INTERFERENCE REDUCTION THROUGH TASK PARTITIONING

IN A ROBOTIC SWARM

Or: “Don’t you Step on My Blue Suede Shoes!”

Giovanni Pini, Arne Brutschy, Mauro Birattari and Marco Dorigo

IRIDIA, CoDE, Universit

e Libre de Bruxelles, Brussels, Belgium

Keywords:

Swarm robotics, Foraging, Self-organized task allocation, Task partitioning, Swarm intelligence.

Abstract:

This article studies the use of task partitioning as a way to reduce interference in a spatially constrained

harvesting task. Interference is one of the key problems in large cooperating groups. We present a simple

method to allocate individuals of a robotic swarm to a partitioned task, and show that task partitioning can

increase system performance by reducing sources of interference. The method is experimentally studied, both

in an environment with a narrow area and an environment without this constraint. The results are analyzed

and compared to the case in which task partitioning is not employed.

1 INTRODUCTION

In collective robotics, interference is a critical prob-

lem limiting the growth of a group: the time each

robot spends in non-task-relevant behaviors such as

obstacle avoidance increases when the density of indi-

viduals rises—see e.g., (Lerman and Galstyan, 2002).

The performance on tasks that suffer from physical

interference can typically be improved by spatial par-

titioning; for example, by keeping each robot in its

own “working area”. A known approach that uses this

rationale is the so called bucket-brigade (Font

an and

Matari

c, 1996; Shell and Matari

c, 2006). In this ap-

proach, robots hand over objects to robots working in

the following area, until the objects reach their des-

tination. As tasks usually cannot be partitioned ar-

bitrarily, this approach effectively limits the number

of robots that can be employed in the task. A pos-

sible solution to this problem, treating working areas

as non-exclusive, raises other problems: How should

individuals be allocated to tasks? How can such an al-

location help in limiting the amount of interference?

In this paper, we study how task partitioning can

help in reducing sources of interference. Additionally,

we show a simple way to achieve self-organized allo-

cation to such a task partition when using a robotic

swarm.

We use the foraging problem, one of the canon-

ical testbeds for collective robotics, as a base for

our studies. In our experiments, a swarm of homo-

geneous robots has to harvest prey objects from a

source area and transport them to a home area. In

this study, we limit ourselves to a harvesting task that

is pre-partitioned by the designer into two subtasks

with a sequential interdependency. We study a sim-

ple threshold-based model of self-organized alloca-

tion and focus on two questions: Under which en-

vironmental conditions is it advantageous to partition

the task? Can this partition reduce interference be-

tween group members? These questions are studied

in two experiments using a simulated robot swarm.

The paper is organized as follows. We ﬁrst review

related works in Section 2. In Section 3 we explain the

task partitioning and the allocation method employed

in this study. Section 4 gives the methods used in the

experiments by describing the environments, the sim-

ulated robots, and the controller. In Section 5 the re-

sults of the experiments are given and discussed. Sec-

tion 6 draws some conclusions and discusses future

work.

2 RELATED WORK

Interference has long been acknowledged as being

one of the key issues in multi-robot cooperation

(Goldberg and Matari

c, 2003). (Lerman and Gal-

styan, 2002) devised a mathematical model that al-

lows a quantiﬁcation of the interference and its effect

on group performance. Probably, the most thorough

study was published by (Goldberg, 2001), who iden-

tiﬁed several types of multi-robot interactions. Gold-

Pini G., Brutschy A., Birattari M. and Dorigo M. (2009).

INTERFERENCE REDUCTION THROUGH TASK PARTITIONING IN A ROBOTIC SWARM - Or: "Don’t you Step on My Blue Suede Shoes!".

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 52-59

DOI: 10.5220/0002195200520059

 SciTePress

berg notes that one of the most common types of in-

terference is physical interference in a central area,

for example the nest. This kind of interference results

from resource conﬂicts, in this case physical space,

and can be arbitrated by either making sure that robots

stay in different areas all the time or by employing a

scheduling mechanism to ensure that robots use the

same space only at different times.

