What Is the Right Bounding Box of a VRU Cluster in V2X

Communication? How to Form a Good Shape?

Leonardo Barbosa da Silva

1 a

, Silas Correia Lobo

, Evelio Mart

ın Garc

ıa Fern

andez

1 b

and Christian Facchi

2 c

Department of Electrical Engineering, Universidade Federal do Paran

a, Curitiba, Brazil

CARISSMA (C-ECOS), Technische Hochschule Ingolstadt, Ingolstadt, Germany

Keywords:

Vulnerable Road Users, VRU Clustering, Cluster Bounding Boxes, V2X Communication, Vulnerable Road

User Awareness Message, VAM, VRU Basic Service.

Abstract:

Among the possible trafﬁc members on a Vehicle-to-Everything network, the term Vulnerable Road User

(VRU) is assigned e.g. to pedestrians and cyclists. The VRU Awareness Message (VAM) is used by VRUs

to inform other users of their presence and ensure they are perceived in a trafﬁc system. Since the number of

VRUs in crowded areas might be very high, the over-the-air trafﬁc might be overloaded. To reduce channel

overload, VAMs offer a clustering feature in which VRUs with similar kinematics and positions can group

themselves so that only one device transmits messages. The VRU Basic Service speciﬁcation describes the

cluster as a bounding box that must cover all its members using a geometric shape so that other vehicles in the

vicinity can avoid colliding with the contained VRUs. This paper contributes to the standardization effort by

introducing a data structure, the Cluster Map, for the clustering in the VRU Basic Service. Furthermore, this

work is the ﬁrst to suggest strategies for forming bounding box shapes. Simulation results show that each of

the geometry types is useful in different situations, thus further research on the topic is advised.

1 INTRODUCTION

Among all the transport groups in an urban environ-

ment, the Vulnerable Road Users (VRUs), including

cyclists, motorcyclists, moped riders, and pedestri-

ans, face elevated accident risks. Data from the Euro-

pean Road Safety Observatory (ERSO) indicates that

in 2021, 48.01% of the 19,484 trafﬁc-related fatalities

in the European Union involved VRUs, with pedestri-

ans accounting for 18.83% (Decae, 2023).

Contributing to trafﬁc safety, Vehicle-to-

Everything (V2X) communication uses wireless

messages to expand awareness in a transport system.

V2X technologies encompass Cellular V2X (C-V2X)

using the Long-Term Evolution (LTE) standard from

the 3GPP and WiFi-based V2X relying on the IEEE

802.11p amendment. This study favors WiFi-based

V2X over C-V2X due to the latter’s limitation

in communicating out-of-coverage, such as when

traversing tunnels (Festag, 2015).

https://orcid.org/0009-0006-3511-6056

https://orcid.org/0000-0003-1707-8595

https://orcid.org/0000-0002-7762-9419

Through the deﬁnition of the Intelligent Transport

Systems (ITS) concept, the WiFi-based ITS-G5 stan-

dard is introduced by the European Telecommunica-

tions Standards Institute [ETSI] (2010). The ITS-G5

services are categorized by the CAR 2 CAR Commu-

nication Consortium [C2C-CC] based on a deploy-

ment roadmap, with the Day 3+ release containing

VRUs actively broadcasting data (C2C-CC, 2019).

To cover this feature, ETSI published the 103

300 series of reports and speciﬁcations that proposes

a VRU Awareness Message (VAM) that advertises a

VRU’s presence to other stations in its range (ETSI,

2021a,b,c). VAMs are the basis for the VRU Basic

Service (VBS), which describes operations, message

generation rules, and transmission trigger conditions.

The generation time depends on channel occupation

through the use of the Decentralized Congestion Con-

trol (DCC) mechanism (ETSI, 2015). Some use cases

of the VBS are collision avoidance and intersection

management (C2C-CC, 2023).

In a region densely populated with VRUs, plenty

of individual VAMs can be exchanged, consuming

spectrum resources and requiring plenty of process-

ing from each V2X device in the local network, lead-

144

Barbosa da Silva, L., Lobo, S., Fernández, E. and Facchi, C.

What Is the Right Bounding Box of a VRU Cluster in V2X Communication? How to Form a Good Shape?.

DOI: 10.5220/0012699100003702

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 10th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2024), pages 144-155

ISBN: 978-989-758-703-0; ISSN: 2184-495X

ing to a higher overhead (ETSI, 2021c). As a solution,

the VBS offers the clustering functionality, grouping

VRUs with similar positions and kinematics and let-

ting a single node called cluster leader be responsible

for transmitting VAMs. To advertise the set of mem-

bers, the leader must include a data ﬁeld in its VAM

that represents the area occupied by the cluster partic-

ipants. These objects can assume three different geo-

metrical shapes: circle, rectangle, or polygon. How-

ever, ETSI does not offer strategies on how to produce

these constructs, nor does it discuss each option’s im-

pact on the service’s performance.

This paper addresses implementation gaps in clus-

tering on the VBS, presenting the ﬁrst comprehen-

sive set of techniques for generating bounding box

shapes. A Cluster Map is introduced as a supporting

data object facilitating the formation and maintenance

of cluster shapes. Testing the proposed strategies is a

simulated trafﬁc scenario implemented in the open-

source framework Artery (Riebl et al., 2015). The

comparison of the impact caused by each shape on the

service uses cluster density (VRUs per bounding box

area), average message size, number of active clus-

ters, and total operations as metrics.

This work is structured as follows: Section 2

presents the state of the art regarding VAMs and VRU

clustering. Section 3 describes an implementation

of the VBS and proposes shape formation strategies,

with Section 4 deﬁning metrics to compare the shapes

generated from these methods. Section 5 describes

the tools used to simulate the service, and Section 6

discusses the obtained results. Section 7 concludes

the paper and suggests future steps.

