Active Steering ProjectActive Steering Project

Andrew OdhamsRichard Roebuck

David Cebon2nd April 2009

ContentsContents

1. Control concept2. Low speed testing3. High speed testing4. Conclusions

ACTIVE STEERINGACTIVE STEERING

– Define Lead point and follow point– Calculate articulation angle of a perfect tracking trailer– Steer in relation to difference between real and ideal

articulation angle– Set individual wheel angles to equalise tyre forces

Lead Point

Follow Point

•Controller

•Low speed

•High speed

•Conclusions

PATH FOLLOWING TESTSPATH FOLLOWING TESTSUK Roundabout Test

5.3m

8.9m11.25m

12.5m

•Controller

•Low speed

•High speed

•Conclusions

LOW SPEED LOW SPEED ROUNDABOUTROUNDABOUT• Unsteered:

•Controller

•Low speed

•High speed

•Conclusions

LOW SPEED LOW SPEED ROUNDABOUTROUNDABOUT• Command Steer:

•Controller

•Low speed

•High speed

•Conclusions

0 10 20 30 40 50 60 70 80 90 100-5

-4

-3

-2

-1

0

1

Time [s]

Offt

rack

ing:

Fro

nt T

ract

or -

5th

Whe

el [m

]

Tail Swing

Cut In

LOW SPEED ROUNDABOUTLOW SPEED ROUNDABOUT• Offtracking of 5th Wheel:

Locked

Command CVDC

•Controller

•Low speed

•High speed

•Conclusions

0 10 20 30 40 50 60 70 80 90 100-5

-4

-3

-2

-1

0

1

Time [s]

Offt

rack

ing:

Fro

nt T

ract

or -

Rea

r Tra

iler [

m]

Tail Swing

Cut In

LOW SPEED ROUNDABOUTLOW SPEED ROUNDABOUT• Offtracking of Trailer Rear:

Locked

Command

CVDC

•Controller

•Low speed

•High speed

•Conclusions

LOW SPEED ROUNDABOUTLOW SPEED ROUNDABOUT• Tail Swing:

Locked Command Path Following

• Tail swings into blind spot

•Controller

•Low speed

•High speed

•Conclusions

• Unsteered:LATERAL TYRE FORCESLATERAL TYRE FORCES

•Controller

•Low speed

•High speed

•Conclusions

LATERAL TYRE FORCESLATERAL TYRE FORCES• Unsteered:

• FIXED TRAILER: 36.6 kN

•Controller

•Low speed

•High speed

•Conclusions

LATERAL TYRE FORCESLATERAL TYRE FORCES• Path following Strategy:

• CT-AT TRAILER: 6.1 kN

•Controller

•Low speed

•High speed

•Conclusions

Rollover PreventionRollover Prevention

• Rationale– Reduce the risk of rollover by controlling the path

of the trailer

• Optimal linear control strategy– Minimise lateral acceleration– Maintain acceptable path error

• Virtual Driver Model– Original path following controller is nonlinear– ‘Virtual driver model’ performs same function using

linear control

•Controller

•Low speed

•High speed

•Conclusions

Virtual Driver ModelVirtual Driver Modelof Trailer Steeringof Trailer Steering

TractorSemi-trailer

Current position of 5th wheel

Y

O X

Snapshot of tractor semi-trailer and path of 5th wheel at time instant k

try

0ry 1ry 2ry rhy

uT

tre

•Controller

•Low speed

•High speed

•Conclusions

Optimal Control StrategyOptimal Control Strategy

0 11 0 0

1 0 0 0d d d

ri

x k x kA B By u k k

y k y kD E

Discrete-time equations for vehicle and path of 5th wheel

1 1 1 1 2 2 2 2 2 2

Tx y

0 1 2T

r r r rhy y y y y

xz

y

The control objectives

where and2

tr

y

eCz Du

a

tru

The cost function

2

22 2

1 20

tr yk

J Q e k Q a k R u k

Path error Lateral Accel’n Steering effort

•Controller

•Low speed

•High speed

•Conclusions

Results continuedResults continuedManoeuvre: Lane changeVehicle speed: 88km/hFixed value of Q1/R=0.05

•Controller

•Low speed

•High speed

•Conclusions

Selection of weighting valueSelection of weighting value

Q2/R=0.005

Manoeuvre: Lane changeVehicle speed: 88km/hFixed value of Q1/R=0.05

25% reduction

Conventional

•Controller

•Low speed

•High speed

•Conclusions

Path errors in lane changePath errors in lane change

0 20 40 60 80 100 120 140 160 180-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

X distance [m]

Path

trac

king

err

or [m

]

Locked [TO=0.35]

PFC(q2/r=0) [TO=0.15]

RSC(q2/r=0.025) [TO=0.31]

RSC(q2/r=0.1) [TO=0.72]

RSC(q2/r=0.0025) [TO=0.07]

q1/r=0.05•Controller

•Low speed

•High speed

•Conclusions

After lane changeAfter lane change

V=88km/h

Locked Path Following Control

•Controller

•Low speed

•High speed

•Conclusions

PERFORMANCE MEASURESPERFORMANCE MEASURES

Performance Measure

Locked

Comm.

SteerPFC RSC

High speed

Transient Off-tracking [m] 0.35 -0.15 0.31

Rearward Amplification 1.18 1.05 0.86

•Controller

•Low speed

•High speed

•Conclusions

Low speed

Steady State Off-tracking [m] 4.3 1.6 1.2

Tail Swing (Entrance) [m] 0.17 0.61 0.0

Peak Tyre Force [kN] 36.6 5.3 6.1

Exit Settling Distance [m] 23.5 8.8 0.6

ConclusionsConclusions

• Improved low-speed manoeuvrability– Improved productivity (LCV)– Improved safety

• Reduced tyre scrub– Reduced tyre wear– Reduced vehicle wear

• Improved high-speed stability– 25% LTR reduction with no increase of PE– Important for LCV