英文文章Handling Studies of Driver-Vehicle Systems.pdf

Handling Studies of Driver-Vehicle Systems M. Lin, A. A. Popov and S. McWilliam School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, University Park, Nottingham NG7 2RD, U.K. Email: eaxmlnottingham.ac.uk The driver-vehicle system approach provides a firm basis for analysing vehicle and driver dynamics in vehicle handling design. The paper aims to provide an analysis of drivers steering and speed control during driver-vehicle interaction. Generic mathematical models of vehicle and driver are implemented, and the handling characteristics in typical manoeuvres are studied through numerical simulations. As information technology and electronic systems are widely introduced for vehicle chassis control nowadays, new human factor problems have been posed in the simulation for vehicle handling studies. The proposed models here provide tools for exploring the effects of active chassis intervention systems on the driver-vehicle. Keywords / driver-vehicle systems, vehicle dynamics, driver behaviour, chassis enhancement systems 1. INTRODUCTION Recently, as virtual prototyping has been increasingly applied in vehicle development, vehicle handling design in a virtual environment has also been widely used in both academic research and the manufacturing area. For vehicle handling simulations, vehicle dynamics simulation models (VDSMs) are necessities for the developers. Since 1960s 35611, VDSMs have been developed for a variety of applications, including dynamic analysis, interactive driving simulation, and vehicle testing. The model complexity and solution procedures are defined according to a given application. It can be seen that the vehicle and driver form a closely coupled man-machine system. The interaction between the dynamics of the vehicle and the driver behaviour plays a paramount role throughout the whole process of the simulation. At the same time, due to the desire for personal mobility, automotive chassis enhancement systems are introduced into vehicles. They are targeting on providing safety, stability and comfort, and minimising the environmental impacts. However, it is argued that in some cases these chassis enhancement systems can cause more harm than good. In 9, Sharp pointed out that the assessment of driver-vehicle dynamics qualities in the context of electronic enhanced vehicles contains many separate quality issues and many design conflicts. This involves driver-vehicle speed control and its relationship with directional/steering control, which has only recently received attention. A detailed review on automotive chassis enhancement systems in heavy vehicles, provided by Palkovics and Fries 8, includes systems such as anti-lock braking system (ABS), traction control system (TCS), rear axle steering system and dynamic stability control system. It is suggested that the driver is kept in the control loop as drivers intention is necessary to activate the systems. By making a vehicle easier to control, drivers may be encouraged to drive closer to the vehicle limits, therefore affecting the intended safety benefits. In the following sections, a basic 4-DOF (longitudinal, lateral, yaw, roll) vehicle model and a driver control model are presented. The driver model is directionally structured to control vehicle heading/yaw angle and lateral position, and longitudinally perceiving the longitudinal acceleration error. In Section 4, driver- vehicle interaction is reviewed. The simulation is then employed in Section 5 to analyse manoeuvres involving double lane change and braking in turn. 2. VEHICLE MODEL The vehicle is represented by a four degrees of freedom model 4, for the longitudinal, lateral, yaw and roll motion. As shown in Fig. 1, although the suspensions are not included in the modelling, the model uses a simplified description of body roll assuming a fixed roll axis defined by the heights of the roll centres of the front and rear axles of the vehicle. Vehicle model parameters are reported in the Appendix. The equations of motion using axes fixed to the vehicle body are given by, sincos)( yf F xf F xr Frvum+=+? sincos)( xf F yf F yr Fruvm+=+? )sincos(sin )sincos( yf F xf F xr Fh yr Fb xf F yf Fap xz Ir z I + +=? )sincos(cos )(sin )()( xfyfyr zrzf rfrfxzx FFFh FFh pcckkrIpI + + =+? (1) mg z yC.G. h r f r u V v L C.G. C.G. ab Fzr Fyr FxfFxr Fzf Fxr Fxf Fyf,r hg x z y x Fzf,r Fyf roll axis Fig.1 Vehicle Model where Fxf, Fxr, Fyf, Fyr, and Fzf, Fzr are vehicle axle longitudinal, lateral and vertical forces, respectively. r is the yaw rate and p and are the roll rate and roll angle. The sideslip angles and static camber angles of the front and rear wheels f , r and f , r can be defined in terms of vehicle motion variables, rr ff rhu hprbv a rhu hprav a ? ? ? ? ? ? ? ? + = ? ? ? ? ? ? ? ? + = sin cos tan sin cos tan (2) rr ff = = (3) When the vehicle is running at constant speed, the longitudinal motion can be uncoupled from the equations of motion. The dynamics of the non-linear vehicle model includes the influence of the non-linear tyre characteristics, which are modelled by the magic formula 7. The effects of lateral and longitudinal load transfers have been evaluated through a steady state approximation 10. Assuming a fixed roll axis position, the expression of the lateral load transfer for the front and the rear axles are, )( )( _ _ hd L hha t mru F hd L hhb t mru F r g r latrz f g f latfz + = + = (4) The longitudinal load transfer, occurring while the varied vehicle forward velocity is taken into account, is calculated as follows, LhFFF gFrfxlongz /)( _ += (5) 3. DRIVER BEHAVIOUR THROUGH PATH PREVIEW Obviously, only the vehicle itself cannot maintain a desired path. This demands a combination with driver model. The driver has visual and motion feedbacks for developing steering control actions. Driver behaviour through path preview involves actions based on perception of commands. For directional/steering control, drivers can use preview behaviour to follow curved paths. A vehicle will follow a curved path for a given steering angle, so the driver can match horizontal road curvature with appropriate steer angle, and the remaining lane displacement can be handled with compensatory control actions. For speed control, the driver tries to match road grade with a throttle angle, although the correct perception of road grade is much more difficult and imprecise than the perception for horizontal curvature. 