Ci a ion: Es e ez, J.; Ga a e, G.;
Lopez-Guede, J.M.; La ea, M.
Re iew o Ae ial T anspo a ion o
Suspended-Cable Payloads wi h
Quad o o s. D ones 2024,8, 35.
h ps://doi.o g/10.3390/
d ones8020035
Academic Edi o : Abdessa a
Abdelke i
Recei ed: 20 No embe 2023
Re ised: 18 Janua y 2024
Accep ed: 23 Janua y 2024
Published: 25 Janua y 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
d ones
Re iew
Re iew o Ae ial T anspo a ion o Suspended-Cable Payloads
wi h Quad o o s
Julian Es e ez 1,* , Go ka Ga a e 1, Jose Manuel Lopez-Guede 2and Mikel La ea 1
1
G oup o Compu a ional In elligence, Facul y o Enginee ing o Gipuzkoa, Uni e si y o he Basque Coun y
(UPV/EHU), 20080 San Sebas ian, Spain; [email p o ec ed] (G.G.); [email p o ec ed] (M.L.)
2G oup o Compu a ional In elligence, Facul y o Enginee ing o Vi o ia, Uni e si y o he Basque Coun y
(UPV/EHU), 01006 Vi o ia, Spain; [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac :
Payload anspo a ion and manipula ion by o o c a d ones a e ecei ing a lo o a en ion
om he mili a y, indus ial and logis ics esea ch a eas. The in e ac ions be ween he UAV and he
payload, plus he means o objec a achmen o manipula ion (such as cables o an h opomo phic
obo ic a ms), may be nonlinea , in oducing di icul ies in he o e all sys em pe o mance. In his
pape , we ocus on he cu en s a e o he a o ae ial anspo a ion sys ems wi h suspended loads
by a single UAV and a eam o hem and p esen a e iew o di e en dynamic cable models and
con ol sys ems. We co e he las six een yea s o he exis ing li e a u e, and we add a discussion o
e alua ing he main ends in he e e enced esea ch wo ks.
Keywo ds: UAVs; suspended payload; collabo a i e; con ol enginee ing; cable modeling
1. In oduc ion
When dealing wi h he ae ial anspo a ion o payloads, he i s app oach his o ically
aken was o deal wi h he p oblem o a load suspended on a c ane. In his p oblem, wo
ypes o models could be used: global-mass models and dis ibu ed-mass models [1].
Lumped-mass models a e cha ac e ized by a massless cable, whe e he payload is
lumped wi h he hook and ep esen ed by a poin mass. This model is simple while
cap u ing he complex dynamics o payload mo ion [2–4].
Dis ibu ed-mass models a e composed o a dis ibu ed-mass cable and a lumped poin
mass modeling he payload. The only model published ha alls in o his ca ego y is he
plana model de eloped by d’And ea-No el e al. and Abdel-Rahman e al. [
1
,
5
]. Howe e ,
Choo and Casa ella [
6
], in hei e iew compa ing se e al modeling me hods, including
some con inuous and disc e e cable models, a i ed a he conclusion ha he lumped-mass
ep esen a ion, despi e he hea y compu e wo kload needed o i s implemen a ion, is he
mos e sa ile o hem all. This echnique models he cable as a ini e se ies o igid links o
lumped masses a he join s.
Focusing on ae ial applica ions, o e he pas ew decades, owed-cable sys ems ha e
been ex ensi ely esea ched o di e se applica ions, o en p omo ed by mili a y in e es s,
such as he deli e y and e ie al o payloads [
7
,
8
], ae os a s [
9
], e he ing sys ems [
10
,
11
]
and ae ial e ueling sys ems [
12
]. A ypical owed-cable sys em is composed o h ee
componen s: a owing ehicle, a cable (s ing o e he ) and a owed body (d ogue) [13].
