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Abstract and Figures

Highly automated vehicles (HAVs) will need to interact with pedestrians in a safe and efficient way. Thus, investigating and modeling vehicle-pedestrian interactions at uncontrolled locations is essential to ensure safety and acceptance of these vehicles. Controlled studies are a valuable tool for these scenarios where all the tasks are not possible to be done in the real world and where some variables should be controlled with high accuracy for the development of models of human behavior. In this paper, a game-theoretic model was tested using data from a distributed simulator study. The study was conducted by connecting a desktop driving simulator to a CAVE-based pedestrian lab, providing a safe environment for testing the model’s ability to capture the gap acceptance behavior of pedestrians when interacting with a Human-Driven (HD) or an Automated Vehicle (AV). The results showed that, overall, the model could capture pedestrian behavior well and the pedestrians had lower crossing probabilities in front of the AV. This was seemingly due to differences in vehicle kinematics. Further analysis of the pedestrians’ data revealed the importance of given instructions to the participants in these types of studies. Lessons learned through this study were also used to suggest further ideas on how to design controlled studies for game-theoretic modelling.
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Vehicle-Pedestrian Interactions at Uncontrolled Locations: Leveraging Distributed
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Simulation to Support Game-Theoretic Modeling
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Amir Hossein Kalantari
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Institute for Transport Studies, University of Leeds, UK
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a.h.kalantari@leeds.ac.uk
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Gustav Markkula
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Institute for Transport Studies, University of Leeds, UK
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g.markkula@leeds.ac.uk
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Chinebuli Uzondu
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Institute for Transport Studies, University of Leeds, UK
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Federal University of Technology, Owerri, Nigeria
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chinebuli.uzondu@futo.edu.ng
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Wei Lyu
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Institute for Transport Studies, University of Leeds, UK
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School of Business Administration, Northeastern University, China
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tswl@leeds.ac.uk
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Jorge Garcia de Pedro
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Institute for Transport Studies, University of Leeds, UK
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j.garcia1@leeds.ac.uk
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Ruth Madigan
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Institute for Transport Studies, University of Leeds, UK
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r.madigan@leeds.ac.uk
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Yee Mun Lee
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Institute for Transport Studies, University of Leeds, UK
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y.m.lee@leeds.ac.uk
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Christopher Holmes
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Institute for Transport Studies, University of Leeds, UK
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Nissan Technical Centre Europe, Cranfield, UK
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tsch@leeds.ac.uk
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Natasha Merat
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Institute for Transport Studies, University of Leeds, UK
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n.merat@its.leeds.ac.uk
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Word Count: 6427 words + 3 table (250 words per table) = 7177 words
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Submitted [31/07/2021]
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ABSTRACT
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Highly automated vehicles (HAVs) will need to interact with pedestrians in a safe and efficient way. Thus,
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investigating and modeling vehicle-pedestrian interactions at uncontrolled locations is essential to ensure
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safety and acceptance of these vehicles. Controlled studies are a valuable tool for these scenarios where all
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the tasks are not possible to be done in the real world and where some variables should be controlled with
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high accuracy for the development of models of human behavior. In this paper, a game-theoretic model
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was tested using data from a distributed simulator study. The study was conducted by connecting a desktop
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driving simulator to a CAVE-based pedestrian lab, providing a safe environment for testing the model’s
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ability to capture the gap acceptance behavior of pedestrians when interacting with a Human-Driven (HD)
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or an Automated Vehicle (AV). The results showed that, overall, the model could capture pedestrian
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behavior well and the pedestrians had lower crossing probabilities in front of the AV. This was seemingly
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due to differences in vehicle kinematics. Further analysis of the pedestrians’ data revealed the importance
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of given instructions to the participants in these types of studies. Lessons learned through this study were
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also used to suggest further ideas on how to design controlled studies for game-theoretic modelling.
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Keywords: Game theory, Pedestrian crossing, Autonomous vehicles, HIKER lab
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INTRODUCTION
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The interaction between vehicles and pedestrians at unmarked pedestrian crossings might cause a
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disruption in vehicular traffic flow and more worryingly, may cause accidents. Situations may arise where
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one agent makes a decision considering the other’s initial state, but the latter changes his decision
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unexpectedly, or both agents misunderstand each other’s intentions simultaneously, resulting in a conflict
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or even an accident. Hence, investigating, modelling, and simulating these types of interactions is an
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important element in the development of Highly Automated Vehicles (HAVs). Despite the previous
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research [1], it is still unclear how these robots are going to share the road with pedestrians and imitate
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human behavior (as drivers) with high accuracy. On one hand, the ‘defensive’ yielding behavior of
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Automated vehicles (AVs) whenever a pedestrian moves towards/jumps in front of them is
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counterproductive to their potential application [2, 3]; and on the other hand pedestrians have been observed
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to have lower tendencies to cross the road when they recognize a vehicle as an AV [4], and their behavior
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and trust are dependent on AV behavior [5].
