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A course on Vehicle Dynamics

By

Vehicle Dynamics Lecture-11

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Prof. Sarvesh Mahajan BITS, PILANI

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Learning !jec"ives #

Lateral Systems Under Commercial Development

Lane Departure Warning

Lane Keeping System


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Kinematic $odel of Lateral Vehicle $otion

%i-cycle $odel of Lateral Vehicle Dynamics

&oad $odel

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La"eral Sys"ems $n%er &ommercial Develo'men" #

Lane departures are the num"er one cause of fatal accidents across the glo"e'

(n the United States it account for more than )*+ of crash-related fatalities'

&eports "y the ,ational igh!ay .ransportation Safety /dministration 0,.S/ state that asmany as 123432555 accidents annually are caused "y distracted drivers - a large percentageof !hich can "e attri"uted to unintended lane departures'


Lane departures are also identified "y ,.S/ as a ma6or cause of rollover incidents involvingsport utility vehicles 0SUVs and light truc7s 0http899!!!'nhtsa'gov'

.hree types of lateral systems have "een developed in the automotive industry that addresslane departure accidents8

Lane departure !arning systems 0LDWS2 Lane 7eeping systems 0LKS and a! sta"ility control systems'

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Lane De'ar"ure (arning #

/ lane departure !arning 0LDW system is a system that monitors the vehicle:s position !ithrespect to the lane and provides !arning if the vehicle is a"out to leave the lane' /ne;ample of a commercial LDW system under development is the /utoVue LDW system "y

(teris2 (nc and as sho!n in "elo! fig' 11-1


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.he /utoVue device is a small2 integrated unit consisting of a camera2 on"oard computerand soft!are that attaches to the !indshield2 dash"oard or overhead'

.he system is programmed to recogni>e the difference "et!een the road and lane mar7ings'

.he unit:s camera trac7s visi"le lane mar7ings and feeds the information into the unit:scomputer2 !hich com"ines this data !ith the vehicle:s speed'


Using image recognition soft!are and proprietary algorithms2 the computer can predict!hen a vehicle "egins to drift to!ards an unintended lane change'

When this occurs2 the unit automatically emits the commonly 7no!n rum"le strip sound2alerting the driver to ma7e a correction

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/utoVue is pu"lici>ed as !or7ing effectively "oth during day and night2 and in most !eatherconditions !here the lane mar7ings are visi"le'

%y simply using the turn signal2 a driver indicates to the system that a planned lanedeparture is intended and the alarm does not sound'

Lane departure !arning systems made "y (teris are no! in use on truc7s manufactured "y


'

(teris: chief competitor2 /ssist!are2 has also had success in the heavy truc7 mar7et8 theirSafe.rac system is no! availa"le as a factory option on Ken!orth truc7s and via direct salesto commercial fleets'

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Lane )ee'ing Sys"em #

/ lane-7eeping system automatically controls the steering to 7eep the vehicle in its lane andalso follo! the lane as it curves around'

@ver the last ten years2 several research groups at universities have developed anddemonstrated lane 7eeping systems'

&esearchers at California A/. demonstrated a lane 7eeping system "ased on the use of


'

.he magnetic field from the em"edded permanent magnets !as used for lateral positionmeasurement of the vehicle 0Buldner2 et' al'2 1**?'

&esearch groups at %er7eley 0.aylor2 et2 al'2 1*** and at Carnegie $ellon 0.horpe2 et' al'2

1** have developed lateral position measurement systems using vision cameras anddemonstrated lateral control systems using vision "ased measurement'

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&esearchers at the University of $innesota have developed lane departure !arning andlane 7eeping systems "ased on the use of differential BAS for lateral position measurements0Donath2 et' al'2 1**4'

Systems are also under development "y several automotive manufacturers2 including,issan'

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- 2

Cima model2 offers automatic steering in parallel !ith the driver'

See7ing to stri7e a "alance "et!een system comple;ity and driver responsi"ility2 the systemis targeted at :monotonous driving: situations'

.he system operates only on :straight-ish: roads 0a minimum radius !ill eventually "especified and a"ove a minimum defined speed'