As UAV esea ch p og essed, he e olu ion o ai anspo using UAVs also began
o gene a e in e es . This esul ed in he possibili y o pe o ming a wide ange o ans-
po asks using UAVs [
14
]. These asks include a ious ac i i ies, such as anspo ing
la ge and di e se objec s, examining and main aining di e en elemen s and su aces and
ca ying ou indus ial and eme gency- ela ed applica ions [
15
]. Mos cu en esea ch is
ocused on he dynamic modeling and con ol o he sys em encompassing he UAVs and
he payload. The coupling o he UAV and he payload in oduces s ong nonlinea i ies
D ones 2024,8, 35. h ps://doi.o g/10.3390/d ones8020035 h ps://www.mdpi.com/jou nal/d ones
D ones 2024,8, 35 2 o 21
in o es ablished equa ions ha depend on he speci ic kind o sys em [
16
]. Two majo
ca ying s a egies ha e been esea ched by he scien i ic communi y: he di ec a achmen
o he payload o he quadcop e body and he suspension o he ca go wi h cables [
17
,
18
].
Fo he o me , he ca go is a ached o he obo body (no mally below he cen e o g a i y)
h ough claws, obo ic hands o elec omagne ic g ippe s [
19
]. This me hod allows o a
quicke a achmen / elease o he load, bu i inc eases he ine ia momen o he sys em,
hus making i slowe and ha de o agile maneu e s and apid a i ude changes [20–22].
Fo he la e , he load suspended wi h cables adds deg ees o eedom o he inhe en ly
unde ac ua ed na u e o he quad o o , al e ing he ligh dynamics [
23
]. In bo h cases,
he sys em con olle needs special equi emen s added o hose used o UAVs wi hou a
load [
24
,
25
]. Howe e , he ul illmen o he special condi ions o ob ain as , s able, apid
and obus ligh has no op imal solu ion, and his lea es he doo open o a la ge numbe
o con olle designs.
This su ey ocuses on he anspo a ion o cable-suspended loads wi h mul i o o s,
namely, quad o o s. A he momen , ecen e iews on he ci il applica ions o UAVs
do no co e all he design possibili ies, including indi idual o collabo a i e schemes,
cable modeling o as maneu e s. Some o he esea ch e iews ela ed o UAV payload
applica ions ha e been published la ely. Fo ins ance, e s. [
26
–
28
] p esen e iews o
mul i o o s anspo ing a payload, bu hey compa e di e en me hods o ha . Among
hese las pape s, se e al designs a e desc ibed: suspended loads, g asping o he usage o
a ms, and speci ic issues, such as in e ac ions wi h objec s and he equi ed senso s, a e
co e ed. Bu hese pape s do no desc ibe he con ol s a egies used in he ield. Ano he
ecen and highly ci ed e iew by Ruggie o e al. [
29
] pays much a en ion o quad o o s
ha ha e a ms and in e ac wi h objec s, which is one o he main a eas o expe ise in hei
esea ch g oup.
The main con ibu ion o ou e iew is he exclusi e s udy o mul i o o s ca ying
suspended loads wi h cables. The nonlinea na u e o d one beha io is u he com-
pounded by a g ea e cons ain han when i lies wi h no load, making i an ex emely
complex p oblem and, a he same ime, challenging o u u e applica ions. We co e
he ma hema ical modeling o cables and con ol s a egies o bo h indi idual obo s and
eams o obo s.
I is impo an o no e ha , in his esea ch e iew a icle, we will no deal wi h
ha dwa e pla o ms o senso s. Ins ead, ou in es iga ion will be di ec ed owa d he
ma hema ical modeling o cables, con ol s a egies and subsequen expe imen al alida ion
s udies (when possible). This delibe a e scope allows us o del e deepe in o he speci ic
a eas o in e es , p o iding a comp ehensi e analysis and aluable insigh s while a oiding
unnecessa y edundancy in he discussion o ha dwa e and senso s, which a e o en well
documen ed elsewhe e in he li e a u e. By na owing ou ocus, we aim o p o ide eade s
wi h a mo e a ge ed and in o ma i e examina ion o he key ace s wi hin he pu iew o
ou s udy.
