IEEE TRANSACTIONS ON CYBERNETICS 1
E olu ion o T ans e able and Sel -O ganized
Communica ion Modules o Sol ing Mul iple
Swa m Robo ics Tasks
Ra ael Send a-A anz , Ál a o Gu ié ez ,Senio Membe , IEEE,
and Ande s Lyhne Ch is ensen ,Senio Membe , IEEE
Abs ac —A key aspec o decen alized mul i obo coo dina-
ion is communica ion. Howe e , beyond simple signaling, he e
a e only ew epo s in he li e a u e on he success ul e olu ion o
communica ion, wi h successes la gely dependen on speci ic asks
and e olu iona y se ups. Thus, he e is a lack o s anda dized
communica ion amewo ks ha can be applied o di e en asks
wi hou he need o edesign, ebuild, o e-e ol e he en i e
sys em o e e y new ask. In his a icle, we p opose a no el
communica ion module ha does no need o be modi ied o
i s use in di e en asks. Each obo has a coo dina e (s a e)
in a i ual communica ion space. The communica ion space
is pa i ioned in o i ual egions, and each egion is linked
o a physical beha io , such as seeking esou ces, pho o axis,
o echa ging he ba e y. A obo ’s indi idual beha io is
de e mined by he egion o which i s cu en communica ion
s a e belongs. Since obo s can na iga e he communica ion space
and con inually b oadcas hei coo dina es o neighbo s wi hin
ange, obo swa ms can e ec i ely coo dina e hei beha io in
a sel -o ganized manne . We demons a e ha he same e ol ed
communica ion module is e ec i e in h ee swa m obo ics asks:
1) he physical agg ega ion o he obo s in o g oups o a desi ed
size; 2) he o ma ion o desi ed swa m geome ies; and 3) a
o aging ask based on empo al ole alloca ion. The esul s
show ha he communica ion module p o ides good and scalable
pe o mance in all asks, ep esen ing a signi ican s ep owa d
a ask-agnos ic communica ion amewo k o obo swa ms.
Index Te ms—Collabo a i e in elligence, communica ion
sys ems, dis ibu ed managemen , e olu iona y obo ics,
o ma ion con ol, swa m obo ics.
I. INTRODUCTION
COMMUNICATION is one o he key pilla s in swa m
obo ics (SR) [1],[2] ha is equi ed o e ec i ely
Recei ed 10 Oc obe 2024; e ised 18 Ma ch 2025 and 1 Sep embe
2025; accep ed 5 Sep embe 2025. This wo k was suppo ed in pa by
he Eu opean Commission wi hin he con ex o he p ojec SMAUG,
h ough EU Ho izon Eu ope unde G an 101121129; in pa by he
MCIN/AEI/10.13039/501100011033 unde G an PID2023-146540OB-C42;
and in pa by he Independen Resea ch Fund Denma k unde G an
0136-00251B. The wo k o Ra ael Send a-A anz was suppo ed by
he “P og ama P opio I+D+i” inanced by he Uni e sidad Poli écnica
de Mad id. This a icle was ecommended by Associa e Edi o P. Shi.
(Co esponding au ho : Ra ael Send a-A anz.)
Ra ael Send a-A anz and Á. Gu ié ez a e wi h he E.T.S. Ingenie os de
Telecomunicación, Uni e sidad Poli écnica de Mad id, 28040 Mad id, Spain
(e-mail: [email p o ec ed]; [email p o ec ed]).
Ande s Lyhne Ch is ensen is wi h he SDU UAS Cen e , MMMI, Uni e si y
o Sou he n Denma k, 5230 Odense, Denma k (e-mail: [email p o ec ed]).
Colo e sions o one o mo e igu es in his a icle a e a ailable a
h ps://doi.o g/10.1109/TCYB.2025.3610013.
Digi al Objec Iden i ie 10.1109/TCYB.2025.3610013
sol e many coope a i e asks (e.g., [3],[4], and [5]).
In e obo communica ion can po en ially be any so o
in o ma ion exchange among he obo s o he swa m. In
SR, communica ion can be ca ego ized as ei he di ec
in e ac ion [6],[7],[8],s igme gy [9],[10],[11],o di ec
communica ion [3],[4],[5]. The hi d ca ego y, di ec
communica ion, equi es explici ansmission and p ocessing
o signals whose meaning is co ela ed o he speci ic
ask. The e a e mul iple wo ks in he li e a u e ha
employ di ec communica ion in SR asks, wi h di e se
communica ion echnologies and di e en eme gen o
designed communica ion seman ics (e.g., [4],[5],[12],[13],
[14], and [15]). Un o una ely, he communica ion mechanics
and seman ics in hese SR wo ks a e speci ically designed
ad hoc o he ask o p oblem s udied [16]. This app oach
ep esen s a signi ican challenge in he SR ield, as he e
is a lack o s anda dized communica ion amewo ks o
me hods ha can be implemen ed ac oss a wide a ie y o
p oblems. This issue is also discussed in [17], highligh ing
he ela ion be ween he lack o s anda diza ion and eal-
wo ld applicabili y in he SRs ield. The e o e, designing and
e ol ing SR communica ion sys ems and mechanics ha a e
ask agnos ic is a key challenge in he ield.
In his a icle, we p opose a sel -o ganized and decen alized
communica ion module whose logic is e ol ed only once and
can be used in di e en SR asks and wi h a ying swa m sizes
wi hou modi ica ion. We demons a e his aluable ea u e by
employing he exac same e ol ed communica ion module in
h ee well-known SR p oblems, namely, agg ega ion o he
obo s in o g oups o desi ed sizes, o ma ion con ol, and
a o aging ask in ol ing dynamic ole alloca ion. We show
ha hese dis inc asks can be success ully sol ed using he
p oposed sys em.
The communica ion module is based on a i ual s a e space,
e e ed o as he communica ion space. Each obo has a
coo dina e in his communica ion space ha co esponds o i s
communica ion s a e. The communica ion space is pa i ioned
in o egions, each o which is associa ed wi h a physical
beha io — o example, beha io s, such as “ ollow ano he
obo ” o “go o a ligh sou ce.” Each obo execu es he
beha io associa ed wi h he egion ha con ains i s cu en
communica ion s a e. Robo s can dynamically change hei
communica ion s a e by i ually na iga ing in he communi-
ca ion space. Fu he mo e, a each con ol cycle, e e y obo
c
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2IEEE TRANSACTIONS ON CYBERNETICS
communica es i s communica ion s a e o i s neighbo s wi hin
ange. Robo s can use he ecei ed s a es o coo dina e hei
i ual na iga ion wi h o he obo s in o de o sol e SR asks.