A simple method for reducing interference by us-

ing the ﬁrst arbitration method mentioned is the so-

called bucket-brigade: robots are forced to stay in

exclusive working areas and to pass objects to the

following robot as soon as they cross the bound-

aries of their area (Font

an and Matari

c, 1996; Shell

and Matari

c, 2006). Recently, this has been ex-

tended to work with adaptive working areas by (Lein

and Vaughan, 2008). To the best of our knowledge,

current works concerned with bucket brigading only

studied the inﬂuence of interference due to obstacle

avoidance. Other sources of interference (e.g., ob-

ject manipulation) were never studied, although they

might have a critical impact on the performance of

any task partitioning approach. To quote (Shell and

Matari

c, 2006): “If the cost of picking up or dropping

pucks is signiﬁcant [. . . ], then bucket brigading may

not be suitable.”

Task allocation for multi-robot systems is a wide

ﬁeld, which can be divided in intentional and self-

organized task allocation. Intentional task allocation

relies on negotiation and explicit communication to

create global allocations, whereas in self-organized

task allocation global allocations result from local,

stochastic decisions. A formal analysis and taxon-

omy that covers intentional task allocation has been

proposed by (Gerkey and Matari

c, 2004). (Kalra

and Martinoli, 2006) recently compared the two best-

known approaches of intentional and self-organized

task allocation.

The ﬁeld of self-organized task allocation is in

its early stages, as most studies tackle simple prob-

lems without task interdependencies. Studies in

self-organized task allocation are mostly based on

threshold-based approaches, taking inspiration from

division of labor in social insects. (Krieger and Bil-

leter, 2000) were among the ﬁrst to propose threshold-

based approaches in multi-robot task allocation. (La-

bella et al., 2006) used threshold-based task alloca-

tion in a multi-foraging task. Similarly, (Campo and

Dorigo, 2007) used a notion of the group’s internal

energy to allocate individuals to a multi-foraging task.

Finally, (Liu et al., 2007) studied a multi-foraging task

while focusing on the inﬂuence of the use of different

social cues on the overall group performance.

3 TASK PARTITIONING

AND ALLOCATION

In this work, we study a collective foraging task. By

spatially partitioning the environment, the global for-

aging task is automatically partitioned into two sub-

tasks: 1) harvesting prey objects from a harvesting

area (source) and 2) transporting them to a home area

(nest). Robots working on the ﬁrst subtask harvest

prey objects from the source and pass them to the

robots working on the second subtask, which store the

objects in the nest. These subtasks have a sequential

interdependency in the sense that they have to be per-

formed one after the other in order to complete the

global task once: delivering a prey object to the home

area.

Robots can decide to switch from one subtask to

the other, thus creating a task allocation problem: in-

dividual robots have to be allocated to subtasks and

different allocations yield different performance. As

a prey object has to be passed directly from one robot

to the other, a robot usually has to wait some time be-

fore passing a prey object to or receiving a prey object

from a robot working on the other subtask. This wait-

ing time can therefore give an indication of the alloca-

tion quality for the respective subtask: if the waiting

time is very long, there might not be enough robots al-

located to the other subtask. Thus, the robots can use

this waiting time to decide whether to switch subtask

or not. Ideally, the waiting time should be the same

for the two subtasks in order for the system to reach a

stable state and deliver optimal performance.

Our robots exploit a simple threshold-based model

to decide when to switch task: when the waiting time

is higher than a threshold Θ, a robot switches its

subtask. The robot’s waiting time is a function of the

average time the robots working in the other subtask

need to complete their task. The task-completion time

of a robot depends on two factors: 1) round-trip-time

(i.e., distance to travel) and 2) time lost due to interfer-

ence. Thus, the robot’s threshold Θ is a function of the

round-trip-time and the interference of the robots in

the other subtask. Therefore, the optimal task switch-

ing threshold depends on the task (i.e., time to harvest

a prey object) and the environment (i.e., distance be-

tween the source and the nest). As the parameters

of the environment are not pre-programmed into the

robots, determining the optimal threshold can be a

complex problem. In this work, we limit ourselves

to a simple method for setting this threshold: at the

start of the experiment, each robot draws a random

threshold that is used as its task switching threshold

throughout the experiment.

