Energy Saving and Safe Driving Assistance System for Light Vehicles : Experimentation and Analysis

This paper presents an EDAS (Eco-Driving Assistance

System) to render a light vehicle low fuel consuming while being safe. A fuel consumption modeling, associated to a speed/gear optimization module, is proposed and used to compute the optimal speed profile and gear ratio to inform the driver in order him to eco-drive. An HMI module is presented and the driver behavior is analyzed face to the indications given by this HMI: are the optimal trajectories easy to be followed? Are the HMI outputs understandable and accepted by the driver? Does this HMI information improve the way of driving in terms of safety, low consumption and comfort? Several experimental results obtained with a prototype vehicle and several drivers are presented in order to evaluate the quality of this EDAS. The analysis deals with the gain obtained for the safety (speed overlaps, headway spacing, speed while approaching a road curve), consumption and covering distance aspects, by comparing a driving without any HMI and a driving with the use of the HMI with a given driver (several drivers have tested this EDAS for the analysis). The experimental results show that this kind of EDAS can save until around 10% of gasoline and more than 50% speed overlaps (compared to the legal speed).

Energy saving; Eco-Driving Assistance System (EDAS); Experimental application;

I.

INTRODUCTION

The sector of the road transports does not escape the trend consisting of not emitting too many main Green House Gas (GHG). It is the second largest CO 2 emitter with 6.6 Gt in 2008 [START_REF]How the energy sector can deliver on a climate agreement in Copenhagen[END_REF][START_REF]CO2 emissions from fuel combustion 2010 -highlights[END_REF]. Nowadays, electric and hybrid vehicles make their appearance, but several technical and technological limits induce still a long time before they will replace our conventional thermal / diesel vehicles. But these electric/hybrid vehicles represent a good alternative to reduce the dependence of our displacements to the fossil energies.

Thanks to the Automated Driving Assistance Systems (ADAS), a today light vehicle is now equipped with several embedded automated systems. These ADAS thus permit to the driver to be safe while improving his comfort. When the automobiles and parts sector appears as one of the main Green House Gas (GHG) transmitter, many efforts must be made to answer to the anti-polluting norms that are more and more restrictive.

One of the fast and low cost solutions consists of reducing the fuel consumption while acting on the changing of the driver behavior. The main objective is then to help the driver to globally adopt a more economical driving, what is more, a more ecological and safer driving. The system advises the driver in any way (speed display, alarms,... [START_REF] Van Der | A prototype fuel-efficiency support tool[END_REF]) via an HMI. But no active driving assistance system has been developed and commercialized yet. According to Evans (1979), a driver could reduce his fuel consumption by as much as 14% without increasing trip time, just by reducing acceleration levels and generally driving more "gently", combined with a skillful avoidance of stops. The experiment conducted by LIVIC lab. in the Versailles area, France, confirms a gain between 10 to 20% can be obtained by changing the driving style. This shows a great potential fuel saving of future actions that will make the driver be awake of economical and ecological driving. Some prototypes of fuel-efficiency tool support are presented through van der Voort et al. [START_REF] Barbé | Gerico : A human centered eco-driving system[END_REF]; Hellstrom et al. [START_REF] Hellstrom | A real-time fuel optimal cruise controller for heavy trucks using road topography information[END_REF]. These works are carried out in the context of the heavy vehicle. In the field of public transport, the PREDIT-ANR-ANGO project [START_REF] Nouveliere | Fuel consumption optimization for a city bus[END_REF] aims at designing a fuel-efficiency driving assistance system for a city bus. Optimal trajectories were computed with a known itinerary and on an exclusive right of way. There are some ADAS on the market like those issued from the GERICO project or from the eco-driving dashboard from HONDA. On the other side, several systems are based on the MDD concept (Modern Drive Devices). The main difference between them comes from the way to give the advice to the driver. The ADAS are able to send the information in realtime, adapted to the journey; the MDD methodology underlines the analysis and devices given to the driver once the journey is finished with some statistical tools in order the driver to improve his next journey.

In this paper, our approach is different from the already existing studies and technical solutions by its strategy used. This one takes into account both infrastructure characteristics and the current vehicle situation. To do that, a digital map containing the road geometry (slopes, curves,…) is used and the legal speed is known [START_REF] Nouveliere | Infrastructure based fuel consumption optimization of a vehicle[END_REF]. The headway spacing is measured and the vehicle longitudinal characteristics are also known [START_REF] Luu | Vehicle Speed Control For A Safety-Economical-Ecological Compromise : Development Of A Driver Assistance System[END_REF][START_REF] Luu | Towards a Safer Ecological Driver Aassistance System[END_REF]. Starting from these data, the problem of optimization of the fuel consumption is formulated and solved with a dynamic programming technique [START_REF] Luu | Dynamic programming for fuel consumption optimization on light vehicle[END_REF]. A real-time strategy is then adopted in order to render the system adaptive to the traffic conditions. A coupling between the safety problem and the low fuel consumption objective is thus reached. After some simulations on MATLAB/SIMULINK, this EDAS (Ecological Driving Assistance System) was tested on a prototype vehicle driving on a national road test track type. An HMI is used to transmit the device to the driver (optimal speed and optimal gear).The experimental results are shown. A first analysis of the economical gain is given.

II. NOMENCLATURE

The nomenclature in Table 1 is used all along the paper and defines the vehicle parameters.

B. Fuel Consumption Modelling

A consumption model developed in [START_REF] Luu | Modélisation de la consommation en carburant d'un véhicule léger à partir de données expérimentales[END_REF] is used The figure 1 shows that the estimation of the parameters of the consumption model ( 2) from experimental values of the fuel consumption for a light vehicle is not very high: less than 2.5% for the major part of the data, until less than 9% for the higher error.

IV. OPTIMIZATION MODULE

The proposed ADAS is based on a Dynamic Programming (DP) method used to calculate the optimal speed profile and the optimal gear ratio to be sent to the driver in real-time.

A. Fuel Consumption Optimization : Methodology

The fuel optimal control problem is formulated under its classical discrete form where

1 k k k k k k U N k N N N U X f J U X X J N k X J k 1 J m 1 N ( k N (3)
with the criterium J expressed as follows

SMOOTH Q T Q FC Q J . . . 3 2 1 Q Q Q
k x x x x k k k k v v A v v A SMOOTH Figure 2.
Optimal speed profiles and gear ratio versus weighed coeff. Qi.

The detailed methodology and an analysis of these results are given [START_REF] Luu | Dynamic programming for fuel consumption optimization on light vehicle[END_REF].

B. Safety Criterion

Two safety values are taken into account: legal speed and safe headway spacing. The legal speed along the trip is known and stored in the road mapping. It is considered as statics safety information. The safe spacing is a dynamics information depending on the speeds of following and preceding vehicles. The 2s safe headway time (French law, 2001) must be respected by the EDAS. A safety margin is calculated and integrated in the optimization module as shown on the figure 3. A fuzzy approach is developed in [START_REF] Luu | Towards a Safer Ecological Driver Aassistance System[END_REF] to obtain the safety margin and the consequence on the optimization module. The figure 4 gives an example of the results obtained with such an EDAS where one can easily see an economical situation (green circle) and a safe situation (red circle).

