Force-based Heterogeneous Traffic Simulationfor Autonomous Vehicle Testing

Qianwen Chao1,2, Xiaogang Jin3, Hen-Wei Huang4, Shaohui Foong2, Lap-Fai Yu5, and Sai-Kit Yeung6

Abstract— Recent failures in real-world self-driving tests havesuggested a paradigm shift from directly learning in real-worldroads to building a high-fidelity driving simulator as an alterna-tive, effective, and safe tool to handle intricate traffic environ-ments in urban areas. To date, traffic simulation can constructvirtual urban environments with various weather conditions,day and night, and traffic control for autonomous vehicletesting. However, mutual interactions between autonomous ve-hicles and pedestrians are rarely modeled in existing simulators.Besides vehicles and pedestrians, the usage of personal mobilitydevices is increasing in congested cities as an alternative tothe traditional transport system. A simulator that considers allpotential road-users in a realistic urban environment is urgentlydesired. In this work, we propose a novel, extensible, andmicroscopic method to build heterogenous traffic simulationusing the force-based concept. This force-based approach canaccurately replicate the sophisticated behaviors of various roadusers and their interactions through a simple and unified way.Furthermore, we validate our approach through simulation ex-periments and comparisons to the popular simulators currentlyused for research and development of autonomous vehicles.

1. INTRODUCTION

Autonomous vehicles have the potential to improve thequality and productivity of the time spent on cars during atrip, increase the safety and efficiency of the transportationsystem, and transform transportation into a utility avail-able to anyone, anytime. Recent advances in the field ofperception [1], planning [2], [3], and decision-making [4]for autonomous vehicles have led to implementation ofseveral prototypes already being tested on roads. Althoughthe development of a variety of machine learning approacheslargely facilitate the decision making and planing throughlearning from the interactions between autonomous vehiclesand real world environments [5]–[7], the limited amount ofreal-world data, which can barely support the complex trafficscenarios, constrain autonomous driving systems in learningdiverse driving strategies. These make the unmanned vehiclesalways adopt the most conservative and inefficient decisionsfor safety reasons. Despite this, it has been reported thatthese autonomous vehicles have caused some fatal accidentsin the real world. Handling the complex interactions withother road users in various traffic scenarios remains a greatchallenge in autonomous driving [8].

1Department of Computer Science, Xidian University,chaoqianwen15@gmail.com

2The Engineering Product Development, Singapore University of Tech-nology and Design.

3State Key Lab of CAD&CG, Zhejiang University.4Koch Institute, Massachusetts Institute of Technology.5Computer Science Department, George Mason University.6The Division of Integrative Systems and Design, Hong Kong University

of Science and Technology.

Fig. 1. Example mixed traffic simulation result generated by our approach.

Due to the past failure cases of autonomous vehicles inreal world, a high-fidelity driving simulator has become analternative and effective tool to provide various kinds oftraffic conditions for motion control of autonomous vehicles,allowing for safety tests before real-world road driving [9]–[11]. Recently, the Apollo simulation platform [12] and Bestet al.’s work [13] make efforts to provide powerful virtualtraffic scenarios for driving strategy testing of autonomousvehicles. Both simulations implement two non-vehicle trafficparticipants: pedestrians and cyclists. However, the behav-iors of these non-vehicle road users have been pre-definedand cannot react to vehicle motions in real time. Besides,an open-source simulator, Carla [14], has been developedto support the development, training, and validation ofautonomous urban driving systems, which offers flexiblespecification of sensor suites and various environmentalconditions. Although dynamic pedestrians are introduced intothe simulation, the interaction between vehicle and pedestrianis handled in a simple predefined way: in an interaction,the pedestrian stops to wait for a few seconds as sensingany vehicles, then walks anyway without considering theexistence of the vehicle. From this point of view, currentexisting simulators merely make decisions of autonomousvehicles motion in a reactive way without considering anymutual influences and real interactions between vehicles andother potential road-users. As bicycle usage and pedestrianwalking have been increasing in many countries in urbanareas due to potential environmental and health benefits,creating a mixed simulation environment (Fig. 1) consistingof mutual influences and interactions among vehicles, two-wheelers, and pedestrians, is highly desired.

