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How does a driver perceive risk when making decision of lane-changing?
13th IFAC/IFIP/IFORS/IEA Symposium on 13th Symposium on Analysis, Design, and Evaluation of Human-Machine Systems 13th IFAC/IFIP/IFORS/IEA IFAC/IFIP/IFORS/IEA Symposium on 13th IFAC/IFIP/IFORS/IEA Symposium on Analysis, Design, and Evaluation of Human-Machine Available onlineSystems at www.sciencedirect.com Aug. 30 Sept. 2, 2016. Kyoto, Japan Analysis, Design, and Evaluation of Human-Machine Systems Analysis, Design, and Evaluation of Human-Machine Systems Aug. 30 Sept. 2, 2016. Kyoto, Japan Aug. Aug. 30 30 -- Sept. Sept. 2, 2, 2016. 2016. Kyoto, Kyoto, Japan Japan
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How does a driver perceive risk when How How does does a a driver driver perceive perceive risk risk when when making decision of lane-changing? making decision of lane-changing? making decision of lane-changing?
Huiping Zhou ∗∗ Makoto Itoh ∗∗ ∗∗ Huiping Zhou ∗∗ Makoto Itoh ∗∗ Huiping Huiping Zhou Zhou Makoto Makoto Itoh Itoh ∗∗ ∗ ∗ Faculty of Engineering, Information and Systems, University of ∗ of Engineering, Information and Systems, University of ∗ Faculty Faculty of Information and Systems, University of Tsukuba, Tennodai, Tsukuba, Ibaraki (e-mail: Faculty1-1-1 of Engineering, Engineering, Information and 305-8573 Systems, Japan University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) ∗∗ [email protected]) Information and Systems, University of [email protected]) ∗∗ Faculty of Engineering, ∗∗ Faculty of Engineering, Information and Systems, University of ∗∗ Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki (e-mail: Faculty of Engineering, Information and305-8573 Systems, Japan University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper shows a case study to show how a driver perceives driving risk in order Abstract: This shows a show driving risk order Abstract: This paper paper shows a case case study study toLane-changing show how how aaa driver driver perceives driving risk indriving order to model decision making of changing lanes.to data perceives are collected under 28in Abstract: This paper shows a case study to show how driver perceives driving risk in order to model decision making of changing lanes. Lane-changing data are collected under 28 driving to model model decision decision making of changing changing lanes. Lane-changing dataon aredriver’s collectedrisk under 28 driving driving conditions throughmaking a driving simulator. Analyses are focused perception to to of lanes. Lane-changing data are collected under 28 through a driving simulator. Analyses are focused on driver’s risk perception conditions through a driving simulator. Analyses are focused on driver’s risk perception to aconditions leading vehicle driving on the host lane and nearest rear and front vehicles driving on to a conditions through a driving simulator. Analyses are focused on driver’s risk perception to aa leading vehicle driving on the host lane and nearest rear and front vehicles driving on aa leading vehicle driving on the host lane and nearest rear and front vehicles driving on targeted lane. The analyses are operation on two stages when a driver decides to change lanes atargeted leadinglane. vehicle driving on the host lane and nearest rear and front vehicles driving on a The analyses are operation on two stages when a driver decides to change lanes targeted lane.on The analyses are operation on he twoorstages stages when a driver driver decides to change change lanes (i.e., turning turn signal),are and then when she iswhen cutting in thedecides target lane in order to targeted lane. The analyses operation on two a to lanes (i.e., turning on turn signal), and then when he or she is cutting in the target lane in order to (i.e., turning on and when he or cutting in target lane in order to comprehend decision making. suggest that driver tends (i.e., turninglane-changing on turn turn signal), signal), and then then whenThe he results or she she is is cutting in aathe the target laneto inprefer orderthe to comprehend lane-changing decision making. The results suggest that driver tends to prefer the comprehend lane-changing decision making. The results suggest that a driver tends to prefer the time to collision (TTC) to the time headway (THW) to the rear vehicle. When the host vehicle comprehend lane-changing decision making. The results suggest that a driver tends to prefer the time to collision the time headway (THW) to the traffic rear vehicle. When the host vehicle time to (TTC) to the headway (THW) to rear When the vehicle is cutting into the(TTC) targetto lane, driver tends to perceive condition through both TTC time to collision collision (TTC) to the aatime time headway (THW) to the rear vehicle. vehicle. When the host host vehicle is cutting into the target lane, driver tends to perceive the traffic condition through both TTC is cutting cutting into the target targetitlane, lane, a driver driver tends to aperceive perceive the traffic traffic condition through both TTC and THW.into Meanwhile, is also implied that driver tries to grasp statusthrough of each both of related is the a tends to the condition TTC and THW. Meanwhile, it is also implied that a driver tries to grasp status of each of related and THW. Meanwhile, it is also implied that a driver tries to grasp status of each of related vehicles driving around itthe host vehicle for executing lane-changing behavior. Theseoffindings and THW. Meanwhile, is also implied that a driver tries to grasp status of each related vehicles driving around the host vehicle for executing These findings vehicles driving around the for lane-changing behavior. These findings illustrates driver’s risk perception of making a decision lane-changing and operatingbehavior. lane-changing vehicles driving around the host host vehicle vehicle for executing executing lane-changing behavior. Thesebehavior, findings illustrates driver’s risk perception of making a decision and operating lane-changing behavior, illustrates driver’s risk perception of making a decision and operating lane-changing behavior, which suggests it is valid to model lane-changing decision making via perceiving driving risk. illustrates driver’s risk perception of making a decision and operating lane-changing behavior, which which suggests suggests it it is is valid valid to to model model lane-changing lane-changing decision decision making making via via perceiving perceiving driving driving risk. risk. which suggests it is valid to model lane-changing decision making via perceiving driving risk. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Risk perception, Lane-changing behavior, decision making. Keywords: Risk Risk perception, Lane-changing Lane-changing behavior, decision decision making. Keywords: Keywords: Risk perception, perception, Lane-changing behavior, behavior, decision making. making. 1. INTRODUCTION ence between any two consecutive vehicles when they cross 1. INTRODUCTION INTRODUCTION between any(Winsum two consecutive consecutive vehicles whenPractically, they cross cross 1. ence between any two vehicles when they aence reference point and Heino (1996)). 