Consensus Coordination in the Network of

Autonomous Intersection Management

Chairit Wuthishuwong and Ansgar Traechtler

Heinz Nixdorf Institute, Control Engineering and Mechatronics Department,

University Paderborn, Fuestenallee, Paderborn, Germany

Keywords: Autonomous Intersection Management, Intelligent Transportation System, Autonomous Vehicle, Vehicle to

Infrastructure Communication, Infrastructure to Infrastructure Communication, Consensus Algorithm.

Abstract: The Autonomous Intersection Management (AIM) will be a future method for the Intelligent Transportation

System. It combines wireless communication and the autonomous vehicle in order to create the new concept

for managing road traffic more safely and efficienly. The distributed control principle is applied to the

intersection network to control the traffic in the macroscopic level. The Vehicle to Infrastructure (V2I) and

Infrastructure to Infrastructure (I2I) communication are used to exchange the traffic information between a

single autonomous vehicle to the network of autonomous intersections The discrete time consensus

algorithm is implemented to coordinate the gross traffic density of an intersection and its neighborhoods in

the network. The boundary condition for the uncongested flow is created by using the Greenshield’s traffic

model. The proposed method represents the ability to maintain the traffic flow rate of each intersection and

operates with the uncongested flow condition. The simulation results of the network of a multiple

autonomous intersection are provided.

1 INTRODUCTION

The traffic congestion problem is increasingly

becoming a severe problem in the road

transportation. The research in the Intelligent

Transportation System tries to find a solution to

improve the traffic safety and efficiency. There were

several researches in controlling the traffic signal

due to the fixed timing traffic signal, indicating a

poor performance in managing traffic. One of the

active solutions is using the technique of the

adaptive traffic signalling. The traffic signal can be

adjusted adaptively based on the current traffic

situation. There are many methods to adjust the

traffic signal. The commercial solution called

SCOOT (Robertson, 1991) determines the period of

green and red light by using the queue length of each

street. In (Chiu, 1993), Fuzzy logic was applied to

update the signal, based on the constructing rules.

The Autonomous Intersection Management

(AIM) concept is a totally autonomous system that

combines the technology of the autonomous vehicle

and the wireless communication. According to the

intelligence of an autonomous vehicle

(Wuthishuwong, 2008), the road accidents that are

caused by human driver errors can be reduced. The

objectives of creating a full autonomous system are

to improve the traffic safety and traffic efficiency by

using autonomous vehicles and an autonomous

intersection manager. The AIM (Dresner, 2008) was

studied based on the multi-agents technique. Vehicle

agents communicate to an intersection agent to

reserve the area. The successful reservation will

have no confliction with the others. Otherwise, the

reservation will be rejected. In (Naumann, 1998),

(Zou, 2003) used the same concept but without the

intersection agent. Vehicle agent negotiates with

each other in order to cross an intersection. In

(Wuthishuwong, 2013) used the V2I communication

to plan the safe trajectory for each vehicle whilst

crossing an intersection. The extend version from a

single AIM to the multiple AIM in (Wuthishuwong,

2013) was studied the technique for maintaining the

traffic flow in the network by coordinating the local

traffic information between its neighbourhood.

In this paper, the authors propose the consensus

algorithm in order to coordinate the traffic

information between each autonomous intersection

in the network. The multiple intersections scenario is

modelled As well, the communication topology

794

Wuthishuwong C. and Traechtler A..

Consensus Coordination in the Network of Autonomous Intersection Management.

DOI: 10.5220/0005148607940801

In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (IVC&ITS-2014), pages 794-801

ISBN: 978-989-758-040-6

Copyright

c

2014 SCITEPRESS (Science and Technology Publications, Lda.)

between Vehicle to Infrastructure (V2I) and

Infrastructure to Infrastructure (I2I) are designed.

Maintaining the continuity of the traffic flow in the

network, the boundary condition of the uncongested

flow is derived based on the Greenshield’s traffic

model. The simulation of a multiple Autonomous

Intersection Management is presented. The results

are plotted and evaluated with the Greenshield’s

model

2 INTERSECTION NETWORK

The intersection network is modelled by connecting

9 single intersections, where each intersection has 4

ways. It is based on the distributed control structure.

Then, a single intersection is considered as an

autonomous agent that has ability to control itself,

whilst the control strategy is dependent on the

information between its neighborhoods.

