Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
h ps://doi.o g/10.1007/s10846-025-02277-6
REGULAR PAPER
A Mul i-UAV App oach o Fas Inspec ion o O e head Powe Lines:
F om Rou e Planning o Field Ope a ion
Al a o Caballe o1
·F ancisco Ja ie Roman-Esco za1
·I an Maza1
·Anibal Olle o1
Recei ed: 30 No embe 2024 / Accep ed: 20 May 2025
© The Au ho (s) 2025
Abs ac
O e head powe lines a e c i ical in as uc u es o ensu e a eliable ene gy supply, and ailu es in he g id can lead o signi ican
se ice dis up ions. Loca ing hese aul s quickly is c ucial bu o en challenging, especially in ha d- o- each a eas such as
moun ainous egions. This pape p esen s an in eg a ed solu ion o he long- ange isual inspec ion o o e head powe lines
in minimum ime using eams o Unmanned Ae ial Vehicles (UAVs). The solu ion, designed o e ec i e ield ope a ion while
mee ing end-use equi emen s, comp ises ou e planning, au onomous execu ion, and moni o ing o he inspec ion mission.
Conce ning ou e planning, a capaci a ed min-max mul i-depo ehicle ou ing p oblem has been o mula ed o compu e
easible ou es ha co e he en i e g id in minimum mission ime. The me hod can be applied o he e ogeneous mul i-
UAV eams in e ms o inspec ion speed and ba e y consump ion, which helps maximise he u ilisa ion o a ailable obo s.
Mo eo e , he planning me hod is complemen ed by an accu a e ba e y-consump ion model based on ene gy p inciples ha
cap u es he e ec o pa ame e s o en o e looked such as UAV mass, inspec ion speed, and wea he condi ions. The model
has shown es ima es wi h ela i e e o s no exceeding 1.34% compa ed o eal measu emen s. The p oposed solu ion has
been expe imen ally alida ed unde eal-wo ld condi ions, enabling he au onomous mul i-UAV inspec ion o mo e han 10
kilome es o eal powe lines in 13 minu es, which ep esen s a ime educ ion o up o 67.21% compa ed o he s a e o he
a . The esul ing ideos enabled he iden i ica ion o a simula ed powe ou age and i s exac loca ion.
Keywo ds Unmanned ae ial ehicles ·Ae ial obo ics ·Inspec ion ·Pa h planning
1 In oduc ion
Powe ansmission lines a e c ucial asse s o ou socie y.
S e ching o e housands o kilome e s, powe g ids deli e
elec ici y na ionwide o millions o people, enabling c i ical
indus ial ac i i ies, suppo ing i al se ices, and con ibu -
ing signi ican ly o he economic s abili y o any egion. To
main ain he eliabili y o elec ici y supply, u ili y compa-
nies alloca e subs an ial inancial esou ces o bo h building
BAl a o Caballe o
al [email p o ec ed]
F ancisco Ja ie Roman-Esco za
[email p o ec ed]
I an Maza
[email p o ec ed]
Anibal Olle o
[email p o ec ed]
1GRVC Robo ics Lab, Uni e si y o Se ille, Camino de los
Descub imien os S/N, Se ille 41092, Spain
he in as uc u e and implemen ing obus Inspec ion and
Main enance (I&M) s a egies o p e en po en ial dis up-
ions in he se ice and he ela ed cos s [1].
O e he pas ew yea s, he use o UAVs (Unmanned
Ae ial Vehicles) in I&M asks o o e head powe lines has
a ac ed inc easing a en ion. The e a e comme cial solu-
ions such as [2] ha aim o p e en human ope a o s om
wo king a heigh , g ea ly enhancing ope a ional sa e y while
dec easing cos s. F om a esea ch pe spec i e, he H2020
AERIAL-CORE p ojec 1has played a pi o al ole in ad anc-
ing he ield. This p ojec add essed a b oad ange o I&M
ope a ions in o e head powe lines, which can be classi-
ied in o long-dis ance inspec ion, ae ial manipula ion, and
ae ial co-wo king. These asks encompass accu a e 3D map-
ping o powe lines [3], au onomous powe -g id inspec ions
using ad anced con ol echniques [4], deploying bi d- ligh
di e e s, senso s, and o he equipmen ia ae ial obo ic
manipula o s [5–7], as well as enabling in e ac ions be ween
1h ps://ae ial-co e.eu/
0123456789().: V,- ol 123
67 Page 2 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
ae ial obo s and humans wo king a heigh o ool hando e
[8], among o he ac i i ies. Pa allel esea ch ini ia i es also
p opose aligned de elopmen s [9–11].
While nume ous speci ic challenges associa ed wi h using
UAVs o I&M asks on o e head powe lines ha e been
add essed in he li e a u e, mos s udies concen a e on wo
p ima y app oaches: p ecise inspec ion o indi idual ans-
mission owe s and long- ange inspec ion o en i e powe
g ids. In bo h scena ios, planning echniques a e c ucial o
achie e use ul ou comes [12–18].
Fo he p ecise inspec ion o indi idual ansmission ow-
e s, he planning app oach ypically in ol es combining
a ious inspec ion goals in o an op imisa ion p oblem o
compu e a pa h ha emains inside a es ic ed wo kspace.
A no able example is p esen ed in [12], whe e an op imisa-
ion p oblem is o mula ed by conside ing ligh ime, image
quali y, and owe co e age. This p oblem is add essed using
pa icle swa m op imisa ion and simula ed annealing, achie -
ing a well-balanced ade-o among hese h ee pe o mance
me ics. Some s udies inco po a e mul iple UAVs o accel-
e a e he inspec ion p ocess. Howe e , his inc eases he
complexi y o planning, as sa e y be ween UAVs mus be
gua an eed h oughou he mission. Signal Tempo al Logic
can be applied o ensu e his sa e y equi emen is me , along
wi h he o he objec i es [13].
In con as , he planning p oblem o long- ange powe -
g id inspec ion ypically comp ises lying la ge dis ances
while op imising ou es and adhe ing o co e age equi e-
men s and ba e y limi a ions. Gi en ha he VRP (Vehicle
Rou ing P oblem) and i s a ia ions ha e p o en e ec-
i eness o planning asks modelled as g aphs [19], mos
s a e-o - he-a app oaches o powe g id inspec ion ea
he planning p oblem as a a ian o his me hod. In his con-
ex , [14] p oposes a gene alisa ion o he TSP (T a eling
Salesman P oblem) o e icien UAV-based ansmission-
line inspec ions. The o mula ion accoun s o he limi ed
ligh ime o UAVs and in oduces mul i- ou s a egies o
ensu e ull co e age o he powe g id. Howe e , he solu-
ion ocuses on he use o single UAVs, which may p o e
inadequa e o p ac ical applica ions due o hei limi ed
endu ance. To add ess his, o he publica ions explo e he
coo dina ed use o UAVs wi h g ound ehicles ha deploy
and eco e hem o ex ended ange ope a ions [15–17], o
conside mul i-UAV s a egies ha inspec all he elec ic
owe s inside a designa ed a ea bu o e look he connec ing
cables [18]. The e a e also con ibu ions p oposing he use o
mul i- obo ne wo ks o gene al moni o ing and inspec ion
ope a ions, which can be adap ed o powe -g id inspec ion
[20].
Despi e he aluable publica ions on ou e planning o
long- ange inspec ion o powe g ids, mos o hese con-
ibu ions p io i ise he o mula ion o heo e ical p oblems
and hei solu ion me hods wi hou ho oughly e alua ing
he e ec i eness o he esul ing plans du ing eal-wo ld
UAV inspec ions. Thus, many o hem ocus on sol ing la ge
g ids, some imes a i icially complex, in bounded compu a-
ion imes. Howe e , hey a e a he same ime dis ega ding
p ac ical aspec s like cu en egula o y cons ain s, he e ec
o wea he condi ions in he planned ou es o equi emen s
imposed by end use s o gua an ee ce ain quali y le el in he
cap u ed images o ideos. In addi ion, hey usually assume
he a ailabili y o in o ma ion ha is some imes no easily
accessible in p ac ice, such as he accu a e loca ion o elec-
ic owe s. To he bes o he au ho s’ knowledge, he e a e
no p io publica ions de o ed o he au onomous long- ange
inspec ion o o e head powe lines using a mul i-UAV eam
wi h e ec i e ope a ion in eal ield expe imen s.
1.1 Con ibu ions and Ou line
This a icle is an ex ension o he con e ence pape [21]. In
ha publica ion, a ou e planning me hod o as inspec-
ion o o e head powe g ids using a eam o UAVs was
i s p esen ed and analysed, and p elimina y expe imen s
we e ca ied ou as a i s p oo o concep . The me hod,
which inco po a es ba e y cons ain s and suppo s he e o-
geneous UAVs in e ms o ligh speed and ba e y capaci y,
can in eg a e a clus e ing app oach o educe compu a ional
load while p ese ing he quali y o he solu ion.
