An Evolutionary Approach to Formation Control with Mobile Robots

Jane Holland, Josephine Grifﬁth and Colm O’Riordan

College of Engineering and Informatics, National University of Ireland, Galway, Ireland

Keywords:

Evolutionary Robotics, Swarm Robotics, Self-organisation, Collective Behaviours, Kilobots.

Abstract:

The ﬁeld of swarm robotics studies multi-robot systems, emphasising decentralised and self-organising be-

haviours that deal with limited individual abilities, local sensing and local communication. A robotic system

needs to be ﬂexible to environmental changes, robust to failure and scalable to large groups. These desired

features can be achieved through collective behaviours such as aggregation, synchronisation, coordination and

exploration. We aim to analyse these emerging behaviours by applying an evolutionary approach to a speciﬁc

robotic system, called the Kilobot, in order to learn behaviours. If successful, not only would the cost and

computation time for evolutionary computation in mobile robotics decrease, but the reality-gap could also

narrow.

1 INTRODUCTION

Swarm robotics is a developing ﬁeld within collec-

tive robotics, which focuses on groups of robots that

interact and cooperate with one another in order to

reach a common goal. This form of robotics can be

compared to a class of natural systems such as so-

cial insects – ants, bees and termites – that can ac-

complish intricate tasks by means of interaction. In

a decentralised, problem-solving system such as this,

insects have very limited capabilities. However, by

working together as a group, the overall performance

can be improved through self-organisation: a process

whereby a system transitions from a disordered state

to an ordered state by exploiting local interactions be-

tween robots and between robots and their environ-

ment (Dorigo et al., 2004; Trianni and Dorigo, 2006;

Baldassarre et al., 2007).

Formation control is an emergent collective be-

haviour of self-organisation inspired by nature, which

traditionally demonstrates a ‘follow-the-leader’ ap-

proach in a swarm of robots through coordination,

synchronisation and communication. These abilities

allow robots to dynamically interact with one another

in order to organise into a complex system so as to

work together effectively. Furthermore, these abil-

ities can result in an organised set of actions, such

as choosing a common sense of direction when in a

group formation. This is essential for a team of robots

to work as a whole entity and it can also establish a

basic building block for the design of more complex

behavioural strategies (Trianni et al., 2008). In order

for the coordination of behaviours to be successful,

robots must be able to deﬁne communication strate-

gies and protocols among the individuals of the group.

Here, simple forms of communication can be enough

to accomplish the coordination of group activities and

can also be easily scaled up with the number of indi-

viduals involved.

The motivation of the work described here is to

use evolutionary techniques to create parallels with

the biodiversity seen in natural systems; that is, to au-

tomate self-organised, collective behaviours using de-

centralised control and local communication. Evolu-

tionary algorithms are noted for their simplicity; the

Darwinian theory of survival of the ﬁttest is a focal

example: only the ﬁtter individuals of a population

are allowed to reproduce. In evolutionary robotics, a

population of genotypes is initialised and then each

genotype is encoded and mapped into each robot con-

troller. The process of evolution then evaluates the

performance of the robots as individuals or as teams.

The robots that perform above average are allowed

to reproduce and their genetic material can be al-

tered by means of mutation and recombination. This

method is repeated several times until one or more

controllers are found that meets the requirements of

an evaluation, or ﬁtness function. The efﬁciency of

the algorithm is dependent on the variance and se-

lection applied to the population and so, the algo-

rithm can be tailored to many different approaches

and multi-modal problems. Not only are evolution-

ary algorithms relatively simple, but they can pro-

duce solutions that are robust and ﬂexible to change.

Holland, J., Grifﬁth, J. and O’Riordan, C.

An Evolutionary Approach to Formation Control with Mobile Robots.

DOI: 10.5220/0006068602250230

In Proceedings of the 8th International Joint Conference on Computational Intelligence (IJCCI 2016) - Volume 1: ECTA, pages 225-230

ISBN: 978-989-758-201-1

225

These abilities to adapt are crucial for practical prob-

lem solving as they signiﬁcantly decrease the cost,

time required and can be evolved on the ﬂy if unex-

pected anomalies occur.

This position paper aims to outline the advantages

of applying evolutionary computation to swarms of

potentially heterogeneous, mobile robots where each

robot has limited functionality. Furthermore, a ge-

netic algorithm is proposed which we believe is ca-

pable of evolving simple swarms of mobile robots to

carry out the collective behaviour of formation con-

trol. We focus on formation control because this be-

haviour not only demonstrates self-organisation, co-

ordination and synchronisation, but it is also a key

component for more complex behavioural strategies.

