A General Method for the Evaluation of Vehicle Manoeuvrability with Special Emphasis on Motorcycles

This paper presents a novel approach to the assessment of the manoeuvrability of vehicles which is not based on the simulation of open-loop manoeuvres, nor does it rely on the modelling of the driver as a control system. Instead, the essence of the method is the solution of a two-point optimal control boundary value problem, in which a vehicle, subject to physical constraints like tyre adherence and road borders, among others, is required to go between given initial and final positions as fast as possible. The control inputs - i.e., the driver's actions - that make the vehicle move between the two states in the most efficient way are found as a part of the solution procedure and represent the actions of a sort of ideal, perfect driver. The resulting motion is called the optimal manoeuvre and, besides being the most efficient way that the given vehicle has for travelling between the two points according to the chosen optimal criterion, may be taken as a reference for meaningful comparisons with other vehicles. The value of the penalty function, used to define the optimal condition occurring at the optimal manoeuvre, may be taken as a measure of manoeuvrability or handling. With this approach the manoeuvrability properties are established as intrinsic to the vehicle, being defined with respect to an ideal perfect driver. Some possible forms of the penalty function, which means slightly different concepts of manoeuvrability and handling, are discussed. In the end, the case of motorcycles and some examples of optimal manoeuvres are given.     

A passenger car driver model for higher lateral accelerations

Due to increasing demands for time and cost efficient vehicle and driver assistant systems development, numerical simulation of closed-loop manoeuvres becomes increasingly important. Thus, the driver has to be considered in the modelling. On the basis of a two-layer approach to model a driver's steering behaviour, the field of application is extended to higher lateral accelerations in this study. An analytical method to determine the driver parameters is presented, which is based on the two-wheel vehicle model. The simulation results are determined using a full vehicle model including all essential nonlinearities. Standard manoeuvres in the nonlinear range of vehicle handling behaviour are performed. A cornering manoeuvre is chosen to show the characteristics of the proposed driver model.     

A passenger car driver model for higher lateral accelerations

Due to increasing demands for time and cost efficient vehicle and driver assistant systems development, numerical simulation of closed-loop manoeuvres becomes increasingly important. Thus, the driver has to be considered in the modelling. On the basis of a two-layer approach to model a driver's steering behaviour, the field of application is extended to higher lateral accelerations in this study. An analytical method to determine the driver parameters is presented, which is based on the two-wheel vehicle model. The simulation results are determined using a full vehicle model including all essential nonlinearities. Standard manoeuvres in the nonlinear range of vehicle handling behaviour are performed. A cornering manoeuvre is chosen to show the characteristics of the proposed driver model.     

Application of Optimal Control Theory to Inverse Simulation of Car Handling

The application of Optimal Control Theory to time-optimal inverse simulation of car handling was investigated. Time-optimal inverse simulation of car handling involves the calculation of driver actions required to perform specified manoeuvres, in as short a time as possible. Driver actions consist of time-histories of front wheel steer rate and longitudinal force. Optimal time-histories of these quantities were calculated using the Gradient method after formulating the problem as one of optimal control. Simulation results are presented for two different cars performing similar lane-changes. These results show significant differences in necessary driver actions for different cars and demonstrate the suitability of the approach taken.     

A novel integrated chassis controller for full drive-by-wire vehicles

In this paper, a systematic design with multiple hierarchical layers is adopted in the integrated chassis controller for full drive-by-wire vehicles. A reference model and the optimal preview acceleration driver model are utilised in the driver control layer to describe and realise the driver's anticipation of the vehicle's handling characteristics, respectively. Both the sliding mode control and terminal sliding mode control techniques are employed in the vehicle motion control (MC) layer to determine the MC efforts such that better tracking performance can be attained. In the tyre force allocation layer, a polygonal simplification method is proposed to deal with the constraints of the tyre adhesive limits efficiently and effectively, whereby the load transfer due to both roll and pitch is also taken into account which directly affects the constraints. By calculating the motor torque and steering angle of each wheel in the executive layer, the total workload of four wheels is minimised during normal driving, whereas the MC efforts are maximised in extreme handling conditions. The proposed controller is validated through simulation to improve vehicle stability and handling performance in both open- and closed-loop manoeuvres.     

