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Driver Perceived Threat in Rear-End Collision Avoidance
Situations – A Statistical Approach
Jitendra Shah
Ford Research Center Aachen
interactIVe Summer School, Korfu, Greece
4-6 July, 2012
2
Agenda
• Objectives of Driver Behaviour Study
• Overview of Rear End Collision Avoidance
• Test Vehicle Setup & Clinic Overview
• Data Analysis
• Perceived Safety
• Conclusions
Summer School 4 - 6 July 2012
3
• For collision avoidance there is always a balance between early
intervention by the systems and delaying the system reaction long enough
until it is ensured that the driver will not (or is no longer able to) intervene.
• Determine the steering onsets when the driver avoids a rear end collision
by steering.
• Determine preferred lateral distance and acceleration
Summer School 4 - 6 July 2012
Objectives of Driver Behaviour Study
4
Agenda
• Objectives of Driver Behaviour Study
• Overview of Rear End Collision Avoidance
• Test Vehicle Setup & Clinic Overview
• Data Analysis
• Perceived Safety
• Conclusions
Summer School 4 - 6 July 2012
5
• Collision avoidance functions
are divided into four sub-functions:
- lane change collision avoidance (LCCA)
- side impact avoidance (SIA)
- run off-road prevention (RORP)
- rear end collision avoidance (RECA)
• Autonomous steering and/or braking intervention in case of imminent threat
• Evaluates the status of the host vehicle as well as of the surrounding traffic
and environment by utilising different sensors (e.g. radar, camera and
ultrasonic sensors and the digital map)
Summer School 4 - 6 July 2012
Overview of Rear End Collision Avoidance
6
Agenda
• Objectives of Driver Behaviour Study
• Overview of Rear End Collision Avoidance
• Test Vehicle Setup & Clinic Overview
• Data Analysis
• Perceived Safety
• Conclusions
Summer School 4 - 6 July 2012
7
• Ford Focus, 2.0 L Diesel
• Automatic transmission
• Equipped with:
• In-Vehicle sensors
- yaw rate
- lateral acceleration
- longitudinal acceleration
- steering angle
- pedal position
• Cameras monitors environment
and driver
• Differential GPS
• Front and rear radar
Test Vehicle Setup & Clinic Overview
8 04 March 2014 Confidential
• 21 drivers + 4 experts
• Ford employees
• Age from 25-65 years
• 7 female and 18 male
Test Vehicle Setup & Clinic Overview
Details of drivers participated in the clinic
9 04 March 2014 Confidential
1 What is the last moment of steering perceived by driver?
2 How much torque and speed do they apply when steering?
3 What is the level of lateral acceleration?
4 How long does it take to control the vehicle after passing the obstacle?
5 What is the lateral distance to the obstacle when passing it?
6 How do driver parameters affect reaction (age, gender etc.)
7 How is the driver reaction affected by level of speed and dv?
8 What is the driver reaction time?
Test Vehicle Setup & Clinic Overview
10
Vehicle Dynamics Area (VDA) of Lommel Proving Ground
Test Vehicle Setup & Clinic Overview
• Experimantal Setup
11
- Steering manoeuvre as per table
- Order of manoeuvre execution is
randomized
- Drivers were requested to conduct the
manoeuvre as late as possible and not to
brake during manoeuvre.
Velocity Scenario
Host vehicle speed [km/h] FREE steering only 2 - LANES steering only 3 - LANES steering only
35 - x -
50 - x -
70 x x x
100 x x x
120 x x -
Test Vehicle Setup & Clinic Overview
• Experimental Setup – Driver Task
12
Clinic in Progress
13
Agenda
• Objectives of Driver Behaviour Study
• Overview of Rear End Collision Avoidance
• Test Vehicle Setup & Clinic Overview
• Data Analysis
• Perceived Safety
• Conclusions
Summer School 4 - 6 July 2012
14
1. The recorded data from sensors has been imported to matlab.
2. The automated script has been written to read, analyze and write metrics in excel
sheet from matlab. The metrics are shown below in the table.