In this paper, we focus on modeling the heterogeneoustraffic composed of various types of road-users by an unifiedapproach that can facilitate autonomous driving strategy test-

ing. Current existing microscopic modeling methods [15]–[17] and traffic simulators (SUMO [18], SimMobility [19]and Vissim [20]) have always separately modeled the be-havior of vehicles, pedestrian, bicycles and their interac-tions. Furthermore, each specific behavior of each typesof road-user, such as vehicle acceleration and lane change,is modeled and controlled individually. Such non-unifiedapproaches are complicated and inefficient in generatingcomplex virtual traffic environments.

Here, we propose a simple, efficient, scalable force-basedframework to uniformly simulate the behaviors of vehicles,pedestrians, bicycles, and the interactions among them, inwhich any detailed behavior for each category of individualscan be attributed to a specific force. We make three contri-butions:• It introduces a novel, scalable framework based on the

force-based concept to generate complex virtual urbantraffic environments for autonomous vehicle testing.

• Unlike previous traffic simulation methods, it introducesa unified model for various detailed behaviors of vehi-cles, including acceleration/deceleration, lane keeping,and lane changing behavior.

• It provides a viable solution for describing the interac-tions among different types of road users in simulation.

Benefits of this method have been verified in experimentaltests at the end of this paper.

2. FORCE-BASED FRAMEWORK

We present a two-layered force-based framework for hy-brid traffic simulation. Specifically, the top layer calculatesthe detailed motions of each kind of road users respectivelyby interpreting them as different forms of force according totheir different behavioral characteristics. In the second layer,the force-based model is extended to describe the interactionbetween different road users. As the simulated environmentis constructed for the unmanned vehicles testing, we wouldmainly focus on the interactions that may influence the deci-sion making of autonomous vehicle, which are the vehicle-pedestrian and vehicle-bicycle interactions.

Inspired by the social force model [21]–[24] for pedestriandynamics, the participants in mixed traffic act as if theywould be subjected to ’force’ from the influences of theirdesire, their neighboring participants and the built environ-ment such as road structures, walls or buildings. Specifically,assuming that individual i is an arbitrary road user in themixed traffic flow, its motion is determined by a combinationof sociopsychological and physical forces. The total effectforce Fi (t) is defined as follows:

Fi (t) = F0i (t)+

∑j(6=i)

Fij (t)+∑

WFiW (t)+

∑oFio (t) ,

(1)where the driving force F0

i (t) reflects the individual’s inten-tion to move to a certain destination and with a desired speed,the repulsive force Fij (t) describes the effects of interactionswith its neighboring individuals j, FiW (t) measures therepulsive effects of the built environment W , and Fio (t) isintroduced to describe the interaction with other categoriesof road users.

The driving force F0i (t) describes the individual i’s moti-

vation to move with an expected velocity v0i (t) by adapting

the actual velocity vi (t) within a certain relaxation time τi[22]:

F0i (t) = mi

v0i (t)− vi (t)

τi= mi

v0i (t)− vi (t)

v0i (t)

ai, (2)

where mi is the mass of individual i and ai represents themaximum acceleration.

In our framework, the repulsive force Fij from a certainneighbor j is presented in different forms according todifferent characteristics of various kinds of road users. For apedestrian, this force is defined as a combination of social-psychological and physical forces, describing the psycho-logical tendency of two pedestrians to stay away from eachother, and the physical contact force when the pedestrianstouch each other, respectively. For vehicles, the repulsiveforce comes from all the neighboring vehicles within sightin the current and adjacent lanes. For a bicycle, the forceis defined as a combination of the direct repulsive force forcollision avoidance and the force for overtaking.