This a icle builds upon he p e ious ou e planne and
enhances i by adding se e al new ea u es. The esul is
an in eg a ed solu ion ha allows a mul i-UAV eam o
au onomously pe o m he e ec i e long- ange inspec ion o
o e head powe g ids in eal-wo ld condi ions (see Fig. 1),
p oducing use ul ideos as he ou pu . Mo e in de ail, he
main con ibu ions o his pape can be enume a ed as ol-
lows:
Fig. 1 Mul i- o o ae ial obo au onomously execu ing a long- ange
mul i-UAV mission o isual inspec ion o a eal o e head powe line
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 3 o 21 67
1. Adap a ion o he inspec ion app oach p esen ed in [21]
so ha he ideos ob ained when UAVs execu e planned
ou es sa is y end-use equi emen s. These equi emen s
ha e been p o ided by e-dis ibución2, he la ges elec ic
powe dis ibu ion company in Spain, and ange om he
ela i e posi ion ha he UAV came a should keep wi h
espec o he powe g id o co e age equi emen s.
2. Accu a e model o ba e y consump ion used o plan
easible ou es ha can be comple ed by hei assigned
UAVs. This model cap u es he e ec on he ene gy
consump ion o he UAV mass, he inspec ion speed
and he wea he condi ions ( empe a u e, a mosphe ic
p essu e, and wind magni ude and di ec ion), among
o he ele an pa ame e s ha a e equen ly neglec ed.
The p esen ed model has been alida ed using s a is ical
esul s ex ac ed om ligh expe imen s.
3. Uni ied so wa e amewo k o e ec i e ield ope a ion.
The p oposed app oach in oduces and in eg a es se -
e al so wa e modules o add ess speci ic aspec s ha
a ise when in ended o usage in eal-wo ld condi ions.
These modules include a GUI (G aphical Use In e ace)
o easily se up and launch mission planning, he in e-
g a ion o hi d-pa y APIs (Applica ion P og amming
In e aces) o ob ain bo h eal- ime wea he o ecas s o
eed he consump ion model and e ain ele a ion mod-
els o accu a ely loca e ansmission owe s, along wi h
he so wa e ha enables au onomous mission execu ion
and moni o ing. All o his so wa e has been eleased as
open sou ce.
4. Fligh expe imen s in eal-wo ld condi ions. The in e-
g a ed solu ion p esen ed in his pape was success ully
es ed du ing he inal li e demons a ion o he Eu opean
p ojec AERIAL-CORE. A he e ogeneous mul i-UAV
eam was able o au onomously inspec a eal powe g id
consis ing o mo e han 10 kilome es o o e head powe
lines wi h se e al o ks in 13 minu es, while s eaming
he cap u ed ideos o a GCS (G ound Con ol S a ion)
and iden i ying a simula ed powe ou age and i s exac
loca ion.
The subsequen sec ions o he manusc ip a e s uc-
u ed as ollows. Fi s ly, Sec ion 2desc ibes he mul i-UAV
inspec ion p oblem. Secondly, Sec ion 3models he p e i-
ous p oblem, ocusing on a g aph-based abs ac ion o i ,
a clus e ing me hod o simpli y he esul ing g aph, and he
de i a ion o a model o ba e y consump ion o UAVs. Nex ,
Sec ion 4is de o ed o he mul i-UAV ou e planning me hod
o as inspec ion o o e head powe g ids. Then, Sec ion 5
add esses he main aspec s ha should be aced o an e ec-
i e ield ope a ion o he app oach p oposed in his pape .
Sec ion 6shows a gene al iew o he esul ing in eg a ed
2h ps://www.edis ibucion.com/
solu ion and he connec ions be ween i s main modules in o-
duced be o e. Once he comple e amewo k is p esen ed,
Sec ion 7 alida es i h ough ligh expe imen s in eal-wo ld
condi ions and compa es i o he s a e o he a . Finally,
Sec ion 8summa ises he conclusions.
2 The Mul i-UAV Inspec ion P oblem
This a icle concen a es on he au onomous inspec ion o
o e head powe g ids using a lee o UAVs endowed wi h
came as while minimising he mission ime. These powe
g ids a e composed o ansmission owe s and he con-
nec ing wi es, and hei cha ac e is ics a e usually known,
including he owe coo dina es (la i ude and longi ude), hei
ype and size, and he wi ing be ween hem. Rega ding he
UAVs, hey may ha e he e ogeneous capabili ies in e ms o
ba e y consump ion and ligh speed, and commanded and
supe ised om a cen alised GCS, each o hem ope a es
om a s a ion whe e i akes o and lands sa ely, exis ing
also he possibili y o echa ging ba e ies au onomously by
con ac o ex ended ope a ions (see Fig. 2).
An inspec ion mission s a s wi h he UAVs wai ing o
a mission in hei espec i e s a ions and consis s o se e al
s eps. Fi s ly, a ou e planning me hod compu es he bes
inspec ion sequence o each UAV. Then, he UAVs should
ack he plan au onomously while hey s eam he cap u ed
ideos o a GCS. This in o ma ion is also eco ded on boa d
he ae ial obo s. Simul aneously, he ansmi ed in o ma ion
can be analysed in eal ime by an ope a o specialised in his
ask o de ec de ec s o ailu es. Finally, he mission inishes
when all he UAVs e u n o hei s a ions a e comple ing
he g id inspec ion.
Conce ning he e ec i eness o he inspec ion, he ideos
ob ained by he UAVs mus sa is y end-use equi emen s.
These equi emen s a e based on hose used in cu en inspec-
ions conduc ed om manned helicop e s (see Fig. 3). The
main equi emen s can be enume a ed as ollows.
Fig. 2 Mul i- o o UAV and i s s a ion o sa e ake-o , landing, and
au onomous ba e y echa ging by con ac
123
67 Page 4 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
Fig. 3 Video snapsho om a cu en inspec ion conduc ed using a
manned helicop e
Requi emen 1 (Video pe spec i e). The ela i e posi ion
ha he UAV came a mus keep wi h espec o he powe g id
(bo h dis ance and o ien a ion) has o be adjus ed o ensu e
ha a good pe spec i e o he powe -g id elemen s can be
cap u ed du ing he inspec ion. This adjus men in ol es
mo ing he ligh pa h la e ally wi h espec o he powe -
line axis, so ha he angle be ween he sho es segmen
connec ing he UAV came a o he powe line and he line
pe pendicula o he g ound is app oxima ely 45 deg ees.
Al hough i is easie o cap u e a zeni hal pe spec i e (0
deg ees) since i in ol es lying di ec ly o e he owe coo -
dina es a a ce ain al i ude, his pe spec i e does no o e ,
o example, a clea iew o he dis ance be ween ege a ion
on he g ound and he powe -line cables.
Requi emen 2 (Powe -g id co e age). The UAV ideos mus
cap u e all he elemen s o he powe g id and i s su ound-
ings, including ansmission owe s and hei ounda ions,
cables, ege a ion, buildings, and po en ial de ec s, while
ensu ing con inuous ideos ha co e he en i e leng h o
he powe lines.
Requi emen 3 (De ec loca ion). The ideo ames mus be
geo e e enced a all imes in o de o iden i y he exac loca-
ion o any de ec ha migh be ound in he powe g id,
ei he du ing he mission execu ion o in subsequen pos -
p ocessing o he eco ded ideos.
3 P oblem Modelling
This sec ion is de o ed o modelling he p oblem desc ibed
abo e, as he ou e planne p esen ed la e in Sec ion 4is
buil upon he de i ed models. As desc ibed he eina e , he
modelling ocuses on h ee aspec s: a g aph-based abs ac-
ion o he inspec ion p oblem, a clus e ing me hod ha can
be used o simpli y he esul ing g aph, and he o mula ion
o a ba e y consump ion model o UAVs.
3.1 Inspec ion G aph
This pape u ilises g aph heo y o model he mul i-UAV
inspec ion p oblem. Gi en he powe g id o be co e ed,
whe e he loca ions o i s ansmission owe s and hei in e -
connec ions a e known, along wi h he a ailable UAVs and
he coo dina es o hei s a ions as inpu s, a g aph-based
abs ac ion o he inspec ion p oblem can be de i ed. Speci i-
cally, he p oblem can be modelled using a di ec ed weigh ed
mul ig aph G=(V,E,W,D), which is depic ed wi h a sim-
ple example in Fig. 4and explained in de ail below.
The se V=P∪O ep esen s he g aph nodes and
consis s o wo componen s: he se o n ansmission ow-
e s P={1,2, ..., n}, and he se o δUAV s a ions O=
{01,02, ..., 0δ}, whe e δdeno es he numbe o agen s a ail-
able in he mul i-UAV eam. This eam is ep esen ed by he
se D, wi h |D|=δ.
The nodes in Va e connec ed by he se o edges E, ep-
esen ing possible UAV ligh pa hs be ween hese nodes.
Associa ed wi h he edges in E, he e is he se o cos s
W=T∪B, whe e he se s Tand Bco espond o he cos s in
e ms o ligh ime and ba e y consump ion be ween nodes,
espec i ely. The ligh imes a e calcula ed based on he
UAV ligh speeds du ing he inspec ion and he loca ions o
he elec ic owe s and he UAV s a ions. Addi ionally, when
he UAVs e u n o hei s a ions o ba e y echa ging, he
cha ging du a ion is ac o ed in o he o al ligh ime. Ba e y
consump ion calcula ions a e add essed la e in Sec ion 3.3.