Collision Avoidance by Steering
Time to Collision(TTC)
Onset Distance
Onset Velocity
Lateral Acceleration
Lateral Displacement
Max. Torque
Max. Steering Wheel Angle
Max. Steering Wheel Velocity
Extract Information from Raw Data
15
Factors:
1. No of Lanes
2. Drivers Skill level (Regular, Expert)
3. Driver Gender (Male, Female)
4. Vehicle Speed ( 35, 50, 70, 100, 120kph)
TTC - Deepdive
16
In research on Traffic Conflicts Techniques, Time-To-Collision (TTC) has proven to be
an effective measure for rating the severity of conflicts.
TTC is defined as: "The time required for two closing vehicles to collide if they
continue at their present speed and acceleration in the same lane".
0 10 20 30 40 50 600
5
10
15
Velocity[kph]
TT
C [s]
=1.0 TTCStr
=0.2 TTCStr
=0.2 TTCBrk
=0.2 TTCBrk
),,( latdStr ayfTTC
),,( longBrk avfTTC
where,
yd = lateral deviation
alat = lateral acceleration
v = vehicle velocity
alon = long. Deceleration
µ = coefficient of friction
Definition - TTC
17
malefemale
3.5
3.0
2.5
2.0
1.5
1.0
Gender
TT
C
Boxplot of Time To Collision when Steering
RegularExpert
3.0
2.5
2.0
1.5
1.0
Skill
TT
C
Boxplot of TTC
120100705035
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Requested Velocity [kph]
TT
C [
s] 2.6
Boxplot of Time-to-Collision(TTC) when Steering
632
3.0
2.5
2.0
1.5
1.0
No of Lanes
TTC
Boxplot of TTC
Effects of factors on TTC
18
420
420
0.999
0.99
0.9
0.5
0.1
0.01
0.001
420
0.999
0.99
0.9
0.5
0.1
0.01
0.001
35
TTC
Pro
ba
bili
ty
50 70
100 120
35
50
70
100
120
ReqVel
Probability Plot of TTCNormal - 95% CI
Panel variable: ReqVel
3.63.02.41.81.20.6
3.63.02.41.81.20.6
20
15
10
5
0
3.63.02.41.81.20.6
20
15
10
5
0
35
TTC
Fre
qu
en
cy
50 70
100 120
Histogram (with Normal Curve) of TTC by ReqVel
• The metrics from time series data have been extracted.
• It is found that data is not in normal distribution at different factor levels.
• To compare metrics even at different factor levels it is required to transform the data
in normal distribution at all factor levels.
The distribution of TTC has been shown in probability plot & histogram
Understanding Raw data
20
0 20 40 60 80 100 1200
10
20
30
40
50
60
70
80
90
100
X: 60
Y: 14.4
Velocity[kph]
Cri
tica
l D
ista
nce
[m
]
X: 28
Y: 15.02
X: 50
Y: 23.69
=0.2 XStr
=1.0 XStr
=0.2 XBrk
=1.0 XBrk
=1.0 XStr
-Driver
=1.0 XBrk
-Driver
With out system and vehicle response delay
Break Even Point for Steering & Braking
21
Spread of TTC
H0 : σ30kph = σ50kph =…= σ120kph
Ha : σ30kph ≠ σ50kph =… ≠ σ120kph
Bartlett test : For normal data
Levene's test : For non- normal data
There is significant variance of TTC
@velocity. The related p-value is less than
0.05 so reject H0.
Inference: The variance in TTC is not same at different
velocity.
The variance in TTC for male and female for
all velocity is same.
Variances in TTC @ speed & gender
120
100
70
50
35
1.11.00.90.80.70.60.50.40.3
Re
qu
este
d V
elo
cit
y [
kp
h]
95% Bonferroni Confidence Intervals for StDevs
Test Statistic 16.56
P-Value 0.002
Test Statistic 4.30
P-Value 0.002
Bartlett's Test
Levene's Test
Test for Equal Variances for TTC
male
female
0.650.600.550.500.450.40
Ge
nd
er
95% Bonferroni Confidence Intervals for StDevs
male
female
4.03.53.02.52.01.51.0
Ge
nd
er
TTC
Test Statistic 1.31
P-Value 0.170
Test Statistic 6.92
P-Value 0.009
F-Test
Levene's Test
22
TTC – Velocity Difference
Metrics/Vehicles TTC (P-value = 0)
L C U
35kph -0.0317 -0.1545 0.3067
50kph -0.3542 -0.1613 0.0317
70kph -0.3067 -0.1545 0.000
100kph -0.4011 -0.2491 0.000
120kph -0.3470 -0.1855 0.000
The hypothesis :
H0 : μ35kph = …= μ120kph
Ha : μ35kph ≠ … ≠ μ120kph
Inference: 1) The mean of transformed TTC is different from atleast one set.
