Op imal T ajec o y Planning o Cinema og aphy
wi h Mul iple Unmanned Ae ial Vehicles
Al onso Alcan a aa, Jesus Capi ana, Ri a Cunhab, Anibal Olle oa
aGRVC Robo ics Labo a o y, Uni e si y o Se ille, Spain.
bIns i u e o Sys ems and Robo ics, Ins i u o Supe io T´
ecnico, Uni e sidade de Lisboa, Po ugal.
Abs ac
This pape p esen s a me hod o planning op imal ajec o ies wi h a eam o Unmanned Ae ial Vehicles (UAVs) pe o ming
au onomous cinema og aphy. The me hod is able o plan ajec o ies online and in a dis ibu ed manne , p o iding coo dina ion
be ween he UAVs. We p opose a no el non-linea o mula ion o his challenging p oblem o compu ing mul i-UAV op imal
ajec o ies o cinema og aphy; in eg a ing UAVs dynamics and collision a oidance cons ain s, oge he wi h cinema og aphic
aspec s like smoo hness, gimbal mechanical limi s and mu ual came a isibili y. We in eg a e ou me hod wi hin a ha dwa e and
so wa e a chi ec u e o UAV cinema og aphy ha was p e iously de eloped wi hin he amewo k o he Mul iD one p ojec ; and
demons a e i s use wi h di e en ypes o sho s ilming a mo ing a ge ou doo s. We p o ide ex ensi e expe imen al esul s bo h
in simula ion and ield expe imen s. We analyze he pe o mance o he me hod and p o e ha i is able o compu e online smoo h
ajec o ies, educing je ky mo emen s and complying wi h cinema og aphy cons ain s.
Keywo ds: Op imal ajec o y planning, UAV cinema og aphy, Mul i-UAV coo dina ion
1. In oduc ion
D ones o Unmanned Ae ial Vehicles (UAVs) a e sp eading
as o ae ial pho og aphy and cinema og aphy, mainly due o
hei maneu e abili y and hei capaci y o access complex ilm-
ing loca ions in ou doo se ings. F om he applica ion poin o
iew, UAVs p esen a ema kable po en ial o p oduce unique
ae ial sho s a educed cos s, in con as wi h o he al e na i es
like dollies o s a ic came as. Addi ionally, he use o eams
wi h mul iple UAVs opens e en mo e he possibili ies o cin-
ema og aphy. On he one hand, la ge-scale e en s can be ad-
d essed by ilming mul iple ac ion poin s concu en ly o se-
quen ially. On he o he hand, he combina ion o sho s wi h
mul iple iews o di e en came a mo ions b oadens he a is-
ic al e na i es o he di ec o .
Cu en ly, mos UAVs in cinema og aphy a e ope a ed in
manual mode by an expe pilo . Besides, an addi ional quali-
ied ope a o is equi ed o con ol he came a du ing he ligh ,
as aking ae ial sho s can be a complex and o e loading ask.
E en so, he manual ope a ion o UAVs o ae ial cinema og-
aphy is s ill challenging, as mul iple aspec s need o be con-
side ed: pe o ming smoo h ajec o ies o achie e aes he ic
ideos, acking ac o s o be ilmed, a oiding collisions wi h
?This wo k was pa ially unded by he Eu opean Union’s Ho izon 2020
esea ch and inno a ion p og amme unde g an ag eemen s No 731667 (Mul-
iD one), and by he MULTICOP p ojec (Jun a de Andalucia, FEDER P o-
g amme, US-1265072).
Email add esses: [email p o ec ed] (Al onso Alcan a a),
[email p o ec ed] (Jesus Capi an), [email p o ec ed] (Ri a Cunha),
[email p o ec ed] (Anibal Olle o)
po en ial obs acles, keeping o he came as ou o he ield o
iew, e c.
The e exis comme cial p oduc s (e.g., DJI Ma ic [1] o Sky-
dio [2]) ha cope wi h some o he a o emen ioned complexi-
ies implemen ing semi-au onomous unc ionali ies, like au o-
ollow ea u es o ack an ac o o simplis ic collision a oid-
ance. Howe e , hey do no add ess cinema og aphic p inciples
o mul i-UAV eams, as e.g., planning ajec o ies conside ing
gimbal physical limi a ions o in e -UAV isibili y. The e o e,
solu ions o au onomous ilming wi h mul iple UAVs a e o in-
e es . Some au ho s [3] ha e shown ha planning ajec o ies
ahead se e al seconds is equi ed in o de o ul ill wi h cine-
ma og aphic cons ain s smoo hly. O he s [4, 5] ha e e en ex-
plo ed he mul i-UAV p oblem, bu online ajec o y planning
o mul i-UAV cinema og aphy ou doo s is s ill an open issue.
In his pape , we p opose a me hod o online planning and
execu ion o ajec o ies wi h a eam o UAVs aking cine-
ma og aphy sho s. We de elop an op imiza ion-based ech-
nique ha uns on he UAVs in a dis ibu ed ashion, aking
ca e o he con ol o he UAV and he gimbal mo ion simul-
aneously. Ou me hod aims a p o iding smoo h ajec o ies
o isually pleasan ideo ou pu ; in eg a ing cinema og aphic
cons ain s imposed by he sho ypes, he gimbal physical lim-
i s, he mu ual isibili y be ween came as and he a oidance o
collisions.
This wo k has been de eloped wi hin he amewo k o he
EU- unded p ojec Mul iD one1, whose objec i e was o c ea e
a comple e sys em o au onomous cinema og aphy wi h mul i-
1h ps://mul id one.eu.
a Xi :2009.04234 2 [cs.RO] 5 Ap 2021
Figu e 1: Cinema og aphy applica ion wi h wo UAVs ilming a cycling e en .