Fo example, in a mul iplace o aging ask, we demons a e
how obo s can use he communica ion module o coo dina e
and decide which obo s o age om each ood sou ce.
The ans e abili y o obo beha io s has been add essed by
mul iple au ho s in he li e a u e. Kegelei s e al. [18] de ine
wo ypes o ans e abili y: 1) design-me hod ans e and
2) embodimen ans e . The o me e e s o he abili y o
use he same au oma ic design me hod o gene a e obo con-
olle s o di e en pla o ms o asks, while he la e implies
ans e ing and deploying he obo con olle ac oss mul iple
scena ios. In his a icle, we ocus on embodimen ans e ,
sligh ly ex ending he de ini ion in [18] owa d communica ion
ans e abili y— he euse o he same e ol ed communica ion
ac oss mul iple missions. Hasselmann e al. [19] p oposed
an au oma ic and modula design me hod o obo swa ms
ha minimizes human in e en ion. P obabilis ic ini e-s a e
machines (PFSMs) we e au oma ically buil o di e en asks
using ANN-based, mission-agnos ic beha io s. Howe e , he
asks conside ed in his wo k did no equi e explici com-
munica ion and, he e o e, communica ion ans e was no
necessa y. Salman e al. [20] p oposed he au oma ic design o
s igme gic communica ion and i s applica ion o a wide a ie y
o asks. E en hough hey achie ed au oma ic communica ion
design and i s applica ion o mul iple asks, he op imiza ion o
communica ion mus s ill be es a ed on a pe -mission basis
(design-me hod ans e ).
P e ious s udies ha e epo ed he use o i ual s uc-
u es o coo dina e obo swa ms [21],[22],[23],[24],[25].
None heless, hese i ual cons uc s a e used as ools o
planning obo mo ion a he han as a means o communica-
ion. A ela ed app oach was p oposed in [26] and ex ended
in [27]. The au ho s in oduced a sel -o ganized di ision o
labo amewo k, called pa i ioning social inhibi ion. Inspi ed
by he di ision o labo in honeybees, each obo acqui es
i s ole acco ding o a densi y-based dis ibu ion along a
i ual segmen . In his a icle, we also use a i ual space o
coo dina ion. Howe e , he e a e se e al di e ences. Fi s , we
explo e sel -o ganiza ion a he obo le el a he han a he
g oup le el, which allows each obo o specialize inhe en ly
in di e en oles. Second, we ocus on he gene aliza ion
o he p oposed communica ion module ac oss di e en SR
asks. Thi d, Zahada e al. [26],[27] es ic ed he i ual
space o a segmen , which is con enien o small swa ms bu
may deg ade pe o mance as swa m size and ole di e si y
inc ease. He e, we conside bo h 1-D and 2-D spaces, which
signi ican ly educes he ime equi ed o swi ch be ween
asks and imp o es o e all sys em con e gence. Finally, in
Sec ion V, we expe imen ally demons a e ha ou sys em
achie es as e con e gence in he sel -o ganiza ion p ocess, a
c i ical ea u e in SR sys ems.
This a icle in oduces a sel -o ganized communica ion
module o obo swa ms ha can success ully be used in
di e se SR asks. The main con ibu ions a e he ollowing.
1) T ans e abili y in SR: The communica ion is e ol ed
only once and ans e ed o mul iple SR asks.
2) New Communica ion Pa adigm: In oduc ion o a no el,
sel -o ganized, and decen alized communica ion mod-
ule o obo swa ms, based on a i ual cons uc ha
obo s use o communica e, in e ac , and sol e common
asks.
3) Pe o mance and ans e abili y is demons a ed in h ee
popula SR asks: a) agg ega ion; b) o ma ion con ol;
and c) o aging.
4) Scalabili y: The esul s show good pe o mance and
scalabili y in swa ms o up o 60 obo s, which lays he
g oundwo k o sol ing many o he SR asks.
II. COMMUNICATION MODULE
Inspi ed by he ields o coope a i e con ol [28] and g aph
neu al ne wo ks [29], we p opose a ans e able decen alized
communica ion module o sol ing SR asks. I is based on a
i ual communica ion s a e space, o simply communica ion
space, whe e each obo has i s own communica ion s a e.
The communica ion space is a pu ely abs ac cons uc wi h
no di ec physical coun e pa —i does no ep esen a spa ial
mapping, opology, o eplica o he eal wo ld in any way.
The communica ion s a es a e he only pieces o in o ma ion
communica ed be ween he obo s. Robo s can change hei
communica ion s a e ia i ual na iga ion. We ca ego ize he
communica ion module as he combina ion o he communi-
ca ion space, he obo s’ i ual na iga ion in ha space, and
he communica ion o s a es be ween neighbo ing obo s.
A. Communica ion S a e Space
Le Sbe he communica ion space. We conside he pa i-
ion Ro Sin oduced as ollows:
R={R1,...,RM}|S=R1∪R2∪···∪RM.(1)
Mo eo e , each egion Rj, wi h j∈{1,...,M}, is ep e-
sen ed by a cen oid o i ual landma k lj∈Rj. Using hese
i ual landma ks, a con enien way o de ine he egions is
shown as ollows:
Rj=s∈S|dSs,lj<dS(s,lk)∀k= j(2)
whe e dS(s,s) e e s o some dis ance me ic wi hin S.In
he special case in which dS(s,lj)=dS(s,lk), he egion is
assigned andomly o one o he candida e egions.
We de ine si∈Sas he communica ion s a e o he i h
obo , conside ing i∈{1,...,N}, whe e Nis he numbe o
obo s o swa m size. Addi ionally, each obo has a i ual
o ien a ion (θi( )), which de ines i s di ec ion o mo emen
wi hin he i ual space S. A obo iis in egion Rja ime
ins an p o ided ha si( )∈Rj.
R(si)=Rk⇐⇒ si∈Rk, whe e he unc ion
Rde e mines he i ual egion o which a gi en obo ’s
s a e belongs. Each i ual egion co esponds o a physical
beha io . Mo eo e , obo s communica e hei indi idual s a e
(coo dina e in he communica ion space) o neighbo s in ange.