1. INTRODUCTION ence between any(Winsum two consecutive vehicles whenPractically, they cross a reference point and Heino (1996)). Subjective estimate of driving risk in dynamical situation atime-headway reference (Winsum Heino Practically, is calculated as equation (1) in car-following atime-headway reference point point (Winsum and and Heino (1996)). (1996)). Practically, Subjective estimate of driving driving risk in dynamical dynamical situation is 1(a)). calculated as equation equation (1) in in (1995) car-following Subjective of in is preferredestimate to objective facts risk associated with asituation hazard time-headway calculated as (1) car-following situations (Fig.is Cutting and Vishton argue Subjective estimate of driving risk in dynamical situation time-headway is calculated as equation (1) in car-following is preferred to objective facts associated with a hazard situations (Fig. 1(a)). Cutting and Vishton (1995) argue is preferred to objective facts associated aa hazard (See Rosenstock (1974), Janz and Becker with (1984)). Note situations (Fig. 1(a)). Cutting and Vishton (1995) argue the accuracy of perceiving distance through several dimenis preferred to objective facts associated with hazard situations (Fig. 1(a)). Cutting and Vishton (1995) argue (See Rosenstock (1974), Janz and Becker (1984)). Note the accuracy of perceiving distance through several dimen(See Rosenstock (1974), Janz and Becker (1984)). Note that driver’s subjective estimate principally depends on the accuracy of perceiving distance several dimensions. Their argument suggests thatthrough it is more accurate to (See Rosenstock (1974), Janz and Becker (1984)). Note the accuracy of perceiving distance through several dimenthat driver’s driver’s subjective estimate principally depends90% on sions. sions. Their Their argument suggests that it is is more more accurate to that subjective depends on visual information, whichestimate counts principally for approximately argument suggests that it accurate to estimate a time headway with comparison with perceivthat driver’s subjective estimate principally depends on sions. Their argument suggests that it is more accurate to visual information, which counts for approximately 90% estimate a time headway with comparison with perceivvisual information, which counts for approximately 90% of all information driving Sivak (1996)). aa time headway comparison with perceiving a distance thewith perceived distance is sensitive visual information, involving which counts for (See approximately 90% estimate estimate timebecause headway with comparison with perceivof all information involving driving (See Sivak (1996)). ing a distance because the perceived distance is sensitive of all involving driving (See Sivak (1996)). What extent a driver perceives driving greatly ing aa distance because perceived sensitive to variations speed. the Furthermore,Winsum and Heino of all information information involving driving (See risk Sivakis ing distancein perceived distance distance is is sensitive What extent a driver driver perceives driving risk is (1996)). greatly to variations variations inbecause speed. the Furthermore,Winsum and Heino What extent a perceives driving risk is greatly dependent upon what extent of information he or she to in speed. Furthermore,Winsum and Heino What extent a driver perceives driving risk is greatly to variations in speed. Furthermore,Winsum and Heino dependent upon what extent of information he or she dependent upon what information she obtains from a changing trafficof andor dependent upon what extent extent of environment, information he he orhow. she obtains from a changing traffic environment, and how. obtains from athat changing traffic environment, how. The reason a difference between and the magobtains fromis changing traffic exists environment, and how. The reason reason is athat that a difference difference exists betweenmagnitude the magmagThe is a exists between the nitude of a physical stimulus and the perceived The reason is that a difference exists between the magnitude of physical stimulus and the the perceived magnitude nitude aaa physical and magnitude of the of stimulus in astimulus psychophysical theory (See Stevens nitude of physical stimulus and the perceived perceived magnitude of the stimulus in a psychophysical theory (See Stevens of the stimulus in aa psychophysical theory (See Stevens (1961), Allan (1979)). In line with the common ground of the stimulus in psychophysical theory (See Stevens (1961), Allan (1979)). In line with the common ground (1961), Allan (1979)). In line with the common in psychophysical laws, In larger the magnitude of a ground stimu(1961), Allan (1979)). line with the common ground in psychophysical laws, larger the magnitude of a stimuin psychophysical larger the of aa stimulus becomes, lowerlaws, it becomes to magnitude precisely perceive the in psychophysical laws, larger the magnitude of stimulus becomes, lower it becomes to precisely perceive the lus becomes, lower it becomes to precisely the difference. Many previous studies (See Lee perceive (1974), Lee lus becomes, lower it becomes to precisely perceive the difference. Many previous studies (See Lee (1974), Lee difference. Many previous studies (See Lee (1974), Lee (1976), Groeger (2000), Groeger (2002) and Kondoh etLee al. difference. Many previous studies (See Lee (1974), (1976), Groeger Groeger (2000), Groeger (2002) and and Kondoh et al. al. (1976), (2000), Groeger (2002) Kondoh et (2008)) have made efforts to illustrate relations between (1976), Groeger (2000), Groeger (2002) and Kondoh et al. (2008)) have made efforts to illustrate relations between (2008)) have made efforts to illustrate relations between physical visual stimulus and driver’s risk estimation in (2008)) have made efforts to illustrate relations between physical visual visual stimulus and(e.g., driver’s risk distance, estimation in physical and driver’s risk estimation in dynamical trafficstimulus conditions headway time physical visual stimulus and driver’s risk estimation in dynamical traffic conditions (e.g., headway distance, time dynamical traffic conditions (e.g., headway distance, time headway and time-to-collision). Those studies have aimed dynamical traffic conditions (e.g., headway distance, time headway and time-to-collision). time-to-collision). Those studies have aimed aimed headway studies have to find a and proximate measure for Those accurately describing the headway and time-to-collision). Those studies have aimed to find a proximate measure for accurately describing the to find a proximate measure for accurately describing the relations under typical car-following situations as shown to find a proximate measure for accurately describing the relations under typical car-following situations as shown relations under in Fig. 1(a). relations under typical typical car-following car-following situations situations as as shown shown in Fig. 1(a). in 1(a). in Fig. Fig.respect 1(a). to one of microscopic flow characteristics, With With respect to one one of of microscopic microscopic flow characteristics, With respect flow characteristics, May (1990)),Winsum Heino (1996), Lewis-Evans et al. With respect to to one and of microscopic flow characteristics, May (1990)),Winsum and Heino (1996), Lewis-Evans et al. al. May (1990)),Winsum and Heino (1996), Lewis-Evans et 1. Car-following situations and lane-changing situa(2010), Risto and Martens (2013) haveLewis-Evans discussed timeMay (1990)),Winsum and Heino (1996), et al. Fig. Fig. tions 1. Car-following Car-following situations and and lane-changing situasitua(2010), Risto and Martens (2013) have discussed time(2010), Risto and (2013) have timeFig. 1. headway (T HW ). ItMartens is originally defined asdiscussed the time differFig. 1. Car-following situations situations and lane-changing lane-changing situa(2010), Risto and Martens (2013) have discussed timetions headway (T HW ). It is originally defined as the time differheadway tions tions headway (T (T HW HW ). ). It It is is originally originally defined defined as as the the time time differdifferCopyright © 2016, 2016 IFAC 66 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 66 Copyright © 2016 IFAC 66 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 66 Control. 10.1016/j.ifacol.2016.10.462
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(1996), Winsum and Brouwer (1997), Risto and Martens (2013) evaluate that drivers preferred to choice of time headway in car following and braking response.