Bo om, ae ial iew o he expe imen wi h wo mo ing cyclis s. Top, images
aken om he came as on boa d each UAV.
ples UAVs in ou doo spo e en s (see Figu e 1). Mul iD one
add essed di e en aspec s o build a comple e a chi ec u e: a
se o high-le el ools so ha he cinema og aphy di ec o can
de ine sho s o he mission [6]; planning me hods o assign and
schedule he sho s among he UAVs e icien ly and conside ing
ba e y cons ain s [7]; ision-based algo i hms o a ge ack-
ing on he came a image [8], e c. In his pape , we ocus on he
au onomous execu ion o sho s wi h a mul i-UAV eam. We as-
sume ha he di ec o has designed a mission wi h se e al sho s;
and ha he e is a planning module ha has assigned a speci ic
sho o each UAV. Then, ou objec i e is o plan ajec o ies in
o de o execu e all sho s online in a coo dina ed manne .
1.1. Rela ed wo k
Op imal ajec o y planning o UAVs is a commonplace
p oblem in he obo ics communi y. A ypical app oach is
o use op imiza ion-based echniques o gene a e ajec o ies
om polynomial cu es minimizing hei de i a i e e ms o
smoo hness, e.g., he ou h de i a i e o snap [9, 10]. This
polynomial ajec o ies ha e also been applied o op imiza ion
p oblems wi h mul iple UAVs [11]. Model P edic i e Con ol
(MPC) is ano he widesp ead echnique o op imal ajec o y
planning [12], a dynamic model o he UAV is used o p edic -
ing and op imizing ajec o ies ahead wi hin a eceding ho i-
zon. Some au ho s [13] ha e also used MPC-based app oaches
o mul i-UAV ajec o y planning wi h collision a oidance and
non-linea models. In he con ex o mul i-UAV a ge ack-
ing, o he s [14, 15] ha e combined MPC wi h po en ial ields o
add ess he non-con exi y induced by collision a oidance con-
s ain s. In [16], a cons ained op imiza ion p oblem is o mu-
la ed o main ain a o ma ion whe e a leade UAV akes pic u es
o inspec ion in da k spaces, while o he s illumina e he a ge
spo suppo ing he ask. The sys em is used o ae ial docu-
men a ion wi hin his o ical buildings.
Addi ionally, he e a e wo ks in he li e a u e jus o a ge
acking wi h UAVs, p oposing al e na i e con ol echniques
like classic PID [17] o LQR [18] con olle s. The main issues
wi h all hese me hods o ajec o y planning and a ge ack-
ing a e ha hey ei he do no conside cinema og aphic aspec s
explici ly o do no plan ahead in ime o ho izons long enough.
In he compu e anima ion communi y, he e a e se e al
wo ks ela ed wi h ajec o y planning o he mo ion o i -
ual came as [19]. They ypically use o line op imiza ion o
gene a e smoo h ajec o ies ha a e isually pleasan and com-
ply wi h ce ain cinema og aphic aspec s, like he ule o hi ds.
Howe e , many o hem do no ensu e physical easibili y o
comply wi h UAV dynamic cons ain s and hey assume ull
knowledge o he en i onmen map. In e ms o op imiza-
ion unc ions, se e al wo ks conside simila e ms o achie e
smoo hness. Fo ins ance, au ho s in [20] model ajec o ies
as polynomial cu es whose coe icien s a e compu ed o min-
imize snap ( ou h de i a i e). They also check dynamic easi-
bili y along he planned ajec o ies, and he use is allowed o
adjus he UAV eloci y a execu ion ime. A simila applica-
ion o design UAV ajec o ies o ou doo ilming is p oposed
in [21]. Timed e e ence ajec o ies a e gene a ed om 3D po-
si ions speci ied by he use , and he inal iming o he sho s
is add essed designing easing cu es ha d i e he UAV along
he planned ajec o y (i.e., cu es ha modi y he UAV eloc-
i y p o ile). In [22], aes he ically pleasan oo age is achie ed
by penalizing he snap o he UAV ajec o y and he je k ( hi d
de i a i e) o he came a mo ion. An i e a i e quad a ic op i-
miza ion p oblem is o mula ed o compu e ajec o ies o he
came a and he look-a poin (i.e., he place whe e he came a is
poin ing a ). They also include collision a oidance cons ain s,
bu he me hod is only es ed indoo s.
Al hough hese a icles on compu e g aphics app oach he
p oblem mainly h ough o line op imiza ion, some o hem
ha e p oposed op ions o achie e eal- ime pe o mance, like
planning in a o ic space [23] o in e pola ing polynomial
cu es [24, 21]. In gene al, hese wo ks p esen in e es ing he-
o e ical p ope ies, bu hey a e es ic ed o o line op imiza ion
wi h a ully known map o he scena io and s a ic o close- o-
s a ic guided ou scenes, i.e., wi hou mo ing ac o s.
In he obo ics li e a u e, he e a e wo ks ocusing mo e on
ilming dynamic scenes and complying wi h physical UAV con-
s ain s. Fo example, au ho s in [25] p opose o de ec limbs
mo emen o a human o ou doo ilming. T ajec o y planning
is pe o med online wi h polynomial cu es ha minimize snap.