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To date, previous studies involving vehicle-pedestrian interaction modelling have employed rule-
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based models like social force [6-9] and cellular automata models [10-15]. While these models are capable
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of simulating pedestrians’ trajectories, they generally assume that pedestrians act mostly like independent
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moving objects without considering other road users’ intentions before taking every decision, which makes
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it hard to account for interdependencies. To this end, researchers have employed Markov decision process
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models [16, 17], Proxemics [18], Decision Field Theory [19], evidence accumulation models [20, 21],
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discrete choice models [22-25] and game theory [11, 26-29] to model how humans solve conflicts at
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uncontrolled locations like zebra crossings. Among these, game-theoretic models provide a good insight on
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agents’ decisions where there is competition over dominating the road space while maintaining the required
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safety. Game theory is a branch of applied mathematics that models social interactions between intelligent
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rational decision-makers. It has the assumption that rational players form their beliefs based on what they
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think other players will do (strategic thinking), after which they make the decision that best fits those beliefs
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(optimization). Players can revise their decisions and beliefs afterwards until they become mutually
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consistent, that is, until equilibrium is reached.
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Gap acceptance is a fundamental factor that affects pedestrians’ crossing decisions at uncontrolled
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locations where the road and traffic environment is less adapted for pedestrians’ necessities, and the
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pedestrians themselves are less compliant with traffic rules. It has been suggested that pedestrians might
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have a critical gap in mind for crossing attempts which can be explained by the crosswalk length, their
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average walking speed and a safety margin (in seconds) which represents pedestrians risk acceptance (i.e.
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higher risk perception results in smaller safety margins) [22]. This margin of safety can be defined as a
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temporal distance of the approaching vehicle, or time-to-contact (TTC) from the pedestrian’s perspective.
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This proved to be a good estimator of the actual TTC in the meta-analysis of the previous studies [30] and
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an indicator of crossing intentions in Cave Automatic Virtual Environment (CAVE) [31]. In comparison
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with head-mounted displays (HMDs) which are one of the two common tools in the virtual reality (VR)
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world to study pedestrian behavior, the CAVE system does not suffer from field of view limitation [32], or
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discomfort or motion sickness (especially regarding older adults) [33]. Pedestrians have also been shown
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to have longer safety margins in CAVE systems, indicating the immersiveness of this type of environment
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[32]. In addition, CAVE systems allow multiple pedestrians to naturally interact with each other, or with
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other physical objects like mobile phones, which makes it a good choice to study distracted pedestrians.
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For a complete review of CAVE systems see [34].
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Controlled studies provide a valuable tool for examining traffic scenarios in a way that would not
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be possible in the real world, allowing some variables to be controlled with a high degree of accuracy to
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facilitate the development of models of human behavior. Controlled studies have been successfully used to
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support game-theoretic modelling in non-traffic contexts [35, 36], however, they have not been used with
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multiple interacting human participants in the traffic context so far. Instead, people have used naturalistic
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data, which has high validity, but the lack of experimental control, and high behavior variability, means
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that such data does not lend itself well to model development; for instance, to determining exactly how to
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formulate the payoffs. In theory, controlled experiments allow us to single out the different factors that
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might be relevant, and study the independent contributions of each of these factors. The contributions of
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this study are as follows:
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1- To take the first step toward investigating how to design controlled studies with two/multiple
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participants for game-theoretic model development using distributed simulation.
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2 - To test a game-theoretic model’s performance at capturing pedestrians’ gap acceptance behavior.
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Hence, this study seeks to test an existing gap acceptance game-theoretic model using a distributed
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simulator study which was conducted by connecting a CAVE-based pedestrian lab to a desktop driving
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simulator. The rest of the paper consists of the following sections: Section 2 explains the methodology,
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Section 3 involves the results and discussion, Section 4 is the general discussion of the lessons learned from
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the paper and Section 5 is conclusion.
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METHODS
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This section first explains the computational model and the experiment design of the study that has
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been used to validate the model.
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Model formulation
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In this paper, the game-theoretic model by Wu et al. [27] was used to model how pedestrians and
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vehicles resolve conflicts. Both agents can either decide to try to cross in front of the other, or wait and let
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the other agent cross first. Therefore, the players are pedestrians and vehicles, , respectively, and
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strategies are: (cross, wait). The model constructs payoffs as sums of utilities relating to (1) the unpleasant
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experience of being on a collision course with another road user, modeled as k = 1/TTC, and (2) the time
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loss incurred if yielding to the other agent, equal to the time it takes for that agent to pass the crossing
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location (explained by ). Wu et al. assumed that both of these utilities are always present in all outcomes,
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with a negative sign in outcomes where they negatively affect a given road user, or a positive sign otherwise.
