Experimental vehicle longitudinal control using a second

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Experimental vehicle longitudinal control using a secondorder sliding modes technique

L. Nouveliere, S. Mammar

To cite this version:L. Nouveliere, S. Mammar. Experimental vehicle longitudinal control using a second order slidingmodes technique. Control Engineering Practice, Elsevier, 2007, Vol15,N°8, p943-954. �hal-00505946�

https://hal.archives-ouvertes.fr/hal-00505946

https://hal.archives-ouvertes.fr

Experimental vehicle longitudinal control using a second order

sliding modes technique

Lydie Nouveliere a Saıd Mammar a

aLIVIC - INRETS/LCPC13, route de la Miniere, 78000 Versailles, France.

Fax : 33 1 40 43 29 30 Email : [email protected]

Abstract

This paper presents the first phase of an experimental implementation of vehicle longitudinal control at low speed.The main objectives are the increase of traffic capacity while improving safety and comfort. Longitudinal controlmethod used is based on second order sliding mode technique. Results are presented either by simulation or byuse of an experimental process with a vehicle prototype which is equipped with needed sensors and actuators.The principle is based on the well management of inter-vehicular spacing in relation to vehicle speed. Examplesobtained with the automatic system are provided for several traffic situations such as stop-and-go, stop on obstacles,car-following with merging/overtaking. Positive impacts of such a system are given in terms of traffic capacityenhancement and collision gravity reduction.

Key words: Vehicles, Longitudinal control, sliding modes, Congested networks

1. Introduction

Large metropolitan areas and their roads havechanged considerably in the last twenty years.The lengthening of home-to-work distances hasincreased the number of motorized weekday trips.At the same time the construction of new subur-ban motorways has been undertaken, but enoughcapacity has never been created to carry the ever-increasing amount of traffic.

In particular, peri-urban networks experiencegrowing daily congestions at peak hours. While innormal steady state driving conditions, traffic ca-pacity of a lane is at around 2200 vehicles per houron peri-urban motorways, it generaly falls to 1200vehicle per hour (Mammar et al , 1998) in theseparticular disturbed unsafe traffic conditions. Inaddition the increase of the spent time and theworkload cause drivers’ displeasure and irritation.

Thus it is advisable to find solutions to solvesuch a constant problem. The automated highways

1 This work is supported by the french research program”la route automatisee”

concept was developed to provide a simultaneousresponse to this triple problem of congestion, roadsafety and pollution (Hedrick et al. , 1998). It hopesto solve the deadlock in the transport system.

Concerning congested peri-urban networks, apossible affordable approach is vehicle automationat low speed. An first of all, longitudinal modeautomation by regulating vehicle speed and range,considering safety and comfort aspects while en-suring guaranteed travel time.

The technical method adopted in this paper isbased on the accumulation of several automaticfunctions in order to tend progressively towards acomplete vehicle automation.

In that way, first step consists in the implemen-tation of a longitudinal shared driving between thedriver and the automat. For such a system, themodel of inter-vehicular spacing for congested traf-fic situations can be considered in order to definerealistic desired inputs (Nouveliere et al. , 2002).Besides, this driving assistance needs low cost ad-ditional equipment with regard to already existingtechnological means and driver’s workload will be

11 February 2005

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Zone de texte

Control Engineering Practice, Vol. 15, Issue 8, August 2007, Pp 943-954 Special Section on Modelling and Control for Participatory Planning and Managing Water Systems, IFAC workshop on Modelling and Control for Participatory Planning and Managing Water Systems doi:10.1016/j.conengprac.2006.11.011 Copyright © 2006 Elsevier Ltd All rights reserved. http://www.sciencedirect.com/science/journal/09670661

reduced.In this paper several scenarios of longitudinal

control are presented, with recent obtained exper-imental results. A short example of simulation ofa car following control is given. Control law uses asecond order sliding mode technique (Levantovsky, 1985; Levant , 1993; Emelyanov et al. , 1986) andcontrol input is the vehicle acceleration (Hedricket al. , 1997; Nouveliere et al. , 2001). A compari-son with the driver’s reaction time is accomplishedand an analysis of experimental results in terms oftraffic capacity and collision gravity is carried out(Mangeas , 2001).