This a icle is di ided in o he ollowing pa s: In Sec ion 2, we p esen he me hodol-
ogy and a icle selec ion c i e ia ha we ollowed in o de o comple e his e iew a icle.
Sec ion 3desc ibes di e en app oaches o cable modeling o he anspo a ion o objec s
using suspended-load anspo a ion wi h quad o o s. Sec ion 3is di ided in o indi id-
ual and collabo a i e anspo . Nex , Sec ion 4discusses con ol s a egies o payload
anspo a ion by ae ial sys ems, including di e en op imiza ion s a egies. Once again,
he sec ion is di ided in o single and collabo a i e g oups o o o c a . The ac ual knowl-
edge in his ield oday, u u e ends in esea ch and echnical challenges ha s ill need o
be deal wi h a e discussed in Sec ion 5. Finally, Sec ion 6gi es some ema ks abou he
p esen ed concep s.
D ones 2024,8, 35 3 o 21
2. Me hodology
The wo ks ci ed in his a icle we e chosen acco ding o hei ele ance and in e es in
he ield o modeling and con ol o he anspo a ion o objec s by single o eams o UAVs,
mo e speci ically, indi idual and eams o quad o o s using cable-suspended payloads.
These sys ems a e complex and nonlinea and equi e elabo a e ma hema ical models
o desc ibe hei dynamics, as well as o design adequa e con olle s. Because o he
complexi y o hese sys ems, he equi emen o ca ying ou p ac ical expe imen s in
addi ion o simula ions was manda o y o he selec ion made in his su ey. Ano he il e
used was he non-inclusion o heses and unpublished disse a ions.
In o de o e alua e hei ele ance and in e es , he aspec s conside ed we e he ech-
nical quali y o models o bo h dynamics and con ol and he inno a ion o he p esen ed
p oposal. Finally, in seeking ele an wo ks in he ield, he selec ed a icles we e manually
pe used and a e p esen ed in a e e ence lis . Table 1summa izes he c i e ia used in
his su ey.
Table 1. A icle selec ion sea ch c i e ia.
C i e ia Da a
Scien i ic Da abase IEEEXplo e, Google Schola , ISI Web o Knowledge, ScienceDi ec
Publica ion Pe iod F om 2007 o No embe 2023
Keywo ds
(“quad o o ” OR “ o o c a ” OR “quadcop e ” “UAV” OR “mul i- o o ”
OR “mul iple quad o o ” OR “swa m obo ” OR “collabo a i e obo s” OR
“ eam o quad o o s”) AND (“deli e y” OR “ anspo a ion” OR “ anspo ”
OR “ e ie al” OR “ca go” OR “cable” OR “payload” OR “suspended
load”)
3. Cable Modeling o Payload T anspo a ion wi h UAVs
In he ollowing pa ag aphs, di e en cable models used o suspended-load ans-
po a ion, bo h wi h indi idual obo s and wi h a eam o obo s, a e p esen ed.
3.1. Indi idual T anspo
Ea ly esea chwo ks abou UAVs anspo ing payloads appea edin he la e 1990s[
30
,
31
].
Fo payload anspo a ion by UAVs, he cable ea men is a key ac o o modeling he
sys em and he exe ed o ces expe ienced by he quad o o when he li ing, anspo and
deli e y s ages ha e dis inc cha ac e is ics [
32
]. Du ing he anspo phase, he payload
ansmi s ension h ough he cable, while in he e y beginning o he li ing s age, he e is
no o ce ans e ed h ough he cable [
33
]. Fo simplici y, esea che s end o educe such
o ce ans e o whe he he cable is au o no [34].
This dynamic model ep esen s he payload as a mass pa icle and he cable as a
massless igid ba ha pe manen ly main ains a cons an dis ance be ween he payload
and he quad o o and can only ansmi axial o ces h ough i . Unde hese condi ions,
in 3D scena ios, he payload sys em is de ined by wo angles in space, while in plana cases,
one angle is enough, simila o a pendulum [35], as can be seen in Figu e 1.