In the following, we study the properties of this

INTERFERENCE REDUCTION THROUGH TASK PARTITIONING IN A ROBOTIC SWARM - Or: "Don't you Step

on My Blue Suede Shoes!"

simple self-organized task allocation strategy, com-

pare this strategy to a strategy without task partition-

ing, and analyze how it can help to reduce interfer-

ence. We refer to the two strategies as partitioned and

non-partitioned, respectively.

4 METHODS

This section describes the environments in which the

experiments are carried out, the simulated robots, and

the robot’s controller. Additionally, we describe how

we run the experiments and we introduce some met-

rics that we use to evaluate the properties of the sys-

tem.

4.1 Environments

We study task allocation in two different environ-

ments. In these two environments, the nest is marked

by a light source that can be perceived by all robots,

thus providing directional information. The environ-

ment is spatially partitioned in two parts: the source

is located on the left and the nest is located on the

right side of the arena. We refer to the two sides

of the arena as harvest area and store area, respec-

tively. The exchange zone is located between these

two areas. Robots working on the left side, called

harvesters, gather prey objects in the source and move

them to the exchange zone, where they pass them to

the robots working on the other side. These are re-

ferred to as storers: their role is to transport prey

objects to the nest and store them there. The nest,

the source, and the exchange zone can be detected

through environmental cues (ground color).

At time t = 0, the robots are randomly placed

in the harvest area. The experiments run for t

max

18,000 time steps (a simulated time of one hour, with

a time step length of 200 ms). The experiments are run

in two different arenas (see Figure 1). The ﬁrst arena

(Figure 1a) is 4.125m long with a width of 1.6m at

the source and exchange zone, whereas the nest is

0.4m wide. The exchange zone is located 3.125m

away from the source. This arena is characterized by

the presence of an area, critical for the task, in which

high interference between robots can be expected (the

nest). Thus, this arena is referred to as the narrow-

nest environment.

The second arena (Figure 1b) has a rectangular

shape: it is 3.75 m long and 1.6 m wide. Here as well

the exchange zone is located 3.125m from the source.

The arena shape does not suggest the presence of any

zone where interference can be higher than in other

Figure 1: Depiction of (a) the narrow-nest environment

used in the ﬁrst experiment and (b) the wide-nest environ-

ment used in the second experiment. The gray stripes are

the source (left), and the nest (right), each 0.25 m deep. The

black stripe is the exchange zone, that is 0.5 m deep. The

light source is marked with “L”.

places. This arena is referred to as the wide-nest en-

vironment.

The area of both arenas is 6 m

, 5 m

for the har-

vest area and 1m

for the store area. The overall area

is the same in the two arenas, so that the same group

size results in the same robot density. Thus, results

are comparable across the two environments.

4.2 Simulation

The experiments are carried out in a custom simula-

tion environment that models geometries and func-

tional properties of simple objects and robots. Our

robots’ model is purely kinematic. Prey objects are

simulated as an attribute a robot can posses and not as

physical entities. Although the experiments are con-

ducted in simulation only, the simulated robots have

a real counterpart: the swarm-bot robotic platform

(Mondada et al., 2004). The platform consists of a

number of mobile autonomous robots called s-bots,

which have been used for several studies, mainly in

swarm intelligence and collective robotics—see for

instance (Groß et al., 2006) and (Nouyan et al., 2008).

The simulated s-bots are of round shape, with a diam-

eter of 0.116 m. Each of them is equipped with 16

infrared proximity sensors, used to perceive obstacles

up to a distance of 0.15 m. Eight ambient light sensors

can be used to perceive light gradients up to a distance

of 5.0 m. The robots are equipped with 4 ground sen-

sors used to perceive nest, source and exchange zone.

A 8 LEDs ring is used to signal when a prey object

is carried. An omnidirectional camera allows the per-

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

ception of LEDs in a circle of radius 0.6m surround-

ing the robot. A uniform noise of 10% is added to all

sensor readings at each simulation step. The robots

can move at a maximum speed of 0.1

/s by means of

a differential drive system.