RPr = 1/T HWr + 4/T T Cr .
T HW = d/vh
Driver’s lane-changing data are collected in different lanechanging situations operated on a driving simulator.
2. METHOD
(1)
In studies of visual control of locomotion, a concept of time-to-collision (T T C) is argued as an optical flow (See Lee (1974), Lee (1976)). Hayward (1972) gives a definition of time-to-collision as: ”The time required for two vehicle to collide if they continue at their present speed and on the same path”. Since the visual information of time-tocollision has been proved to be a crucial predictor for estimating collision risk in car-following situations (See Cavallo and Laurent (1988), Groeger (2000), Groeger (2002)) time-to-collision is discussed in collision avoidance systems (See van der Horst (1991),van der Horst and Hogema (1993), Winsum and Heino (1996)). Generally, it is manipulated as equation (2) in cases of car-following situations. T T C = d/(vh − vf )
(6)
2.1 Apparatus A fixed-base driving simulator is used in the data collection. It can simulate driving on an expressway with two lanes (See Fig. 2). A speed governor is set up for preventing the host vehicle from a limited velocity vM ax. .
(2)
In recent studies, it is pointed that driver’s subjective estimation of driving risk strongly depends on the global optical flow (i.e., inverse of time-headway) and the local optical flow (i.e., inverse of time-to-collision) in cases of a host vehicle approaching to a slower forward one (See Kondoh et al. (2008), Kondoh et al. (2014)). The studies quantify the subjective estimation as Risk Perception (RP ) according to the following formula (equation (3)).
Fig. 2. A fixed-base driving simulator. 2.2 Participants
RP = 1/T HW + 4/T T C
(3)
Seven females and five males, ranging from 28 to 45 years old (Mean = 38.3, SD = 5.3), participate in the data collection. Each participant holds a valid driver’s license. After receiving an explanation of the data collection, all of them signed in information consent for participating the data collection.
Those studies of visual information in risk perception have focused on traffic accidents in the car-following situations. Accurately obtaining visual information of a rear car in lane-changing situations (e.g., Fig. 1(b)) is more difficult than a forward car in car-following situations (e.g., Fig. 1(a)). Concretely, perceiving risk is through direct and continuous visual information in cases of the forward vehicle. In cases of the rear vehicles, the visual information is indirect and discontinuous. Understanding driver’s subjective perception of risk to a rear car is an essential issue to driving safety in lane-changing behavior. Consequently, this study directs driver’s risk estimation to a rear vehicle that approaches to the host vehicle on the passing lane in the lane-changing situations.
2.3 Driving scenario and driving task One lane-changing scenario is designed in each trial. There are 28 trials in the whole data collection. Driving initial conditions (i.e., RP0 , vh , vr and d0 ) in the 28 trials are sorted in terms of the index of RP as shown in Table (1). Following instructions are given to each of participants: (1) Each participant is requested to accelerate the host vehicle’s velocity (vh ) and to reach the limited velocity vM ax. on the cruising lane after starting a trial, where the headway distance (D) between two vehicles driving on the passing lanes is set a same value (See Fig. 3(a)); (2) he or she is given a piece of acoustic message at the time point t0 when the third vehicle on the passing lane is passing the host vehicle (See Fig. 3(b)); (3) he or she has to make a choice whether he or she can change lanes after receiving the acoustic message. The time point is defined as td when he or she turns on the right turn signal for claiming he or she makes a choice to change lanes;
The purpose of the present paper is to clarify relations of driver’s estimation of collision risk to an approaching rear car in lane-changing situations to choices of time-headway, time-to-collision, RP as well as headway distance. The relations are argued in lane-changing for choice and lanechanging implementation of decision-making behaviors. From the viewpoint of a host vehicle, these measures are redefined as equation (4) - (6). T HWr = −d/(−vh ) = d/vh .
(4)
T T Cr = −d/(−vh − (−vr )) = d/(vr − vh ).
(5) 67
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Table 1. Initial driving condition in each trial.
(4) he or she is instructed to implement the lane-change behavior as soon as possible after making the choice of changing lanes. The time point is defined as ti when the host vehicle’s body firstly touches the center line. Note that after the host vehicle passed the center line, the limited velocity of vh is canceled. (5) In cases of giving up a lane-changing choice, he or she is requested to turn on the left turn signal.
N o.
RP0
vh
vr
d0
N o.
RP0
vh
vr
d0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.75 0.75 0.75 0.75 1.00 1.00 1.00 1.00 1.25 1.25 1.25 1.25 1.50 1.50
60 60 90 90 60 60 90 90 60 60 90 90 60 60
85 95 100 110 85 95 100 110 85 95 100 110 85 95
59 74 48 70 44 55 36 53 36 44 29 42 30 37
15 16 17 18 19 20 21 22 23 24 25 26 27 28
1.50 1.50 2.00 2.00 2.00 2.00 2.50 2.50 2.50 2.50 3.00 3.00 3.00 3.00
90 90 60 60 90 90 60 60 90 90 60 60 90 90
100 110 85 95 100 115 85 95 100 115 85 85 100 115
24 35 22 28 18 26 18 22 14 21 15 19 12 18
Unit of velocity is km/h. Unit of distance is m.
host vehicle’s body firstly touches the center line. In order to investigate driver’s perceiving driving risk during his/her decision making for changing lanes, this study investigates following measures at lane-change choice and implementation:
Fig. 3. Driving scenario. 2.4 Procedure
• Necessary time to decide lane changes that is time length from t0 to td when the right turn signal is turned on. • time-headway, time-to-collision, RP , and headwaydistance to the nearest rear vehicle on the passing lane at ti , which are defined as T HWinit. , T T Cinit. , RPinit. and dinit. , respectively. • Subjective assessment to each lane-change scenario
Each participant is given an explanation of the driving simulator’s operation and the instructions during driving task. Then, he or she does approximately 5-minute driving exercise for being familiar with the driving simulator. After 5-minute rest, he or she is instructed to experience the 14 trials. After 5-minute rest, he or she experiences the other 14 trials. All participants are divided into two groups in order to counterbalance order effects. One group is operated in an ascending order of RP , the other is in a descending order.
