Cooperative Maneuvers of Highly Automated Vehicles at Urban

Intersections: A Game-theoretic Approach

orn Koopmann, Stefan Puch, G

unter Ehmen and Martin Fr

anzle

OFFIS e.V., Escherweg 2, 26121 Oldenburg, Germany

Keywords:

Highly Automated Driving, Cooperative Driving, Intelligent Transportation Systems, Trafﬁc Management,

Intersection Management, Intelligent Infrastructure, Collaborative Sensing, Trajectory Planning, Trafﬁc

Efﬁciency, Road Safety, Vehicle-to-Everything Communication, Game Theory, Trafﬁc Simulation.

Abstract:

In this paper, we propose an approach how connected and highly automated vehicles can perform cooperative

maneuvers such as lane changes and left-turns at urban intersections where they have to deal with human-

operated vehicles and vulnerable road users such as cyclists and pedestrians in so-called mixed trafﬁc. In

order to support cooperative maneuvers the urban intersection is equipped with an intelligent controller which

has access to different sensors along the intersection to detect and predict the behavior of the trafﬁc participants

involved. Since the intersection controller cannot directly control all road users and – not least due to the legal

situation – driving decisions must always be made by the vehicle controller itself, we focus on a decentralized

control paradigm. In this context, connected and highly automated vehicles use some carefully selected game

theory concepts to make the best possible and clear decisions about cooperative maneuvers. The aim is to

improve trafﬁc efﬁciency while maintaining road safety at the same time. Our ﬁrst results obtained with a

prototypical implementation of the approach in a trafﬁc simulation are promising.

1 INTRODUCTION

Mobility is a vital basis for individual freedom, an

indicator of social prosperity, and an important fac-

tor for economic growth (Lemmer, 2019). The ris-

ing need for mobility of people and goods poses ma-

jor challenges to administrations of cities and munic-

ipalities and stresses the existing infrastructure. In

the long term, the structural maintenance and replace-

ment of transport infrastructure is expected to involve

increasingly higher investment costs (Federal Min-

istry of Transport and Digital Infrastructure, 2016).

Besides the growing challenges for municipal ad-

ministrations, the increased trafﬁc load also reduces

the quality of life of the citizens through increased

emissions and delays due to congestion. In 2018, Ger-

man drivers spent on average of more than 120 hours

in trafﬁc jams (INRIX, 2019). At the same time, long

congestion periods and unadapted driving styles exac-

erbate the problems associated with increased air pol-

lution and environmental impact. Discussions on road

closures and driving bans resulting from high levels of

nitrogen oxides and particulates – whether effective or

not – can be heard in the press almost every day (Zeit,

2018; Tagesspiegel, 2019; Spiegel, 2019).

Figure 1: Exemplary Conﬂict Areas.

Intersections are a key element of today’s trans-

port infrastructure and have a signiﬁcant impact on

inner-city trafﬁc efﬁciency. At these junctions traf-

ﬁc ﬂows from different directions meet, which them-

selves consist of different road users – each with indi-

vidual goals and their own driving styles. Depending

on the active trafﬁc light phase, conﬂict areas with

other road users arise while crossing the intersection.

Figure 1 shows an example of these areas resulting

from a left-turn scenario. After passing through on-

coming trafﬁc (1), the orange-colored vehicle must

take crossing cyclists and pedestrians (2) into account.

Koopmann, B., Puch, S., Ehmen, G. and Fränzle, M.

Cooperative Maneuvers of Highly Automated Vehicles at Urban Intersections: A Game-theoretic Approach.

DOI: 10.5220/0009351500150026

In Proceedings of the 6th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2020), pages 15-26

ISBN: 978-989-758-419-0; ISSN: 2184-495X

While human drivers can have difﬁculties assess-

ing the speeds of other vehicles and the remain-

ing gaps in ﬂowing trafﬁc (Yan et al., 2007), dedi-

cated sensor systems can reliably perform this task.

The use of connected and highly automated vehi-

cles (CHAVs) in inner-city trafﬁc could therefore help

to improve the use of remaining free spaces and to

achieve a higher capacity. In addition, however, fur-

ther challenges arise in the reliable detection of cy-

clists and pedestrians – also called vulnerable road

users (VRUs) – that share green light phases with

motorized road users. Due to the possibility of be-

ing covered by vehicles parked at the roadside and the

high complexity of their dynamic behavior, this task

poses a high degree of difﬁculty for human drivers in

human-operated vehicles (HVs) as well as for assis-

tance systems and automated driving functions.

In order to master the challenges of connected

and highly automated driving at urban intersections,

a common approach is to support the vehicle sen-

sors with infrastructural sensors and communicating

information systems to increase sensing ranges and

reliability (Burgstrahler, 2017). At the same time,

this solution enables connected participants to receive

comprehensive real-time information about the pre-

vailing trafﬁc situation in remote and poorly visi-

ble areas. In addition, trafﬁc light phases as well

as information about the future signal course can

be transmitted. Equipped with vehicle-to-everything

(V2X) transceivers and suitable environmental sen-

sors, specialized systems like trafﬁc management sys-

tems (TMS) could ultimately generate behavior rec-

ommendations to actively support CHAVs in a safe

and efﬁcient crossing of intersection areas.

Current research gives reason to assume that co-

operation of CHAVs with each other, HVs, and VRUs

can increase trafﬁc efﬁciency while ensuring at least

the same level of road safety. For this reason, it is

likely that in the future not only the automation of in-

dividual vehicles, but also their safe interaction with

different road users will be an important aspect. With

the increasing prevalence of automated vehicles and

their growing pervasion in mixed trafﬁc the consid-

eration of cooperation brings new challenges. In this

context, the following research questions are of par-

ticular importance for the present work:

1. How can unambiguous, joint decisions be made

whether or not to perform cooperative maneuvers,

taking into account global and local goals?

2. Is it possible to increase trafﬁc efﬁciency at urban

intersections through cooperation?