The graph theory (Murray, 2009) is used to

visualize and interpret the interaction of a network.

Technically, each intersection manager is assigned

by a node and the connection between each node is

represented by an edge. However, there are 2 classes

of a node relationship.

2.1 Street Network

The street network is modeled based on the real

physical connection of each intersection. Typically,

an intersection is connected through an incoming

and outgoing street. Hence, the street network is a

set of street that connects a group of neighbored

intersections as illustrated in Fig.1. At the street

network, a single intersection acts as a central

manager. Each single intersection collects the local

traffic density on the connected street by counting

Figure 1: Network of streets with the direction flow of all

intersection.

the requested messages that are transmitted from the

incoming vehicles over the V2I communication.

Therefore, each intersection manager in the network

is identical and it responds to manage only its own

local intersection. The collected traffic density

information of each intersection can be determined

by summing the traffic density of all incoming

streets to intersection.

∈

,

,∈

(1)

Where,

is the gross incoming traffic density of the

intersection,

is the incoming traffic density of a

street has traveled from intersection to intersection

, and

,

is the external incoming traffic from the

sources , connect to the intersection .

2.2 Communication Network

The communication topology of the intersection

network is illustrated in Fig. 2. The connection

between couple of nodes uses the bi-directional

communication. Each node, which represents an

intersection manager, can either receive or transmit

the data package to their destination node

Figure 2: Intersection communication network topology.

The properties of a graph theory are used to

represent the relationship of the intersection

network. The adjacency element

, will have value

1 when there is an edge between each node,

otherwise the value is equal to 0.

1,

,

∈

0,

;,

∈

(2)

The degree matrix describes the number of

connections at each intersection.

ConsensusCoordinationintheNetworkofAutonomousIntersectionManagement

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,

,

0,

;,

∈

(3)

The Laplacian matrix describes the complete

relationship of the intersection network. The simple

way to determine the Laplacian matrix is subtracting

the degree matrix with the adjacency matrix.

(4)

Where; is the row element of the matrix, is the

column element of the matrix,

is the adjacency

matrix,

is the degree matrix, and is the

Laplacian matrix.

3 CONSENSUS COORDINATION

OF AIM

In this work, the discrete consensus algorithm is

implemented for coordinating the traffic information

in AIM in order to balance the overall traffic flow in

the network. The consensus algorithm has been

recently studied in robot application such as robot

formation in (Ren, 2007; Olfati-Saber, 2003; Olfati-

Saber, 2007). Naturally, it is the distributed control

that gives the convergence property, which fits for

the large scale system. The system architecture of

the multiple, autonomous intersections management

is illustrated in Fig. 3.

Figure 3: The system architecture of the multiple

autonomous intersections management.

Each intersection acts as the centralized

controller. The traffic density of each intersection is

collected in the street network layer by using V2I

communication and this information is distributed to

its neighborhoods in the intersection network layer

over I2I communication. The AIM will compute the

control command, based on the traffic density of

itself and its neighborhoods.

The consensus algorithm is applied to coordinate

the traffic information among the intersections in the

group. The traffic density is used as the coordinated

information, as well as, representing the state of an

intersection. The dynamics of each local intersection

and a global network can be expressed as the

following equation.

∈

(5)

(6)

Substituting the gross traffic density of each

intersection, which is defined in Eq.1, the consensus

of a collective AIM can be derived as:

⋮

∙

⋮

∙

⋮

(7)

The discrete time consensus is derived by applying

the difference equation. Then, the discrete time

consensus for a local intersection and a global

network can be expressed as the following equation.

1

∈

(8)

1

(9)

Where, is a Perron matrix and is the

step size 0. The sufficient conditions for the

stability of a consensus in the network are provided

in [9].

The control system of a mulitple autonomous

intersections is composed of nine units of AIM,

which is the distributed control schema. Thus, each

intersection control strategy is identical. The closed

loop control block diagram of the autonomous traffic

control of a single intersection is illustrated in Fig.4.

The autonomous vehicle is used in AIM system

and practically AIM can only prioritze the timing of

crossing an intersection. Thus, the control variable is

the incoming time which can be transformed to the

average velocity when the distance between a

vehicle and intersection is known. Basically, every

vehicle has to send the requesting message to AIM

before crossing an intersection. With this point, the

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traffic density and number of vehicles approaching

an intersection, is measured through the V2I

communication. It counts the number of messages of

the incoming vehicles and substracts the number of

outgoing vehicles. However, the information is in a

discrete time domain after sampling.