In the following, this EDAS is implemented on a prototype light vehicle. An HMI was studied and is presented with an analysis about the driver perception. The HMI module was conceived with the use of the Qt library in C++. As it is presented on the figure 5, the current vehicle speed is displayed by the black needle. The white triangle on the circular contour shows the optimal speed from the optimization module. The contour of the speedometer is coupled to a colored code If the difference between the optimal speed computed by the optimization module and the current speed stays in the definite slot (a margin on either side of the optimal speed), the contour is green.

V. HUMAN-MACHINE INTERFACE MODULE

If the optimal speed is superior to the current speed, the contour is blue.

If the optimal speed is inferior to the current speed, the contour is red.

This HMI part permits to know the current driver behavior. In order to add a quantitative perception of the difference between both speeds, a colored shaded off is used.

A small window on the right of the speedometer indicates the current gear ratio. The same colored code is used for it on the up/down arrows ("up" to engage the next up gear ratio, "down" to downshift). With these displays, an immediate information feedback can be given to the driver and the EDAS can propose to him the speed and the gear ratio to be reached.

Besides, the information related to the safety aspect seems to be interesting to show to the driver that the sent data are reliable. That is the reason why a road sign was added and is reflected in an indication relative to the legal speed on the speedometer.

A 150 m journey is then built on the bottom of the screen, with the follower vehicle displayed at the beginning of this journey. The preceding vehicle is at the headway spacing from the follower vehicle. The length of both parallel black lines on the displayed road represent the safe headway spacing (2s headway time). With this information, the driver knows the safety context in which he is evolving. When the vehicle becomes too closely from the preceding vehicle, a new road sign is displayed to give an alert to the driver (a sound bip can accompany this road sign).

When a particular event occurs not manageable by the HMI module, this one is at the moment desactivated, but when the event disappears, the driver automatically receives the new information from the HMI.

VI. VEHICLE IMPLEMENTATION

A. Vehicle Equipment

For our tests, two vehicles are used: a follower vehicle which is a RENAULT Clio Eco2 and a preceding vehicle equipped with a wifi system, a GPS receiver and an on board computer.

In each vehicle, an on-board computer executes the different processing. The preceding vehicle receives the GPS data, its longitudinal speed, its longitudinal acceleration and its covered distance thanks to the odometer of the follower vehicle. The follower vehicle uses its one to manage all the processing of data acquisition, searching the vehicle positions on the digital map, computing the optimal trajectories, transmitting the outputs to the driver via the HMI module. The data transfer from one vehicle to the other is achieved by a wifi connecting channel. Each vehicle has a GPS receiver. A map matching algorithm in the follower vehicle permits it to determine the position of both vehicles on the digital map. This one acquires some data from the CAN bus: speed, acceleration, covered distance, engine speed. The engaged gear ratio is rebuilt from the speed and the engine speed. A laser based radar measures the headway spacing that permits to obtain the relative speed.

B. Test Scenarios

The tests are achieved with 8 voluntary drivers distributed onto 2 phases: P1: two drivers drive under a free circulating (no traffic constraint), in order to validate the fuel economy effect. Only the legal speed is considered as a safety constraint. P2: six drivers drive the same vehicle on the same itinerary but with a preceding vehicle (safe headway spacing), to take into account the traffic conditions.

Each driver must realize two different itineraries with two passing on each. The first two passing are covered without the EDAS, and it is demanded to the driver to make some effort about his eco-driving style. During their two last passing, the HMI display is offered to the driver. The objective is to see if the EDAS will bring a fuel gain compared to the eco-driving rules.

P1 Phase. Regarding the driver B on the Table 2, he obtains a 1.8% economical gain. The driver M achieved a 9.7% economical gain. One can note that the driver B did not have a very high gain, compared to the driver M. How to convince the driver B to use this EDAS? On this same Table, the trip time increased of around 8% with the HMI, thus the question is: is it acceptable by the driver? In a accident gravity point of view, it can be viewed as a way to reduce the average speed thus to decrease the number of accidents.

The Table 3 shows that the use of the HMI brings a very very high gain in respecting the legal speed even with the driver B, it is another one of the advantages of this EDAS. The figure 8 presents the speed and engine torque profiles of the driver B on a 2.5km journey, with two passing (with and without HMI). A negative value of the torque corresponds to the use of the engine braking. The pink plot is the engine brake use: when "0", there is no brake. When there is the first legal speed changing, the driver begins to use the engine braking at the same moment on both trips. If we compare both trips with and without the HMI, one can see that without the HMI, the speed profile is always up to the one with the HMI. The reason is the following: as the EDAS has an electronic horizon, it can anticipate on the different events to be coming, contrarily to the driver without the HMI. By this way, the HMI advice being anticipative, the driver can also anticipate his action by following the HMI output, at some moments where the eco-driving rules can be difficult to be applied without an indication like with an electronic horizon.

Furthermore, for the driver B, the engine braking is used at 29.96% of the total time during his two first passing face to 26.25 on his two last passing. This means that the engine braking can create an influence on the fuel consumption but it is not a dominant variable. P2 Phase. Now, the traffic conditions are taken into account. Considering the Table 4, all the drivers induce a fuel economy just by following the instructions of the HMI. This gain varies from 1.6% to 12.9%, in function of the considered driver. These gains begin to be significative for several drivers. Besides, without the HMI, all the drivers had made some efforts to eco-drive by applying the rules. So when we compare both experiences (with and without HMI), the gains are supposed a few larger than the ones given in the Table 4. The fuel consumption average of all the drivers without the HMI is 6.61 l/100km. With the HMI, it is 6.12 l/100km. The obtained fuel economy is then 7.55%, what is the more, in real traffic conditions. In real traffic conditions, it can be noted that, in a safety point of view, the gains are quite high with the use of the ADAS. Table 5 shows the percentage of legal speed overshoots for all the drivers with and without HMI and computes the resulted gain between both situations. One can note the high gains and the diversity among the drivers.

VII. CONCLUSION

An Ecological Driving Assistance System is presented in its experimental phase. From the vehicle and fuel consumption modeling, consumption optimization, a HMI module is developed in order to test this EDAS and evaluate the gains obtained in terms of economy, ecology and safety. After several experimental tests with 8 different drivers, the results permit to affirm that the conception of EDAS is promising, by obtaining around 9 to 12% fuel gain while improving the safety aspects.

θ

  Road slope (rad)III. VEHICLE AND CONSUMPTION MODELLINGA. Vehicle ModellingA non slip longitudinal vehicle model is used to simulate the optimization module in order the vehicle to low fuel consume

Figure 1 .

 1 Figure 1. Estimation error of the fuel consumption.

  control input which gathers the engine torque and the gear ratio. The DP method is then written )

  and T is the trip time.SMOOTH is the penalty induced by a speed change. It is tuned 1

Figure 3 .

 3 Figure 3. Safety / Optimization modules structure (PV/FV:Preceding/Follower Vehicles).

Figure 4 .

 4 Figure 4.Optimal profiles with Q1=Q2=Q3=1.

Figure 5 .

 5 Figure 5. HMI for the proposed EDAS.

Figure 6 .