2) The variation of TTC is 1.32s
Individual 95% CIs For Mean Based on Pooled StDev
Level N Mean StDev ------+---------+---------+---------+---
35 22 0.7247 0.2962 (--------*---------)
50 19 0.5634 0.2889 (----------*---------)
70 64 0.5702 0.3344 (-----*----)
100 65 0.4755 0.2483 (-----*----)
120 43 0.5392 0.2071 (------*------)
------+---------+---------+---------+---
0.48 0.60 0.72 0.84
Pooled StDev = 0.2785
Hsu’s Multiple Comparison with Best
23
Tukey‘s Test – pairwise comparison of TTC ReqVel = 35 subtracted from:
ReqVel Lower Center Upper --+---------+---------+---------+-------
50 -0.4012 -0.1613 0.0787 (-----------*-----------)
70 -0.3438 -0.1545 0.0349 (--------*---------)
100 -0.4381 -0.2491 -0.0602 (---------*--------)
120 -0.3863 -0.1855 0.0153 (---------*---------)
--+---------+---------+---------+-------
-0.40 -0.20 -0.00 0.20
ReqVel = 50 subtracted from:
ReqVel Lower Center Upper --+---------+---------+---------+-------
70 -0.1934 0.0068 0.2069 (---------*---------)
100 -0.2877 -0.0879 0.1119 (---------*---------)
120 -0.2353 -0.0243 0.1868 (----------*---------)
--+---------+---------+---------+-------
-0.40 -0.20 -0.00 0.20
ReqVel = 70 subtracted from:
ReqVel Lower Center Upper --+---------+---------+---------+-------
100 -0.2296 -0.0947 0.0403 (-----*------)
120 -0.1821 -0.0310 0.1200 (------*-------)
--+---------+---------+---------+-------
-0.40 -0.20 -0.00 0.20
ReqVel = 100 subtracted from:
ReqVel Lower Center Upper --+---------+---------+---------+-------
120 -0.0870 0.0636 0.2142 (------*-------)
--+---------+---------+---------+-------
-0.40 -0.20 -0.00 0.20
24
TTC – Gender Differences
malefemale
3.5
3.0
2.5
2.0
1.5
1.0
Gender
TT
C
Boxplot of Time To Collision when Steering
Two-Sample T-Test and CI: TTC, Gender
Two-sample T for TTC
Gender N Mean StDev SE Mean
female 75 2.084 0.535 0.062
male 138 1.655 0.466 0.040
Difference = mu (female) - mu (male)
Estimate for difference: 0.4289
95% CI for difference: (0.2899, 0.5679)
T-Test of difference = 0 (vs not =): T-Value = 6.08 P-Value = 0.000
DF = 211
Both use Pooled StDev = 0.4915
Inference Previously, we have seen that variances are equal.
There is sufficient evidence exist that mean TTC
for male and female exist.
p-values <0.05 &
CI does not include zero.
The estimated difference is 0.43s(approx)
25
Regression of TTC among Estimates
0.500.250.00-0.25-0.50
0.50
0.25
0.00
-0.25
-0.50
-0.75
First Component
Se
co
nd
Co
mp
on
en
t
ActVel
No_of_Lane
Abs_SWA
Abs_LatAcc_BoxCox
Abs_latDist_BoxCox
Abs_LongDist_BoxCox
TTC_BoxCox
Loading Plot of Estimates
Statistian‘s View
Engineer’s View
4.03.22.4 1.51.00.5 210
1.5
1.0
0.5
0.0
531
1.5
1.0
0.5
0.0
1208040 642
Abs_LongDist_BoxCox
TTC
_B
oxC
ox
Abs_latDist_BoxCox Abs_LatAcc_BoxCox
Abs_SWA_BoxCox ActVel No_of_Lane
Scatterplot of TTC_BoxCox
26
Criteria Conclusions
Velocity 1. Theoretically, TTC for steering is independent of vehicle velocity.