3. RESULTS 3.1 Driver’s lane-changing behavior
After each trial, they are asked to report their subjective assessment to the experienced scenario by using a paperquestionnaire as shown in Fig. 4.
Fig. 5 indicates averaged horizontal position at each 1second time period as a function of time for 5-second time period prior and 3-second time period posterior to the time point td . Results show that lane-changing behaviors are operated in a good manner while time-to-collision is large but time-headway is small in such trials shown in Fig. 5(a). As time-to-collision becomes smaller and timeheadway becomes larger, the driving behaviors posterior to td tend to become in a disorder in such trials shown in Fig. 5(b) and (d). The disorder tendency becomes much clearer when both of time-to-collision and time-headway become smaller in such trials shown in Fig. 5(c). Note that the disorders also occur prior to td . Furthermore, host vehicle’s transition in the horizontal direction while changing lanes retards as RP becomes great.
Fig. 4. Questionnaire sheet that is used for reporting subjective assessment to each scenario after each trial.
3.2 Driver’s lane-changing choice 2.5 Measures Fig. 6 plots necessary time of making a choice whether to change lanes, or not, related to each of initial driving conditions (i.e., T HW0 , T T C0 , RP0 and d0 ). It is indicated that more dangerous the traffic condition is, more time is spent on make the choice. Linear regression analysis is performed between the necessary time and each of measures.
Since all participants are instructed to turn on the turnsignal once they make a choice of changing lanes in the near future, it can be considered that lane-change choice is made at td . Furthermore, ti denotes the time point when lane-change implementation is initiated, i.e., the 68
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Fig. 5. Horizontal moving position of the host vehicle. Note that zero of the horizontal axis is the time point td at which a driver turns on the right turning signal. Each of coordinate values of Y- axis is an average horizontal position during every 1-second time period from 5 s prior and 3 s posterior to td for 12 participants. Dotted horizontal line denotes a center-position of the cruising lane.
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Fig. 6. Necessary time for making a choice of lane-changing behavior to-collision but also time-headway to an approaching rear car. In comparison that a driver refers to perceiving only time-to-collision for lane-changing choice, he or she prefers to both of time-to-collision and time-headway for lanechanging implementation. It is suggested that a driver intends to perceive a rear-collision risk dependently on both a global optical flow and a local optical flow while he or she implements a lane change.
Results show strongly positive correlation between T T C0 and the necessary time (r = 0.60, p < 0.01 ) than T HW0 and d0 (See Table (2)). It is indicated that a driver tends to perceive the driving risk through time-to-collision information to an approaching rear car for making a choice whether it is executable to change lanes under the current traffic condition, or not. It is implied that driver’s subjective risk estimation depends greatly on a local optical flow. Table 2. Statistical parameters resulting from the linear regression analysis between the necessary time to make a choice and the four measures (T HW0 , T T C0 , RP0 and d0 ) M easures T HW0 T T C0 RP0 d0
r2 0.090 0.294 0.289 0.200
r 0.30 0.54 0.54 0.45
Parameters Df MS 26 1.560 26 1.21 26 0.443 26 241.0
F 2.569 10.81 10.56 6.49
p 0.12 0.002 0.003 0.02
3.3 Driver’s lane-changing implementation Fig. 7 indicates relationships of four measures under conditions of lane-change implementation versus initial traffic conditions, i.e., T HW0 , T T C0 , RP0 and d0 . Linear regression analysis is operated on each of four measures between lane-change implementation versus traffic conditions. According to the results, strong correlations (r = 0.62 - 0.97) are observed on each of four measures (See Table (3)). Especially, greatly significant positive correlation is showed on both T HW0 (r = 0.97, p < 0.01) and T T C0 (r = 0.97, p < 0.01).
Fig. 7. Relationship of four measures between lane-change implementation and initial traffic conditions.
It is argued that a driver implements lane-changing behavior while perceiving driving risk through not only time69
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• drivers tend to prefer time-to-collision information for perceiving driving risk for making a choice whether it is possible to change lanes in current traffic conditions with comparison to traffic flow like time-headway and headway-distance; • drivers’ lane-changing implementations are greatly dependent on subjective risk perception through time-to-collision and time-headway information. • though drivers prefer time-to-collision and timeheadway information for lane-change choice and implementation to RF , their subjective estimations of driving risk are consistent with the index of RF .
Table 3. Statistical parameters resulting from the linear regression analysis on four measures (time-headway, time-to-collision, RP and headway-distance) between lane-change implementation and initial traffic conditions M easures T HW0 T T C0 RP0 d0
r2 0.95 0.93 0.385 0.607
r 0.97 0.96 0.62 0.78
Parameters Df MS 26 0.052 26 0.894 26 0.384 26 118.5
F 475.3 363.8 16.26 40.09
p 0.00 0.00 0.0004 0.00
3.4 Subjective assessment
Since the index of RP involves two concepts of timeto-collision and time-headway information, it is believed that RP would be a significant index to quantify driver’s subjective perception of proximity risk by a rear vehicle through optimizing weights on T T C and T HW .
Mean subjective assessment to each trial is plot to each of four measures of initial traffic conditions, i.e., T HW0 , T T C0 , RP0 and d0 in Fig. 8. Higher the score is, more dangerous the scenario is thought. Results in Fig. 8 show a same tendency on all the four measures. More definite correlation is indicated between the subjective assessment and values of T T C0 . It is argued that a driver prefers visual information of time-to-collision for evaluating what extent the situation is, that is, visual stimulus in the local optical flow field affects greatly on his/her subjective assessment to the rear-collision risk.
