DISTRIBUTED TEAM FORMATION

FOR HUMANOID ROBOT SOCCER

Onuralp Ulusoy and Sanem Sariel-Talay

Department of Computer Engineering, Istanbul Technical University, Istanbul, Turkey

Keywords: RoboCup competitions, Humanoid robot soccer, Team strategy, Multi-robot cooperation, Distributed team

formation.

Abstract: In this paper, we propose an adaptive team formation strategy for humanoid robot soccer. The proposed

strategy involves distributed cooperative decisions through both communication and observations. Two

agent groups, namely defenders and attackers, are formed by a case-based group formation method.

Attackers are formed for constructing an attacking formation around the ball and scoring a goal whenever

possible while defenders are for blocking and constructing a defensive obstacle against the opponent team.

Cooperative decisions are made using communication among team members. Distribution of agents on the

field is ensured by Voronoi cell construction of each agent through observations in a distributed manner.

Experiments are set in the RoboCup 3D Soccer Simulation League environment where our method is

compared to earlier team formation methods. The results illustrate that a distributed Voronoi cell

construction method combined with a case-based grouping algorithm outperforms the others. Furthermore,

it has been shown that our method is also robust to communication failures.

1 INTRODUCTION

RoboCup competitions provide convenient tools to

test and validate multi-agent team strategies.

Specifically, simulation competitions are suitable for

analyzing complicated team strategies in the face of

realistic constraints such as limitations on

observability, communication and teleoperation.

This paper presents a team formation approach for

humanoid soccer teams which deal with both

competition and cooperation issues. Just like real

soccer games, the main objective of a humanoid

soccer team is scoring goals against an opponent

team. Efficiency of cooperation is an important key

factor to win a game. There are mainly two

behaviors which involve cooperation issues, namely,

passing the ball to a teammate or spreading out to

the field of play to gain control of the ball whenever

needed. Both behaviors require agents to be in

appropriate positions to achieve the desired

outcomes. These positions usually belong to special

formations which may dynamically change their

shapes for different situations during a game. The

performance of the overall team is highly dependent

on these adaptive formations and the corresponding

positions of robotic agents. Contrary to human

soccer games, there are not generic formations for

humanoid soccer especially because these are also

dependent on the underlying motion model.

Therefore, the set of mobility constraints of a team

plays an important role in the selection of an

appropriate team strategy.

We propose an adaptive team formation strategy

which can be applied to robot soccer. However, the

focus of this paper is on the RoboCup 3D simulated

humanoid soccer competitions. Our team strategy is

used in the top layer of the software for team

beeStanbul (Asta et al., 2011) for RoboCup 3D

Soccer Simulation League (SSL). Experiments are

set in the RoboCup 3D SSL Environment, Simspark

(Simspark Official Website, 2011). Simspark

provides an environment for multiplayer soccer

games of two competing teams of simulated

autonomous humanoid agents (RoboCup 2011 3D

Simulation League hosted 9 x 9 agent games on a

21x14 m field.). The team scores more goals in a

ten-minute-long match wins the game. Simspark

uses ODE (Open Dynamics Engine) for physical

agent simulation of Nao humanoid robots by

Aldebaran Robotics (Aldebaran Robotics Official

Website, 2011). The real Nao robot has a height of

57 cm, a weight of 4,5 kg and 22 degrees of

605

Ulusoy O. and Sariel-Talay S..

DISTRIBUTED TEAM FORMATION FOR HUMANOID ROBOT SOCCER.

DOI: 10.5220/0003881006050613

In Proceedings of the 4th International Conference on Agents and Artiﬁcial Intelligence (SSIR-2012), pages 605-613

ISBN: 978-989-8425-95-9

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

freedom. The robot is equipped with special sensors

including a gyroscope, an accelerometer and a force

resistance perceptor on each foot. Simspark can

simulate all these features and model some realistic

limitations including sensor and actuator noise. The

simulator also provides limited communication

among robots through special effectors and

perceptors and visual information in the form of

noisy distance and angle values for the objects in the

viewpoint of agents.