 6 Figure 6. Different HMI scenarios.

Figure 7 .

 7 Figure 7. Vehicles equipment.

Figure 8 .

 8 Figure 8. Speed and engine torque profiles of driver B: use of engine braking.

Figure 9 .

 9 Figure 9. Speed and headway spacing for several drivers under traffic conditions.

TABLE II .

 II TESTS WITHOUT ANY TRAFFIC CONSTRAINT.

			Legal Speed Overshoots (%)
	Driver	Trip Time (s)	Covered Distance (m)	Cumulated Consumption (l)	Middle Consumption (l/100km)
	B without HMI	651	10624	0.6263	5.8944
	B with HMI	710 (+8.31%)	10633	0.6151 (-1.79%)	5.7851 (-1.85%)
	M				6.724
	without	630	10667	0.7160
	HMI
	M with HMI	691 (+8.83%)	10674	0.6465 (-9.71%))	6.0566 (-9.93%)

TABLE III

 III

		.	LEGAL SPEED OVERSHOOTS
	Driver	Legal Speed Overshoots (%) Without HMI With HMI	Gain (%)
	B	18.3	3.38	-79.23
	M	21.3	7.11	-66.62

TABLE IV .

 IV T ESTS WITH THE PRECEEDING VEHICLE (IN TRAFFIC CONDITIONS).

	Driver	Trip Time (s)	Covered Distance (m)	Cumulated Consumptio n (ml)	Middle Consumptio n (l/100km)
	D without HMI	683.13	10708.5	0.7314	6.8297
	D with HMI	707.04 (+3.5%)	10710.6	0.7007 (-4.19%)	6.5423 (-4.2%)
	S without HMI	662.24	10666.8	0.7910	7.4152
	S with HMI	686.78 (+3.7%)	10675.3	0.6914 (-12.6%)	6.4760 (-9.1%)
	F without HMI	712.97	10688.8	0.7672	7.1770
	F with HMI	768.33 (+7.7%)	10689.0	0.6706 (-12.59%)	6.2734 (-12.59%)
	G without HMI	642.43	10679.2	0.6674	6.2490
	G with HMI	730.81 (+13.76)	10700.0	0.6186 (-7.3%)	5.7809 (-7.35)
	A without HMI	684.78	10693.4	0.6459	6.0404
	A with HMI	781.58 (+14.13 %)	10709.4	0.6182 (-4.2%)	5.77287 (-4.6%)
					Driver	Trip Time (s)	Covered Distance (m)	Cumulated Consumptio n (ml)	Middle Consumptio n (l/100km)
					C without HMI	678.92	10693.7	0.6410	5.9946
					C with HMI	715.60 (+5.4%)	10669.0	0.6307 (-1.6%)	5.9117 (-1.36%)

TABLE V .

 V L EGA L SPEED OVERSHOOTS IN TRAFFIC REAL CONDITIONS.

	Driver	Legal Speed Overshoots (%) Without HMI With HMI	Gain (%)
	B	18.3	3.38	-79.23
	C	13.71	9.24	-32.6%
	D	5.67	4.17	-26.4%
	S	9.34	9.3	-0.42%
	F	6.33	2.35	-62.8%
	G	18.87	5.02	-73.39%
	A	9.35	3.76	-59.78%

This work is supported by the ANR (French National Research Agency) VTT program, and developed in the ANR VTT ABV (Low Speed Automation) research project (2009-2013).

ACKNOWLEDGMENT

This work is supported by the ANR (French National Research Agency) VTT program, and developed in the ANR VTT ABV (Low Speed Automation) research project (2009)(2010)(2011)(2012)(2013). The validation of this system is going to be validated within the EU FP7 ecoDriver project.


André Benine-Neto

Saïd Mammar

Piecewise affine output

I. INTRODUCTION

The development of autonomous vehicles has increased attention of researchers in the recent years. An overview of these activities is presented in [START_REF] Shladover | Path at 20 -history and major milestones[END_REF]. Regarding vehicle lateral control, it can be noted that the research has evolved from automated lane keeping in which the lateral accelerations are generally low (see [START_REF] Rosseter | Lyapunov based performance guarantees for potencial field lane keeping assistance system[END_REF] and [START_REF] Minoiu-Enache | Assistance active de prévention des sorties de voie. prise en compte des virages[END_REF]) to more recent work which deals with the control of the vehicle in extreme dynamics to avoid accidents ( [START_REF] Mammar | Lane keeping automation at tire saturation[END_REF] and [START_REF] Benine-Neto | Piecewise affine state feedback controller for lane departure avoidance[END_REF]). For that, it is required to develop systems that are able to operate in the complete domain of tire forces, including the nonlinear behavior, as many accidents occurs due to the vehicle loss of control when the tire forces are saturated.

The lane keeping assistance system (LKAS) presented in [START_REF] Mammar | Lane keeping automation at tire saturation[END_REF] takes into account the nonlinear behavior of the lateral tire forces for the design of a parallel distributed controller based on a Takagi-Sugeno model. In [START_REF] Benine-Neto | Piecewise affine state feedback controller for lane departure avoidance[END_REF] a Piecewise Affine (PWA) state feedback controller is developed to avoid the tire saturation on the lane departure avoidance maneuvers.

PWA systems have also been used in the development of other driver assistance systems. In [START_REF] Borrelli | A Hybrid Approach to Traction Control[END_REF] the longitudinal tire forces are approximated by PWA functions for a traction control system. The lateral tire forces have also been considered in PWA form to design yaw rate controllers in [START_REF] Bernardini | Driveby-wire vehicle stabilization and yaw regulation: A hybrid model predictive control design[END_REF], [START_REF] Benine-Neto | Vehicle yaw rate control based on piecewise affine regions[END_REF] and [START_REF] Palmieri | Constrained robust design of lateral vehicle dynamics control systems[END_REF].

In this paper, similar approximations of the lateral tire forces are used to design an output-feedback PWA controller for a LKAS, which is able to operate in the entire domain of the tire forces. As an extension of the work presented in [START_REF] Benine-Neto | Piecewise affine state feedback controller for lane departure avoidance[END_REF], the measurement of the vehicle sideslip angle requires sensors that are not available in currently commercialized vehicles, therefore an estimator is designed to drive the switches of the PWA controller. Following the results obtained in [START_REF] Rodrigues | Observer based control of piecewise-affine systems[END_REF], the control synthesis is casted as a Bilinear Matrix Inequality (BMI) optimization problem which is solved using the V-K method. This interactive procedure allows the BMI to be transformed into two Linear Matrix Inequalities (LMI) optimization problems which can be solved more efficiently to find simultaneously the output feedback gain and a Piecewise Quadratic Lyapunov (PWQL) function that ensures stability of the closed loop system. The vehicle model for control synthesis is described in Section II, followed by the controller design shown in Section III. The simulation results obtained on a nonlinear model are presented in Section IV. Section V wraps up the work and provides some perspective for the future work.

