through haptic feedback a model was developed and tested that returned a warning to the driver about too high vehicle speed. This was realised by modifying the experienced steering wheel torque as a function of the lateral acceleration. The hypothesis for this work was that drivers of heavy vehicles will perform with more margin of safety to the rollover threshold if the steering feel is altered by means of decreased or additionally increased steering wheel torque at high lateral acceleration. Therefore, the model was implemented in a test truck with active steering with torque overlay and used for a track test. Thirty-three drivers took part in the investigation that showed, depending on the parameter setting, a significant decrease of lateral acceleration while cornering.     

Steady Turning of Two-Wheeled Vehicles

When driving along a circular path, the driver of a motorcycle controls the vehicle mainly by means of steering torque. If low steering torque is necessary, the driver feels that the vehicle is manoeuvrable. In this paper, a mathematical model concerning steering torque is developed; it takes into account the actual kinematic behaviour of the vehicle and the properties of motorcycle tyres. Tyre forces act at the contact points of toroidal tyres, which are calculated according to kinematic analysis. Non-linear equations are solved using an iterative approach. Several numerical results are presented, and the influence of tyre properties and some geometrical and inertial properties of the vehicle on steering torque are discussed.     

Steady Turning of Two-Wheeled Vehicles

When driving along a circular path, the driver of a motorcycle controls the vehicle mainly by means of steering torque. If low steering torque is necessary, the driver feels that the vehicle is manoeuvrable. In this paper, a mathematical model concerning steering torque is developed; it takes into account the actual kinematic behaviour of the vehicle and the properties of motorcycle tyres. Tyre forces act at the contact points of toroidal tyres, which are calculated according to kinematic analysis. Non-linear equations are solved using an iterative approach. Several numerical results are presented, and the influence of tyre properties and some geometrical and inertial properties of the vehicle on steering torque are discussed.     

Common underlying steering curves for motorcycles in steady turns

We study the steady turn behaviours of some light motorcycle models on circular paths, using the commercial software package ADAMS-Motorcycle. Steering torque and steering angle are obtained for several path radii and a range of steady forward speeds. For path radii much greater than motorcycle wheelbase, and for all motorcycle parameters including tyre parameters held fixed, dimensional analysis can predict the asymptotic behaviour of steering torque and angle. In particular, steering torque is a function purely of lateral acceleration plus another such function divided by path radius. Of these, the first function is numerically determined, while the second is approximated by an analytically determined constant. Similarly, the steering angle is a function purely of lateral acceleration, plus another such function divided by path radius. Of these, the first is determined numerically while the second is determined analytically. Both predictions are verified through ADAMS simulations for various tyre and geometric parameters. In summary, steady circular motions of a given motorcycle with given tyre parameters can be approximately characterised by just one curve for steering torque and one for steering angle.     

Vehicle steering returnability with maximum steering wheel angle at low speeds

In this paper, an analytical model with suitable vehicle parameters, together with a multi-body model is proposed to predict steering returnability in low-speed cornering with what is expected to be adequate precision as the steering wheel moves from lock to lock. This model shows how the steering response can be interpreted in terms of vertical force, lateral force with aligning moment, and longitudinal force. The simulation results show that vertical steering rack forces increase in the restoring direction according to steering rack displacement for both the inner and outer wheels. As lateral forces due to side-slip angle are directed toward the medial plane of the vehicle in both wheels, the outer wheel pushes the steering wheel in the returning direction while the inner wheel does not. In order to improve steering returnability, it is possible to increase the total steering rack force in both road wheels through adjustments to the kingpin axis and steering angle. This approach is useful for setting up a proper suspension geometry during conceptual chassis design.     

Additional 4WS and Driver Interaction

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

Tyre–road grip coefficient assessment – Part II: online estimation using instrumented vehicle,extended Kalman filter,and neural network

The main objective of this work is to determine the limit of safe driving conditions by identifying the maximal friction coefficient in a real vehicle. The study will focus on finding a method to determine this limit before reaching the skid, which is valuable information in the context of traffic safety. Since it is not possible to measure the friction coefficient directly, it will be estimated using the appropriate tools in order to get the most accurate information. A real vehicle is instrumented to collect information of general kinematics and steering tie-rod forces. A real-time algorithm is developed to estimate forces and aligning torque in the tyres using an extended Kalman filter and neural networks techniques. The methodology is based on determining the aligning torque; this variable allows evaluation of the behaviour of the tyre. It transmits interesting information from the tyre–road contact and can be used to predict the maximal tyre grip and safety margin. The maximal grip coefficient is estimated according to a knowledge base, extracted from computer simulation of a high detailed three-dimensional model, using Adams^® software. The proposed methodology is validated and applied to real driving conditions, in which maximal grip and safety margin are properly estimated.     