Some rules of humanoid soccer are different

from real soccer due to the limitations of mobility of

agents. At present, fouls are not penalized in the

RoboCup 3D SSL but crowding the ball. According

to the crowding rule, at most two players are

allowed to be in the 0.8 m radius circle around the

ball; only a single player from a team in a circle with

a radius of 0.4 m and at most two teammates in a

circle with a radius of 1 m. Failure to comply with

either of these rules results in a repositioning of an

agent out of the field. All these rules should be taken

into account in the team strategy for avoiding any

penalties.

Our proposed approach considers the mentioned

rules to escape from penalties. According to our

strategy, robots can be in four different roles,

namely, goalkeeper, defender, midfielder and

forward. Forward and goalkeeper roles have their

own planners. Midfielder and defender roles share

the same planner but they differ in positioning on the

field. Goalkeeper is a static role which is assigned to

an agent for the entire match. The forward role is

assigned dynamically based on a voting mechanism

through communication. Each agent sends its time

cost to be able to control the ball and determine

whether it can be in the forward role based on the

information from the incoming messages and a self-

calculation.

Two groups (attackers and defenders) are formed

with a case-based group formation method and the

remaining roles are assigned based on the messages

from the team’s captain (goalkeeper is selected as

the captain due to its widest viewpoint). When there

is a failure in communication, agents decide on their

roles based on only observations.

The attackers group involves the forward agent

and the midfielders. Attackers usually target to

control the ball and score a goal, while defenders

prevent the opponent from scoring. Team formation

is shaped by the positions of defender or midfielder

agents. These agents calculate their next positions

based on a distributed Voronoi cell construction

which is the main contribution of this work. Voronoi

cell decomposition method is previously applied to

robot soccer. However, our method differs from

earlier work in the construction of cells both as the

calculation and the way the overall diagram is

formed. First, there is no supervision of cell

construction which is performed in a completely

distributed manner. Second, our method neither

relies on communication nor need a high

communication bandwidth among agents. However,

if communication is available, this channel is also

used to improve the solution quality. Since the

approach is not heavily dependent on explicit

communication, failures in communication could

also be handled. This feature is especially useful in

real-world settings. Another contribution of our

method lies in the automatic online determination of

targets for agents. Therefore, there is no need to

previously determine special formations.

This paper’s structure is as follows: Section 2

reviews earlier work in the field. Section 3 presents

the main team strategy for robotic soccer games and

the proposed procedures: the case-based group

formation approach and the distributed adaptive

formation. Experimental results and performance

analysis of the approach in terms of ball possession

ratio and use of communication are presented in

Section 4. Finally, Section 5 concludes the paper.

2 RELATED WORK

Dynamic team formation problem has been

investigated in earlier work for both humanitarian

and military applications (Balch and Arkin, 2000;

Stone and Veloso, 1999). Successful results of these

works have been used in RoboCup environments as

well (Candea, Hu, Iocchi, Nardi and Piaggio, 2011;

Nair, Tambe and Marsella, 2003; Röfer, 2003).

Multirobot coordination approaches used in

RoboCup environments mostly rely on continuous

communication among agents. However, RoboCup

3D SSL doesn’t provide a supervisor and

communication among agents is limited.

Several team formation algorithms were applied

in RoboCup soccer competitions (Dashti et al., 2006;

Nakanishi, Murakami and Naruse, 2008; Reis, Lau

and Oliviera, 2001; Ros, Arcos, de Mantaras and

Veloso, 2009). Dashti et al. (2006) use Voronoi cells

to position and distribute players in the field for

RoboCup 2D SSL. With this method, each agent

calculates its own Voronoi cell and moves to the

center of its own cell. Dynamically calculating the

cells ensures the agents to scatter throughout the

field. After the distribution is achieved, agents move

to better positions by attraction vectors and calculate

ICAART 2012 - International Conference on Agents and Artificial Intelligence

606

their Voronoi cells dynamically to be distributed in

the field again. Even though this method is efficient

for fast-moving 2D soccer agents, slower humanoid

agents in 3D SSL should maintain proximity to each

other in order to gain control of the ball quickly

when it is lost. Therefore, distributing the agents

throughout the field may not result in the desired

outcome in 3D SSL.