II. VEHICLE MODEL

In order to design the control law for the LKAS, a PWA system is derived from a simple nonlinear vehicle model, in which the lateral translational and yaw motions are considered and the roll and pitch motions are neglected. The wheels of the front and rear axles are lumped into one located at the axle center leading to a bicycle model. The equations describing this model are given by:

mv( β + r) = f sf + f sr J ṙ = l f f sf -l r f sr , (1)
where the involved variables consist of the vehicle yaw rate, denoted r and the vehicle sideslip angle, β. Concerning the fixed parameters for the model, v represents the longitudinal vehicle speed, m is the vehicle mass, l f (l r ) is the distance from the front (rear) axle to the center of gravity (CG), J is the vehicle inertia with respect to the vertical axle through the CG. All numerical values of these parameters are presented in Table I. The lateral forces f sx , with x = f, r, for the front and rear tires can be modeled according to the Pacejka tire model [START_REF] Pacejka | Tire and Vehicle Dynamics[END_REF]:

f sx (α x ) = D x sin(C x atan((1-E x )B x α x +E x atan(B x α x ))), (2)
where α x stands for the front (rear) tire sideslip angle. Considering that the angles remain small, the sideslip angles for front and rear tires are given by:

α f = δ f -β - l f r v , α r = -β + l r r v , (3)
where δ f is the steering angle. The Pacjeka tire model is depicted by the solid line in Fig. 1.

The simple nonlinear model [START_REF] Ackermann | Robust Control[END_REF] shows, as well known in literature (see for example [START_REF] Ono | Bifurcation in vehicle dynamics and robust front wheel steering control[END_REF]), a limited stability region which also depends on the driver steering wheel angle, two unstable equilibrium points and a stable one (bifurcation analysis). The causes of the instability are due to the nonlinear behavior of the tire-road forces which are taken into account in the PWA vehicle model described below.

A. Piecewise affine approximation of lateral tire forces

Considering that the front and rear tire forces described by (2) are approximated by the following PWA functions:

f sf (α f ) = e f i + d f i α f f sr (α r ) = e ri + d ri α r (4)
where d f i , d ri , e f i and e ri depend on the front and rear tire forces and the index (i) corresponding to the partitioning of the tire force domain, based on the tire sideslip angles, as illustrated by the dotted lines on Fig. 1 for the front wheel.

For the region containing the origin (i = 2), a simple linear approximation is considered, in this case d f 2 = c f , d r2 = c r , e f 2 = 0, and e r2 = 0. The cornering coefficients are related to the Pacejka parameters as

; cf = B f C f D f , and c r = B r C r D r .
Replacing the PWA approximation of lateral tire forces (4) in the vehicle model (1) leads to the PWA system:

ẋd = A d i x d + B d i u + a d i , (5)
with the corresponding dynamics:

A d i = - d f i +dri mv -1 - d f i l f -drilr mv 2 drilr -d f i l f J - d f i l 2 f +dril 2 r Jv , (6)
B d i = d f i mv d f i l f J , a d i = e f i +eri mv e f i l f -erilr J . ( 7
)
where the control input is the front wheel steering angle u = δ f and the state variables are the vehicle sideslip angle, β and the vehicle yaw rate, r,

x d = [β, r] T .
Even though this approximation can be refined, it is shown in the simulation section that improved performance can be obtained by simply approximating the tire forces with the proposed PWA functions.

B. Additional dynamics for lane keeping

For lane keeping purposes, the model ( 5) has to be expanded with the dynamics of the relative yaw angle and the lateral displacement with respect to the lane centerline. These measurements are provided by a video sensor. Let ψ L = ψ -ψ d be the yaw angle error which is the angle between the vehicle orientation and the tangent to the road. The road reference curvature ρ ref is defined by ( ψd = vρ ref ), and the following equality can be derived:

ψL = r -vρ ref . (8)
Denoting by l s the look-ahead distance, the equation giving the evolution of the measurement of the lateral offset y L from the centerline at sensor location is obtained by

ẏL = v(β + ψ L ) -l s r. (9)
Equations ( 8) and ( 9) are included in system (5) and the PWA system describing the vehicle dynamics and positioning is described by:

ẋp = A p i x p + B p i u + B p ρ ρ ref + a p i ( 10
)
where x p = [β, r, ψ L , y L ] T and

A p i =   A d i 0 0 0 1 0 0 v l s v 0   , B p i = (B d i ) T 0 0 T , B p ρ = 0 0 -v 0 T , a p i = (a d i ) T 0 0 T . (11)
An illustration of the state variables is provided in Fig. 2 III. CONTROL STRATEGY

The algorithm presented in [START_REF] Rodrigues | Observer based control of piecewise-affine systems[END_REF] is applied for the design of the proposed LKAS. It provides an efficient procedure for designing a PWA output feedback controller, by means of a BMI optimization procedure, based on the search of a PWQL function.

According to (3), the partitions defined by the front wheel sideslip angles, α f =±ᾱ f , depend on the state variables and control input. As mentioned in [START_REF] Rodrigues | Observer based control of piecewise-affine systems[END_REF] the switching between the regions should depend only on the state x, so models in which there is a feed-through from u to a nonlinearity should be avoided. This can be done by the inclusion of a first order actuator which is also useful to enforce continuity of the control input at the boundaries. Therefore, the steering angle is included as an additional state to the system as follows:

δf = -τ δ f + u c , (12)
where u c becomes the control input of the augmented plant and τ = 10.

As most vehicles have understeering behavior, it is assumed that the front tire forces tend to saturate firstly, therefore only the front tire forces are approximated by PWA functions according to (4), and a simply linear approximation is assumed for the rear tires. Nevertheless, an analogous approach can be considered in order to design assistances for oversteering vehicles.

Disturbances and exogenous inputs, such as the road curvature, are not taken into account in the control synthesis, therefore the PWA model describing the vehicle dynamics, positioning [START_REF] Ono | Bifurcation in vehicle dynamics and robust front wheel steering control[END_REF] and first order actuator (12) can be written as:

ẋ = A i x + B i u + a i , y = C i x (13)
with x = [β, r, ψ L , y L , δ f ] T and y is the system output. The matrices defining the dynamics are:

A i = A p i B p i 0 0 0 0 -τ , B i = 0 0 0 0 τ T , a i = (a p i ) T 0 T , (14)
Since the vehicle sideslip angle is not available for measurement, the matrix defining the system output y is given by:

C i =     0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1     . ( 15
)
Each of the regions R i (with i = 1, 2, 3) can be described as the intersection of the half spaces:

R i = {x|H T i x -g i < 0} (16)
Since these regions are slab, it is preferred to express them as degenerated ellipsoids, as suggested in [START_REF] Rodrigues | Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization[END_REF] and [START_REF] Rodrigues | Observer based control of piecewise-affine systems[END_REF], because they describe exactly the slab regions and it often requires fewer parameters than the polytopic description [START_REF] Shladover | Path at 20 -history and major milestones[END_REF].

The degenerated ellipsoids can be described by:

||E i x + f i || 2 ≤ 1 ∀x ∈ R i , (17)
and if R i = {x|d < c T i x < d} then the degenerated ellipsoid is described by d-d), as shown in [START_REF] Rodrigues | Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization[END_REF].