Fig. 1(a) illus a es a 1-D communica ion space wi h six
i ual egions {Ri}6
i=1 ep esen ed by hei associa ed i ual
landma ks {li}6
i=1. In his example, he e a e eigh obo s whose
communica ion s a es a e ep esen ed by whi e ci cles. In his
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SENDRA-ARRANZ e al.: EVOLUTION OF TRANSFERABLE AND SELF-ORGANIZED COMMUNICATION MODULES 3
Fig. 1. Hypo he ical communica ion spaces and p imi i e selec o . (a) Hypo he ical 1-D communica ion space wi h six i ual egions (Ri)and hei espec i e
landma ks li(deno ed as s a s). (b) Hypo he ical 2-D communica ion space wi h six i ual egions as in (a). In bo h (a) and (b), he e a e eigh obo s, whose
communica ion s a es a e ep esen ed as whi e ci cles. (c) Example o a p imi i e selec o ha maps i ual egions in S o p imi i es i o be execu ed by
he obo s. (d) Sc eensho o he eigh obo s execu ing hei co esponding p imi i es. The geome ic shape displayed on op o each obo ep esen s he
p imi i e being execu ed, while he colo o he obo ’s LED indica es i s cu en i ual egion (acco ding o he colo s shown in (a) and (b)).
igu e, he e is one obo in R1, woinR2, woa einR3,
wo in R4, one in R6, and none in R5. Addi ionally, Fig. 1(b)
illus a es he analogous 2-D communica ion space wi h he
same numbe o i ual egions and landma ks.
B. Connec ion Be ween Vi ual Regions and Robo Beha io s
Simila o he le els o compe ence in [30] and he beha io
p imi i es in [31], we de ine a p imi i e pool F={ 1,..., K},
which is a se o p imi i e beha io s designed o sol e speci ic
and simple asks. Some examples o p imi i es a e “explo e
he a ena,” “app oach a ligh sou ce” (pho o axis), “mo e away
om a ligh sou ce,” “ ollow ano he obo ,” “s ay in a nes ,”
and “ o age om a esou ce a ea.” These p imi i es ha e
access o he obo senso eadings and can modi y he s a e o
he obo ’s ac ua o s. In his a icle, we only conside manually
designed p imi i es, bu he se could also include e ol ed,
lea ned, o hyb id p imi i es. Each i ual egion is associa ed
wi h exac ly one beha io p imi i e. We he e o e de ine a
mapping be ween he i ual egions in Rand he p imi i es
in F. This implies ha a obo whose communica ion s a e
belongs o a i ual egion execu es he p imi i e o ha
egion. We e e o his mapping be ween he se s Rand F
as he p imi i e selec o . In his a icle, e e y obo has he
same se o p imi i es, and he p imi i es and p imi i e selec o
a e manually designed o each speci ic ask being sol ed.
An example o a p imi i e selec o is illus a ed in Fig. 1(c),
whe e six i ual egions o ei he Fig. 1(a) o (b) a e mapped
on o ou p imi i es { 1,..., 4}( ep esen ed g aphically as
di e en geome ic shapes). Fig. 1(d) shows a swa m o eigh
obo s ha a e sol ing a ce ain ask. The p imi i e ha each
obo o he igu e is execu ing is g aphically ep esen ed wi h
a 3-D geome y acco ding o he obo ’s communica ion s a e
in Figs. 1(a) and (b) and he p imi i e selec o in Fig. 1(c).
C. Na iga ion in he Communica ion Space
The communica ion s a e o each obo is subjec o i ual
na iga ion ha modi ies i s coo dina es in S. Fu he mo e, a
na iga ion policy de ines he ules and dynamics o i ual
na iga ion, which a e d i en by a goal o con e gence c i e-
ion. To be e ec i e, such na iga ion policy should ake in o
conside a ion he i ual landma ks and he communica ion
s a es o he neighbo s (wi h neighbo hood in he communi-
ca ion space de ined as ollows)
si,sja e neighbo s ⇐⇒ R(si)= Rsj.(3)
In his a icle, we es ablish he na iga ion policy goal as
ollows:
∀si,sj∈{s1,...,sN},si= sj⇒ R(si)= Rsj.(4)
This a ge condi ion is me when each obo ’s communica ion
s a e belongs o a unique i ual egion, ensu ing no wo
obo s sha e he same egion. To complemen (4), no ice
ha he i ual egions o m a pa i ion o S, so ha any
communica ion s a e always belongs o only one i ual egion,
ega dless o he na iga ion policy. The na iga ion goal in (4)
has been delibe a i ely es ablished o sol e he SR asks o
his a icle. Howe e , al e na i e objec i es can be designed o
mee o he ask equi emen s (e.g., allowing mul iple obo s’
communica ion s a es o con e ge o he same i ual egion).
To ul ill he imposed policy, he i ual na iga ion is
con olled by he communica ion con olle ( comm).The
communica ion con olle is a dis inc uni and should no
be con used wi h he con en ional con olle esponsible o
he obo ’s physical beha io . The la e maps senso eadings
o ac ua o ac ions, while he o me go e ns he i ual
na iga ion o he obo s in he communica ion space. The com-
munica ion con olle o he i h obo is gene ically de ined as
ollows:
ai,θ
a ,i= comm(si,scs ,lcs ,l a )(5)
whe e he ou pu s a e he no malized na iga ion speed ai∈
[0,1] and he a ge i ual o ien a ion θ a ,io obo iin
he communica ion space S. Al e na i ely, he communica ion
con olle ecei es as inpu s ou ec o s, namely, he closes
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4IEEE TRANSACTIONS ON CYBERNETICS
communica ion s a e among he neighbo s in S(scs ), he
closes landma k (lcs , which is he landma k associa ed wi h
he i ual egion R(si)), a a ge landma k (l a ), and i s
own communica ion s a e (si). The uple (si,scs ,lcs ,l a )
summa izes all he in o ma ion equi ed by comm o ul ill
(4), while a oiding he high dimensionali y and dynamic size
issues ha would a ise i all he i ual landma ks and all he
neighbo communica ion s a es we e p o ided.
Be o e explaining he compu a ion o he a ge landma k
l a ,le pi∈NM
0(N0=N∪0)be a ec o o p io i ies, whe e
0 ep esen s he highes p io i y, and p io i y dec eases wi h
inc easing numbe s. The p io i ies in pia e associa ed one-
o-one wi h each o he i ual egions, so ha pi(m)is he
p io i y o egion Rm o all m∈{1,...M}acco ding o obo
i. The subsc ip io piis used o deno e ha he p io i ies
a e subjec i e o each obo i∈{1,...,N}, so ha each obo
can ha e di e en i ual egion p io i ies (see Sec ions II-D
and II-E o mo e de ails).