In [26, 3], hey p esen an in eg a ed sys em o ou doo cin-
ema og aphy, combining ision-based a ge localiza ion wi h
ajec o y planning and collision a oidance. Fo op imal ajec-
o y planning, hey apply g adien descen wi h di e en iable
cos unc ions. Smoo hness is achie ed minimizing ajec o y
je k; and sho quali y by de ining objec i e cu es ul illing cin-
ema og aphic cons ain s associa ed wi h ela i e angles w. . .
he ac o and sho scale. Cinema og aphy op imal ajec o ies
ha e also been compu ed in eal ime h ough eceding ho izon
wi h non-linea cons ain s [27]. The use inpu s aming ob-
jec i es o one o se e al a ge s on he image, and e o s o
he image a ge p ojec ions, sizes and ela i e iewing angles
a e minimized; sa is ying collision a oidance cons ain s and
a ge isibili y. The me hod beha es well o online nume ical
2
Re e ences Online Scene UAVs
Dynamics
Collision
A oidance
Mu ual
Visibili y Ou doo s Mul iples UAVs
[23] No S a ic No No No No No
[20] No S a ic Yes No No Yes No
2 [22] No S a ic Yes Yes No No No
[21] No S a ic Yes Ac o No Yes No
[24] No Dynamic No No No No No
[27] Yes Dynamic Yes Yes No No No
[4] Yes Dynamic Yes Ac o Yes No Yes
[25] Yes Dynamic Yes Ac o No Yes No
[5] Yes Dynamic Yes Yes Yes No Yes
[26] Yes Dynamic Yes Yes No Yes No
[3] Yes Dynamic Yes Yes No Yes No
Ou s Yes Dynamic Yes Yes Yes Yes Yes
Table 1: Rela ed wo ks on ajec o y planning o UAV cinema og aphy. We indica e whe he compu a ion is online o no , he ype o scene and cons ain s hey
conside , and hei capaci y o handle ou doo applica ions and mul iple UAVs.
op imiza ion, bu i is only es ed in indoo se ings.
Some o he a o emen ioned au ho s om obo ics ha e also
app oached UAV cinema og aphy applying machine lea ning
echniques. In pa icula , lea ning om demons a ion o imi-
a e p o essional came aman’s beha io s [28] o ein o cemen
lea ning o achie e isually pleasan sho s [29]. In gene al,
mos o hese ci ed wo ks on obo ics p esen esul s qui e in e -
es ing in e ms o ope a ion ou doo s o online ajec o y plan-
ning, bu hey always es ic o a single UAV.
Rega ding me hods o mul iple UAVs, he e is some ela ed
wo k which is wo h men ioning. In [4], a non-linea op imiza-
ion p oblem is sol ed in a eceding ho izon ashion, aking in o
accoun collision a oidance cons ain s wi h he ilmed ac o s
and be ween he UAVs. Aes he ic objec i es a e in oduced by
he use as i ual e e ence ails. Then, UAVs ecei e cu en
plans om all o he s a each planning i e a ion and compu e
collision- ee ajec o ies sequen ially. A UAV o ic space is
p oposed in [5] o ensu e ha cinema og aphic p ope ies and
dynamic cons ain s a e ensu ed along he ajec o ies. Non-
linea op imiza ion is applied o gene a e polynomial cu es
wi h minimum cu a u e a ia ion, accoun ing o a ge is-
ibili y and collision a oidance. The mo ion o mul iple UAVs
a ound dynamic a ge s is coo dina ed by means o a cen alized
mas e -sla e app oach o sol e con lic s. E en hough hese
wo ks p esen p omising esul s o mul i-UAV eams, hey a e
only demons a ed a indoo scena ios whe e a Vicon mo ion
cap u e sys em p o ides accu a e posi ioning o all a ge s and
UAVs. These wo ks p esen qui e aluable con ibu ions o
cinema og aphy wi h mul iple UAVs, bu hey a e e alua ed in
indoo se ings. The speci ics o he ou doo scena ios consid-
e ed in ou wo k a e di e en in se e al aspec s, as he en i on-
men is less con olled: UAVs equi e mo e payload o ca y on-
boa d came as wi h be e lenses and equipmen o la ge ange
communica ion; achie ing smoo h ajec o ies is mo e complex
due o ex e nal ac o s such as wind gus s o communica ion de-
lays; UAV posi ioning is less accu a e in gene al; and so on.
To sum up, Table 1 shows he main ela ed wo ks on ajec-
o y planning o UAV cinema og aphy and hei co espond-
ing p ope ies. We indica e whe he compu a ion is online o
o line, whe he he scene con ains dynamic a ge s o be ilmed
and whe he UAV dynamics a e included as cons ain s. We
also analyze he ype o collision a oidance: none (No), wi h
he ac o being ilmed (Ac o ) o wi h ex e nal obs acles and
o he UAVs (Yes). Wo ks which add ess mu ual isibili y con-
s ain s be ween mul iple came as a e men ioned speci ically.
Finally, we indica e whe he each me hod includes e alua ion
in ou doo se ings and whe he i can handle mul iple UAVs.
1.2. Con ibu ions
We p opose a no el me hod o plan online op imal ajec o-
ies o a se o UAVs execu ing cinema og aphy sho s. The
op imiza ion is pe o med in a dis ibu ed manne , and i aims
o smoo h ajec o ies complying wi h dynamic and cinema o-
g aphic cons ain s. We ex end ou p e ious wo k [30] in op-
imal ajec o y planning o UAV cinema og aphy as ollows:
(i) we cope wi h mul iple UAVs in eg a ing new cons ain s o
in e -UAV collisions and mu ual isibili y; (ii) we p esen ad-
di ional simula ion esul s o e alua e he me hod wi h di e en
ypes o sho s; and (iii) we demons a e he sys em in ield ex-
pe imen s wi h mul iple UAVs ilming dynamic scenes. The e-
o e, he main no el y o ou me hod is he mul i-UAV coo -
dina ion o combine he execu ion o se e al ypes o sho s si-
mul aneously in ou doo scena ios, wi h he speci ic challenges
ha hose en i onmen s in ol e. Mo e pa icula ly, ou main
con ibu ions a e he ollowing:
•We p opose a no el o mula ion o he ajec o y planning
p oblem o UAV cinema og aphy. We model bo h UAV
and gimbal mo ion (Sec ion 2), bu decouple hei con ol
ac ions.