E i = 2c T i /( d-d) and f i = -( d+d)/(
For the PWA system (13), the ellipsoids describing the slab regions are: The ellipsoidal cell description is used to relax the constraints when searching the PWQL function. In order to ensure the continuity of the PWQL function across the boundaries, a parametric boundary description is needed [START_REF] Hassibi | Quadratic stabilization and control of piecewise-linear systems[END_REF].

E T 1 = [-1, - l f v , 0, 0, 1] 2 -ᾱf -d , f 1 = - -ᾱf +d -ᾱf -d , E T 2 = [-1, - l f v , 0, 0, 1] 1 ᾱf , f 2 = -ᾱf -ᾱf ᾱf + ᾱf = 0, E T 3 = [-1, - l f v , 0, 0, 1] 2 d-ᾱf , f 3 = - d+ ᾱf d-ᾱf , (18)
Each facet boundary between the neighboring regions R i and R j is contained in the hyperplanes described by:

{x|c T ij x -d ij = 0}. ( 19
)
an the boundary parametric description can be obtained by:

Ri ∩ Rj ⊆ {x|l ij + F ij s|s ∈ R n-1 } (20)
where F ij ∈ R n×n-1 (full rank) is the matrix whose columns span the null space of c ij , and 13) the parametric description of the boundaries is given by:

l ij ∈ R n is given by l ij = c ij (c T ij c ij ) -1 d ij For the LKAS model (
F 1,2 =       1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 l f v 0 0       , F 2,3 =       1 0 0 - l f v 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0       , l 1,2 = ᾱf 2+l 2 f /v 2 , ᾱf l f /v 2+l 2 f /v 2 , 0, 0, -ᾱf 2+l 2 f /v 2 , l 2,3 = -ᾱf 2+l 2 f /v 2 , -ᾱf l f /v 2+l 2 f /v 2 , 0, 0, ᾱf 2+l 2 f /v 2 . ( 21
)
A. PWA Output-feedback control synthesis Due to the symmetry of the lateral tire forces with respect to the origin, only regions R 1 and R 2 are considered in the control synthesis. The same gains obtained for region R 1 can be applied for region R 3 .

The goal is to stabilize (13) with a PWA dynamic controller with state space representation of each region of the form:

ẋc (t) = A ci x c + L i y + b ci u = K i x c + m i (22)
An augmented state x = [x, x c ] T is defined, so the closed loop system can be written as:

ẋ = Ãi x + bi (23)
where;

Ãi = A i B i K i L i C i A ci and bi = b i + B i m i b ci (24)
The PWQL function for the augmented system (23) has the form:

V i (x) = xT Pi x + 2q T i x + ri . ( 25
)
where

Pi = P T i , Pi ∈ R 2n×2n , qi ∈ R 2n and ri ∈ R. V i (x) is a Lyapunov function with a decay rate α i , for the region R i if, for a fixed ǫ ≥ 0, x ∈ R i , V i (x) > ǫ||x -x eq || 2 d dt V i (x) < -α i V i (x), (26)
where x eq is the equilibrium point of the closed loop system. Under strong lateral solicitations, the controller should bring the vehicle to the condition where the tire forces behavior is linear (R 2 ). In order to do so, the desired equilibrium point of the closed loop system is placed at the origin (x eq = 0). The equilibrium point must also be the extrema of the Lyapunov function candidate for the corresponding region (see [START_REF] Rodrigues | Observer based control of piecewise-affine systems[END_REF]). In consequence, q 2 = 0 2n×1 and r 2 = 0 to ensure that V (0) = 0.

As the closed loop system has a single equilibrium point, the equilibrium points of R 1 , denoted x eq1 and R 3 , x eq3 , must not be contained in its own region, enforcing a transition through the boundaries with R 2 . This can be done using the constraint:

Ãi

x eqi + bi = 0. ( 27
)
The stability of system (23) can be guaranteed by Sprocedure [START_REF] Boyd | Linear Matrix Inequalties in System and Control Theory[END_REF], using the ellipsoidal cell description (17) on conditions (26), if there exists Pi = P T i ≻ 0, and positive constants λ 1 and γ 1 that satisfy:

                P1 -ǫI n + λ 1 ẼT 1 Ẽ1 q1 + ǫx eq + λ 1 ẼT 1 f 1 * r1 -ǫx T eq x eq +λ 1 (f T 1 f 1 -1)    ≻ 0 P2 -ǫI n ≻ 0 (28)                     ÃT 1 P1 + P1 + Ã1 -γ 1 ẼT 1 Ẽ1 + α 1 P1 P1 b1 + ÃT 1 q1 -γ 1 ẼT 1 f 1 + α 1 q1 * 2 bT 1 q1 + α 1 r1 -γ 1 (f T 1 f 1 -1)      ≺ 0 ÃT 2 P2 + P2 + Ã2 + α 2 P2 ≺ 0 (29) where * means transposed and Ẽi = [E i , 0].
The parametric description of the boundaries (21) are adjusted to the augmented system as:

Fij = F ij 0 0 I and lij = l ij 0 (30)
so that the continuity of the PWQL function candidate is ensured by:

     F T 12 ( P1 -P2 ) F12 = 0 F T 12 ( P1 -P2 ) l12 + F T 12 q1 = 0 lT 12 ( P1 -P2 ) l12 + 2q T 1 l12 + r1 = 0 (31)
The switches of the controller can be driven only by the system outputs, therefore controller has to be designed with the structure of a regulator and an estimator. Thus, the front wheel sideslip angle must be computed with the estimate of the vehicle sideslip angle and the measurements of yaw rate and steering angle, according to [START_REF] Benine-Neto | Vehicle yaw rate control based on piecewise affine regions[END_REF]. For that, the following constraints is added:

A ci = A i + B i K i -L i C i b ci = B i m i + b i + (A i -L i C i )x eq (32)
Defining a performance criterion as: J = min i α i , The goal is to find A ci , K i L i , m i , b ci , and a a PWQL function (25) that maximize the performance criterion J. This optimization problem can be cast as a BMI as:

max min i α i
such that: (27), (28), (29), (31), (32),

ǫ > 0 γ 1 > 0 λ 1 > 0 α 1,2 > l 0 > 0 -l 1 < K i < l 1 -l 2 < m i < l 2 (33)
where l 0 is a scalar bound, l 1 and l 2 are vector bounds.

B. Solution of BMI optimization problem

The BMI problem (33) was solved using the V-K method, in which LMIs are solved in an iterative fashion. For that, the equilibrium point of the dynamics corresponding to the affine region x eq1 , is chosen a-priori, such that it is not located in R 1 . For the specific lane keeping problem, the algorithm becomes.

V-step: Given a fixed controller, and a fixed α i , solve:

Find: P 1 , q 1 , r 1 and P 2 , such that: (31), ( 28), (29),

ǫ > 0, γ 1 > 0, λ 1 > 0, (34)
K-step: For P 1 , q 1 , r 1 and P 2 fixed at the previous step, solve: max min i α i such that ( 27), ( 28), ( 29), (32),

ǫ > 0, γ 1 > 0, λ 1 > 0, α 1,2 > l 0 > 0, -l 1 < K i < l 1 , -l 2 < m i < l 2 , (35)
For each iteration of the K-step, the decay rates α 1 and α 2 must be greater than the value computed at the previous iteration. The loop must be repeated until there is no significant improvement on the cost or the LMIs become infeasible.

