Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Controller Development and Evaluation

SUMMARY

Due to increased traffic congestion and travel times, research in Advanced Vehicle Control Systems (AVCS) has focused on automated lateral and headway control. Automated vehicles are seen as a way to increase freeway capacity and vehicle speeds while reducing accidents due to human error. Recent research in automated lateral control has focused on vehicle control during low-g maneuvers. To increase safety, automated lateral controllers will need to recognize and react to emergency situations.

This paper investigates the effects of vehicle and tire model order on the response of automated vehicles to an emergency step lane change using a controller based on linear vehicle and tire models. From these studies it is concluded that control strategies based solely on linear vehicle and tire models are inadequate for emergency vehicle maneuvers.

A strategy is then proposed to automatically control vehicles through emergency maneuvers. Here the response of a nonlinear vehicle model is used with a linear state model to optimize controller gains for nonlinear maneuvers. An emergency step lane change is used as a preliminary test of the method.     

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.     

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.     

Control of Longitudinal and Lateral Platoon Using Sliding Control

SUMMARY

This paper initially introduces a vehicle model that can be utilized for simulation tests in the field of AVCS studies. This model contains the non-linear elements of the engine, the torque converter, the automatic gear shift and the tire. The vehicle model has 3 degrees of freedom and it can be used for multiple vehicle simulations in AVCS as well as in ATIMS. This paper applies the model to the study and analysis of vehicle “platooning” for automated driving. In this paper, it is shown that platooning can be realized both longitudinally and laterally by the application of the sliding control.     

Messungen von Fahrbahn-Unebenheiten paralleler Fahrspuren und Anwendung der Ergebnisse

Measurement of two track road inputs and theoretical application of the results

The calculation of vehicle response to road-surface irregularity inputs requires the spectral densities of the left and right longitudinal track and their statistical dependence

This paper presents some resluts of parallel profile measurements, three typical german roads have been chosen

Random vibration of two vehicle types are digital-simulated. The dynamic tire load shows that independent suspension systems are more advantageous than beam axles, because by wheel tramp this type increases the dynamic tire load.     

Fuzzy Logic Traction Controllers and their Effect on Longitudinal Vehicle Platoon Systems

This paper presents two fuzzy logic traction controllers and investigates their effect on longitudinal platoon systems. A fuzzy logic approach is appealing for traction control because of the nonlinearity and time-varying uncertainty involved in traction control systems

The fuzzy logic traction controllers we present regulate brake torque to control wheel slip, which is the normalized difference between wheel and vehicle speed. One fuzzy controller estimates the peak slip corresponding to the maximum tire-road adhesion coefficient and regulates wheel slip at the peak slip. The controller is attractive because of its ability to maximize acceleration and deceleration regardless of road condition. However, we find through simulations the controller's performance degrades in the presence of time-varying uncertainties. The other fuzzy logic controller regulates wheel slip at any desired value. Through simulations we find the controller robust against changing road conditions and uncertainties. The target slip is predetermined and not necessarily the peak slip for all road conditions. If the target slip is set low, stable acceleration and deceleration is guaranteed, regardless of road condition

We also study the effect of traction control on longitudinal vehicle platoon systems using simulations. The simulations include acceleration and deceleration maneuvers on an icy road. The results indicate traction control may substantially improve longitudinal platoon performance, especially when icy road conditions exist.     

Autonomous Lateral Control of Vehicles in an Automated Highway System

Lateral control of vehicles in IVHS requires the installation of on-board sensors as well as the installation of roadway hardware such as cables, magnets, etc. Existing control approaches in PATH require road curvature and vehicle lateral position (with respect to the center of the lane) information. Hence these approaches rely on roadway sensors to obtain relative lateral position. These methods will necessitate infrastructural changes to the highway.

This paper introduces the concept of autonomous lateral control or auto-tracking. The method allows us to use only line-of-sight sensor information to effect vehicle control. We present a detailed vehicle model. Controllers have been proposed to demonstrate the effectiveness of the proposed auto-tracking scheme. We also examine the possibilities of using this method for lane change purposes in an automated highway system.     

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.     