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They also included a multiplier to account for the extra waiting time needed if both agents try to cross
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simultaneously, and thus need to avoid a collision, e.g., by emergency braking.
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Table 1 shows the parameters of the model:
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Table 1 Parameters of the study
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Parameter
Description
Scenario-based parameters (parameters of the experiment)
vehicle speed (m/s)
distance between the vehicle and the pedestrian (m)


risk perception for pedestrians/ vehicles
waiting time of pedestrians or drivers (s)
time the vehicles take to pass the crossing location
time the pedestrians take to pass the crossing location
Model parameters
multiplier for the utility of delay (emergency brake) when both agents
want to cross

Weight coefficient: Varies from scenario to scenario and based on this
assumption: The more the pedestrian waits, the higher the chance of
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considering delay loss more important than risk perception. In the
original paper is modeled as varying with cumulative waiting time for
the pedestrian, which is not considered here.
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In Wu et al. [27], the payoff matrix is formulated as:
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Table 2 Payoff matrix (the vehicle is the row player and the pedestrian is the column player)
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Pedestrian wait
Vehicle cross
 
Vehicle wait

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The first expression of each row in Table 2 belongs to the vehicle payoff, and the second one is for
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the pedestrian. From Table 2, it can be seen that the game has no unique Nash equilibrium, and has two
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dominant strategies ((pedestrian cross, vehicle wait), (pedestrian wait, vehicle cross)) which can be
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calculated using the mixed strategy algorithm which equates expected utilities of each player [37]. The
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probability for the pedestrian to cross/wait can be defined as follows:
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Ppc, Ppw = ( 

 (1)
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The model also predicts cross/wait probabilities for the vehicle, but as will be clear from the below, the
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driver behavior was partially constrained by the instructions in the empirical study. For this reason, only
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the pedestrian crossing probabilities were modeled in this paper.
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Empirical Study
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A subset of a dataset obtained from a distributed simulator study was used to test the model. The study
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was conducted by connecting the University of Leeds desktop driving simulator to the Highly Immersive
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Kinematic Experimental Research (HIKER) lab [38].
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Apparatus
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The HIKER lab is a 9 × 4 m CAVE-based pedestrian simulator with four plate glass walls and a
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wooden floor (Figure 1). Virtual scenes are projected at 120 Hz to the floor and walls using eight Barco
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F90 4k projectors. The whole scene responds to the participant’s head position and gaze, using a head and
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controller tracking system, consisting of ten VICON Vero v2.2 (2.2MP) cameras, using VICON Tracker
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3.7. The BabySim (aka the Leeds desktop driving simulator) (Figure 1) consists of a screen, a Logitech G27
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Racing Wheel for steering, accelerator/brake pedals placed on the floor, and sound system to imitate the
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sound of the vehicle’s engine. The pedestrians had fourteen body markers attached to their body to track
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their position, while they moved freely during the experiment. The virtual environment was built in Unity
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3D in a way that the pedestrian in the HIKER lab and the driver behind the wheel of the BabySim could
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see it at the same time, each from their own perspective. Unity communicated with the VICON tracking
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system built into the HIKER environment, and received the pedestrian orientation and position,
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continuously updating the scene. The BabySim was placed behind one of the HIKER’s screens to ensure
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that participants could not see each other during the experiment, other than in the virtual environment. The
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pedestrian was visualized as a set of graphical spheres to the driver (Figure 2), with each sphere
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corresponding to the body tracking markers attached to the head, arms, chest, pelvis, elbows, hands, thighs,
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ankles and feet (see also [38]).
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Figure 1 The HIKER pedestrian lab (left) and the BabySim (right) at the University of Leeds
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Figure 2 The driver’s view (left) vs the pedestrian’s view (right) (Note that the two photos do not
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show the exact same situation.)
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Participants
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50 participants including 25 drivers (12 female, Age: M = 41.75, SD = 11.43) and 25 pedestrians
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(13 female, Age: M = 32.64, SD = 9.97) took part in the study. Each driver was paired with a pedestrian.
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Every driver held UK/EU license and had at least 3 years’ driving experience (range 3–46) with annual
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mileage of 9,264 miles (SD = 8,631). All pedestrians had lived in the UK for at least 1 year (range: 157).
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The study was approved by the University of Leeds Ethics Committee (Ref: LTTRAN-113).