To design the initial controller for the first iteration on the V-step, it was supposed that all the state variables are available for measurement. A state feedback only for R 2 was computed using the algorithm from [START_REF] Minoiu-Enache | Assistance active de prévention des sorties de voie. prise en compte des virages[END_REF], and the gain for the observer was computed by pole-placement such that its poles are 10 times faster than the closed loop of the state feedback. The regulator and estimator structure was obtained from (32), and the same structure was considered for R 1 and R 3 .

The resulting gains from the V-K method after 4 iterations are:

K 1 = [ -0.8505 -0.2780 -1.5037 -0.7683 -0.5072], K 2 = [ -0.7278 -0.3558 -1.7699 -0.9394 -0.8112], K 3 = K 1 , m 1 = -m 3 = 0.023, m 2 = 0 α 1 = 16.
IV. SIMULATION RESULTS

Simulation have been carried out on the Matlab/Simulink environment, in order to verify the performance of the PWA controller. The dynamics of the model used for simulation consists of nonlinear 4-wheels vehicle according to [START_REF] Ackermann | Robust Control[END_REF], which is considered to capture the essential vehicle lateral steering dynamics:

m( vy + rv) = f sf cos δ f + f sr J ṙ = l f f sf cos δ f -l r f sr (37)
where v y is the lateral velocity, and the lateral forces are given by [START_REF] Benine-Neto | Piecewise affine state feedback controller for lane departure avoidance[END_REF]. The sideslip angles α f,r are given by:

α f (lef t) = δ f -arctan vβ+rl f v-a 2 r α f (right) = δ f -arctan vβ+rl f v+ a 2 r α r(lef t) = -arctan vβ-rlr v-a 2 r α r(right) = -arctan vβ-rlr v+ a 2 r (38)
The vehicle model has been submitted to the obstacle avoidance maneuver defined in ISO 3888-2 standard, at a constant longitudinal velocity of v = 21m/s. Fig. 3 shows the displacement of the vehicle within the area delimited by the cones, confirming that the maneuver was successfully achieved.

It can be seem from Fig. 4 that the vehicle reaches the nonlinear behavior of tire lateral forces, overshooting the The control input required to perform the maneuver, as well as the corresponding steering angle are depicted respectively in the upper and bottom subplots of Fig. 5.

The vehicle sideslip angle and yaw rate are shown in subplots of Fig. 6. The relative yaw angle and lateral offset at look-ahead distance, representing the vehicle positioning on the road are depicted in Fig 7 .   V. CONCLUSION In this paper the design and simulation of a PWA controller for LKAS has been described. The nonlinear behavior of the lateral tire forces are approximated by PWA functions. As only understeering vehicles are considered in this work, the regions describing the PWA vehicle model can be exactly described as degenerated ellipsoids which are used to relax the conditions for the existence of a PWQL function. The simultaneous search of a PWQL function and a PWA observer based output-feedback gain has been casted as a BMI optimization problem and its solution has been computed using the V-K method in which the BMIs are transformed into two LMI optimization procedures that have been solved iteratively. The resulting PWA controller has been tested according to the double lane change standard maneuver ISO-3888-2, showing that the PWA controller can handle the nonlinearity of the tyre lateral force. The switches are based on the state estimation, avoiding measurement of the vehicle sideslip angle, which requires a sensor that is not available in currently commercialized vehicles and are also very costly.

System robustness with respect to parameter variations, as for example vehicle longitudinal speed and load transfers should be taken into account in the future work as well as implementation on prototype vehicle.

Fig. 1 .

 1 Fig. 1. Front tire forces described by the Pacejka magic formula and corresponding PWA approximations and partitions.

Fig. 2 .

 2 Fig. 2. Single track vehicle model.

  where d and d can be arbitrarily set, such that d < -ᾱf and d > ᾱf .

2349 and α 2

 2 = 14.8648.

Fig. 3 .

 3 Fig. 3. Displacement of the vehicle equipped with PWA output-feedback controller in standardized maneuver ISO-3888-2.

Fig. 4 .

 4 Fig. 4. Active region for PWA control and front wheels estimated sideslip angle

Fig. 5 .

 5 Fig. 5. Control input and Steering angle for vehicles with PWA controller

Fig. 6 .Fig. 7 .

 67 Fig. 6. Vehicle dynamics response

TABLE I VALUES

 I OF THE VEHICLE PARAMETERS.

	Parameter	Value
	c f , front cornering stiffness	40000 N/rad
	cr, rear cornering stiffness	35000 N/rad
	l f , distance form CG to front axle	1.22 m
	lr, distance form CG to rear axle	1.44 m
	ls, look-ahead distance	0.95 m
	m, total mass	1600 kg
	J, vehicle yaw moment of inertia	2454 kgm 2
	v, longitudinal velocity	17 m/s

IFSTTAR -LIVIC, 14 Route de la Minière, 78000 Versailles, France (andre.benine-neto@ifsttar.fr)3 IBISC -EA 4526 UEVE, 40 rue du Pelvoux CE1455, 91020, Evry, Cedex, France (e-mail: said.mammar@inrets.fr)


Lydie Nouveliere

Ifsttar Im -Livic

Qi Cheng

Olivier Orfila

ECO-DRIVING ASSISTANCE SYSTEM: A NEW WAY OF HOW TO SAVE ENERGY

Keywords: Eco-Driving Assistance System (EDAS), CO2, emissions, driver support, low carbon vehicles, vehicle modeling, optimization

The work developed in this paper is realized within the ecoDriver EU FP7 project that is shortly presented in the first part of the paper. Among the several main objectives underlined by this project, one consists in developing a vehicle and energy consumption model to be validated and then used to help the driver to better drive in terms of consumption and safety, advised by a HMI (Human-Machine Interface) module. Several experimental results are shown to illustrate the obtained energy saving with such an EDAS and the legal speed respect.

INTRODUCTION

In 2005 in France, 553 million tons of greenhouse gas (GHG) were emitted, thus decreasing the French crude emissions of 2% between 1990 and 2005. But in the same time, the emissions due to the transportation have increased by 22%, and the transport represents one third of the total energy consumption. The governmental objective consists in reducing by 20% the energy consumption and the greenhouse emissions in the transports by 2020. The fuel consumption is responsible for 35% of the nation-wide emissions of CO 2 . The main GHG effect of rejections increases because of the strong raise of displacements (ADEME source, France). Besides, because of the high oil prices/economical crisis and the stakes of the greenhouse effect reduction, more and more vehicle drivers look for a low energy consumption behavior. The economical-ecological way of driving (eco-driving) is a citizen driving behavior, which allows to reduce the energy consumption up to 15%, limiting the GHG effect responsible for the climatic warming, and to decrease the risk of accidents (by 10 to 15%).

