Collision Risk Evaluation Index Based on Deceleration for Collision ...

Collision Risk Evaluation Index Based on Deceleration for Collision Avoidance (First Report) - Proposal of a new index to evaluate collision risk against forward obstacles Toshihiro HIRAOKA,a Masaki TANAKA,a,b Hiromitsu KUMAMOTO,a Tatsuya IZUMIc and Kenichi HATANAKAc a

Department of Systems Science, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan b

He currently works at Bosch Corporation. c

Sumitomo Electric Industries, Ltd.,

1-1-3, Shimaya, Konohana-ku, Osaka 554-0024, Japan Received Y XXX 2007: received in revised form Y XXX 2007

Abstract This paper proposes deceleration for collision avoidance (DCA) as a new index to evaluate collision risk against forward obstacles. Cases in which the vehicle in front maintains its current acceleration or decelerates abruptly are defined as overt- and potential DCAs, respectively. Numerical simulations are performed to compare the DCA values with time-to-collision and margin-to-collision, which are well-known indices used to evaluate the potential collision risk in a situation where the possibility of collision with a forward obstacle is high. 1. Introduction

braking force according to the amount of brake pedal

In an attempt to realize a zero-traffic-accident society,

depression, and 3) an automatic brake function that applies

the five-year Eighth Fundamental Traffic Safety Program [1]

the brakes automatically to reduce collision velocity and to

aims to reduce the number of traffic deaths and traffic

mitigate collision damage when the system deems that a

casualties to 5,500 and a million or fewer, respectively, by

collision is unavoidable.

2010. The White Paper on Traffic Safety in Japan 2008 [2]

This paper describes the deceleration required to avoid

reported that the number of traffic deaths had decreased over

collision using a deceleration for collision avoidance (DCA)

the past seven years to 5,744, and that the number of traffic

index, which can be applied to determining the warning

casualties has also decreased over the past three years to

provision threshold of a forward obstacle collision warning

1,034,445. The decreasing trend is steady, but it is readily

system (FOCWS). This is equivalent to the collision

apparent that we have to make greater efforts in order to

warning function mentioned above. Moreover, in a situation

achieve the proposed target.

where the collision risk with the preceding vehicle becomes

The Traffic Safety Program [1] proposes various

high, the DCA values are compared with those from other

measures to reduce traffic accidents, one of which is

indices,

research and development into the advanced safety vehicle

margin-to-collision (MTC), which are used in conventional

(ASV),

FOCWSs.

which

is

an

intelligent

vehicle

utilizing

such

as

time-to-collision

(TTC)

and

information-communication technology. One of the practical technologies

employed

in

the

ASV

is

a

forward

2. FOCWS

collision-damage mitigation braking system, which consists

2.1 Three processes of driving behavior and driving

of 1) a collision warning function that warns drivers when

support systems

the system detects the possibility of a collision with forward

Driving behavior consists of three processes: perception,

obstacles, 2) a brake assist function which amplifies the

judgment, and operation. Except for unforeseen accidents,

Driving environment ① Perception support

Environmental Information, Vehicle state, etc.

Following vehicle (FV)

Direct driving support system ② Judgment support

vf, af

③ Operation support

Camera image, …

Alarm sound, Warning sign,….

Automatic brake / steering,…

Perception

Judgment

Operation

Steering, Gas / Brake pedals, Switches, etc.

xf

Preceding vehicle (PV) v p , ap

xp

x

Fig. 2: Definition of variables ④ Environmental improvement

FOCWS detects not only the preceding vehicle, but also a

Road shape improvement, Drainage pavement, Hump, etc.