Although evolutionary computation has been prac-

tised on Khepera robots (Mondada et al., 1994) and

S-Bots (Mondada et al., 2002), there has been no re-

search carried out on robots with a high level of hard-

ware and software restraints.

The outline of the paper is as follows: initially,

we outline our motivations and challenges in section

2; these include system design, cost, time and the

reality-gap. Next, an overview is given of the robots

which will be used in the work (Kilobots). In sec-

tion 4, we discuss related work in the areas of self-

assembly and decision making, both of which demon-

strate the process of self-organisation. In section 5,

we put forward a methodology, describing our forma-

tion control experiment in detail, making reference to

our chosen evolutionary algorithm and ﬁtness func-

tion evaluations. Lastly, conclusions and future work

are discussed in section 6.

2 MOTIVATIONS AND

CHALLENGES

Designing a control system for robots is a challeng-

ing and complex task as the system needs to be de-

composed into two phases: the behaviours of the in-

dividual and the behaviour of the system. The global

behaviour is a result of dynamical interactions among

its components, be it interactions between individuals

or interactions between individuals and the environ-

ment (Trianni and Dorigo, 2006). As these dynami-

cal interactions are hard to foresee, it is a good idea

to use an evolutionary technique to avoid decompo-

sition at both levels. Such an approach relies on the

evaluation of the system as a whole, particularly on

the emergence of the desired global behaviour start-

ing from the deﬁnition of the individual behaviours

(Trianni et al., 2008). By using this approach, the

evolutionary process eliminates unsought behaviours

and selects only the desirable behaviours based on an

evaluation function.

Other challenges that need to be taken into ac-

count are the costs and time required. For instance,

although the evolutionary approach bypasses decom-

position, artiﬁcial evolution can take a long time to

compute on a physical robot. Furthermore, if robots

were to be damaged during this evolution period,

costs would increase as hardware would need to be

replaced. It is for these reasons that simple, mobile

robots need to be used. As Kilobots have a low cost

price of around $14 for parts and only take 5 min-

utes to assemble, they can be easily produced in large

numbers (Rubenstein et al., 2012). The evolution of

their controllers can also be done through simulation

and then the most successful individuals can be run on

the physical robots in order to speed up the process.

However, evolving robot behaviours through the use

of simulation can present some other problems such

as a reality-gap: programs may work well on simu-

lated robots, but they can fail on real robots due to the

different actuation and sensing abilities as it can be

very difﬁcult to simulate the actual dynamics of the

real world (Brooks, 1992).

3 KILOBOT

The Kilobot (Rubenstein et al., 2012), shown in Fig-

ure 1, is a low-cost robot designed to make testing col-

lective algorithms on a large number of robots easily

manageable. The Kilobot has an Atmega328 proces-

sor controller, running at 8MHz with 32K of memory.

The controller has two main functions; it is used to

run a user-deﬁned program as well as operating as an

interface between electronics such as motors, power

circuitry and LEDs. It can regulate the speed of the vi-

bration motors by using two pulse width modulation

channels and can measure the intensity of the incom-

ing infra-red signals through 10-bit analog-to-digital

converters.

This robot does not have traditional characteris-

tics as it uses vibration motors for movement, and

reﬂective infra-red light and distance sensing in or-

der to communicate with other robots. The Kilobot

uses an infra-red LED transmitter and receiver that

allows the robot to receive messages from every di-

rection. When the transmitter is in use, a neighbour-

ing robot can receive light emitted by the transmit-

ting robot once it has been reﬂected off the surface

on which the Kilobot has been placed. The locomo-

tion of these motors prevent against travelling long

distances by providing noisy locomotion without po-

sition feedback. However, by using measured dis-

ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications

226

Figure 1: Graphical visualisation of the Kilobot robot in V-

Rep simulation software.

tances between neighbours as feedback, the robot’s

movement can be corrected, as well as being used to

promote the use of collective behaviours (Rubenstein

et al., 2012).

As previously mentioned, the limited range and

lack of bearing systems in the Kilobot make coordi-

nated navigation difﬁcult to implement. Kilobots can

only perceive the distance between each other, but not

the direction their neighbours are travelling in. To

combat this, robots need to continuously communi-

cate and measure the distances between themselves

and their neighbours in order to calculate their neigh-

bour’s pose, that is their orientation and position.