No mally, ex a es ic ions a e conside ed in he dynamic modeling o hese sys-
ems [33,36,37]:
1. The quad o o is modeled as a symme ic igid body.
2.
The cable is modeled as inex ensible, massless and a ached o he cen e o he
quad o o , and he payload is modeled as a poin mass a ached o he cable.
3.
The mass o he payload is small compa ed o he mass o he quad o o , which
implies ha i s mo ion has li le impac on he mo ion o he quad o o .
4.
The e ec s o he payload and he cable a e ea ed as an ex e nal o ce applied o
he UAV.
D ones 2024,8, 35 4 o 21
Figu e 1. Payload wi h au -cable modeling in 3D (le ) and 2D ( igh ) scena ios.
Tau -cable app oaches became success ul because hey pe mi ed an easie s abiliza ion
o he UAV posi ioning. Lupashin and D’And ea [
38
] p oposed a e he ed quad o o and
modeled he cable as au , and hey used his cable as a use in e ac ion medium o a
low-cos , small ho e ing UAV in o de o s abilize he o ien a ion and he posi ion. Wi h he
au cable, esea che s p o ed ha simple ine ial measu emen senso s a e enough o he
quad o o o eco e i s posi ion and a i ude a e ex e nal pe u ba ions. Following his
app oach, S eena h e al. [
39
] modeled he cable o a suspended load as au o bo h he
ense-cable and ze o- ension cases. In a 3D scena io and a model wi h nonze o cable ension,
he equa ion dynamics o he sys em u n ou o ha e 8 deg ees o eedom, wi h 4 deg ees
unde ac ua ed. On he con a y, when he cable ansmi s no ension, hey conside ed ha
he UAV and cable o m sepa a e sys ems, and he load is in ee all. In bo h cases, hey
alida ed he models using simula ions and eal expe imen a ion using au cables, which
pe mi s a high ealis ic pe o mance o ajec o ies wi h cu es.
Despi e he simplici y o payload modeling, i is a widely accep ed echnical solu ion
among scien is s, as di e en wo ks om he las wo yea s e eal [
40
–
43
], whe e he
ma hema ical o mula ion and cons ain s o he model ha e emained unchanged.
The limi a ions o he model o a au cable a e e ealed when he quad o o pe o ms
ce ain c i ical asks [
17
,
44
,
45
]. Klausen e al. [
46
] es ed a au -cable model o agg essi e
maneu e s and highligh ed ha he e is a subs an ial load de lec ion du ing sudden
accele a ions and ha he payload keeps oscilla ing when he UAV eaches he ho e ing
s a e, despi e being low-ampli ude swings. These limi a ions a e he eason o o he cable
model p oposals.
One o hose c i ical asks is he li ing o he load om he g ound, whe e he quad o o
and payload sys em expe ience di e en dynamics and a au cable no longe makes sense.
C uz e al. [
47
,
48
] p oposed a hyb id model o he cable and UAV, consis ing o di iding
he p ocess, om li ing he payload o comple ely sepa a ing i om he g ound, in o h ee
phases (Se up,Pull and Raise), and o each o hem, hey de eloped di e en swi ching
dynamics. These swi ching dynamics, known as cable collision [
49
], a ise when he cable
s a e passes ins an aneously om slack o au ; mo eo e , he UAV unde goes ano he
ension jump when he load is comple ely in he ai . These h ee s eps can be seen in
Figu e 2.
The Se up phase is de ined solely by he dynamics o he UAV, while he payload has
no e ec . A he p ecise momen he UAV makes he cable e ical, i changes he ension
om slack o au , and i is calcula ed by he collision e ec p esen ed in [
49
]. Nex , in
he Pull phase, he payload is s ill in con ac wi h he g ound, and hus, esea che s ake
in o accoun he no mal o ce ha he g ound is exe ing on he pa icle mass; al hough
he cable is s ill no ully ense, i is al eady conside ed au . Finally, in he Raise phase,
he cable is ense, and he pa icle loses con ac wi h he g ound.