Section 2 presents the considered shared drivingmodes. Section 3 gives the vehicle model used forcontrol synthesis (Hedrick et al. , 1997) while sec-tions 4 and 5 provide the control synthesis proce-dure with some simulation results. Finally section6 is devoted to the obtained experimental resultsand their analysis.

2. Control modes for shared driving

� � � � � � � � � � � � � � � � � � �� AUTO

� � � � � � � � � � � � � � � � � � � � � � � � �� Instrumented Mode� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � ��

Warning Mode� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � �� Limit Mode� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � �� Regulated Mode

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

5 Control

Modes for

Shared Driving

� � � � � � � � � � � � � � � � � � � � � � � � �� Automated Mode

� � � � � � � � � � � � � � � � � � �� AUTO� � � � � � � � � � � � � � � � � � �� AUTO


� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � ��

Warning Mode� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � �� Limit Mode� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � �� Regulated Mode

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

5 Control

Modes for

Shared Driving

� � � � � � � � � � � � � � � � � � � � � � � � �� Automated Mode

� � � � � � � � � � � � � � � � � � � � � � � � �� Instrumented Mode


� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � ��

Warning Mode

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � ��

Warning Mode� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � �� Limit Mode

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � �� Limit Mode� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � ��

Regulated Mode

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

5 Control

Modes for

Shared Driving

� � � � � � � � � � � � � � � � � � � � � � � � �� Automated Mode

Fig. 1. Five control modes for shared driving

Longitudinal control concept at low speed ismainly devoted to the enhancement of traffic con-ditions and safety while reducing driver’s workloadin sub-urban congested traffic situations. However,the vehicle can only be in automatic mode undera certain threshold. From realtime observed trafficdata, it was estabilished that more than 90% ofspeeds during daily peak-hours are under 60Km/h.But in such conditions, the traffic can becomefluid at certain times, then the driver must havethe means of taking manual driving again. Theprimary objective is thus not only to achieve a fullautomated vehicle but also to provide to the drivera permanent informative or active assistance sys-tem. This kind of assistance with vehicle sharedcontrol must integrate the priority to the driverto drive in manual mode. Actually, five assistancemodes for shared driving have been established:– Instrumented mode : this mode gives an indica-

tion of the state or the value of a helpful variable

to the driver, as for example the vehicle velocityor actual headway time.

– Warning mode : It informs the driver that thereis a limit not to overshoot like the maximal au-thorized speed onto the traffic network or alerthim when the minimum safety headway time isreached.

– Limited mode : this mode notifies the driver ofnot overshooting an enforced limit. A typical ex-ample is the system of active gas pedal.

– Regulated mode : an automated system con-strains the controlled vehicle to follow a desiredreference signal such as a desired speed or spac-ing.

– Automated mode : the vehicle is completely au-tomated.The experimental vehicle is designed methodi-

cally by adding technical modules. In other words,it is desired to implement and to evaluate sev-eral experimental tools including sensors, actua-tors and HMI that can be used after to graduallyconceive more elaborated safety systems. The ex-perimental vehicle is designed in such a way thatthe driver can always easily override any actionperformed by the controller.

The following section gives a summary of thevehicle model used for control synthesis.

3. Vehicle model

3.1. Model equations

The vehicle model used for control synthesis is asimplified non-linear model (Hedrick et al. , 1997).First of all, the longitudinal equation of the drive-train is described by

(m +(Jwr + Jwf )

h2)a =

Ts − Tb − Mrr

h− Fa − mg sin(θ)(1)

with a non slip assumption like

v = Rghωe (2)

Te = RgTs (3)

with a non slip assumption (v = Rghωe) and (Te =RgTs) one can eliminate the term of traction effortin equation (1) which becomes

Te − Rg(Tb + Mrr + hFa + mgh sin(θ)) = Ita (4)

with

It =(Je + R2

g(Jwr + Jwf + mh2))