4 RELATED WORK

Much of the previous work in this area has dealt with

collective algorithms that demonstrate basic function-

ality in Kilobots, such as the ability to move within

an environment and communicate with neighbour-

ing robots (Rubenstein et al., 2012). More recently,

Rubenstein et al. (2014) have developed a self-

assembly algorithm which demonstrates edge follow-

ing, gradient formation, localisation and collective

transport. The aim of this work was to create artiﬁcial

swarms with the capabilities of natural ones. Further-

more, decision making within a self-organised system

has also been studied by Valentini et al. (2015), which

examines the trade-off between speed and accuracy

when making collective decisions as a swarm. The

decision strategy used was successfully implemented

on 100 robots, proving feasibility in large swarms and

robustness to robot failures.

This type of research tends to gravitate towards

more physics and mathematical based models, rather

than evolutionary developments. Although the no-

free-lunch theorem (Wolpert and Macready, 1997)

states that there cannot be an algorithm that is capable

of solving all problems, evolutionary algorithms can

surpass other methods in respect to solving problems

where heuristics are either not readily available, or do

not give a good performance. For instance, evolution-

ary algorithms may not outrival traditional methods

with simple issues, but in real-world function opti-

misation, where problems can have non-linear con-

straints, non-stationary conditions or even noisy en-

vironments, classic optimization techniques cannot

compare (Fogel, 1997).

Although there has been research carried out that

uses an evolutionary approach to produce emerging

behaviours in robot populations, there has been noth-

ing conducted speciﬁcally on Kilobots. The goal is

to have a deeper understanding of, and new evolu-

tionary algorithmic insights, into the emergence of

collective behaviours in these limited individuals and

how we can improve their robustness, ﬂexibility and

scalability. These insights could lead to real-world

potential applications in areas that are too danger-

ous for humans, such as search and rescue and detec-

tion of environmental hazards. Furthermore, swarm

robotics could be used in the nano-medical domain

for early diagnosis of disease or to ﬁght tumour cells

(Mavroidis and Ferreira, 2013).

5 METHODOLOGY

Formation control experiments traditionally have

robots lined up facing a leader that moves in a forward

direction while all the following robots trail along be-

hind in the same path (Figure 2a). This is a typical

ﬁnite state machine: the model requires robots to ei-

ther wait or go. For instance, robotA will stay in the

wait state until robotB and robotC are also in the wait

state, then robotA will switch to the go state, whereby

it continuously measures its distance to the robot in

front of it, trying to reduce it. When the distance is

reduced, robotA will switch back to the wait stage and

the process is repeated.

In contrast to this method, we will use a decen-

tralised algorithm which does not require any states.

In a decentralised problem-solving system composed

of simple interacting entities, such as an ant colony,

there is no leader that determines the activities of the

group, nor are there individuals informed of a global

pattern to be executed. Therefore, this type of algo-

rithm can be seen as more robust and ﬂexible com-

pared to others as the system’s behaviours can arise

through the interaction of individual robots. Further-

more, we will change the overall formation structure

from a linear to a hexagon shape (Figure 2b). By

using a hexagon shape, robots will need to continu-

ously measure their distance between their surround-

ing neighbours rather than just the robots in front and

An Evolutionary Approach to Formation Control with Mobile Robots

227

(a)

(b)

Figure 2: A graphic visualisation of a) the traditional forma-

tion control structure and b) our proposed formation control

structure.

behind. Furthermore, a hexagon shape promotes a

high density; we penalise robots that detract from the

density of the group.

In this experiment, formation behaviour is inte-

grated with a navigational behaviour to enable a team

of robots to reach a goal while avoiding obstacles

and simultaneously remaining in formation. Teams

are rewarded when the average distance of all the

Kilobots from the group centre of mass is minimised.

The robots are randomly placed in an enclosed square

arena with cylindrical obstacles (Figure 3), whereby

they need to reach a set of coordinates on the grid.

Through the use of proximity sensors, individuals can

measure their distance between neighbouring robots

and obstacles. The Kilobot controller uses the read-

ings from the proximity sensors as input nodes and

two output nodes control the robot’s motors. As the

Kilobot has a limited amount of memory and process-

ing power, we will carry out simulations using V-Rep

(Rohmer et al., 2013), a 3D world simulation tool

speciﬁcally developed by Coppelia Robotics for de-

signing and evaluating control algorithms. The best

controllers will then be downloaded onto real Kilo-

bots and our hypotheses will be further tested.