•We p opose a non-linea , op imiza ion-based me hod o
ajec o y planning (Sec ion 3). Using a eceding ho i-
zon scheme, ajec o ies a e planned and execu ed in a
dis ibu ed manne by a eam o UAVs p o iding mul iple
iews o he same scene. The me hod conside s UAV dy-
namic cons ain s, and imposes hem o a oid p ede ined
3
Figu e 2: De ini ion o e e ence ames used. The o igins o he came a and
quad o o ames coincide. The came a poin s o he a ge .
no- ly zones o collisions wi h o he s. Cinema og aphic
aspec s imposed by sho de ini ion, came a mu ual isibil-
i y and gimbal physical bounds a e also add essed. T ajec-
o ies smoo hing UAV and gimbal mo ion a e gene a ed o
achie e aes he ic ideo oo age.
•We desc ibe he comple e sys em a chi ec u e on boa d
each UAV and he di e en ypes o sho conside ed (Sec-
ion 4). The a chi ec u e in eg a es a ge acking wi h
ajec o y planning and i is such ha di e en UAVs can
be execu ing di e en ypes o sho simul aneously.
•We p esen ex ensi e expe imen al esul s (Sec ion 5) o
e alua e he pe o mance o ou me hod o di e en ypes
o sho . We p o e ha ou me hod is able o com-
pu e smoo h ajec o ies educing je ky mo emen s in eal
ime, and complying wi h he cinema og aphic es ic-
ions. Then, we demons a e ou sys em in ield expe i-
men s wi h h ee UAVs planning ajec o ies online o ilm
a mo ing ac o (Sec ion 6).
2. Dynamic Models
This sec ion p esen s ou dynamic models o UAV cine-
ma og aphe s. We model he UAV as a quad o o wi h a came a
moun ed on a gimbal o wo deg ees o eedom.
2.1. UAV model
Le {W}deno e he wo ld e e ence ame wi h o igin ixed
in he en i onmen and Eas -No h-Up (ENU) o ien a ion. Con-
side also h ee addi ional e e ence ames (see Figu e 2): he
quad o o e e ence ame {Q}a ached o he UAV wi h o igin
a he cen e o mass, he came a e e ence ame {C}wi h z-
axis aligned wi h he op ical axis bu wi h opposi e sign, and
he a ge e e ence ame {T}a ached o he mo ing a ge ha
is being ilmed. Fo simplici y, we assumed ha he o igins o
{Q}and {C}coincide.
The con igu a ion o {Q}wi h espec o {W}is deno ed by
(pQ,RQ)∈SE(3), whe e pQ∈R3is he posi ion o he o igin
o {Q}exp essed in {W}and RQ∈SO(3) is he o a ion ma-
ix om {Q} o {W}. Simila ly, he con igu a ions o {T}and
{C}wi h espec o {W}a e deno ed by (pT,RT)∈SE(3) and
(pC,RC)∈SE(3), espec i ely.
We model he quad o o dynamics as a linea double in eg a-
o model:
˙
pQ= Q
˙
Q=aQ,(1)
whe e Q=[ x y z]T∈R3is he linea eloci y and aQ=
[axayaz]T∈R3is he linea accele a ion. We assume ha he
linea accele a ion aQ akes he o m:
aQ=−ge3+RQ
T
me3,(2)
whe e mis he quad o o mass, g he g a i a ional accele a ion,
T∈R he scala h us , and e3=[0 0 1]T.
Fo he sake o simplici y, we use he 3D accele a ion aQ
as con ol inpu ; al hough he h us Tand o a ion ma ix RQ
could also be eco e ed om 3D eloci ies and accele a ions.
I we es ic he yaw angle ψQ o keep he quad o o ’s on
poin ing o wa d in he di ec ion o mo ion such ha :
ψQ=a an2( y, x),(3)
hen he h us Tand he Z-Y-XEule angles λQ=
[φQ, θQ, ψQ]Tcan be ob ained om Qand aQacco ding o:
T=mkaQ+ge3k
ψQ=a an2( y, x)
φQ=−a csin((aycos(ψQ)−axsin(ψQ))/kaQ+ge3k)
θQ=a an2(axcos(ψQ)+aysin(ψQ),az+g)
(4)
2.2. Gimbal angles
Le λC=[φC, θC, ψC]Tdeno e he Z-Y-XEule angles ha
pa ame ize he o a ion ma ix RC, such ha :
RC=Rz(ψC)Ry(θC)Rx(φC).(5)
In ou sys em, we decouple gimbal mo ion wi h an indepen-
den gimbal a i ude con olle ha ensu es ha he came a is
always poin ing owa ds he a ge du ing he sho , as in [3].