Sensitivity of Driver-Vehicle Performance to Vehicle Characteristics Revealed in Open-loop Tests

The advantages of being able to objectively specify desirable vehicle handling characteristics, which can be determined without recourse to closed-loop tests on a prototype vehicle, are widely recognised. This paper reviews the studies that have attempted to find a relationship between closed-loop task performance, and driver subjective opinion, and various steady-state and transient characteristics revealed in open-loop tests of the vehicle. It is found that the level of definition of these relationships is not sufficient to justify mandatory regulations for vehicle design. However, the basic requirements for steering control sensitivity, and the rapidity and stability of the fixed-control dynamic response of vehicles in normal manoeuvres, are beginning to emerge. Data are particularly lacking for the closed-loop effects of vehicle sideslipping characteristics, free-control responses and vehicle behaviour in limit manoeuvres.     

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.     

Comparison of various double-lane change manoeuvre specifications

One of the commonly used performance measures to quantify a vehicle's handling transient dynamics is the maximum forward speed (MFS) while passing a certain specified double-lane change (DLC) manoeuvre without violating the boundary and tyre lift-off. The MFS is directly associated with the minimum curvature radius (MCR) of the vehicle centre of gravity (CG) trajectory controlled by the driver during the manoeuvre. The MCR is further affected by the vehicle dimensions to meet the boundary condition. In this study, a single heavy vehicle CG trajectory is assumed to be a combination of three straight lines and two third-order spline curves. A heavy vehicle multi-body system model established with ADAMS/Car is correlated with test data for step-steer and constant radius cornering events, and then the model is used to demonstrate that the assumptions considered in the formulation applied in this paper are valid for this specific vehicle category. The MCRs of four heavy vehicles are maximised among all the possible choices of the vehicle CG trajectory during each of five specific DLC manoeuvres, including North Atlantic Treaty Organization (Allied Vehicle Testing Publication 03-160W), International Organization for Standardization (ISO) 3888-1, ISO 3888-2, Consumer Union Short Course and Test Operations Procedure 2-2-609. The maximised MCR (MMCR), considered as the best possible choice of vehicle CG trajectories, is further solved as a function of the vehicle width and length. The results will show the sensitivity of the MMCR to the vehicle length and width, thus the impact on the vehicle transient handling dynamics. Finally, the comparison of five DLC specifications may help users to correlate a vehicle's MFS from one specification to others.     

A theoretical justification of the sine with dwell manoeuvre

The sine with dwell (SWD) manoeuvre has received much attention within the context of vehicle stability testing. This manoeuvre is used in a test developed by the NHTSA, designed to certificate electronic stability control systems in light vehicles. The test is used in legislations as well as in consumer tests all over the globe. The SWD manoeuvre was designed using test vehicles on a test track and experimentally validated. The paper at hand uses optimal control theory to theoretically justify the use of the SWD manoeuvre to produce a severe lateral motion and over-steering based on steering input. It is shown that a manoeuvre similar to the SWD manoeuvre can be obtained from an optimal control problem using simple vehicle dynamics models. The optimal control method is further used to analyse the manoeuvre's robustness with respect to vehicle dimensions and tyre properties. It is shown that the manoeuvre is robust in dimensions, which theoretically motivates its application for various sizes of vehicles.     