Rgh(5)

2

Tb Brake torque (N.m)

Mrr Rolling resistance torque (N.m)

h height of the center of the wheel (m)

Fa aerodynamic force (N)

g gravity (9.81 m.s−2)

θ Road slope angle (deg)

a acceleration (m.s−2)

Jwr Jwf Rear/front wheel inertias (1.2825 kg.m2)

Je Engine/ transmission inertias(0.2630 kg.m2)

Rg gear ratio ( final gear included)

Ts Shaft torque (N.m)

v vehicle speed (m.s−1)

ωe Engine speed (rpm)

m Vehicle mass (kg)

Table 2: Vehicle model parameters

Te

Tb

Fa

Mrr

Rg

x

v

a

Vehicle

alpha* alpha

Throttle actuator

alpha

delta

Td

ma

we

Te

Engine

Tb* Tb

Brake actuator

Sep=-lambda_e.Se

1-Sliding Modes

Te* ma*

Conversion

Tb*

Rg

Te*

Mrr

a

Fa

v

x

we

ma

[t,delta]

Td

Fig. 2. Global diagram

3.2. Switching criterion (Hedrick et al. , 1997)

Switching from throttle to brake is performedusing an acceleration threshold ath: if a∗ ≥ ath,throttle control is activated, and if a∗ < ath, thesystem is braking. a∗ is the desired acceleration. Inthis way, a residual engine torque Tct correspond-ing to a closed throttle must be calculated (Hedricket al. , 1997). Then, the engine torque can be di-vided into two parts: Te which is submitted to con-trol and Tct. Equation 4 can be written

Te − RgTb = Rg(Mrr + hFa + mgh sin(θ)) + Ita − Tct(6)

In the absence of control inputs, ath can be calcu-lated

ath =1

It

[Tct − Rg(Mrr + hFa + mgh sin(θ))] (7)

Then, the expressions of desired engine and braketorques are

T ∗

e = Ita∗ + Rg(Mrr + hFa + mgh sin(θ)) (8)

and

T ∗

b =Tct − Ita

∗

Rg

− (Mrr + hFa + mgh sin(θ)) (9)

Tct is determined experimentally.The engine torque is generated from the model of

an engine (Powell , 1979; Powell and Cook , 2000).Engine state equations are

ma = maci− maco

(10)

ωe = kn(Te − Tl) (11)

where Tl is the load torque at engine output. Airmass flow rate ma in the intake manifold is ob-tained by subtraction between flow rates at inputmaci

and output maco.

The longitudinal controller is now designed onthe basis of the model presented above.

3.3. Model analysis

The model is simulated with Td = 10 mN, 15◦ ≤δ ≤ 18◦, Mrr = 70 mN, θ = 0◦ and Rg = 0.3521which corresponds to the third gear. The same ac-tuator as before is used for the throttle body andthe brake actuator is represented by a first orderfilter with a time constant: τb = 0.072 sec. Figure3 shows that the accelerations a∗ and a are con-fused. It means that the vehicle acceleration cor-rectly follows the desired acceleration input, witha sufficient engine torque.

0 5 10 15 20 25 300

50

100

Thr

ottle

ang

lede

g

0 5 10 15 20 25 300

50

100

Pm

kPa

0 5 10 15 20 25 300

100

200

Te

mN

0 5 10 15 20 25 30−1

0

1

Acc

el°

m/s

ec/s

ec

0 5 10 15 20 25 300

50

100

Spe

edkm

/h

0 5 10 15 20 25 300

500

1000

time − sec

Pos

ition

m

ath

a, a*

Fig. 3. Simulation for sinusoidal acceleration input

3

4. Synthesis procedure

A second order sliding mode technique is used forlongitudinal control. This method is well adaptedfor non-linear systems, and permits considerablereduction of the inherent chattering phenomenon.This is achieved by applying the algorithm not di-rectly on the control input u but on its derivative.Besides sliding modes are robust to sensor noisewhich is very important for experiments knowingthat several sensors are required for longitudinalcontrol.