2 VRU BASIC SERVICE

On the VBS, transmission of a VAM occurs when

one of its trigger conditions is satisﬁed, for exam-

ple, due to elapsed time or a change in either speed,

orientation, or position above a predeﬁned threshold.

The interval between consecutive message generation

ranges from a minimum of 100 ms up to 5 s. A VAM’s

structure consists of the mandatory containers: ITS

Protocol Data Unit (PDU) Header, Basic Container,

and High Frequency Container. These are sent in ev-

ery message and contain, among other elements, each

device’s Station ID, message generation time, VRU

proﬁle, position, and kinematics (ETSI, 2021c).

VAMs might also contain the optional containers:

Low Frequency Container, Cluster Information Con-

tainer (CIC), Cluster Operation Container (COC), and

Motion Prediction Container. The VBS also offers the

optional VRU cluster management function that han-

dles clustering events and parameters. Subsections

2.1, 2.2, and 2.3 provide an overview of VBS stan-

dalone and cluster operations based on (ETSI, 2021c).

2.1 Standalone VRU Operation

The default role of a VRU on the VBS is standalone,

meaning that it will periodically send VAMs disclos-

ing its presence and keep listening for updates from

other devices. The VRUs store knowledge about ob-

jects in their surroundings by receiving and parsing

awareness messages. They maintain this information

in a facility called Local Dynamic Map (LDM), that

can be used to support various ITS applications, such

as collision risk assessment (ETSI, 2014). When the

cluster manager is enabled, standalone VRUs will

keep monitoring their LDM in search of opportunities

to create a cluster or join a compatible one.

2.2 VRU Cluster Creation

During the process of clustering, nodes are compat-

ible if their distance and speed difference fall below

predeﬁned thresholds: maxClusterDistance (default:

5 m) and maxClusterVelocityDifference (default: 5%).

The VRU’s cluster manager inspects the LDM and

considers a group of perceived users as a cluster can-

didate when at least numCreateCluster (default: 3) of

them, including the ego VRU, meet these criteria.

The VRU that notices this situation ﬁrst changes

its role from standalone to cluster leader and emits

a VAM advertising a clustering opportunity. Cluster

VAMs must always possess a CIC containing clus-

ter identiﬁcation number (ClusterID), bounding box

shape, number of nodes contained (cardinality), and

type of VRUs present (e.g., pedestrians, cyclists, and

moped riders). For the ﬁrst cluster VAM, the leader

must generate a random ClusterID and produce a

shape that contains only itself.

2.3 VRU Cluster Updating

When a standalone VRU receives a cluster VAM and

deems itself compatible, it may send a join notiﬁca-

tion for 3 s. This message includes the COC with

the ClusterJoinInfo data ﬁeld, specifying the target

cluster’s ID and the duration for which the VRU will

continue sending standalone VAMs. After success-

fully joining, the VRU assumes a passive role, ceasing

VAM transmission but monitoring leader messages to

ensure that speed difference and distance are still suit-

able. A VRU can only join clusters with cardinality

below maxClusterSize (default: 20 VRUs).

What Is the Right Bounding Box of a VRU Cluster in V2X Communication? How to Form a Good Shape?

145

A member can decide to leave a cluster due to:

incompatible kinematics with the group, no VAM re-

ceived from the leader within 2 s, or the triggering of

a break-up by the leader. Complementary to the join

message, the leave VAM also includes a COC, but in

this case with the ClusterLeaveInfo data ﬁeld, con-

taining the target cluster’s ID and stating the reason

for the operation. The VRU must transmit the leave

notiﬁcation for 1 s.

During a cluster’s lifespan, the leader sends VAMs

containing a CIC that describes a geometry encapsu-

lating every member. This shape, named bounding

box, can be one of three possible types: circle, rect-

angle, or polygon, each taking a varying amount of

parameters as shown in Figure 1. The circle is de-

ﬁned by a center point (C.a) and radius (C.b), the rect-

angle is formed by a center point (R.a), half-length

(R.b), half-width (R.c), and orientation (R.d), while

the polygon is described by a sequential list of all the

offset points (P.a.1, ..., P.a.n) that form the vertices of

the shape, with no explicit upper bound. Depending

on how each bounding box is declared in the CIC, the

chosen shape can signiﬁcantly inﬂuence message size

and, consequently, the channel load.

P.a.1

P.a.2

P.a.3 P.a.4

P.a.5

C.a

C.b

R.d

R.a

R.b

R.c

Figure 1: Parameters that are used to describe a Bounding

Box shape in the CIC.

The leader listens for VAMs containing COCs ad-

dressed to its ClusterID, updating the bounding box

according to valid join and leave notiﬁcations. And,

if necessary, it triggers a breakup operation by includ-

ing a COC with the clusterBreakupInfo data ﬁeld in

the VAM. The message contains a reason for the dis-

solution (e.g., insufﬁcient cardinality) and the time at

which the leader will stop sending cluster VAMs.

2.4 Functional Gaps of the VBS

As the current ETSI 103 300 VBS standard by ETSI

(2021c) is still in development, it has functional gaps

hindering complete clustering implementation. This

subsection describes the enhancements proposed by

Lobo et al. (2023) which were incorporated in this

study. In the last paragraph, an original enhancement

is suggested to cover another identiﬁed gap.

On heavily occupied channels, consecutive mes-

sage generations from a VRU using the VBS might

take up to 5 s. If the VRU in question is a cluster

leader, this would lead the members to wrongfully

trigger a “leader-lost” leave operation due to a lack

of received leader VAMs in the span of timeCluster-

Continuity (default: 2 s). To prevent this issue, Lobo

et al. propose the reduction of the maximum gener-

ation delta time (T GenVamMax) for cluster leaders

from 5 to 2 s.

Another suggested addition from Lobo et al. is

a “Cluster creation failed” event. Currently, a leader

creating a cluster will wait indeﬁnitely for join VAMs

while the cardinality is below numCreateCluster.