Rega ding he numbe o edges be ween wo nodes and
hei cha ac e is ics, wo key aspec s mus be aken in o
accoun . Fi s , since he UAVs may be he e ogeneous, he
ligh cos be ween wo nodes a ies depending on he spe-
ci ic UAV used. Second, he ligh cos may also be in luenced
by he ligh di ec ion, o ins ance, due o wind condi ions.
As a esul , he numbe o edges connec ing wo nodes is
Fig. 4 G aph-based abs ac ion o he mul i-UAV inspec ion p oblem.
Simple example wi h wo connec ed owe s and wo he e ogeneous
UAVs
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 5 o 21 67
2×δ, excep in cases whe e one node belongs o he se O,
since each UAV mus ope a e om i s designa ed s a ion. In
hese cases, he numbe o edges is 2. Nodes wi hin he se O
a e no connec ed be ween hem. Thus, he edge ei,j|k∈E
ep esen s he possible ligh o UAV k om node i o node
j(i= j), which akes ime i,j|k∈Tand uses ba e y
ene gy bi,j|k∈B, no malised ela i e o ull ba e y capac-
i y. Gene ally, i,j|k= j,i|kand bi,j|k= bj,i|k,aswellas
i,j|k= i,j|qand bi,j|k= bi,j|q, whe e q∈Dand q= k.
Despi e he p e ious conside a ions, he edges in Ecan be
di ided in o wo dis inc se s: E=C∪U. On one hand, he
se Ccomp ises all edges connec ing wo nodes wi hin he
se P, when hese nodes ep esen ansmission owe s ha
a e physically connec ed in he ac ual powe g id, as shown
in Fig. 4 o nodes 1 and 2 (dashed edges). On he o he hand,
he se Uconsis s o he emaining edges no included in C
(do ed edges in Fig. 4).
3.2 Powe -G id Clus e ing
The sea ch o op imal solu ions in g aphs like he one p e-
sen ed in he p e ious subsec ion is widely ecognised as
an NP-ha d (Non-de e minis ic Polynomial- ime ha d) p ob-
lem, whe e he compu a ional load escala es d as ically as
he numbe o ehicles and nodes inc eases. As a esul ,
inding exac solu ions wi hin a easonable ime becomes
challenging as he p oblem size g ows. To ackle his issue,
heu is ic me hods a e commonly employed [22]. These
me hods p o ide al e na i e s a egies o he op imisa ion
p ocess, yielding subop imal solu ions ha a e accep able
wi hin bounded compu a ion imes. In addi ion o educ-
ing compu a ional complexi y h ough heu is ics, ano he
app oach is he adop ion o clus e ing me hods [23], which
can help o simpli y he g aph ep esen a ion o he mul i-
UAV inspec ion p oblem.
A clus e ing me hod was i s p oposed in he p e ious
pape o he au ho s [21], and i s ope a ion basis has been
ou lined he e o he sake o comple eness. As depic ed in
Fig. 5, he clus e ing me hod g oups segmen s o he powe
g id loca ed wi hin he same b anches based on a consump-
ion c i e ion, c ea ing simpli ied b anches ha ep esen he
o iginal ones. Thus, e e y clus e ensu es ha he ba e y
h eshold α∈(0,1)is ne e exceeded o any UAV in he se
D. I is impo an o no e ha his p ocess main ains ace-
abili y be ween he edges o o iginal and clus e ed powe
g ids as illus a ed in Fig. 5. The e o e, ou e planning can
be o mula ed on he simpli ied g aph and, once a solu ion
is ound, his can be ep esen ed in ela ion o he o iginal
powe g id. Fo mo e de ails abou his clus e ing me hod,
please e e o Sec ion IV in pape [21].
Fig. 5 G aphical ep esen a ion o he clus e ing me hod: o iginal ( op)
and clus e ed (bo om) powe g ids
3.3 Ba e y Consump ion
The g aph-based abs ac ion p esen ed in Sec ion 3.1 asso-
cia es es ima es o ba e y consump ion wi h he edges in he
g aph. These cos s will be used o ou e planning, and conse-
quen ly, he easibili y o he compu ed solu ions will depend
on he accu acy o he cos es ima es. Fo his eason, his
sec ion in oduces a model o ene gy consump ion designed
o accu a ely es ima e he elec ic powe equi ed by mul i-
o o UAVs when lying be ween ansmission owe s and
s a ions, and by ex ension, he le el o ba e y ha is d ained.
This model cap u es he impac on he ene gy consump-
ion o UAV mass, inspec ion speed, and wea he condi ions
( empe a u e, a mosphe ic p essu e, and wind magni ude and
di ec ion), among o he ele an pa ame e s ha a e o en
o e looked.
Since mos o he ligh ime in missions like inspec ions o
powe g ids is spen lying ho izon ally a cons an speed o e
inspec ion a ge s, he p esen ed consump ion model ocuses
on o wa d ligh s. Mo eo e , sho ansi ions in ol ing axial
ligh s, such as ascen and descen du ing ake-o and land-
ing, do no signi ican ly con ibu e o he o al consump ion
in such missions as hey usually ep esen less han 5% o
he o al ligh ime (e.g., 1-2 minu es in missions a ound 40
minu es), and p ac ical applica ions ha e shown ha hese
axial ansi ions a e ypically pe o med a low speeds. Con-
sequen ly, he associa ed ene gy consump ion is simila o he
consump ion in ho e ing ligh condi ions [24,25], which is
a pa icula case o o wa d ligh wi h a o wa d speed equal
o ze o.
123
67 Page 6 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
The model o ene gy consump ion desc ibed he e is based
on ene gy p inciples and makes use o he ae odynamic
powe in i s de i a ion. Thus, s a ing om he se o pa am-
e e s lis ed in Table 1, he di e en componen s o he
ae odynamic powe equi ed o any gi en mission can be
es ima ed. Then, he P inciple o Conse a ion o Ene gy
can be le e aged o ob ain he associa ed elec ic powe
demanded om he UAV ba e ies. Finally, he ba e y cha ge
equi ed o sa is y he elec ici y demand can be deduced
om such elec ic powe . Mo e de ails a e p o ided below.
Inspi ed by he P inciples o Helicop e Ae odynamics
[24], he ae odynamic powe Pao a mul i- o o UAV can be
modelled as
Pa=n (Pi+P0)+P (1)
whe e Piis he induced powe o speed up he o o ai low
and p oduce h us , P0is he p o ile powe associa ed wi h
he d ag o he o o blades, and P is he pa asi ic powe
equi ed o coun e ac he d ag o he ai ame. In con as
o o he simpli ied consump ion models used o planning
pu poses, whe e he ae odynamic powe is equen ly es i-
ma ed only o ho e condi ions and he con ibu ions o he
blade p o ile powe and he pa asi ic powe a e neglec ed,
he model p esen ed he e is mo e complex bu leads o mo e
accu a e es ima es.
Conce ning he induced powe Pi o each o o , he e is
he ollowing ela ion wi h he h us Texe ed by he o o
and i s induced eloci y i
Pi=κT i(2)
Table 1 Pa ame e s used as inpu s in he model o ba e y consump ion
Pa ame e Desc ip ion
mUAV mass (including payload)
gG a i y accele a ion
n Numbe o o o s
nbNumbe o o o blades
RRadius o he o o s
cBlade cho d
QBa e y ene gy
ClLi coe icien ( o o blade)
CdD ag coe icien ( o o blade)
ρAi densi y
Equi alen la -pla e a ea ( uselage)
κInduced powe ac o
KμNume ical cons an
ηAe odynamic e iciency
Addi ionally, acco ding o he Momen um Theo y [24], he
induced eloci y i ul ils
i=− ∞sin(α ), (3)
whe e ∞is he UAV ai speed, α he angle o a ack o he
o o s and a a iable whose alue can be compu ed using
again he Momen um Theo y om
− ∞sin(α )−T
2ρπR2 2
∞cos2(α )+2=0.(4)
Going back o Equa ions (2)-(4), he h us Tand he angle
o a ack α can be compu ed by es ablishing equilib ium o
o ces o he ehicle in o wa d ligh
T=mg
n cos(α )(5)
an(α )=D
mg ,(6)
being D he d ag o he ai ame, which can be modelled as
D=1
2ρ 2
∞ .(7)
The pa ame e is known as he equi alen la -pla e a ea
and accoun s o he d ag o he ai ame [24]. I may be
de ined as =CD S e , whe e S e is a e e ence a ea
whose de ini ion may no be unique, and CD is he ai ame
d ag coe icien based on ha e e ence a ea. Howe e , he
di ec use o he pa ame e helps o a oid po en ial ambi-
gui ies associa ed wi h he choice o S e .
Rega ding he blade p o ile powe P0, he applica ion o
he Blade Elemen Theo y [24] gi es ise o
P0=ρR43nbcCd
81+Kμ ∞cos(α )
R2(8)
=6T
ρnbcR3Cl
−3
2 ∞cos(α )
R2
,(9)
whe e is he o a ional speed o he o o s.