Similarly, for different types of road users, the forceFiW (t) from the built environment is defined in differentforms, depending on their specific locations and relatedbehaviors. Specifically, FiW is introduced to describe pedes-trian i’s interaction with environment borders and obstaclesW . For a bicycle, the repulsive force FbW from laneboundary W makes the bicycle b keep a certain distancefrom lane boundaries for safety. Analogously for vehicles,FcW (t) measures the repulsive force from the lane boundaryW . But different from bicycles, a distinctive force Fcl

c (t) isintroduced to model vehicle behaviors in the lane-changingprocess.

We define the interaction force Fio (t) as the environmen-tal influence respectively for the interactions between vehi-cles and pedestrians, as well as vehicles and bicycles. Theinteracting individuals treat each other as the environmentalinfluence and compute the feedback to themselves. It is worthnoticing that the pedestrian behaviors are computed using thesocial force model. More details can be found in [21], [22].

3. FORCES FOR BEHAVIORS IN MIXED TRAFFIC

3.1. Force-based Model for VehiclesThe force-based simulation model for vehicles is designed

according to the characteristics of vehicle movements:• Drivers mainly drive in a car-following fashion. How-

ever, the vehicle’s movement is also affected by allvehicles in the field of view.

• Drivers must keep driving within the lane marks, andfollow the traffic laws and regulations.

• Drivers tend to change lanes to take advantage of theallowable speed in a target lane or to cope with someimperative factors such as end of current lane.

3.1.1) Repulsive Forces between Vehicles: When movingalong a traffic flow, a vehicle c is subjected to repulsive forcesfrom all the neighboring vehicles within sight in its currentand adjacent lanes. As illustrated in Fig. 2, due to the lane-keeping rules in traffic, the impact of the vehicle q in adjacentlanes on vehicle c is far less than that of the front vehicle p in

c

q

pFcq

Fcp

v

Signt Range

FcWL

FcWU

WU

WL

Fig. 2. The sight range (in red sector) of an vehicle c and its repulsiveforces Fcp and Fcq from surrounding vehicles in the current and adjacentlanes. The repulsive forces FcWU

and FcWLfrom two-side lane boundaries

(WU and WL) are also shown here.

the current lane in the absence of lane changing. Therefore,we design the repulsive force Fcj from a certain neighbor jin different forms.

Influence from vehicles in adjacent lanes: The forcefrom a neighboring vehicle q in the adjacent lane (bluevehicle in Fig. 2) is mainly associated to its distance anddirection to vehicle c, defined as follows:

Fncq (t) = Ucqe

− rcqRcq ncq, (3)

where Ucq is the scale factor of the repulsive force Fncq (t),

rcq is the distance between the vehicle q and c, Rcq is thesensitivity coefficient of the repulsive force to the distance,and ncq is the unit vector pointing from vehicle q’s centerto vehicle c’s center.

Influence from the vehicle in current lane: Accordingto the car-following phenomenon [25] in real-world traffic,vehicle c’s behavior in the current lane is mainly a responseto its leading vehicle p (green vehicle in Fig. 2), for purposeof maintaining a safe gap to vehicle p while seeking forits desired velocity during driving. Here, we utilize thebraking deceleration term in the popular and well-calibratedintelligent driver model (IDM) [26], [27] to approximate therepulsive force Ff

cp of vehicle c from its leading vehicle p.Specifically, the force Ff

cp can be defined as a function ofthe vehicle c’s velocity vc, its bumper-to-bumper distance sand relative velocity ∆v to the leading vehicle p:

Ffcp (t) = −bc

(s∗

s

)2

nc,

s∗ = s0 + vcTc +vc∆v

2√acbc

,

(4)

where the parameters (ac, bc, s0, Tc) are constant for eachvehicle, which describe its basic driving capability, ac andbc are respectively the vehicle c’s maximum acceleration andcomfortable deceleration, s0 is jam space headway and Tcis the desired safety time headway, nc is the unit vectordenoting the current direction of vehicle c’s movement.