The a ge landma k (l a )is selec ed acco ding o he
ollowing c i e ia, lis ed acco ding o hei impo ance in he
selec ion.
1) Whe he he i ual egion R a o l a is al eady occu-
pied by one o mo e neighbo s.
2) The p io i y o he landma k’s egion.
3) The dis ance, dS, om he obo ’s communica ion s a e
o he landma k.
The communica ion con olle is esponsible o gene a ing
a i ual na iga ion eloci y and o ien a ion. The dynamics o
he i ual o ien a ion o a obo ia e cha ac e ized as ollows:
τθ
∂θi( )
∂ =θ a ,i( )−θi( )(6)
while he dynamics o he communica ion s a e a e de ined as
ollows:
τs∂si( )
∂ =ai( )·cos(θi( ))
sin(θi( )).(7)
The ixed ime cons an s τθand τsalso in luence he linea
and angula speeds o he i ual na iga ion, and a e se o
20·∂ in bo h cases. P elimina y s udies e ealed ha hey a e
a good adeo be ween smoo hness and as esponse in he
i ual na iga ion.
Equa ions (6) and (7) a e speci ically designed o 2-D com-
munica ion spaces. Thus, in he case o 1-D communica ion
spaces, he dynamics educe o (8) as he e is no longe a need
o include o ien a ion
τs∂si( )
∂ =ai( )·θ a ,i( ). (8)
In (8), he a iable θ a ,i∈{−1,1}has wo possible alues,
each ep esen ing one o he wo na iga ion di ec ions along
he single dimension o he communica ion space.
Fig. 2(a) summa izes he s ages o he i ual na iga ion
p ocess o a obo in he communica ion space. Fi s , scs ,
lcs , and l a a e compu ed. Subsequen ly, hese ec o s a e
ed o he communica ion con olle comm, which gene a es
he desi ed na iga ion speed and i ual o ien a ion. The
communica ion s a e o he obo is ul ima ely upda ed based
on (6) and (7).
Fig. 2. Diag am o he o e all sys em. (a) Communica ion module. (b) Robo
con olle .
D. Robo Con olle
The obo con olle , illus a ed in Fig. 2(b), is esponsible
o he physical beha io o a obo . In each con ol cycle, he
p imi i e selec o is used o pick one o he p imi i es a ailable
inap imi i e pool, based on he cu en egion o he obo in
he communica ion space. Mo eo e , he selec ed p imi i e is
execu ed using he cu en senso y eadings, deno ed as φ( ).
In addi ion, he obo con olle is also composed by he
p io i y selec o . A i ual egion’s p io i y de e mines i s
ela i e impo ance o a gi en obo and is conside ed when
he obo pe o ms i ual na iga ion. The p io i y selec o is
de ined as ollows:
pi( )=P io i ySelec o (φ( ))(9)
so ha i s ou come is he ec o pi, esul ing om he conca e-
na ion o he p io i ies o all he p imi i es o he i h obo .
The p io i ies can be se o ixed alues, o ins ance, as in he
agg ega ion and o ma ion asks (see Sec ions IV-A and IV-B).
Howe e , p io i ies can also be dynamically upda ed using
condi ional ules and he cu en senso eadings, φ( ).Asan
example, a change in he p io i y o a p imi i e can happen
when a obo uns low on ba e y and needs o c i ically
p io i ize a “ echa ge ba e y” beha io . In his scena io, he
p io i y selec o would simply check whe he some ba e y
le el h eshold was c ossed, and modi y he “ echa ge ba e y”
p io i y acco dingly.
E. In e ac ions Be ween he Communica ion Module and he
Robo Con olle
Fig. 2shows an o e iew o he communica ion module,
he obo con olle , and he da a low be ween hem. The
bidi ec ional in e ac ions be ween hese wo componen s a e
he ollowing.
1) In luence o he Communica ion Module on he Robo
Con olle : The communica ion module modi ies he
beha io o he obo s in he physical en i onmen
h ough he p imi i e selec o and he communica-
ion s a e. Speci ically, he communica ion s a e o a
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SENDRA-ARRANZ e al.: EVOLUTION OF TRANSFERABLE AND SELF-ORGANIZED COMMUNICATION MODULES 5
Fig. 3. Flowcha o he communica ion module phases.
obo and he i ual egion o which i belongs de e -
mine he physical beha io p imi i e execu ed by a
obo . Simila ly, ansi ioning om one i ual egion
o ano he also causes a change in he obo ’s physical
beha io .
2) In luence o he Robo Con olle on he Communica ion
Module: The obo con olle can al e he i ual na -
iga ion ha cha ac e izes he communica ion module
by means o he p io i y ec o pi( )local o each
obo i. Consequen ly, pi( )o a obo ide e mines he
i ual egions ha his obo should occupy wi h highes
p io i y a ime ins an . The obo con olle can modi y
he alues o pia each con ol cycle based on he senso
eadings.
F. E olu ion and Deploymen Phases
The pa ame e s o he ANN de ining he communica ion
con olle ( comm)a e op imized wi h he ul ima e goal o
sa is ying (4). The communica ion con olle is e ol ed p io
o he design o he physical obo con olle . Acco dingly,
i ope a es in wo s ages: 1) he e olu ion phase and 2) he
deploymen phase.
The e olu ion phase ocuses exclusi ely on op imizing he
communica ion con olle , whe e obo s lea n o na iga e in
he communica ion space. A his s age, he con olle is
agnos ic o he SR ask pe o med in he physical en i onmen ,
and no p imi i e beha io s a e associa ed wi h he i ual
egions.
The deploymen phase begins once e olu ion is comple e.
He e, he communica ion module is con igu ed o a speci ic
SR ask by assigning p imi i e beha io s o i ual egions and
de ining bo h he p imi i e selec o and he p io i y selec o .
While his s udy employs manually designed p imi i es and
selec o s, hese componen s could also be e ol ed o lea ned
depending on ask-speci ic equi emen s.
A key ad an age o he p oposed module is i s ask-
agnos ic na u e: i can be eused ac oss di e se asks wi hou
edesign, e-e olu ion, o e aining, a p ope y we e e o
as ans e abili y [18]. Adap ing he module o a new ask
equi es only i s con igu a ion du ing deploymen . In his
s udy, we e ol e a single communica ion con olle and deploy
i ac oss mul iple asks: agg ega ion, o ma ion con ol, and
o aging (Fig. 3).
Fig. 4. Example showing how he communica ion module and obo
con olle can sol e a simple o aging. (a) Communica ion space showing
example ajec o ies o wo coope a ing obo s sol ing a simple o aging.