This state, if kept for prolonged durations, is inef-

ﬁcient as it drains the VRU’s power resources and

overloads the channel more than in standalone mode.

The suggested event interrupts cluster creation when

a leader does not receive sufﬁcient valid joins in the

span of timeLeaderWaiting (default: 2 s).

Since the standard does not offer a method to con-

struct the initial bounding box, Lobo et al. suggest

that this geometry shall always be a circle with a

radius of half the distance to the closest compatible

VRU. This shape type needs the least number of data

elements to be described, and the suggested radius en-

sures non-negative areas covering only the leader.

Regarding bounding boxes, Lobo et al. also pro-

pose an optional buffer distance

B f

= v

V RU

·t

VAM

, (1)

added to the edge of all shapes, increasing the cov-

ered area. The padding distance (d

B f

) uses the highest

VRU velocity within the cluster members (v

V RU

) and

the VAM assembly time (t

VAM

) as parameters. This

functionality prevents VRUs from being at the exact

edge of the geometry, leading to them being wrongly

determined inside/outside the bounding box due to la-

tency, time delays, or position errors.

Furthermore, this present work identiﬁes and

solves an additional gap. When a leader receives leave

notiﬁcations from its cluster members, it recalculates

the bounding box and reduces the cardinality. How-

ever, when a cluster contains less than three VRUs, it

is impossible to form a rectangle or polygon since the

VRUs’ positions would amount to a single line seg-

ment. This study suggests that a cluster should dis-

solve whenever a leader identiﬁes that the cardinal-

ity is below numCreateCluster for the duration time-

LeaderWaiting. This parameter provides some time

for join requests to be received and processed by the

leader while also matching the suggested timeout for

the initial formation of the cluster.

2.5 Related Works - VAMs

Current research on VAMs often focuses on the VRU

in a standalone capacity. For instance, Lobo et al.

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146

discuss the enhanced VRU detection time provided

by the VBS and explore the advantages of using this

service along with ETSI’s other solutions, such as the

Collective Perception Message (Lobo et al., 2022).

Through ﬁeld testing, Lusvarghi et al. suggest that

the rules for triggering VAM generation should dif-

fer depending on the proﬁle of the VRUs (Lusvarghi

et al., 2023). Zoghlami et al. advocate for a context-

aware message transmission scheme based on posi-

tion and kinematics, leading to adaptive VAM gener-

ation (Zoghlami et al., 2022).

Concerning VRU Clustering, Rupp and Wischhof

show that this VBS feature reduces the number of

VAMs sent in trafﬁc scenarios, particularly for higher

cardinalities. However, it also leads to an increase

in position error when compared to individual VAMs.

Finally, they recommend improving cluster effective-

ness by either increasing maxClusterVelocityDiffer-

ence to a minimum of 25% or adjusting it to con-

sider velocity averages rather than instantaneous val-

ues (Rupp and Wischhof, 2023).

Also analyzing clustering performance on the

VBS, Lobo et al. compare simulation results on a

scenario with and without clustering enabled. The ob-

tained data shows that clustering reduces channel oc-

cupation, thus making communication more reliable

by minimizing the message latency and Packet Error

Rate. This behavior is related to the DCC function of

the service operating closer to its threshold when only

individual VAMs are present, leading to the formation

of queues and message drops (Lobo et al., 2023).

2.6 Related Works - Bounding Boxes

To the best of the author’s knowledge, at the moment,

no other research related to the geometrical shaping

of the VRU clusters has been published. This topic is

particularly challenging since the ETSI 103 300 stan-

dard by ETSI (2021c) does not offer strategies to pro-

duce the cluster bounding box shapes. Furthermore,

through the literature review of the state of the art

on wireless network technologies, the production of

these geometries appears to be an unsolved issue to

the VBS since most clustering functionalities do not

need to worry about the shape that their list of mem-

bers produces.

For example, clustering applications for Wireless

Sensor Networks and Radio Frequency Identiﬁcation

both deal with the grouping of various devices based

on their positions (Shahraki et al., 2020; Gomes et al.,

2022). Both, however, do not take into consideration

kinematics or the shape formed by the set of objects,

treating clusters as amorphous point clouds.

In image processing, bounding boxes are used to

contour the result of a classiﬁcation algorithm (Lak-

shmanan et al., 2021). They are, however, limited to

forming only axis-aligned rectangles.

The Bounding Volumes (BV) concept presents a

similar goal to the cluster bounding boxes within the

VBS. The formation of BVs uses a variety of compu-

tational geometry strategies to represent one or more

complex geometries through simpler shapes (e.g., cir-

cles, rectangles, and polygons), both in 2D and 3D.

This approach is used in collision detection algo-

rithms to produce objects that are easier to process,

which is ideal for ray-tracing and hitbox detection in

physics simulators, computer animations, and video

games (Ericson, 2004).

Research in Light Detection and Ranging (Li-

DAR) also beneﬁts from BV strategies, using them

to represent a perceived object in a 3D space. In au-

tonomous driving, some applications of LiDARs are

object detection (V and Pankaj, 2021), assessment of

object orientation (Liu et al., 2020), and collision de-

tection (Wang et al., 2019).

3 VBS CLUSTERING

IMPLEMENTATION

To evaluate the viability of clustering on the VBS

and the particular effect of each shape, previous im-

plementations of the standard on Artery were ex-

tended. In (Lobo et al., 2022), the VAM contain-

ers and the message transmission triggers were de-

veloped for standalone VRUs, providing the basis for

the VBS in the framework. Continuing the VBS de-

velopment, (Lobo et al., 2023) implements the cluster

management functionality, enabling VRU clustering

with polygonal shapes. Each device with VBS has

a cluster management instance responsible for stor-

ing the VRU’s role, parsing the Cluster Information

and Operations containers, managing the bounding

box construction, and monitoring the LDM for con-

ditions to trigger cluster events (creation, join, leave,

and breakup).