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

Additional 4WS and Driver Interaction

SUMMARY

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

Asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles

This paper shows that, for a four-wheel steering vehicle, a proportional-integral (PI) active front steering control and a PI active rear steering control from the yaw rate error together with an additive feedforward reference signal for the vehicle sideslip angle can asymptotically decouple the lateral velocity and the yaw rate dynamics; that is the control can set arbitrary steady state values for lateral speed and yaw rate at any longitudinal speed. Moreover, the PI controls can suppress oscillatory behaviours by assigning real stable eigenvalues to a widely used linearised model of the vehicle steering dynamics for any value of longitudinal speed in understeering vehicles. In particular, the four PI control parameters are explicitly expressed in terms of the three real eigenvalues to be assigned. No lateral acceleration and no lateral speed measurements are required. The controlled system maintains the well-known advantages of both front and rear active steering controls: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres and improved manoeuvrability. In particular, zero lateral speed may be asymptotically achieved while controlling the yaw rate: in this case comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced. Also zero yaw rate can be asymptotically achieved: in this case additional stable manoeuvres are obtained in obstacle avoidance. Several simulations, including step references and moose tests, are carried out on a standard small SUV CarSim model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tyre forces, pitch, roll and driver dynamics. The simulations confirm the decoupling between the lateral velocity and the yaw rate and show the advantages obtained by the proposed control: reduced lateral speed or reduced yaw rate, suppressed oscillations and new stable manoeuvres.     

Haptic steering support for driving near the vehicle’s handling limits; skid-pad case

Current vehicle dynamic control systems from simple yaw control to high-end active steering support systems are designed to primarily actuate on the vehicle itself, rather than stimulate the driver to adapt his/her inputs for better vehicle control. The driver though dictates the vehicle’s motion, and centralizing him/her in the control loop is hypothesized to promote safety and driving pleasure. Exploring the above statement, the goal of this study is to develop and evaluate a haptic steering support when driving near the vehicle’s handling limits (Haptic Support Near the Limits; HSNL). The support aims to promote the driver’s perception of the vehicle’s behaviour and handling capacity (the vehicle’s internal model) by providing haptic (torque) cues on the steering wheel. The HSNL has been evaluated in (a) driving simulator tests and (b) tests with a vehicle (Opel Astra G/B) equipped with a variable steering feedback torque system. Drivers attempted to achieve maximum velocity while trying to retain control in a circular skid-pad. In the simulator (a) 25 subjects drove a vehicle model parameterised as the Astra on a dry skid-pad while in (b) 17 subjects drove the real Astra on a wet skid-pad. Both the driving simulator and the real vehicle tests led to the conclusion that the HSNL assisted subjects to drive closer to the designated path while achieving effectively the same speed. With the HSNL the drivers operated the tires in smaller slip angles and hence avoided saturation of the front wheels’ lateral forces and excessive understeer. Finally, the HSNL reduced their mental and physical demand.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation.     

Integrated chassis control for a three-axle electric bus with distributed driving motors and active rear steering system

This paper describes an integrated chassis control framework for a novel three-axle electric bus with active rear steering (ARS) axle and four motors at the middle and rear wheels. The proposed integrated framework consists of four parts: (1) an active speed limiting controller is designed for anti-body slip control and rollover prevention; (2) an ARS controller is designed for coordinating the tyre wear between the driving wheels; (3) an inter-axle torque distribution controller is designed for optimal torque distribution between the axles, considering anti-wheel slip and battery power limitations and (4) a data acquisition and estimation module for collecting the measured and estimated vehicle states. To verify the performances, a simulation platform is established in Trucksim software combined with Simulink. Three test cases are particularly designed to show the performances. The proposed algorithm is compared with a simple even control algorithm. The test results show satisfactory lateral stability and rollover prevention performances under severe steering conditions. The desired tyre wear coordinating performance is also realised, and the wheel slip ratios are restricted within stable region during intensive driving and emergency braking with complicated road conditions.     

A path-following driver–vehicle model with neuromuscular dynamics,including measured and simulated responses to a step in steering angle overlay

An existing driver–vehicle model with neuromuscular dynamics is improved in the areas of cognitive delay, intrinsic muscle dynamics and alpha–gamma co-activation. The model is used to investigate the influence of steering torque feedback and neuromuscular dynamics on the vehicle response to lateral force disturbances. When steering torque feedback is present, it is found that the longitudinal position of the lateral disturbance has a significant influence on whether the driver’s reflex response reinforces or attenuates the effect of the disturbance. The response to angle and torque overlay inputs to the steering system is also investigated. The presence of the steering torque feedback reduced the disturbing effect of torque overlay and angle overlay inputs. Reflex action reduced the disturbing effect of a torque overlay input, but increased the disturbing effect of an angle overlay input. Experiments on a driving simulator showed that measured handwheel angle response to an angle overlay input was consistent with the response predicted by the model with reflex action. However, there was significant intra- and inter-subject variability. The results highlight the significance of a driver’s neuromuscular dynamics in determining the vehicle response to disturbances.