This educes he complexi y o he planning p oblem and al-
lows us o con ol he came a based on local pe cep ion eed-
back i a ailable, accumula ing less e o s. We also conside
ha he ime-scale sepa a ion be ween he ” as e ” gimbal dy-
namics and ”slowe ” quad o o dynamics is su icien ly la ge
o neglec he gimbal dynamics and assume an exac ma ch be-
ween he desi ed and ac ual o ien a ions o he gimbal. In o de
o de ine RC, le us in oduce he ela i e posi ion:
q=hqxqyqziT=pC−pT,(6)
and assume ha he UAV is always abo e he a ge , i.e., qz>0,
and no di ec ly abo e he a ge , i.e., [qxqy],0. Then, he
gimbal o ien a ion RC ha gua an ees ha he came a is aligned
4
wi h he ho izon al plane and poin ing owa ds he a ge is
gi en by:
RC=−q×q×e3
kq×q×e3k
q×e3
kq×e3k
q
kqk
=
∗qy
√q2
x+q2
y∗
∗−qx
√q2
x+q2
y∗
√q2
x+q2
y
√q2
x+q2
y+q2
z
0qz
√q2
x+q2
y+q2
z
.(7)
To eco e he Eule angles om he abo e exp ession o RC,
no e ha i he came a is aligned wi h he ho izon al plane, hen
he e is no oll angle, i.e. φC=0, and RC akes he o m:
RC=
cos(ψC) cos(θC)−sin(ψC) cos(ψC) sin(θC)
cos(θC) sin(ψC) cos(ψC) sin(ψC) sin(θC)
−sin(θC) 0 cos(θC)
,(8)
and we ob ain:
φC=0
θC=a an2(−qq2
x+q2
y,qz)
ψC=a an2(−qy,−qx)
(9)
Ou cinema og aphy sys em is designed o pe o m smoo h
ajec o ies as he UAVs a e aking hei sho s, and hen using
mo e agg essi e maneu e s only o ly be ween sho s wi hou
ilming. I UAVs ly smoo hly, we can assume ha hei ac-
cele a ions axand aya e small, and hence, by di ec applica-
ion o Eq. (4), ha hei oll and pi ch angles a e small and
Rx(φQ)≈Ry(θQ)≈I3. This assump ion is ele an o alle ia e
he non-linea i y o he model and achie e eal- ime nume ical
op imiza ion. Mo eo e , i is easonable du ing sho execu ion,
as ou ajec o y planne will minimize explici ly UAV accele -
a ions, and will limi bo h UAV eloci ies and accele a ions.
Unde his assump ion, he o ien a ion ma ix o he gimbal
wi h espec o he quad o o Q
CRcan be app oxima ed by:
Q
CR=(RQ)TRC
≈Rz(ψC−ψQ)Ry(θC)Rx(φC),(10)
and he ela i e Eule angles QλC( oll, pi ch and yaw) o he
gimbal wi h espec o he quad o o a e ob ained as:
QφC=φC=0
QθC=θC=a an2(−qq2
x+q2
y,qz)
QψC=ψC−ψQ=a an2(−qy,−qx)−a an2( y, x)
(11)
Acco ding o Eq. (4), (9) and (11), λQ,λCand QλCa e com-
ple ely de ined by he ajec o ies o he quad o o and he a -
ge , as explici unc ions o q, Q, and aQ.
3. Op imal T ajec o y Planning
In his sec ion, we desc ibe ou me hod o op imal ajec o y
planning. We explain how ajec o ies a e compu ed online in a
eceding ho izon scheme, conside ing dynamic and cinema o-
g aphic cons ain s; and hen, how he coo dina ion be ween
mul iple UAVs is add essed. A e wa d, we de ail how o exe-
cu e he ajec o ies and con ol he gimbal. Las , we include a
ho ough discussion abou some c i ical aspec s o he me hod.
3.1. T ajec o y planning
We plan op imal ajec o ies o a eam o nUAVs as hey
ilm a mo ing ac o o a ge whose posi ion can be measu ed
and p edic ed. The main objec i e is o come up wi h ajec-
o ies ha sa is y physical UAV and gimbal es ic ions, a oid
collisions and espec cinema og aphic concep s. This means
ha each UAV needs o pe o m he kind o mo ion imposed
by i s sho ype (e.g., s ay beside/behind he a ge in a la -
e al/chase sho ) and gene a e smoo h ajec o ies o minimize
je ky mo emen s o he came a and yield a pleasan ideo
oo age. Each UAV will ha e a sho ype and a desi ed 3D po-
si ion (pD) and eloci y ( D) o be eached. This desi ed s a e
is de e mined by he ype o sho and may mo e along wi h he
eceding ho izon. Fo ins ance, in a la e al sho , he desi ed
posi ion (pD) mo es wi h he a ge , o place he UAV beside i ;
whe eas in a lyby sho , his posi ion is such ha he UAV ge s
o e he a ge by he end o he sho . Mo e de ails abou he
di e en ypes o sho and how o compu e he desi ed posi ion
will be gi en in Sec ion 4.
We plan ajec o ies o each UAV in a dis ibu ed manne ,
assuming ha he plans om o he neighbo ing UAVs a e com-
munica ed (we deno e his se o neighbo ing UAVs as Neigh).
Fo ha , we sol e a cons ained op imiza ion p oblem o each
UAV whe e he op imiza ion a iables a e i s disc e e s a e wi h
3D posi ion and eloci y (xk=[pQ,k Q,k]T), and i s 3D accele -
a ion as con ol inpu (uk=aQ,k). A non-linea cos unc ion is
minimized o a ho izon o N imes eps, using as inpu a each
sol ing i e a ion he cu en obse a ion o he sys em s a e x0.
In pa icula , he ollowing non-con ex op imiza ion p oblem is
o mula ed o each UAV:
minimize
x0,...,xN
u0,...,uN
N
X
k=0
(w1||uk||2+w2Jθ+w3Jψ)+w4JN(12)
subjec o x0=x0(12.a)
xk+1= (xk,uk)k=0,...,N−1 (12.b)
min ≤ Q,k≤ max (12.c)
umin ≤uk≤umax (12.d)
pQ,k∈ F (12.e)
||pQ,k−pO,k||2≥ 2
col,∀O(12. )
θmin ≤QθC,k≤θmax (12.g)
ψmin ≤QψC,k≤ψmax (12.h)
cos(βj
k)≤cos(α),∀j∈Neigh (12.i)
As cons ain s, we impose he ini ial UAV s a e (12.a) and
he UAV dynamics (12.b), which a e ob ained by in eg a ing
nume ically he con inuous model in Sec ion 2 wi h he Runge-
Ku a me hod. We also include bounds on he UAV eloci y
5
(12.c) and accele a ion (12.d), o ensu e ajec o y easibili y.