3.1.2) Force from Lane Boundaries: The repulsive forceFcW from two-side lane boundaries W is introduced toprompt the vehicle c to stay within the lane marks and closeto the lane’s central line. As shown in Fig. 2, the repulsiveforces from the upper (WU ) and lower (WL) boundariesof the lane, where the vehicle c is located, are respectivelycalculated, and their vector sum (FcWU

+ FcWL) represents

the vehicle c’s repulsive force from all lane boundaries.When the vehicle is in the middle of the lane, the repulsiveforces from WU and WL would compensate to each other.For each boundary W , the force is associated with thedistance rcW between vehicle c and lane boundary W ; thatis, the closer the vehicle is to the lane boundary, the greaterthe repulsive force it receives is. The formula of force FcW

can be defined akin to Eq. 3.3.1.3) Force for Lane Changing: A vehicle generally

performs lane changing if it can go faster in a target lane.According to the lane-changing model proposed by Kestinget al. [28], the incentive condition for a lane-changingdecision of the vehicle c is fulfilled if the utility of a possiblelane change for vehicle c is larger than the influence on theinvolved neighbors (the original follower o in the originallane and the new follower n in a target lane), which istypically measured in acceleration values:

ac − ac + p (an − an + ao − ao) > ∆ath, (5)

where the first two terms refer to the acceleration gainof a possible lane changing for vehicle c and the otherterms indicate the acceleration loss of the original and newfollowers, ac denotes the new acceleration for vehicle c aftera prospective lane changing, and ac denotes its accelerationbefore the lane changing. The politeness factor p determinesto which degree these successors influence the lane-changingdecision of vehicle c. ∆ath is the lane-changing thresholdwhich prevents lane changes for marginal advantage [16].

If the incentive criterion (Eq. 5) is satisfied, the lanechanging is performed by introducing an attraction force Fcl

c

from the target lane to vehicle c. As the attraction force isto counteract the lane-keeping constraint from current laneboundary, Fcl

c can be computed akin to the repulsive forceFcW from current lane boundaries, using Eq. 3.

3.2. Force-based Model for Bicycles

Unlike the way pedestrians and vehicles interact with theirneighbors, bicyclists have their own characteristics wheninteracting with neighbors. First, bicycles generally do notmove in a car-following manner and utilize lateral spaceto a greater extent than motor vehicles do. Second, unlikepedestrians, bicyclists tend to adjust their motions rather thancompletely stop and wait when an event happens, so as toreduce the amount of required physical exertion.

Therefore, we describe a bicycle k’s repulsive force Fkj

from its neighbor j with two force components: the directrepulsive force FR

kj for collision avoidance and the force FEkj

for overtaking:

Fkj (t) = FRkj (t) + FE

kj (t) . (6)

The direct repulsive force FRkj for collision avoidance

is used to describe a cyclist’s conscious response to avoidcollisions with other bicycles nearby. In accordance with abicycle’s shape, we use an ellipse to define a bicycle’s safetyspace in a certain period of time, and use the semi-minoraxis of the ellipse to measure the degree of other bicycles’influence. As shown in Fig. 3, B is the semi-minor axis of theellipse and the relative velocity (∆v = vk − vj) of bicyclek to j lies on the semi-major axis of the ellipse. The position

−

Fig. 3. Bicycle k’s repulsive forces from its neighbor bicycle j. Thegreen ellipse area denotes the safety space of bicycle k. The bicycle k’srepulsive force Fkj from its neighbor j can be decomposed into two forcecomponents: one direct repulsive force FR

kj for collision avoidance and oneforce FE

kj perpendicular to it for overtaking.

of bicycle k is the focus of the ellipse and the neighboringbicycle j is located on the circumference of the ellipse. Asmaller B means shorter distance between bicycle k and j,which results in a larger repulsive force FR

kj . Formally, theforce can be computed as follows:

FRkj (t) = Ukje

−B/Rkjnkj , (7a)

B =1

2

√(‖rkj‖+ ‖rkj −∆v∆t‖)2 − (‖∆v∆t‖)2, (7b)

where rkj is the vector that points from bicycle k to j, ∆tis a time step, Ukj and Rkj are constant factors, and nkj isthe unit vector from bicycle j’s to k.