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Experiment design
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In this study, the pedestrian was asked to cross between two vehicles: A white car followed by a
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blue one. The behavior of the white vehicle was always handled by software, while the blue vehicle was
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controlled by the human driver (HD) in 50% of the trials and by the automated vehicle (AV) in the other
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50%. The vehicles always travelled at the same speed (30 mph/13.41 m/s), and had headways from 3.16 to
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8.28 s which was increased by 0.16 s for each consecutive trial, resulting in 32 crossings per
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driver/pedestrian pair.
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An overview of the design used for the 32 trials is shown in Table 3. This resulted in 16 conditions
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for the HD (8 braking, 8 non-braking) and 16 conditions for the AV (8 braking: 4 soft braking, 4 hard
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braking, 8 non-braking). These trials were randomized within a block per pedestrian, to account for order
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effects.
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Table 3 Experimental conditions of the study
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Blue car
condition
Braking condition
Description
Human Driver
(HD)
Braking (HDB)
HD instructed to yield to the pedestrian
Non-Braking (HDNB)
HD asked not to brake (but encouraged to do so,
if pedestrian stepped into the road)
Automated
Vehicle (AV)
Soft Braking (AVSB)
AV decelerated from 40 m away, and stopped
at a distance of 4 m away from the pedestrian
Hard Braking (AVHB)
AV decelerated from 40 m away, and stopped
at a distance of 12 m away from the pedestrian
Non-Braking (AVNB)
AV did not brake
Procedure
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After reading the relevant participant information sheet and signing the consent form, pedestrians
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began each experimental trial standing at a designated point at the edge of the virtual road, where they were
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asked to look to their right and wait for the two approaching cars. The instruction to the pedestrians was to
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cross the road naturally between the two oncoming vehicles (i.e. after the white vehicle had passed), if they
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felt safe to do so. After crossing the road, they had to walk back to the starting position and start the next
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trial.
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The drivers were asked to follow instructions on the screen before the start of each trial. These
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instructions notified them if the driving mode in the upcoming trial was automated or not (AV/HD), and
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also regulated the braking condition (Braking or Non-Braking). As outlined above, the blue vehicle was
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handled by drivers on 50% of trials. For these trials, the blue vehicle initiated its trip in automated mode,
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to allow the same uniform speed profile and time gap with the white vehicle as the AV conditions. For the
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HD conditions, a simple interface at the bottom half of the windscreen, changed from green to yellow when
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the vehicle was 80m away from the pedestrian, alerting drivers that they should be ready to resume control.
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After another 20m, when the vehicle was 60m away from the pedestrian, this light changed to red, and
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drivers were asked to resume control by taking hold of the steering wheel as soon as possible. At this point,
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drivers either kept on driving and passed the pedestrians (the non-braking conditions) or braked to let the
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pedestrians cross the road (braking trials). Note that it was not visible to the pedestrian whether the vehicle
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was in AV or HD mode in a given trial. Figure 3 shows the sketch of the experiment.
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Figure 3 Road scenario of the experiment; illustrating the relation between pedestrian’s crossing
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position, and the distance at which each braking event/HMI condition happened
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MODEL FIT
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As mentioned above, early deceleration/braking was by design a part of the scenario in AVSB and
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AVHB conditions, and in HDB the most common behavior of the human drivers was to commence yielding
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directly from the 60 m takeover point. This means no actual game-theoretic interaction happened in these
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trials as the driver had no choice but to stop at a certain distance from the pedestrian and the pedestrian also
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already observed that the vehicle had stopped for him even before deciding whether or not to cross. Thus,
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only non-braking trials have been used to test the model. Although the vehicle in AVNB condition never
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yielded, the trials were randomized per block per pedestrian, and since the pedestrian had no way of
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knowing if the vehicle was going to stop for him or not, the game-theoretic model is applicable for these
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trials. Moreover, as mentioned earlier, the driver in HDNB condition was asked to brake if the pedestrian
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stepped into the road, and therefore the situation was not of a game-theoretic nature for the drivers in this
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experiment, so the model was just tested for the pedestrian.
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The raw data were extracted and the model, similar to Wu et al. [27], was fitted using headway
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intervals (time gaps) for each non-braking condition and its free parameters which are and . Thus, three
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pairs of free parameters were used for AVNB, HDNB and combined (both AVNB and HDNB) conditions.
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It should be noted that unlike Wu et al.’s [27] naturalistic study dataset, this study has no concept of waiting
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time, as participants only had the chance to cross the road after the first vehicle passed and before the arrival
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of the second one. Before model fitting, the following exclusion criteria were applied so that only actual
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crossings were considered: a) data missing due to technical issues, b) pedestrian crossed before the first
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vehicle, and finally, c) pedestrian initiated crossing behavior but did not finish crossing. To this end,
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pedestrian number 5 was identified as an outlier due to the total ignorance of the instructions and was
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excluded.