Indirect driving support system

pedestrian. This paper adopts the same variables and

Fig. 1: Three processes of driving behavior and various driving support systems

definitions as the previous study [4], which assessed the relationship among different collision risk indices. As shown

most traffic accidents occur as a result of human error, which may happen in any of the three processes. Consequently,

supporting

perception,

judgment,

and

operation will reduce the number of traffic accidents; for example, mechanisms that facilitate "information provision" for perception support, "warning provision" for judgment support, and "operation intervention" for operation support. In a previous paper [3], we classified driving support systems according to the relationship between the driver and the system. Judgment support evaluates a given situation based on certain criteria, and provides the results to the driver via a warning message and an audio alarm. This is followed by operation support, which then intervenes in the driving operation. A system that gets directly involved with driving behavior through either judgment or operation support is defined as "a direct driving support system." In contrast, a system that provides information to drivers for perception

support

or

which

improves

the

driving

environment through a road shape improvement and a drainage pavement are defined as "indirect driving support systems," because drivers make their own decisions and

in Fig. 2, the reference points of the following vehicle and the preceding vehicle are defined as the tip and the rear-end point of the vehicles, respectively, because the FOCWS evaluates the collision risk based, not on the distance between the centers of gravity, but on inter-vehicular distance. The positions, velocities and accelerations of the following vehicle and the preceding vehicle are defined as x f , v f , a f , x p , v p , a p , and the relative position, relative velocity, and relative acceleration are defined as xr , vr , ar .

Note that the relative position xr ( = x f − x p )

becomes

negative when the following vehicle is behind the preceding vehicle. Therefore, the inter-vehicular distance of the following state can be calculated by multiplying the relative position xr by minus. The relative velocity vr is defined as positive when the velocity of the following vehicle is higher than that of the preceding vehicle. The relative acceleration ar is defined as positive when both vehicles accelerate and the acceleration of the following vehicle is greater than that of the preceding vehicle, or when both vehicles decelerate and the deceleration of the following vehicle is lower than that of the preceding vehicle.

drive the vehicle themselves. Figure 1 illustrates the relationship between the two types of driving support systems and the three processes of driving behavior. The FOCWS has a function that warns the driver when the risk of collision with a forward obstacle is high. The system is thus considered to be a direct driving support system because it concludes that a collision-avoidance action is necessary based on the relation between the forward obstacles and the vehicle, and then provides a warning.

2.3. Conventional indices 2.3.1. TTC One of the most representative indices for assessing the warning provision timing of the FOCWS is TTC [5]. The symbol tc depicts the TTC and it is defined as follows: x f − xp x tc = − r = − (1) vr v f − vp The TTC represents the predicted time to collision on the assumption that the current relative velocity is maintained. Morita et al. [6] suggest that an inverse of the TTC is closely

2.2 Definition of principle symbols Figure 2 shows the variables used in this paper. The preceding vehicle is drawn as the forward obstacle, while the

related to the driver’s braking behavior because it is equivalent to the time rate of change of the visual angle to

the forward obstacle.

abruptly, even if the following vehicle also decelerates

A night vision enhancement system [7] with an infrared

abruptly at the same time. There is no essential difference

image of the forward view provides a pedestrian warning

between MTC and SD, except that MTC does not consider a

based on the TTC. Simulator experiments verify that this

response delay on the part of the driver of the following

pedestrian warning system is effective in helping a driver

vehicle.

avoid pedestrians dashing out into the road [8]. 2.3.4. Other indices and relations 2.3.2. Stopping distance

Many indices to evaluate the risk of the current situation

Assume that the preceding vehicle suddenly decelerates

other than TTC, SD, and MTC have been studied. In the

and that the following vehicle then decelerates after the

previous study [4], eight evaluation indices were compared

reaction time T , the inter-vehicular distance d when the

based on the definition of the indices, and the relations

two vehicles stop can be described as follows: ⎛ v 2f v 2p ⎞ ⎟ d = − xr − v f ⋅ T + ⎜ − ⎜ 2a f 2a p ⎟ ⎝ ⎠

among them were discussed theoretically; TTC, 1/TTC

(2)

The FOCWS based on a stopping distance algorithm

(Inverse

of

TTC),

KdB,

τ

,

TTC2nd

(the

second-order-predicted TTC), THW (time-headway), MTC, and RF (risk feeling). The nine indices that include these

(SDA) gives the collision warning when the calculated

eight indices and the SD mentioned above are classified as

inter-vehicular distance d , called the stopping distance

follows:

(SD), becomes smaller than the safety distance d s . The SD is one of the indices used to determine the collision warning timing of the FOCWS. The velocities v f , v p of Eq. (2) are not preset, but are updated constantly, while the driver reaction time T and the decelerations a f , a p are set by predefined parameters. Consequently, the warning provision

1) Indices defined by only relative movement of the two vehicles TTC, 1/TTC, KdB, τ , TTC2nd 2) Indices defined by the status of both movements THW, RF, MTC, SD 3) Indices for evaluating the appropriateness of driver braking

timing can be changed by adjusting these parameters.