At the same time, the overtaking force FEkj is introduced to

describe bicycle k’s flexible behavior when confronted withobstacles or congestion. The direction of FE

kj is perpendic-ular to the direct repulsive force FR

kj and the magnitude isproportional to FR

kj :

FEkj (t) = α

∥∥FRkj (t)

∥∥nVkj , (8)

where nVkj is the unit vector perpendicular to FE

kj , and α isthe scale factor set as 0.3 in our experiments.

3.3. Interactions in Mixed Traffic

In this section, we model vehicle-bicycle interactions, aswell as interactions between a vehicle and a pedestriancrossing a road. In keeping with our force-based frameworkfor each kind of road users, the mutual influences of theinvolved interacting individuals are measured in terms offorces and encoded as environmental feedbacks into theirown behavioral control models.

3.3.1) Vehicle-Bicycle Interactions: To model vehicle-bicycle interactions, the interaction force is designed to takeone of two different forms depending on the positionalrelationship between the bicycle k and vehicle c (see Fig. 4).

For vehicle c, if there is a side-by-side bicycle k in thesight range (the light green area), it will receive a lateralforce from k for collision avoidance (Fig. 4 (a)). On theother hand, if bicycle k is traveling in the near front, vehiclec will receive a rearward force for deceleration (Fig. 4

(b) k in front(a) k by side

Fig. 4. Vehicle c receives repulsive force Fck from bicycle k in interaction.

(b)). Accordingly, the vehicle c’s interaction force Fck frombicycle k is defined as:

Fck (t) =

Ucke− sck

Rck nck, k by side

−bc ∗(

s0+vcTc

sck

)2nc, k in front

(9)

where sck denotes the distance between vehicle c and bicyclek, vc is the velocity of the vehicle, nck is the unit vectorpointing from bicycle k to vehicle c, and nc representsthe moving direction of vehicle c. The constant parameters(bc, Tc, s0) describe the vehicle c’s basic driving capability,which have the same meanings as those in Eq. 4. Uck andRck are constant factors.

Similarly, the interaction force Fkc subjected on bicyclek can take one of two different forms depending on thepositional relationship between k and c: whether the vehicleis by side or in front. The force is formulated akin to Eq. 9.

3.3.2) Interactions with a Road-crossing Pedestrian:When a pedestrian is about to cross a road in a mixedtraffic environment, he/she perceives the surrounding traf-fic conditions, and the approaching vehicles correspond tohis/her stimuli. Based on this perception, the pedestrian imakes a walk-or-wait decision based on gap acceptance [29],[30] to judge whether the current distance gap betweenhim/her and the approaching vehicle c can ensure a safecrossing. Both the pedestrian’s predicted crossing time ti andthe vehicle’s estimated passing time tc are computed. Thecrossing is considered as safe if ti is less than tc. Otherwise,the pedestrian needs to wait for the next longer gap.

When the pedestrian i is walking, he/she usually slowsdown at the beginning of crossing due to the concerns aboutvehicle c’ arrival time, and after successfully cutting in,the pedestrian tends to accelerate significantly due to thepsychological impact of wanting to leave the danger zone.Inspired by Steven’s psychophysical power law [31], wemodel this kind of dynamic behavior pattern and compute theinteraction force Fic received by pedestrian i from vehicle cas follows:

Fic (t) = βs0.67ic nic, (10)

where sic is the distance between pedestrian i and vehicle cand nic is the unit vector pointing from c to i. β is a constantscale factor set as 0.5 in our experiments.