Nakanishi et al. (2008) propose Dominant

Region (DR) diagrams to create a formation. DR

diagrams look like Voronoi diagrams, but the

required calculation is based on the arrival time of

all agents to their future positions. Each agent forms

its region based on an area where it can reach to

faster than its teammates. Players can move in their

regions in order to be positioned on the field. With

this approach, the agent which is closest to the ball

approaches to the ball and the others can follow it

while staying in their dominant regions. This method

can be useful in 3D humanoid soccer but needs a

supervisor or a high communication bandwidth

among the agents to calculate a general DR diagram.

Therefore, it may not be suitable for environments

with limited communication.

Situation Based Strategic Positioning (SBSP)

(Reis et al., 2001) is another team formation

approach which uses game information including the

current position of the agent and its current role, the

selected formation for the team and the positions of

others. Maintaining this information, agents move to

their positions according to their roles. This method

requires dynamically assigning roles to the agents

during the game. SBSP suffers from a complicated

rule-based algorithm to reach a final formation in

non-deterministic and noisy environments like

RoboCup 3D SSL due to the computation

requirements.

Forming groups in the team usually results in

better team performance. Ayanian, Kumar and

Koditschek (2011) introduce a method which

coordinates the agents within each group by explicit

communication. Forming groups with optimal

number of agents can prevent unnecessary crowds.

Therefore, agents in different groups can achieve

multiple tasks which might help completing those

tasks faster. While inter-group communication is

kept limited, intra group communication demands

are high.

Ros et al. (2009) propose a Case-Based

Reasoning (CBR) method to position the agents.

Cases represent both the action sequences and the

formations by keeping the game situations including

positions of the agents, game time, current score etc.

CBR is an applicable formation method but in some

of the CBR methods, the cases should be hand-

coded before and usually the number of them is

limited. Some of the CBR approaches update their

case libraries in runtime to modify cases but this is a

costly process.

Our approach uses Voronoi cell decomposition

as in Dashti et al. (2006) but differs from this

approach by its initial frame construction and its

adaptability based on the ball location. The objective

is not spreading out all players on the field but

constructing a formation around the ball to easily

possess it whenever possible.

3 DISTRIBUTED TEAM

STRATEGY

The proposed distributed team formation strategy

involves four sequential processes to determine a

target for an agent. Figure 1 presents the main

modules for the team strategy. Initially two groups,

namely attackers and defenders, are formed by using

a Case-Based group formation strategy (Aamodt and

Plaza, 1994). The role of each agent is determined

based on these groups. The attackers group involves

the forward and the midfielder agents while the

defenders group involves only the defender agents.

Our adaptive formation method relies on the

construction of Voronoi cells, which are generated

distinctly by each agent that has the role of

midfielder or defender. The centers of these cells

form the initial targets for these agents. Target

locations are finalized by applying Potential Fields

Method (Arkin, 1998) for obstacle avoidance and

path planning. Because controlling the ball is crucial

in soccer, its location is used in cell initialization and

forming groups. All agents except goalkeeper

continuously send their time costs to control the ball

and they decide on the forward agent role according

to the incoming cost information and a self-

calculation.

The Partial Fourier Series (PFS) model is used as

the motion model for our RoboCup 3D SSL

beeStanbul team software (Asta and Sariel-Talay,

2011). Different types of body motions, including

straight walks (forward, back, diagonal and side

walk), inward turn, outward turn, rotate, kick and

stand-up are available for agents. Based on the

assigned role of an agent, the corresponding planner

is activated. Each plan has a set of behaviors which

activate a set of motions. Figure 2 shows the

decomposition of an example plan (dribble-to-goal)

for an agent that has the forward role.