4.3 Controller

All the robots share the same, hand coded, ﬁnite state

machine controller depicted in Figure 2. The con-

troller consists of two parts, each corresponding to a

possible subtask a robot can perform. Gray states re-

fer to the harvest subtask, white states to the store

subtask. Since all the robots start in the harvest

area, their controller is initially set to perform anti-

phototaxis. In this way they will reach the source,

where they can start retrieving prey objects. The be-

havior of each robot is a function of the task it is per-

forming. Harvesters not carrying a prey object move

towards the source, where they can ﬁnd prey. Har-

vesters carrying a prey object, move to the exchange

zone and wait for a free storer. Upon arrival of such

a storer, the harvester passes the prey object to it.

Storers carrying a prey object move towards the nest,

where they can deposit the object. Storers not car-

rying a prey object head to the exchange zone and

search for a harvester with a prey object. Robots can

detect other robots carrying a prey on the basis of the

color of their LED ring. While moving, each robot

avoids obstacles (walls and other robots).

Task switches can occur: a harvester carrying a

prey object can decide to become a storer, and a storer

not carrying a prey object can decide to become a har-

vester. As mentioned before, robots switch task de-

pending on an internal threshold Θ, representing the

maximum amount of control cycles they can spend in

the transfer zone waiting to pass (harvesters) or re-

ceive (storers) a prey object. If a robot remains in the

transfer zone longer than its threshold without pass-

ing or receiving prey objects (t

> Θ), it switches its

task. The optimal threshold value is not trivial to de-

termine. In the work presented here, we use a sim-

ple method to set the threshold Θ: at the beginning

of the experiment, each robot draws a random thresh-

old, sampled uniformly in the interval [0, 1000]. We

chose this method because it is independent of the en-

vironment and does not rely on complex approxima-

tion techniques. The threshold value does not change

during the experiment. In case of the non-partitioned

strategy, the threshold is set to Θ = 0, causing the

robots to switch subtask immediately as soon as they

reach the exchange zone.

Figure 2: Simpliﬁed state diagram of the controller of the

robots. Gray states belong to the harvest task, white states

to the store task. The obstacle avoidance state has been

omitted for clarity, as it is applicable in all states of the

robot. t

is the time spent in the exchange zone and Θ is

the threshold.

4.4 Experiments

The goal of the experiments is to investigate whether

task partitioning can reduce interference in task-

critical zones, and how to allocate a robotic swarm to

partitions. As pointed out by (Lerman and Galstyan,

2002), interference is related to the number of indi-

viduals in the system. Additionally, the physical in-

terference between robots is also a function of the en-

vironment the robots act in. The higher the group size,

the higher the density, resulting in a higher amount of

physical interference. Thus, in order to study interfer-

ence in our experiments, we increase the size of the

group in each of the two environments shown in Fig-

ure 1, while using both strategies (non-partitioned and

partitioned). We study the performance of the system

when the group size N ranges in the interval [1,40].

We run 50 repetitions for each value of N and each

experimental settin.

4.5 Metrics

In order to quantify the inﬂuence of interference, we

measure the group performance P by the number of

prey objects collected by the swarm at the end of the

experiment (t

max

= 1 hour). From the group perfor-

mance measure we can derive the individual efﬁciency

as follows:

eff

= P/N, (1)

where N is the size of the group. Individual efﬁciency

can help to understand the effect of interference on

the performance.

In order to measure the inﬂuence of environmen-

tal features on the interference, we deﬁne an inter-

ference measure taking inspiration from (Rosenfeld

et al., 2005). In their work, interference is measured

INTERFERENCE REDUCTION THROUGH TASK PARTITIONING IN A ROBOTIC SWARM - Or: "Don't you Step

on My Blue Suede Shoes!"

0 10 20 30 40

0 100 200 300 400

Prey objects retrieved (P)

●

non−partitioned

partitioned

●

0 10 20 30 40 50

Number of robots (N)

Prey objects retrieved

by individual robot (I

eff

)

●

Figure 3: (a) Performance P and (b) individual efﬁciency I

eff

for increasing number of robots in the narrow-nest environment.

The black continuous line refers to the case of no task partitioning, the black dashed line to the case of partitioning. Gray

lines indicate the 95% conﬁdence interval on the expected value.

as the time spent performing actions not strictly re-

lated to the task, but rather lost due to negative inter-

actions with the environment (e.g., obstacle avoidance

maneuvers). By registering the number of collisions

for each area of the arena, we can draw conclusions

about where physical interferences happen most of-

ten. We measure interference through the state of the

controller: in our case a robot is experiencing inter-

ference each time its controller perceives an obstacle.

