Analysis of Multi-Robot Cooperation using Voronoi Diagrams

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1 Δεκ 2013 (πριν από 3 χρόνια και 11 μήνες)

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Analysis of Multi
-
Robot Cooperation
using Voronoi Diagrams


This paper presents an analysis of using voronoi diagrams for simulated 2D soccer game play on FIRA.
The writer built a spatial model and used voronoi

diagrams rather than cellular automata to process
video data for space
-
time possession analysis. The paper focusses on not only examining victory
conditions but searching for relationships which exist throughout the game.

I. INTRODUCTION


The paper descri
bes the usual human behavior where humans, being part of a small autonomous team
or large hierarchical organizations are capable of forming both practical work groups to undertake tasks
on the spur of the moment and coordinate by committee to plan for futu
re events. It further explains
the endeavor to achieve the same complex relationships to create robotic teams that are capable of a
wider variety of tasks and more effective operation.

The objective is defined as, how can we get robots to plan, divide work
load, coordinate, and interact to
make teams more capable than the sum of their parts?

This objective is explored further in the field of playing soccer and the writer explains that teams are
reaching a stage where there are diminishing returns in having t
he fastest robots, highest resolution
vision system, or most accurate control algorithms. There is a need for robots to use teamwork to win.

It explains that football provides an excellent foundation to investigate challenges of implementing
cooperation by

encompassing traditional problems associated with multi
-
robot research, such as
machine vision, communication, task allocation and planning, but does so in a highly dynamic and
competitive environment.

A. Microsoft Robot Football

Microsoft Robot Football
is regulated under FIRA. This paper focuses on the 11
-
a
-
side competition.

Robots are identified by color patch on their top sides, and controlled remotely from a PC. The vision
system identifies the position and orientation of each robot, and the position
of the ball, and passes this
information to the strategy software, which calculates the actions of each robot and broadcasts them
via a radio link.

Strategies in Microsoft Robot Football are currently based on hierarchical roles, plays and strategies.

Any
apparent cooperation is usually short lived and the effect of a pre
-
programmed set piece, such as a
kick off, where robots might be issued with a set sequence of passes and moves. At other times, players
tend to work collaboratively, working towards the sa
me goal, and supporting one another, but there is
no explicit cooperation between them. Each player, in this case, is usually only a back up in case a player
goes foul.

B. Multi
-
Agent Architectures

This section outlines three popular cooperative task alloc
ation schemes:



Auctions and markets

-

based on the contract net protocol. An auctioneer agent broadcasts a
task for execution. Each agent makes a bid for that task based on its estimated costs. By holding
a number of rounds of auction, a near optimal solut
ion can be found. In some systems it is
possible to sub
-
auction tasks.



Voting
-

each agent votes on which task it should perform based on it's perception of the
situation and it's abilities.



Motivation

-

agents are motivated by concepts such as impatience
and acquiescence. If an agent
spends too long doing a task, another agent will take over or if one fails over repeatedly to
perform a task and can sense failure, it will retire.

The second problem is cooperative task execution and this section introduces t
he following:



Behavior exchange

-

the sensors of one robot cause motors on another robot to act.



Leader follower

-

one agent becomes leader and delegates tasks to other team members for
cooperative execution.



Markets

-

similar to the auctions scheme for ta
sk allocation but uses shorter duration tasks and
hold auctions more frequently. Works well for loosely coupled jobs.

The above mentioned schemes appear trivial to implement, however, the major issue is not figuring out
how to implement them, it is about h
ow to translate a complex problem so that these schemes can
work. An example of a complex scheme is to move the object BALL to point GOAL while avoiding
OPPOSITION. The term 'avoiding' adds complexity to the task.

The paper discusses and describes experime
nts in representing the tasks of robot soccer at a team level
by analyzing the spatial distribution of agents using Voronoi diagrams.

C. Spatial Awareness and Perception

The section describes how human footballers train in set piece (dead ball) situations
and can then
generalize their learning to actual game play. The important factor here is that humans are aware of
their environment and surroundings and do not require direct or explicit input from their sensors. They
can also reconstruct the playing field

using partial information fairly accurately. These are some of the
challenges faced by robots as such skills are not present in them.

Another important tactic in actual football is to force the opponent into a disadvantageous position,
such as making a fa
lse run, looking at the wrong player while passing the ball to someone else, etc.
These weaknesses are also not present in non
-
human opponents and therefore cannot be leveraged in
game play.

II. THE SPACE
-
TIME POSSESSION GAME

The writer had previously work
ed on a concept of spatial representation from football by creating a
space
-
time possession game, a cellular automata in which two teams of agents competed to control
space on a 2
-
dimensional pitch. The pitch is divided into cells, each of which is owned b
y the closest
agent and therefore, the agent’s team. By outmaneuvering the opponent, the teams tried to control a
larger area on the pitch. Experiments and results from this work showed that teams that had
cooperating agents outperformed the ones that didn
’t have cooperating agents.

