longitudinal vehicle dynamics control for improved … · longitudinal vehicle dynamics control for...
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Longitudinal Vehicle Dynamics Control for
Improved Vehicle Safety Name: Herman Hamersma
Supervisor: Prof Schalk Els
Date: 19 September 2013
Identifying the problem
𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹
=𝒕𝒕𝑹𝑹𝒕𝒕𝒕𝒕𝒕𝒕 𝒘𝒘𝒘𝒘𝒘𝒘𝒕𝒕𝒘𝒘𝟐𝟐𝒘𝒘𝑹𝑹𝒘𝒘𝒉𝒉𝒘𝒘𝒕𝒕 𝑹𝑹𝒐𝒐 𝑪𝑪𝑪𝑪
Aim of Research • Develop an autonomous longitudinal control
system for path planning and following • Control system will improve vehicles safety by
preventing the vehicle from exceeding vehicle’s limits.
Approach 1. Develop a longitudinal model of the Land Rover
in Adams (Automated dynamic analysis of mechanical systems).
2. Optimize the route the vehicle follows. 3. Develop control system and evaluate
performance in Adams. 4. Implement the control system on the Land
Rover. 5. Compare experimental results with simulated
results.
Modelling the Land Rover: Supply Forces
Measured engine torque Modelled engine torque
020
4060
80100
10001500200025003000350040004500-50
0
50
100
150
200
250
Throttle position [%]
Modelled engine torque
Engine speed [rpm]
Torq
ue [
Nm
]
0
50
100
150
200
Modelling the Land Rover: Demand Forces
Coast down test Demand forces
0 10 20 30 40 50 60 70 80 900
10
20
30Vehicle speed as a function of time
Time [s]
Spee
d [m
/s]
0 10 20 30 40 50 60 70 80 90-0.8
-0.6
-0.4
-0.2
0Vehicle acceleration as a function of time
Time [s]
Acce
lera
tion
[m/s
2 ]
17 18 19 20 21 22 23 24 25 26900
950
1000
1050
1100
1150
1200
1250
1300
Vehicle speed [m/s]
Dem
and
forc
e [N
]
Demand force as a function of vehicle speed
Measured Force
ax2+c fit
Engine Brake Torque Deceleration due to braking
500 1000 1500 2000 2500 3000 3500 4000 4500-40
-35
-30
-25
-20
-15
-10Engine brake torque as a function of engine speed
Speed [RPM]
Torq
ue [N
m]
Modelling the Land Rover: Demand Forces
-1 0 1 2 3 4 5 6 7-2
-1
0
1
2
3
4
5 g p
Hydraulic pressure [MPa]
Decele
rati
on
[m
/s2]
Measured dataFitted function
Adams Model - Summary
• Engine map modelled as a function of engine speed and throttle position
• Drag and rolling resistance modelled as a function of vehicle speed
• Engine braking torque was modelled as a function of engine speed
• Braking deceleration was modelled as a function of brake line pressure
Control System Development • Rollover threshold given by:
𝑨𝑨𝒚𝒚𝒉𝒉
=𝒕𝒕𝒘𝒘𝟐𝟐𝒘𝒘
• Lateral acceleration given by: 𝑨𝑨𝒚𝒚 =
𝑽𝑽𝟐𝟐
𝑹𝑹
• Thus, increase radius of path leads to a higher permissible speed or lowers lateral acceleration
• Leads to trajectory planning
Trajectory Planning • Racetrack discretised into sections
– Coordinates of right and left side of track – Position on section of the track indicated by α – α = 0 → LH side of track – α = 1 → RH side of track
300 350 400 450-640
-620
-600
-580
-560
-540
-520
-500
-480
Track discretisation
x-coordinate
y-co
ordi
nate
Left boundaryRight boundary
α = 0
α = 1
Trajectory Planning • Optimisation:
– Curvature requires second derivative – Use finite difference methods to approximate
curvature – Minimise the “global” curvature of the trajectory
– Standard quadratic form → use quadratic
programming to optimise
𝜿𝜿 = 𝜶𝜶 𝑻𝑻 𝑯𝑯 𝜶𝜶 + 𝒃𝒃 𝑻𝑻 𝜶𝜶
Trajectory Planning
0 200 400 600 800 1000
-700
-600
-500
-400
-300
-200
-100
0
100
Bird's eye view of Gerotek's ride and handling track
Distance x [m]
Dist
ance
y [m
]
Road boundariesTrajectory
50 100 150 200 250 300 350 400 450
-550
-500
-450
-400
-350
-300
-250
x-coordinate [m]
y-co
ordi
nate
[m]
Discretised track with minimum curvature trajectory
Longitudinal Control System
• The reference speed (V) must now be determined.