Drive control system design for stability and maneuverability of a 6WD/6WS vehicle

This paper describes a drive controller designed to improve the lateral vehicle stability and maneuverability of a 6-wheel drive / 6-wheel steering (6WD/6WS) vehicle. The drive controller consists of upper and lower level controllers. The upper level controller is based on sliding control theory and determines both front and middle steering angle, additional net yaw moment, and longitudinal net force according to the reference velocity and steering angle of a manual drive, remotely controlled, autonomous controller. The lower level controller takes the desired longitudinal net force, yaw moment, and tire force information as inputs and determines the additional front steering angle and distributed longitudinal tire force on each wheel. This controller is based on optimal distribution control and takes into consideration the friction circle related to the vertical tire force and friction coefficient acting on the road and tire. Distributed longitudinal/lateral tire forces are determined as proportion to the size of the friction circle according to changes in driving conditions. The response of the 6WD/6WS vehicle implemented with this drive controller has been evaluated via computer simulations conducted using the Matlab/Simulink dynamic model. Computer simulations of an open loop under turning conditions and a closed-loop driver model subjected to double lane change have been conducted to demonstrate the improved performance of the proposed drive controller over that of a conventional DYC.     

Minimum order bang-bang guidance for feedforward obstacle avoidance steering maneuvers of vehicles

In this paper, a new methodology is presented for computing time-optimal obstacle avoidance maneuvers for ground vehicles. Usually, the problem of obstacle avoidance is addressed in two parts. In the first part a path is planned. In the second an appropriately designed vehicle controller tracks the desired path. In view of the fact that the main problem concerning emergency maneuvers remains the development of an optimal control for minimum time and maximum maneuverability — with respect to the slip risk due to saturation of the tire forces — the authors propose an alternative approach. Considering that the time optimal control according to Pontryagin’s Maximum Principle (PMP) is of bang-bang type the investigations concern the minimum order and magnitude bang-bang control for “feedforward” steering maneuvers with the target of minimizing the computation time and simplifying the algorithm. This is accomplished by keeping the basic PMP logic but transforming the computational algorithm from an exact to a least squares control problem. Furthermore, the paper addresses how to solve the problem of guiding the vehicle from a non rest to a rest position. Simulations of obstacle avoidance maneuvers illustrate the performance of the controller.     

Analysis of the Dynamic Response of a Rolling String-Type Tire Model to Lateral Wheel-Plane Vibrations

A theory has been developed for the analysis and prediction of the dynamic frequency response of lateral force and moment acting upon a pneumatic tire when the wheel is moved laterally and swivelled about the vertical axis. The theory establishes the force and moment response of a tire model which consists of a stretched circular string with mass, elastically supported to the wheel-center-plane. The analysis is confined to small deviations from rectilinear motion such that it is permissible to assume that sliding does not occur in the contact area. In this manner, the equations are kept linear.

The theory which gives an exact analysis of the dynamic response of the model adopted shows satisfactory qualitative agreement with experiments. The change in the moment response due to tire inertia reduces the tendency to shimmy at higher frequencies and higher speeds. The lateral force response, however, changes in an unfavorable fashion which, for castered wheels, may result in a decrease of the effective damping about the king-pin at higher speeds and frequencies.     

Vehicle Motion Analysis in Relation to Vehicle Safety

The influence of vehicle handling on the possible avoidance of accident situations is discussed. lit is shown that accident reconstruction at present does not provide the necessary information to relate the cause of accidents to the lack of road worthiness of vehicles. It follows that the vehicle behavior in proximity of its performance limit must be determined in order to infer its accident avoidance potential.

The paper presents a review of the state-of-the-art of vehicle modeling, simulation of vehicle maneuvers and full scale testing. The application of the direct method of the stability theory is suggested as a possible means of obtaining performance limit envelopes which are necessary for establishing standards of the performance of vehicles.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

Preview Control Algorithms for the Active Suspension of an Off-Road Vehicle

The potential performance improvement using preview control for active vehicle suspension was first recognized in the late nineteen sixties. All work done since that time has been based on optimal control theory using simple vehicle models.

In this article, the performance of quarter vehicle preview controllers when applied to a real off-road vehicle is simulated using both two degree of freedom quarter and ten degree of freedom full vehicle models. The results, which are compared with non-preview active and conventional passive suspensions, confirm that preview control reduces vertical acceleration of the body centre of gravity, which results in improved ride quality. Further, reductions in pitch and roll motion result from smaller vertical displacements of the vehicle quarters. Coupling between quarters, through the vehicle body, appears to have a smoothing effect on the control.

As an alternative to optimal control theory based controllers, a simple ad hoc preview controller based on isolating the vehicle body from dynamic loads transmitted through the suspension is proposed. Simulation results show that such a controller outperforms the optimal control theory based controllers over small discrete disturbances but responds poorly to disturbances encountered from other than steady state.     