When facing a pedestrian i trying to cross a road, vehiclec tends to decelerate for safety. This situation is similar tothe sudden crossing of a bicycle as depicted in Fig. 4(b).Therefore, we calculate the interaction force Fci received byvehicle c from pedestrian i similarly as Fck in Eq. 9.

On-line Simulation: Up to now, each road user’s detailedbehavior in the mixed traffic flow has been modeled by

applying the described force-based method. Based on giveninitial states (position and velocity) of each road user, ourmethod can reconstruct the sophisticated behaviors of variousroad users and their interactions. Taking into account thepotentially complex environment required for autonomousvehicle testing, more microscopic behaviors of arbitraryroad user can be easily integrated into current simulationframework by adding more specific forces.

For autonomous vehicle testing, an autonomous vehiclecan be easily added into the simulation environment and con-trolled by its own sensing and planning algorithms. Mannedvehicles, pedestrians and bicycles in the system will senseand react to the dynamic status of autonomous vehicle. It isworth mentioning that the proposed forced-based approach iscompatible with commercialized simulators for autonomousvehicle testing, such as Carla and Apollo. The interactionsbetween different types of road-users in Carla and Apollo canbe simply replaced with the proposed unified force approach.

4. SIMULATION RESULTS

To ensure the robustness and safety of autonomous ve-hicles traveling on real-world roads, autonomous drivingsystems should be tested in virtual yet realistic traffic en-vironments before real-world deployment. To validate ourforce-based simulation framework, we generate mixed traf-fic flow on a road without any traffic signs, which canbe regarded as a complex traffic scenario for autonomousvehicle testing (Fig. 1). Table I summarizes the key parametervalues used in our experiments. Note that we do not listthe parameter values used in the pedestrian’s social forcemodel, as they are set as the same as those in [22]. Theparameters (v0c , ac, bc, s0, Tc) for each vehicle are initializedby empirical values which are then added with some randomperturbations to reflect individual diversity in locomotion.

TABLE IPARAMETER VALUES USED IN OUR EXPERIMENTS.

Parameter Value Unit Descriptionv0c [2,6] m/s vehicle’s optimal velocity

ac [2,3.5] m/s2 vehicle’s maximum accelerationbc [2,3.5] m/s2 vehicle’s comfortable decelerations0 [1.5,2.5] m jam space headwayTc [0.5,0.6] s desired safety time headway

∆ath 0.5 m/s2 lane changing thresholdp 0.4 / politeness factor in lane changing

Ucq 3.3 / scale factor of Fncq

Rcq 3.0 / sensitivity coefficient of Fncq

Ukj 3.5 / scale factor of FRkj

Rkj 2.0 / sensitivity coefficient of FRkj

Uck 3.5 / scale factor of FckRck 2.0 / sensitivity coefficient of Fck

As the simulated environments are constructed for un-manned vehicles testing, the following experiment resultswould only focus on the interactions between various ve-hicles, vehicles and pedestrians, as well as vehicles andbicycles, respectively. In addition, the animations of all thementioned comparisons are shown in the supplemental video.Although the interactions between individual pedestrians,individual bicycles, as well as pedestrians and bicycles arenot shown in the main results, they are all incorporated intothe mixed traffic simulation.

Timing performance: To determine the timing perfor-mance of our force-based simulation method, we conducted aseries of experiments with different numbers of individuals inthe mixed traffic, in which the ratio of vehicles, bicycles andpedestrians was 1:2:3. All the timings were obtained witha 64-bit laptop machine with a 2.90 GHz Intel CoreTMI9-8950HK processor, 32GB memory, and an Nvidia GeForceGTX 1080 video card. The results of our performancetests shows that the computational costs scale approximatelylinearly with the number of road users simulated. Moreover,our approach can simulate about 800 agents in real time(30 fps) and over 1,200 agents at interactive simulationrates (10 fps). The efficient time performance indicatesthat our approach can be straightforwardly plugged intovarious existing traffic simulation systems for autonomousvehicle testing and data generation. It is noticeable that ourapproach is collision-free because the repelled force betweeneach road-users significantly increases with the decrease oftheir distance. When the environment becomes crowded,pedestrians, bicycles and vehicles tend to keep in their lanesand reduce any interactions with each other.