Driver steering and muscle activity during a lane-change manoeuvre

The article reports an experimental study of driver steering control behaviour in a lane-change manoeuvre. Eight test subjects were instrumented with electromyography to measure muscle activation and co-contraction. Each subject completed 30 lane-change manoeuvres with one vehicle on a fixed-base driving simulator. For each driver, the steering torque feedback characteristic was changed after every ten manoeuvres; the response of the vehicle to steering angle inputs was not changed. Drivers' control strategies were found to be robust to changes in steering torque feedback. Path-following errors, muscle activity and muscle co-contraction all reduce with the number of lane-changes performed by the driver, suggesting the existence of a learning process. Comparing the test subjects, there was some evidence that high levels of co-contraction were used to allow high-frequency steering inputs to be generated. The results contribute to the understanding of vehicle–driver (and more generally, human–machine) dynamic interaction.     

Modeling multi-unit vehicle dynamics for low-speed path-following assessment off-highway

This paper proposes a non-linear dynamics model for articulated vehicles. This model is able to capture common low-speed behaviours of any articulated vehicles off-highway, such as operating for a corner or roundabout on a cambered or slippery surface. It can be used to assess the low-speed manoeuvrability of articulated vehicles under such manoeuvres and conditions. The vehicle model was validated by comparing its path tracking performance to that of the field tests.     

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.     

Driver steering and muscle activity during a lane-change manoeuvre

The article reports an experimental study of driver steering control behaviour in a lane-change manoeuvre. Eight test subjects were instrumented with electromyography to measure muscle activation and co-contraction. Each subject completed 30 lane-change manoeuvres with one vehicle on a fixed-base driving simulator. For each driver, the steering torque feedback characteristic was changed after every ten manoeuvres; the response of the vehicle to steering angle inputs was not changed. Drivers' control strategies were found to be robust to changes in steering torque feedback. Path-following errors, muscle activity and muscle co-contraction all reduce with the number of lane-changes performed by the driver, suggesting the existence of a learning process. Comparing the test subjects, there was some evidence that high levels of co-contraction were used to allow high-frequency steering inputs to be generated. The results contribute to the understanding of vehicle-driver (and more generally, human-machine) dynamic interaction.     

Automotive Steering Control in a Split-µ Manoeuvre Using an Observer-Based Sliding Mode Controller

Summary In this paper a sliding mode integral action controller and sliding mode observer are used to enhance vehicle stability in a split- µ manoeuvre. Anti-lock braking systems (ABS) have become an integral part of modern cars, and they have dramatically improved vehicle handling in braking manoeuvres. However, when a vehicle attempts to brake on a surface with uneven friction coefficient such as on wet or icy roads, a so-called split- µ scenario, the yaw moment generated by the asymmetric braking can prove demanding for an inexperienced driver. The controller presented hereworks in conjunction with a conventional ABS system to provide safe and effective braking through steer-by-wire. This paper extends previous state-feedback work by only using certain measurable quantities in the controller, estimating further signals by employing an observer.     

Automotive Steering Control in a Split-µ Manoeuvre Using an Observer-Based Sliding Mode Controller

Summary In this paper a sliding mode integral action controller and sliding mode observer are used to enhance vehicle stability in a split- µ manoeuvre. Anti-lock braking systems (ABS) have become an integral part of modern cars, and they have dramatically improved vehicle handling in braking manoeuvres. However, when a vehicle attempts to brake on a surface with uneven friction coefficient such as on wet or icy roads, a so-called split- µ scenario, the yaw moment generated by the asymmetric braking can prove demanding for an inexperienced driver. The controller presented hereworks in conjunction with a conventional ABS system to provide safe and effective braking through steer-by-wire. This paper extends previous state-feedback work by only using certain measurable quantities in the controller, estimating further signals by employing an observer.     

Implementation of active steering on longer combination vehicles for enhanced lateral performance

A steering-based controller for improving lateral performance of longer combination vehicles (LCVs) is proposed. The controller steers the axles of the towed units to regulate the time span between the driver steering and generation of tyre lateral forces at the towed units and consequently reduces the yaw rate rearward amplification (RWA) and offtracking. The open-loop effectiveness of the controller is evaluated with simulations and its closed loop or driver in the loop effectiveness is verified on a test track with a truck–dolly–semitrailer test vehicle in a series of single- and double-lane change manoeuvres. The developed controller reduces the yaw rate RWA and offtracking considerably without diminishing the manoeuvrability. Furthermore, as a byproduct, it decreases the lateral acceleration RWA moderately. The obtained safety improvements by the proposed controller can promote the use of LCVs in traffic which will result in the reduction of congestion problem as well as environmental and economic benefits.     