Vergleich einiger Rechen- und Messergebnisse zum Fahrverhalten von Sattelzügen

In this paper some results of theoretical and experimental investigations on the dynamic directional properties of heavy tractor-semitrailer vehicles are presented.

A nonlinear digital computer model was developed on which the theoretical system analysis is based. This model takes account of the nonUnear tire properties and the friction couple of the fifth wheel. A combination of numerical computation methods (Runge-Kutta and Newton-Raphson techniques) is used for the digital computer simulation.

Full scale road tests with articulated vehicles of 38 ton total weight were conducted for experimental validation of the used theoretical model. As input signals to the vehicle, predetermined steering wheel angle functions were used. The system output signals corresponding to these input functions were measured and stored.

A comparison of the obtained theoretical and experimental results shows a very good qualitative agreement and hence leads to the conclusion that the developed theoretical model can give consistent estimates of the basic dynamic vehicle properties.     

Control Algorithms for Active Cab Suspensions on Agricultural Tractors

This paper describes active agricultural tractor cab suspensions based on optimal control theory. Control algorithms based on time invariant state feedback and on adaptive control are developed and studied. The influence of different observers and measurement noise levels on the vibration damping capacity are studied as well as the power consumption for the suspensions.

The principle for the adaptive algorithm is based on the parameters in the penalty matrices being varied so that the resulting controller always strives to make optimum use of available travel space. The feedback and observer gains are also changed depending on the characteristics of the vehicle's frame movements.

The results show that it is possible to design an effective active suspension, but that the choice of feedback gains must be dependent on the surface characteristics to reach satisfactory vibration damping performance.     

Investigation into untripped rollover of light vehicles in the modified fishhook and the sine maneuvers. Part I: Vehicle modelling, roll and yaw instability

Vehicle rollovers may occur under steering-only maneuvers because of roll or yaw instability. In this paper, the modified fishhook and the sine maneuvers are used to investigate a vehicle's rollover resistance capability through simulation. A 9-degrees of freedom (DOF) vehicle model is first developed for the investigation. The vehicle model includes the roll, yaw, pitch, and bounce modes and passive independent suspensions. It is verified with the existing 3-DOF roll-yaw model. A rollover critical factor (RCF) quantifying a vehicle's rollover resistance capability is then constructed based on the static stability factor (SSF) and taking into account the influence of other key dynamic factors.

Simulation results show that the vehicle with certain parameters will rollover during the fishhook maneuver because of roll instability; however, the vehicle with increased suspension stiffness, which does not rollover during the fishhook maneuver, may exceed its rollover resistance limit because of yaw instability during the sine maneuver. Typically, rollover in the sine maneuver happens after several cycles.

It has been found that the proposed RCF well quantifies the rollover resistance capability of a vehicle for the two specified maneuvers. In general, the larger the RCF, the more kinetically stable is a vehicle. A vehicle becomes unstable when its RCF is less than zero. Detailed discussion on the effects of key vehicle system parameters and drive conditions on the RCF in the fishhook and the sine maneuver is presented in Part II of this study.     

Dynamic Measurements in the Research and Development of Rail Vehicles

This paper reviews the measurements which are necessary to all aspects of vehicle dynamics as applied to rail vehicles. Although an attempt has been made to introduce some reference to measurements made in Europe and America, the detailed discussion has been limited to those techniques employed by British Rail. This has the advantage that the discussion can be first hand and therefore more specific.

For convenience the measurements have been collected together under four broad headings.

1. Measurements of rail system data.

2. Measurements of vehicle parameters.

3. Measurements to validate theory and predictions.

4. Measurements of vehicle performance.     

Overturning Stability of Three Wheeled Motorized Vehicles

Three wheeled motorized vehicles are a major mode of public transport in many countries. These vehicles are prone to overturning even during normal turning and obstacle avoidance maneuvers. This paper presents a parametric analysis of a mathematical model of the vehicle and evolves guidelines for improving the overturning stability in terms of vehicle geometry and suspension properties.

Differential equations governing the dynamic behavior of the vehicle are derived on the basis of a six degree of freedom model. The vehicle response to variations in steering, engine power and braking inputs is then numerically simulated. The effects of vehicle geometry and elasto-damping suspension coefficients on the vehicle stability are presented. The results indicate an optimum position of the center of gravity where the vehicle is most stable. While stiffer suspensions favour stability, there exists an optimum value of suspension damping for which the minimum wheel load is a maximum.