As the size of the pitch increased, the complexity of calculating cells increased. This also had a direct
relation with the camera resolution in use. The writer needed to come up with some other mechanism
that didn’t require vis
ual data from camera for faster computations. To solve this, the writer used
Voronoi diagram.

A. The Voronoi Diagram

The following figure shows a bounded Voronoi diagram where each ‘+’ is a player on the pitch.

Since the Voronoi
diagram is calculated
dire
ctly from the
positions of players, it
is much more efficient
in segmenting large
areas than the cellular
automata, which
analyses the empty
spaces.

The complexity of
Voronoi diagram
increases with the
number of players,
since there are smaller
number of p
layers (at
most 22) as compared
to the available space
on the pitch, it makes
the computations
faster and straight forward.

The writer ran an experiment and compared the run
-
time for both
v
oronoi diagram based as well as
c
ellular
automata based games and s
howed that the latter’s run
-
time increased exponentially. It is
further established that
analyzing one video frame using voronoi diagram based technique can be done
at 43 fps which is higher than the actual video frame rate (30 fps).

III. ROBOCUP SIMULATIO
N LEAGUE ANALYSIS

Using the model constructed earlier, the writer examined the dynamics of team space during a match.
The aim was to find out whether there is a relationship between the distribution of team space and the
states of play during a match.

The
writer mentions a similar work done earlier by S. Kim, “Voronoi Analysis of a Soccer Game”
. Kim
examined player space with relation to victory conditions in a simulation of real football. He concluded
that to win, a team did not necessarily have to control

the largest area on average during the game, but
that in order to score a goal, a team did need to be in control of a larger area of pitch at that moment.


The writer based their tests on data from the RoboCup simulation league. In this league, teams of 1
1
agents compete in a simulated environment. The simulator logs information about the agents and the
ball, for every match played. Using possession game, seven different matches representing a variety of
winning conditions were examined. Observations were
made changes in team space, player space, goals
scored and the ball position during game play.

A. Team Space Analysis

Measurements were recorded for the amount of pitch owned by either team in each of the seven
matches and compared with average ownership t
o the number of goals scored. The results from the
paper are reproduced below:

Match

Score (A
-
B)

Average team possession
as % of pitch

A B

Average
possession
difference

Maximum team
possession as % of pitch

A B

1

0


0

44⸸9

55⸱1

10⸲2

74⸴2

78⸵0

2

10


0

51⸷3

48⸲7

3⸴.

71⸵4

78⸵9

3

1


2

48⸳9

51⸶1

3⸲.

75⸴1

75⸸6

4

0


0

54⸴8

45⸵2

8⸹.

74⸹5

79⸱3

5

0


6

42⸱4

57⸸6

15⸷2

76⸰1

79⸰7

6

4


3

54⸲3

45⸷7

8⸴.

80⸳6

74⸶8

7

3


0

51⸲8

48⸷2

2⸵.

76⸷6

74⸸1

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Further research was conducted on Match 5 by analyzing the change in possessio
n. Monitoring key
events such as an intercepted pass, relationships between the definition of team space and the changing
game state were established. The following figure shows how Team A controlled specific quantities of
pitch.

The total area of the pit
ch is 7140 units and
Team A controls a small portion of it around
2500 units. The low ownership is reflected by
Team B being in possession of the ball for
78% of the match and Team A playing
defensively. Possession scores of 3600
(about half of the pitch)
is an effect of the
time spent in kickoff position after each goal
is scored and is not a representation that
Team A had influence on the pitch.

It was also observed that larger team spaces
usually correspond to attacking game plays
and smaller ones to def
ensive ones. In terms
of spatial configurations, larger team spaces facilitates easier passing and movements to intercept stray
balls which helps in build up for attacking game play. In contrast, smaller team spaces indicate tight
configurations better sui
ted to protect specific small areas, intercept passes through and shots in that
region.

However, from the data recorded it is not conclusive that larger team spaces would mean that a team in
on attack alone. The team must also be in possession of the ball.

B. Movement of the Ball

The relationship between team space and ball position was examined. In the figure below, positive
values indicate more control exerted by Team A, and negative values indicate increased control by Team
B. The plot of ball x
-
positio
n has been rescaled in amplitude, but has not been altered frame wise. The x
-
axis of ball position is defined as the line passing
through the center of both goal mouths.

A relationship can be seen between the two plots,
with both having similar major featu
res. These
features appear in close phase to one another with a
difference varying between 20 to 30 frames. This
relationship
is evident in all of the seven matches.

The experiments indicate that once a team has
possession of the ball, it adopts a broad sp
atial
configuration, which facilitates passing and safe
movement about the pitch.