5.1 The Evolutionary Algorithm

We use a genetic algorithm for the synthesis of the

robot controllers; this will represent the way in which

the controller will interact with the environment. To

delineate the robot controller, we use a look-up table

(LUT) with two columns: the set of circumstances in

which the robot can ﬁnd itself and the actions that cor-

relate to each circumstance (Table 1). The input from

the Kilobot’s sensors are used to look-up the speciﬁc

situation and ﬁnd the corresponding action. A sim-

Figure 3: The proposed experimental arena containing 17

randomly placed obstacles.

ple example of a situation could refer to obstacles in

front, left or right of the Kilobot; 1 representing an

obstacle in a speciﬁc direction and 0 illustrating an

obstacle free path. The actions within the table are

linked to the robot’s actuators.

The initial population is composed of 100 geno-

types, all of which are binary encoded and are mapped

into the controller of each Kilobot. The robots are

homogeneous by design and genetically similar, but

as they carry out a random action at the beginning

of each run and respond to external stimuli, robots

can exhibit heterogeneous behaviours. Each run of

the experiment lasts a ﬁxed number of generations

and the population in subsequent generations is pro-

duced by a combination of tournament selection and

crossover. In every generation, we evaluate the geno-

types of the population by means of a ﬁtness func-

tion. The best performing genotypes of every popu-

lation are allowed to reproduce in order to create new

offspring where are all subject to a low level of muta-

tion.

Table 1: A simple example of a LUT.

Situation Action

000 Forward

001 Forward

010 Forward

011 Forward

100 Left

101 Left

110 Right

111 Stop

5.2 The Fitness Evaluation

The ﬁtness of the genotype is computed by measur-

ing the performance of the corresponding robot in a

group. The function F is calculated by evaluating the

ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications

228

behaviour of the group of Kilobots for a number of

trials and then averaging the obtained values. This ﬁt-

ness function is designed to favour exploration, fast

reaction to obstacles and coordinated motion. For

simplicity’s sake, we have split the function into two

parts F

and F

. F

is a weighted average of the

components F

(collision) and F

(exploration).

, (1a)

where T

is the number of cycles prior to the occur-

rence of a collision and T is the total number of cy-

cles. Here, the Kilobots evolve to avoid collision by

using the LUT. When the robot ﬁnds the correct ac-

tion for their situation, their ﬁtness is increased.

The second component rewards Kilobots that ex-

plore the arena:

z(T

)

Z(T

)

, (1b)

where z(T

) is the number of zones visited by cycle T

and Z(T

) is the maximum number of zones that can

be visited in T

cycles.

is calculated as the average density of the robot

group throughout the simulation:

∑

i=1

density(t

)

, (2a)

where there are T intervals.

The density of the group at time t

is calculated as

the average Euclidean distance of the n robots to the

centroid of the group:

density(t

) =

∑

j=1

dist( j, centroid)

(2b)

We evolve the Kilobots by averaging the ﬁtness

functions F

and F

. As the robots exhibit poten-

tially heterogeneous behaviours, their individual ﬁt-

ness values in F

are dependent on the other robots

in the current population, which introduces a further

complexity to the problem. That is, if one robot per-

forms poorly in the formation, the other robots’ ﬁt-

nesses will also be affected.

6 CONCLUSIONS

In this position paper we outlined the advantages of

using evolutionary computation on individuals with

limited capabilities. We also proposed an evolution-

ary algorithm which we believe is simple, yet robust

and ﬂexible enough to evolve a swarm of potentially

heterogeneous, mobile robots to carry out collective

behaviours, in particular, formation control. Further-

more, by evolving robots with limited sensing abili-

ties, we contend that the reality-gap can be more eas-

ily overcome as there are less parameters that need to

be validated in comparison to other robots that have a

more complicated set of sensors and motors. Despite

this, there is still a potential chance of a reality-gap,

so simulations need to be carefully modelled to retain

as many features of the robot as possible.

In future work, we intend to examine the system’s

behaviour and the individuals’ behaviours with the

evolutionary approach outlined in this paper by ad-

dressing two main issues: composition and a method

for selection. Robots must either have the same rules

or employ different ones (genetically homogeneous or

heterogeneous) and they will be evaluated using a new

ﬁtness that combines individual ﬁtnesses and team ﬁt-

nesses. Developing upon this, we will then use the

best controller on the hardware to test our hypothe-

ses further. As discussed in this position paper, this

may be easier to accomplish by using simple swarms

of robots, thereby reducing cost and time as well as

diminishing the reality-gap.

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