Swi ching o he pa asi ic powe P , his is by de ini ion
P =D ∞.(10)
Once he ae odynamic powe Paused o li he ehicle
is compu ed, he elec ic powe Pegene a ed by he UAV
ba e ies can be es ima ed h ough he Law o Conse a ion
o Ene gy. Acco ding o his law, he elec ic powe Peis
ans o med in o he ae odynamic powe Pa, wi h ce ain
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 7 o 21 67
powe losses quan i ied h ough he e iciency pa ame e η.
Consequen ly,
Pe =Pa
η.(11)
whe e he ae odynamic e iciency ηcan be conside ed a
cons an pa ame e , as i has been demons a ed o mo o -
p opelle combina ions ecommended by manu ac u e s and
wo king a ypical ope a ing condi ions [26].
Finally, he ba e y cha ge Ee, e e enced wi h espec o
he maximum ba e y capaci y Q(Ee∈[0,1]), equi ed o
p o ide he elec ic powe Pedu ing a ligh ime can be
deduced om
Ee=1
Q
0
Ped .(12)
This ba e y cha ge Eeis used o he g aph-based ep esen-
a ion o he inspec ion p oblem, gi ing he alues o bi,j|k
in Sec ion 3.1.
Figu e 6shows he e olu ion o he elec ic powe Pe,
compu ed acco ding o p e ious equa ions, wi h espec o
he ai speed ∞and he mass m o a s anda d UAV. As can
be obse ed, he elec ic powe dec eases wi h inc easing low
o wa d speeds [27]. In con as , his powe inc eases d ama -
ically a high speeds due o pa asi ic losses. The combina ion
o bo h e ec s leads o he exis ence o an op imal alue o
he o wa d speed ha maximises he ime ha he ehicle
can ly wi hou echa ging ba e ies. Based on [24], an es i-
ma e o his op imal o wa d speed ∗
∞adap ed o mul i- o o
UAVs is gi en by
∗
∞=mg
ρπR2κπR2
3n 1/4
.(13)
Aligned wi h he la e , he esul s demons a e ha o he
simpli ied models, such as he one adop ed in [25], whe e
he ae odynamic powe is always app oxima ed by he one
equi ed in ho e condi ions ( ∞=0), gi e an o e es i-
ma e o he elec ic powe . Al hough hose models could be
assumed alid o low speeds and imply es ima es on he side
o sa e y, hey may esul in signi ican e o s. Figu e 6also
shows how he elec ic powe always inc eases wi h he UAV
mass, which is an expec ed phenomenon.
The ai speed ∞used in he p e ious de i a ions is he el-
a i e ho izon al speed ha he UAV expe iences wi h espec
o he ai . Howe e , he g ound speed gis used in his pape
as a e e ence since i is di ec ly ela ed o he speed ha
ensu es a p ope in o ma ion cap u e due o came a senso
limi a ions. The ela ion be ween bo h ai and g ound speeds
is gi en by
∞= 2
g+ 2
w−2 g wcos(θw), (14)
whe e wis he wind speed, and θwis he angle be ween
he g ound speed and he wind speed ec o s. This equa ion
means ha bo h speeds coincide only when he e is no wind.
In he es o he cases, lying a ce ain g ound speed implies
ha he wind has an e ec on he ene gy consump ion. This
e ec can be bene icial o no depending on he magni ude
Fig. 6 E olu ion o he elec ic
powe Pedemanded by a
s anda d UAV wi h espec o i s
o wa d ai speed ∞and i s
mass m
123
67 Page 8 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
and o ien a ion o he wind wi h espec o he UAV mo e-
men and can be es ima ed by in eg a ing Equa ion (14)in o
Equa ions (1)-(12).
I should be highligh ed ha he e ec on he ba e y con-
sump ion o o he wea he a iables like empe a u e Tand
a mosphe ic p essu e pis also cap u ed in he de i ed model
h ough he ai densi y ρ. In his sense, he Ideal Gas Law
o e s he ollowing ela ion ha can be adop ed he e
ρ=Mmp
RgT,(15)
whe e Mmis he mola mass o he ai , and Rgis he uni-
e sal gas cons an . O he simpli ied models like he ISA
(In e na ional S anda d A mosphe e) model assume ixed
s anda d-day empe a u e and p essu e and he e o e canno
cap u e me eo ological a ia ions (e.g., ba ome ic luc ua-
ions due o wind condi ions, o daily empe a u e swings)
ha signi ican ly a ec he powe consump ion h ough he
ai densi y. To p o ide mo e accu a e ene gy es ima es, Equa-
ion (15) needs o be e ained, compu ing densi y om
he ac ual ambien p essu e and empe a u e measu emen s
a he han om nominal alues.
4 Rou e Planning
The calcula ion o e icien ou es o he inspec ion o o e -
head powe lines by only one UAV ends o be ela i ely
simple, bu such inspec ions may equi e signi ican ime o
be comple ed. To o e come his limi a ion, mul i-UAV s a e-
gies a e commonly implemen ed o accele a e he inspec ion.
Howe e , de e mining op imal ou es ha minimise he o e -
all mission du a ion becomes mo e challenging when powe
g ids ha e complex opologies and mul iple UAVs, po en-
ially wi h he e ogeneous capabili ies in ba e y consump ion
and ligh speed, a e in ol ed. In his con ex , his sec ion
p esen s a ou e planning app oach designed o compu e he
op imal assignmen and inspec ion sequence o each ae ial
obo .
4.1 Capaci a ed Min-Max Mul i-Depo Vehicle
Rou ing P oblem
S a ing om he g aph-based abs ac ion p esen ed in
Sec ion 3.1, o i s clus e ed e sion acco ding o Sec ion 3.2,
he inspec ion mission can be e o mula ed as an op imisa-
ion p oblem on he g aph G, whe e he op imal assignmen
and inspec ion sequence mus be de e mined o each UAV.
Speci ically, each UAV in se Ds a s and inishes a i s s a-
ioninse O, lying be ween he nodes in se P o ully co e
all edges in he se C, ei he in one di ec ion o in he opposi e,
wi hin he sho es mission ime as de e mined by he cos s
in se T. This mus be achie ed while espec ing he UAV
ba e y capaci y cons ain s, e i ied using he cos s in se B
and compu ed acco ding o Sec ion 3.3. This implies ha i
he inspec ion ask exceeds he UAV anges on a single ba -
e y cha ge, hey mus e u n o hei s a ions o echa ge he
ba e ies be o e esuming he mission.
The p oblem ou lined abo e can be app oached as a a i-
an o he VRP, named he e capaci a ed (UAVs wi h limi ed
ba e y) min-max (minimisa ion o he inspec ion ime o he
UAV ha akes he longes ime) mul i-depo (UAVs ope a -
ing om di e en s a ions) VRP, and i s exac solu ion can
be ob ained using MILP (Mixed In ege Linea P og am-
ming). To achie e his, a se o decision a iables Xneeds
o be de ined, whe e he bina y a iables xi,j|k∈Xindica e
whe he he edges ei,j|k∈Ea e co e ed (xi,j|k=1) o no
(xi,j|k=0). Addi ionally, i should be no ed ha op imising
he mission du a ion o he mul i-UAV eam equi es min-
imising he inspec ion ime o he UAV ha akes he longes
ime o comple e i s ou e, as he mission concludes only once
he las UAV has e u ned o i s s a ion. To accommoda e his
min-max objec i e, which is inhe en ly nonlinea , he objec-
i e can be e o mula ed o MILP by minimising he sum
o inspec ion imes o all UAVs, while aiming o keep hese
imes balanced. To inco po a e his balance wi hin he op i-
misa ion p oblem, eal a iables y ,q≥0 a e in oduced o
each pai o UAVs and qin se D, whe e <q. These a i-
ables cap u e he di e ences in inspec ion imes be ween he
pai s o UAVs indica ed by hei subsc ip s (e.g., be ween he
pai s o agen s {1,2},{1,3}and {2,3}i he e a e 3 a ailable
UAVs).
Taking in o accoun all he p eceding aspec s, he MILP
p oblem can be p esen ed in he ollowing manne
min
xi,j|k,y ,q
{i,j}∈V
i= j
k∈D
i,j|kxi,j|k+
{ ,q}∈D
<q
y ,q(16)
s. .
j∈P
x0k,j|k≥1∀k∈D(17)
i∈P
xi,0k|k≥1∀k∈D(18)
j∈V
j=ixi,j|k−xj,i|k=0∀i∈V,∀k∈D(19)
k∈Dxi,j|k+xj,i|k≥1∀{i,j}|ei,j|k∈C,i<j(20)
{i,j}∈V
i= j i,j| xi,j| − i,j|qxi,j|q−y ,q≤0
∀{ ,q}∈D, <q(21)
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 9 o 21 67
{i,j}∈V
i= j i,j|qxi,j|q− i,j| xi,j| −y ,q≤0
∀{ ,q}∈D, <q(22)
i∈S
j/∈S
k∈D
xi,j|k+xj,i|k≥2h(S)∀S⊂P(23)
In his o mula ion, he objec i e unc ion in Equa ion (16)
aligns wi h he op imisa ion app oach ou lined be o e. Con-
s ain s (17) and (18) ensu e ha all UAVs s a and inish
he mission a hei designa ed s a ions. These cons ain s
also pe mi UAVs o e isi he s a ions i ba e y echa g-
ing is needed. Cons ain s (19) main ain con inui y a each
node o each UAV, meaning ha i a UAV eaches a node, i
mus also depa om ha node. Cons ain s (20) ensu e ull
co e age o he powe g id, as hey equi e a leas one edge
be ween e e y pai o connec ed owe s in se C o be chosen,
in ei he di ec ion. Cons ain s (21) and (22) a e se o bal-
ance inspec ion imes be ween UAVs. By including he sum
o decision a iables y ,qin he objec i e unc ion, minimis-
ing his sum en o ces minimisa ion o indi idual y ,q alues,
he eby balancing inspec ion imes o each UAV pai and
qacco ding o hese cons ain s. Finally, Cons ain s (23)a e
commonly known as he sub ou elimina ion cons ain s and
hei implemen a ion has been widely s udied in he li e a u e
[28,29]. They p e en he c ea ion o sub ou s unconnec ed
o any s a ion o ou s ha su pass he UAV ba e y capaci ies.