(b) P imi i e selec o showing i e p imi i e beha io s ( i)and how hey a e
associa ed o he egions o he communica ion space. I also p o ides a sho
desc ip ion o each goal o each p imi i e. (a) also shows mul iple callou s
wi h he alues o he p io i ies o he obo s du ing speci ic pa s o he
ajec o ies (illus a ed wi h he s yle o he cu es, being ei he solid, dashed,
o do ed). Fo he sake o cla i y, in his example we conside ei he ON
and OFF p io i y alues, so ha ON means ha he co esponding egion has
p io i y and he obo is a ac ed o i , and OFF implies ha he co esponding
egion can be neglec ed. Fo example, he ec o (OFF,OFF,OFF,OFF,ON)
indica es ha only egion R5has p io i y, and, hus, he obo ’s a ge beha io
would be 5(“Re u n o nes ”).
G. Illus a i e Example
A simple mul iplace o aging ask is used as an example
o illus a e he ope a ion o he communica ion module. This
o aging ask is composed o a nes zone and wo ood a eas.
The aim o he obo s is o ind he ood a eas and, he ea e ,
anspo as many ood elemen s as possible o he nes by
pe o ming ound ips be ween he co esponding esou ce
a ea and he nes . Addi ionally, he obo s mus pe o m
con inual ask alloca ion so ha each obo seeks and o ages
om a di e en ood a ea.
This example wi h wo obo s is shown in Fig. 4.Fig.4(a)
depic s he communica ion space and he i ual na iga ion o
each o he wo obo s (as whi e and black cu es, espec-
i ely). The e a e i e i ual egions (R1,...,R5), each
linked o a dis inc p imi i e beha io ( 1,..., 5)acco ding o
he p imi i e selec o shown in Fig. 4(b). The callou s show
he 5-D p io i y ec o s wi h hei alues se o ei he OFF
o ON o each o he i e egions. The s yle o he cu e
(do ed, dashed, o solid) depic s he pa o he ajec o ies
in which he p io i ies o he callou s a e used by each obo .
The alue OFF means ha he obo ’s i ual na iga ion
will no be a ac ed owa d i . Fo example, he ec o
(OFF,OFF,OFF,OFF,ON)indica es ha only egion R5has
p io i y, while he es can be neglec ed. Consequen ly, he
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6IEEE TRANSACTIONS ON CYBERNETICS
obo should na iga e owa d R5wi h he aim o execu ing
beha io 5(“Re u n o nes ”).
Focusing on he ajec o y o obo 1 (in whi e), he i ual
na iga ion is he sequence {R1,R3,R5,R3,R5,...}, so ha
he p imi i es execu ed by his obo a e { 1, 3, 5, 3, 5...}.
In e ms o obo beha io s, his sequence is as ollows:
1) he obo sea ches o a ood a ea by explo ing he
en i onmen , and once ood a ea 1 is ound, 2) i con in-
ually anspo s esou ces om ha ood a ea o he nes .
The i ual na iga ion o obo 2 (in black) is he se ies
{R2,R4,R5,R4,R5,...}and he sequence o obo 2 p im-
i i es a e { 2, 4, 5, 4, 5,...}. In his case, obo 2 s a s
execu ing he p imi i e “Find ood a ea 2,” because obo 1
is al eady looking o he o he ood sou ce. Subsequen ly,
obo 2 pe o ms a ound ip o aging om he ood a ea
2 and he nes . The alues o he p io i y ec o s play a
c ucial ole in his example. Fo ins ance, he ound ips
be ween R3and R5a e p oduced because when a obo
acqui es ood, he obo con olle upda es he p io i y ec o
o (OFF,OFF,OFF,OFF,ON), indica ing ha only egion R5
is ac i e, and he new a ge beha io o he obo is e u ning
o he nes (p imi i e 5).
III. EVOLUTION OF THE COMMUNICATION CONTROLLER
The communica ion module, comm, should enable obo s
o i ually na iga e he communica ion space in a man-
ne ha sa is ies (4).Fo comm, we use an ANN whose
pa ame e s and opology a e e ol ed using he neu oe olu-
ion o augmen ing opologies (NEAT) algo i hm [32].E en
hough comm can, in p inciple, be op imized using o he
e olu iona y algo i hms ha a ge ixed neu al s uc u es, he
use o NEAT is mo i a ed by i s abili y o simul aneously
e ol e bo h ANN pa ame e s and opology. NEAT begins
wi h minimal a chi ec u es and p og essi ely inc eases he
numbe o neu ons and synapses, seeking balance be ween
pe o mance and complexi y. Mo eo e , NEAT inco po a es
niching s a egies ha p omo e model di e si y and alle ia e
p ema u e con e gence o subop imal solu ions.
In each gene a ion o NEAT, e e y indi idual is e alua ed
in a obo ics simula o (see Sec ion IV). In each simula ion, a
swa m o en obo s na iga es a i ual communica ion space
di ided in o en egions. A each con ol cycle, e e y obo
ansmi s i s communica ion s a e (si) o neighbo ing obo s.
One i e a ion o he communica ion module [wi h i s con ol
low and main s ages shown in Fig. 2(a)] is hen compu ed,
p oducing he nex communica ion s a e o each obo .
The objec i e o e olu ion in his s udy is o op imize he
communica ion con olle so ha obo s a e dis ibu ed wi h
exac ly one obo pe egion, he eby sa is ying (4). The ini ial
communica ion s a es o he obo s a e uni o mly dis ibu ed
ac oss he en i e communica ion space. The coo dina es o
he i ual landma ks in he communica ion space a e also
andomly sampled, subjec o a minimum dis ance cons ain
be ween landma ks. This minimum dis ance is a hype pa-
ame e ha depends on he o al numbe o landma ks. Fo
en landma ks, we empi ically se his alue o 0.3, ensu ing
su icien sepa a ion be ween landma ks.
Fig. 5. Communica ion space con igu a ion, opologies, and i ual na i-
ga ion con ol. (a) Ci cle communica ion space embedded in a 3-D space.
Rema k: he hickness o he ci cle is only ep esen ed o isualiza ion
pu poses, albei he s uc u e is a compac 1-D mani old. (b) Un olded ci cle
communica ion space. (c) To us communica ion space embedded in a 3-D
space. (d) Un olded o us communica ion space. (e) A chi ec u e o he
CTRNN model used o con ol he i ual na iga ion o he obo s in he
communica ion space.