• Reference speed limited by: – Maximum lateral acceleration: – Friction available (friction circle) – Vehicle’s longitudinal performance capabilities
(supply and demand forces)
𝒕𝒕𝒚𝒚 =𝑽𝑽𝟐𝟐
𝑹𝑹
Maximum Lateral Acceleration
• Minimising the curvature is the same as maximising the radius
• To determine the radius of curvature:
𝒕𝒕𝒚𝒚 =𝑽𝑽𝟐𝟐
𝑹𝑹
𝑹𝑹𝒘𝒘 = 𝒙𝒙𝑹𝑹,𝒘𝒘 − 𝒙𝒙𝒘𝒘𝟐𝟐 + 𝒚𝒚𝑹𝑹,𝒘𝒘 − 𝒚𝒚𝒘𝒘
𝟐𝟐
Friction Available (Friction Circle)
• Friction force available is the vector subtraction of lateral force (generated by cornering) from the limit:
𝑨𝑨𝒙𝒙,𝒘𝒘 = 𝑨𝑨𝒙𝒙,𝒎𝒎𝒕𝒕𝒙𝒙 𝟏𝟏 − 𝑨𝑨𝒚𝒚,𝒘𝒘 𝑨𝑨𝒚𝒚,𝒎𝒎𝒕𝒕𝒙𝒙⁄ 𝟐𝟐
Vehicle’s Performance
0 50 100 1500
1
2
3
4
Vehicle speed [km/h]
Acc
eler
atio
n [m
/s2 ]
Maximum acceleration available as a function of speed
0 50 100 150-6.15
-6.1
-6.05
-6
-5.95
Vehicle speed [km/h]
Acc
eler
atio
n [m
/s2 ]
Maximum deceleration available as a function of speed
Speed Profile Algorithm
• Preview distance • Speed at each point
on the trajectory determined with limiting longitudinal acceleration
• Speed limit of 130km/h
𝒘𝒘𝒑𝒑𝑹𝑹𝑹𝑹𝑹𝑹 = 𝑽𝑽𝑽𝑽 −𝟏𝟏𝟐𝟐𝒕𝒕𝒎𝒎𝒕𝒕𝒙𝒙,𝑹𝑹𝑹𝑹𝒍𝒍𝒉𝒉𝑽𝑽𝟐𝟐 + 𝒕𝒕𝑹𝑹𝒍𝒍𝒄𝒄𝒕𝒕
𝑽𝑽𝒘𝒘+𝟏𝟏 = 𝑽𝑽𝒘𝒘𝟐𝟐 + 𝟐𝟐𝑨𝑨𝒙𝒙∆𝒄𝒄𝒘𝒘
0 500 1000 1500 2000 2500 3000 3500 4000 45000
20
40
60
80
100
120
140Reference speed for Gerotek
Distance travelled [m]
Spee
d [k
m/h
]
Reference speed
Maximum speed V2/R
ADAMS/View Simulation • Obtain GPS coordinates for various tracks around
the world – Silverstone – Imola – Zandvoort – Gerotek’s ride and handling track
• Generate a trajectory (path) and speed profile for each track
• Specify acceleration limits (longitudinal and lateral) • SIMULATE!