He e, he unc ion h(S)p o ides a lowe bound on he UAV
en ies and exi s ha e e y subse Sin P equi es. Howe e , as
he numbe o subse s Scan be subs an ial, hese cons ain s
a e gene ally omi ed ini ially and added inc emen ally when
unme [30]. To u he expedi e he op imisa ion p ocess,
hese addi ional ba e y cons ain s can also be inco po a ed
{i,j}∈V
i= j
bi,j|kxi,j|k≤
j∈P
x0k,j|k∀k∈D(24)
These cons ain s equi e ha he o al ba e y consumed by
each UAV along i s ope a ion (le -hand side o he inequal-
i y) does no exceed he numbe o imes i depa s om i s
s a ion ( igh -hand side o he inequali y), unde he assump-
ion ha he UAVs always lea e hei s a ions wi h ully
cha ged ba e ies.
4.2 Rou e Recons uc ion
The solu ion o he MILP p oblem in he p e ious subsec-
ion p o ides he se o decision a iables xi,j|kwi h a bina y
alue o 1, hus yielding he se E∗o selec ed g aph edges
e∗
i,j|k o be co e ed by he mul i-UAV eam. Nex , he edges
e∗
i,j|kassigned o a pa icula UAV kcan be easily iden i ied,
as hese a e al eady indexed by k. Subsequen ly, he inspec-
ion sequence o each UAV kcan be de e mined in o de by
s a ing om i s edge e∗
i,j|kwhe e index iis equal o 0kand
sequen ially linking edges un il eaching i s edge e∗
i,j|kwhe e
jequals 0k. In cases whe e mul iple edges e∗
i,j|kha e indices
iequal o 0k o he same UAV k, his indica es he p esence
o mul iple ou s o ha UAV. Ne e heless, all hese ou s
can be handled as a single mul i- ou sequence, assembled
by linking each ou h ough he node 0k. This app oach ul i-
ma ely p o ides each UAV kwi h an op imised ou e Rk,
ep esen ed as a so ed se o nodes di ec ly de i ed om he
p eceding edge sequence, as ollows
Rk={0k,A,B..., C, ..., D,E,0k}∀k∈D,(25)
whe e A,B,C,D, and E ep esen he nodes ( ansmission
owe s) ha UAV kmus isi du ing he inspec ion mission.
Nodes such as B,C,o Dmay also ep esen he s a ion 0k.
5 Conside a ions o Effec i e Field
Ope a ion
The app oach in oduced so a es ablishes a solid s a egy
o compu e easible ou es ha can lead he mul i-UAV eam
o he e icien inspec ion o o e head powe g ids. Nex ,
he main aspec s ha mus be aced o an e ec i e ield
ope a ion ha e been add essed along his sec ion.
5.1 Accu a e UAV Posi ioning
The ou e planne p esen ed in Sec ion 4gi es he sequences
o ansmission owe s and s a ions ha he UAVs mus ol-
low o pe o m hei mission. Then, hese sequences mus be
ans o med o he WPs (Waypoin s) ha e e y UAV mus
ack. Since he elemen s in he powe g id a e he inspec-
ion a ge s, he UAV posi ioning will be calcula ed ela i e
o he powe -g id loca ion. The e o e, he 3D loca ion o he
ansmission owe s in he g id mus be known.
Acco ding o in o ma ion p o ided by he powe dis-
ibu ion company e-dis ibución, he coo dina es o he
ansmission owe s (la i ude and longi ude), hei ypes and
sizes, and he wi ing be ween hem a e commonly s o ed
in accessible da abases, bu hei al i udes a e no included.
This lack o al i ude in o ma ion may ha e a limi ed impac
on inspec ions wi h a zeni hal pe spec i e, as ep esen ed in
Fig. 7(le ), whe e inaccu acies in he UAV e ical posi ion-
ing ela i e o he powe line s ill allow sa is ying co e age
equi emen s. Howe e , hese same inaccu acies can lead o
ine ec i e esul s o inspec ions acco ding o Requi emen 1
in Sec ion 2, as depic ed in Fig. 7( igh ).
123
67 Page 16 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
7.2 Real Powe -G id Inspec ion
The in eg a ed solu ion o he inspec ion o o e head powe
lines using a mul i-UAV eam has been expe imen ally ali-
da ed unde eal-wo ld condi ions. These expe imen s we e
pa o he inal li e demons a ion o he Eu opean H2020
p ojec AERIAL-CORE, conduc ed a he ATLAS Fligh Tes
Cen e 11 (Villaca illo, Spain). Figu e 13 shows he expe i-
men al se up. As depic ed in he igu e, he e is an o e head
powe g id in he su oundings o he cen e ha s e ches
o mo e han 10 kilome es, including mul iple o ks and
89 ansmission owe s, ma ked as ed do s in he igu e.
The e, a powe ou age was simula ed a an unknown loca ion
o he powe g id by hanging a piece o g eenhouse plas ic
shee om one o he wi es connec ing wo owe s. In o de
o loca e he o igin o he powe ou age in minimum ime,
a eam o h ee he e ogeneous UAVs, shown in he igu e,
was deployed. This eam consis ed o one ixed-wing UAV
wi h VTOL (Ve ical Take-O and Landing) capabili ies,
Del aQuad P o12, equipped wi h a Fli Duo P o R came a
(4000 ×3000px esolu ion, 56◦×45◦ ield o iew), and
wo mul i- o o UAVs, DJI M210 RTK13, one equipped wi h
he Zenmuse X5S came a (4096 ×2160px esolu ion, 72◦
diagonal ield o iew) and he o he wi h he Zenmuse XT2
came a (3840 ×2160px esolu ion, 57.12◦×42.44◦ ield o
iew). The echnical speci ica ions o his mul i-UAV eam
a e included in Table 4. Each ae ial obo used a Raspbe y
Pi 4 Model B14 as he onboa d compu e . The UAVs we e
deployed along he unway o he ATLAS cen e, oge he
wi h hei echa ging s a ions (Skycha ge BOLO S115 dock-
ing sys ems wi h he se up shown in Fig. 2), while he en i e
mission was planned, execu ed, and moni o ed using a s an-
da d lap op (In el Co e i7-1165G7 CPU, 16GB RAM, 512GB
SSD, Ubun u 22.04.3 LTS ope a ing sys em) ope a ed om
he main building o he cen e.
The mission began wi h planning he op imal pa hs o
he mul i-UAV eam o inspec he en i e powe g id in mini-
mum ime. Fo his, he GUI o mission planning was used,
se ing i up wi h he planning pa ame e s lis ed in Table 5.
Fo ou e planning, he MILP p oblem associa ed wi h he
capaci a ed min-max mul i-depo VRP was p og ammed in
Ma lab R2023a and sol ed using he in linp og16 sol e o
he Op imiza ion Toolbox. The esul ing pa hs, au oma ically
s o ed in he inspec ion da abase as an expo able kml ile, a e
ep esen ed in Fig. 14. These pa hs, compu ed in 19 seconds,
11 h ps://www.a lascen e .ae o/en/
12 h ps://www.del aquad.com/p oduc s/p o/
13 h ps://www.dji.com/suppo /p oduc /ma ice-200-se ies
14 h ps://www. aspbe ypi.com/p oduc s/ aspbe y-pi-4-model-b/
15 h ps://www.skycha ge.de/d one-cha ging-pad
16 h ps://www.ma hwo ks.com/help/op im/ug/in linp og.h ml
Table 4 Technical speci ica ions o he mul i-UAV eam
Pa ame e Del aQuad P o DJI M210
Mass 5kg 5.15kg
Dimensions 235 ×90 ×17cm 89 ×88 ×41cm
Max. ligh ime 88min 41min
Max. speed 28m/s23m/s
S all speed 12m/s−
Max. wind 9m/s12m/s
Max. al i ude 4000m3000m
Resolu ion (Fli ) 4000 ×3000px −
FoV (Fli ) 56 ×45◦−
Resolu ion (X5S) −4096 ×2160px
FoV (X5S) −72◦(diagonal)
Resolu ion (XT2) −3840 ×2160px
FoV (XT2) −57.12 ×42.44◦
The ac onym FoV s ands o Field o View
ha e he cha ac e is ics summa ised in Table 6and allow co -
e ing he en i e powe g id e icien ly. As can be obse ed,
he mission can be comple ed in 765 seconds, which co -
esponds o he maximum ligh ime, wi h ligh imes as
e enly balanced as he powe g id con igu a ion allows, e en
i he ligh dis ances di e as a consequence o he di e -
en inspec ion speeds o he he e ogeneous mul i-UAV eam.