Interaction with Road-crossing Pedestrians: We com-pare our force-based approach for pedestrian crossing to twopopular open-source simulation platforms: Apollo [12] andCarla [14]. Fig. 5 shows the comparison results betweenApollo simulation and our method. It is observed that inApollo simulation (Fig. 5(a)), the autonomous vehicle (inblue) reacted to a pedestrian (represented as yellow rect-angle) crossing the road with an initially defined constantvelocity of 2.24 km/h. Since the pedestrian’s reaction tothe real-time behavior of the vehicle was not consideredin Apollo simulation platform, the pedestrian continued tofollow the predefined path after the vehicle had completelystopped, thereby colliding with the vehicle (at the 880thframe in Fig. 5(a)). By contrast, our force-based approachattempted to mimic the real pedestrian-vehicle interaction inwhich both the pedestrian and vehicle made decisions basedon the other one’s instantaneous status (Fig. 5(b)).

Fig. 6 shows the velocities of both the pedestrian (inyellow lines) and vehicle (in blue lines) through (a) Apollosimulation and (b) our force-based approach. It is observedin our approach that the vehicle and the pedestrian bothdecelerated for safety as they sensed each other. Subse-quently after the vehicle completely stopped, the pedestrianaccelerated to cross the lane as quickly as possible. Finally,both of them recovered to their original status after theinteraction. However, in the result of Apollo simulationshown in Fig. 6 (a), the autonomous vehicle braked urgentlywhen the pedestrian came close and the pedestrian did notreact to the vehicle’s behaviors.

The Carla simulation platform models pedestrian-vehicleinteractions with a simple rule-based approach: when a vehi-cle appears on the pedestrian’s planned route, the pedestrianmomentarily stops moving. After waiting for a couple ofseconds, the pedestrian will continue to walk even if thereis a vehicle in front of the pedestrian.

Through the above comparisons, it is clearly shown thatthe force-based approach models pedestrian-vehicle interac-tions in a more realistic and smooth manner in the pedestrian

Frame #717 Frame #880 Frame #1060(a) Apollo Simulation Platform [12]

(b) Our Force-based ApproachFrame #398 Frame #700 Frame #830

Fig. 5. Simulation results of the intersection scenario that a pedestrian (inyellow rectangle) tends to cross the road when a blue vehicle is coming,using (a) Apollo simulation platform and (b) our force-based method. Thepedestrian’s movement was predefined with a constant velocity of 2.24 km/hin Apollo simulation, while the pedestrian reacted to the real-time behaviorof the blue vehicle in our approach.

(a) Apollo Simulation Platform [12]

300 500 700 900 1100 1300Frames

Vehi

cle’

s vel

ocity

(m/s

)

3

2

1

0

4

Pede

stria

n’s v

eloc

ity (m

/s)

0.7

0.5

0.3

0.1

0.9

(b) Our Force-based Approach

pedestrianvehicle

Vehi

cle’

s vel

ocity

(m/s

)

Pede

stria

n’s v

eloc

ity (m

/s)

6

4

2

0200 400 600 800 1000

Frames

0.7

0.5

0.3

0.1

0.9pedestrianvehicle

Fig. 6. The comparison of the velocities of both the pedestrian and vehiclebetween Apollo simulation platform (a) and our approach (b).

road-crossing scenario. We believe our approach can beincorporated into Apollo and Carla simulation platform tosimulate pedestrian-vehicle interactions more realistically.

