Active Steering Project
Andrew Odhams
Richard Roebuck
David Cebon
2nd April 2009
Contents
1.
2.
3.
4.
Control concept
Low speed testing
High speed testing
Conclusions
ACTIVE STEERING
•Controller
Lead Point
•Low speed
•High speed
Follow Point
•Conclusions
– 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
PATH FOLLOWING TESTS
•Controller
UK Roundabout Test
•Low speed
•High speed
•Conclusions
11.25m
8.9m
12.5m
5.3m
LOW SPEED ROUNDABOUT
• Unsteered:
•Controller
•Low speed
•High speed
•Conclusions
LOW SPEED ROUNDABOUT
• Command Steer:
•Controller
•Low speed
•High speed
•Conclusions
LOW SPEED ROUNDABOUT
•Controller
• Offtracking of 5th Wheel:
•Low speed
1
Tail Swing
•Conclusions
Offtracking: Front Tractor - 5th Wheel [m]
•High speed
0
Locked
Cut In
-1
Command
CVDC
-2
-3
-4
-5
0
10
20
30
40
50
Time [s]
60
70
80
90
100
LOW SPEED ROUNDABOUT
•Controller
• Offtracking of Trailer Rear:
•Low speed
1
Tail Swing
•Conclusions
Offtracking: Front Tractor - Rear Trailer [m]
•High speed
0
CVDC
Cut In
-1
-2
Command
-3
Locked
-4
-5
0
10
20
30
40
50
Time [s]
60
70
80
90
100
LOW SPEED ROUNDABOUT
•Controller
• Tail Swing:
•Low speed
•High speed
•Conclusions
Locked
Command
• Tail swings into blind spot
Path Following
LATERAL TYRE FORCES
• Unsteered:
•Controller
•Low speed
•High speed
•Conclusions
LATERAL TYRE FORCES
• Unsteered:
•Controller
•Low speed
•High speed
•Conclusions
• FIXED TRAILER: 36.6 kN
LATERAL TYRE FORCES
• Path following Strategy:
•Controller
•Low speed
•High speed
•Conclusions
• CT-AT TRAILER: 6.1 kN
Rollover Prevention
•Controller
•Low speed
•High speed
•Conclusions
• 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
Virtual Driver Model
of Trailer Steering
•Controller
Y
Current position
of 5th wheel
•Low speed
•High speed
Semi-trailer
•Conclusions
Tractor
etr
ytr
yr 0
yr1
yr 2
yrh
X
O
uT
Snapshot of tractor semi-trailer and path of 5th wheel at time instant k
Optimal Control Strategy
•Controller
•Low speed
•High speed
Discrete-time equations for vehicle and path of 5th wheel
 x  k  1   Ad


 y  k  1   0
0   x k   0 
 B0 d 
 B1d 

y

u
k


   ri         k 

D   y  k   E 
 0 
 0 
•Conclusions
x  1 1
y   yr 0
yr 1
1  1 2 2
yr 2
yrh 
2  2
T
y2  2 
T
The control objectives
 etr 
 a   Cz  Du
 y2 
 x
z    and
 y
where
u   tr
The cost function




J   Q1  etr  k    Q2 a y2  k   R  u  k  
k 0
Path error
2
2
Lateral Accel’n
2

Steering effort
Results continued
•Controller
•Low speed
•High speed
•Conclusions
Manoeuvre: Lane change
Vehicle speed: 88km/h
Fixed value of Q1/R=0.05
Selection of weighting value
•Controller
•Low speed
Manoeuvre: Lane change
Vehicle speed: 88km/h
Fixed value of Q1/R=0.05
•High speed
•Conclusions
25% reduction
Conventional
Q2/R=0.005
Path errors in lane change
•Controller
0.8
q1 /r=0.05
•Low speed
RSC(q2 /r=0.1) [TO=0.72]
0.6
•High speed
•Conclusions
RSC(q2 /r=0.025) [TO=0.31]
Path tracking error [m]
0.4 Locked [TO=0.35]
RSC(q2 /r=0.0025) [TO=0.07]
0.2
0
-0.2
PFC(q2 /r=0) [TO=0.15]
-0.4
-0.6
-0.8
0
20
40
60
80
100
X distance [m]
120
140
160
180
After lane change
•Controller
•Low speed
•High speed
•Conclusions
V=88km/h
Locked
Path Following Control
PERFORMANCE MEASURES
•Controller
•Low speed
•High speed
High speed
•Conclusions
Performance
Measure
Locked
Transient Off-tracking [m]
Comm.
Steer
Low speed
PFC
RSC
0.35
-0.15
0.31
Rearward Amplification
1.18
1.05
0.86
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
Conclusions
• 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