DISTRIBUTED TEAM FORMATION FOR HUMANOID ROBOT SOCCER

607

Figure 1: General structure of the distributed team

formation method.

As described in Section 1, goalkeeper positions

itself around the defense area regardless of the team

formation. The forward agent (i.e., the closest agent

to the ball) always targets to possess the ball. While

goalkeeper is a static role assigned to an agent, the

remaining agents switch between the other roles

according to their time costs to reach to the ball.

Figure 2: The decomposition of an example plan for an

agent that has the forward role. Lower level components

are hierarchically activated by selection at a higher level.

At the lowest level, primitive actions are selected and the

corresponding motion commands are sent to the server.

3.1 Case-based Group Formation

The current setup of the RoboCup 3D SSL involves

nine team players in each team. A single player is

assigned to the goalkeeper role. Our strategy divides

the rest of the team into two groups, namely,

defenders and attackers, for offensive and defensive

strategies. Attackers are formed for constructing an

attacking formation around the ball and scoring a

goal whenever possible. This group involves the

forward agent and the midfielders which usually

target to control the ball and score a goal. Defenders

are formed for blocking and constructing a defensive

obstacle against the opponent team. This strategy

prevents the opponent team from scoring.

We use a case-based group formation method

(Aamodt and Plaza, 1994) to determine the number

of defender agents and midfielder agents

dynamically. Since two agents are assigned to the

goalkeeper and the forward roles, the remaining

seven agents are to be assigned to these roles.

Instead of using a predetermined number for these

roles, a case-based method is applied to determine

the best separation.

The current game score and the positions of

agents and the ball are considered in the problem

description of cases. The general structure of cases is

shown in (1). Each case corresponds to a certain

number of agents for defenders and midfielders. For

example, if the team is losing in the middle of the

game, more players could be assigned as midfielders

to tie the game with more attacker agents while

taking the risk of conceding a goal.

 = { , ,



 , ,

  }

(1)

The case library initially involves 12

predetermined cases which are allowed to be

modified in runtime according to the success of

applying them.

The maximum bandwidth for RoboCup 3D SSL

agents is 20 B for each cycle which can be used by a

single agent. This communication channel can be

used by a single agent to send role assignments for

group formations. We have selected the goalkeeper

as the captain of the team because it has the widest

line of sight of the field. The time period to

communicate is shared effectively by each agent.

The goalkeeper is responsible to send group

formation messages according to the results of the

case-based grouping method while other agents send

their costs to reach at the ball position. If agents fail

to communicate with each other, they behave

according to their field knowledge and observations.

Figure 3 shows each agent’s role selection

strategy and its decision for joining to a group. The

agent that is closest to the ball assigns itself the

forward role and directly looks for ball possession to

score against the opponent. The other agents in the

ICAART 2012 - International Conference on Agents and Artificial Intelligence

608

attackers group take midfielder role and follow the

forward agent in a close proximity for handling

passes or failures. The defenders position themselves

at a distance behind the ball to defend the goal.

Goalkeeper continuously sends the ball position and

the numbers of the teammates that are going to be in

attackers group according to the case-based

grouping method. If a player hears its number in the

latest message string, it positions itself as one of the

attackers. Otherwise, it takes the defender role. If

the goalkeeper fails to send messages to the others

due to falling down or any other reason, it sends a

failure message to inform them. If the other players

don’t hear any messages or hear the failure message,

they act on their behalf through observation. In this

case, five players closest to the ball assign

themselves the attackers group and three players the

defenders group in a static manner. If a player

observes five teammates that are closer to the ball

than itself, it acts like a defender and uses a

defensive Voronoi cell calculation method. In the

opposite situation, it acts as either the forward agent

or a midfielder agent. Midfielder agents calculate

Voronoi cells to determine their targets while the

forward agent directly targets the ball.

Figure 3: FSM for agents’ group formation behavior

according to the team captain messages or observations.

: i

lowest Euclidean distance between the ball and the

agents in the viewpoint, d: Euclidean distance between the

agent and the ball, k: the maximum number of attackers.