In case of a partitioned task, there is another

source of inefﬁciency that adds to interference: the

time lost in the exchange zone. We deﬁne the strat-

egy cost C as the sum of time lost because of physical

interference and time lost in the exchange zone:

C = T

int

+ T

part

, (2)

where T

int

is the amount of time steps during which

the controller perceives an obstacle, and T

part

is the

total amount of time steps spent in prey passing

maneuvers. By using this metric, the cost of the

non-partitioned strategy is purely due to interference

part

= 0), while in case of the partitioned strategy,

prey passing costs add to interference costs. In a way,

passing a prey object produces another kind of inter-

ference in the system. The strategy cost captures this

effect, thus allowing for a comparison of strategies.

5 RESULTS AND DISCUSSION

The graphs in Figures 3a and 4 show the perfor-

mance P for different group sizes in the narrow-nest

and wide-nest environment respectively. Figure 3b

shows the individual efﬁciency I

eff

of the robots in

the narrow-nest environment. Black curves are the

average computed over the 50 repetitions of each set-

ting, gray curves indicate the 95% conﬁdence inter-

val on the expected value. The performance graph

in Figure 3a shows that the partitioned strategy im-

proves performance in the narrow-nest environment.

The graph shows that the non-partitioned strategy per-

forms better than the partitioned strategy for small

group sizes (up to N = 13 robots). However, increas-

ing the group size makes the non-partitioned strategy

collapse: the number of gathered prey objects drops

dramatically for groups larger than 13. The individual

efﬁciency graph (Figure 3b) can explain the behavior

of the system. The robots employing the partitioned

strategy are less efﬁcient, for small group sizes, than

those performing the non-partitioned strategy. How-

ever, the addition of more individuals affects the ef-

ﬁciency of the non-partitioned group in a more dra-

matic way. At a certain point, the drop in efﬁciency

becomes very steep for the non-partitioned strategy.

On the other hand, the partitioned strategy scales bet-

ter: individual efﬁciency drops smoothly. This ex-

plains why a group using the partitioned strategy per-

forms better: it can beneﬁt from the work of more

individuals and therefore collects more prey objects.

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

0 10 20 30 40

0 200 400 600 800

Number of robots (N)

Prey objects retrieved (P)

●

non−partitioned

partitioned

●

Figure 4: Performance P for increasing number of robots in the wide-nest environment. The black continuous line refers

to the case of no task partitioning, the black dashed line to the case of partitioning. Gray lines indicate the 95% conﬁdence

interval on the expected value.

Strategy cost (C)

0 5000 10000 15000 20000

Collision costs

Partition costs

Strategy cost (C)

0 5000 10000 15000 20000

0 5 10 15 20 25 30 35 40

Number of robots (N)

partitioned strategy

non−partitioned strategy

Figure 5: Cost of interference in the narrow-nest environ-

ment. Bars represent the cost C, sum of interference time

int

and partition time T

part

(i.e., waiting times). For easy

reference, the outline of the bars of the respective other

graph has been added to each graph. (a) Costs for the par-

titioned strategy, where interference cost stem from waiting

times and collisions. (b) Cost in case of the non-partitioned

strategy, where only physical interference through colli-

sions exists.

These considerations do not hold in the wide-nest en-

vironment. The performance graph in Figure 4 shows

that the non-partitioned strategy performs better than

the partitioned strategy for group sizes N < 33. In

both the environments, independently of the strat-

egy used to accomplish the task, the system collapses

when the area is saturated by the swarm.

Figure 5 shows the effect on the cost of increas-

ing the number of robots in the narrow-nest environ-

ment. The graph compares the cost C of each of the

two strategies for different group sizes. In case of the

partitioned strategy (Figure 5a), the graph shows each

component of the cost (T

int

and T

part

). Clearly, task

partitioning has the effect of reducing the cost due

to interference but has the disadvantage of increasing

the cost due to time lost. The probability of two or

more robots encountering each other increases with

the robot density. Although this determines a higher

interference cost (i.e., T

int

), it decreases the cost due to

lower waiting time (i.e., T

part

) in the case of the parti-

tioned strategy. Partitioning performs better when the

gain from interference reduction is greater than the

loss of performance due to partitioning inefﬁciencies.