Simulation Results - Gerotek
0 500 1000 1500 2000 2500 3000 3500 40000
50
100
150
Distance travelled [m]
Spee
d [km
/h]
Speed as a function of distance travelled
ADAMS/View model speedLong ref speedMax lateral speed
0 500 1000 1500 2000 2500 3000 3500 4000-10
-5
0
5
10
Distance [m]
Acce
lerati
on [m
/s2 ]
Acceleration as a function of distance
LateralLongitudinalLimits
-1.5 -1 -0.5 0 0.5 1 1.5
-0.5
0
0.5
Friction circle
Lateral [g]
Long
itudi
nal [
g]
0 500 1000
-600
-400
-200
0
Path followed
x coordinates [m]
y coo
rdin
ates [
m]
Gerotek ride and handling simulation results
Simulation Results - Silverstone
0 500 1000 1500 2000 2500 3000 3500 40000
50
100
150
Distance travelled [m]
Spee
d [k
m/h
]
Speed as a function of distance travelled
ADAMS/View model speedLong ref speedMax lateral speed
0 500 1000 1500 2000 2500 3000 3500 4000-10
-5
0
5
10
Distance [m]
Acce
lera
tion
[m/s
2 ]
Acceleration as a function of distance
LateralLongitudinalLimits
-1 0 1-1
-0.5
0
0.5
1Friction circle
Lateral [g]
Long
itudi
nal [
g]
-500 0 500
-800
-600
-400
-200
0Path followed
x coordinates [m]
y co
ordi
nate
s [m
]Silverstone simulation results
Simulation Results Discussion • Trajectory planning used to minimise curvature • Lateral acceleration, friction and vehicle
performance limit used to determine maximum longitudinal acceleration
• Speed profile developed and implemented in Adams
• The model was able to negotiate several racetracks while maintaining control
Experimental Validation • Procedure:
– Record the path to be driven by driving at low speed.
– Define the maximum allowable lateral and longitudinal acceleration.
– Calculate the speed profile – Perform a severe double lane change
manoeuvre – Hope the vehicle brakes
Experimental Results
0 100 200 300 400 500 600-4
-2
0
2Path followed
x-coordinate [m]
y-co
ord
inat
e [m
]
-10 -5 0 5 10
-202
g-g diagram
Lateral acceleration [m/s2]
Lo
ng
itu
din
al
ac
cele
rati
on
[m
/s2 ]
0 100 200 300 400 500 6000
20
40Speed as a function of distance travelled
Distance travelled [m]
Sp
eed
[m
/s]
Measured speedDesired speed
0 100 200 300 400 500 6000
1
2Brake line pressure as a function of distance travelled
Distance travelled [m]
Bra
ke P
ress
ure
[M
Pa]
Measured pressureDesired pressure
0 100 200 300 400 500 600-4
-2
0
2
4Acceleration as a function of distance travelled
Distance travelled [m]
Acc
eler
atio
n [
m/s
2 ]
Longitudinal accelerationLateral acceleration
DLC - Lateral 5m/s2 ; Longitudinal 8m/s2
Experimental Results • Lateral acceleration of vehicle was kept below
prescribed limit • Vehicle reduced speed when exceeding speed
limit and tracked the speed limit • Control system was found to be
conservative(brakes early)
Conclusion • Aim was to develop a control system that limits lateral
acceleration by controlling vehicle speed • Longitudinal dynamics modelled in ADAMS:
– Engine map – Demand forces – Brakes – Engine braking
• Longitudinal control system developed • Control system performance was simulated in ADAMS • Control system implemented experimentally
Future Work • Investigate control system’s performance on test
track that resembles public roads
• Optimise the trajectory in real-time
• Integrate the developed control system with lane departure warning and obstacle detection
Thank you