3. If so, what conditions must be met in order to pro-

mote an efﬁciency gain? Which conditions may

lead to deteriorations?

In order to provide a solution for the ﬁrst ques-

tion as well as some hints on answering questions two

and three, we will present a novel, decentralized co-

operation approach that was developed within the na-

tional research project Digitaler Knoten 4.0 (Digitaler

Knoten 4.0, 2019). The deﬁned concepts explicitly

address the prevalence of mixed trafﬁc that can be ex-

pected in the long transition phase of CHAVs to reg-

ular operation and could be evaluated directly in the

ﬁeld. We propose a game-theoretic approach which

can be implemented algorithmically and allows coop-

eration candidates to take their own view into account

when making decisions about performing a cooper-

ative maneuver or rejecting a speciﬁc request. As a

prerequisite, we assume the existence of an intelligent

TMS equipped with sensors and actuators, which has

a global view of the trafﬁc situation and – based on

predictive path planning – can derive and communi-

cate assessments for meaningful cooperative maneu-

vers. The approach is evaluated by using a proto-

typical implementation on the basis of Simulation of

Urban Mobility (SUMO) (German Aerospace Center,

2018) that enables us to see some ﬁrst effects.

This paper is structured as follows. In Section 2,

existing work on the interaction of CHAVs at urban

intersections is discussed. Afterwards, we provide a

brief overview of a selected set of game theory con-

cepts. In Section 4, the top-level architecture and a de-

scription of relevant characteristics of the trafﬁc par-

ticipants involved are given. Section 5 presents the

developed concepts. This includes the time division

of an intersection crossing by a CHAV into phases as

well as a detailed investigation of the cooperation ap-

proach. In order to analyze the effects of the selected

approach, we ﬁrst describe the implementation of the

trafﬁc simulation and the individual experiments in

Section 6. Subsequently, a discussion of the results

is conducted. In Section 7, we conclude the paper and

give an outlook on future enhancements.

2 STATE OF THE ART

According to (Wu et al., 2012), cooperative driving

was ﬁrst introduced through the use of inter-vehicle

communication to perform lane changes and merging

maneuvers in the context of platooning. It was fol-

lowed by a line of research to guide vehicles through

intersections using the Autonomous Intersection Man-

agement (AIM) (Dresner and Stone, 2008; Dresner,

2009) approach. The focus is dedicated to avoid crit-

ical situations as well as collisions and to adapt the

passing sequence of approaching vehicles in order to

improve the junction’s capacity.

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

A major challenge regarding the trajectory plan-

ning algorithms is noted to be the “complexity of

cooperative driving planning”, because every vehicle

has to be considered individually. To this category

belong Frese and Beyerer with their work about plan-

ning cooperative motions of cognitive automobiles by

proposing a tree search algorithm and Gr

egoire et al.

who propose a mathematical framework to decom-

pose the cooperative motion planning problem for ve-

hicles at intersections to “a discrete scheduling prob-

lem (priority graph) and a continuous problem formu-

lated in the abstract coordination space” (Frese and

Beyerer, 2010; Gregiore et al., 2012). Kneissl et al.

presented a model predictive control based algorithm

for automated intersection crossings whereby vehi-

cles do not have to share private data (Kneissl et al.,

2018). All these approaches are based on a central

controller for CHAVs or at least on autonomously ex-

ecuted cooperative maneuvers. Liu et al. extended

the previous research by suggesting a hybrid approach

where an intersection management system plans col-

lision free trajectories but vehicles are able to arrange

their trajectory individually (Liu et al., 2019). This

approach is simpliﬁed by the fact that conﬂict areas

ﬁrst have to be reserved and vehicles drive as platoon

over the intersection at constant speed.

None of the previously mentioned approaches

considered the execution of cooperative maneuvers in

mixed trafﬁc where the somewhat optimal path plan-

ning result from AIM has to be combined with uncon-

trolled trafﬁc participants, whose dynamic behavior is

hardly predictable. According to Sharon and Stone,

“AIM has been shown to provide little or no improve-

ment” if less than 90 % of the vehicles are driving au-

tonomously so that the approach cannot be smoothly

applied to mixed trafﬁc. They addressed this gap with

the development of the Hybrid Autonomous Intersec-

tion Management protocol (Sharon and Stone, 2017).

It builds upon a reservation-based “First Come, First

Served” extension of the AIM protocol and shall im-

prove the transition period from mostly HVs to solely

CHAVs comprised trafﬁc. In (Sharon et al., 2018), a

centralized manager controls a set of so-called com-

pliant agents while other self-interested agents coex-

ists within the network. However, cooperative maneu-

vers between CHAVs are not taken into account.

All existing approaches for the interaction of

CHAVs and HVs have in common that they only con-

sider global goals such as collision avoidance or an

increase of trafﬁc efﬁciency. They do not take into

account the individual pursuit of local goals, which

may result from manufacturer-speciﬁc features or the

individual preferences of vehicle occupants. The im-

portance of this limitation is further strengthened by

legal and safety constraints of the implementing man-

ufacturers. In this context, a common paradigm is

the strict rule that every safety-critical driving deci-

sion must be made by the vehicle controller itself. To

comply with this demand, all conceivable information

provided by other participants and infrastructure sys-

tems must only be used to extend a vehicle’s “ﬁeld of

view” and to increase the conﬁdence of its own situa-

tion assessment. Only if external requests to achieve

global goals are consistent with local goals, then they

may inﬂuence driving decisions. This style of nego-

tiating cooperative driving maneuvers, taking into ac-

count global and local goals while exclusively relying

on vehicle-based decision making, is – to the best of

our knowledge – not subject of current research.