Figure 4: Closed loop control block diagram of a single

intersection.

In order to control the traffic flow of an

intersection, the traffic density of the neighborhoods

is inputted through I2I communication. The

consensus algorithm coordinates the information

from itself with its neighborhood in order to

determine the desired value of the traffic density

following the Eq. 9. Therefore, the error term of

each intersection is the difference between the

desired traffic density and the current traffic density

value. It can be expressed as the following equation.

1

(10)

Technically, the consensus algorithm try to

balance the traffic density between the local

intersections. This means it will maintain the level of

traffic density closed to its neighborhoods, to keep

the low variation between them. Theoretically, the

error term must be minimized and approach zero in

the finite time in order to make the current traffic

density equal to the desired traffic density.

Refering to the field of transportation engineer, the

traffic model is composed of three corresponding

parameters: traffic density, traffic flow rate and

average velocity. These relationships are used to

represent the macroscopic traffic. In this work, the

Greenshield’s model is used as the reference traffic

model. For controlling the traffic, the condition of

the congested and uncongested traffic are defined by

using the empirical data of the traffic density,

average velocity and traffic flow rate. the

relationship between the average velocity and the

traffic density with the boundary of congested and

uncongested traffic is illustrated in Fig.5.

Figure 5: Greenshield’s traffic model: the relationship

between the average velocity and the traffic density.

According to the parameters of the Greenshield’s

model (Hall, 1996), the free flow velocity

is

given at 91 km/hr and the jamming density

is

given at 78 vehicles/km/lane. The velocity at

capacity

is given at 46 km/hr. The velocity at

capacity is the lower boundary of the average

velocity that vehicles can drive under the

uncongested traffic. The traffic will begin to congest

after this boundary, if the vehicles cannot keep the

driving velocity at least at this level. Consequently,

the traffic density at capacity

is the maximum

number of vehicles on the street that still keeps the

average velocity within the boundary. It can be

determined as:

1

(11)

The traffic density at capacity is round up to 38

vehicles/km/lane. The boundary condition of the

uncongested traffic can be summarized into the

following equations.

0

(12)

The uncongested traffic is satisfied when the average

velocity is higher than the velocity at capacity and

less than the free flow velocity, as well as, the traffic

density being greater than zero and less than the

traffic density at capacity. On the other hand, the

congested traffic conditions are vice versa.

The second relationship represents the relationship

between the traffic flow rate and the traffic density.

ConsensusCoordinationintheNetworkofAutonomousIntersectionManagement

797

The relationship between these two parameters is

defined by a parabolic function. With the provided

parameters, the traffic flow at capacity

can be

determined as:

(13)

The traffic flow rate at the capacity will be

approximately 1,800 vehicles/hr. It can be said that

the boundary of the uncongested traffic is 0

. However, this boundary condition cannot be

alone used to indicate the traffic situation. The

uncongested traffic and congested traffic condition

share the same boundary since the relationship is the

parabolic function. The traffic flow of the

uncongested traffic is in the left region of the graph

and the derivative gives the positive value. That

means the average velocity is increasing from zero

until it reaches the boundary of the traffic flow at

capacity. Meanwhile, the traffic flow under the

congested traffic is on the other side with the

negative slope. The flow rate is gradually decreased

to zero after the point of traffic flow at capacity is

reached. The Greenshield’s model of the relationship

between the traffic flow rate and the traffic density

with the boundary of congested and uncongested

traffic is illustrated in Fig.6.

Figure 6: Greenshield’s traffic model: the relationship

between the traffic flow rate and the traffic density.

The Greenshield’s model of the relationship between

the average velocity and the traffic flow rate with the

boundary of congested and uncongested traffic is

illustrated in the Fig. 7. The uncongested traffic is

represented in the upper part of the graph. On the

contrary, the lower part of the graph represents the

congested traffic condition. In addition, the graph

shows that at the equilibrium point, the average

velocity at capacity and the traffic flow rate at

capacity provides the value of the traffic density at

capacity.

Figure 7: Greenshield’s traffic model: the relationship

between the average velocity and the traffic flow rate.