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Fig. 8. Plots of subjective assessment versus T HW0 , T T C0 , RP0 and d0 4. CONCLUSION This study collected lane-changing data under different traffic conditions. Driver’s lane-change choice and implementation have been investigated on measures of timeheadway, time-to-collision, RP and headway-distance. Results show that: 70
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comfort. Accident Analysis & Prevention, 42(6), 1926– 1933. May, A. (1990). Traffic Flow Fundamentals. Prentice-Hall, NJ. Risto, M. and Martens, M.H. (2013). Time and space: The difference between following time headway and distance headway instructions. Transportation Research Part F: Traffic Psychology and Behaviour, 17, 45–51. Rosenstock, I. (1974). The health belief model and preventive health behavior. Health Educ. Mono., 2, 354– 386. Sivak, M. (1996). The information that drivers use: is it indeed 90% visual? Perception, 25, 1081–1089. Stevens, S. (1961). To honor fechner and repeal his law. Science, 133(3446), 80–86. van der Horst, A. (1991). Time-to-collision as a cue for decision-making in braking. In A.G. et al. (ed.), Vision in Vehicles III, 19–26. Elsevier Science Publishers B.V., Amsterdam. van der Horst, A. and Hogema, J. (1993). Time-tocollision and collision avoidance systems. Proceedings of the 6th ICTCT Workshop: Safety Evaluation of Traffic Systems: Traffic Conflicts and Other Measures, 109–121. Winsum, W.V. and Brouwer, W. (1997). Time headway in car following and operational performance during unexpected braking. Perceptual and Motor Skills, 84, 1247–1257. Winsum, W. and Heino, A. (1996). Choice of timeheadway in car-following and the role of time-to-collision information in braking. Ergonomics, 39(4), 579–592.
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How does a driver perceive risk when How How does does a a driver driver perceive perceive risk risk when when making decision of lane-changing? making decision of lane-changing? making decision of lane-changing?
Huiping Zhou ∗∗ Makoto Itoh ∗∗ ∗∗ Huiping Zhou ∗∗ Makoto Itoh ∗∗ Huiping Huiping Zhou Zhou Makoto Makoto Itoh Itoh ∗∗ ∗ ∗ Faculty of Engineering, Information and Systems, University of ∗ of Engineering, Information and Systems, University of ∗ Faculty Faculty of Information and Systems, University of Tsukuba, Tennodai, Tsukuba, Ibaraki (e-mail: Faculty1-1-1 of Engineering, Engineering, Information and 305-8573 Systems, Japan University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) ∗∗ [email protected]) Information and Systems, University of [email protected]) ∗∗ Faculty of Engineering, ∗∗ Faculty of Engineering, Information and Systems, University of ∗∗ Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki (e-mail: Faculty of Engineering, Information and305-8573 Systems, Japan University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper shows a case study to show how a driver perceives driving risk in order Abstract: This shows a show driving risk order Abstract: This paper paper shows a case case study study toLane-changing show how how aaa driver driver perceives driving risk indriving order to model decision making of changing lanes.to data perceives are collected under 28in Abstract: This paper shows a case study to show how driver perceives driving risk in order to model decision making of changing lanes. Lane-changing data are collected under 28 driving to model model decision decision making of changing changing lanes. Lane-changing dataon aredriver’s collectedrisk under 28 driving driving conditions throughmaking a driving simulator. Analyses are focused perception to to of lanes. Lane-changing data are collected under 28 through a driving simulator. Analyses are focused on driver’s risk perception conditions through a driving simulator. Analyses are focused on driver’s risk perception to aconditions leading vehicle driving on the host lane and nearest rear and front vehicles driving on to a conditions through a driving simulator. Analyses are focused on driver’s risk perception to aa leading vehicle driving on the host lane and nearest rear and front vehicles driving on aa leading vehicle driving on the host lane and nearest rear and front vehicles driving on targeted lane. The analyses are operation on two stages when a driver decides to change lanes atargeted leadinglane. vehicle driving on the host lane and nearest rear and front vehicles driving on a The analyses are operation on two stages when a driver decides to change lanes targeted lane.on The analyses are operation on he twoorstages stages when a driver driver decides to change change lanes (i.e., turning turn signal),are and then when she iswhen cutting in thedecides target lane in order to targeted lane. The analyses operation on two a to lanes (i.e., turning on turn signal), and then when he or she is cutting in the target lane in order to (i.e., turning on and when he or cutting in target lane in order to comprehend decision making. suggest that driver tends (i.e., turninglane-changing on turn turn signal), signal), and then then whenThe he results or she she is is cutting in aathe the target laneto inprefer orderthe to comprehend lane-changing decision making. The results suggest that driver tends to prefer the comprehend lane-changing decision making. The results suggest that a driver tends to prefer the time to collision (TTC) to the time headway (THW) to the rear vehicle. When the host vehicle comprehend lane-changing decision making. The results suggest that a driver tends to prefer the time to collision the time headway (THW) to the traffic rear vehicle. When the host vehicle time to (TTC) to the headway (THW) to rear When the vehicle is cutting into the(TTC) targetto lane, driver tends to perceive condition through both TTC time to collision collision (TTC) to the aatime time headway (THW) to the rear vehicle. vehicle. When the host host vehicle is cutting into the target lane, driver tends to perceive the traffic condition through both TTC is cutting cutting into the target targetitlane, lane, a driver driver tends to aperceive perceive the traffic traffic condition through both TTC and THW.into Meanwhile, is also implied that driver tries to grasp statusthrough of each both of related is the a tends to the condition TTC and THW. Meanwhile, it is also implied that a driver tries to grasp status of each of related and THW. Meanwhile, it is also implied that a driver tries to grasp status of each of related vehicles driving around itthe host vehicle for executing lane-changing behavior. Theseoffindings and THW. Meanwhile, is also implied that a driver tries to grasp status of each related vehicles driving around the host vehicle for executing These findings vehicles driving around the for lane-changing behavior. These findings illustrates driver’s risk perception of making a decision lane-changing and operatingbehavior. lane-changing vehicles driving around the host host vehicle vehicle for executing executing lane-changing behavior. Thesebehavior, findings illustrates driver’s risk perception of making a decision and operating lane-changing behavior, illustrates driver’s risk perception of making a decision and operating lane-changing behavior, which suggests it is valid to model lane-changing decision making via perceiving driving risk. illustrates driver’s risk perception of making a decision and operating lane-changing behavior, which which suggests suggests it it is is valid valid to to model model lane-changing lane-changing decision decision making making via via perceiving perceiving driving driving risk. risk. which suggests it is valid to model lane-changing decision making via perceiving driving risk. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Risk perception, Lane-changing behavior, decision making. Keywords: Risk Risk perception, Lane-changing Lane-changing behavior, decision decision making. Keywords: Keywords: Risk perception, perception, Lane-changing behavior, behavior, decision making. making. 1. INTRODUCTION ence between any two consecutive vehicles when they cross 1. INTRODUCTION INTRODUCTION between any(Winsum two consecutive consecutive vehicles whenPractically, they cross cross 1. ence between any two vehicles when they aence reference point and Heino (1996)). 