τ , TTC2nd, MTC, SD

The first indices are calculated based on relative

2.3.3. MTC MTC [9] is an index defined based on a similar

position, relative velocity, and relative acceleration. It is

perspective to SD. The index also represents the possibility

reasonable to assume that drivers evaluate the collision risk

of collision in a case where the preceding vehicle and the

by using 1/TTC or KdB, because they can be estimated

following vehicle decelerate abruptly at the same time (the

based on the visual information on the part of the following

abrupt deceleration is assumed to be 0.7 [G] (=6.9 [m/s2])).

drivers. However, when the relative velocity and the relative

MTC is defined by a ratio of the summation of the

acceleration become zero, the five indices cannot evaluate

inter-vehicular distance − xr and the stopping distance of

the difference of the collision risk of the long and short

the preceding vehicle d p divided by the stopping distance

inter-vehicular distances.

of the following vehicle d f . Therefore, MTC is a nondimensional parameter as shown in Eq. (3), while SD is

The second indices can evaluate that the shorter inter-vehicular distance case has a greater risk than the

provided in meters because it depicts the inter-vehicular

longer distance case, even when the relative velocity or the

stopping distance.

relative acceleration are zero. MTC and SD evaluate the

MTC =

− xr + d p df

− xr − = −

potential collision risk, because the indices are calculated

v 2p 2a p

v 2f

not by the current decelerations, but the assumed abrupt

(3)

2a f

An MTC of less than 1 indicates a high likelihood of collision in a case where the preceding vehicle decelerates

decelerations. The indices in the third category evaluate the appropriateness of the braking behavior of the following vehicle. Lee [5] clarified that the driver should control the

deceleration to satisfy the inequality, τ > −0.5 , in order to

of indices to evaluate the collision risk, which is defined by

avoid a collision with the preceding vehicle. Therefore, τ

DCA. One of the indices is an ODCA (Overt DCA), which

is not an index to evaluate the risk of collision with the

describes the DCA when the preceding vehicle keeps the

preceding vehicle, but an index to regulate correct braking

current acceleration, and the other index is a PDCA

behavior to avoid the collision. The other three indices do

(Potential DCA), when it is supposed to decelerate abruptly.

not regulate braking behavior to avoid a collision. TTC2nd indicates the time to collide with the preceding vehicle when

3.2. ODCA

the relative acceleration is constant. MTC and SD indicate

3.2.1. Basic formulae

the margin to collision when the following vehicle and the

The current time is set to zero, and x p 0 , v p 0 describe the

preceding vehicle are supposed to slow down with the

position and the velocity of the preceding vehicle at that

assumed abrupt deceleration.

time. Here, assume that the preceding vehicle starts a uniformly accelerated motion with acceleration a p 0 , and

3. Deceleration for Collision Avoidance

that the following vehicle also performs a uniformly

3.1. Problems of warning timing of FOCWS

accelerated motion with acceleration a f 0 after a uniform

A previous paper [10] proposed a situation-adaptive

motion for the driver’s reaction time T . The velocities and positions

of the preceding

warning timing based on the visibility of forward obstacles,

v p (t ), v f (t )

and verified the effectiveness of the proposed FOCWS

vehicle and the following vehicle at time T

system; the TTC threshold for collision warning for

expressed by the following equations, respectively.

pedestrians is set to be short during the daytime, and long at night. However, the proposed warning timing has two problems. The first is the inconsequence of warning’s meaning derived from the difference of the pedestrian warning timing corresponding to the situation. The TTC threshold during the daytime is set to 2 [s], and it indicates that a collision will happen if the driver does not take

x p (t ), x f (t )