Howe e , Alo hman e al. [
50
] p esen ed wo k in which hey esea ched he ansi ion
om li ing o anspo ing he payload, and hey spli he dynamic equa ions in o wo.
In he i s s age, he quad o o has no ension a all, and he dynamic equa ions do no ake
he ca go in o accoun . In he ollowing phase, when he ae ial obo exceeds he heigh o
D ones 2024,8, 35 5 o 21
he cable leng h, he sys em is ans o med in o a UAV and a slung-load sys em, modeling
he cable as au . The ansi ion om one phase o he o he is mo e ab up han in he case
o [
47
], and hey alida ed he model only wi h simula ions. Simila ly, Es e ez e al. [
51
]
de eloped a au cable modeled as a pendulum o he li ing phase, conside ing no ic ion
wi h he g ound. They did no ge id o any swi ching dynamics be ween he phases and
alida ed i h ough expe imen s. Mo eo e , acco ding o he ends in ecen yea s, his
payload-li ing p ocedu e emains he simples possible, and he cable keeps swi ching
om a slack o a au phase when exceeding a heigh h eshold [52–56].
Figu e 2. The li maneu e : (a)Se up, (b)Pull, and (c)Raise.
While wo ks seen un il now modeled he cable as a massless igid link, Ko a u e al. [
17
]
conside ed he cable o be elas ic, and hey alida ed hei model by ocusing on obo ic
applica ion s udies, whe e cable elas ici y canno be igno ed and hus, he igid- od model
is no longe alid. Fo ha , hey included a damping and a sp ing in hei cable model (see
Figu e 3) and es ed he sys em s abili y unde pe u ba ions and wi h di e en damping
and s i ness alues; howe e , hei s udy was alida ed only h ough simula ions. The p o-
cedu e o modeling his cable as a dampe combined wi h a sp ing has been applied o
he s udy o o he UAV-na iga ion- ela ed asks [
57
], which sugges s ha he model is s ill
conside ed alid o cap u ing he men ioned speci ic payload e ec s, pa icula ly la ge
payload swings.
Figu e 3.
Cable model wi h damping and linea sp ing.
C
and
k
a e damping and s i ness coe icien s,
l e e s o he cable leng h, and xQand xL e e o quad o o and load posi ions.
La e , Gooda zi e al. [
24
] in oduced ano he lexible-cable model, o med by a se ies
o weigh ed segmen s o di e en sizes connec ed wi h sphe ical join s (see Figu e 4).
The links be ween join s can elonga e, and he esea che s aimed o ob ain a mo e p ecise
dynamic model o he agg essi e maneu e s o UAVs, wi h payloads modeled as a se ial
chain o
n
connec ed links, which aimed o p o e he s abili y o a coupled sys em composed
D ones 2024,8, 35 6 o 21
o a e he ed cable and a UAV pe o ming ligh maneu e s in 3D. The au ho s conside ed
he ib a ions o he cable h ough ib a ions o he
n
connec ed links. Ne e heless, o he
knowledge o he au ho s o he cu en a icle, his schema has no been widely ollowed
in he li e a u e.
Figu e 4. Cable model de eloped by [24].
In e ms o landing, he esea ch communi y has co e ed he p ocess o UAVs no
ca ying payloads [
58
,
59
]. Howe e , he challenge o landing wi h a payload has no been
s udied in dep h [
32
], and he li e a u e e lec s jus some a emp s. One o hem was
de eloped by Gooda zi [
60
], who used a a iable-leng h cable o lowe he payload o he
g ound, and he alida ed he esea ch h ough simula ions. Nex , Qian e al. [
32
] p o ed,
h ough eal expe imen a ion, ha wi h a p ecise con ol design, he assump ion o a au
cable is alid o he deli e y o a slung payload on he g ound.