1. INTRODUCTION ence between any(Winsum two consecutive vehicles whenPractically, they cross a reference point and Heino (1996)). Subjective estimate of driving risk in dynamical situation atime-headway reference (Winsum Heino Practically, is calculated as equation (1) in car-following atime-headway reference point point (Winsum and and Heino (1996)). (1996)). Practically, Subjective estimate of driving driving risk in dynamical dynamical situation is 1(a)). calculated as equation equation (1) in in (1995) car-following Subjective of in is preferredestimate to objective facts risk associated with asituation hazard time-headway calculated as (1) car-following situations (Fig.is Cutting and Vishton argue Subjective estimate of driving risk in dynamical situation time-headway is calculated as equation (1) in car-following is preferred to objective facts associated with a hazard situations (Fig. 1(a)). Cutting and Vishton (1995) argue is preferred to objective facts associated aa hazard (See Rosenstock (1974), Janz and Becker with (1984)). Note situations (Fig. 1(a)). Cutting and Vishton (1995) argue the accuracy of perceiving distance through several dimenis preferred to objective facts associated with hazard situations (Fig. 1(a)). Cutting and Vishton (1995) argue (See Rosenstock (1974), Janz and Becker (1984)). Note the accuracy of perceiving distance through several dimen(See Rosenstock (1974), Janz and Becker (1984)). Note that driver’s subjective estimate principally depends on the accuracy of perceiving distance several dimensions. Their argument suggests thatthrough it is more accurate to (See Rosenstock (1974), Janz and Becker (1984)). Note the accuracy of perceiving distance through several dimenthat driver’s driver’s subjective estimate principally depends90% on sions. sions. Their Their argument suggests that it is is more more accurate to that subjective depends on visual information, whichestimate counts principally for approximately argument suggests that it accurate to estimate a time headway with comparison with perceivthat driver’s subjective estimate principally depends on sions. Their argument suggests that it is more accurate to visual information, which counts for approximately 90% estimate a time headway with comparison with perceivvisual information, which counts for approximately 90% of all information driving Sivak (1996)). aa time headway comparison with perceiving a distance thewith perceived distance is sensitive visual information, involving which counts for (See approximately 90% estimate estimate timebecause headway with comparison with perceivof all information involving driving (See Sivak (1996)). ing a distance because the perceived distance is sensitive of all involving driving (See Sivak (1996)). What extent a driver perceives driving greatly ing aa distance because perceived sensitive to variations speed. the Furthermore,Winsum and Heino of all information information involving driving (See risk Sivakis ing distancein perceived distance distance is is sensitive What extent a driver driver perceives driving risk is (1996)). greatly to variations variations inbecause speed. the Furthermore,Winsum and Heino What extent a perceives driving risk is greatly dependent upon what extent of information he or she to in speed. Furthermore,Winsum and Heino What extent a driver perceives driving risk is greatly to variations in speed. Furthermore,Winsum and Heino dependent upon what extent of information he or she dependent upon what information she obtains from a changing trafficof andor dependent upon what extent extent of environment, information he he orhow. she obtains from a changing traffic environment, and how. obtains from athat changing traffic environment, how. The reason a difference between and the magobtains fromis changing traffic exists environment, and how. The reason reason is athat that a difference difference exists betweenmagnitude the magmagThe is a exists between the nitude of a physical stimulus and the perceived The reason is that a difference exists between the magnitude of physical stimulus and the the perceived magnitude nitude aaa physical and magnitude of the of stimulus in astimulus psychophysical theory (See Stevens nitude of physical stimulus and the perceived perceived magnitude of the stimulus in a psychophysical theory (See Stevens of the stimulus in aa psychophysical theory (See Stevens (1961), Allan (1979)). In line with the common ground of the stimulus in psychophysical theory (See Stevens (1961), Allan (1979)). In line with the common ground (1961), Allan (1979)). In line with the common in psychophysical laws, In larger the magnitude of a ground stimu(1961), Allan (1979)). line with the common ground in psychophysical laws, larger the magnitude of a stimuin psychophysical larger the of aa stimulus becomes, lowerlaws, it becomes to magnitude precisely perceive the in psychophysical laws, larger the magnitude of stimulus becomes, lower it becomes to precisely perceive the lus becomes, lower it becomes to precisely the difference. Many previous studies (See Lee perceive (1974), Lee lus becomes, lower it becomes to precisely perceive the difference. Many previous studies (See Lee (1974), Lee difference. Many previous studies (See Lee (1974), Lee (1976), Groeger (2000), Groeger (2002) and Kondoh etLee al. difference. Many previous studies (See Lee (1974), (1976), Groeger Groeger (2000), Groeger (2002) and and Kondoh et al. al. (1976), (2000), Groeger (2002) Kondoh et (2008)) have made efforts to illustrate relations between (1976), Groeger (2000), Groeger (2002) and Kondoh et al. (2008)) have made efforts to illustrate relations between (2008)) have made efforts to illustrate relations between physical visual stimulus and driver’s risk estimation in (2008)) have made efforts to illustrate relations between physical visual visual stimulus and(e.g., driver’s risk distance, estimation in physical and driver’s risk estimation in dynamical trafficstimulus conditions headway time physical visual stimulus and driver’s risk estimation in dynamical traffic conditions (e.g., headway distance, time dynamical traffic conditions (e.g., headway distance, time headway and time-to-collision). Those studies have aimed dynamical traffic conditions (e.g., headway distance, time headway and time-to-collision). time-to-collision). Those studies have aimed aimed headway studies have to find a and proximate measure for Those accurately describing the headway and time-to-collision). Those studies have aimed to find a proximate measure for accurately describing the to find a proximate measure for accurately describing the relations under typical car-following situations as shown to find a proximate measure for accurately describing the relations under typical car-following situations as shown relations under in Fig. 1(a). relations under typical typical car-following car-following situations situations as as shown shown in Fig. 1(a). in 1(a). in Fig. Fig.respect 1(a). to one of microscopic flow characteristics, With With respect to one one of of microscopic microscopic flow characteristics, With respect flow characteristics, May (1990)),Winsum Heino (1996), Lewis-Evans et al. With respect to to one and of microscopic flow characteristics, May (1990)),Winsum and Heino (1996), Lewis-Evans et al. al. May (1990)),Winsum and Heino (1996), Lewis-Evans et 1. Car-following situations and lane-changing situa(2010), Risto and Martens (2013) haveLewis-Evans discussed timeMay (1990)),Winsum and Heino (1996), et al. Fig. Fig. tions 1. Car-following Car-following situations and and lane-changing situasitua(2010), Risto and Martens (2013) have discussed time(2010), Risto and (2013) have timeFig. 1. headway (T HW ). ItMartens is originally defined asdiscussed the time differFig. 1. Car-following situations situations and lane-changing lane-changing situa(2010), Risto and Martens (2013) have discussed timetions headway (T HW ). It is originally defined as the time differheadway tions tions headway (T (T HW HW ). ). It It is is originally originally defined defined as as the the time time differdifferCopyright © 2016, 2016 IFAC 66 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 66 Copyright © 2016 IFAC 66 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 66 Control. 10.1016/j.ifacol.2016.10.462
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(1996), Winsum and Brouwer (1997), Risto and Martens (2013) evaluate that drivers preferred to choice of time headway in car following and braking response.