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,issan:s premise is that drivers feel tired after long hours of continuous e;press!ay drivingas a result of having to constantly steer their vehicles slightly to 7eep them in their lane'

.he LKS attempts to reduce such fatigue "y improving sta"ility on the straight high!ay road'

%ut the driver must remain engaged in actively steering the vehicle -- if he9she does not2 theLKS gradually reduces its degree of assistance' .he practical result is that you can:t Etune

E


'

,issan:s argument is that this approach achieves the difficult "alance "et!een providingdriver assistance !hile maintaining driver responsi"ility'

.he lo! level of steering force added "y the control isn:t enough to interfere !ith the

driver:s manoeuvres'

.he system uses a single CCD camera to recogni>e the lane demarcation2 a steering actuatorto steer the front !heels2 and an electronic control unit'

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.he camera estimates the road geometry and the host vehicle:s position in the lane'

%ased on this information2 along !ith vehicle velocity and steering !heel angle2 the control

unit calculates the steering torFue needed to 7eep !ithin the lane'

,issan is also developing a LDW system called its Lane Departure /voidance 0LD/ system

:


the lane in addition to providing !arning through audio signals and steering !heelvi"rations'

,issan:s LD/ creates a lateral E"ufferE for the driver2 and 7ic7s into action to automaticallysteer if the vehicle starts to depart the lane'

%ut2 unli7e a true co-pilot2 the system !on:t continue to handle the steering 6o" -- !ithhaptic feed"ac7 in the steering !heel2 the driver is alerted to the system activation and ise;pected to re-assert safe control "y himself or herself'

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.he automatic steering assist is steadily reduced over a period of several seconds' So2 a roaddeparture crash is still possi"le2 "ut is e;pected "e less li7ely unless the driver is seriouslyincapacitated'

LD/ is accomplished using the same "asic components of LKS8 a camera2 a steering actuator2an electronic control unit2 and a "u>>er or other !arning device'


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*a+ S"a!ili"y &on"rol Sys"ems #

Vehicle sta"ility control systems that prevent vehicles from spinning and drifting out have"een developed and recently commerciali>ed "y several automotive manufacturers'

Such sta"ility control systems are also often referred to as ya! control systems or electronicsta"ility control systems'

=igure 11-# schematically sho!s the function of a ya! control system'


(n this figure2 the lo!er curve sho!s the tra6ectory that the vehicle !ould follo! in responseto a steering input from the driver if the road !ere dry and had a high tire-road frictioncoefficient'

(n this case the high friction coefficient is a"le to provide the lateral force reFuired "y the

vehicle to negotiate the curved road'

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(f the coefficient of friction !ere small or if the vehicle speed !ere too high2 then thevehicle !ould "e una"le to follo! the nominal motion reFuired "y the driver - it !ouldinstead travel on a tra6ectory of larger radius 0smaller curvature2 as sho!n in the upper

curve of fig 11-#


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.he function of the ya! control system is to restore the ya! velocity of the vehicle as muchas possi"le to the nominal motion e;pected "y the driver'

(f the friction coefficient is very small2 it might not "e possi"le to entirely achieve thenominal ya! rate motion that !ould "e achieved "y the driver on a high friction coefficientroad surface'

:


2

closer to the e;pected nominal ya! rate2 as sho!n "y the middle curve in =igure 11-#'

$any companies have investigated and developed ya! control systems during the last tenyears through simulations and on prototype e;perimental vehicles'

Some of these ya! control systems have also "een commerciali>ed on production vehicles'G;amples include the %$W DSC) 0Leffler2 et' al'2 1** and the $ercedes GSA2 !hich !ereintroduced in 1**32 the Cadillac Sta"ilitra7 system 0ost2 1**? introduced in 1**? and theChevrolet C3 Corvette /ctive andling system in 1**4 0offman2 et'al'2 1**'

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.hree types of sta"ility control systems have "een proposed and developed for ya! control8

Differen"ial Braing sys"ems !hich utili>e the /%S "ra7e system on the vehicle to apply

differential "ra7ing "et!een the right and left !heels to control ya! moment'