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For the model fit, for each of the three conditions, the time gap was divided into three intervals:
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(3,5], (5,7] and (7,9] and the middle value of each interval was selected to represent and which is
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in Equation (1). The observed value of  was calculated based on the number of performed crossings
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divided by the total number of crossings and non-crossings within that headway interval in the dataset. Any
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combination of two selected intervals and observed  in those intervals could specify the values for the
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two free parameters and . Here, the combination of the first and third interval was used.
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One benefit of controlled studies over naturalistic studies is that it is possible to study individual
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differences in interaction behavior. Therefore, going beyond the population-level fitting implemented by
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Wu et al. [27], the current model was then calibrated per individual using the sum of squares and a grid
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search of the free parameters ( and ) to minimize the deviation between observed and model-predicted
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behavior:
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 
  (2)
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where n represents the number of trials for each pedestrian, is the observed choice of crossing and 
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is the predicted probability of crossing in Equation 1. This is similar to the fitting method used by Liu et al.
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[39]. The 95% Wilson confidence intervals for each individual's data were also calculated based on the
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following formula:
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





 (3)
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where  are lower and upper bounds, respectively, is the 
quantile of a standard normal
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distribution corresponding to the target error rate, which here is 0.05 and therefore , is the
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proportion of performed crossings to the total number of trials ( in each headway interval.
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RESULTS AND DISCUSSION
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HDNB vs AVNB
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Figure 4 shows the results per 24 participants in 190, 187 and 377 trials for HDNB, AVNB and all
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non-braking conditions combined, respectively. The panels on the left show the model prediction based on
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the current lab data. To compare the behavior that has been observed in the lab to its naturalistic counterpart.
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We used Wu et al. study’s reported free parameters [27] and set the waiting time of the pedestrians to zero
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to make the two sides comparable. The results of this model can be seen by purple lines on the right panels.
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The values of the free parameters for each condition are provided under the titles. The left side of Figure 4
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shows that for all three conditions, there is a good match between the observed and predicted data and an
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increasing trend in crossing probability over time gap is evident this is in line with previous studies, but
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the probabilities at the higher time gaps are somewhat smaller than previously observed [40, 41]. One
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reason for this could be the exclusion criteria as we only included fully completed crossings. Other potential
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reasons can be explained by analyzing the same plot per pedestrian (see Section 3.2). For the AVNB
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condition, this increase is less noticeable. One of the main reasons for this could be that there were more
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excluded trials where pedestrians initiated their crossing behavior but aborted it in the AVNB condition (12
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trials) compared with HDNB condition (6 trials). In these situations, it would appear that the pedestrian
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started crossing with the hope that the vehicle was going to yield for them (especially if they had
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experienced a braking trial before), but soon recognized that there was no sign of yielding, and thus, to
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avoid a collision they went back to the starting point, meaning no crossing happened. Possibly the main
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reason for the greater crossing tendency in the HDNB condition than AVNB was that the human drivers
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were in favor of slowing down slightly after taking over, as can be seen in Figure 5; the AV kept a relatively
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constant speed with little fluctuation in the range of  to   ( to  ), whereas the HD
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shows, on average, a consistent decline in speed after taking over ( ), reaching under   when
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it was close to the pedestrian, resulting in higher probabilities of crossing.
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The right side of Figure 4, as mentioned, illustrates that with the free parameters obtained from Wu
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et al’s naturalistic data; the model still shows the pattern of higher crossing probabilities for larger time
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gaps, but with a weaker effect of time gap, and lower probabilities overall. This was not unexpected as
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setting the waiting time to zero resulted in a very small value for which led to the lower probabilities.
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Overall, the group level results show that the Wu et al. model can be fitted to capture the general trends in
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the study.