3.2. Collabo a i e T anspo
Collabo a i e sys ems a e use ul o he anspo a ion and o ien a ion o he payload.
Ac ually, he use o mul iple UAVs can manage o pe o m mo e complex asks and o e -
come he limi a ions o an indi idual load, such as he enhancemen o he load capaci y
and be e con ol o oscilla ions [
61
]. Howe e , hese p os come a he cos o inc easing he
sys em complexi y and ae ial ehicle coo dina ion, which mus a oid collisions wi h one
ano he [
62
]. Thei dynamics and addi ional con ol equi emen s a e ex ensi ely discussed
in [29,63,64]. The e o e, he op imiza ion o hese a iables is no sol ed ye .
The li e a u e has in oduced solu ions in ol ing he igid a achmen o mul iple
quad o o s o objec s, as de ailed in [
65
,
66
]. Howe e , hese cases ha e demons a ed
ha manipula ion is conside ably mo e challenging o achie e han anspo a ion. This
di icul y a ises om he unde ac ua ion p ope y o mul i o o s [
67
]. To add ess hese
limi a ions, a eliable al e na i e has eme ged in he o m o igid links connec ed h ough
sphe ical join s o he payload, as e idenced in [
68
–
71
]. This app oach ensu es he ull
ac ua ion o he pla o m by obo s. Fu he mo e, subs i u ing igid links wi h cables
enables he design o lexible loa ing anspo a ion s uc u es. No ably, hese cables
acili a e he pa ial decoupling o he ehicle’s o a ional dynamics om ha o he ca ied
payload. Addi ionally, employing sphe ical join s enhances he lexibili y o obo o ma-
ion shapes, while he ligh weigh na u e o he cables signi ican ly inc eases he obo s’
payload capaci y.
Many pape s conside he usage o massless igid links due o hei lowe complex-
i y [
34
,
64
,
72
]. Michael e al. [
73
] p esen ed a model o anspo a disc- ype payload ia
owed cables wi h quad o o s. The p oblem is analogous o ha o cable-ac ua ed pa allel
manipula o s ope a ing in h ee dimensions, as bo h ypes o manipula o s a e designed
o con ol he pose o he payload wi h a ying obo posi ions and in ae ial sys ems, and
he payload o ien a ion is modi ied wi h ae ial cable owing pe o med by quad o o s (see
Figu e 5). They used h ee di e en app oaches o sol e he p oblem: in e se kinema -
ics o he payload and UAVs, he di ec p oblem and an op imiza ion o ha las di ec
p oblem. Mo eo e , he same esea ch g oup modeled he anspo a ion o a suspended
DLO (de o mable linea objec ) [
74
] and designed a deep ma hema ical backg ound o he
D ones 2024,8, 35 7 o 21
o mula ion o he sys em’s s abili y and con ol, bu wi h se e e dynamic limi a ions and
quasis a ic condi ions.
Figu e 5. A eam o h ee poin -model obo s manipula es a payload in h ee dimensions [73].
Ano he cable al e na i e was p oposed by Pize a e al. [
62
], who used a model o
elas ic cables, and hey elied on hei ac ion o ce o ejec he dis u bances c ea ed by
he payload on he UAV. Mo eo e , hey p o ed ha hei p oposal is alid o li ing he
payload om he g ound, using a single sys em o dynamics and a se ies o assump ions:
(1) he cable is massless; (2) when he load is on he g ound and he cable is slack, he e is
no e ec on he ehicles; (3) he ae odynamic e ec s on he load and ehicle a e negligible.
They simula ed hei sys em wi h wo UAVs conside ing only he longi udinal plane o
payload swings.
The g oup anspo a ion and o ien a ion o a igid wo-dimensional payload is
achie ed by using a cable sys em ha is modeled as a se ies o connec ed links [
75
] (see
Figu e 6), as demons a ed in he wo ks p esen ed in he p e ious sec ions, [
24
,
76
], which
demons a e he obus ness o his app oach o payload anspo a ion wi h UAVs.