3 GAME THEORY

To design a mechanism enabling a joint, unambigu-

ous negotiation process for cooperating CHAVs, we

employ a set of commonly used game theory concepts

(von Neumann and Morgenstern, 1953). According

to Maschler, game theory subsumes the “methodol-

ogy of using mathematical tools to model and analyse

situations of interactive decision making” (Maschler

et al., 2013). The so-called players with possibly dif-

ferent goals inﬂuence the further outcome of other

players with each of their decision. It can provide

valuable services in the analysis of complex eco-

nomic phenomena as well as in everyday decisions,

because it deals with an enormous variety of differ-

ent decision-making situations and makes suggestions

how good decisions can be achieved (Winter, 2015).

An important question that has to be answered be-

fore applying game theory is which kind of game ﬁts

best for the given situation. It is possible to distin-

guish between static or dynamic games and games

with complete or incomplete information (Winter,

2015). In static games, players act simultaneously

without knowing how other players have behaved or

will behave. They are also commonly known as si-

multaneous or concurrent games (de Alfaro and Hen-

zinger, 2000). Conversely, in dynamic games, which

are often referred to as turn-based, sequential, or re-

peated games, players act in a ﬁxed order (de Al-

faro and Henzinger, 2000; Maschler et al., 2013). In

games with complete information, each player is well

informed about the other players and can practically

put himself in their shoes. A player is also aware of all

scores, but usually has no knowledge of the individual

strategies. Games with incomplete information can

result, for example, from strongly restrictive rules, in-

formation hiding policies or technical limitations.

Cooperative Maneuvers of Highly Automated Vehicles at Urban Intersections: A Game-theoretic Approach

Within a game each player can have an amount of

strategies – good ones which lead to “win” the game

as well as bad ones which lead to “loose”. A strategy

combination describes a combination of one strategy

per player, a set of all strategy combinations deﬁne

all possible game sequences. Each player can rate his

strategies with a measure. This indicates the advan-

tage or beneﬁt of the outcome of the game from the

player’s perspective. Within the framework of game

theory, this measure is referred to as payoff.

The objective of game theory is to ﬁnd an optimal

strategy combination based on the payoffs of the in-

dividual players. From a player’s point of view, the

primary goal is to achieve the highest possible payoff

by selecting the “best” strategy combination in order

to “win” the game. In this context, an optimal strat-

egy combination from a global perspective is referred

to as Nash equilibrium (Nash, 1951). If the equilib-

rium is played, none of the players would unilaterally

change their mind, because no other strategy could

achieve a higher payoff or an improvement. It there-

fore allows distributed strategy ﬁnding without addi-

tional communication, just by rational reasoning.

A common representation for games with a lim-

ited number of strategies are so-called payoff matri-

ces. They list the strategies of one player in rows and

the strategies of another in columns. Each cell thus

contains the combined payoffs for the combination of

both individual strategies. We will use this form of

representation and the underlying theory to select the

best possible strategy combination and to decide in a

distributed manner whether or not to perform the re-

sulting cooperative driving maneuver.

4 TOP-LEVEL ARCHITECTURE

In order to control the ﬂow of mixed trafﬁc at urban

intersections, the Digitaler Knoten 4.0 project consor-

tium developed a reference architecture, which can be

understood as a blueprint for the digitalization of ur-

ban intersections. Here, the extensive expert knowl-

edge and know-how from previous projects of the in-

dustrial and academic partners involved were used to

provide a comprehensive and consistent architecture

to guide the development of future transport systems.

At the highest level, the proposed reference archi-

tecture is divided into two (sub-)architectures Auto-

mated Vehicle and Trafﬁc Management System, which

are illustrated in Figures 2 and 3. While the commu-

nication between these subsystem classes is realized

by means of a third reference architecture Communi-

cation Channel, their individual components are not

explained in detail for the sake of simplicity.

Planning + Control

Signal

Capturing/

Processing

Feature

Extraction

Situation

Assessment

- Odometry

- …

Environment

Model

Sensor /

Actuator

Model

- Object Recognition

- Object Tracking

- …

- Digital Maps

- Road Markings

- …

- Ego Vehicle Motion

- …

Trajectory Planning

Safe Corridor Prediction

Trajectory Segment

Execution

Desired Trajectory Segment

Dynamic Control

Feedback control for micro

segments / curves

Sensor Actuator Control

Feedback control for

driving dynamics

Decision Making

Routing, Navigation, Cooperation

Vehicle

Dynamics

Model

Mission

Space

Model

Vehicle

Sensors

Environmental Sensors

Localization Sensors

Selection of

Relevant Messages

HMI

Actuators

Communi

cation

Knowledge

Base

Commu

nication

HMI

Referenzarchitektur „Automatisiertes Fahrzeug“1

Funktionaler Architekturentwurf (Ver. 1.2)

Informationsfluss

Rückkopplung

Modellintegration

Figure 2: (Sub-)Architecture Automated Vehicle.

Referenzarchitektur „Verkehrsinfrastruktur“2

Funktionaler Architekturentwurf (Ver. 1.2)

Informationsfluss

Rückkopplung

Modellintegration

Evaluation

Situation

Assessment

Planning + Control

Decision Making

Signal

Capturing/

Processing

Feature

Extraction

- Object Recognition

- Object Tracking

- …

Environment

Model

Selection of

Relevant Messages

Infrastructure

Model

Environmental Sensors

Traffic

Lights

Communi

cation

Actuators

Sensor Actuator Control

Feedback control for

traffic guidance systems

Determination of

Traffic Light Status

Infrastructure Control

Selection of traffic light phases

and necessary notifications

Communi

cation

Handling of

Dynamic

Objects

Handling of

Static

Obstacles

Recommendations

- (Virtual) green filter arrow

- Lane change advices

- Cooperation initiations

Directives

- (Preventive) lane closures

- Road map adaptations

Information Services

- Signal predictions

- Hazard warnings

- Traffic monitoring

Knowledge

Base

Figure 3: (Sub-)Architecture Trafﬁc Management System.