A. Communica ion Space
The communica ion amewo k is assessed in expe imen s
wi h bo h 1-D and 2-D communica ion spaces. We de ine
he 1-D communica ion space as he line segmen S1=
[−L/2,L/2)wi h he addi ional p ope y ha he wo
endpoin s −L/2 and L/2 a e connec ed—in ac , hey a e he
same poin in he communica ion space. Fig. 5(a) shows he
1-D communica ion space as a ci cle in a 2-D space, while
Fig. 5(b) illus a es i as a line segmen . Bo h ep esen a ions
co espond o he same communica ion space. The dis ance
me ic ha cha ac e izes S1is de ined as ollows:
dS1s,s=mins−s,L−s−s(10)
whe e s,s∈S1.
The 2-D communica ion space is de ined as an un olded
o us in S2=[−W/2,W/2)×[−H/2,H/2). The uppe and
lowe bounda ies o S2a e connec ed, and he le and igh
bounda ies a e connec ed as well. Fig. 5(c) shows S2as a o us
in a 3-D space, while Fig. 5(d) illus a es he un olded o us.
As in he 1-D case, he communica ion spaces ep esen ed
in bo h igu es a e equi alen . The dis ance me ic o S2is
o mula ed as ollows:
dS2s,s=
⎛
⎝
mins1−s
1,W−s1−s
1
mins2−s
2,H−s2−s
2⎞
⎠
2
(11)
whe e s=(s1,s2)and s=(s
1,s
2)and s,s∈S2.
B. Communica ion Con olle
The ANN model used in comm is he con inuous- ime
ecu en neu al ne wo k (CTRNN) [33], which is an ANN
wi h eedback connec ions ha ope a es in con inuous ime.
The use o a CTRNN is mo i a ed by he con inuous dynamics
o i ual na iga ion in he communica ion space, which
p esen s a scena io whe e a eac i e eed- o wa d model may
no su ice.
Fig. 5(e) shows he CTRNN a chi ec u e used in he
expe imen s. The bo om nodes o he igu e ep esen he inpu
neu ons o he neu al ne wo k, and he op nodes ep esen he
ou pu neu ons. Recall om Sec ion II-C ha comm ecei es
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SENDRA-ARRANZ e al.: EVOLUTION OF TRANSFERABLE AND SELF-ORGANIZED COMMUNICATION MODULES 7
as inpu he closes neighbo ’s communica ion s a e (scs ), he
closes landma k (lcs ), and he a ge landma k (l a ).The
CTRNNexecu ionisp ecededbyap ep ocessings ageinwhich
hese ec o s a e con e ed in o he dis ance and angle be ween
he obo communica ion s a e and he co esponding ec o .
Fo ins ance, dS(si,scs )and ϕS(si,scs )a e, espec i ely, he
dis ance and angle be ween siand scs in S. In con as , he
ou pu s o he CTRNN a e he i ual na iga ion eloci y and
a ge o ien a ion o obo i.
C. E olu iona y Se up
The i ness unc ion FFien o ces ha only one obo should
occupy each i ual egion in o de o achie e he goal de ined
in (4). The ins an aneous i ness unc ion o a single obo i,
used by he NEAT algo i hm o op imize he CTRNN model,
is shown as ollows:
FFi( )=⎧
⎨
⎩
e−α·dS(si( ), l∗
i( )),i sj/∈R∗
i( )∀j= i
0,o he wise.
(12)
whe e R∗
i( )is he i ual egion o which he communica ion
s a e o obo icu en ly belongs (si∈R∗
ia ime s ep ), and
l∗
i e e s o he i ual landma k co esponding o egion R∗
i.
The alue o FFiinc eases exponen ially as he dis ance
o l∗
idec eases, p o ided ha obo iis he only obo
whose communica ion s a e lies wi hin i ual egion R∗
i.
The pa ame e αmodula es he a e a which i ness decays
as he dis ance o he i ual landma k inc eases. Based on
p elimina y expe imen s, we se α=8 oa oidspa se
i ness landscapes while p e en ing obo s om being o e ly
ewa ded when loca ed a he bo de s o he i ual egions.
The inal i ness sco e o a simula ion is compu ed as he
a e age o FFi( )ac oss all obo s in he swa m and all
simula ion ime s eps. Addi ionally, he i ness unc ion is
e alua ed en imes ( uns), wi h andom and independen
ini ializa ions.
The NEAT popula ion is composed o 100 indi iduals, wi h
wo eli es p ese ed ac oss gene a ions. Main aining wo eli es
was ound o imp o e pe o mance in p elimina y expe imen s.
Each pa ame e o he CTRNN model is mu a ed wi h p ob-
abili y 0.1, using Gaussian mu a ion wi h a mu a ion powe
o 0.05. Fu he mo e, a new node is added wi h p obabili y
0.05, and a new synap ic connec ion is c ea ed wi h p obabili y
0.2. The emaining hype pa ame e s ollow he con igu a ion
p oposed by he au ho s o NEAT [32] and by p e ious s udies
o NEAT applied o SR [34]. Speci ically, we use c1=1, c2=
1, and c3=0.4 as he compa ibili y coe icien s, and δ =
3 as he compa ibili y h eshold. These pa ame e s a e used
du ing he specia ion p ocess o iden i y compa ible species.
The weigh s and biases a e cons ained o he ange [−10,10]
and ini ialized wi h a Gaussian dis ibu ion o ze o mean and
s anda d de ia ion σ=1.
IV. EXPERIMENTS
To assess he communica ion amewo k, we use h ee
popula SR asks: 1) agg ega ion; 2) geome ic o ma ions;
and 3) o aging wi h obo ba e y dependence. We use he
same communica ion module, e ol ed acco ding o he de ails
and hype pa ame e s p esen ed in Sec ion III, o all asks,
bu con igu ed wi h di e en beha io p imi i es, p imi i e
selec o , and p io i y selec o o each ask. All he expe imen s
a e implemen ed using he pybulle lib a y [35] o eal-
ime collision de ec ion and mul iphysics simula ions. The
obo s a e equipped wi h eigh IR-based p oximi y senso s
dis ibu ed along hei pe ime e , a GPS o know hei absolu e
posi ion in he a ena, and communica ion ansmi e s and
ecei e s ha enable he sha ing o hei communica ion s a es
wi h neighbo s wi hin ange. In he case o he o aging
expe imen , each obo is also equipped wi h eigh ligh
senso s posi ioned along i s pe ime e and a g ound senso ha
de ec s he colo o he loo below he obo . Communica ion
anges o 2 m a e used in expe imen s wi h swa m sizes
below 20, while he communica ion ange is inc eased o
4 m when swa m sizes la ge han 20 a e conside ed. The
obo ics simula ions, NEAT algo i hm, CTRNN models, and
obo and communica ion con olle s a e public and a ailable
in a gi hub eposi o y called Me eli.1
A. Agg ega ion in G oups
In he agg ega ion ask, obo s ha e o o m a desi ed
numbe o g oups wi h a gi en numbe o obo s in each
g oup. Mo eo e , he obo s o each g oup ha e o agg ega e as
closely as possible o he o he membe s o hei g oup, while
a oiding collisions. We de ine Gas he numbe o g oups, and
Gi,i∈{1,...,G}as he numbe o a ge membe s o each
g oup. The ea e , he e a e Gp imi i es wi h he ollowing
meanings:
i−→ “Go o he cen e o mass coo dina es
o he neighbo s also belonging o g oup i.”