The UAV posi ion is es ic ed in wo manne s. On he one
hand, i mus s ay wi hin he olume F ∈ R3(12.e), which
is a space no necessa ily con ex excluding p ede ined no- ly
zones. These a e s a ic zones p o ided by he di ec o be o e
he mission o keep he UAVs away om known haza ds like
buildings, high ees, c owds, e c. On he o he hand, he UAV
mus s ay a a minimum dis ance col om any addi ional obs a-
cle Ode ec ed du ing ligh (12. ), in o de o a oid collisions.
pO,k ep esen s he obs acle posi ion a imes ep k. One o hese
cons ain s is added o each o he UAV in he eam o model
hem as dynamic obs acles, using hei communica ed ajec o-
ies o ex ac hei posi ions along he planning ho izon. How-
e e , o he dynamic obs acles, e.g. he ac o o be ilmed, can
also be conside ed. Fo ha , a model o p edic he u u e posi-
ion o he obs acle wi hin he ime ho izon is equi ed. Besides,
mechanical limi a ions o he gimbal o o a e a ound each axis
a e en o ced by means o bounds on he pi ch (12.g) and yaw
angles (12.h) o he came a wi h espec o he UAV. Las , he e
a e mu ual isibili y cons ain s (12.i) o each o he UAV in
he eam, o ensu e ha hey do no ge in o he ield o iew
o he came a a hand. Mo e de ails abou how o compu e his
cons ain a e gi en in Sec ion 3.2.
Rega ding he cos unc ion, i consis s o ou weigh ed
e ms o be minimized. The e minal cos JN=||xN−[pD D]T||2
is added o guide he UAV o he desi ed s a e imposed by he
sho ype. The o he h ee e ms a e ela ed wi h he smoo hness
o he ajec o y, penalizing UAV accele a ions and je ky mo e-
men s o he came a. Speci ically, he e ms Jθ=|Q˙
θC,k|2and
Jψ=|Q˙
ψC,k|2minimize he angula eloci ies o penalize quick
changes in gimbal angles. De i ing analy ically (11), Jθand
Jψcan be exp essed in e ms o he op imiza ion a iables and
he a ge ajec o y. We assume ha he a ge posi ion a he
ini ial imes ep is measu able and we apply a kinema ic model
o p edic i s ajec o y o he ime ho izon N. An app op ia e
uning o he di e en weigh s o he e ms in he cos unc ion
is key o en o ce sho de ini ion bu gene a ing a smoo h came a
mo ion.
3.2. Mul i-UAV coo dina ion
Ou me hod plans ajec o ies o mul iple UAVs as hey pe -
o m cinema og aphy sho s. The coope a ion o se e al UAVs
can be used o execu e di e en ypes o sho simul aneously o
o p o ide al e na i e iews o he same subjec . This is pa ic-
ula ly appealing o ou doo ilming, e.g. in spo e en s, whe e
he di ec o may wan o o ches a e he iews om mul iple
came as in o de o show su oundings du ing he line o ac-
ion. In his sec ion, we p o ide u he insigh in o how we
coo dina e he mo ion o he se e al UAVs while ilming.
The i s poin o highligh is ha we sol e ou op imiza ion
p oblem (12) on boa d each UAV in a dis ibu ed manne , bu
being awa e o cons ain s imposed by neighbo ing eamma es.
This is e lec ed in (12. ) and (12.i), whe e we o ce UAV a-
jec o ies o es ablish a sa e y dis ance wi h o he s and o s ay
ou o o he s’ ield o iew o aes he ic pu poses. Fo ha , we
assume ha UAVs a e ope a ing close o ilm he same scene,
wha allows hem o communica e hei compu ed ajec o ies
a e each planning i e a ion. Howe e , he e a e di e en al-
e na i es o synch onize he dis ibu ed op imiza ion p ocess
so ha UAVs ac in a coo dina e ashion. Le us discuss o he
app oaches om key ela ed wo ks and hen ou p oposal.
In he li e a u e he e a e mul iple wo ks o mul i-UAV op i-
mal ajec o y planning, bu as we showed in Sec ion 1.1, only
ew wo ks add essed cinema og aphy aspec s speci ically. A
mas e -sla e app oach is applied in [5] o sol e con lic s be-
ween mul iple UAVs. Only one o he UAVs ( he mas e ) is
supposed o be shoo ing he scene a a ime, whe eas he o h-
e s ac as elay sla es ha p o ide complemen a y iewpoin s
when selec ed. The sla e UAVs ly in o ma ion wi h he mas-
e a oiding isibili y issues by s aying ou o i s ield o iew.
Con e sely, ully dis ibu ed planning is pe o med in [4] by
means o a sequen ial consensus app oach. Each UAV ecei es
he cu en planned ajec o ies om all o he s, and compu es a
new collision- ee ajec o y aking in o accoun he whole se
o u u e posi ions om eamma es and he es o es ic ions.
Besides, i is ensu ed ha ajec o ies o each UAV a e planned
sequen ially and communica ed a e each planning i e a ion. In
he i s i e a ion, his is equi alen o p io i y planning, bu no
in subsequen i e a ions, yielding mo e coope a i e ajec o ies.
We ollow a hie a chical app oach in be ween. Con a y
o [5], all UAVs can ilm he scene simul aneously wi h no p e -
e ences; bu he e is a scheme o p io i ies o sol e mul i-UAV
con lic s, as in [4]. Thus, he UAV wi h op p io i y plans i s
ajec o y igno ing o he s; he second UAV gene a es an op i-
mal ajec o y applying collision a oidance and mu ual isibil-
i y cons ain s gi en he planned ajec o y om he i s UAV;
he hi d UAV a oids he wo p e ious ones; and so on. This
scheme helps coo dina ing UAVs wi hou deadlocks and e-
duces compu a ional cos as UAV p io i y inc eases. Mo eo e ,
we do no ecompu e and communica e ajec o ies a e each
con ol imes ep as in [4]; bu ins ead, eplanning is pe o med
a a lowe equency and, meanwhile, UAVs execu e hei p e-
ious ajec o ies as we will desc ibe in nex sec ion.