The two architectures in focus are layered archi-

tectures whose horizontal design is based on the com-

monly used “Sense-Plan-Act” paradigm. In this con-

text, each subarchitecture consists of six columns

that structure the underlying components according

to their functional purpose. Triggered by the input

events of the sensor components, the collected in-

formation is propagated successively through the in-

dividual segments and is aggregated to an encom-

passing real-time situational overview on which either

driving or control decisions can be made.

The (abstract) functional components, each rep-

resenting a set of possible implementations of re-

quired tasks, are arranged at different abstraction lev-

els according to their time resolution or activation fre-

quency – ranging from control-based algorithms on

lower levels to service-oriented concepts on higher

layers. While the ﬁrst subarchitecture contains up to

ﬁve abstraction levels, the Trafﬁc Management Sys-

tem has a simpliﬁed vertical design due to the lack of

proper motion and the comparatively low complexity

of the control tasks assigned to it.

In the following, some general properties of the

considered trafﬁc participants will be put into con-

crete terms. While the reference architecture al-

ready provides a good overview of the functionality

of the technical systems involved, the assumptions

used about the equipment of the TMS have to be

concretized. In addition, suitable assumptions about

the physical properties and the dynamic behavior of

CHAVs, HVs, and VRUs will be formulated.

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

4.1 Trafﬁc Management System

As explained above, the use of an intelligent TMS is

a key element of our approach. In our vision, such

a system has the capability to send and receive V2X

messages with a minimum reception range of 200 m.

In addition, we assume it to be equipped with environ-

mental sensors that detect and track static obstacles

and dynamic objects within a sensing range of 150 m

in order to maintain a real-time situational overview

and to predict the future behavior of all participants.

As a third source of information, a TMS should be

linked to the trafﬁc light system, which provides ac-

cess to the signal phases and future signal courses.

Based on the situational overview aggregated in

the environment and infrastructure models, the Deci-

sion Making component analyzes the current and an-

ticipated trafﬁc situation in the intersection area. It

brings intelligence to the TMS and takes all high-level

control decisions related to the ﬂow of mixed trafﬁc.

Besides the transmission of infrastructure-to-vehicle

(I2V) messages, such as behavior recommendations

and hazard warnings, it controls the infrastructure ac-

tuators (e.g., variable message signs), and provides

evaluation services for trafﬁc analyses.

4.2 Highly Automated Vehicles

While the CHAVs in focus are assumed to have au-

tomation levels from 4 to 5 (SAE International, 2018),

their individual driving tasks are (almost) completely

taken over. In accordance with the explanations on

the TMS, all decisions are drawn by a central Deci-

sion Making component. Every CHAV has the capa-

bility to send and receive V2X messages and comes

with a suitable set of environmental sensors.

Each CHAV moves at a maximum speed of

50 km/h and complies with all trafﬁc regulations. Due

to the high degree of automation and the lack of hu-

man reaction time, a CHAV should also adapt to ex-

ternal events in signiﬁcantly less than 1 s. At the same

time, conservative estimates of distances and time

gaps are used – the vehicle thus drives very defen-

sively and with foresight. While all CHAVs behave

prudently when interacting with other road users, it

is assumed that no cooperative maneuvers are per-

formed without using the proposed approach.

4.3 Human-operated Vehicles

In contrast to CHAVs, all HVs are assumed to have

automation levels ranging from 0 to 3 (SAE Interna-

tional, 2018). The driving task is therefore primarily

taken over by the human driver. For this reason, the

driving behavior is signiﬁcantly inﬂuenced by his per-

sonality and state of health as well as his local knowl-

edge and individual goals, e.g., resulting from time

pressure or being on a “sightseeing tour”. The com-

munication with other road users is usually done by

simple light and hand signals. Although top-of-the-

range vehicles may already have the option to receive

V2X or I2V messages at these automation levels, it is

not considered to be the case for the majority.

Depending on the passenger’s preferences, a typ-

ical HV drives at a higher maximum speed of up to

60 km/h. In most cases, the driver adheres to the traf-

ﬁc rules, but deviates from them in certain situations.

In addition, his reaction time is about 1 s. During the

journey of a HV the driver under- or overestimates

distances and time gaps due to the natural limitations

of his perception. The possibility of mental over-

load in unexpected situations results in a higher fail-

ure probability compared to CHAVs.

4.4 Cyclists and Pedestrians

The non-motorized road users, consisting of cyclists

and pedestrians, exhibit a comparatively low speed

compared to CHAVs and HVs. At the same time,

the safe prediction of their dynamic behavior poses

a major challenge due to the high complexity of the

underlying models and the possibility of fast direc-

tional changes. While appropriate concepts to handle

non-compliant behaviors exist, we limit ourselves to

the assumption that VRUs move on bicycle paths or

sidewalks and behave according to the trafﬁc rules.

5 COOPERATION APPROACH

There is a wide variety of conceivable scenarios that

can provide beneﬁts for the participating road users

and municipal administrations. In the further course,

the cooperative lane change (CLC), whose basic prin-

ciple is illustrated in Figure 4, will be subjected to

closer examination. It was extensively studied as a

further part of the Digitaler Knoten 4.0 project.

At the beginning of the scenario, the orange-

colored CHAV



approaches a static obstacle



such as a vehicle at the end of a congestion or a nar-

rowing of the roadway. While the CHAV in focus

would normally have to wait, a negotiation with the

turquoise-colored CHAV



on the adjacent lane al-

lows an agreement on performing a CLC that enables

an efﬁcient merge into ﬂowing trafﬁc. In order to

avoid unnecessary strong effects on the second coop-

eration partner or other dangerous situations, a thor-

Cooperative Maneuvers of Highly Automated Vehicles at Urban Intersections: A Game-theoretic Approach

= Traffic Management System

= Static Obstacle

= Cooperation Partner 1

= Cooperation Partner 2

Figure 4: Cooperative Lane Change.

ough analysis of the trafﬁc situation and suitable con-

cepts for a distributed assessment are required.