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Figure 4 The probability of crossing over time gap for all non-braking trials; left: current
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study and right: Wu et al. study
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Figure 5 Second vehicle speed profile over distance to the pedestrian
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Differences among pedestrians
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Figure 6 shows the probability of crossing over the time gap for 14 participants considering all non-
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braking trials (377 trials). Those participants who never crossed the road in these trials were omitted from
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the figure. In order to do per-participant analysis, we pooled each individual’s data across AVNB and
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HDNB with an average of 5 data points per pedestrian per headway interval. 95% confidence intervals
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along with the values of the free parameters for each pedestrian can be seen in each plot. As can be seen
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from the figure, two participants (i.e., 8 & 17) always crossed the road irrespective of the time gap, which
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may suggest they always preferred to save time rather than worrying about their safety. On the contrary,
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two participants (i.e., 11 & 13) did not cross in most of the trials. The behavior of these participants along
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with those 10 participants who never crossed the road can be the main reason for the overall lower
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probabilities. Moreover, some participants (i.e., 7, 18, 22, 24), showed lower probabilities in higher time
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gaps which was surprising. The interpretation that these participants were relatively insensitive to the time
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gap (as suggested by their model fits) is equally compatible with the data, as shown by the confidence
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intervals. The results for the remaining participants are in correspondence with the literature which suggests
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higher time gaps usually result in higher probabilities of crossing. Overall, the model was more successful
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in predicting the behaviors that were in line with the findings from the literature which is not surprising. It
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should be noted that, as mentioned above, the number of data points in each panel was few which makes it
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hard to draw concrete conclusions.
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Figure 6 Probability of crossing over time gap per individual
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LESSONS LEARNED AND FUTURE DIRECTION
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To date, some studies have used a controlled design with human participants to test a game-
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theoretic model regarding pedestrians interactions with each other [42] and with robots [35, 36, 43, 44] in
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non-traffic domains. Turnwald et al. found that pedestrians’ comfort level depends on the level of
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cooperation and distance from the robot at which the interaction happens. They then found that participants
22
could distinguish the motions generated by a social force planner from human motions but not by those
23
based on a game-theoretic planner[36]. These studies show that game theory is a useful method for
24
simulating the interactions among a crowd of pedestrians and proved to be a capable tool when used for
25
programming a motion planner in robots. This suggests that future AVs can benefit from a game-theoretic
26
controller as part of their design algorithms which has been confirmed by the later experimental traffic
27
studies by Camara and colleagues [29, 45]. However, these studies have been either conducted in a non-
28
traffic environment, for instance, by using a board game type paradigm [2, 46] with two humans; or in a
29
real-traffic scenario, but with only one human and one AV agent [29]. The unrealistic nature of the board
30
13
game method was also evident in Camara et al.’s later paper using VR, in which their results contradicted
1
earlier papers by showing that avoiding a collision was far more important to pedestrians in traffic
2
situations, than the time loss for them [29]. Therefore, the current paper tried to take the first step toward
3
exploring the use of a controlled study for a game-theoretic model using two human agents. While there
4
are many models of gap acceptance capable of fitting the lab data, a game-theoretic model’s performance
5
at capturing gap acceptance has not really been tested before.
6
This paper, among its novelties, has several limitations: First and from the payoff formulation
7
perspective, the Wu et al model assumes that the delay penalty when the pedestrian is waiting is the
8
pedestrian’s own crossing time , whereas intuitively it seems more logical to consider the delay as the
9
time it takes for the vehicle to pass . Moreover, it would be interesting to accommodate psychosocial
10
metrics like Social Value Orientation (SVO) similar to [47] into the players’ utility functions to measure
11
how individuals weigh their reward against the rewards of the other player. This seems essential as previous
12
research revealed that individuals have different reward functions in this respect [44]. Second, and
13
regarding experiment design, the approaching vehicle had only one constant velocity which may suggest a
14
constant representation of risk perception. Manipulating the speed of the approaching vehicle could be
15
beneficial, as previous studies have shown the effect of different vehicle speeds on the pedestrians crossing
16
behaviors in the CAVE [31, 32]. Additionally, the driver’s task was to yield to the pedestrian, if required
17
to avoid a collision, in all conditions; whereas the AV was preprogrammed to either yield or not yield,
18
regardless of the situation. This made it impossible to account for the car/AV decisions as an interactive
19
player in the game.
20
Future distributed simulator studies should be designed in a way to make sure that both agents do
21
play the game in each interaction, and such that none of them will become passive after a number of trials.
22
One way to do this may be to create time-based incentives (e.g., time-based scores or time limits) to create
23
an element of time pressure, or just instructing them to imagine that they are in hurry (e.g., late for a
24
meeting), while asking them to drive/cross safely as well. However, excessive time pressure could lead to
25
a situation where the pedestrian steps into the road in small time gaps, forcing the driver to brake hard to
26
avoid a collision, which might lead to problems with subsequent behavioral adaptation, driving simulator
27
sickness in the driver, or both. It seems that a key principle here lies in carefully designing and constraining
28
the spatiotemporal area in which the interaction happens. Not limiting the participants to stay within a
29
constrained conflict zone in this type of study would let them either avoid any conflicts completely, or
30
always wait for the other agent to go first. Thus, identifying a proper time (i.e., a temporal distance) for the
31
agents to initiate an interaction is crucial. All in all, the results of this paper emphasized the importance of
32
the instructions given to the participants in experimental studies as this can easily lead to divergence from
33
the behaviors that usually are expected to be observed in reality. Therefore, initiatives should be taken to
34
design the experimental paradigm and the instructions such that participants can behave as much as possible
35
as if they are interacting in real traffic, while still constraining their behavior sufficiently so as to force them
36
to interact with each other.