Over the last few years, the French government has then incited the cars and trucks manufacturers and vehicle equipment manufacturers to bring some new concepts in vehicles development and their associated accessories (climate systems, rain sweeps,…) in such a way that these systems will consume less and less. The French National Agency for the research also support the ABV project (low speed automation) for the development of new ADAS (Advanced Driving Assistance Systems) that will be safer and low energy consuming. In that sense, the European Union (EU) underlines this run-up through several EU research projects: HAVEit [START_REF]HAVEit EU FP7 Project[END_REF], eFuture [START_REF]eFuture EU FP7 Project[END_REF] or ecoDriver [1]. This paper shortly presents the EU ecoDriver project (FP7), by insisting on the energy optimizing part. The principles of modeling the energy consumption are based on the calculation of the energy consumption (fuel, electricity) for a given traffic on a given road network.

Low energy consumption strategies and low emissions systems would require models, currently designed to follow the vehicles fleet behavior, able to characterize the fine kinematics variations of a single vehicle. Here an advisor system is presented, with some simulation and experimental results, for a light vehicle low consumption. The vehicle and consumption modeling are described with their inputs/outputs scheme. A first analysis in terms of obtained gain in consumption and legal speed respect is developed.

ECODRIVER PROJECT: PRESENTATION

The project ecoDriver -Supporting the driver in conserving energy and reducing emissions -addresses the need to consider the human element when encouraging "green" driving, since driver behaviour is a critical element in energy efficiency. The focus of the project is on technology working with the driver. The project aims to deliver the most effective feedback to drivers on green driving by optimizing the driver-powertrainenvironment feedback loop. It will carry out a substantial programme of work to investigate how best to win the support of the driver to obtain the most energy-efficient driving style for best energy use. Feedback coverage will include preview of the upcoming situation, optimizing the current driving situation as well as post-drive feedback and learning. The project will address this across a wide range of vehicles -e.g. cars, light trucks and vans, medium and heavy trucks and buses -covering both individual and collective transport, and will optimize feedback to drivers for both nomadic devices (smartphones, tablets) and built-in systems and compare the effectiveness of each. The project will evaluate HMIs and feedback to drivers via both nomadic devices and built-in systems and compare the effectiveness of each. In each case a range of HMIs and feedback styles will be assessed. The project aims to examine driving not only with present and near-term power trains but also with a full range of future vehicles, including various types of hybrid and plug-in electric vehicles. A comprehensive evaluation will be carried out both in the laboratory (a variety of driving simulators) and in real world driving in both the private and fleet contexts. Scenarios will be developed to assess the implications for the future effectiveness of green driving support. The target of ecoDriver is to deliver a 20% improvement in energy efficiency by autonomous means alone, which opens up the possibility of greater than 20% savings in combination with cooperative systems.

BUILT-IN SYSTEM IN A MANUAL TRANSMISSION CAR

Among the four test vehicles considered in the ecoDriver project for the powertrain model for green-driving, a middleclass passenger car with a conventional powertrain having at its disposal a manual transmission is chosen. The energy used is petrol and this test vehicle is already inserted in the commercial market and can be considered as a "man in the street" car (see Annex A for its description).

Introduction and main outputs of the model

A model will be used to compute an optimal speed profile and an optimal gear number to be followed by the driver if he wants to ecodrive "in the ecoDriver way". This driving assistance system is based on the knowledge of the incoming road cartography in its longitudinal and vertical axis. The model is built based on the vehicle dynamics (engine, gearbox, Differential, wheel, aerodynamic, road slope).

It has to be noted that the emissions will not be modeled, but an information feedback from the vehicle CAN bus can be made about the CO 2 emissions (as the estimated output of the CAN bus CO 2 internal model). The functional description of the powertrain model is presented on figure 1. The approach considers that from road and vehicle data, an optimal profile in terms of speed and gear number is computed and sent to the HMI module developed in the project, this one being in interaction with the driver. The ambition of the specified model is to combine safety requirements and fuel consumption reduction by optimizing the vehicle speed and the gear management. It then needs to know several kinds of data issued from the vehicle (speed, position, gear number), environment (longitudinal headway spacing), road (legal speed limitation, road geometrical attributes) to compute such an optimal profile.

Functional description of the model

The geometrical road attributes are interesting to compute a limit speed to enter a curve to be coming based on the curve geometry and the vehicle dynamics.

Model family

The vehicle model is based on the powertrain dynamics considering the different efforts interacting between the vehicle, the road and the environment. The fuel consumption is physically modeled from experimental data issued from the test vehicle (Annex A), under a physical relation.

Model parameters

Several parameters to be tuned are considered in the model : vehicle mass, wheel radius, wheel inertia, engine inertia, gearbox inertia, drag coefficient, rolling resistance, air mass density, differential ratio, gear ratios, gearbox efficiency, maximum engine torque (at given rpm), maximum power (at given rpm).

Model accuracy

The vehicle and fuel consumption models must be designed and tuned in order to obtain at the least a 1s refreshment of the HMI, this is coherent with the driver perception. Furthermore, the real-time constraint for the final experimental application in ecoDriver makes an electronic horizon use being compulsory. It will use the road data and the cartography.

On board auxiliaries

The only auxiliary taken into account in the model is the air conditioning in terms of spent power. This fuel consumption model was determined in comparison with the different models encountered in the literature [START_REF] Ahn | Microscopic fuel consumption and emission modeling[END_REF][START_REF] Ahn | Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration levels[END_REF][START_REF] Thomas | Developpement of second-bysecond fuel use and emissions model based on an early 1990s composite car[END_REF]. This relation is a function with the engine speed and the engine torque. Obviously, when the vehicle does not accelerate (engine braking), the engine torque is regarded as negative and only the engine speed is taken into account. In [START_REF] Luu | Modélisation de la consommation en carburant d'un véhicule léger à partir de données expérimentales[END_REF], it is shown that the estimation of the parameters of the consumption model ( 2) from experimental values of the fuel consumption for a light vehicle is not very high: less than 2.5% for the major part of the data. The figure 2 illustrates the experimental validation of this model with measured data.

Vehicle modeling TABLE I. NOMENCLATURE -VEHICLE PARAMETERS

Optimization Module

The proposed ADAS is based on a Dynamic Programming (DP) method used to calculate the optimal speed profile and the optimal gear number to be sent to the driver in real-time.

Fuel Consumption Optimization: Methodology

The fuel optimal control problem is formulated under its classical discrete form where

U k k k k k k N k N N N U X f J U X X J N k X J ))) , ( ( ) , ( min( ) ( 0 ... 1 for ) ( 1 (3)
with the criterium J expressed as follows

SMOOTH Q T Q FC Q J . . .

Safety Criterion

The legal speed and the safe headway spacing are two safety variables that are considered in this optimization module. The legal speed along the trip is known and stored in the embedded cartography and is regarded as a static safety information. The safe headway spacing is a dynamic out of the speeds of both following and preceding vehicles.

A safety margin is calculated and integrated in the optimization module as shown on the figure 4. A fuzzy approach is developed in [START_REF] Luu | Towards a Safer Ecological Driver Assistance System[END_REF] to obtain the safety margin and the consequence on the optimization module. The figure 4 gives an example of the results obtained with such an EDAS where one can easily see an economical situation (green circle) and a safe situation (red circle). This EDAS is then implemented on a prototype light vehicle (Annex A).

