Advanced vehicle-infrastructure-driver speed profile for road departure accident prevention C. SENTOUH*†, S. GLASER‡ and S. MAMMAR† † Laboratoire Systèmes Complexes 40, rue de Pelvoux 91020 Evry France. ‡ LCPC-LIVIC, 13 route de la minière, 78000 Versailles, France Correspondence
*Université d’Evry Val d’Essonne CNRS FRE 2494 LSC, 40 rue du Pelvoux CE1455, 91025 Evry Cedex France. Email:
[email protected]
Abstract In this paper, we present a new method for the calculation of the maximal authorized speed in curve. Where the three elements of the situation which are the vehicle, the driver and the infrastructure were well taken into account. The vehicle dynamics are represented by a four wheels model which includes longitudinal slip and side slip angle of the vehicle. The driver behaviour considers his ability in deceleration taking into account his mobilized friction while the infrastructure characteristics introduce a precise definition of the road geometry and the maximal available friction. Keywords: Speed Profile; Vehicle model; Driver behaviour; Modeling; 1 Introduction In France, road departure accounts for more than 30% off all in-vehicle fatalities. Previous work on preventing road departure accidents mostly makes use of Road Departure Warning Systems (RDWS). These systems predict if a dangerous situation is expected, and trigger an alarm to warn the driver. The use of a too summary description of the infrastructure such as the curvature is generally not sufficient to develop a relevant warning system for excessive speed when approaching a curve. The presence of many false alarms strongly decreases the acceptance of the system by the driver. Many researchers are implied today with the development of enhanced digital maps specification such as the NexMap project (2000-2002) in Europe that evaluates the technical and economical feasibilities of enhanced digital road maps for safety applications or EdMap (2001-2004) in the United State that determines safety application performance improvements and extensions using enhanced map data [6]. The ADAS applications require a combination of precise positioning technology and the enhanced digital maps. The map database is used to predict the road geometry ahead of the vehicle. This kind of assistance gives warning to the driver and is often in the range of 3 to 6 seconds. At the opposite, in emergency situations, the side slip and the longitudinal slip are necessary to detect a sliding or a skidding behaviour of the vehicle, which may have normal yaw rate. Moreover in these situations, the longitudinal vehicle speed can not be exactly measured by wheel speed because of excessive longitudinal slip of the wheel. However, side slip angle and the longitudinal slip are not directly measured on vehicles and
C. Sentouh et al. therefore must be estimated [3,4,5]. A precise description of the infrastructure and more accurate vehicle dynamic characteristics make possible to consider the development of a more relevant warning system. This paper presents a computational method of the highest safe speed for driving the upcoming curve. The interaction of the three actors which are the vehicle, the driver and the infrastructure are taken into account. The vehicle dynamics are represented by a four wheels model which includes longitudinal slip and side slip angle. The driver behaviour considers his ability in deceleration while the infrastructure characteristics introduce a precise definition of the road geometry (curvature, slope and superelevation) and the maximal available friction. We also study the influence of the various parameters of the infrastructure and the vehicle dynamics on the calculated speed model. We present then the results in the form of an experimental validation using an instrumented vehicle running on a test track. 2 Existing Speed Models in Curves The maximum safe speed in a curve depends on the road geometry, the surface conditions, the skill (or tolerance for discomfort) of the driver, and the rollover stability of the vehicle. The geometric factors of a curve that are always fixed are its radius of curvature, its slop and its superelevation or banking. The other road-dependent factor is the maximum lateral friction factor that can be generated by the road surface. The friction factor can vary from vehicle to vehicle; it varies with the temperature of the surface, precipitation on the surface, the tires and speed of the vehicle. Neglecting any other parameter than the curvature ρ, the maximum speed at which a vehicle can be kept on the road while moving at a constant speed on a circular section is given by: (1) Where g is the acceleration due to gravity and µlat is the maximum available side friction. The friction coefficient µ depends on the characteristics of the interface between the tire and the road surface. Due to the lack of any other road geometry attribute than curvature in currently available map databases, most Curve Warning Systems under development do actually use this simple model. The determination of the safe speed in a curve is generally based on the information on lateral acceleration. These constraints express in particular, the maximum road curvature according to acceptable maximum lateral acceleration (between 0.2g and 0.3g) [7]. One can go one step further by taking into account the superelevation φ and driver behaviour. For instance, the NHTSA [2] guidelines for the design and development of Curve Warning Systems state that the maximum safe speed at the apex of an approaching curve (Vmax) should be determined from the equation: (2) In this model (NHTSA) the description of the road is more precise compared to the first model (traditional model). In [1], a step further is accomplished, a model of the maximum speed authorized in a curve was developed; this model is carried out starting from a precise description of the road, in particular the curvature, the superelevation, the slope and maximum available friction.