2. Practically, it is found that the only difference in TTC exist between
35kph and 100kph for steering.
3. The break-even point for steering and braking is 60kph at 14.5m
without system delay.
4. The break-even point for steering and braking is 40kph at 14.5m with
system delay.
5. The break-even point for steering and braking is 50kph at 24.0m for
drivers.
Enviro 1. The number of available free lanes does not affect TTC.
Driver 1. Beautiful gender take significantly more TTC than the handsome
gender.
2. The ascending driving skills reduces the required TTC.
Summary of TTC findings
Summary of TTC findings
27
Factors:
1. No of Lanes (2,3,Free(6))
2. Drivers Skill level (Regular, Expert)
3. Driver Gender (Male, Female)
4. Vehicle Speed ( 35, 50, 70, 100, 120kph)
Lateral Acceleration – deep dive
28
Regression – Latacc vs velocity
12011010090807060504030
5.5
5.0
4.5
4.0
3.5
3.0
2.5
Requested Velocity [kph]
La
tera
l A
cce
lera
tio
n [
m/
s^
2]
S 0.0751838
R-Sq 99.6%
R-Sq(adj) 99.2%
Regression
95% CI
95% PI
The lateral accelerations achieved by drivers has quadratic relationship with velocity.
2000376.00815.0693.0 vvamean
29
Factors:
1. No of Lanes (2,3,Free(6))
2. Drivers Skill level (Regular, Expert)
3. Driver Gender (Male, Female)
4. Vehicle Speed ( 35, 50, 70, 100, 120kph)
Lateral Distance – deep dive
30
Criteria Conclusions
Velocity 1. Lateral displacement has equal variance is all velocities
2. The lateral distance targetted by driver at different velocities are not
significantly different from each other
Enviro 1. The number of available free lanes does affect lateral displacement.
2. 2 lanes or 3 lanes scenario has no significant difference
3. Free space and 2 lanes or 3 lanes scenario is significantly diferent by
1.1m
Driver 1. Beautiful genders take significantly more lateral distance than the
handsome genders by 1.16m
2. The ascending driving skills reduces the required lateral distance.
Summary of lateral displacement findings
31
Factors:
1. No of Lanes (2,3,Free(6))
2. Drivers Skill level (Regular, Expert)
3. Driver Gender (Male, Female)
4. Vehicle Speed ( 35, 50, 70, 100, 120kph)
Longitudinal Distance - Deepdive
32
Regression
12011010090807060504030
60
50
40
30
20
10
Requested Velocity [kph]
Me
an
On
se
t D
ista
nce
[m
]
S 1.74810
R-Sq 98.8%
R-Sq(adj) 98.4%
Regression
95% CI
95% PI
vxonset 03937.0352.5
Regression among onset distance and vehicle velocity
33
Criteria Conclusions
Velocity 1. Longitudinal distance has equal variance is all velocities
2. The longitudinal distance targetted by driver at different velocities are
significantly different from each other execpt between 35kph and 50kph
Enviro 1. The number of available free lanes does effect longitudinal distance.
2. 2 lanes or 3 lanes scenario has no significant difference
3. Free space and 3 lanes scenario is significantly diferent .
Driver 1. Beautiful genders take significantly more longitudinal displacement
than the handsome genders by 10m
2. The ascending driving skills reduces the required longitudinal
displacement by 13.7m
Summary of longitudinal distance findings
34
Steering Torque – Deep Dive
Factors:
1. No of Lanes (2,3,Free(6))
2. Drivers Skill level (Regular, Expert)
3. Driver Gender (Male, Female)
4. Vehicle Speed ( 35, 50, 70, 100, 120kph)
35
Regressions
1086420
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Abs. Max. Lateral Acceleration[m/s^2]
Ab
s.