Preceding vehicle: ⎧v p (t ) = v p 0 + a p 0 t ⎪ ⎨ 1 2 ⎪ x p (t ) = x p 0 + v p 0t + a p 0 t 2 ⎩ Following vehicle: ⎧v f (t ) = v f 0 + a f 0 (t − T ) ⎪ ⎨ 1 2 ⎪ x f (t ) = x f 0 + v f 0T + v f 0 (t − T ) + a f 0 (t − T ) 2 ⎩

can be

(4)

(5)

avoidance action such as depressing the brake pedal. At night, the threshold is set to 5 [s], and it suggests a caution to remind the driver of a forward pedestrian. Furthermore, the driver cannot confirm the presence of a pedestrian visually at night, and therefore, the driver would be misled into thinking that the pedestrian warning is false because the warning timing at night is different from that during the daytime. The second problem is that the system does not provide a warning when the relative velocity is zero. This is because TTC, as shown in Eq. (1), is defined as the ratio of the inter-vehicular distance divided by the relative velocity. The warning is not provided when the relative velocity is zero even if the inter-vehicular distance is very short, and the warning is provided suddenly after the preceding vehicle decelerates. Consequently, the system cannot evaluate the collision risk properly. To solve these problems, this paper proposes two types

3.2.2. Condition to prevent collision within driver’s reaction time As mentioned above, the DCA is defined based on the assumption that the following vehicle starts to decelerate after the reaction time T . Therefore, the driver cannot avoid the collision in a case where the collision will occur during the reaction time—even if the FOCWS provides a warning. The condition for collision avoidance within the reaction time T is that the position of the following vehicle at time T is behind the position of the preceding vehicle. In other words, the relative position at time T has only to be minus. xr (T ) = x f (T ) − x p (T ) < 0

(6)

Substitution of Eqs. (4) and (5) into this inequality yields 1 xr 0 + vr 0T − a p 0T 2 < 0 (7) 2 where xr 0 = x f 0 − x p 0 , vr 0 = v f 0 − v p 0 . This subsection explains how to calculate DCA on the

90 v f0 = 60 [km/h], v p 0 = 30 [km/h]

x f 0 = 0 [m], x p 0 = 20 [m] v f 0 = 60 [km/h], v p 0 = 30 [km/h]

60

a f 0 = -3.12 [m/s ] (t > 1.2 [s ])

a f0 = -3.47 [m/s ] (t > 1.2 [s ])

50

parenthesis in the above becomes negative. Therefore, a

2

2

a p 0 = 0 [m/s ]

a p 0 = 2[m/s ]

X [m]

50 PV

40

40

negative discriminant of Eq. (9) leads to the following

PV

inequality:

30

30 20 FV 10

10

0

0 1

2 3 Time [s] ( a)

4

5

2 3 Time [s]

4

5

PV (go back)

FV (go back) X [m]

20

25

2

v f 0 = 60 [km/h ], v p 0 = 60 [km/h] 2

a f 0 = 0 [m/s ] (t ≦ 1.2 [s ])

10

a f 0 = 0 [m/s ] (t ≦ 1.2 [s ]) a f 0 = -7.5 [m/s ] (t > 1.2 [s])

2

a p 0 = -5 [m/s ]

3.2.4. Case 2: Preceding vehicle decelerates

0 0

1 (c)

2 3 Time [s]

4

5

0

v p0

a p < 0, T < t1 < − a

(11)

a f 0 = -6.6 [m/s ] (t > 1.2 [s])

5

2

a p 0 = -3 [m/s ]

0

) )

2

2

5

( (

x f 0 = 0 [m], x p 0 = 15 [m]

15

v p 0 = 50 [km/h]

10

where a f 1 is calculated by Eq. (10). ⎧ 0 a p 0 ≥ 0, v p 0 ≥ v f 0 ⎪ αo = ⎨ ⎪−a f 1 a p 0 ≥ 0, v p 0 < v f 0 ⎩

FV

20

x f 0 = 0 [m], x p 0 = 10 [m] v f 0 = 60 [km/h ],

15

occurring. In the case of v p 0 < v f 0 , ODCA becomes − a f 1

FV (go back)