Thus, he planne exploi s he di e en inspec ion speeds
o une enly alloca e he powe g id, ensu ing he mission
is comple ed in he sho es possible ime. All UAVs can
comple e he ope a ion wi hou he need o echa ge ba e ies
du ing he mission execu ion, as none o he pa hs exceeds
he ene gy capaci y ha can be p o ided by a single ba -
e y se . Also, Fig. 14 (bo om) highligh s he impo ance o
inco po a ing e ain ele a ion in o he planning p ocess o
Table 5 Planning pa ame e s o he mul i-UAV inspec ion unde eal-
wo ld condi ions
Pa ame e Value
Inspec ion eloci y (Del aQuad P o)15m/s
Inspec ion eloci y (bo h DJI M210)7m/s
Dis ance o powe g id (Del aQuad P o)30m
Dis ance o powe g id (bo h DJI M210)10m
Video pe spec i e (all UAVs) 45◦
Tempe a u e114.2◦C
A mosphe ic p essu e1102100Pa
Wind eloci y14.61m/s
Wind di ec ion1248◦
Ba e y h eshold αused o clus e ing 0.1
1Da a au oma ically acqui ed om he API o wea he es ima es
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 17 o 21 67
Fig. 14 Pa hs planned o he mul i-UAV inspec ion unde eal-wo ld condi ions: g ound p ojec ions ( op) and ligh al i udes (bo om)
accu a e UAV e ical posi ioning ela i e o he powe line,
since i shows signi ican a ia ions along he pa hs ha may
lead o inspec ion inaccu acies o e en UAV c ashes i hey
a e no conside ed.
Once he mission plan was eady, i was au oma ically
expo ed o a yaml ile o mission execu ion and moni o ing
om he GCS. A e app o al by he ope a o , he mul i-UAV
eam au onomously execu ed he inspec ion, as illus a ed
in Fig. 1, while s eaming he eco ded ideos o he GCS.
Figu e 15 shows wo examples wi h snapsho s o he cap u ed
ideos. O e all, hese ideos ul il he Requi emen s 1-3
in Sec ion 2, since hey p o ide a sui able ideo pe spec-
i e, cap u e all he elemen s o he powe g id and i s
su oundings, co e he en i e leng h o he powe lines, and
a e geo e e enced a all imes in o de o pinpoin he exac
loca ion o any de ec ha migh be ound in he powe g id.
Thanks o hese ea u es, he simula ed powe ou age and
i s exac loca ion we e success ully iden i ied (see he bo -
om side o Fig. 15). The la e educes cos s and enables
a as esponse o he p oblem by allowing he subsequen
deploymen o human ope a o s di ec ly o he a ge place,
ha ing an o e iew o he aul e en be o e a i ing, which
helps o p epa e a epai plan and he equipmen needed in
ad ance. Also, i should be highligh ed ha he expe imen
was a ec ed by mode a e wind condi ions as shown in Fig. 15
(bo om), e idenced by he mo emen o he piece o plas ic
Table 6 Pa hs planned o he mul i-UAV inspec ion unde eal-wo ld condi ions: main cha ac e is ics. The mos signi ican alues o each me ic
ha e been highligh ed in bold
UAV Fligh ime Fligh dis ance Co e ed powe -g id dis ance Ba . consump ion
Del aQuad P o 765s 11481m 5506m 14.49%
DJI M210 (X5S) 639s4475m2408m25.98%
DJI M210 (XT2) 759s5312m2576m30.85%
123
67 Page 18 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
Fig. 15 Snapsho s o he geo e e enced ideos eco ded by he mul i-
UAV eam du ing he au onomous mission execu ion unde eal-wo ld
condi ions: example o ansmission owe ( op) and piece o g eenhouse
plas ic shee hanging om one o he wi es connec ing wo owe s and
simula ing a powe ou age (bo om)
shee hanging om he wi e. Howe e , his windy condi ions
did no signi ican ly impac he quali y o he esul s hanks
o he s able pe o mance o all he UAVs and he e ec i e
ideo s abiliza ion capabili ies o hei onboa d came as.
The planning esul s ha e also been compa ed o hose
ob ained using he s a e-o - he-a app oach p oposed in
[14]. This ou e planne ex ends he well-known TSP o
he inspec ion planning o powe ansmission lines. The
me hod is designed o mul i- ou one-depo scena ios and
assumes he use o a single UAV, bu i he inspec ion mis-
sion exceeds he ime ha he UAV can ly in one ou , he
app oach p oposes ha he mul i- ou solu ion can be dis-
ibu ed be ween mul iple obo s o expedi e he inspec ion.
Ne e heless, all UAVs a e es ic ed o ope a e om he
same loca ion and mus ha e iden ical capabili ies in e ms
o inspec ion speed and ba e y consump ion. Consequen ly,
he e ogeneous mul i-UAV eams, like he one selec ed in his
pape , canno be accommoda ed.
Figu e 16 depic s he pa h planned using he s a e-o - he-
a app oach. The pa h emains he same whe he he mission
is compu ed o he mul i- o o o he ixed-wing UAVs. In
bo h cases, he mission can be comple ed wi h a single se
o ba e ies, which p e en s he planne om p oposing he
deploymen o a mul i-UAV eam, e en wi h homogeneous
capabili ies. Mo eo e , Table 7summa ises he main cha ac-
e is ics o he pa h when i is planned o he ixed-wing UAV
Del aQuad P o o a mul i- o o UAV DJI M210. Al hough
hese pa hs can be compu ed in less han one second, he able
shows longe mission imes compa ed o he one compu ed
in Table 6wi h he no el app oach o mula ed in his pape ,
a he ime ha he emaining a ailable UAVs a e no used
in he inspec ion. In his sense, he no el app oach achie es
a educ ion o 29.81% and 67.21% in he o al ime ha is
needed o plan and execu e he mission when compa ed o
he single use o he ixed-wing UAV Del aQuad P o o a
mul i- o o UAV DJI M210, espec i ely.
Finally, i is impo an o emphasise ha he s a e-o -
he-a app oach [14] does no implemen se e al ea u es
in oduced in his pape , such as accu a e UAV posi ion-
ing ela i e o he powe g id, pa h adap a ion o ensu e
an app op ia e ideo pe spec i e, o in eg a ion o an accu-
a e ba e y-consump ion model. These ea u es ha e been
iden i ied o be essen ial o he e ec i e ope a ion in eal
inspec ions.
8 Conclusion
This a icle has p esen ed an in eg a ed solu ion o he as
inspec ion o o e head powe lines by eams o UAVs. The
solu ion add esses he main aspec s ha mus be aced o
an e ec i e ield ope a ion and simpli ies i s use by ope a-
o s o planning, au onomous execu ion, and moni o ing o
he inspec ion mission. Fu he mo e, he app oach also p o-
ides esul s ha mee end-use equi emen s and enables
he exploi a ion o he e ogeneous mul i-UAV eams in e ms
o inspec ion speed and ba e y consump ion, which helps o
maximise he u ilisa ion o a ailable obo s. In his con ex ,
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 19 o 21 67
Fig. 16 Pa h planned using he me hod desc ibed in [14] o he inspec ion unde eal-wo ld condi ions. The pa h emains unchanged ega dless o
whe he he mission is execu ed wi h he ixed-wing UAV Del aQuad P o o a mul i- o o UAV DJI M210
comme cial UAVs wi h high le els o eliabili y, obus -
ness, and sa e y ha e been combined wi h cus om so wa e
speci ically designed o add ess he pa icula i ies o he
au onomous inspec ion o o e head powe g ids, o e ing a
good balance be ween lexibili y and pe o mance. All he
a o emen ioned so wa e has been eleased as open sou ce,
ei he in his publica ion o in p e ious con ibu ions.
The pape has also de i ed an accu a e model o ba e y
consump ion, which is used du ing he planning p ocess o
compu e easible ou es. The model allows cap u ing he
impac on ene gy consump ion o ele an pa ame e s ha
a e o en o e looked, such as UAV mass, inspec ion speed,
o wea he condi ions, including empe a u e, a mosphe ic
p essu e, and wind magni ude and di ec ion. Compa isons
wi h expe imen al esul s ha e endo sed he alidi y o he
p oposed model o es ima e eal ene gy consump ion accu-
a ely, showing ela i e e o s ha do no exceed 1.34%.