While the interaction of multiple trafﬁc partici-

pants would be conceivable and could have more far-

reaching effects on trafﬁc efﬁciency, we will focus on

the cooperation of only two CHAVs to explain the ba-

sic principles of the underlying concepts.

5.1 Time Subdivision into Phases

In order to guide the development of the overall coop-

eration approach and to enable a structured analysis

of the resulting trafﬁc situations, we decided to divide

the journey of each CHAV through the intersection

area into three so-called cooperation phases.

5.1.1 Subscription Phase

The aim of this ﬁrst phase is to improve the situa-

tional awareness of the CHAV in focus and the TMS

by communicating vehicle-speciﬁc data and exchange

information about the trafﬁc situation to set the stage

for cooperative maneuvers. In a ﬁrst step, a unique

vehicle ID, a global driving intention (e.g., turn left,

straight ahead, turn right), and the intended destina-

tion lane are sent to the TMS. The reception of the

message is conﬁrmed to the CHAV by sending a de-

tailed response containing the current signal phase of

the trafﬁc lights, their future signal course, a digital

map of the intersection as well as comprehensive in-

formation about static obstacles and dynamic objects.

According to the assumptions made in Sec-

tion 4.1, it is assumed hereinafter that the subscription

phase is completed at least 150 m before the stop line

of the respective lane. If the subscription of a CHAV

is not completed in time, the crossing must take place

without making any beneﬁts from the additional ser-

vices provided by the TMS, including the support in

cooperative maneuvers. Of course, an adaptation of

the assumed range constraint is possible to accommo-

date other intersection geometries.

5.1.2 Execution Phase

From the perspective of a CHAV, the primary aim

of the execution phase is to cross the intersection

safely and as efﬁciently as possible. During the rule-

compliant approach of the CHAV to the stop line,

the interaction with other road users takes place as it

would do even without the existence of an intelligent

TMS. Based on the information acquired in the ﬁrst

phase, however, an earlier decision can be made for

or against passing the intersections trafﬁc lights.

At the same time, the TMS aims to increase the

junction’s capacity, prevent congestion, and reduce

emissions. It makes use of all available information

about the current positions, velocities, driving inten-

tions, and the planned destination lanes of the sub-

scribed CHAVs and other participants, its knowledge

about the intersection geometry, static obstacles as

well as dynamic objects, and identiﬁes potential con-

ﬂict situations between CHAVs to be solved. In a sec-

ond step, the TMS tries to derive feasible solutions

to these conﬂicts that increases trafﬁc efﬁciency, e.g.,

through behavioral predictions and the recognition of

previously learned patterns within the trafﬁc scene.

Subsequently, promising solutions are delivered to

the participating CHAVs in the form of cooperation

recommendations. The CHAVs initiate distributed as-

sessments of the trafﬁc situations based on their own

situational overviews and exchange their evaluations,

which can ultimately lead to joint decisions and the

execution of the proposed cooperative maneuvers.

5.1.3 Unsubscription Phase

In the course of the unsubscription phase, the infor-

mation collected during the crossing of the intersec-

tion is fed back to the TMS. By receiving the pe-

riodically sent positions and velocities of all exiting

CHAVs, further information can be obtained on traf-

ﬁc density and the likelihood of congestion in the

individual exits. After leaving the reception area of

the V2X transceiver, each CHAV is indirectly unsub-

scribed by its removal from the situational overview.

5.2 Cooperation Procedure

In contrast to almost all existing publications, we pro-

pose a decentralized cooperation approach for the ne-

gotiation of cooperative maneuvers. For this purpose,

the TMS serves as a central source of information

and recommendations that actively supports the ap-

proaching CHAVs as they cross the intersection. At

the same time, it includes other trafﬁc participants

using suitable sensors and actuators. The involved

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

TMS CHAV 1 CHAV 2

D D

Subscription 1

Subscription 2

R , R

Recommendation

R , R

Recommendation

Evaluation 1

Evaluation 2

par

Figure 5: Time Sequence of Communication.

CHAVs agree decentrally on recommended driving

maneuvers or decide against their execution.

In order to give a clearer insight into the under-

lying concepts, Figure 5 provides an overview of the

intended communication ﬂow. Following the distribu-

tion of a cooperation recommendation to the two in-

volved CHAVs



, an assessment of the proposed co-

operative maneuver and the resulting strategy combi-

nations is performed locally. Each vehicle then com-

municates the results of its assessment by means of

an evaluation



. The messages sent are also received

by the TMS and can be used to monitor the coopera-

tion process and improve behavioral predictions. As

a ﬁnal step, the decision is made for or against the

execution of the cooperative maneuver



5.2.1 Cooperation Recommendation

As already described in Section 5.1.2, the TMS makes

use of all available information about the current po-

sitions, velocities, driving intentions, and the planned

destination lanes of trafﬁc participants, its knowledge

about the intersection geometry, static obstacles as

well as dynamic objects, and identiﬁes potential con-

ﬂict situations between CHAVs to be solved. If such

a situation is identiﬁed in which an increase in efﬁ-

ciency can be expected through the execution of a co-

operative driving maneuver, it is ﬁrst checked whether

the vehicles involved are CHAVs. If so, their unique

IDs are stored to prepare the message exchange. Ad-

ditionally, the vehicle beneﬁting directly from in-

creased trafﬁc efﬁciency is designated as ﬁrst coop-

eration candidate (CHAV 1), while the other one is

denoted as second cooperation candidate (CHAV 2).

In the further course, suitable strategies for both

vehicles are identiﬁed or extracted from a strategy

catalogue based on expert knowledge and feedback

received from preceding vehicles during their indi-

vidual unsubscription phases. A strategy consists of

a pair of (abstract) longitudinal and lateral behavior

descriptions, which can be derived directly from the

cooperative maneuver and the given trafﬁc situation.