30

FV

25

preceding vehicle travels at a constant velocity (Fig. 3 (a)) or

cannot collide with each other without deceleration

35

30

(10)

v p 0 ≥ v f 0 , ODCA α o becomes zero, because both vehicles

PV

40

35

(= a f 1 )

vehicle is faster than that of the following vehicle, PV (go back)

45

PV

2 xr 0 + 2vr 0T − a p 0T 2

accelerates (Fig. 3 (b)). When the velocity of the preceding

ap = 0

50

40

X [m]

1 (b )

ap > 0

45

vr20 + 2a p 0 xr 0

Here let us consider the case of a p 0 ≥ 0 when the 0

50

af 0
T ) can be described as xr (t ) = x f (t ) − x p (t ) =

avoided. Here, let us calculate the condition that the two curved

1 1 ⎛ ⎞ ar 0 t 2 + vr 0 − a f 0T t + ⎜ xr 0 + a f 0T 2 ⎟ 2 2 ⎝ ⎠

(

positive when the vehicles stop, and this means a collision is

)

(8)

where ar 0 = a f 0 − a p 0 .

lines intersect in the range of T < t ≤ − a , as shown in Fig. vp0

p0

3 (c). A solution of xr (t ) = 0 is defined as t1 , which is equivalent to an intersection of the two curved lines.

When the inequality of Eq. (7) is satisfied, the condition

Substitution of the condition of the deceleration of the

to avoid a collision between the following vehicle and the

following vehicle satisfies a f 0 = a f 1 in the case when the

preceding vehicle at time t (> T ) is that the two curved lines

two curved lines intersect into the solution yield. v p0 2x + v T T < t1 = r 0 r 0 ≤ − . a p 0T − vr 0 a p0

x f (t ) and x p (t ) do not intersect. To satisfy the condition,

the equation xr (t ) = 0 must not have a solution, that is, a discriminant as follows has to be negative.

(12)

Second, let us consider the ODCA in a case where the inequality of Eq. (12) is not satisfied. As mentioned above,

Start

Start

Does a collision happen within a reaction time?

Does a collision happen within a reaction time?

No

No

1 xr 0 + vr 0T − a ' p 0 T 2 < 0 2

1 xr 0 + vr 0T − a p 0T 2 < 0 2

Unable to calculate ODCA (Unable to avoid a collision)

Yes Is the preceding vehicle decelerating? a p0 < 0

Is the following condition satisfied?

Yes

T < t '1 ≤ −

No

Is the following condition satisfied? v p0 T < t1 ≤ − a p0

Yes

No α o = −a f 2 Is the preceding vehicle faster than the following vehicle?

Unable to calculate PDCA (Unable to avoid a collision)

Yes

α o = −a f 1

Yes

v p0

a' p 0

No α o = −a ' f 1

α o = −a ' f 2

Fig. 5: Method for calculating PDCA

As mentioned in Sec. 2.3, SD and MTC assume that

Yes

both the preceding vehicle and the following vehicle

v p0 ≥ v f 0

decelerate abruptly. PDCA is defined as the DCA on the

No α o = −a f 1

αo = 0

assumption that the preceding vehicle suddenly starts to decelerate with a constant deceleration 0.6 [G] (=5.88

Fig. 4: Method for calculating ODCA

[m/s2])), and it is expressed as α p in this manuscript.

in order to avoid a collision in this case, the inter-vehicular

Except for a substitution of -5.88 [m/s2] into the acceleration

distance at stop has to be larger than zero. The stopping

a p 0 of the preceding vehicle, a calculational procedure of

distance of the following vehicle and the preceding vehicle

PDCA is essentially the same with that of ODCA.

are −

v 2f 0 2a f 0

,−

v 2p 0 2ap0

, respectively, therefore, it derives the

following inequality:

x f 0 + v f 0T −

v 2f 0 2a f 0

< x p0 +

v 2p 0

(13)

2a p 0

⎧−a ' f1 ⎪ αp = ⎨ ⎪−a ' f 2 ⎩

( T