A Mathematical Model for Driver Steering Control,with Design,Tuning and Performance Results

A mathematical model for the steering control of an automobile is described. The structure of the model derives from linear optimal discrete time preview control theory but it is non-linear. Its parameter values are obtained by heuristic methods, using insight gained from the linear optimal control theory. The driver model is joined to a vehicle dynamics model and the path tracking performance is demonstrated, using moderate manoeuvring and racing speeds. The model is shown to be capable of excellent path following and to be robust against changes in the vehicle dynamics. Application to the simulation of manoeuvres specified by an ideal vehicle path and further development of the model to formalise the derivation of its parameter values and to put it to other uses are discussed.     

A Mathematical Model for Driver Steering Control, with Design, Tuning and Performance Results

A mathematical model for the steering control of an automobile is described. The structure of the model derives from linear optimal discrete time preview control theory but it is non-linear. Its parameter values are obtained by heuristic methods, using insight gained from the linear optimal control theory. The driver model is joined to a vehicle dynamics model and the path tracking performance is demonstrated, using moderate manoeuvring and racing speeds. The model is shown to be capable of excellent path following and to be robust against changes in the vehicle dynamics. Application to the simulation of manoeuvres specified by an ideal vehicle path and further development of the model to formalise the derivation of its parameter values and to put it to other uses are discussed.     

A closed-loop dynamic simulation-based design method for articulated heavy vehicles with active trailer steering systems

This paper presents a closed-loop dynamic simulation-based design method for articulated heavy vehicles (AHVs) with active trailer steering (ATS) systems. AHVs have poor manoeuvrability at low speeds and exhibit low lateral stability at high speeds. From the design point of view, there exists a trade-off relationship between AHVs’ manoeuvrability and stability. For example, fewer articulation points and longer wheelbases will improve high-speed lateral stability, but they will degrade low-speed manoeuvrability. To tackle this conflicting design problem, a systematic method is proposed for the design of AHVs with ATS systems. In order to evaluate vehicle performance measures under a well-defined testing manoeuvre, a driver model is introduced and it ‘drivers’ the vehicle model to follow a prescribed route at a given speed. Considering the interactions between the mechanical trailer and the ATS system, the proposed design method simultaneously optimises the active design variables of the controllers and passive design variables of the trailer in a single design loop (SDL). Through the design optimisation of an ATS system for an AHV with a truck and a drawbar trailer combination, this SDL method is compared against a published two design loop method. The benchmark investigation shows that the former can determine better trade-off design solutions than those derived by the latter. This SDL method provides an effective approach to automatically implement the design synthesis of AHVs with ATS systems.     

Integrated evasive manoeuvre assist for collision mitigation with oncoming vehicles

Development and deployment of steering based collision avoidance systems are made difficult due to the complexity of dealing with oncoming vehicles during the evasive manoeuvre. A method to mitigate the collision risk with oncoming vehicles during such manoeuvres is presented in this work. A point mass analysis of such a scenario is first done to determine the importance of speed for mitigating the collision risk with the oncoming vehicle. A characteristic parameter was identified, which correlates well with the need to increase or decrease speed, in order to reduce the collision risk. This finding was then verified in experiments using a Volvo XC90 test vehicle. A closed-loop longitudinal acceleration controller for collision mitigation with oncoming vehicles is then presented. The longitudinal control is combined with yaw stability control using control allocation to form an integrated controller. Simulations in CarMaker using a validated XC90 vehicle model and the proposed controller showed consistent reductions in the collision risk with the oncoming vehicle.