4.1. Problem formulation

Let it be X = [ma, ωe, x, x]t the state vector ofthe system to be controlled. State representation is

X = f(X, t, u) (12)

System input u is Te or Tb but from experimentalpoint of view, it is easier to use acceleration in-put which is simpler to measure. Then in order tocontrol the vehicle from a leader speed profile, thedesired input of the system is

u = a∗ = Te − Rg(Tb + Mrr + hFa + mgh sin(θ))(13)

To be able to control the vehicle in acceleration,vehicle engine must be controlled (Hedrick et al. ,1997; Nouveliere et al. , 2001). This is performedusing a simple first order sliding mode on the throt-tle angle (figure 2).

4.2. Algorithm

The sliding surface chosen for the control is ofthe form

S = (x − xl) + (L + hx) (14)

where xl is the position of the followed vehicle, Lrepresents the inter-distance while stopping and his the headway time. This surface S was chosenbecause of the recent french law that specifies todrivers not to leave a headway time inferior to 2seconds. When inferior, safety is not assured.

With such a sliding surface, the system has a rel-ative degree equal to 1. The Twisting Algorithm(Levantovsky , 1985; Levant , 1993; Emelyanov etal. , 1986) is then applied to the vehicle model tosimulate an automatic car-following control. Algo-rithm is

u =

−u if |u| > |ueq|

−KMsign(S) if SS > 0 and |u| 6 |ueq|

−kmsign(S) if SS 6 0 and |u| 6 |ueq|

(15)

where ueq is the equivalent control satisfying S =0. Coefficients km and KM are determined to re-spect the four conditions of applications of theTwisting Algorithm which is a second order slid-ing mode algorithm that converges in finite time(Levant , 1993).

5. Simulation results

0 5 10 15 2034

36

38

40

42

44

46

48

Time (s)

Spe

ed (

km/h

)

0 5 10 15 200

50

100

150

200

250

300

Time (s)

Pos

ition

s (m

)

0 5 10 15 201.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

Time (s)

Hea

dway

tim

e (s

)

Fig. 4. Simulation of a car-following control - (-) leader (...)controlled vehicle - L=5m, h=1s

Congested traffic experimental data analysisshows that 75% of headway times are under 1s. Inorder to prove the effectiveness of the developedwhelicle following controller, a headway time of1s is chosen in the sliding surface. The controlleris implemented with L = 5 m, h = 1 s, km = 30and KM = 120. Figure 4 shows results obtainedfor car following in reaction to speed variations ofthe preceding vehicle. One can note that the posi-tion of the controlled vehicle is well regulated andheadway time is always greater than 1 s. Further-more, once the control has converged, the speed ofthe controlled vehicle follows the imposed speedprofile.

6. Experimental tests

Simulation tests have lead to satisfactory re-sults for longitudinal control. Then an experimen-tal phase has been carried out with the develop-ment of a prototype vehicle. Several tests are pro-posed in the following in order to analyze the be-havior of the controlled vehicle face to a typicalscenario. The objectives are thus to evaluate thesystem and validate it in order to determinate if itcan be used as an assistance system sharing withthe driver.

4

At first, a short description of the experimentalvehicle is given, both at the equipment level andarchitectural one.

6.1. Vehicle equipment

Fig. 5. Vehicle equipment : a) Vehicle prototype - b) Stere-ovision sensors - c) Braking pedal modified - d) Embeddeddata processing

The prototype vehicle is a Renault Scenic (figure5 a)), which has been instrumented with severalsensors. For the developed control strategy, fourdifferent measures are necessary at each sampletime : inter-vehicular spacing, relative speed, speedand acceleration of the controlled vehicle.

6.1.1. SensorsAccording to figure 5 b), a video system using

stereovision technique (Labayrade and Aubert ,2002, 1998) permits to know the value of inter-vehicular spacing and relative speed. his system isalso used to detect obstacles on the traffic lane, itneeds only a calibration test before normal oper-ating. Vehicle speed is obtained by an odometerwhile an inertial unit returns the longitudinal ac-celeration of the controlled vehicle.