Figu e 6.
Quad o o UAVs wi h a igid-body payload. Cables a e modeled as a se ial connec ion o
an a bi a y numbe o links.
Howe e , au cables a e no he only mechanical elemen s ha ha e been esea ched
in o de o achie e a be e ep esen a ion o eali y, and [
77
] de eloped wha hey call
enseg i y muscles. This elemen consis s o a ini e numbe o enseg i y p ism cells, whe e
each p ism cell is made o e he s and igid ba s, and hey can apply ension and com-
p ession e o s. The key o hei app oach is o conside hese elemen s as a con inuum
de o mable elemen , which pe mi s hem o scale he numbe o UAVs in he ae ial ans-
po ask, hus gaining some ad an ages, such as an inc ease in obus ness, econ igu a ion
D ones 2024,8, 35 8 o 21
capabili ies and he abili y o he sys em o na iga e in cons ained en i onmen s, such as
na ow channels.
Ca ena ies a e widely accep ed by he scien i ic communi y as a dynamic cable model
ep esen a ion and ha e been used in subma ine moo ing cable simula ions [
78
–
80
]. How-
e e , models based on ca ena ies ha e no been ully exploi ed o ae ial owing, despi e
he p omising esul s p esen ed in p e ious wo ks [
78
,
81
,
82
]. Wo ks using his cable o -
mula ion de end he ad an ages o ca ena ies o hei quasis a ic con igu a ion, ease o
compu a ion and well-es ablished igid–solid mechanics equa ion. Ca ena ies can be used
o o mula e disc e e o con inuous models. Es e ez e al. [
83
] p esen ed a collabo a i e
quad o o sys em o DLO anspo a ion using ca ena ies, as shown in Figu e 7. They
c ea ed an equiload quad o o heigh con igu a ion o he anspo a ion o a cable wi h
he same e ical load o each obo unde he ollowing assump ions:
•
The cable diame e is negligible compa ed o i s leng h. Thus, he cable can be modeled
as a 1D objec .
• The mass pe uni leng h o he cable is cons an .
• The cable canno elas ically leng hen (Young’s modulus is la ge).
• The e is no o sion in he cable.
Figu e 7. T anspo a ion o DLO wi h a eam o quad o o s.
The same esea ch g oup e ol ed hei wo k and u ned hei p oposal in o a hy-
b id pa abola and ca ena y swi ching model, so he eam o UAVs does no collapse he
ca ena ies when hey ge oo close in agg essi e maneu e s o sha p ajec o ies [
84
].
The app oach o modeling cables wi h ca ena ies has been adop ed by o he esea ch
g oups, such as [
85
,
86
], who expe imen ally es ed he alidi y o he solu ion. Howe e ,
bo h o hem jus use wo o o c a in he o ma ion.
Howe e , e y ew o he mul i- obo anspo p oposals in his sec ion ake in o
accoun li -o o landing p ocedu es. Al hough Gooda zi and Lee [
87
] and Michael
e al. [
73
] pe o med expe imen s showing ha hei sys ems a e able o li and land, hey
do no desc ibe he ma hema ical modeling o he cable o a ansien egime. Including
he dynamic p ope ies o he cable du ing hese phases inc eases he cos o compu a ion.