This work enhances (Lobo et al., 2023) by im-

plementing all three cluster bounding box shapes de-

scribed in ETSI’s standard (ETSI, 2021c), determin-

ing strategies based on computational geometry to

form these structures. The introduction of a new

data structure, the Cluster Map, supports the cur-

rent VBS clustering functionality. This object stores

data from cluster-compatible VRUs, providing a stan-

dalone VRU with means to determine if it should cre-

ate a cluster while also providing the cluster leader

with data regarding its members. Additionally, an

Artery simulation scenario enables the evaluation of

What Is the Right Bounding Box of a VRU Cluster in V2X Communication? How to Form a Good Shape?

147

the effects of clustering using the different shape

types, comparing the beneﬁts and drawbacks of each

on a VBS.

3.1 Cluster Map Concept

This study introduces the Cluster Map (CM) concept

as a tool to support the cluster management func-

tionality of the VBS. A CM uses the data objects of

the LDM to store perceived VRUs that are cluster-

compatible, containing information such as position,

kinematics, and station ID. The purpose of the CM, as

illustrated in Figure 2, is to generate a specialized data

structure that is simpler to iterate as part of the VBS

functional cycle, supporting the creation and manage-

ment of clusters. A CM is instantiated in every VRU

as it assumes a standalone or cluster leader role.

Moving and static objects perceived

by a VRU through V2X services

All vehicles, VRUs and

road infrastructure present in a region

Clustering-compatible VRUs

Figure 2: Funneling of perceived trafﬁc nodes in a region.

Cluster Map acts as a specialized LDM.

Initially, the CM stores a list of cluster-compatible

VRUs perceived in the LDM, with the ego standalone

VRU using this structure to evaluate if it could create

a new cluster and become a leader. In these situa-

tions, the CM is used to determine the expected car-

dinality and calculate the radius of the ﬁrst iteration

of the bounding box. Cardinality is determined by

summing the number of VRUs on the CM and adding

one to the total to account for the leader. After suc-

cessful cluster creation, the initial CM is purged and

is only updated by the leader through valid join and

leave VAMs from compatible nodes. This change en-

sures proper cluster management by the leader who

must validate the received operations and keep track

of the members’ positions, enabling it to construct an

appropriate bounding box.

3.2 Bounding Box Generation

The development of VRU Clustering on Artery pre-

sented in this work addresses the absence of speci-

ﬁed Bounding Box formation strategies in the stan-

dard (ETSI, 2021c) by determining and implement-

ing its methodologies. The adopted approaches stem

from the literature review of bounding boxes in the

realm of computational geometry, being the ﬁrst to

offer strategies for clustering on a VBS.

The VBS incorporates the generation of bound-

ing boxes through an instance of the cluster manage-

ment module in each VRU. A device shall only have

access to this functionality if either they are a stan-

dalone VRU attempting to generate a new cluster or

if they are already a leader. In both these cases, a

Cluster Map will be used to produce a point cloud

that indicates the position of a set of VRUs. The CM

is the primary data source for the proposed bounding

box generation strategies. For simplicity, this study

assumes that all devices in a test scenario use the same

default shape type and that no type change is possible

except the one that occurs at the transition between

the cluster formation and the maintenance phases.

3.2.1 Initial Bounding Box

For the initial bounding box, ETSI 103 300 deter-

mines that the ﬁrst iteration of a cluster must contain

only the leader, with a cardinality of one (minCluster-

Size), and a bounded area covering only the VRU cre-

ating the cluster (ETSI, 2021c). At this moment, the

standalone ego VRU creates an empty initial Cluster

Map (iCM). Next, it iterates the LDM, searching for

all the perceived VRUs (P) and comparing if they are

compatible with the ego (E). The ﬁrst parameter eval-

uated for this decision is the Euclidean distance

d =

− x

)

+ (y

− y

)

, (2)

calculated between the positions of each perceived

VRU (x

) and the ego VRU (x

). Since this

study does not consider elevation differences, only 2D

coordinates are used. The nodes E and P are compat-

ible if the distance (d) is less than 5 m. The second

parameter, speed difference (v

di f f

), is given by

di f f



− v



· 100% , (3)

the ratio of the absolute values for the speed of both

ego (v

) and perceived (v

) nodes, with a maximum

suitable difference of 5%. If P has both d and v

di f f

within the acceptable ranges, the VRU’s data object is

appended to the iCM. During this assessment, the ego

VRU must store the overall smallest valid distance

min

) among all the d’s calculated from the iCM, us-

ing it later to generate the initial cluster bounding box.

After evaluating all the VRUs in the LDM, the ego

VRU veriﬁes the size of the resulting iCM. If it con-

tains at least two VRUs, the potential cluster reaches a

cardinality of numCreateCluster, and a cluster is pos-

sible. Next, the ego VRU switches roles and becomes

a leader, starting the cluster-creation process. Algo-

rithm 1 summarizes this decision workﬂow.

For the ﬁrst cluster VAM, the initial shape shall

always be a circle since this is the shape that needs

VEHITS 2024 - 10th International Conference on Vehicle Technology and Intelligent Transport Systems

148

Data: Ego VRU’s status and LDM

Result: Cluster Creation Decision

initialization;

while VRU’s role is standalone do

update LDM;

check LDM for compatible VRUs;

generate iCM with compatible VRUs;

if iCM size ≥ 2 then

set VRU’s role as cluster leader;

produce initial cluster bounding box;

generate random cluster ID;

include CIC in VAM;

send initial cluster VAM;

else

send standalone VAM;

end

Algorithm 1: Cluster creation decision workﬂow.

the least amount of data elements, being described

by a node center point (C.a) and a radius (C.b). The

ﬁrst element is a tuple of x and y offset distances in

centimeters between the cluster leader and the actual

center of the proposed bounding box. Since the initial

geometry must contain only the leader, the bounding

box is centered on its position, resulting in a node cen-

ter point of (0,0). The radius is given in decimeters

and calculated by dividing d

min

by half, placing the

edge of the shape at a balanced distance between the

leader and the closest compatible VRU.