With the Greenshield’s traffic model, the traffic of

an intersection is controllable. In order to manage

the current traffic density to meet the desired traffic

density, the Greenshield’s relationship of an average

velocity and a traffic density is implemented. Since

the model gives the direct relationship between

them, it is obvious that changing an average velocity

is the way to minimize the traffic density error of an

intersection. The average velocity in the discrete

time can be derived as:

̅

̅

1

(14)

In the control block diagram, the filter is

implemented for smoothing the output response in

order to remove the short term fluctuation. The

technique of the moving average is applied by

weighting the value between the current computed

value with the previous desired value. The weighting

coefficient is called the degree of filtering and the

summation of them will be unity. It is called the

exponential moving average filter. Technically, the

function of this filter is identical to the first order

low pass filter in the electronics circuit, suppressing

the amplitude of a signal so that the frequency is

higher than the cut-off frequency. The exponential

moving average filter for the desired average

velocity can be expressed as:

̅

∗

̅

1

̅

∗

1

(15)

Where, ̅

∗

is the desired average velocity for an

intersection at time step , ̅

is the computed

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average velocity from the Greenshield’s model at

time step , ̅

∗

1 is the previous time step

1 of a desired average velocity and is the

weight coefficient, ∈

0,1

.

Since, the intersection network is designed,

based on the distributed control, every intersection

control structure is identical as presented in Fig. 4.

For this reason, the collective of all sub systems,

intersection manager, represents the characteristic of

the intersection network. The closed loop control

block diagram of the intersection network can be

illustrated in Fig.8.

Figure 8: Closed loop control block diagram of the

intersection network.

4 SIMULATION RESULTS

The simulation results of the multiple autonomous

intersection management, which were implemented,

based on the consensus algorithm with the

Greenshield’s traffic model, is presented. The

inputted traffic flow rate of all 12 sources is assigned

randomly. The range of the traffic flow rate is set

between 1,000-2,000 vehicles/hr.

All vehicles generate their own route randomly. The

results of the relationship between 3 traffic

parameters of each intersection are plotted. The

paired relationship between average velocity, traffic

density and traffic flow rate is shown in Fig. 9, 10,

and 11 respectively. In addition, the collecting plots

of all intersections, compared to the Greenshield’s

model are shown in Fig12, 13 and 14 respectively.

The corresponding plot of all traffic parameters of 9

intersections is shown in Fig.15.

Figure 9: The average velocity and the traffic density

relationship of each intersection in the network.

Figure 10: The average velocity and the traffic flow rate

relationship of each intersection in the network.

Figure 11: The traffic flow rate and the traffic density

relationship of each intersection in the network.

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Figure 12: Collecting plot of the average velocity and the

traffic density, compared with the Greenshield’s model.

Figure 13: Collecting plot of the average velocity and the

traffic flow rate, compared with the Greenshield’s model.

Figure 14: Collecting plot of the traffic flow rate and the

traffic density, compared with the Greenshield’s model.

Figure 15: Summary plot of all traffic parameters, traffic

flow rate, traffic density and average velocity of 9

intersections.

The results show all intersections can maintain the

level of traffic density, average velocity and the

traffic flow rate, within the uncongested condition.

As well, AIM provides better efficiency in traffic

flow rates, compared to the theoretical value that

given by Greenshield’s model.

5 CONCLUSIONS

This work introduces the coordination method for

multiple, autonomous intersections by using discrete

consensus algorithm with the Greenshield’s model.

In this paper, the proposed method presents the

success performance in managing the traffic in the

network of multiple autonomous intersections. The

simulation results show every intersection in the

network can operate under the uncongested flow

condition and provides a contribution in traffic flow

rate capability. The attached video presents the

success driving under the green wave concept that

all vehicles can maintain continuous driving and

crossing multiple intersections without stop.

ACKNOWLEDGEMENTS

This research is funded by Ministry of Innovation,

Science, Research, and Technology of the Federal

State North-Rhine-Westphalia, Germany through the

International Graduate School (IGS) of Dynamic

Intelligent System. This research work is the

continued project of the Autonomous Intersection

Management under the supervision of Prof. Ansgar

Traechtler, Heinz Nixdorf Institute, Control

engineering and Mechatronics department,

University of Paderborn.

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