The in eg a ed solu ion has been expe imen ally alida ed
unde eal-wo ld condi ions. Speci ically, he inspec ion o
o e 10 kilome es o eal o e head powe lines was planned
and au onomously execu ed in 13 minu es by a he e oge-
neous mul i-UAV eam comp ising one ixed-wing UAV wi h
VTOL capabili ies and wo mul i- o o UAVs. This ep e-
sen s a ime educ ion o up o 67.21% when compa ed o
he s a e o he a [14]. Finally, he UAV ideos s eamed
du ing he mission execu ion p o ed o be aluable in o -
ma ion o de ec ailu es in he powe g id and de e mine
hei exac loca ions. E en i he p esen ed solu ion elied on
isual ideos, cap u ed wi h he e ogeneous came a models,
he senso -agnos ic na u e o he o mula ed planning ame-
wo k also enables he in eg a ion o al e na i e payloads such
as he mal came as o LiDAR (Ligh De ec ion and Ranging)
scanne s wi hou equi ing modi ica ion.
Fu u e wo k includes eal- ime moni o ing o ene gy con-
sump ion on boa d he UAVs du ing mission execu ion o
indi ec ly es ima e wind-induced unce ain ies and igge
dynamic e-planning whene e de ia ions may comp omise
he o iginal plan. I also includes he in eg a ion o image-
based con ol loops so ha he o ien a ion o he came as
on boa d he UAVs can be au oma ically adjus ed o keep
he powe line cen ed in e e y ame. Addi ionally, aul -
de ec ion me hods based on a i icial in elligence can be
deployed o au oma ically highligh anomalies in powe lines
e en unde poo con as , cloudy skies o hea y shadows,
elimina ing he need o specialised ope a o s o analyse he
esul ing inspec ion ideos. Finally, machine lea ning and
heu is ic/me aheu is ic sea ch me hods o ou e planning
can also be explo ed o ackle la ge and mo e complex powe
g ids.
Table 7 Pa hs planned using he me hod desc ibed in [14] o he inspec ion unde eal-wo ld condi ions: inspec ion using he ixed-wing UAV
Del aQuad P o ( op) and inspec ion using a mul i- o o UAV DJI M210 (bo om)
UAV Fligh ime Fligh dis ance Co e ed powe -g id dis ance Ba . consump ion
Del aQuad P o 1116s(1)16733m10490m21.14%
DJI M210 2390s(2)16733m10490m97.15%
(1)The app oach in his pape achie es a educ ion o 29.81% in he o al ime needed o plan and execu e he mission
(2)The app oach in his pape achie es a educ ion o 67.21% in he o al ime needed o plan and execu e he mission
123
67 Page 20 o 21 Jou nal o In elligen & Robo ic Sys ems (2025) 111:67
Acknowledgemen s The au ho s would like o hank Vic o M. Vega,
Miguel Gil and Al a o R. Poma o hei suppo in conduc ing he
expe imen s p esen ed in his a icle, and Jesus Zamb ano, as an end
use ep esen ing he company e-dis ibución, o p o iding he equi e-
men s adop ed in his pape o he e ec i e inspec ion o o e head
powe lines.
Au ho Con ibu ions All au ho s con ibu ed o he s udy concep ion
and design. Ma e ial p epa a ion, da a collec ion and analysis we e pe -
o med by Al a o Caballe o and F ancisco Ja ie Roman-Esco za. The
i s d a o he manusc ip was w i en by Al a o Caballe o and all
au ho s commen ed on p e ious e sions o he manusc ip . All au ho s
ead and app o ed he inal manusc ip .
Funding This wo k has been suppo ed by he Eu opean P ojec s
AERIAL-CORE, AEROSUB and SIMAR, unded by he Ho izon 2020
and he Ho izon Eu ope esea ch and inno a ion p og ammes o he
Eu opean Commission unde g an ag eemen s 871479, 101189723 and
101070604, espec i ely.
Decla a ions
Compe ing In e es s The au ho s ha e no ele an inancial o non-
inancial in e es s o disclose.
Code a ailabili y The so wa e associa ed wi h he planne p esen ed
in his a icle is publicly a ailable in he ollowing Gi hub eposi o y:
h ps://gi hub.com/g c- obo ics-lab/mul iUAV_planne / (accessed on
30 No embe 2024).
E hics app o al No applicable.
Consen o pa icipa e No applicable.
Consen o publish No applicable.
Open Access This a icle is licensed unde a C ea i e Commons
A ibu ion 4.0 In e na ional License, which pe mi s use, sha ing, adap-
a ion, dis ibu ion and ep oduc ion in any medium o o ma , as
long as you gi e app op ia e c edi o he o iginal au ho (s) and he
sou ce, p o ide a link o he C ea i e Commons licence, and indi-
ca e i changes we e made. The images o o he hi d pa y ma e ial
in his a icle a e included in he a icle’s C ea i e Commons licence,
unless indica ed o he wise in a c edi line o he ma e ial. I ma e ial
is no included in he a icle’s C ea i e Commons licence and you
in ended use is no pe mi ed by s a u o y egula ion o exceeds he
pe mi ed use, you will need o ob ain pe mission di ec ly om he copy-
igh holde . To iew a copy o his licence, isi h p://c ea i ecomm
ons.o g/licenses/by/4.0/.
Re e ences
1. Kü eo˘glu, S., e al.: Economic impac s o elec ic powe ou ages
and e alua ion o cus ome in e up ion cos s. PhD hesis, Aal o
Uni e si y, Helsinki (Finland) (2015)
2. PLP: UAV-ins alled bi d di e e s. h ps://plp.com/ene gy/dis i
bu ion/wildli e-p o ec ion/ua -ins alled-bi d-di e e s. Accessed
30 No 2024
3. Paneque, J., Valseca, V., Ma ínez-de Dios, J., Olle o, A.:
Au onomous eac i e LiDAR-based mapping o powe line inspec-
ion. In: 2022 In e na ional Con e ence on Unmanned Ai c a
Sys ems (ICUAS), pp. 962–971 (2022). IEEE
4. Xing, J., Cio i, G., Hidalgo-Ca ió, J., Sca amuzza, D.:
Au onomous powe line inspec ion wi h d ones ia pe cep ion-
awa e MPC. In: 2023 IEEE/RSJ In e na ional Con e ence on
In elligen Robo s and Sys ems (IROS), pp. 1086–1093 (2023).
IEEE
5. Caballe o, A., Silano, G.: A signal empo al logic mo ion planne
o bi d di e e ins alla ion asks wi h mul i- obo ae ial sys ems.
IEEE Access. 11, 81361–81377 (2023)
6. Cacace, J., O ozco-So o, S.M., Sua ez, A., Caballe o, A., O sag,
M., Bogdan, S., Vasilje ic, G., Ebeid, E., Rod iguez, J.A.A., Olle o,
A.: Sa e local ae ial manipula ion o he ins alla ion o de ices on
powe lines: AERIAL-CORE i s yea esul s and designs. Appl.
Sci. 11(13), 6220 (2021)
7. I e sen, N., K ambe ge , A., Scho ield, O.B., Ebeid, E.: Pneuma ic-
mechanical sys ems in UAVs: au onomous powe line senso uni
deploymen . In: 2021 IEEE In e na ional Con e ence on Robo ics
and Au oma ion (ICRA), pp. 548–554 (2021). IEEE
8. A i i, A., Co sini, G., Sable, Q., Aboudo a, Y., Sidob e, D.,
F anchi, A.: Physical human-ae ial obo in e ac ion and collabo a-
ion: explo a o y esul s and lessons lea ned. In: 2023 In e na ional
Con e ence on Unmanned Ai c a Sys ems (ICUAS), pp. 956–962
(2023). IEEE
9. He, T., Zeng, Y., Hu, Z.: Resea ch o mul i- o o UAVs de ailed
au onomous inspec ion echnology o ansmission lines based on
ou e planning. IEEE Access. 7, 114955–114965 (2019)
10. Yang, L., Fan, J., Liu, Y., Li, E., Peng, J., Liang, Z.: A e iew
on s a e-o - he-a powe line inspec ion echniques. IEEE T ans.
Ins um. Meas. 69(12), 9350–9365 (2020)
11. Foudeh, H.A., Luk, P.C.-K., Whidbo ne, J.F.: An ad anced
unmanned ae ial ehicle (UAV) app oach ia lea ning-based con-
ol o o e head powe line moni o ing: A comp ehensi e e iew.
IEEE Access. 9, 130410–130433 (2021)
12. Baik, H., Valenzuela, J.: Unmanned ai c a sys em pa h plan-
ning o isually inspec ing elec ic ansmission owe s. Jou nal
o In elligen & Robo ic Sys ems. 95, 1097–1111 (2019)
13. Silano, G., Baca, T., Penicka, R., Liuzza, D., Saska, M.: Powe line
inspec ion asks wi h mul i-ae ial obo sys ems ia signal empo al
logic speci ica ions. IEEE Robo ics and Au oma ion Le e s. 6(2),
4169–4176 (2021)
14. Neko a , F., Faigl, J., Saska, M.: Mul i- ou se a eling sales-
man p oblem in planning powe ansmission line inspec ion. IEEE
Robo . Au om. Le . 6(4), 6196–6203 (2021)
15. Liu, Y., Shi, J., Liu, Z., Huang, J., Zhou, T.: Two-laye ou ing o
high- ol age powe line inspec ion by coope a ed g ound ehicle
and d one. Ene gies 12(7), 1385 (2019)
16. Pe i p ez, E., Geo ges, F., Raballand, N., Be and, S.: Deploymen
op imiza ion o a lee o d ones o ou ine inspec ion o ne -
wo ks o linea in as uc u es. In: 2021 In e na ional Con e ence
on Unmanned Ai c a Sys ems (ICUAS), pp. 303–310 (2021).