In e ms o mul i-UAV coo dina ion, cons ain (12. ) copes
wi h collisions be ween eamma es and (12.i) wi h mu ual isi-
bili y. We conside all neighbo ing UAVs as dynamic obs acles
whose ajec o ies a e known (plans a e communica ed), and we
en o ce a sa e y in e -UAV dis ance col along he en i e plan-
ning ho izon N. The p ocedu e o o mula e he mu ual isibil-
i y cons ain is illus a ed in Figu e 3. The objec i e is o en-
su e ha each UAV’s came a has no o he UAVs wi hin i s ield
o iew ( he angle o iew is deno ed as α). We app oxima e he
ac ual ield o iew o he came a wi h a ci cula shape, and α
is he semi-cone angle o he cone su ounding he eal ield o
iew. We hink his is a good app oxima ion o long- ange
sho s and i simpli ies he o mula ion o he mu ual isibil-
i y cons ain s, which alle ia es he p oblem non-linea i y and
helps compu ing a solu ion. Geome ically, we model UAVs as
poin s ha need o s ay ou o he ield o iew, bu selec α
la ge enough o accoun o UAV dimensions. I we conside
he UAV ha is planning i s ajec o y a posi ion pQ,kand an-
o he neighbo ing UAV ja posi ion pj
Q,k, hen βj
k e e s o he
angle be ween ec o s qk=pQ,k−pT,kand dj
k=pQ,k−pj
Q,k:
6
βj
kα
dj
k=pQ,k−pj
Q,k
qk
pT,k
Ac ion poin
UAV j
Figu e 3: Mu ual isibili y cons ain o wo UAVs. The UAV on he igh
(blue) is ilming an ac ion poin a he same ime ha i keeps he UAV on op
( ed) ou o i s angle o iew α.
cos(βj
k)=qk·dj
k
||qk||·||dj
k||,(13)
being cos(βj
k)≤cos(α) he condi ion o keep UAV jou o he
ield o iew.
Finally, i is impo an o no ice ha he e may be ce ain
si ua ions whe e ou p io i y scheme o apply mu ual isibili y
cons ain s could ail. I we plan a ajec o y o he UAV wi h
p io i y 1, and hen, ano he one o he UAV wi h lowe p i-
o i y 2; ensu ing ha UAV 1 is no wi hin he ield o iew o
UAV 2 does no imply he way a ound, i.e., UAV 2 could s ill
appea on UAV 1’s ideo. Howe e , hese si ua ions a e a e in
ou cinema og aphy applica ion, as he e a e no many came as
poin ing in andom di ec ions, bu only a ew and all o hem
ilming a a ge ypically on he g ound. Mo eo e , since we
a o smoo h ajec o ies, we expe ienced in ou es s ha ou
sol e ends o a oid c ossings be ween di e en UAVs’ ajec-
o ies, as ha would esul in mo e cu es. The e o e, es ab-
lishing UAV p io i ies in a sma way, based on hei heigh o
dis ance o he a ge , was enough o p e en issues ela ed wi h
mu ual isibili y.
3.3. T ajec o y execu ion
Ou ajec o y planne s p oduce op imal ajec o ies con-
aining UAV posi ions and eloci ies sampled a he con ol
imes ep, which we can deno e as ∆ . As we do no ecompu e
ajec o ies a each con ol imes ep o compu a ional easons,
we use ano he independen module o ajec o y ollowing,
whose ask is lying he UAV along i s cu en planned ajec-
o y. This module is execu ed a a a e o 1/∆ Hz and keeps
a ack o he las compu ed ajec o y, which is eplaced a e
each planning i e a ion. Each ajec o y ollowe compu es 3D
eloci y e e ences o he eloci y con olle on boa d he UAV.
Fo his pu pose, we ake he closes poin in he ajec o y o
he cu en UAV posi ion, and hen, we selec ano he poin in
he ajec o y a leas Lme e s ahead. The 3D eloci y e e -
ence is a ec o poin ing o ha look-ahead waypoin and wi h
he equi ed speed o each he poin wi hin he speci ied ime
in he planned ajec o y.
A he same ime ha UAVs a e ollowing hei ajec o ies,
a gimbal con olle is execu ed a a a e o 1/∆ GHz o poin
he came a owa d he a ge being ilmed. We assume ha he
gimbal has an IMU and a low-le el con olle ecei ing angu-
la a e commands, de ined wi h espec o he wo ld e e ence
ame {W}. Using eedback abou he a ge posi ion, we gen-
e a e e e ences o he gimbal angles o ack he a ge and
compensa e he UAV mo ion and possible e o s in ajec o y
planning. These e e ences a e sen o an a i ude con olle
ha compu es angula eloci y commands based on he e o
be ween cu en and desi ed o ien a ion in he o m o a o a-
ion ma ix Re=(RC)TR∗
C, whe e he desi ed o a ion ma ix
R∗
Cis gi en by (8). Recall ha we assumed ha RCins an a-
neously akes he alue o R∗
C. To design he angula eloci y
con olle , we use a s anda d i s -o de con olle o s abiliza-
ion on he Special O hogonal G oup SO(3), which is gi en by
ω=kω(Re−RT
e)∨, whe e he ee ope a o ∨ ans o ms 3 ×3
skew-symme ic ma ices in o ec o s in R3[31]. Mo e spe-
ci ic de ails abou he ma hema ical o mula ion o he gimbal
con olle can be seen in [32].