With regard to the example shown in Figure 4, the

vehicle approaching the obstacle, which is referred to

as CHAV 1, is recommended to perform a CLC with

CHAV 2. Table 1 contains a list of exemplary strate-

gies that can be used to solve the imminent conﬂict

situation from the perspective of CHAV 1.

Table 1: Strategies for CHAV 1.

ID Longitudinal

Behavior

Lateral

Behavior

S1.1 Continue Lane change

S1.2 Decelerate Continue

On the other hand, the vehicle on the adjacent

lane, denoted as CHAV 2, is recommended to support

the CLC of its cooperation partner CHAV 1. Again, a

selected set of suitable strategies is listed in Table 2.

Of course, in realistic situations, considerably more

strategies would have to be taken into account, such

as changing lanes with simultaneous accelerations or

varying degrees of intensity of certain maneuvers.

Table 2: Strategies for CHAV 2.

ID Longitudinal

Behavior

Lateral

Behavior

S2.1 Decelerate Continue

S2.2 Continue Continue

Following the derivation of suitable strategies for

both participants, the initial payoff matrix R is gen-

erated, which is shown in Table 3. Each of its cells

represents a strategy combination that results from the

selection of one strategy for each cooperation candi-

date. At this point of time, all entries are empty, since

Cooperative Maneuvers of Highly Automated Vehicles at Urban Intersections: A Game-theoretic Approach

Table 3: Initial Payoff Matrix.

CHAV 2

S2.1 S2.2

CHAV 1

S1.1

( – , – ) ( – , – )

S1.2

( – , – ) ( – , – )

no valuations of the strategy combinations exist.

As a ﬁnal step, the initial payoff matrix R as

well as the recommended strategy combination R,

which represents the most valuable solution in terms

of global goals, are transmitted to the CHAVs.

5.2.2 Evaluation and Decision Making

After receiving the recommendation, an indepen-

dent, in-vehicle evaluation of all strategy combina-

tions generated by the TMS is initiated. For this pur-

pose, each cooperation candidate evaluates the so-

lutions based of its own situational overview. Be-

sides the speeds of the road users involved, distances

between them and differential speeds, the predicted

future behavior of dynamic objects and local goals

of the CHAV could be included. While the evalua-

tion approach is manufacturer- and implementation-

speciﬁc, the payoffs can be understood as a function

of the results of two separate safety and efﬁciency

evaluations. The calculated payoffs are then ﬁlled into

the matrix entries as illustrated in Table 4.

Table 4: Evaluation of the Cooperative Maneuver.

CHAV 2

S2.1 S2.2

CHAV 1

S1.1

( 4 , – ) ( 3 , – )

S1.2

(-2 , – ) ( 1 , – )

CHAV 2

S2.1 S2.2

CHAV 1

S1.1

( – , 2 ) ( – , -2 )

S1.2

( – , 1 ) ( – , 0 )

Once all strategy combinations have been suc-

cessfully assessed, the exchange of the (so far only

half-ﬁlled) payoff matrices E

and E

proceeds in or-

der to merge them into two complete and consistent

copies of matrix D, one for each vehicle. In order

to make the game fair and safe, communication must

take place (almost) simultaneously. For the practi-

cal implementation of this approach, it is crucial that

no prematurely received evaluations of other players

must be used as a basis for one’s own evaluation. In

terms of game theory, it has to be a static game.

Table 5: Decision Making.

CHAV 2

S2.1 S2.2

CHAV 1

S1.1

( 4 , 2 ) ( 3 , -2 )

S1.2

(-2 , 1 ) ( 1 , 0 )

In Table 5, the determination of the Nash equi-

librium for the previously merged payoff matrix D

is shown. For this purpose, the strategy combination

with the highest payoffs for both cooperation candi-

dates is selected. If there is only one Nash equilibrium

(condition 1) that corresponds to the original cooper-

ation recommendation (condition 2), a clear, joint so-

lution has been found. If condition 1 does not apply,

the cooperation is rejected for safety reasons.

5.2.3 Execution of Cooperative Maneuvers

Within our approach, the determination of a Nash

equilibrium is deﬁned as signing a binding contract

for performing the agreed strategy combination. Fol-

lowing an update of the situational overview, the

planned cooperative maneuver is executed using in-

vehicle trajectory planning and control algorithms.

In order to achieve a higher safety level during ex-

ecution, time bounds or reserved lane areas, for exam-

ple, could be agreed in advance. Further cooperative

maneuvers may be recommended by the TMS until

the participating CHAVs leave the intersection area.

6 EVALUATION

The evaluation of our cooperation approach builds

upon a comprehensive simulation setup that includes

virtual sensors, controllers for the TMS and all ve-

hicles involved, local situational overviews and inter-

nal states for all automated participants, specialized

subscription and unsubscription procedures, a lim-

ited, prototypical implementation of the proposed ap-

proach as well as an omniscient evaluation framework

with extensive monitoring and logging capabilities.

Despite the large implementation effort, we are

aware that our setup is useful only for demonstration

purposes, but not sufﬁcient to fully answer the second

and third research questions. We therefore plan to en-

hance this setup in follow-up activities and to publish

more differentiated results in further contributions.

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

6.1 Implementation

To evaluate the cooperation approach simulatively,

the developed concepts were prototypically imple-

mented as a Python wrapper for the simulator Sim-

ulation of Urban Mobility (SUMO, version 1.1.0). As

a widely used and commonly accepted open source

trafﬁc simulation, SUMO offers a large community,

extensive documentation, numerous application ex-

amples, and a plethora of scientiﬁc publications.

The simulation setup employs a TCP-based ar-

chitecture and makes use of Trafﬁc Control Interface

(TraCI) to manipulate the behavior of all automated

trafﬁc participants. As a ﬁrst step, a TMS controller

is instantiated into the model. In each simulation

step, an external simulation routine is triggered ﬁrst,

which adds new road users to the simulation. Each

newly created vehicle is then equipped with an ex-

ternal CHAV or HV controller that can inﬂuence the

participant’s behavior in all subsequent steps.