Advanced Vehicle - Infrastructure - Driver Speed Profile
(3)
Where θ is the road slope, λlat µmax (resp. λlong µmax) represents the side friction (longitudinal friction) mobilized by the driver, H is the height of the centre of gravity of the vehicle and Lav (resp. Lar) is the distance between the centre of gravity and the front axle (resp. rear axle). In the following an enhancement of this model is considered. 3 Approach Used for Speed Profile Generation The model of the maximum speed authorized in curve developed in [1] is more precise compared with that developed in [2] because the slope and the driver behaviour are taken into account. However, the vehicle dynamics is not entirely taken into account. The following enhancements are considered here: 1. A four wheels vehicle model which takes into account at the same time the forces at each the tire/road contact point and the load transfer due to the longitudinal and lateral accelerations. 2. Lateral and longitudinal mobilized frictions on each wheel are computed. The highest safe speed is defined considering the maximum friction. As we consider a four-wheel vehicle model, his speed is computed by resolving the maximum of the four mobilized frictions. . 3. The driver acceleration profile, knowing that the driver is constrained within coupled longitudinal and lateral acceleration maximum. The speed in circular parts is considered constant while the speed profile algorithm in the clothoid which precedes the circular portion is based on the driver mobilizable friction. 3.1 Vehicle Model One of the most difficult bodies of the vehicle to study and to model is with no doubt the tire. The aforementioned is the interface between the road and the vehicle and has as a role to transmit the efforts. Several models of road vehicle exist. We chose a simplified model of vehicle with four wheels of which two are directors and that is sufficiently precise to approximate lateral dynamics in the curves, but also longitudinal dynamics by taking into account the longitudinal slip (Wheel-slip).
Fig. 1. The four wheels vehicle model
C. Sentouh et al. We chose a model of the vehicle which takes into account at the same time the forces at the tire/road contact point and the load transfer due to the longitudinal and lateral accelerations. We will describe the three types of the vehicle' s movements. The longitudinal dynamics are given by: (4) Where Flong represents the longitudinal force acting on the tires and which is according to the longitudinal slipκ, Faerolon is the aerodynamic force into longitudinal. (5) Where Kpi is the coefficient of stiffness of the tires (supposed to be the same for all wheels), sat represents the saturation function. κmax is the positive maximum value of the longitudinal slip κ. The lateral movement is described by two equations which represent the effect of the lateral forces on the lateral movement and the yaw rateψ . (6) Where Faerolat is the aerodynamic force into lateral, Flat is the lateral force exerted on the tires Flat =
4 i =1
Fyi , it
can be regarded as proportional to the slip angle of the tire. One can as follows express the lateral forces on the four wheels:
(7)
Where µmax is maximum available friction, δ is the steering angle, Sb is the length of the axles and lf (resp. lr) represents the distance between the centre of gravity and the front axle (resp. rear axle). In dynamic conditions, load can transfer to the front wheels during braking, the rear wheels during acceleration, and side to side during cornering. Determining the axle loads under arbitrary conditions is an important step in the analysis of approaching a curve because the axle loads determine the tractive and steering forces available at each wheel, affecting acceleration, braking performance and thus authorized speed in curve. When a vehicle is a curve, tire lateral forces will have to generate the centrifugal force necessary to follow the curve. When the vehicle is accelerating, normal forces on the four tires can be obtained as follows:
(8)
Advanced Vehicle - Infrastructure - Driver Speed Profile Where Kf is the vehicle lateral weight-shift distribution on front wheels, Kr is the vehicle lateral weight-shift distribution on rear wheels. 3.2 Tire-Road Interface The tire is one of the main components of the vehicle. It indeed represents the interface of the aforementioned with the external environment which is the road. It transmits the guidance and braking/tractive efforts. The tire dynamic behaviour is very complex and is linear only under certain restricted conditions of operation. One observes various phenomena like skidding and blocking. The Coulomb friction model is used to obtain the mobilized friction µmob. Thus the transversal force Ft and the normal force Fz are such that: (9) 2 Where µmax is the maximum available friction. Since: Ft 2 = Flat2 + Flong we have:
(10)