3.2 Target Selection by Adaptive

Voronoi Cell Construction

The midfielder and defender agents need to position

themselves for maintaining close proximity to the

forward agent and defending the goal respectively.

This is accomplished by a distributed Voronoi cell

construction approach in which each agent

calculates its own cell independent from that of the

others. Therefore, every agent has a different shaped

cell and these can overlap.

In conventional Voronoi diagram computation,

Fortune Algorithm (FA) (de Berg, van Kreveld,

Overmars, and Schwarzkopf, 2000) is used. Our

approach differs from FA in the construction of the

final cell. The initial cell is constructed by

considering the ball location and then, iteratively

narrowed down to get the final cell for the agent. In

FA, the lines that construct the cells are

perpendicular bisectors of the line segment between

teammate locations. In our approach, a line from the

corresponding teammate position parallel to the

perpendicular bisector is used. The main procedure

for our distributed cell construction approach for

each agent is given in Algorithm 1.

After constructing the cell for itself, each agent

determines the center of the cell as its new target.

Agents become closer to each other by using this

strategy, which is more beneficial for attacking in

soccer. However, RoboCup 3D SSL league have

some rules to prevent crowding an area with

multiple agents. According to these rules, a player is

repositioned out of the field if it is in a circle that has

a radius of 1 meter with two other teammate players.

In order to overcome the situation where there is a

teammate closer than 2 m, the cell is adjusted to

keep at least 1 m distance from that teammate.

Applying these alterations on the construction of a

cell, the distance to any teammate is guaranteed to

be greater than 1 m. In RoboCup 3D SSL, each

agent has a 120 degrees angle of view. Therefore,

agents only consider the positions of teammates they

can see and the ball’s last seen position to construct

their Voronoi cells. Euclidean distance is used for

distance calculations. (2) shows the distance formula

for two coordinates (A(x

), B(x

)) that is used in

Algorithm 1.



(

, 

)



(



−



)



+(



−



)



(2)

Algorithm 1: Voronoi cell construction for agent a

Input:

: the ball’s last seen position (b

)

: the current position of a

)

: the midpoint of the team’s goal line

: the initial cell start point

l: the distance limit for cell initialization (4 m)

m: the distance limit for the crowding rule (2 m)

Output:

cell

: the Voronoi cell for a

the center of

cell

: target destination of a

DISTRIBUTED TEAM FORMATION FOR HUMANOID ROBOT SOCCER

609

: Line between L

and L

: Slope of L

if agent = midfielder

= P

end if

if agent = defender

= (P

+ P

)/2

end if

: Line between P

and P

= P

, L

= P

)

: Line between L

and L

where

1 ⊥

), P

∈L



(





,



)

=



(





,



)

=

(





,



)

=/2

: Line between L

and L

where (L

2 ⊥

)

, P

∈L



(





,



)

=



(





,



)

=

(





,



)

=/2

: Line between L

and L

, where m

= m

: Line between L

and L

, where m

= m

create cell

which is the enclosed area between the

intersection points of L

, L

and L

for all teammates (a

≠ a

) in point of view

p: Coordinate to draw line according to a

: Line between P

and P

if 

(





,



)

>

p = P

else if 

(





,



)

≤/2

p = x where x ∈ L

, 

(

,



)

=/2

else

p = x where x ∈ L

, 

(

,



)

=

(





,



)

– /2

end if

create line L where p∈L, (L

⊥

)

if L intersects cell

//L divides cell

into 2 cells: cell

and cell

cell

= cell

(j ∈{1,2}andP

∈cell

)

end if

end for

calculate center coordinate of cell

(c)

calculate t

by altering c according to obstacles using

Potential Fields

Algorithm 1 is used for both midfielders and

defenders. Defenders create their cells with the same

algorithm, but their initial cell is calculated

according to the midpoint of the line connecting the

ball position and the center of the team’s goal

position while midfielders use the ball location.