RPr = 1/T HWr + 4/T T Cr .
T HW = d/vh
Driver’s lane-changing data are collected in different lanechanging situations operated on a driving simulator.
2. METHOD
(1)
In studies of visual control of locomotion, a concept of time-to-collision (T T C) is argued as an optical flow (See Lee (1974), Lee (1976)). Hayward (1972) gives a definition of time-to-collision as: ”The time required for two vehicle to collide if they continue at their present speed and on the same path”. Since the visual information of time-tocollision has been proved to be a crucial predictor for estimating collision risk in car-following situations (See Cavallo and Laurent (1988), Groeger (2000), Groeger (2002)) time-to-collision is discussed in collision avoidance systems (See van der Horst (1991),van der Horst and Hogema (1993), Winsum and Heino (1996)). Generally, it is manipulated as equation (2) in cases of car-following situations. T T C = d/(vh − vf )
(6)
2.1 Apparatus A fixed-base driving simulator is used in the data collection. It can simulate driving on an expressway with two lanes (See Fig. 2). A speed governor is set up for preventing the host vehicle from a limited velocity vM ax. .
(2)
In recent studies, it is pointed that driver’s subjective estimation of driving risk strongly depends on the global optical flow (i.e., inverse of time-headway) and the local optical flow (i.e., inverse of time-to-collision) in cases of a host vehicle approaching to a slower forward one (See Kondoh et al. (2008), Kondoh et al. (2014)). The studies quantify the subjective estimation as Risk Perception (RP ) according to the following formula (equation (3)).
Fig. 2. A fixed-base driving simulator. 2.2 Participants
RP = 1/T HW + 4/T T C
(3)
Seven females and five males, ranging from 28 to 45 years old (Mean = 38.3, SD = 5.3), participate in the data collection. Each participant holds a valid driver’s license. After receiving an explanation of the data collection, all of them signed in information consent for participating the data collection.
Those studies of visual information in risk perception have focused on traffic accidents in the car-following situations. Accurately obtaining visual information of a rear car in lane-changing situations (e.g., Fig. 1(b)) is more difficult than a forward car in car-following situations (e.g., Fig. 1(a)). Concretely, perceiving risk is through direct and continuous visual information in cases of the forward vehicle. In cases of the rear vehicles, the visual information is indirect and discontinuous. Understanding driver’s subjective perception of risk to a rear car is an essential issue to driving safety in lane-changing behavior. Consequently, this study directs driver’s risk estimation to a rear vehicle that approaches to the host vehicle on the passing lane in the lane-changing situations.
2.3 Driving scenario and driving task One lane-changing scenario is designed in each trial. There are 28 trials in the whole data collection. Driving initial conditions (i.e., RP0 , vh , vr and d0 ) in the 28 trials are sorted in terms of the index of RP as shown in Table (1). Following instructions are given to each of participants: (1) Each participant is requested to accelerate the host vehicle’s velocity (vh ) and to reach the limited velocity vM ax. on the cruising lane after starting a trial, where the headway distance (D) between two vehicles driving on the passing lanes is set a same value (See Fig. 3(a)); (2) he or she is given a piece of acoustic message at the time point t0 when the third vehicle on the passing lane is passing the host vehicle (See Fig. 3(b)); (3) he or she has to make a choice whether he or she can change lanes after receiving the acoustic message. The time point is defined as td when he or she turns on the right turn signal for claiming he or she makes a choice to change lanes;
The purpose of the present paper is to clarify relations of driver’s estimation of collision risk to an approaching rear car in lane-changing situations to choices of time-headway, time-to-collision, RP as well as headway distance. The relations are argued in lane-changing for choice and lanechanging implementation of decision-making behaviors. From the viewpoint of a host vehicle, these measures are redefined as equation (4) - (6). T HWr = −d/(−vh ) = d/vh .
(4)
T T Cr = −d/(−vh − (−vr )) = d/(vr − vh ).
(5) 67
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Table 1. Initial driving condition in each trial.
(4) he or she is instructed to implement the lane-change behavior as soon as possible after making the choice of changing lanes. The time point is defined as ti when the host vehicle’s body firstly touches the center line. Note that after the host vehicle passed the center line, the limited velocity of vh is canceled. (5) In cases of giving up a lane-changing choice, he or she is requested to turn on the left turn signal.
N o.
RP0
vh
vr
d0
N o.
RP0
vh
vr
d0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.75 0.75 0.75 0.75 1.00 1.00 1.00 1.00 1.25 1.25 1.25 1.25 1.50 1.50
60 60 90 90 60 60 90 90 60 60 90 90 60 60
85 95 100 110 85 95 100 110 85 95 100 110 85 95
59 74 48 70 44 55 36 53 36 44 29 42 30 37
15 16 17 18 19 20 21 22 23 24 25 26 27 28
1.50 1.50 2.00 2.00 2.00 2.00 2.50 2.50 2.50 2.50 3.00 3.00 3.00 3.00
90 90 60 60 90 90 60 60 90 90 60 60 90 90
100 110 85 95 100 115 85 95 100 115 85 85 100 115
24 35 22 28 18 26 18 22 14 21 15 19 12 18
Unit of velocity is km/h. Unit of distance is m.
host vehicle’s body firstly touches the center line. In order to investigate driver’s perceiving driving risk during his/her decision making for changing lanes, this study investigates following measures at lane-change choice and implementation:
Fig. 3. Driving scenario. 2.4 Procedure
• Necessary time to decide lane changes that is time length from t0 to td when the right turn signal is turned on. • time-headway, time-to-collision, RP , and headwaydistance to the nearest rear vehicle on the passing lane at ti , which are defined as T HWinit. , T T Cinit. , RPinit. and dinit. , respectively. • Subjective assessment to each lane-change scenario
Each participant is given an explanation of the driving simulator’s operation and the instructions during driving task. Then, he or she does approximately 5-minute driving exercise for being familiar with the driving simulator. After 5-minute rest, he or she is instructed to experience the 14 trials. After 5-minute rest, he or she experiences the other 14 trials. All participants are divided into two groups in order to counterbalance order effects. One group is operated in an ascending order of RP , the other is in a descending order.