The scien i ic li e a u e in his ield is e y sca ce and elies on some simpli ica ions o
ease he calculus and compu a ional cos [
88
]. Fo ins ance, Bacela e al. [
89
] p esen ed
wo AR D one 2.0 quad o o s o anspo ing a suspended load and speci ied ha hey
a e always assumed o be au . Nex , Pize a e al. [
90
,
91
] p oposed a sys em o wo
quad o o s anspo ing a poin -mass load wi h wo cables o med by poin -like masses
joined by sp ings and dampe s (Kel in–Voig models). This cable model is able o abso b
he con ac wi h he g ound and linea ly educe he ension o he cables. Geng e al. [
92
]
and Goodman e al. [
93
] used he same cable dynamic model. La ely, some o he esea che s
ha e ep oduced his schema o loading ba - o od-shaped payloads, as can be seen in
Figu e 8. While elas ic cables o e he ad an age o mi iga ing impulsi e o ces on he ba ,
excessi e oscilla ions can induce unwan ed o ce ul mo emen s, po en ially jeopa dizing
he sa e y o he collabo a i e ask. The e o e, he implemen a ion o elas ic cables wi h
enhanced s i ness and damping is c ucial o sa egua d he ba du ing he anspo a ion
D ones 2024,8, 35 9 o 21
p ocess. Fo ins ance, Goodman e al. again alida ed hei esul s wi h simula ions in [
94
],
while Gabellie i e al. [95] alida ed hei p oposal wi h eal expe imen s.
Figu e 8.
Quad o o s anspo ing a cable-suspended ba (
le
) and cable sec ion ep esen ed by
mass–sp ing–dampe sys ems ( igh ).
Finally, Shi ani e al. [
88
] p esen ed a ma hema ically simple cable collapse-and-
collision model o li -o and landing based on he geome ic coo dina es and dis ance
be ween he UAVs and he payload. Su p isingly, he end in ecen yea s has been o
ex end he cable model ha swi ches he s a e o he cable om slack o au when a
heigh h eshold is achie ed wi h a eam o o o c a [
69
,
91
,
96
,
97
], which is appa en ly he
simples o mula ion, ma hema ically speaking. This slung-load op ion p e ails as one o
he mos used al e na i es, bo h o expe imen s including payload li ing and o hose
wi hou i . Howe e , o he o me , hese s udies a e limi ed o smoo h maneu e s.
4. Con ol S a egies
Dynamic models o mul i o o - ype UAVs usually conside ha he geome y and
mass dis ibu ion a e symme ical, which allows o some simpli ica ions o he dynamic
equa ions. The mass dis ibu ion o an ae ial obo wi h a payload is no longe symme -
ical, as i a ies widely wi h he mo emen o he manipula o o cable mass. In he
ollowing pa ag aphs, we discuss he s a e o he a in con ol design o se e al o he
abo e con igu a ions.
4.1. Indi idual T anspo
Du ing ligh , he payload adds passi e dynamic e ec s, which could come om ei he
he cable o he payload, and gene a es swinging ha modi ies he dynamics o he UAV
and al e s i s dynamic pe o mance. The mos common way o deal wi h he pe u ba-
ions caused by he payload is o s abilize he sys em, minimizing he load swings
[36,98]
.
Al e na i ely, some wo ks used eedback con ol o ack he desi ed load ajec o ies o
ajec o y-planning algo i hms o he quad o o -wi h-load mul i-body sys em [
99
]. Some
o he esea che s di ided he cable model in o di e en subsys ems. In hese hyb id dy-
namic models, each subsys em has i s speci ic and specialized con olle , and he swi ching
among he simple con olle s is pe o med by a supe iso y sys em [
39
,
47
]. In con as ,
o he g oups wo ked on he sea ch o a gene al solu ion o he p oblem o suspended-cable
anspo , no ma e wha s age he mission is in [23,50,100].
The dynamic sys em o a quad o o wi h a hanging payload in 3D has eigh deg ees o
eedom and only ou con ol inpu s. Thus, he same ou model simpli ica ions men ioned
in Sec ion 3.1 e e ing o he UAV and payload a e assumed, bu s ill, he ou deg ees o
unde ac ua ion make he con olle design challenging [
101
]. This subsec ion is di ided
in o h ee di e en con ol-o ien ed app oaches o he UAV and he payload sys em.
They include swing a enua ion o he payload, op imal ajec o y acking and con ol o
agg essi e maneu e s.
D ones 2024,8, 35 16 o 21
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