Bicycle-Vehicle Interactions: In Fig. 7, we show thesnapshots of bicycle-vehicle interactions in two differentsituations described in Section 3-3.1: (a) a cyclist ridingin front of a vehicle; (b) a cyclist riding near the side ofa vehicle. For each case, we also show the velocities ofboth the bicycle and vehicle for comparison. The solid linesrepresent the velocities in the forward moving direction andthe dashed lines indicate those in the lateral direction. As canbe seen from Fig. 7, when the bicycle was driving in the nearfront of the vehicle (from about 430th to 530th frame), thevehicle decelerated significantly in the forward direction, andits lateral movement did not change significantly. In contrast,when the bicycle was traveling near one side of the vehicle(from about 170th to 205th frame), the vehicle obviouslyavoided collision with the bicycle in the lateral direction ofmovement. At the same time, there was a slight decelerationin the forward moving direction of the vehicle. It is worthnoting that in both interaction situations, while the vehiclewas reacting, the bicycle also accelerated away from theirinteraction area and returned to its lane. As depicted in Fig. 7,there was apparent acceleration behavior in both directionsof bicycle movement.

5. CONCLUSION AND DISCUSSION

In this paper, we devised a virtual mixed-traffic envi-ronment that can approximately emulate the intricate urbantraffic for autonomous vehicle testing. Pedestrians, bicycles,

300 350 400 450 500 550 600-20

2

4

6

8

10

12

100 150 200 250 300-101234567

Framesvehicle’s forward velocity vehicle’s lateral velocity bicycle’s forward velocity bicycle’s lateral velocity

Velo

city

(m/s

)

Velo

city

(m/s

)

Frames

(a) (b)

Fig. 7. The snapshots for two kinds of bicycle-vehicle interaction scenariosand the velocities of both the cyclist and vehicle in their interaction process:(a) the cyclist riding in front of the vehicle; (b) the cyclist riding near the sideof the vehicle. For the scenario in (a), the vehicle decelerated significantly inthe forward moving direction as response to the front bicycle’s movement,while in scenario (b), there is an obvious avoidance behavior in the vehicle’slateral moving direction to prevent collision with the bicycle by side.

and vehicles are considered as the main road users. Theirbehaviors are encoded in a general, unified force-basedframework, whose forces can be classified as the desire forceto a target, the repulsive forces with neighbors and the builtenvironment, and interaction forces between different kindsof road-users. Our approach offers a simple, efficient, andextensible method to simulate different behavioral charac-teristics of different road users and the realistic interactioneffects in complex urban traffic environments. Experimentalresults have been conducted to validate the performance ofour approach by comparing with two popular simulationplatforms specifically for autonomous vehicle testing .

Although the simulation results are promising, the ap-proach presented in this paper is still preliminary and canbe improved in several aspects. First, the simulation pa-rameters can be set optimally by calibration using real-world traffic data, rather than being set empirically as in thecurrent experiments. Second, it will be more interesting ifpedestrians, bicyclists and drivers’ personalized behavioralcharacteristics can be modeled to generate heterogeneouscrowd behaviors, thus generating more versatile and real-istic simulations. Third, for pedestrian crossing scenarios, apedestrian’s decision-making process is far more complex inreal-world traffic than that in our current model. Besides thegap acceptance criterion, there are possibly other factors thatneed to be considered in making the walk-or-wait decisions,such as the total number of pedestrians crossing the roadtogether and the waiting time.

ACKNOWLEDGMENT

This research project is partially supported by the NationalScience Foundation (No. 1565978) and an internal grantfrom HKUST (R9429). Qianwen was supported by Vir-tual Singapore (No. NRF2015VSGAA3DCM001-014) andthe National Natural Science Foundation of China (No.61702393). Xiaogang Jin was supported by the National KeyRD Program of China (No. 2017YFB1002600) and ArtificialIntelligence Research Foundation of Baidu Inc.

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