3.1 Directional/Steering Control For drivers visual feedback, a two-level (preview and compensatory) driver steering model based on the control strategy proposed by Donges 3 is presented here. The driver exerts steering control to maintain lane position through preview control, and to manoeuvre the vehicle during curve negotiation, lane change or obstacle avoidance. Unpredictable road disturbances can randomly move the vehicle within the lane, and the driver must counteract these disturbances with compensatory control. For preview control, Weir and McRuer 12 suggested that, systems structured to control vehicle heading/yaw angle and lateral position or path angle and lateral position offer good closed-loop characteristics. Therefore, it is assumed here that the driver develops steering corrections based on perceived heading/yaw and lane position errors. By setting a preview point P on the vehicle-fixed x axis, a sort of predictive behaviour is incorporated into the system. Fig. 2 illustrates drivers behaviour through path preview. A composite heading error of the preview point relative to the desired path at the preview point is given by, )(/ PPec Ly+= (6) where ye is the lane position error, LP is the preview distance, is the heading angle and P is the heading angle between x axis and AP line. Instead of separately perceiving both heading and lane position errors, the driver needs only to perceive the angular error c to the preview point down the road. The preview distance LP here is the product of vehicle forward speed and preview time constant TP. This is consistent with our everyday experience that driver sees nearer distance at lower speeds and further distance at higher speeds. Following McRuers crossover model 6, drivers compensatory feedback control can be defined by the transfer function of the steering angle to the composite heading error, s I L c e sT sT G s s + + =) 1 1 ( )( )( (7) It includes three components: a gain G which sets the magnitude of road steering angle corrections for given heading error c ; a lead term ) 1(+sTLthat the driver adopts to counteract vehicle tyre delay; a lag term ) 1(+sTIcorresponding to the neuromuscular delay; and , a time delay s e approximating drivers reaction time delay. For drivers motion feedback, it provides information on motion performed by human organs and on orientation with respect to the gravitational direction. In 1, Allen noted that the yaw rate information can be used as a motion feedback element. The motion feedback gain Km provides a lead that the driver can use to compensate for the vehicle yaw rate lag. 3.2 Speed Control Speed control is important in a variety of scenarios, including maintaining safe lateral acceleration levels while following curved paths, responding to speed limits, and slowing down during emergency avoidance. During straight running the driver continues at specified speed. When the driver detects curvature, speed is then reduced accordingly in order to maintain desired lateral acceleration. The driver speed control law can then be described as Fig.3 (a). The driver commands deceleration consistent with a desired speed change, and perceives deceleration errors. Especially, when electronic chassis controls, such as ABS, TCS, etc., are involved, speed control will be essential. As we can see from the operating principles of these control systems, most of them are activated under emergency situations. Speed changing is therefore inevitable. For example, by adding an effective ABS, the relationship between the brake pedal force and vehicle deceleration is illustrated in Fig.3 (b). With the application of this relationship and the speed control law described above, the assessment of effects of these electronic controls is feasible. A c Preview point P P LP y x X Y ye / LP Desired path P Fig.2 Driver Model through Path Preview Fig.3 (b) Driver Speed Control Law (a) ABS System Characteristic 4. DRIVER-VEHICLE INTERACTION 4.1 Driver-Vehicle Dynamics without Speed Control Given the above dynamic characteristics for the vehicle and driver, a block diagram of the overall driver-vehicle system model without speed control can be structured as shown in Fig.4. It is assumed that the vehicle is travelling at constant forward speed. Vehicle lateral velocity v, yaw rate r and roll rate p are generated by steering inputs to the vehicle equations of motion. Vehicle lateral velocity v and yaw rate r are then under direct control of the driver. Although the roll motion is not controlled by the driver directly, it also influences driver behaviour, especially when the variation of vehicle forward velocity is taken into account. Kinematical equations then provide vehicle heading angle and lateral lane position from lateral velocity and yaw rate. Finally, steering corrections will be made by the driver based on the composite heading error. For the closed-loop analysis, there are two system inputs, one is the path command yc, and the other is the initial heading angle command P . The vehicle will be steered to follow path commands, and P will help implement the correction of visual error. However, with the application of the crossover model merely, a lateral deviation can be found in the simulation (Fig.5 (a). It is assumed that the driver continues to steer until the