The leader then adds C.a and C.b to the CIC, start-

ing to send cluster VAMs shortly after. The broad-

cast of the initial shape continues until the cluster cre-

ation is concluded by having at least numCreateClus-

ter members or is interrupted due to an elapsed time

above the timeLeaderWaiting threshold.

After generating the initial cluster VAM, the clus-

ter manager discards the iCM, and an empty mainte-

nance Cluster Map (mCM) is created to store the data

objects of the cluster participant VRUs. The main

difference between these CMs is that the iCM con-

tains a list of all the VRUs that are cluster-compatible

within the LDM, acting as a list of potential members,

while the mCM possesses only valid member VRUs

that have actively sent join VAMs to the leader.

When the mCM has sufﬁcient members (num-

CreateCluster) added through join VAMs, the clus-

ter management enters a maintenance mode and

stops sending the initial cluster VAM. At this point,

the leader must send VAMs every generation time

(T GenVam) with a CIC containing a bounding box

and cardinality representing all its participants. The

manager stays in this state until a breakup occurs due

to insufﬁcient cardinality or other reasons mentioned

in (ETSI, 2021c). The cluster maintenance routine

executed by the leader is described in Algorithm 2.

Data: mCM and received VAMs

Result: Updated cluster

initialization;

while VRU Role is leader do

parse received VAMs;

if VAM’s COC contains cluster ID then

if Operation is Join then

add new VRU to mCM;

update bounding box;

else if Operation is Leave then

remove VRU from mCM;

if mCM size < 3 for over 2 s then

trigger breakup Operation;

include COC to VAM;

set VRU’s role as standalone;

else

update bounding box;

end

include CIC to VAM;

send cluster VAM;

end

Algorithm 2: Cluster maintenance by the leader.

The update bounding box segments of Algorithm

2 vary depending on the chosen shape type. Subsec-

tions 3.2.2, 3.2.3, and 3.2.4 describe the strategies em-

ployed to generate each geometry type. All of these

approaches initiate from the mCM, which serves as

the initial reference point, supplying the positions of

all cluster members. These methods aim to generate

the essential bounding box data elements for the CIC,

as detailed in subsection 2.3.

The use of the Axis Aligned Bounding Box

(AABB) supports the formation of the circle and rect-

angular shapes. This strategy, of time complexity

O(n), uses the cartesian coordinates of the VRUs in

the mCM to determine the lowest-leftmost and the

highest-rightmost VRUs, calling these points min and

max, respectively. These two points describe the min-

imum possible non-rotated rectangular envelope that

covers all the mCM nodes (Ericson, 2004).

3.2.2 Circular Bounding Box

A circular geometry on the VBS needs two data ele-

ments: the node center point C.a and the radius C.b.

The most straightforward strategy to determine the

shape’s center would be to take the average of the

What Is the Right Bounding Box of a VRU Cluster in V2X Communication? How to Form a Good Shape?

149

point cloud coordinates. However, this approach may

result in a radius twice as large as necessary when the

points are not uniformly distributed. Thus, another

method to determine the center of a point cloud is to

ﬁrst create an AABB around it and consider the center

of the resulting geometry as the cloud center (Ericson,

2004). For the circle radius, it is only necessary to de-

termine the distance d

max

between the furthest VRU

of the mCM and the AABB center. The creation of

this box follows Algorithm 3. The time complexity of

this algorithm is also O(n).

Data: mCM

Result: Circle CIC data elements

initialization;

calculate AABB from mCM;

obtain min and max from AABB;

get center C from min and max;

// Get largest distance to center

for each VRU object in mCM do

get current VRU position P;

get distance d

between C and P;

if d

> d

max

then

max

← d

;

end

obtain leader position P

leader

;

C.a ← offset between P

leader

and C;

C.b ← d

max

;

return C.a and C.b;

Algorithm 3: Circular Bounding Box formation.

3.2.3 Rectangular Bounding Box

A rectangular bounding box is described by a node

center point R.a, half-length R.b, half-width R.c, and

orientation R.d. The strategy adopted to build an

orientation-dependent rectangle is to iterate the point

cloud from the mCM at different rotations and gener-

ate an AABB each time, calculating the resulting area

on each step and selecting the smallest (AAABB

min

To obtain the half-length and half-width, the (min,

max) pair from AAABB

min

are used by comparing

the x and y coordinates separately. The process fol-

lows Algorithm 4 and has time complexity O(n).

3.2.4 Polygon Bounding Box

The VBS deﬁnes a Polygon in the CIC through a list

of offsets from one vertice to the next. In this im-

plementation, the VRUs positions from the mCM are

all candidates to form the geometry’s vertices, result-

ing in a max number of 20 (maxClusterSize) offsets.

However, implementing a strategy to select which

points to use is fundamental, as a simple ordered list

with all the candidates could lead to holes and spikes

in the bounding box.

Data: mCM

Result: Rectangle CIC data elements

initialization;

create a point cloud from mCM;

// Get smallest rotated cloud area

for θ within (0, 2π) do

rotate cloud θ counterclockwise;

calculate AABB from rotated cloud;

calculate area A from AABB;

if A < A

min

then

min

← A;

AABB

min

← current AABB;

min

← current θ;

end

increment 0.1 to θ;

end

get min and max from AABB

min

;

R.a ← center from min and max;

R.b ← (max.x − min.x) * 0.5;

R.c ← (max.y − min.y) * 0.5;

R.d ← θ

min

;

return R.a, R.b, R.c, and R.d;

Algorithm 4: Rectangular Bounding Box formation.