37
38
CONCLUSION
39
In this paper, a game-theoretic model was tested with a distributed simulator study, by connecting
40
a desktop driving simulator to the HIKER pedestrian lab. The results showed that, overall, the controlled
41
study was a good match for a computational model which is basically built on human naturalistic behavior.
42
This suggests that distributed simulation could generate a gap acceptance dataset with respect to both AV
43
and HD conditions that is close to the reality. Analyzing the data suggested the important role of the
44
instructions given to the participants in these kinds of experiments, to minimize the number of invalid
45
crossings and/or any other eccentric behavior. As experimental studies are a valuable tool for scenarios
46
which would not be possible to manipulate in the real world, and where some variables should be controlled
47
with high accuracy, future experiments should be designed in a way that promises more naturalistic
48
14
behavior from the interactive agents, simultaneously constraining the participants such that interaction is
1
required, while still permitting this interaction to take place in as natural a way as possible. This is a
2
challenging yet, interesting objective to pursue.
3
ACKNOWLEDGMENTS
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The simulator experiment was carried out as part of the HumanDrive project, funded by Innovate
5
UK and the Centre for Connected and Automated Vehicles (TS/P012035/1). The remainder of the work
6
reported in this paper was carried out within the SHAPE-IT project, receiving funding from the European
7
Commission's Horizon 2020 Framework Programme (Grant agreement 860410).
8
9
AUTHOR CONTRIBUTIONS
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The authors confirm contribution to the paper as follows: Experimental study conception and design: N.
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Merat, C. Uzondu, W. Lyu, J. Pedro, R. Madigan and Y.M. Lee; data collection: C. Uzondu, W. Lyu, R.
12
Madigan, Y.M. Lee and C. Holmes; analysis and interpretation of results: A.H. Kalantari and G.Markkula;
13
draft manuscript preparation: A.H. Kalantari, G.Markkula and R. Madigan. All authors reviewed the results
14
and approved the final version of the manuscript.
15
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... L'étude de ces phénomènes constitue une perspective de recherche intéressante. En effet, dans des situations réelles, un piéton pourrait finalement décider de ne pas traverser la voie devant le VA ou ce dernier pourrait ajuster sa vitesse pour passer devant le piéton ou au contraire, le laisser passer (Jayaraman et al., 2019 ;Nunez Velasco et al., 2019 ;Kalantari et al., 2021). La perception du risque d'un passager de VA naviguant parmi des piétons pose également la question du style de conduite souhaitée. ...
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Interactive pedestrian simulators have become a valuable research tool for investigating street-crossing behavior and developing solutions for improving pedestrian safety. There are two main kinds of pedestrian simulators: one uses a technology based on rear-projection screens (Cave Automatic Virtual Environment, or CAVE), the other a head-mounted display (HMD). These devices are used indiscriminately, regardless of the research objective, and it is not yet known whether they are equally effective for studying street crossing. The present study was aimed at comparing the street crossing behavior and subjective evaluations of younger and older adult pedestrians when they are using a CAVE-like or HMD-based (HTC Vive Pro) pedestrian simulator. Thirty younger adults and 25 older adults performed 36 street-crossing trials (combining different speeds, two-way traffic conditions, and gap sizes) on each of the two types of simulators. The results indicated that participants in the HMD condition crossed the street significantly more often (58.6 %) than in the CAVE condition (42.44%) and had shorter safety margins. The most striking difference pertained to crossing initiation, which occurred considerably earlier (1.78 s) in the HMD condition than in the CAVE condition. Synchronization of crossing initiation with oncoming traffic was not as good in the CAVE condition because visual information in front of the pedestrian was missing due to the absence of ground projection. In both simulators, older adults caused more collisions than did younger ones, had shorter safety margins, and a slower crossing speed. Hence, the HMD reproduced classical age-related differences in most street-crossing behaviors already found on the CAVE. Usually observed speed effects were also found for both simulators. Neither cybersickness nor any adverse effects on stereoacuity or postural balance were found for either simulator. The HMD produced a higher level of presence and preference than the CAVE did. These findings provide evidence that HMDs have a clear potential for studying pedestrian behaviour.
