Driver Perceived Threat in Rear-End Collision Avoidance ... · Driver Perceived Threat in Rear-End...

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


Objectives of Driver Behaviour Study

4

Agenda




• Data Analysis


• Conclusions


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)


Overview of Rear End Collision Avoidance

6

Agenda




• Data Analysis


• Conclusions


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


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?


10

Vehicle Dynamics Area (VDA) of Lommel Proving Ground


• 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 -


• Experimental Setup – Driver Task

12

Clinic in Progress

13

Agenda




• Data Analysis


• Conclusions


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:


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



100 -0.2296 -0.0947 0.0403 (-----*------)

120 -0.1821 -0.0310 0.1200 (------*-------)

--+---------+---------+---------+-------

-0.40 -0.20 -0.00 0.20



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))




Lateral Acceleration – deep dive

28

Regression – Latacc vs velocity

12011010090807060504030

5.5

5.0

4.5

4.0

3.5

3.0

2.5


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:





Lateral Distance – deep dive

30


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:





Longitudinal Distance - Deepdive

32

Regression

12011010090807060504030

60

50

40

30

20

10


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


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:





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




• Data Analysis


• Conclusions


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


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




• Data Analysis


• Conclusions


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

[email protected]

+49 241 9421 425

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