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Active Steering ProjectActive Steering Project
Andrew OdhamsRichard Roebuck
David Cebon2nd April 2009
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ContentsContents
1. Control concept2. Low speed testing3. High speed testing4. Conclusions
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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
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PATH FOLLOWING TESTSPATH FOLLOWING TESTSUK Roundabout Test
5.3m
8.9m11.25m
12.5m
•Controller
•Low speed
•High speed
•Conclusions
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LOW SPEED LOW SPEED ROUNDABOUTROUNDABOUT• Unsteered:
•Controller
•Low speed
•High speed
•Conclusions
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LOW SPEED LOW SPEED ROUNDABOUTROUNDABOUT• Command Steer:
•Controller
•Low speed
•High speed
•Conclusions
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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
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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
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LOW SPEED ROUNDABOUTLOW SPEED ROUNDABOUT• Tail Swing:
Locked Command Path Following
• Tail swings into blind spot
•Controller
•Low speed
•High speed
•Conclusions
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• Unsteered:LATERAL TYRE FORCESLATERAL TYRE FORCES
•Controller
•Low speed
•High speed
•Conclusions
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LATERAL TYRE FORCESLATERAL TYRE FORCES• Unsteered:
• FIXED TRAILER: 36.6 kN
•Controller
•Low speed
•High speed
•Conclusions
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LATERAL TYRE FORCESLATERAL TYRE FORCES• Path following Strategy:
• CT-AT TRAILER: 6.1 kN
•Controller
•Low speed
•High speed
•Conclusions
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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
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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
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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
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Results continuedResults continuedManoeuvre: Lane changeVehicle speed: 88km/hFixed value of Q1/R=0.05
•Controller
•Low speed
•High speed
•Conclusions
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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
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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
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After lane changeAfter lane change
V=88km/h
Locked Path Following Control
•Controller
•Low speed
•High speed
•Conclusions
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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
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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