3. RESULTS 3.1 Driver’s lane-changing behavior
After each trial, they are asked to report their subjective assessment to the experienced scenario by using a paperquestionnaire as shown in Fig. 4.
Fig. 5 indicates averaged horizontal position at each 1second time period as a function of time for 5-second time period prior and 3-second time period posterior to the time point td . Results show that lane-changing behaviors are operated in a good manner while time-to-collision is large but time-headway is small in such trials shown in Fig. 5(a). As time-to-collision becomes smaller and timeheadway becomes larger, the driving behaviors posterior to td tend to become in a disorder in such trials shown in Fig. 5(b) and (d). The disorder tendency becomes much clearer when both of time-to-collision and time-headway become smaller in such trials shown in Fig. 5(c). Note that the disorders also occur prior to td . Furthermore, host vehicle’s transition in the horizontal direction while changing lanes retards as RP becomes great.
Fig. 4. Questionnaire sheet that is used for reporting subjective assessment to each scenario after each trial.
3.2 Driver’s lane-changing choice 2.5 Measures Fig. 6 plots necessary time of making a choice whether to change lanes, or not, related to each of initial driving conditions (i.e., T HW0 , T T C0 , RP0 and d0 ). It is indicated that more dangerous the traffic condition is, more time is spent on make the choice. Linear regression analysis is performed between the necessary time and each of measures.
Since all participants are instructed to turn on the turnsignal once they make a choice of changing lanes in the near future, it can be considered that lane-change choice is made at td . Furthermore, ti denotes the time point when lane-change implementation is initiated, i.e., the 68
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Fig. 5. Horizontal moving position of the host vehicle. Note that zero of the horizontal axis is the time point td at which a driver turns on the right turning signal. Each of coordinate values of Y- axis is an average horizontal position during every 1-second time period from 5 s prior and 3 s posterior to td for 12 participants. Dotted horizontal line denotes a center-position of the cruising lane.
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Fig. 6. Necessary time for making a choice of lane-changing behavior to-collision but also time-headway to an approaching rear car. In comparison that a driver refers to perceiving only time-to-collision for lane-changing choice, he or she prefers to both of time-to-collision and time-headway for lanechanging implementation. It is suggested that a driver intends to perceive a rear-collision risk dependently on both a global optical flow and a local optical flow while he or she implements a lane change.
Results show strongly positive correlation between T T C0 and the necessary time (r = 0.60, p < 0.01 ) than T HW0 and d0 (See Table (2)). It is indicated that a driver tends to perceive the driving risk through time-to-collision information to an approaching rear car for making a choice whether it is executable to change lanes under the current traffic condition, or not. It is implied that driver’s subjective risk estimation depends greatly on a local optical flow. Table 2. Statistical parameters resulting from the linear regression analysis between the necessary time to make a choice and the four measures (T HW0 , T T C0 , RP0 and d0 ) M easures T HW0 T T C0 RP0 d0
r2 0.090 0.294 0.289 0.200
r 0.30 0.54 0.54 0.45
Parameters Df MS 26 1.560 26 1.21 26 0.443 26 241.0
F 2.569 10.81 10.56 6.49
p 0.12 0.002 0.003 0.02
3.3 Driver’s lane-changing implementation Fig. 7 indicates relationships of four measures under conditions of lane-change implementation versus initial traffic conditions, i.e., T HW0 , T T C0 , RP0 and d0 . Linear regression analysis is operated on each of four measures between lane-change implementation versus traffic conditions. According to the results, strong correlations (r = 0.62 - 0.97) are observed on each of four measures (See Table (3)). Especially, greatly significant positive correlation is showed on both T HW0 (r = 0.97, p < 0.01) and T T C0 (r = 0.97, p < 0.01).
Fig. 7. Relationship of four measures between lane-change implementation and initial traffic conditions.
It is argued that a driver implements lane-changing behavior while perceiving driving risk through not only time69
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• drivers tend to prefer time-to-collision information for perceiving driving risk for making a choice whether it is possible to change lanes in current traffic conditions with comparison to traffic flow like time-headway and headway-distance; • drivers’ lane-changing implementations are greatly dependent on subjective risk perception through time-to-collision and time-headway information. • though drivers prefer time-to-collision and timeheadway information for lane-change choice and implementation to RF , their subjective estimations of driving risk are consistent with the index of RF .
Table 3. Statistical parameters resulting from the linear regression analysis on four measures (time-headway, time-to-collision, RP and headway-distance) between lane-change implementation and initial traffic conditions M easures T HW0 T T C0 RP0 d0
r2 0.95 0.93 0.385 0.607
r 0.97 0.96 0.62 0.78
Parameters Df MS 26 0.052 26 0.894 26 0.384 26 118.5
F 475.3 363.8 16.26 40.09
p 0.00 0.00 0.0004 0.00
3.4 Subjective assessment
Since the index of RP involves two concepts of timeto-collision and time-headway information, it is believed that RP would be a significant index to quantify driver’s subjective perception of proximity risk by a rear vehicle through optimizing weights on T T C and T HW .
Mean subjective assessment to each trial is plot to each of four measures of initial traffic conditions, i.e., T HW0 , T T C0 , RP0 and d0 in Fig. 8. Higher the score is, more dangerous the scenario is thought. Results in Fig. 8 show a same tendency on all the four measures. More definite correlation is indicated between the subjective assessment and values of T T C0 . It is argued that a driver prefers visual information of time-to-collision for evaluating what extent the situation is, that is, visual stimulus in the local optical flow field affects greatly on his/her subjective assessment to the rear-collision risk.
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Fig. 8. Plots of subjective assessment versus T HW0 , T T C0 , RP0 and d0 4. CONCLUSION This study collected lane-changing data under different traffic conditions. Driver’s lane-change choice and implementation have been investigated on measures of timeheadway, time-to-collision, RP and headway-distance. Results show that: 70
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