Ma
xT
ors
ion
Ba
r T
orq
ue
[N
m]
S 0.202320
R-Sq 86.0%
R-Sq(adj) 85.8%
Regression
95% CI
95% PI
201246.004074.0262.2 yytrq aaTbar
The regression among steering wheel torque and lateral acceleration is shown below
36
Agenda
• Objectives of Driver Behaviour Study
• Overview of Rear End Collision Avoidance
• Test Vehicle Setup & Clinic Overview
• Data Analysis
• Perceived Safety
• Conclusions
Summer School 4 - 6 July 2012
37
Perceived Safety - Questionnaire
The responses of the drivers to the questionnaire form a natural order. It is a natural
option to fit a ordinal logistic regression model.
The questionnaire has 5 levels of safety feel to choose after each maneuver.
- How safe or unsafe did you feel during the last maneuver?
very somewhat neither somewhat very
Unsafe Safe
Scale 1 2 3 4 5
38
Attribute data – Feeling safe
12011010090807060504030
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Requested Velocity [kph]
Fe
eli
ng
Sa
fe [
-]
ReqVel
Gender
120
100705035
male
female
male
female
male
fem
ale
male
female
male
fem
ale
5.0
4.5
4.0
3.5
3.0
Fe
eli
ng
Sa
fe [
-]
Interval Plot of Feeling safe95% CI for the Mean
The rating scale is not explored by drivers!
Variable Value Count
Feeling Safe
2 4
3 13
4 98
5 98
0.500.250.00-0.25-0.50
0.75
0.50
0.25
0.00
-0.25
-0.50
First Component
Se
co
nd
Co
mp
on
en
t
Feeling safe
Abs_SWA_BoxCox
Abs_LatAcc_BoxCox
Abs_latDist_BoxCoxAbs_LongDist_BoxCox
TTC_BoxCox
Loading Plot
Strong influence: Lateral Distance,
Longitudinal Distance
Weak Influence : TTC
39
Estimate Model
Suppose we have k ordered levels of our categorical variable (Safety feel) k = 5,
The proportional Odds model is :
Note that b0k is different for each level of categorical variable.
Odds and Odd ratios are very informative way of expressing the relationship between
categorical varaibles.
Odds is defined as the probability of an event occuring divided by probability of the
event not occuring
40
Significant Factors in OLR
Logistic Regression Table
Odds 95% CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Const(1) -15.6640 4.61745 -3.39 0.001
Const(2) -14.0564 4.59080 -3.06 0.002
Const(3) -11.0319 4.54698 -2.43 0.015
TTC_BoxCox -2.27400 1.26578 -1.80 0.072 0.10 0.01 1.23
Abs_latDist_BoxCox 3.95001 0.987757 4.00 0.000 51.94 7.49 359.97
Abs_LongDist_BoxCox 2.18964 1.05043 2.08 0.037 8.93 1.14 70.00
Abs_LatAcc_BoxCox -0.164366 0.975453 -0.17 0.866 0.85 0.13 5.74
Abs_SWA_BoxCox 0.340979 0.761455 0.45 0.654 1.41 0.32 6.26
Small p-values
The factors chosen to be part of ordinal regression model are as
- Time to Collision
- Lateral Distance
- Longitudinal Distance
- Lateral Acceleration
- Steering Wheel Angle
Only the factors with small p-values has significant effect on „Safety feel“.
41
Probability of Perceived Safety
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00
Pro
ba
bilit
y o
f P
erc
eiv
ed
Sa
fety
Score
Some what Unsafe(2)
Neither(3)
Some what safe(4)
Very Safe(5)
42
Agenda
• Objectives of Driver Behaviour Study
• Overview of Rear End Collision Avoidance
• Test Vehicle Setup & Clinic Overview
• Data Analysis
• Perceived Safety
• Conclusions
Summer School 4 - 6 July 2012
43
Conclusion
1. The driver clinic really shows the threat that can be accepted by driver with
out feeling unsafe.
2. Ordinal logistic regression shows the fit of the driver response to the
engineering metric.
3. Lateral acceleration preferred by drivers is saturated to 0.5g.
4. The steering torque required to do manoeuvres is linearly increasing with
increasing lateral acceleration.
5. TTC for steering is constant for all velocity which is matching with
enginnering findings.
6. The system delay compensation is required during autonomous system
intervention to avoid getting the break even point below the driver perceived
break even point.
44
Thank you.
Jitendra Shah
Research Engineer
Ford Research Center Aachen, Germany
+49 241 9421 425