The numbe o i ual egions o he communica ion space
equals he swa m size and, o each i, he p imi i e selec o
maps Gidi e en i ual egions o he p imi i e i.Fig.6(a)
illus a es an example o he agg ega ion in g oups wi h 21
obo s, G=3 g oups, h ee p imi i es { 1, 2, 3}, and Gi=
7∀i. All he a ge g oups o his ask ha e he same
impo ance and all he i ual egion p io i ies a e ixed o he
same alue o 1. The e o e, he p io i y selec o used in his
expe imen is simply
pi( )=(1,...,1)∀ ∀i∈{1,...,N}.(13)
A he beginning o he ask execu ion, he a ge numbe
o g oups and obo s pe g oup is manually se . The obo s’
posi ions a e ini ialized andomly wi hin a squa e a ea o ei he
2×2 m o swa ms wi h less han 20 obo s, o 3 ×3m
o swa m sizes g ea e han 20. The o ien a ions o he obo s
a e andomly ini ialized be ween 0 and 2π. The agg ega ion
in g oups is a highly impo an ask ha goes beyond simple
agg ega ion, as i can be used o con enien ly di ide he
labo o he swa m ac oss eams in eal-wo ld geog aphically
dis ibu ed asks [36],[37], such as i e igh ing o sea ch and
escue.
1h ps://gi hub.com/Robolabo/Me eli/ ee/VCommModule
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8IEEE TRANSACTIONS ON CYBERNETICS
Fig. 6. Illus a ion o he p oposed SR expe imen s. (a) Agg ega ion in g oups o desi ed sizes. (b) Fo ma ion o a ge swa m geome ies. (c) Basic o aging
wi h a nes a ea (black), wo ood a eas (g ay), and h ee ed ligh sou ces whe e he obo s can echa ge hei ba e ies. The aim is o pe o m a empo al
ole alloca ion so ha he e a e always N/4 obo s o aging om each o he esou ces (N/2 o age s in o al), while he emaining swa m membe s a e ei he
echa ging hei ba e ies o wai ing inside he nes .
B. Fo ma ion
The second ask is he o ma ion o desi ed swa m geome-
ies (e.g., [38] and [39]). The o ma ion is ela i e o he
cen e o mass o he obo s, implying ha i can be es ablished
anywhe e in he en i onmen . The only equi emen is ha
he dis ances be ween obo s a e app oxima ely p ese ed
acco ding o he geome y o he speci ied o ma ion. As an
example, Fig. 6(b) illus a es a a ge o ma ion wi h nine
obo s.
Le he a ge o ma ion o Npoin s be o mula ed as
ollows:
{x∗
1( ),...,x∗
N( )}={c( )+1,...,c( )+N}(14)
whe e c∈R2is he cen e o mass o he swa m and ∀i∈
{1,...,N},i∈R2
+is he o se ec o ha de ines he
coo dina es o he poin x∗
i ela i e o cin he o ma ion.
In his expe imen , he p imi i e selec o is an injec i e
mapping be ween R={R1,...,RN}and F={ 1,..., N},
so ha each p imi i e has he ollowing meaning:
i−→ “Go o coo dina es x∗
i( )=c( )+i”.
All he spo s o he a ge o ma ion ha e he same impo -
ance and, he e o e, all he i ual egion p io i ies a e ixed
o he same alue o 1 [see (13)]. A he beginning o he
ask execu ion, he a ge o ma ion geome y is manually
se . Mo eo e , obo s’ physical posi ions and o ien a ions a e
andomly ini ialized as in he agg ega ion ask (Sec ion IV-A).
C. Fo aging
The hi d ask is o aging. The en i onmen has a nes
a ea and wo esou ce a eas loca ed a opposi es sides o he
nes . Addi ionally, each obo is equipped wi h a ba e y ha
discha ges when he obo is ou side he nes and can be
echa ged in he p oximi y o a ligh sou ce. The aim is o
main ain 25% o he obo s o aging om ood 1 and ano he
25% ha o age om ood 2. The emaining 50% o he obo s
ei he wai inside he nes o echa ge hei ba e ies. Thus,
he e a e ou oles engaged by he obo s, namely: s ay in
nes , o age ood 1, o age ood 2, and echa ge ba e y.No e
ha his ask equi es dynamic ole alloca ion because when
a o age obo uns low on ba e y and goes o echa ge,
ano he idling obo has o upda e i s ole o o age in i s
place. Fig. 6(c) depic s he o aging expe imen wi h N=12
obo s accomplishing he ask wi h he op imal dis ibu ion o
oles. The igu e also illus a es he loca ions o he nes (black
g ound a ea), he ood a eas (g ay g ound a eas), and he ed
ligh sou ces whe e he obo s can echa ge hei ba e ies.
The ba e y le el o each obo iis deno ed as bi( )∈[0,1]
and is subjec o he dynamics in (15) and (16) o i s cha ge
and discha ge, espec i ely
∂b( )
∂ =γ1−b( )2(15)
∂b( )
∂ =b(16)
whe e γand ba e he cha ge and discha ge coe icien s, and
as ini ial condi ions, we ix b(0)=1.
The e a e N+1 i ual egions, and we de ine ou beha io
p imi i es
1−→ “S ay in he nes a ea,”
2−→ “Fo age om ood a ea 1,”
3−→ “Fo age om ood a ea 2,”
4−→ “Recha ge ba e y (pho o axis”).
Addi ionally, he p imi i e selec o pe o ms he ollowing
mapping be ween i ual egions and p imi i es:
Rnes ={R1,...,RN
2}−→ 1
R ood1 ={RN
2+1,...,R3N
4}−→ 2
R ood2 ={R3N
4+1,...,RN}−→ 3
Rba =RN+1−→ 4.