Lateral and longitudinal available friction on each wheel are computed by using the equations (10) and by making the following approximations of the yaw rate, lateral and longitudinal acceleration: (11) Under the assumption of the low values of the angles (superelevation, slope and slip angle of vehicle), and according to (10) the expressions of the lateral friction to each wheel are:
(12)
According to (10) the expressions of the longitudinal friction to each wheel are:
(13)
C. Sentouh et al. The highest safe speed is defined considering the maximum friction. As we consider a four-wheel vehicle model, we have to find the maximum of the four mobilized frictions, so: (14) 3.3 Driver Behaviour The driver is unceasingly obliged, according to information which it takes on the environment, to define a speed and a position appropriate to the situation of control. Here the capacities of the driver in acceleration are taking into account. The driver can not mobilize the same level of acceleration into longitudinal and lateral, and for this reason we have to distinguish between the maximum friction in longitudinal and lateral modes: (15) For comfort and safety reasons, and under good weather conditions, a driver generally does not mobilize all the available lateral and/or longitudinal friction; therefore we represent the driver behaviour with through two adimensional coefficients λlat and λlong and a maximum friction µmax [1]. (16) It is well known that driver behaviour adapts according to maximum available friction. We considered that the driver behaviour varies inversely proportional to maximum friction µmax. (17) With: (18) Where λ Dry (resp. λ Slip) represents the quantity of maximum friction that the driver can mobilize on a dry road (resp. slipping road). 4 Generation of Speed Profile The speed in circular parts is considered constant, therefore longitudinal acceleration at the entry of the curve is zero (γlon = 0). The algorithm of the speed profile in the clothoid which precedes the circular portion is based on mobilizable friction by the driver. By replacing the equations (12) and (13) in (15) and after calculation the expressions of safe speeds for at each wheel:
(19)
Advanced Vehicle - Infrastructure - Driver Speed Profile Then, the final safe speed Vmax in a curve is obtained from: Vmax = min {V1, V2, V3, V4}. This safe speed model in curve is according to intrinsic parameters (mass, inertia), extrinsic parameters (road geometry, available friction) and driver behaviour (driver ability in deceleration). This model takes into account the lateral dynamics of the vehicle in curve due to the load transfer and the vehicle side slip, and longitudinal dynamics by considering the longitudinal slip on each wheel. The expressions of η1, η2, η3 et η4 are given by:
(20)
Finally the speed profile can has to be adapted for the case of successive curves. For example consider a successions of curves, the first has a radius of 300m, the second turn has a radius of curvature weaker than the first, it is of 150m. Figure 2 shows how the algorithm treats the influence of the second turn on the first. Therefore if speed at the end of the first turn is too high compared to that at the entry of the second turn, the calculation of the speed profile on the first turn must take into account this influence.
Fig. 2. Comparison of Advanced Vehicle Infrastructure Driver Speed Profiles to those developed in [1].
5 Parameter effects analysis This section illustrates the influence of the three parameters of the infrastructure model (the slope, the superelevation and the assumed road friction) and the influence of the vehicle model dynamics (the longitudinal slip and the side slip angle). The road section considered here is a clothoid of length L = 50m such that ρ (0) = 0m −1 and ρ ( L) = 1 / 300m −1 . Results are shown on figure 3.
C. Sentouh et al. 5.1 Influence of the Superelevation The main purpose of the road superelevation is to counteract the lateral acceleration. In figure 3-a, the curve simulated is a left curve (ρ > 0). A left curve normally has a negative superelevation (φ < 0). One can see that the speed difference at the beginning of the clothoid can be high: for a superelevation of -6°, the speed is 2.6 m.s-1 higher than a superelevation of 0°. At opposite, strongly superelevated curves are known to be very dangerous (ρ > 0 & φ > 0). One can see that our speed estimate for a superelevation of 6° in a left curve leads to a speed profile 3 m.s-1 below the one computed for a 0°. 5.2 Influence of the Slope The second parameter of the infrastructure model is the slope. To keep a constant longitudinal speed in a curve, the driver must accelerate or brake the vehicle according to the sign of the slope, therefore it will mobilize part of maximum available friction. So, maximum speed in a curve with a slope (positive or negative) is lower than that calculated for a horizontal road. Figure 3-b presents the variation of the speed profile for different slopes, the safe speed decreases as the absolute value of the slope increases.
Fig. 3. Parameters effect: (a) the superelevation, (b) the slope, (c) the longitudinal slip, (d) the side slip angle.