To avoid holes and spikes in a polygon, it must be

convex, meaning that all the interior angles must be

under 180 degrees. To ensure convex polygon gen-

eration, a Convex Hull algorithm that implements the

Graham Scan is used (Shamos, 1978). This approach

uses the point cloud from the mCM, ﬁrst searching

for V RU

low

, the single lowest vertical position or the

leftmost if multiple points share the y-lowest position.

It then produces a list by sorting the cloud based on

the polar coordinates related to this reference point.

Next, it iterates the resulting list starting at V RU

low

selecting triplets of consecutive points, with the cen-

tral point as a vertex candidate.

At every loop iteration, it evaluates through a cross

product if the two segments formed between the can-

didate and the neighbor points generate a left (coun-

terclockwise) turn, meaning it has an interior angle

under 180 degrees (Shamos, 1978). If true, the al-

gorithm moves one position down the list and checks

the next triplet. If not, the candidate generates a right

turn or is collinear to its neighbors and should thus

be removed from the list. Next, the selection is back-

tracked in one position, using a previously approved

vertex and checking if, with the new right neighbor

point, it still produces a left turn (Shamos, 1978).

VEHITS 2024 - 10th International Conference on Vehicle Technology and Intelligent Transport Systems

150

The scan, summarized in Algorithm 5, ends when the

list of potential vertices is exhausted, containing only

left turns and with the last segment reaching the ﬁrst

point. The lowest point selection is of time complex-

ity O(n), while the scan is O(n logn).

Data: mCM

Result: Polygon CIC data elements

initialization;

get point list from mCM;

iterate list and get V RU

low

;

// Produce the convex hull

sort list by polar coordinates to V RU

low

;

list starts and ends at V RU

low

;

while right of vertex not VRU

low

get vertex candidate C;

get left L and right R adjacent points;

CL ← (x

− x

, y

− y

);

CR ← (x

− x

, y

− y

);

P ← CL ×CR;

if P > 0 then

keep candidate in the list;

get next candidate;

else

remove candidate from the list;

move to previous vertex;

end

get the list of n ∈ N vertices;

calculate the offset of consecutive vertices;

each offset is assigned to a P.a.n;

return all P.a.n offsets;

Algorithm 5: Polygonal Bounding Box formation.

An example of the resulting bounding boxes ob-

tained from the same set of points by using the strate-

gies from Algorithms 3, 4, and 5 is shown in Fig-

ure 3. In an initial assessment, one can observe that

the three methods can construct shapes that optimally

cover all the points while occupying the smallest pos-

sible area. However, it is noticeable that a circular

shape yields a larger bounding box for the same point

cloud, whereas the rectangle and polygon produce a

more well-ﬁtted perimeter.

4 METRICS DEFINITION

It is necessary to determine parameters to compare the

effects of the different bounding boxes on the VBS.

The main goal is to verify the pros and cons of each

geometry type, enabling the study to draw conclu-

sions on which shape is better suited for each use case.

Figure 3: Different bounding boxes generated with the same

set of points.

In the VBS, since VAMs do not contain the pre-

cise position of every member, a bounding box must

be treated as a solid object by external nodes to avoid

collisions. Thus, it is crucial to refrain from generat-

ing a much larger shape than what is needed to cover

all participants, as boxes might block trafﬁc on seg-

ments of sidewalks or streets. Another potential issue

of excessive size is the overlap of nearby cluster ge-

ometries, which could confuse a VRU about which

cluster to join and a vehicle about how to avoid the

clusters properly. The cluster density

D =

cluster cardinality

bounding box area

(4)

is used to evaluate how well a geometry type covers

its participants without occupying excess space.

As in subsection 2.3, each geometry type implies

a different amount of data elements added to the CIC

of a VAM. A circular bounding box in the VBS takes

two parameters, offering the smallest increase to the

CIC. Polygons, on the other hand, lead to the largest

potential increment in VAM size since they need be-

tween three and twenty offsets to form, depending on

cluster cardinality and the number of vertices selected

by the Convex Hull. As an intermediate option, the

rectangle requires four variables, needing more data

than circles but less than most polygons.

Thus, a method to compare the geometry types

is by evaluating the average VAM size in a simu-

lation scenario. This metric is relevant because, in

a crowded environment, it is particularly relevant to

reduce as much as feasible the message size so that

the sent VAMs contribute less to channel congestion.

Moreover, evaluating the average number of clusters

and the number of operations triggered is relevant to

observe their inﬂuence in the message size and detect

different behaviors caused by each shape type.

5 SIMULATION STACK

To test the presented shaping strategies and compare

the geometries using the metrics deﬁned in Section 4,

What Is the Right Bounding Box of a VRU Cluster in V2X Communication? How to Form a Good Shape?

151

a simulation stack based on trafﬁc and network sim-

ulators was used. The following subsections offer a

brief overview of the tools and setup parameters.

5.1 Trafﬁc Scenario

Simulation of Urban MObility (SUMO) (Lopez et al.,

2018) handles the trafﬁc simulation, being responsi-

ble for generating the trips of pedestrians and vehicles

on a given map. Aiming to create a trafﬁc scenario re-

sembling a real-world application, a crowded pedes-

trian crossing from Ingolstadt (Germany) provided by

InTAS (Lobo et al., 2020) was used. It occupies an

area of roughly 5.082 m

and comprises a pair of two-

way streets, one with 5 lanes, and one with 6. A set of

1,487 pedestrians and 35 vehicles are inserted at ran-

dom instants and coordinates in the simulation. The

steady increase in active actors in the simulated area

produces various clustering opportunities and opera-

tion triggers, also causing a rise in channel occupa-

tion over time. The simulation spans 15 s, processed

in steps of 0.10 s each. At the simulation end, 1,478

pedestrians and 32 vehicles were in the crossing. One

known issue of this tool is that pedestrians do not have

an associated physical size, meaning they are a single

point in the simulation and might overlap.