IEEE
17. Wang, J., Wang, G., Hu, X., Luo, H., Xu, H.: Coope a i e ans-
mission owe inspec ion wi h a ehicle and a UAV in u ban a eas.
Ene gies 13(2), 326 (2020)
18. Li, K., Yan, X., Han, Y.: Mul i-mechanism swa m op imiza ion o
mul i-UAV ask assignmen and pa h planning in ansmission line
inspec ion unde mul i-wind ield. Appl. So Compu . 150, 111033
(2024)
19. Zhang, H., Ge, H., Yang, J., Tong, Y.: Re iew o ehicle ou ing
p oblems: models, classi ica ion and sol ing algo i hms. A chi es
o Compu a ional Me hods in Enginee ing, 1–27 (2021)
20. Hayajneh, M., Al Mahasneh, A.: Guidance, Na iga ion and Con ol
Sys em o Mul i-Robo Ne wo k in Moni o ing and Inspec ion
Ope a ions. D ones. 6(11), 332 (2022)
21. Caballe o, A., Roman-Esco za, F.J., Maza, I., Olle o, A.: A Mul i-
UAV Rou e Planning Me hod o Fas Inspec ion o Elec ic
123
Jou nal o In elligen & Robo ic Sys ems (2025) 111:67 Page 21 o 21 67
Powe T ansmission Lines. In: 2024 In e na ional Con e ence on
Unmanned Ai c a Sys ems (ICUAS), pp. 835–842 (2024). IEEE
22. Lapo e, G.: The a eling salesman p oblem: An o e iew o exac
and app oxima e algo i hms. Eu . J. Ope . Res. 59(2), 231–247
(1992)
23. Cos a, J.G.C., Mei, Y., Zhang, M.: Clus e -based hype -heu is ic
o la ge-scale ehicle ou ing p oblem. In: 2020 IEEE Cong ess
on E olu iona y Compu a ion (CEC), pp. 1–8 (2020). IEEE
24. Leishman, G.J.: P inciples o Helicop e Ae odynamics. Cam-
b idge Uni e si y P ess, Camb idge (2006)
25. Do ling, K., Hein ichs, J., Messie , G.G., Magie owski, S.: Vehicle
ou ing p oblems o d one deli e y. IEEE T ansac ions on Sys-
ems, Man, and Cybe ne ics: Sys ems. 47(1), 70–85 (2016)
26. Baue s eld, L., Sca amuzza, D.: Range, endu ance, and op imal
speed es ima es o mul icop e s. IEEE Robo ics and Au oma ion
Le e s. 7(2), 2953–2960 (2022)
27. Ka ydis, K., Kuma , V.: Ene ge ics in obo ic ligh a small scales.
In e ace ocus. 7(1), 20160088 (2017)
28. Lapo e, G.: Gene alized sub ou elimina ion cons ain s and con-
nec i i y cons ain s. Jou nal o he Ope a ional Resea ch Socie y.
37(5), 509–514 (1986)
29. Achu han, N., Cacce a, L., Hill, S.: A new sub ou elimina ion
cons ain o he ehicle ou ing p oblem. Eu . J. Ope . Res. 91(3),
573–586 (1996)
30. Lapo e, G.: Wha you should know abou he ehicle ou ing p ob-
lem. Na . Res. Logis . 54(8), 811–819 (2007)
31. Gil-Cas illa, M., Caballe o, A., Maza, I., Olle o, A.: In eg a ion
o Cus omized Comme cial UAVs wi h Open-Sou ce Tools in a
He e ogeneous Mul i-UAV Sys em o Powe -Lines Inspec ion.
In: 2024 In e na ional Con e ence on Unmanned Ai c a Sys ems
(ICUAS), pp. 1362–1369 (2024). IEEE
32. Poma, A.R., Caballe o, A., Maza, I., Olle o, A.: Open-Sou ce Web-
Based G ound Con ol S a ion o Long-Range Inspec ion wi h
Mul iple UAVs. In: 2024 In e na ional Con e ence on Unmanned
Ai c a Sys ems (ICUAS), pp. 1385–1392 (2024). IEEE
33. Quigley, M., Ge key, B., Conley, K., Faus , J., Foo e, T., Leibs,
J., Be ge , E., Wheele , R., Ng, A.: ROS: an open-sou ce Robo
Ope a ing Sys em. In: IEEE In e na ional Con e ence on Robo ics
and Au oma ion Wo kshop on Open Sou ce So wa e (2009). IEEE
34. Alejo, D., Conde, R., Cobano, J.A., Olle o, A.: Mul i-UAV collision
a oidance wi h sepa a ion assu ance unde unce ain ies. In: 2009
IEEE In e na ional Con e ence on Mecha onics, pp. 1–6 (2009).
IEEE
Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju is-
dic ional claims in published maps and ins i u ional a ilia ions.
Al a o Caballe o ecei ed he Ph.D. deg ee in Ae ial Robo ics om he
Uni e si y o Se ille, Spain, in 2022. Since 2014, he has been in ol ed
in EU- unded p ojec s such as AEROARMS, HYFLIERS, AERIAL-
CORE, OMICRON o AEROSUB. He has also been pa icipa ing in
echnology ans e ac i i ies in collabo a ion wi h leading companies
such as Na an ia o Endesa. He comple ed a esea ch s ay a he Mul i-
Robo Sys ems (MRS) g oup a he Czech Technical Uni e si y (CTU)
in P ague. He is he au ho o co-au ho o mo e han 20 scien i ic
publica ions. His main esea ch in e es s include mo ion planning o
ae ial obo s in inspec ion and main enance.
F ancisco Ja ie Roman-Esco za ecei ed he Bachelo ’s Deg ee in
Elec onics, Robo ics, and Mecha onics Enginee ing om he Uni-
e si y o Se ille and he Uni e si y o Malaga, wi h a specializa ion
in Robo ics and Au oma ion in 2023. He is cu en ly pu suing an
M.Sc. in Robo ics a Miguel He nández Uni e si y o Elche. Since
2023, he has been wi h he GRVC Robo ics Lab, Uni e si y o Se ille,
in ol ed in he AERIAL-CORE and ePa k+ p ojec s. His wo k has
been ocused on planning o ae ial obo s and de eloping simula ion
ools o inspec ion and main enance asks.
I an Maza is Associa e P o esso a he Uni e si y o Se ille (Spain),
ecei ed he Telecommunica ion Enginee ing Deg ee in 2000 and
joined he GRVC Robo ics Lab. He has made esea ch s ays a he
Au oma ion Technology Labo a o y a he Helsinki Uni e si y o
Technology and a he LAAS-CNRS in Toulouse. His Thesis was
awa ded wi h he Robo nik P ize o he Bes Doc o al Disse a ion on
Robo ics gi en by he Spanish Commi ee o Au oma ion in 2010. He
au ho ed mo e han 80 publica ions on Robo ics including mo e han
30 jou nal pape s indexed in he JCR da abase and he co-edi ion o
a book published in he Sp inge STAR Se ies. His esea ch in e -
es s include unmanned ae ial ehicles, mul i- obo sys ems, symbolic
and mo ion planning and ask alloca ion echniques. He pa icipa ed
as PI om he Uni e si y o Se ille in he ARCAS P ojec (2011-
2015) de o ed o he de elopmen and expe imen al alida ion o he
i s coope a i e ee- lying obo sys em o assembly and s uc u e
cons uc ion. In addi ion, he has pa icipa ed as co-PI om he Uni e -
si y o Se ille in he SAFEDRONE P ojec (2018-2020) unded by EU
SESAR JU o he demons a ion wi h d ones o U-Space se ices a
he ATLAS ligh es cen e . He has been also PI in se e al R&D con-
ac s ela ed o di e en UAV echnologies wi h companies such as
Boeing Resea ch and Technology Eu ope, Na an ia and TSK. He has
ecei ed he “Manuel Losada Villasan e Awa d” in 2021 o excellen
esea che s in he Inno a ion ca ego y o his wo k on d one a ic
managemen wi hin he U-space con ex .
Anibal Olle o is a Full P o esso , he Head o he GRVC Robo ics Lab,
and he Scien i ic Ad iso o he Cen e o Ae ospace Technologies
(CATEC) in Se ille, Spain. He has au ho ed mo e han 900 publica-
ions. He led mo e han 190 esea ch p ojec s, pa icipa ing in mo e
han 41 p ojec s o he Eu opean esea ch p og ams, being coo dina o
o 7. He has also been ecognized wi h 33 awa ds, including he Span-
ish Na ional Resea ch Awa d in Enginee ing, he Rei Jaume I in New
Technologies, he O e all In o ma ion and Communica ion Technolo-
gies Inno a ion Rada P ize 2017 o he Eu opean Commission, and
se e al bes pape awa ds in con e ences.
123