Sensors previously quoted are for the most ofthem noisy. Particularly inter-vehicular spacing,vehicle speed and acceleration are filtered numer-ically so as to obtain data which can be exploitedfor driver warning or vehicle control.

6.1.2. Control moduleThe controller block is managed by a DLL (Dy-

namic Link Library) which computes the desiredacceleration via the presented Twisting Algorithmand sends a desired algebraic acceleration to theactuator module. The control loop runs at a sam-ple time of 23ms.

6.1.3. Actuators moduleBraking pedal is lined by an electrical jack which

is controlled in position by a numerical PID con-troller (see figure 5 c)). Throttle angular positionis directly controlled by the vehicle integrated elec-tronic control unit.

CONTROL METHOD : 2-order Sliding Mode Control

Longitudinal

Control

Desired

Acceleration Throttle

Braking pedalPosition

Vehiclespeed

Acceleration

Embedded Data Processing

ARCHITECTURE

Actuators

Control

Inertial System

Relativespeed

SensorsOdometer

Inter-vehicularspacing

Desired

Braking

Differentialodometers byradio-modem

or Stereovision

CONTROL METHOD : 2-order Sliding

Longitudinal

Control

Throttle


Vehiclespeed

Acceleration

Processing

Actuators

Control

Inertial System

Relativespeed

SensorsOdometer



or Stereovision

LabVIEW

CONTROL METHOD : 2-order Sliding Mode Control

Longitudinal

Control

Desired

Acceleration Throttle


Vehiclespeed

Acceleration

Embedded Data Processing

ARCHITECTURE

Actuators

Control

Inertial System

Relativespeed

SensorsOdometer


Desired

Braking


or Stereovision

CONTROL METHOD : 2-order Sliding

Longitudinal

Control

Throttle


Vehiclespeed

Acceleration

Processing

Actuators

Control

Inertial System

Relativespeed

SensorsOdometer



or Stereovision

LabVIEW

Fig. 6. Global system architecture

6.1.4. System architectureAll the previous described modules are man-

aged by a LabVIEW interface which allows processmemory management for real-time realization. Anembedded data processing has been installed in thevehicle boot (figure 5 d)). System architecture issummed up on figure 6.

This vehicle equipment makes possible the ex-perimental evaluation of several scenarios of longi-tudinal assistance in both warning and shared con-trol modes. However, due to space limitation, onlythe regulated mode is detailed in this paper.

6.1.5. Switch automatic/manual modesIt was said before that the system considered

calls on the shared control with the priority tothe driver. Then it is important for such a systemthat the transition from automatic driving mode tomanual driving mode is carried out during a veryshort time in the case for instance the driver wantsto reach the leader faster. That is the reason whyas soon as the driver presses on the pedal, a detec-tor orders the system to change of driving mode.This action is immediate and reversible.

6.1.6. Switch automatic/manual modesIt was said before that the system considered

calls on the shared control with the priority tothe driver. Then it is important for such a systemthat the transition from automatic driving mode tomanual driving mode is carried out during a veryshort time in the case for instance the driver wantsto reach the leader faster. That is the reason whyas soon as the driver presses on the pedal, a detec-tor orders the system to change of driving mode.This action is immediate and reversible.

6.2. Experimental scenarios

In the following are given the results obtained forsome scenarios tested during experimental phaseand validated during the IEEE Intelligent Vehi-cle Symposium IV2002. The desired accelerationis calculated in order to ensure a headway time

5

greater than 2 s with respect to the new french lawon time headway. Control law is the one which ispresented in 4.2. the derivative of the sliding sur-face is easily computed using the available sensors,.