S"eer-!y-(ire sys"ems !hich modify the driver:s steering angle input and add a correctionsteering angle to the !heels'


Ac"ive Torue Dis"ri!u"ion sys"ems !hich utili>e active differentials and all !heel drivetechnology to independently control the drive torFue distri"uted to each !heel and thusprovide active control of "oth traction and ya! moment'

%y large2 the differential "ra7ing systems have received the most attention from researchers

and have "een implemented on several production vehicles'

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)inema"ic Mo%el of La"eral Vehicle Mo"ion #

Under certain assumptions descri"ed "elo!2 a 7inematic model for the lateral motion of avehicle can "e developed'

Such a model provides a mathematical description of the vehicle motion !ithoutconsidering the forces that affect the motion'

.he eFuations of motion are "ased purely on geometric relationships governing the system'


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(n the "icycle model2 the t!o left and right front !heels are represented "y one single!heel at point /' Similarly the rear !heels are represented "y one central rear !heel atpoint %'

.he steering angles for the front and rear !heels are represented "y /fand /r respectively'

.he model is derived assuming "oth front and rear !heels can "e steered'

0or fron"-+heel-only s"eering, "he rear s"eering angle 1,. can !e se" "o 2ero.

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.he center of gravity 0c'g' of the vehicle is at point C'

.he distances of points / and % from the c'g' of the vehicle are lfan% lr 2 respectively'

.he !heel"ase of the vehicle is L 3 lf4 lr

.he vehicle is assumed to have planar motion' .hree coordinates are reFuired to descri"e


, '

0I2 are inertial coordinates of the location of the c'g' of the vehicle'

J descri"es the orientation of the vehicle'

.he velocity at the c'g' of the vehicle is denoted "y V and ma7es an angle 7 !ith thelongitudinal a;is of the vehicle'

.he angle 7 is called the slip angle of the vehicle'

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Assum'"ions

.he ma6or assumption used in the development of the 7inematic model is that the velocity

vectors at points / and % are in the direction of the orientation of the front and rear !heelsrespectively'

(n other !ords2 the velocity vector at the front !heel ma7es an angle /f!ith the


'

Li7e!ise2 the velocity vector at the rear !heel ma7es an angle /r 2 !ith the longitudinal a;isof the vehicle'

.his is eFuivalent to assuming that the Eslip anglesE at "oth !heels are >ero' .his is a

reasona"le assumption for lo! speed motion of the vehicle 0for e;ample2 for speeds lessthan 3 mls'

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/t lo! speeds2 the lateral force generated "y the tires is small'

(n order to drive on any circular road of radius & 2 the total lateral force from "oth tires is


'

forces are small2 it is indeed very reasona"le to assume that the velocity vector at each!heel is in the direction of the !heel'

.he point 5 is the instantaneous rolling center for the vehicle'

.he point 5 is defined "y the intersection of lines /5 and %@ !hich are dra!n perpendicularto the orientation of the t!o rolling !heels'

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.he radius of the vehicle:s path & is defined "y the length of the line @C !hich connects thecenter of gravity C to the instantaneous rolling center 5'

.he velocity at the c'g' is perpendicular to the line @C'

.he direction of the velocity at the c'g' !ith respect to the longitudinal a;is of the vehicle iscalled the slip angle of the vehicle '


.he angle J is called the heading angle of the vehicle'

.he course angle for the vehicle is M J N '

/pply the sine rule to triangle @C/'

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/pply the sine rule to triangle @C%'


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(f !e assume that the radius of the vehicle path changes slo!ly due to lo! vehicle speed2then the rate of change of orientation of the vehicle 0i'e' JO must "e eFual to the angularvelocity of the vehicle'

Since the angular velocity of the vehicle is V9& 2 it follo!s that


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&emar7ere it is appropriate to include a note on the E"icycleE model assumption' %oth the left andright front !heels !ere represented "y one front !heel in the "icycle model' (t should "e

noted that the left and right steering angles in general !ill "e appro;imately eFual2 "ut note;actly so' .his is "ecause the radius of the path each of these !heels travels is different'Consider a front !heel steered vehicle as sho!n in =igure 11-

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