lane departure warning - university of...

Modelling of Automotive Systems 1

Lane Departure Warning

-The LDW system is developed (by Iteris and used by Merceds and Freightliner)

-provides warning if the vehicle is about to leave the lane

- consists of camera, computer and lane recognising software to track visible lane markings


Lane Keeping Systems

-LKS automatically controls the steering to keep the vehicle in its laneand follow the lane as it curves around.

-Research in USA universities and some car manufacturers (such asNISSAN) have demonstrated working based on machine vision

- The current systems can operate only on ‘straight-ish’ roads and with limited speed range.


Yaw Stability Control Systems - The function of yaw control system is to avoid spinning and overturn when theground friction is not high enough to provide centripetal force. - Some systems have already applied to commercial vehicles.

Lateral force (centrifugal force) from two wheels

RmV 2


Yaw Stability Control Systems Yaw control is implemented by -Differential braking between the left and right wheels. - Steer-by-wire: system correct the steering. - Active torque distribution: independent torque is applied to individual wheels.


Consider road bank angle φ

φsin where

ma y

mgF

FFF

bank

bankyryf

=

++=


Lateral acceleration:

ψ&&& xVy +=ya


Dynamic Model in terms of Error with respect to road y - Vehicle position (measured from O) ψ -Yaw Define

:errorn Orientatio e)errorposition (

road of line centre and c.g.between Distance e

2

1

desψψ −=

radius road velocity,llongitudia

where

,

onaccelerati yaw and velocity yaw Desired2

R-V

VR

VRV

x

desxx

desx

des

−

=== ψψψ &&&&

Acceleration: ( ) ( )desxdesxxdesxy VyVVyVa ψψψψψ &&&&&&&&&&& −+=−+=−=1e

Velocity ( )desxVy ψψ −+= &&1e


( ) ( )

( ) ( )

using

20

20

20

20

1000

20

20

0010motion of equations lateral theFrom

22

δ

ψψ

ψψ

α

α

αααα

αααα

+

+−

−−

−−−

+−

=

z

ff

f

xz

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x

rf

ICl

mC

yy

VIlClC

VIlClC

mVlClC

VmV

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dtd

&

&

&

&

( )des

desxVyψψ

ψψ&&&&&&

&&&&&&

−=−+=

2

1

ee


( ) ( ) ( )

( ) ( ) ( )

( )

( )

des

des

xz

rrff

x

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z

ff

f

xz

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xz

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x

rf

BBAeeeeee

e

LetVI

lClC

mVlClC

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mVlClC

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eeee

dtd

ψδ

ψδ

αα

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α

α

αααααα

αααααα

&&

&

&

&

&

&

&

&

21

2

2

1

1

22

2

2

1

1

22

2

2

1

1

...,

20

20

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2220

1000

2220

0010

++=

=

+−

−−−

+

+

+−

−−−

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=


( ) ( ) ( )

( ) ( ) ( )

( )

( )

+−

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=

+−

−−−

−−

++−

=

+=

=

++=

xz

rrff

x

rrffx

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ff

f

xz

rrff

z

rrff

xz

rrff

x

rrffrf

x

rf

des

des

VIlClC

mVlClC

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ICl

mC

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VIlClC

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VIlClC

mVlClC

mCC

mVCC

A

whereBAee

Then

LetBBAee

22

3

22

3

21

20

20

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20

,

2220

1000

2220

0010

loopOpen

αα

αα

α

α

αααααα

αααααα

ζ

ψδ

ζ

ψδ

&

&

&&

∫ dt1B

A

ee&δ

2Bdesψ&


=

=

+=+=

00000000

,

1000010000100001

form controlin Write

3

DC

whereDCezBAeeζζ&

)1000mR bendcircular ,/30(/03.0 === smspeedsraddesψ&

∫ dt C3B

A

D

ee&δ z


road_profile

To Workspace3

t

lat_error

To Workspace1

yaw_error

To Workspace

20

Time

Terminator1

Terminator

delta

Steering Angle

x' = Ax+Bu y = Cx+Du

State-Space

Scope3 Scope2

Scope1

Scope

PulseGenerator1

PulseGenerator

0.03

Constant

Clock

Add1


0 5 10 15 200

100

200

300

time (sec)

Late

ral E

rror (

m)

0 5 10 15 20-0.5

0

0.5

1

time (sec)

Yaw

Rat

e E

rror (

rad/

s)

0 5 10 15 200

1

2

3

time (sec)

Ste

erin

g an

gle

(deg

rees

)

0 5 10 15 200

0.05

0.1

time (sec)

Des

ired

yaw

rate

(rad

/s)


[ ]

( )

[ ]T

des

des

jjp

pK

BeKBAethen

kkkkKwhereKe

BBAee

1073535

asgiven are seigenvalue where),Bplace(A,K

function Matlab using found becan

feedback stateApply

feedback)(with loop Closed

1

21

4321

21

−+−−−=

=

+−=

=−=

++=

ψ

δψδ

&&

&&

It can be foundK= [0.5764 0.0807 3.2974 0.2291]

Steering Control for automated Lane Keeping


∫ dt1B

A

ee&δ

2Bdesψ&

K

+

++

−

0=r

Steering Control for automated Lane Keeping


Closed loop control for automated lane keeping

desired_yaw_rate

To Workspace3

lat_error

To Workspace1

yaw_error

To Workspace

Terminator1

Terminator

delta

Steering Angle

x' = Ax+Bu y = Cx+Du

State-Space

Scope3

Scope2

Scope1

Scope

PulseGenerator

-1

Gain1

KK

Gain

Add


0 5 10 15 20-0.05

0

0.05

time (sec)

Late

ral E

rror (

m)

0 5 10 15 20-0.05

0

0.05

time (sec)

Yaw

Rat

e E

rror (

rad/

s)

0 5 10 15 20-5

0

5

time (sec)

Ste

erin

g an

gle

(deg

rees

)

0 5 10 15 20-0.05

0

0.05

time (sec)

Des

ired

yaw

rate

(rad

/s)


Dynamic Model in terms of Error with respect to road + road bank

errorn orientatioeroad of line centre and c.g.between distancee

2

1

−−

( ) ( ) ( )

( ) ( ) ( )

( )

( )φψδ

αα

αα

α

α

αααααα

αααααα

sin

00

0

20

20

20

20

2220

1000

2220

0010

22

2

2

1

1

22

2

2

1

1

+

+−

−−−

+

+

+−

−−−

−−

++−

=

g

VIlClC

mVlClC

V

ICl

mC

eeee

VIlClC

IlClC

VIlClC

mVlClC

mCC

mVCC

eeee

dtd

des

xz

rrff

x

rrffx

z

ff

f

xz

rrff

z

rrff

xz

rrff

x

rrffrf

x

rf

&

&

&

&

&

φψδ sinor

421 BBBAee des +++= &&


[ ]

=

=

++=

φψ

ξ

ξδ

sin

equation state-state loop-open The

425

51

des

BBBwhere

BBAee

&

&

[ ]

( ) ξ

δ

51

4321

feedback stateApply

BeKBAethen

kkkkKwhereKe

+−=

=−=

&

lane departure warning - university of...

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