6.2.1. Scenario 1 : Low speed car-following control

2040 2060 2080 2100 2120 21400

5

10

15

20

25

30

35

Time (s)

Inte

r−ve

hicu

lar

spac

ing

(m)

2040 2060 2080 2100 2120 21400

5

10

15

20

25

30

35

Time (s)

Spe

ed o

f con

trol

led

vehi

cle

(km

/h)

2040 2060 2080 2100 2120 21400

10

20

30

40

50

60

70

Time (s)

Hea

dway

tim

e (s

)

Fig. 7. Low speed car-following control by differentialodometry - (-) leader (...) controlled vehicle - L=8m, h=3s

Figure 7 shows a car-following control with h =3s and L = 8m. One can note that the controlledvehicle follows correctly the leader at low speedbecause measured spacing is near desired spacing.The curve is quite smoother than the desired spac-ing because of filtered data.

6.2.2. Scenario 2 : Stopping on obstaclesEach stop on obstacle comes after a car-following

control.Fallen motorbike

3085 3090 3095 3100 3105

5

10

15

20

25

30

35

40

45

Time (s)

Inte

r−ve

hicu

lar

spac

ing

(m)

3090 3095 3100 3105−5

0

5

10

Time (s)

Spe

ed o

f con

trol

led

vehi

cle

(km

/h)

3090 3095 3100 3105

0

10

20

30

40

50

60

Time (s)

Hea

dway

tim

e (s

)

Fig. 8. Stop on obstacle - (-) leader (...) controlled vehicle- L=10m, h=3s

Stereovison is very useful to detect an obstacleon the lane. In this scenario the controlled vehicle

has to stop automatically in front of a fallen mo-torbike on the road. On figure 8, one can see thatthe controlled vehicle stops at around 11 m fromthe motorbike. Headway time indicates that thestopping is carried out safely since headway timeis always greater than 2 seconds.

Pedestrian crossing

4030 4040 4050 4060 4070

10

15

20

25

30

35

40

45

Time (s)

Inte

r−ve

hicu

lar

spac

ing

(m)

4030 4040 4050 4060−5

0

5

10

15

20

25

30

35

Time (s)

Spe

ed o

f con

trol

led

vehi

cle

(km

/h)

4030 4040 4050 4060 4070

0

10

20

30

40

50

Time (s)

Hea

dway

tim

e (s

)Fig. 9. Stop on pedestrian crossing by stereovision - (-)leader (...) controlled vehicle - L=8m, h=3s

This scenario wants to show how the controlledvehicle reacts face to a pedestrian crossing on thelane between both vehicles. Stereovision quicklydetects the pedestrian and returns to the systemthe inter-distance value. The controlled vehicle canautomatically determine if it is necessary to stop oronly to slow down when the pedestrian walks on theroad as it is described on figure 9. For the example,the vehicle stops briefly before restarting as we cansee with the measured headway time that is infinitewhen the pedestrian is in front of the controlledvehicle. The law with respect to headway time isalways respected.

6.2.3. Scenario 3 : Stop-and-GoAs the main paper interest is low speed longitu-

dinal control, the third scenario is the realizationof a stop-and-go automatic car-following. Figure10 indicates the reaction of the controlled vehiclewhen the preceding one carries out successive stop-ping and restarting. We can note that the evolu-tion of the measured spacing closely follows the de-sired one. These speed variations are comparableto those of a congested traffic situation however,the time headway safety criterion is still satisfied.

6.2.4. Scenario 4 : Car-following withmerging/overtaking

In congested traffic situations, merging and over-taking are frequent. For example a merging causes

6

4820 4840 4860 4880 4900

10

15

20

25

30

Time (s)

Inte

r−ve

hicu

lar

spac

ing

(m)

4820 4840 4860 4880 49000

5

10

15

20

25

30

Time (s)

Spe

ed o

f con

trol

led

vehi

cle

(km

/h)

4820 4840 4860 4880 49000

20

40

60

80

100

120

140

Time (s)

Hea

dway

tim

e (s

)

Fig. 10. Stopgo with stereovision - (-) leader (...) controlledvehicle - L=8m, h=3s

4870 4880 4890 4900 4910 4920 4930

10

15

20

25

30

35

40

Time (s)

Inte

r−ve

hicu

lar

spac

ing

(m)