By de aul , he p io i ies o each i ual egion a e 2 o
he egions in Rnes , 1 in he case o R ood1 and R ood2,
and 3 o Rba . Consequen ly, o aging om one o he ood
a eas has he highes p io i y, s aying in he nes has medium
p io i y, and echa ging he ba e y is a low-p io i y p imi i e.
None heless, when he condi ion bi( )<0.4 is me , he p io i y
o Rba is upda ed o 0, u ning ba e y eco e y in o he
p imi i e wi h highes p io i y. When he ba e y le el is abo e
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SENDRA-ARRANZ e al.: EVOLUTION OF TRANSFERABLE AND SELF-ORGANIZED COMMUNICATION MODULES 9
Fig. 7. Resul s o communica ion module in isola ion. (a) Resul s o h ee
independen simula ions o he i ual na iga ion in he 1-D communica ion
space S1wi h en i ual landma ks and en obo s. (b) Resul s o he i ual
na iga ion in he 2-D communica ion space S2wi h 20 i ual egions and 20
obo s. Red s a s indica e he coo dina es o he i ual landma ks and ci cles
ep esen he communica ion s a es o he obo s. (c) Box plo showing he
e olu ion o he numbe o e o s in he i ual na iga ion du ing a simula ion
wi h 30 obo s. An e o occu s when a obo mo es in o a i ual egion ha
is occupied by ano he obo .
0.9 again, he p io i ies o he co esponding obo e u n o
hei de aul alues. Speci ically, he ollowing p io i y selec o
is used in he o aging ask:
pi( )=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
⎛
⎜
⎝1,...,1
N/2
,2,...,2
N/2
,3⎞
⎟
⎠,i ba e y echa ged
⎛
⎜
⎝1,...,1
N/2
,2,...,2
N/2
,0⎞
⎟
⎠,i ba e y deple ed.
The en i onmen is composed o a nes a ea (ci cula black
g ound a ea), wo ood a eas (ci cula g ay g ound a eas) o
equal adius, and h ee ed ligh sou ces ha can be sensed
om e e y poin in he en i onmen (see Fig. 6). The nes
a ea is always loca ed a he cen e o he a ena and has a
adius wice as la ge as he ood a eas. Speci ically, he nes
adius is ixed o 1 m o swa m sizes smalle han 40 and
2 m o swa ms wi h mo e han 40 obo s. The ood a eas
a e loca ed symme ically a ei he sides o he nes , being
he nes - o- ood dis ance: 3 m o swa ms up o 40 obo s,
and 5 m o swa m sizes g ea e han 40. The obo posi ions
a e ini ialized andomly wi hin a squa e cen e ed a he nes ’s
o igin, o ei he 2 ×2 and 3 ×3 o swa m sizes in he anges
[1,40)and [40,60], espec i ely. The ba e y is always ully
cha ged a he beginning o e e y simula ion, and γand b
a e always ixed o 0.01 and 0.001.
V. RESULTS
A. Communica ion Module in Isola ion
We i s p esen he esul s o he e ol ed communica-
ion module in isola ion, assessing whe he he na iga ion
goal in (4) is ul illed du ing i ual na iga ion in bo h S1
and S2. Focusing i s on he 1-D communica ion space S1,
Fig. 7(a) shows he esul s o i ual na iga ion wi h en i ual
landma ks ( ed s a s) and obo s (whi e ci cles) ac oss h ee
independen execu ions (ho izon al lines). In his case, he
Fig. 8. Resul s o he agg ega ion in g oups wi h swa ms o 20 obo s.
(a) Agg ega ion in wo g oups o en obo s. (b) Agg ega ion in h ee g oups
wi h i egula sizes o 5, 6, and 9 obo s. (c) Agg ega ion in ou g oups o
i e obo s. (d) Agg ega ion in i e g oups o ou obo s.
i ual na iga ion success ully mee s he con e gence c i e ion
de ined in (4). In addi ion, Fig. 7(b) depic s he esul s in
S2using 20 i ual egions and 20 obo s. Fig. 7(c) shows
he e olu ion o he numbe o e o s o e simula ion ime
s eps, in a swa m o 30 obo s using S2as he communica ion
space. E e y 100 ime s eps, he dis ibu ion o e o s is
summa ized as a box plo based on 50 independen uns. The
con e gence ime o each a median e o ( ed segmen s) o
5 is app oxima ely 700 ime s eps, while achie ing a median
e o o 0 equi es a ound 2400 i e a ions. Mo eo e , he
s eady-s a e solu ion exhibi s a s able median alue o 0 and
low a ia ion.
B. Agg ega ion in G oups
Fig. 8shows he posi ions o he obo s in he inal ame
o simula ions wi h 20 obo s and wi h di e en numbe s o
g oups in he agg ega ion ask. In all he uns, he ask is
success ully sol ed, demons a ing ha he swa m is capable
o alloca ing and dis ibu ing i s membe s o di e en g oups
o i he a ge sizes. Addi ionally, i should be no ed ha
he clus e s o agg ega ed obo s end o emain dispe sed,
p e en ing clus e me ge s.
C. Fo ma ion
The swa m o ma ion ask is also sol ed wi h p omising
esul s. Fig. 9(a)–(e) illus a e he con e gence owa d ou
di e en o ma ion geome ies, showing he ajec o ies as
well as he ini ial and inal o ma ions. In all ep esen a ions,
he colo s o he ci cles indica e he ime ins an o he
co esponding o ma ion, acco ding o he imeline in he colo
ba in Fig. 9(g). The sho black lines deno e he o ien a ion
o he obo s. All o ma ions a e eached wi h high accu acy,
s a ing om andomly selec ed ini ial posi ions. Mo eo e ,
Fig. 9( ) p esen s a simula ion in which he a ge o ma ion
is swi ched h ee imes du ing he expe imen . The desi ed
o ma ion geome y is se by explici ly upda ing he i
ec o s o he p imi i es (see Sec ion IV-B). In eal-wo ld
applica ions, he a ge geome y upda e could be eleope a ed
o p ep og ammed.
In addi ion o o ma ion swi ching, Fig. 9( ) also shows
coo dina ed mo emen o he swa m while p ese ing he
con e ged o ma ion. Recall om Sec ion IV-B ha he aim
o he p imi i es is o d i e he obo s owa d he o ma ion
poin s {c( )+1,...,c( )+N}. Thus, once he swa m has
success ully con e ged o he desi ed o ma ion, he en i e
swa m can be con olled by simply adding an o se o bias
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