vehicles attitude intersects the preview point down the road. This strategy finally eliminates vehicle attitude errors but does not correct lane position errors. Therefore, an additional feedback is needed that accumulates error whenever vehicle is not correctly positioned laterally in the lane. By adding a parallel integrator in the system, this offset error can be eliminated (Fig.5 (b). The function of this integrator is to compensate for the composite heading error, which accumulates both the vehicle heading error and the lane position error (Fig.4). It develops much quicker compensation than having the integrator compensate for lane position error only. The transfer function of the steering angle to the composite heading error can then be defined as, )1 () 1 1 ( )( )( s K e sT sT G s s s I L c + + + = (7) Fig. 4 Driver-Vehicle System Directional Control Model Brake Pedal Force + _ deceleration error Without ABS With ABSVehicle deceleration Speed Control Vehicle Longitudinal Dynamics brake Pedal force actual deceleration deceleration command (b) (a) (a) without integrator (b) with integrator Fig. 5 Effect of the Parallel Integrator 4.2 Driver-Vehicle Dynamics with Speed Control When speed control is concerned, driver-vehicle interaction is the result of drivers longitudinal and lateral controls, which reflects the driver control behaviour in a more tactical level. Fig.6 represents the structure of the interaction. The upper part of Fig.6 describes the driver directional control behaviour, and the lower part describes the speed control behaviour. By looking at the path information and feedback of vehicle responses, the relationship between them can be processed. Fig.6 Driver-Vehicle Interaction with Speed Control 5. PERFORMANCE ANALYSIS 5.1 Double Lane Change at a Constant Speed Driver-vehicle model without speed control is applied here for a double lane change manoeuvre. Refer to the Appendix for vehicle parameters. Fig.7 shows the system responses. It can be seen that path information inputs make possible the analysis of the vehicles performances. The driver steers along a standard ISO double lane change manoeuvre with the constant forward speed 80km/h, and tracks the desired path using the two- level control. Therefore, drivers steering input is determined by the motion of the desired path to be followed by the preview point through the coupling of the preview distance LP, and also by drivers behaviour of the inverse dynamics of the vehicle. As shown in Fig.7 (a), the manoeuvre requires the vehicle to travel for 15m in the original lane, to change lane with a lateral displacement of 3.5m in 30m, to stay in this lane for 25m and to return to the original lane in 25m. The driver successfully performed the required manoeuvre without touching the cones delimiting the lanes. The action of the driver is with a short delay, and with a small gain, not to induce instability. The other results show the characteristic W shape of the double lane change responses. The system responds with a peak road steering wheel angle 1.6 (Fig.7 (b), which results in peak lateral accelerations of about 0.4g (Fig.7 (c). This value is above average drivers preference 2. It stems from the tyre saturation near the peak value. The oscillations are characterised by the natural frequency and damping of the model. (a) cones (b) (c) Fig.7 Transient Response in Double Lane Change Constant Speed V = 80km/h (Driver parameters: G = 0.35, = 0.1s, TL = 0.1s, TI = 0.2s, K = 0.05, Km = 0.01, TP = 1s) 5.2 Braking in Turn Scenario Now consider the combined steering and speed control driver-vehicle model for the braking in turn manoeuvre. Fig.8 illustrates the characteristic responses of the model. The driver enters a 300m-radius turn with a speed of 100km/h. Since the turn is sharper than expected, the manoeuvre results in excessive lateral acceleration ay, about 0.3g in Fig.8. Statistically 2, a cautious driver applies low to moderate deceleration while driving, with the result of reducing ay below 0.26g. The driver model is therefore set up to reduce ay to some percentage below 0.26g, corresponding with a reduced speed at around 88km/h. The speed control law is previously described in section 3.2, and the command braking deceleration is set at 0.2gs. One should note that when the lateral acceleration exceeds 0.3gs (Fig.8 (b), the driver model begins braking, which is subsequently brought up to the longitudinal command level of 0.2gs (Fig.8 (a). The vehicle goes into oversteer as evidenced by the actual trajectory crossing the desired during the braking process (Fig.8 (c). This is a result of a reduction in the rear axle + _ Steering Wheel Angle + _ path command Speed Control Vehicle Longitudinal Dynamics brake Pedal force actual deceleration deceleration command Directional/Steering Control Vehicle Lateral Dynamics path information actual path cornering stiffness. The driver is then able to reduce speed and bring the vehicle back under stable control in understeer condition after the vehicle reaches the desired speed, as evidenced in the steady state of lateral acceleration. (a) (b) (c) Fig.8 Driver-Vehicle Response in Braking in Turn 6. CONCLUSIONS AND FURTHER RESEARCH Rational driver directional/steering and speed control models have been specified based on vehicle attitude, lateral position and longitudinal deceleration controls. Driver-vehicle system performances in double lane change and braking in turn scenarios are studied. The analysis has demonstrated stable control of the system simulation. Steering control stability has been achieved with preview-compensatory model over a speed range. The proposed models in the paper are aimed at the assessment of effects of electronic chassis enhancement systems. They provide tools for the exploration of the effects of active chassis intervention systems on the driver-vehicle interaction