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Objective To contribute to the validation of virtual reality (VR) as a tool for analyzing pedestrian behavior, we compared two types of high-fidelity pedestrian simulators to a test track. Background While VR has become a popular tool in pedestrian research, it is uncertain to what extent simulator studies evoke the same behavior as nonvirtual environments. Method An identical experimental procedure was replicated in a CAVE automatic virtual environment (CAVE), a head-mounted display (HMD), and on a test track. In each group, 30 participants were instructed to step forward whenever they felt the gap between two approaching vehicles was adequate for crossing. Results Our analyses revealed distinct effects for the three environments. Overall acceptance was highest on the test track. In both simulators, crossings were initiated later, but a relationship between gap size and crossing initiation was apparent only in the CAVE. In contrast to the test track, vehicle speed significantly affected acceptance rates and safety margins in both simulators. Conclusion For a common decision task, the results obtained in virtual environments deviate from those in a nonvirtual test bed. The consistency of differences indicates that restrictions apply when predicting real-world behavior based on VR studies. In particular, the higher susceptibility to speed effects warrants further investigation, since it implies that differences in perceptual processing alter experimental outcomes. Application Our observations should inform the conclusions drawn from future research in pedestrian simulators, for example by accounting for a higher sensitivity to speed variations and a greater uncertainty associated with crossing decisions.
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Introduction Pedestrian gap acceptance has been studied by many researchers for evaluating pedestrian facilities. However, these studies could not relate the gap acceptance at uncontrolled mid-block crosswalks have varied roadway features with pedestrian behaviour under mixed traffic conditions. In this context, the goal of the proposed study is to understand the probability of pedestrian gap acceptance while crossing uncontrolled mid-blocks and pedestrian risk taking behaviour considering the effect of pedestrian behaviour and different roadway characteristics. Method Video surveys were conducted at selected uncontrolled crosswalk locations with varied roadway characteristics which includes number of lanes, median etc. in Mumbai city, India. The pedestrian individual and behavioural characteristics as well as roadway, traffic and vehicle characteristics were observed and noted from the processed videos. The binary logit models were developed with extracted data at each selected location by using NLOGIT 4 software package, considering pedestrian gap acceptance behaviour (accept or reject) as the response variable and set of remaining data as explanatory variables. Further, the generic model was developed with combined data by cross validation method. Results The results show that the important explanatory variables affecting the pedestrian gap acceptance behaviour are vehicular gap size, frequency of attempt, pedestrian rolling behaviour and type of vehicle, which play a major role in pedestrian gap acceptance and risk taking behaviour while crossing the road. It is also identified that the pedestrian risk taking behaviour increases with increase in number of lanes by usage of pedestrian behavioural aspects. Conclusions The study concluded that pedestrian behavioural characteristics needs to be controlled to reduce the pedestrian risky behaviour during road crossing at uncontrolled mid-block crosswalks. Study findings concluded that the increase in number of traffic lanes increases the risk of pedestrian road crossing. The model results from the study may be useful for practitioner, planners and policymakers to formulate suitable traffic management guidelines to control pedestrian-vehicle conflicts at different uncontrolled mid-block crosswalks.
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The interaction between pedestrians and vehicles is an inevitable phenomenon at unsignalized midblock crosswalks. This study aims to contribute to a better understanding of the interaction between vehicle yielding and pedestrian gap acceptance (VY and PGA). A microscopic traffic flow model was established to describe the interaction and explores its effect on traffic flow. The VY and PGA behaviors were converged into the proposed model. The proposed model was accomplished in a time step simulation. The results stability and descriptive power of the proposed model were analyzed. The proposed model was also validated using empirical data. The effects of the traffic and geometric factors on the operation of the unsignalized midblock crosswalks were discussed based on numerical experiments. Accordingly, the recommendations on choosing the proper control mode of midblock crosswalks (unsignalized or signalized) were proposed.
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Thanks to technological advancements, virtual reality has become increasingly flexible and affordable, resulting in a growing number of user studies conducted in virtual environments. Pedestrian simulators, visualizing traffic scenarios from a pedestrians’ perspective, have thereby emerged as a powerful tool in traffic safety research. However, while both the interest in this technology and the concern for vulnerable road users is high, a systematic overview of research employing pedestrian simulators has not been provided so far. The present literature survey is based on 87 studies published during the past decade, investigating pedestrian behaviour by means of virtual traffic scenarios. Results were categorized according to the research question, technical setup, experimental task, and participant sample. Identifying trends and gaps in knowledge and highlighting differences between methodological approaches, this work serves as an assessment of the current state and a baseline from which to develop future research questions. It aims to demonstrate both opportunities and challenges of this relatively new methodology. Thereby, it is hoped to foster the awareness of existing limitations, support the reasonable interpretation of the available data, and guide pedestrian research towards reliable and generalizable insights enhancing pedestrian mobility, comfort, and safety.