The time complexity of the algorithm is O(n

)

where n is the number of agents in the team. Figure

4 shows the iterations for calculating the final cell

and the corresponding target as the center of this cell

for agent #2 (a

), which is a midfielder and draws its

initial cell according to the ball position. As

mentioned before, only teammates in the viewpoint

(a) (b)

Figure 4: Step-by-step calculation of the Voronoi cell for

. (a) construction of the initial cell according to the ball

position, (b) cell iteration due to the intersections with a

, (d) the

final cell for a

. The corresponding target position is

marked with a red point.

of the agent are considered. The area that is out of

’s point of view is shown as the shaded area.

Figure 4 (a) shows the initial cell construction by

considering the ball position (P

). In Figure 4 (b),

(c), and (d), the cell is modified according to the

locations of a

, a

and a

, respectively. The line

for a

doesn’t have any intersection points with the

current cell, so it doesn’t make any changes in the

cell. The final Voronoi cell of a

is shown with the

red frame and the center of that cell is marked with a

red point in Figure. 4 (d).

Agents continually form their Voronoi cells and

move toward their targets. Due to the distributed

calculation of cells, a complete diagram is not

formed. Cells of different agents may overlap in

some situations, but the relevant precautions taken to

overcome the crowding rule and the Potential Fields

Method ensures that the targets are not too close to

ICAART 2012 - International Conference on Agents and Artificial Intelligence

610

each other. This approach also protects agents from

collusions.

4 EXPERIMENTAL RESULTS

Two sets of experiments are set to analyze the

performance of our proposed team strategy.

rcssserver3d is used for the simulation, which is the

official server software for RoboCup 3D SSL

competitions and RoboViz (Stoecker and Visser,

2011) as a visualization tool.

In soccer game, keeping possession of the ball is

one of the key factors for scoring a goal. Our first

experiment targets to analyze this issue and the

average position of the ball in the field. Ball position

fields are determined by dividing the 21 x 14 m field

horizontally into 3 equal areas (defense, midfield and

forward) each 7 x 14 m. The area next to the team’s

goal is called the defense area, the area next to the

opponent’s goal is called the forward area and the

area between these two fields is the midfield area.

The proposed method is compared to our earlier

method Situation Based Strategic Positioning

(SBSP) that we used in RoboCup German Open

2011 competitions, our previous Voronoi cell based

method which uses a static grouping strategy instead

of case-based grouping and DPVC method (Dashti

et al., 2006). In DPVC, Voronoi cells are used to

scatter the agents throughout the field. In SBSP,

each agent has a predetermined role and they shape

formations according to predefined positions around

the ball based on their roles. All the approaches are

applied on the latest motion model of our team.

RoboCup 2011 binary of Nao Team Humboldt

(Burkhard et al., 2011)

is used as an opponent because

the motion model of Nao Team Humboldt

is close in

speed to that of our PFS model. Also Nao Team

Humboldt

has a successful defensive team formation

which blocks the opponent. We run 10 games for

each method against Nao Team Humboldt. A

snapshot is shown in Figure 5 from an instance

during these games where the blue agents are from

beeStanbul team and the red agents from Nao Team

Humboldt. This figure also illustrates the Voronoi

cell of each midfielder agent in beeStanbul. The

agent closest to the ball assigns itself the forward

role while the rest of them are assigned to the

midfielder role in the attackers group. As can be

seen from the figure, the Voronoi cells of

midfielders may overlap as it is allowed. However,

target positions as the centers of these cells are

always different if agents see each other.

Table 1 shows the overall results of all methods.

These results illustrate that, the new approach

outperforms our previous approaches and DPVC in

terms of ball possession, keeping control of the ball

and carrying the ball to the opponent’s area. Our

previous approach that uses Voronoi cells combined

with a static grouping method also gives good

results but using a case-based method for grouping

further improves the overall performance. According

to these results, the key factors for the success of the

proposed team strategy can be listed as the

distributed online construction of Voronoi cells and

dynamic positioning to the centers of these cells.