5.2 Network Simulator

OMNeT++

is a discrete-event network simulator,

with sequential simulation steps. This fact makes

it possible to synchronize OMNeT++ and SUMO

events, establishing a bidirectional ﬂow of data and

commands between the two tools, using TraCI

. Sup-

port for the Access Layers (PHY and MAC) of the

ITS-G5 V2X protocol are provided by INET

During the initial testing of the scenario, DCC

acted to alleviate channel overload caused by a high

volume of simultaneous transmissions from multiple

nodes at the 10-second mark of the simulation. This

timeframe was selected as the warm-up period to en-

sure a comparative analysis of shaping techniques in

a busy channel environment. The triggering of events

on OMNeT++ does not occur at the exact instant in

every run, having an innate probabilistic behavior.

Results originate from the average of simulations us-

ing six different seeds.

https://omnetpp.org

https://sumo.dlr.de/docs/TraCI.html

https://inet.omnetpp.org

5.3 V2X Framework

Regarding the ITS-G5 stack, the messaging protocol

Vanetza

manages the GeoNetworking and DCC fea-

tures. The V2X simulator Artery (Riebl et al., 2015)

handles the Application layer, with the services de-

ployed and managed in each node through middle-

ware modules. This VBS implementation builds upon

the work from Lobo et al. (2023), who ﬁrst introduced

VRU clustering to Artery. This work’s main contribu-

tion is an extension of the framework, introducing the

Cluster Map structure, through which the proposed

bounding box generation techniques are possible.

In every simulation, all present VRUs have the

clustering function enabled and will actively look for

opportunities to interact with existing clusters or cre-

ate new ones. As an introduction to the study of the

impact of geometry types on the service, this work

considers only one shape type per simulation run. So,

for example, there is no scenario in which rectangular

and polygonal bounding boxes coexist. Table 1 con-

tains the parameters of the simulation stack.

Table 1: Simulation parameters.

Parameter Value

Simulated time 15.00 s

Simulation step 0.100 s

Warm-up time 10.00 s

Seeds 0, 23, 42, 1337, 0815, 4711

Trafﬁc model InTAS

Number of actors 1,487 pedestrians, 35 cars

Min. cluster size 3 VRUs

Max. Cluster Size 20 VRUs

Cluster Distance 5 m

Speed Difference 5%

6 RESULTS AND DISCUSSION

The VBS containing clustering functionalities and the

proposed shaping strategies was deployed on the de-

veloped InTAS-based trafﬁc scenario. Simulations

using the stack from Section 5 were executed for the

three distinct bounding box types with six random

seeds. This setup resulted in eighteen simulations,

with the following results being the average values

obtained from each iteration. The parameters mea-

sured are the cluster density and the message size, as

proposed in Section 4.

It can be observed in Figure 4 that circular bound-

ing boxes offer the lowest cluster density values. This

behavior suggests that this shape type needs to occupy

https://www.vanetza.org

VEHITS 2024 - 10th International Conference on Vehicle Technology and Intelligent Transport Systems

152

larger areas to cover the participating nodes of a clus-

ter. The polygon presents the highest density overall,

reaching more than ﬁve times the amount of VRUs

per squared meter as the circle at 12.4 s. The rectan-

gle is the second best, surpassing the polygon brieﬂy

at 11.2 s. These results indicate that both the rectan-

gle and the polygon have better ﬁtness to the original

point cloud when compared to the circle since there

is less area occupied without necessity. These high-

density values are also associated with the limitations

of pedestrian simulations in SUMO since it is unreal-

istic for twelve VRUs to occupy the same squared me-

ter. However, the results should still be interpreted as

an upper bound of the service, illustrating the higher

clustering potential of rectangles and polygons.

Figure 4: Cluster density for each shape.

Moreover, the rectangles and polygons also

present more spikes in the curves, as shown in Figure

4. A possible cause is that the shapes are more sus-

ceptible to sudden cardinality changes as the VRUs

join and leave clusters due to the bounding box be-

ing tighter-ﬁtted around the point cloud. After 12.4

s, there is a noticeable decline in the densities for

the three shape types, which can be associated with

the VRUs drifting apart due to them taking different

routes, resulting in a more sparse point cloud.

Regarding the average message size, Figure 5

shows that the circular bounding boxes offer the

smallest values with an average of about 36.85 bytes,

conﬁrming the assumption that this type yields the

smallest increment to the CIC. Polygons result in

the largest VAM sizes among the geometries and the

highest difference between minimum and maximum

reached values, respectively, 37.35 and 37.67 bytes.

This gap could be associated with polygons being the

only shape type that changes the amount of data el-

ements included in the message depending on each

cluster. As the average cluster cardinality grows due

to more VRUs entering the crossing, the number of

data elements needed also increases. Once again,

rectangles are an intermediate option, with an aver-

age message size larger than circles but smaller than

polygons, standing approximately at 37.05 bytes.

Figure 5: Average message size (left) and average number

of active clusters (right) for each shape.

When observing the number of active clusters af-

ter the DCC starts operating, Figure 5 indicates that

as time passes, the number of clusters present in the

crossing increases similarly for all shape types. This

increase helps explain the rising trend in average mes-

sage size, with varying results based on the increment

that each geometry type adds to the CIC.

Evaluation of these parameters highlights an inter-

esting aspect of the clustering of VRUs on the VBS.

The circular bounding boxes offer the smallest mes-

sage increment and, therefore, are suited for applica-

tions in which channel efﬁciency is desired, with the

drawback that the generated shape has low density.

These characteristics mean that when using circular

bounding boxes, it is hard to determine the position

of the VRUs within the cluster.