As a result of the controller initialization, selected

parameters of the SUMO default vehicle models are

overwritten with suitable values to represent the typ-

ical characteristics of CHAVs and HVs described in

Section 4, which are compared in Table 6.

Table 6: Comparison of Vehicle Controller Parameters.

Parameter CHAV-C HV-C

Maximum Speed v

max

50 km/h 60 km/h

Speed Deviation δ

0 0.1

Driver Imperfection σ 0.1 0.5

Reaction Time t

0.6 s 1 s

As they approach the intersection, all CHAVs sub-

scribe themselves by calling respective methods of the

TMS controller. The TMS senses the trafﬁc situation

at the intersection using virtual sensors and generates

simpliﬁed cooperation recommendations for CLCs,

which are then forwarded to the CHAV controllers. In

order to evaluate the strategy combinations indepen-

dently, each vehicle uses both virtual sensors and a

randomly generated cooperative factor f

∈ [0, 1] that

models the general willingness to cooperate. Follow-

ing the evaluations, the two payoff matrices are ex-

changed via further method calls and a decision is

made. If the CHAVs decide to execute the maneu-

ver, the driving behavior of the involved vehicles is

manipulated by calling the changeLane(...) and

slowDown(...) TraCI methods. If not, the vehicles

continue their journey without being affected.

6.2 Execution

A simulation model of the research intersection in

Brunswick provided by the Institute of Transporta-

tion Systems of the German Aerospace Center serves

as a basis for the simulation-based evaluation. It com-

prises a true-to-scale representation of the physical in-

tersection as part of the Application Platform for In-

telligent Mobility including an integrated trafﬁc light

sequence and a realistic lane layout. Besides ﬁve in-

coming lanes from east, south, and west as well as

three incoming lanes from north, each intersection

arm has two additional outgoing lanes.

The simulation model also includes recorded, real

trafﬁc data with a duration of one hour, in which ar-

rival times and lanes, types, and destinations of all

trafﬁc participants (passenger cars, trucks, cyclists,

and pedestrians) are deﬁned. A previously created,

deterministic mechanism divides passenger cars into

CHAVs and HVs according to a selected distribution.

In preparation for the simulation experiments, we also

instantiated two vehicles with a ﬁxed position and a

constant speed of 0 km/h used as static obstacles to

provoke CLCs in the western and southern approach

in close proximity to the intersection area.

The ﬁrst component of the evaluation was the ex-

ecution of eleven simulation runs with an increasing

percentage of CHAVs (0, 10, . . . , 100 %) without be-

ing inﬂuenced by our cooperation approach. The goal

of these simulations was to create a baseline for as-

sessing the impact of cooperation. The trucks in-

cluded in the trafﬁc data were exclusively used with-

out any automated controller. In addition, the behav-

ior of cyclists and pedestrians remained unchanged.

To increase the variance, ten repetitions of each sim-

ulation run were performed with different allocations

of CHAV and HV controllers. The generated simula-

tion results thus contain ten hours of simulated traf-

ﬁc per run, in each of which approximately 19.200

CHAVs, HVs, and trucks as well as 1.200 cyclists and

1.860 pedestrians pass the intersection area.

As a second evaluation component, eleven addi-

tional simulation runs with the same allocations of

CHAV and HV controllers were carried out, incorpo-

rating the presented cooperation approach. By using

the same simulation environment and the same input

data, the simulation results can be used to assess the

impact of cooperation on trafﬁc efﬁciency.

6.3 Results

Since the ﬁrst research question has already been ad-

dressed by the presentation of our cooperation ap-

proach in Section 5, we will focus on our simulation

results to give some ﬁrst hints on answering the subse-

quent questions. At ﬁrst, a look into the global obser-

vations shall give an impression on the effects of au-

tomation and cooperation in general. A second rather

Cooperative Maneuvers of Highly Automated Vehicles at Urban Intersections: A Game-theoretic Approach

0 20 40

80 100

100

200

300

400

500

Percentage of CHAVs [%]

Number of Cooperating Vehicles [#]

Total

West

South

North

Figure 6: Numbers of Cooperating Vehicles.

detailed look focuses on individual parts of the inter-

section and investigates the inﬂuence of cooperative

maneuvers on individual road users.

The potential options for assessing trafﬁc efﬁ-

ciency are manifold. While municipal administrations

usually consider capacities or maximum congestion

lengths, human drivers or passengers evaluate trafﬁc

efﬁciency on the basis of crossing durations or the

presence of directly perceptible delays. As the evalu-

ation is based on a ﬁxed simulation environment and

real trafﬁc data, it does not make sense to consider the

junction’s capacity as no vehicle gets stuck. Instead,

the crossing duration will be taken into account, as it

implicitly includes time losses and waiting times.

6.3.1 Global Observations

Starting with Figure 6, it can be observed that the

total number of cooperating vehicles grows with an

increasing percentage of CHAVs from 2 at a rate of

10 % to 500 at a rate of 100 %. A division of the num-

ber of vehicles by two results in the number of coop-

erative maneuvers, since one cooperation always in-

volves two participating CHAVs. As expected, a ma-

jority of cooperative maneuvers can be observed on

the lanes coming from west and south.

By putting this ﬁgure in direct relation with Fig-

ure 7, it can be determined that along with an in-

creased percentage of CHAVs – with and without

cooperation – the mean crossing duration decreases,

which can be expected through strict compliance with

legal requirements such as minimum distance and

maximum speed of CHAVs in contrast to HVs. It

is noteworthy that only from a rate above 50 % of

CHAVs cooperative maneuvers bring an additional,

albeit small, improvement in comparison to the base-

line without cooperation. At rates below they can

0 20 40

80 100

56.5

57.5

58.5

59.5

Percentage of CHAVs [%]

Mean Crossing Duration [s]

Baseline

Cooperative

Figure 7: Mean Crossing Durations.

even have a negative impact, e.g., at 30 % with a pro-

longation of the mean crossing duration by 0.24 s.