Even when the forward agent falls over during an

attack, by this approach, midfielders maintain close

proximity with the forward agent and regain control

of the ball. Communication is also used to

dynamically form attacker and defender groups.

Another advantage of the new approach is the

unpredictability of the team strategy as a competitive

strategy. There are not fixed formations that can be

learned and predicted by the opponent during a

game.

Figure 5: An instance from a game using rcssserver3d of

Simspark for simulation and RoboViz for the visualization.

Blue polygons indicate the cells of the agents and red

circles indicate their centers.

As expected, the performance of DPVC is better

than that of SBSP in terms of carrying the ball to the

opponent’s area due to the dynamism. In SBSP, on

the other hand, predetermined formations are easy to

be predicted by the opponent in a later time step

during the game. However, ball possession

performance of DPVC is worse than that of SBSP

because it scatters the agents throughout the field. In

that case, if the motion model of the agents is not

fast enough, they may not responsively regain the

control of the ball when it is lost.

DISTRIBUTED TEAM FORMATION FOR HUMANOID ROBOT SOCCER

611

Table 1: Comparison among the methods used in beeStanbul team software against Nao Team Humboldt in terms of ball

possession and ball position.

Distributed Voronoi

Approach with case-

based grouping

Distributed Voronoi

Approach with static

grouping

DPVC SBSP

Ball Possession

Ratio

53.23177%

(σ = 0.04441)

52.92768%

(σ = 0.08248)

47.83140%

(σ = 0.07796)

50.45958%

(σ = 0.06877)

Ball in Own

Area

15.95018%

(σ = 0.04423)

17.11815%

(σ = 0.11013)

27.76341%

(σ = 0.13851)

37.04670%

(σ = 0.18277)

Ball in Midfield

37.48712%

(σ = 0.08912)

38.37606%

(σ = 0.14637)

31.74228%

(σ = 0.11037)

33.22326%

(σ = 0.10827)

Ball in

Opponent Area

46.56270%

(σ = 0.11047)

44.50579%

(σ = 0.18259)

40.49431%

(σ = 0.13937)

29.73004%

(σ = 0.24710)

(a) (b)

Figure 6: Test results for each message loss rate presented as the averages of 5 games against Nao Team Humboldt. (a)

Average goal difference (positive values show the scores in favor of our team) (b) Average ball possession ratio of our

team.

In the second set of experiments, we measure the

performance of our method for different message

loss rates. In rcssserver3d, a team is allowed to send

a message periodically in 0.06 seconds. In our

current implementation, we use all the available

messaging periods in order to perform better. In this

experiment, we manually switched off

communication based on the message loss rate to

simulate communication failure. The reported results

indicate that our method is robust to communication

failures for most of the instances. Even for no

communication cases, agents can still make

decisions and calculate their Voronoi cells based on

observations and they position themselves to

appropriate target locations for maintaining an

efficient formation. This is achieved by the

distributed implementation of Voronoi cell

construction. However, as expected, ball possession

performance is degraded gradually with the worst

value 47.7%.

5 CONCLUSION AND FUTURE

WORK

We have presented an adaptive team formation

method for RoboCup 3D SSL. Our proposed

Voronoi Diagram based formation generation

method requires less computational cost than the

standard Voronoi Diagram generation. The ball

position is also taken into account during these

calculations. We combined our Adaptive Voronoi

Diagram with a Case-Based group formation method

controlled by an agent (i.e., goalkeeper) through

explicit communication. The agents are divided into

-2

-1

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Goal Difference

Message Loss Rate

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Ball Possession Ratio

Message Loss Rate

ICAART 2012 - International Conference on Agents and Artificial Intelligence

612

defender and attacker groups according to this

agent’s messages. We compared our method against

our previous Voronoi cell approach that is combined

with a static group formation algorithm, and earlier

methods. The results illustrate that the new approach

outperforms the other approaches. In our future

work, we plan to change the team leader to

determine the group behaviors dynamically in run

time. In order to provide a better formation, we plan

to assign the captain role to the agent that has the

best angle of view on the field dynamically.

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