5.3 Influence of the Vehicle Dynamics This section illustrates the influence of the vehicle dynamics on the maximum safe speed in curve. Figure 3-c illustrates the effect of the longitudinal slip on the maximum safe speed in curve. The safe speed at the end of the clothoid decreases as the value of the longitudinal slip increases. V0.02(50) = 25.1m.s-1 and V0.024(50) = 21.5 m.s-1. Figure 3-d presents the variation of the speed profile for different values of side slip angle. For a
Advanced Vehicle - Infrastructure - Driver Speed Profile side slip angle β = 0.02 rad, the speed at the end of the clothoid is V0.02(50) = 32 m.s-1. For a side slip angle β = 0.08 rad, the safe speed is 9 m.s-1 below the one computed for β = 0.02 rad. 6 Test Track Tests and HMI Aspects The developed method is tested on an experimental vehicle equipped with GPS and a digital map enhanced with infrastructure attributes. The detection of alarms will be done in three steps: We calculate the three speed profiles, corresponding to the parameters λlon = λlat = 0.3, 0.4 and 0.5 on the road section at every moment t. Then by knowing the speed of the vehicle and its lateral acceleration at the moment t, we will be able to estimate his speed at the moment t+T, where T is a temporary horizon selected at 3s (higher than the driver reaction time). The difference between vehicle speed predicted with t+T and acceptable maximum speed with t+T given by the profiles speed calculated for 0.3g, 0.4g and 0.5g allows to evaluate a risk level for excessive speed in curve. M Iz lf lr H Sb Csi Kp
Table1. Parameters of experiment vehicle “Scénic”. Vehicle mass kg Yaw moment of inertia Kg.m2 distance between centre of gravity and the front axle m distance between centre of gravity and the rear axle m height of the centre of gravity m height of the centre of gravity m lateral stiffness coefficient of the tire N.rad-1 longitudinal stiffness coefficient of the tire N
1500 2200 1.0065 1.4625 0.5 1.5 57500 12000
Fig. 4. : The three Speed profiles prediction corresponding to the parameters λlon = λlat = 0.3, 0.4 and 0.5
Figure 5-a provides the speed profile prediction with the associated warning levels when the prediction is outside the fixed boundary limit of 0.5g. The HMI module will use visual, acoustic and haptic output signals to warn the driver using different modalities. Various levels and modalities of warnings are considered, according to the risk level assessment. Figure 5-b presents also the developed HMI with vehicle location display, actual speed, predicted speed profile, risk... The results obtained during the experimental tests are very encouraging because there were no not-detected dangerous situations neither false alarm.
C. Sentouh et al.
(a)
Fig. 5. : (a) Speed profile prediction and associated warning levels, (b) In-board HMI
(b)
6 Conclusion In this paper, a new method for the calculation of the highest safe speed for driving the upcoming curve was proposed. This safe speed model takes into account the infrastructure characteristics using an accurate description of the road geometry (radius of curvature, slope and superelevation), and the estimated maximal available friction, the vehicle dynamics and driver behaviour. Parameter effects analysis has been performed. Using an instrumented vehicle, experiments are carried out to validate the generated speed profiles, and, mainly the chosen thresholds. Moreover, the involvement of the vehicle dynamics can be wider, by using observers to estimate the longitudinal slip and the vehicle side slip angle. These aspects will be incorporated in prototype vehicle and tested. Acknowledgments This work has been carried out in the context of the wireless local danger warning (WILLWARN) project within the PReVENT research program, funded by the European Union. References [1] Glaser, S. : Modélisation et analyse d'un véhicule en trajectoire limites Application au développement de systèmes d'aide à la conduite. Thèse de l' Université d' Evry Val d' Essonne, 2004. [2] Department of Transportation U. S. (NHTSA): Run-Off-Road Collision Avoidance Using IVHS Countermeasures. Final Report, December 1999. [3] Ryu, J., Rossetter, E. J. and Gerdes, J. C. : Vehicle Sideslip and Roll Parameter Estimation using GPS. 2002. [4] Miller, S. L. , Youngberg, B., Millie, A., Schweizer, P. and Gerdes, J. C.: Calculating Longitudinal Wheel slip and Tire Parameters Using GPS Velocity. Proceeding of the American Control Conference, Arlington, VA June 25-27, 2001. [5] Hac, A. and Simpson, M. D.: Estimation of Vehicle Side Slip Angle and Yaw Rate. Delphi Automotive Systems, 2000. [6] Crash Avoidance Metrics Partnership (CAMP): Enhanced Digital Mapping Project. Final Report, November 2004. [7] Lauffenburger, J. P., ”Contribution à la surveillance temps-réel du système Conducteur - Véhicule Environnement” : élaboration d’un système intelligent d’aide à la conduite, Thèse de l’Université de Haute Alsace, 2002.