VEHICLE IMPLEMENTATION

For the EDAS tests, two vehicles are used: a follower vehicle which is a RENAULT Clio 3 Eco2 and a preceding vehicle equipped with a wifi system, a GPS receiver and an on-board computer.

In each vehicle, an on-board computer executes the different processing. In the preceding vehicle, it is the GPS data, its longitudinal speed, its longitudinal acceleration and its covered distance thanks to the odometer of the follower vehicle. The follower vehicle uses its one to manage all the data acquisition processing, looking for the vehicle positions on the digital map, computing the optimal trajectories, transmitting the outputs to the driver via an HMI module whose development will be a main part of the ecoDriver project. The data transfer from one vehicle to the other is achieved by a wifi connecting channel. Each vehicle has a GPS receiver. A mapmatching algorithm in the follower vehicle permits it to determine the position of both vehicles on the digital map. This one acquires some data from the CAN bus: speed, acceleration, covered distance, engine speed. The engaged gear ratio is rebuilt from the speed and the engine speed. A laser radar measures the headway spacing that permits to obtain the relative speed.

Tests Objectives Such a suggestive system efficiency highly depends on the driver reactions. It is then obvious to make several drivers driving in different ways in order to collect their first impression.

A free circulating scenario is proposed to these drivers to know their way of driving. Following this one, traffic conditions are added to take into account the safe headway (simulated by the preceding vehicle behavior in acceleration). The evaluation is then oriented into 3 directions: environmental (potential economical gain), mobility (trip time) and safety (improvement).

Tests scenarios

Eight voluntary drivers have realized the following scenarios distributed on 2 phases: PH1: two drivers drive under a free circulating (no traffic constraint), in order to validate the fuel economy effect. Only the legal speed is considered as a safety constraint. PH2: six drivers drive the same vehicle on the same itinerary but with a preceding vehicle (safe headway spacing), to take into account the traffic conditions.

Each driver must realize two different itineraries with two passing on each. The first two passing are covered without the EDAS, and it is demanded to the driver to make some effort about his eco-driving style. During their two last passing, the HMI display is offered to the driver. The objective is to see if the EDAS will bring a fuel gain compared to the eco-driving rules.

PH1 phase

Among the two considered drivers in PH1, one obtains a 1.8% economical gain face to the second one that achieves a 9.7% economical gain. The question is : how to convince the first one to use this EDAS in spite of its weak economical gain? Furthermore, the trip time increased of around 8% with an speed/gear number advice via a HMI, then the second question is: is it acceptable by the driver? In a accident gravity point of view, it can be viewed as a way to reduce the average speed thus to decrease the number of accidents.

Regarding now the legal speed overshoots, the use of the HMI brings a very high gain in respecting the legal speed even the first driver (gain of more tan 79%), it is another one of the advantages of this EDAS.

The figure 5 presents the speed and engine torque profiles of the first driver on a 2.5km journey, with two passings (with and without HMI). A negative value of the torque corresponds to the use of the engine braking. The pink plot is the engine brake use: when "0", there is no brake. When there is the first legal speed changing, the driver begins to use the engine braking at the same moment on both trips. If we compare both trips with and without the HMI, one can see that without the HMI, the speed profile is always up to the one with the HMI. The reason is the following: as the EDAS uses an electronic horizon, it can anticipate on the different events to be coming, contrarily to the driver without any HMI. By this way, the HMI advice being anticipative, the driver can also anticipate its action by following the HMI output, at some moments where the ecodriving rules can be difficult to be applied without any indication like with an electronic horizon. Furthurmore, for the first driver, the engine braking is used at 29.96% of the total time during its two first passings face to 26.25 on his two last passings. This means that the engine braking can create an influence on the fuel consumption but it is not a dominant variable.

PH2 Phase Now, a preceding vehicle is added in order the traffic conditions to be taken into account. All the six drivers (C, D, S, F, G, A) induce a fuel economy just by following the instructions of the HMI. This gain varies from 1.6% to 12.9%, in function of the considered driver. These gains begin to be significative for several drivers. Besides, without the HMI, all the drivers had made some efforts to eco-drive by applying the rules. So when we compare both experiences (with and without HMI), the gains are supposed a few. The fuel consumption average of all the drivers without the HMI is 6.61 l/100km. With the HMI, it is 6.12 l/100km. The obtained fuel economy is then 7.55%, what is the more, in real traffic conditions. It can be noted that, in a safety point of view, the gains are quite high with the use of the ADAS. The table II indicates the different gains won in terms of legal speed overshoots by using the presented EDAS with some very encouraging results and so promising for this kind of built-in system. The ecoDriver project thus aims to improve these results in terms of the different objectives listed in this paper.

Besides, this experimental work was realized with a trial HMI, it is obviously not an ergonomic HMI. The ecoDriver project will help in delivering such an ergonomic HMI module, that will be usefull to prove the system efficiency.

CONCLUSION

The European FP7 ecoDriver project is presented in broad outline. An Ecological Driving Assistance System (EDAS), developed in ecoDriver project is presented in its built-in form.

From the vehicle and fuel consumption modeling, energy consumption optimization, several tests are achieved with this EDAS and induce the evaluation of the gains obtained in terms of economy, ecology and safety. After several experimental tests with 8 different drivers, the results affirm that the conception of EDAS is promising, by obtaining around 9 to 12% fuel gain while improving the safety aspects.

Fig. 1 -

 1 Fig. 1 -Schematic diagram of the powertrain model.

xFig. 2 -

 2 Fig. 2 -Comparison of the consumption model (2) with experimental data.

  input which gathers the engine torque and the gear ratio. The DP method is then written k

Fig. 3 -

 3 Fig. 3 -Optimal speed profiles and gear ratio versus weighed coefficient Q i .

Fig. 4 -

 4 Fig. 4 -Optimal profiles with Q1=Q2=Q3=1.

Fig. 5 -

 5 Fig. 5 -Speed and engine torque profiles of the first driver: use of engine braking.

TABLE II . LEGAL SPEED OVERSHOOTS IN TRAFFIC REAL CONDITIONS. Driver Legal Speed Overshoots (%)

 II

		Without HMI	With HMI	Gain (%)
	1 st driver of PH1	18.3	3.38	-79.23
	C	13.71	9.24	-32.6%
	D	5.67	4.17	-26.4%
	S	9.34	9.3	-0.42%
	F	6.33	2.35	-62.8%
	G	18.87	5.02	-73.39%
	A	9.35	3.76	-59.78%

ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Union Seventh Framework Programme under grant agreement n° 288611 -ecoDriver project.

ANNEX A VEHICLE DESCRIPTION FOR EDAS BUILT-IN SYSTEM

The aim of this model is to be mainly used on ICE (Internal Combustion Engine) vehicles. Parameters for each vehicle have to be set in the application. A "standard" vehicle can be selected if these parameters are not available. The application is tested on a RENAULT Clio 3 Eco 2 equipped with CAN bus fuel consumption measurements and fuel flow meters. For the experimental applications, this test vehicle is also equipped with a datalogger named RTMAPS (Intempora France) that makes the interface between the C/C++ algorithm issued from the MATLAB/SIMULINK algorithms and the sensors/actuators.

The figure 6 and Table III respectively give a general view of the test vehicle and the main technical data about it.