Polygons exhibit larger average message sizes,

which escalate along with cardinality. However, they

offer increased cluster density, indicating a better-

ﬁtted resulting geometry. This accuracy improves

safety as it is easier for other road users to avoid col-

liding with the member VRUs described by a poly-

gon. Thus, this shape type is advantageous in less

crowded scenarios where message sizes and channel

occupation are less critical.

Rectangles offer a compromise between circles

and polygons, with the second-best density and mes-

sage size. New metrics can prove fundamental for this

line of study, as further research into the impact of

rectangles on the VBS is necessary to determine use

cases in which this shape type can be beneﬁcial. Some

parameters to evaluate in the future are the position er-

ror among the members, average cluster lifetime, and

rate of VRUs clustered versus non-clustered.

When the average number of cluster creation, join,

leave and breakup events are taken into account, it

can be noted that the shape choice also affects the

clustering dynamics. For instance, Table 2 demon-

strates comparable creation and breakup rates across

all shapes, consistent with the number of active clus-

What Is the Right Bounding Box of a VRU Cluster in V2X Communication? How to Form a Good Shape?

153

ters in Figure 5. Rectangles exhibit more join and

leave occurrences, followed by polygons. This be-

havior ﬁts the assumptions related to the spikes from

Figure 4, that the tight-ﬁtting nature of these shapes

leads to more VRUs entering and leaving a cluster

coverage despite the use of the padding distance d

B f

(Equation 1). Rectangles appear to be especially sus-

ceptible to this issue, probably due to the constraints

that this shape type presents when covering a point

cloud due to its limited number of vertices.

Table 2: Average amount of cluster events per shape type.

Event Circle Rectangle Polygon

Creation 100.333 100.333 102.167

Join 10,325.333 10,477.167 10,373.833

Leave 10,080.833 10,296.833 10,181.667

Breakup 60.167 58.167 60.000

One possible future work is the simulation of the

same scenario with different numbers of actors, test-

ing if, for less crowded use cases, the cluster cre-

ation and operations behave the same. Evaluating

ETSI 103 300’s default values for cluster compati-

bility and message generation times is recommended

since the different VRU types should present very dif-

ferent kinematic behavior.

Moreover, simulating different trafﬁc scenarios

could conﬁrm if different bounding box types are

more suited for particular use cases, leading to the

deﬁnition of parameters to decide which shape to cre-

ate. Another topic to be explored is the overlap of

bounding boxes, as long and frequent occurrences

could indicate a shape is inadequate for a use case

since it could pose a safety or operational issue due

to the region of uncertainty generated by two clusters

occupying the same area.

Even if the average message sizes are distinct,

their maximum difference is an arguably small value

of about one byte. At the same time, many cluster

events occurred on the 5 s of data recorded. There-

fore, more metrics, such as the Channel Busy Ra-

tio (CBR) from the DCC (ETSI, 2015), should also

be used to verify if the geometry choice is signiﬁ-

cant to the channel performance. These parameters

could even lead to a dynamic change of the clustering

parameters and shape type based on the state of the

channel occupation and the current trafﬁc situation.

7 CONCLUSION

This work has extended the VRU Basic Service from

the ITS-G5 standard by introducing the data structure

Cluster Map to assist in clustering. Also, as a con-

tribution, bounding box formation strategies for all

the shape types determined by ETSI TS 103 300 were

suggested, using the Cluster Map and computational

geometry strategies. Summarizing these methods are

Algorithms 3, 4 and 5. Furthermore, this work sug-

gests a new condition to start a cluster breakup trig-

gered by the leader when it detects insufﬁcient cardi-

nality for a determined elapsed time. This condition

assists the VBS by proposing a timeout for an unsuc-

cessful cluster creation event.

This work proposes and uses the cluster density

and average message size parameters to evaluate how

each shape behaves in a crowded trafﬁc use case. The

ﬁrst parameter measures how well a bounding box

uses its coverage space to contain all member VRUs,

which means that a higher density indicates that a

cluster does not occupy much unnecessary space to

protect its participants. Average message size is a

measurement to determine which shapes contribute

the most to channel occupation through their incre-

ment to the CIC.

Those functionalities, shaping methodologies, and

metrics were then implemented computationally in

V2X simulations using the Artery framework, with

the support of the InTAS trafﬁc model simulated

through SUMO. The test scenario contains several

pedestrians in a single crossing, resulting in many op-

portunities to form clusters and interact with other

VRUs and vehicles. Eighteen simulations, six for

each bounding box shape type, were executed.

Simulation results show that circular bounding

boxes are indicated when a use case prioritizes

smaller messages over spatial efﬁciency or shape rep-

resentation accuracy. This performance is adequate

for busy wireless channel scenarios, so reducing con-

gestion is the priority. Polygons are ﬁt for the op-

posite situation, where the VBS can afford to send

larger messages with the beneﬁt of representing the

points contained in the cluster with a tighter, more

detailed bounding box. Rectangles offer moderate

cluster density and message size. Thus, identify-

ing use cases where rectangular bounding boxes are

best suited poses a considerable opportunity for fu-

ture work. Knowing more about the situations in

which each geometry type excels could lead to im-

provements to the VBS as it could, in the future, con-

tain speciﬁc purposes for each shape type.

Additionally, introducing metrics related to chan-

nel performance is a research path that could lead

to new insights into the management of the cluster-

ing operations. For instance, an intriguing investiga-

tion would involve assessing the viability of a spe-

ciﬁc shape type when the channel occupation exceeds

a designated CBR threshold.

VEHITS 2024 - 10th International Conference on Vehicle Technology and Intelligent Transport Systems

154

ACKNOWLEDGEMENTS

The authors would like to acknowledge and thank the

Bayerisches Staatsministerium f

ur Wirtschaft, Lan-

desentwicklung und Energie for partially funding this

work through the ”RealFutuRe” project (DIK-2105-

0051//DIK0281/02).

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