These considerations hold in the narrow-nest environ-

ment, where the likelihood of physical interference in

a task-critical zone is very high. In the wide-nest en-

vironment, interference in the nest is as likely as inter-

ference in the exchange zone. Thus, it is not beneﬁ-

cial to pay the cost of waiting and the non-partitioned

strategy performs better for any group size.

The mechanism by which partitioning reduces in-

terference costs can be deduced by comparing the in-

terference graphs in Figure 6. The graphs show the

number of times that physical interference (as de-

ﬁned in Section 4.5) was registered in each region

of the narrow-nest environment. The total area was

discretized in squares of 1 cm

. Figure 6 shows the

results obtained with 18 robots, in the case of the

non-partitioned strategy (Figure 6a) and in the case

of the partitioned strategy (Figure 6b). The graphs

show that the use of the non-partitioned strategy leads

to high interference in the nest, which becomes con-

INTERFERENCE REDUCTION THROUGH TASK PARTITIONING IN A ROBOTIC SWARM - Or: "Don't you Step

on My Blue Suede Shoes!"

−2

−1

−0.5

0.0

0.5

Interference

100

partitioned

strategy

−2

−1

−0.5

0.0

0.5

Interference

100

non−partitioned

strategy

Figure 6: Mean interference values registered for (a) the partitioned strategy and (b) the non-partitioned strategy, both in the

narrow-nest environment. Shown values are observation means of 50 repetitions with N = 18 robots. Coordinates on the x-

and y-axis are given in meters. The arena is stretched along the y-axis for better visualization. The dashed white line marks

the location of the exchange zone.

gested. Partitioning the task reduces the robot den-

sity in the nest, thus spreading the interference more

uniformly across the arena. In addition, the overall

interference diminishes because the exchange zone is

wider: the robots have more freedom of movement

and collide less often. Although the graphs show only

data collected with 18 robots, experiments with dif-

ferent group sizes produced similar results.

6 CONCLUSIONS AND FUTURE

WORK

Interference can be an issue when working with

swarms of robots. In this work, we used task parti-

tioning and allocation to reduce interference between

robots sharing the same physical space. We manu-

ally partitioned the environment and employed a sim-

ple self-organized strategy for allocating individuals

to subtasks. Results show that a partitioning strategy

improves performance in a constrained environment.

Additionally, we identiﬁed cases in which partition-

ing is not advantageous and a non-partitioned strategy

should be used. The proposed strategy is fairly simple

and far from being an optimal solution, nevertheless

we improved the performance of the swarm when in-

terference was costly.

Future work will concern the identiﬁcation of the

optimal allocation in the studied environments as well

as the development and study of a strategy that can

ﬁnd this optimal allocation in a self-organized and

adaptive way. In addition, the interference metric pro-

posed in Section 4.5 could be used by the robots to

decide whether to partition the task. In this way, we

could achieve even better performance, since parti-

tioning would be employed only when strictly needed.

Finally, the goal is to validate the system using the

real robots.

ACKNOWLEDGEMENTS

This work was supported by the SWARMANOID

project, funded by the Future and Emerging Tech-

nologies programme (IST-FET) of the European

Commission, under grant IST-022888 and by the

VIRTUAL SWARMANOID project funded by the

Fund for Scientiﬁc Research F.R.S.–FNRS of Bel-

gium’s French Community. The information provided

is the sole responsibility of the authors and does not

reﬂect the European Commission’s opinion. The Eu-

ropean Commission is not responsible for any use that

might be made of data appearing in this publication.

Marco Dorigo and Mauro Birattari acknowledge sup-

port from the Fund for Scientiﬁc Research F.R.S.–

FNRS of Belgium’s French Community, of which

they are a research director and a research associate,

respectively.

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INTERFERENCE REDUCTION THROUGH TASK PARTITIONING IN A ROBOTIC SWARM - Or: "Don't you Step

on My Blue Suede Shoes!"