However, when interpreting the results it must be

taken into account that with respect to the small size

of the trafﬁc area under consideration only minor time

differences are to be expected, especially if the per-

centage of CHAVs is low. A further limitation is

the simpliﬁed implementation of the TMS controller,

which only generates cooperation recommendations

for a selected set of trafﬁc situations. As already men-

tioned in Section 2, a number of publications exclu-

sively deal with algorithms for possible path planning

that could be applied to improve the quality of the

generated recommendations in future work.

6.3.2 Local Observations

In the following, we focus on the western intersection

approach, where the largest number of cooperative

maneuvers can be observed. Thereby, the inﬂuence of

cooperative maneuvers on both cooperating and non-

cooperating vehicles is investigated more deeply.

In Figures 8 and 9, the variation of crossing du-

rations is plotted on the y-axis along with the preva-

lence of CHAV in percentage on the x-axis. A neg-

ative value represents an improvement (faster cross-

ing) whereas a positive value represents a deteriora-

tion (slower crossing). The variation is to be inter-

preted in relation to the crossing time needed without

cooperative maneuvers (baseline at constant 0) and

therefore only those vehicles were considered, which

experienced a change of their crossing duration.

The effects on cooperating vehicles are depicted

in Figure 8. It can be seen that no cooperations were

observed below a prevalence rate of CHAVs of 20 %.

The medians of all subsequent distributions are al-

ways around zero and vary slightly in the ﬁrst decimal

place. The boxes which represent 50 % of the vehicles

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

0 20 40

80 100

−50

−25

Percentage of CHAVs [%]

Variation of Crossing Durations [s]

Figure 8: Effects on Cooperating Vehicles (West).

are also around zero. However, with an increasing

percentage of automated vehicles (exception at 60 %)

it can be stated that the vehicles from the upper quar-

tile experience only a small time loss, whereas the ve-

hicles from the lower quartile can achieve a greater

time gain in comparison. The outliers to be observed

are caused by the use of time-controlled trafﬁc lights

and the changed arrival times of the involved CHAVs.

As a red phase lasts up to 50 s, corresponding time

gains and losses can be found. Since there are more

outliers downwards than upwards, the mean values –

represented by diamonds – are below zero above 50 %

of CHAVs with an exception at 60 % with 0.67 s.

Figure 9 shows the effects on non-cooperating ve-

hicles. The medians as well as the mean values and

boxes are around zero, again. With an increasing per-

centage of CHAVs the box sizes decrease slightly,

probably due to a smoother trafﬁc ﬂow. It is notice-

able that the only cooperation that is observed at 10 %

– located in the southern approach – has a clearly vis-

ible effect on the trafﬁc situation in the western inter-

section arm. The reason for this seems to come from

SUMO, which varies some parameters of newly in-

stantiated vehicles depending on the prevailing trafﬁc

situation. The distribution of outliers in terms of time

gains and losses is again inﬂuenced by the behavior of

the trafﬁc lights, but can be regarded as balanced, so

that neither a particular advantage nor disadvantage

can be determined on non-cooperating vehicles.

7 CONCLUSION

In this paper, we proposed a decentralized, game-

theoretic approach for the negotiation of coopera-

tive maneuvers of CHAVs at urban intersections. To

support these maneuvers, we assumed the existence

0 20 40

80 100

−75

−50

−25

Percentage of CHAVs [%]

Variation of Crossing Durations [s]

Figure 9: Effects on Non-Cooperating Vehicles (West).

of an intelligent TMS with a global view on the

whole scenery in order to derive cooperation recom-

mendations without directly controlling the CHAVs.

This combination enables a mutually consistent, dis-

tributed decision making on cooperative driving ma-

neuvers, taking into account global and local goals.

Due to the large implementation effort, the evalua-

tion results are preliminary with regard to a possible

increase in trafﬁc efﬁciency and the identiﬁcation of

causal relationships. We therefore plan to enhance

our evaluation, e.g., by investigating the inﬂuence of

different trafﬁc densities or controller conﬁgurations,

and to report on more elaborated results.

Until now, it can be stated that both cooperat-

ing and non-cooperating vehicles are inﬂuenced posi-

tively and negatively in the sense of shorter and longer

crossing durations. A trend shows that the advantages

for cooperating vehicles seem to be much greater than

the disadvantages, although (so far) not for all per-

centages of CHAVs. Positive and negative impacts on

non-cooperating vehicles compensate each other. The

results may vary depending on the geometry and other

characteristics such as the number of the lanes.

Taking into account the fact that the approach only

considers a single intersection without any cascading

effects and that initially only two CHAVs are able to

perform a cooperative maneuver, it was possible to

create a solid basis for further evaluations. The pro-

totypical implementation of required methods for the

generation of cooperation recommendations can cer-

tainly be improved on the basis of existing research.

Also the CHAV controller could be reﬁned, e.g., by

including more realistic virtual sensors or behavioral

predictions. In addition, we plan to extend our ap-

proach in a granted follow-up project to support the

interaction of cooperating vehicle groups in signiﬁ-

cantly larger trafﬁc areas with multiple intersections.

Cooperative Maneuvers of Highly Automated Vehicles at Urban Intersections: A Game-theoretic Approach

The associated potential to increase trafﬁc efﬁciency

still offers plenty of scope for further research.

ACKNOWLEDGMENTS

This work has been funded by the Federal Ministry of

Transport and Digital Infrastructure (BMVI) as part

of Digitaler Knoten 4.0 (reference no. 16AVF1008F)

and ViVre (reference no. 01MM19014E).

We would like to thank all project partners for

their trust and cooperation in discussions on the ini-

tial cooperation concept and the joint development of

the presented reference architecture.

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