4870 4880 4890 4900 4910 4920 49305

10

15

20

25

30

35

40

Time (s)

Spe

ed o

f con

trol

led

vehi

cle

(km

/h)

4860 4880 4900 4920 49400

10

20

30

40

50

60

Time (s)

Hea

dway

tim

e (s

)

Fig. 11. Merging/overtaking influence - (-) leader (...) con-trolled vehicle - L=8m, h=2s

a large input disturbance for the controlled vehi-cle because inter-vehicular spacing is suddenly re-duced. Automatic system has to avoid collisions,as it is shown on figure 11. Headway time is alwayssuperior to 2 seconds.

6.3. Reaction time

0

2

4

6

8

10

12

14

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0

2

4

6

8

10

12

14

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

Fig. 12. Distribution of a driver’s reaction time

One can note that all figures of experimental re-sults present a time delay due to the delay betweenthe measured and the desired accelerations (fig-ure 12 b)). It is mainly a consequence of the timeresponse of the engine, its value is around 0.7 s.Considering that the distribution of drivers’ reac-tion time is centered on 1.2 s (see figure 12 a) andMangeas (2001)), such a shared control systemimproves thus this reaction time. The objective innear future is to reduce further this reaction time,knowing that the vehicle engine has actually a timedelay of only 0.3 s.

6.4. Capacity/Gravity consequences

2000 2500 3000 35000

0.20.40.60.81

1.21.41.61.8

2

Capacity (veh/h)

Nb of dead and serious injured humans

1.2s

0.7sWithoutcomm

0.7sWith comm

0.3s2000 2500 3000 3500

00.20.40.60.81

1.21.41.61.8

2

Capacity (veh/h)

Nb of dead and serious injured humans

1.2s

0.7sWithoutcomm

0.7sWith comm

0.3s

Fig. 13. Relation between traffic capacity and gravity

The impact of such a system on the traffic capac-ity and collision gravity is directly linked to the re-action time as it is shown on figure 13. Without au-tomated systems, actual maximum traffic capacityis 2200 vehicles/hour at 50 km/h. The associatedaccident gravity is of 0.3 dead or serious injuredhumans per accident. Then at constant capacity,reducing reaction time leads to gravity reduction.At constant gravity, reducing reaction time per-mits to considerable increase of traffic capacity. Asa conclusion, a compromise has to be achieved be-tween safety and capacity.

7. Conclusion

According to a non-linear vehicle model, a sec-ond order sliding mode control is applied for longi-tudinal control of vehicle at low speed. In additionto the automatic mode, several driving assistancemodes are declined. After a simulation phase, ex-perimental results are given with different scenar-ios like car-following control, stop-and-go, stop onobstacles using stereovision detection. Safety as-pect is considered by integrating the headway timein the desired spacing. Results are illustrated byreal data collected during experiments. It is shown

7

that the developed assistance system improves re-action time. The impact of such a system is thenanalyzed in terms of traffic capacity and gravity.

References

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B.K. Powell, A dynamic model for automo-tive engine control analysis, CH1486-0/79/0000-0120$00.75 IEEE, 1979.

B.K. Powell, J.A. Cook, Nonlinear low frequencyphenomenological engine, INST CNRS, 2000.

R. Labayrade, D. Aubert, J.P. Tarel, Realtimeobstacle detection on non flat road geometrythrough ” V-disparity ” representation, IEEE In-telligent Vehicle Symposium IV2002, Versailles,France, June 2002.

R. Labayrade, D. Aubert, Robust and fast stereo-vision based road obstacles detection for drivingsafety assistance, IAPPR Workshop on MachineVision, Applications, Nara, Japan, Dec. 2002.

S. Mammar et al., Route automatisee : Analyseet Evaluation d’un Scenario d’Autoroute Peri-urbaine, Convention DSCR N◦9770013, Nov1999.

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tance system with respect to capacity and safety,Intelligent Vehicle Symposium IV 2001, Tokyo,June 2001.

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Documents

Experimental vehicle longitudinal control using a second