3.4. Discussion
In his sec ion, we discuss some c i ical aspec s o ou
me hod o ajec o y planning. In pa icula , i s op imali y and
con e gence ime, as well as how i deals wi h issues such as
delays compu ing solu ions, ex e nal dis u bances due o bad
wea he o obs acle ep esen a ion.
Op imali y. We apply nume ical me hods o sol e he op i-
miza ion p oblem desc ibed in Sec ion 3.1, hus con e ging
o an op imal solu ion o a single UAV. E en hough he e
a e no heo e ical gua an ees o achie ing he global op imum
when sol ing a non-linea and non-con ex op imiza ion p ob-
lem, we expe ienced good esul s wi h he nume ical sol e ha
we used bo h in e ms o local op imali y and compu a ion ime.
A p ope sol e ini ializa ion is essen ial o as con e gence,
so we use he las compu ed ajec o y o ini ialize he solu-
ion sea ch. None heless, as we a e conside ing a o mula ion
wi h mul iple UAVs ac ing simul aneously, ou me hod does
no achie e he op imal solu ion o he comple e eam. This
is because we impose a p io i y scheme and sol e each UAV
ajec o y assuming o he s’ ajec o ies ixed o he gi en ime
ho izon. E en hough i would be mo e op imal o ecompu e
and exchange solu ions a e each execu ion ime s ep o all
UAVs [4], he quali y o ou solu ions was enough o he pu -
pose o he applica ion. Mo eo e , in ou expe imen s, UAV
p io i ies we e ixed, bu he me hod could be adap ed easily o
conside p io i ies ha a y du ing he mission depending on
ce ain ci cums ances o be mo e e icien . We lea e as u u e
wo k a u he analysis o es ablish bounds on he quali y deg a-
7
da ion o ou solu ion compa ed wi h he comple e mul i-UAV
op imum.
Con e gence ime. Ou ajec o y planning p oblem is a non-
linea and non-con ex op imiza ion ha is complex o sol e;
e en i he eam o UAVs does no encoun e ex e nal obs a-
cles, hey need o conside in e -UAV collision a oidance and
mu ual isibili y. The e o e, he ime o con e ge o a solu ion
is no negligible. We ackle his by limi ing he ime ho izon
o ajec o y planning (which educes compu a ion ime) and
using di e en a es o ajec o y planning and execu ion. T a-
jec o y planning is pe o med a lowe a es o educe compu-
a ion (be ween 0.5 and 2Hz in ou expe imen s). Besides, we
limi he compu a ion ime o he sol e and keep ollowing he
las compu ed ajec o y un il i con e ges o a new solu ion. In
case ha he maximum compu a ion ime is eached wi hou
con e gence, he e a e no gua an ees ega ding he quali y o
he solu ion compu ed, so we ecalcula e changing he p ob-
lem ini ializa ion wi h he cu en UAV s a e, which is usually
enough o con e ge o a new solu ion. In he unlikely case o
eaching he end o he p e ious compu ed ajec o y wi hou
new solu ion, he UAV would s ay ho e ing and ecompu ing
ajec o ies wi h di e en ini ial solu ions un il con e gence.
In addi ion, we do no assume ha solu ions a e gene a ed in-
s an ly and we deal wi h delays when planning ajec o ies. The
gene a ed ajec o ies ha e ime s amps associa ed wi h each
waypoin . The ajec o y ollowe componen desc ibed in Sec-
ion 3.3 ecei es hese ajec o ies wi h ce ain delay (due o he
solu ion compu a ion ime) and synch onizes hem by disca d-
ing he ini ial waypoin s co esponding o ime ins an s al eady
gone by.
Pe o mance unde ex e nal pe u ba ions. Keeping ligh s a-
bili y and smoo h ajec o ies e en unde ex e nal dis u bances
such as bad wea he condi ions is c i ical in ou me hod. In he
p esence o bad wea he , he ajec o y planning componen s
(Sec ion 3.1) would s ill gene a e smoo h ajec o ies; howe e ,
windy condi ions could esul in an inaccu a e ajec o y ol-
lowing due o ex e nal pe u ba ions. The e o e, he key o
imp o e s abili y unde bad wea he condi ions would be im-
plemen ing mo e obus UAV con olle s. In ou case, we im-
plemen ed a ajec o y ollowe based on a pu e pu sui algo-
i hm wi h a look-ahead pa ame e and a eloci y con olle .
None heless, al e na i e con ol echniques [13, 33] aking in o
accoun ex e nal pe u ba ions and unce ain ies o in eg a ing
non-linea models o he UAV could be applied o inc ease
ligh s abili y in case o wind gus s. Besides, in e ms o a-
jec o y planning, we could also adap he weigh s o he cos
unc ion in case o bad wea he , penalizing mo e hose cos s
based on UAV accele a ions and gimbal angula eloci ies, and
elaxing he cos associa ed wi h he desi ed inal s a e. Thus,
he gene a ed ajec o ies would be mo e conse a i e om he
smoo hness poin o iew, which would help ollowing ajec-
o ies in hese ad e se condi ions.
Obs acle ep esen a ion. In ou p oblem o mula ion, we in-
clude p ede ined no- ly zones and addi ional dynamic obs acles.
The o me a e used o indica e s a ic haza ds wi h known po-
si ions, like buildings, a eas wi h ees, e c. The la e consis s
o o he UAVs in he eam o ex e nal obs acles, e.g., he a -
ge being ilmed, o he ac o s in he scene, e c. As explained
in Sec ion 3.1, we ep esen hese dynamic obs acles by means
o sphe ical objec s o adius col, since he cons ain included
is o keep ha sa e y dis ance be ween he 3D obs acle posi-
ion and he co esponding UAV. We also explained ha we
need a p edic ion model o es ima e objec ajec o ies wi hin
he planning ho izon ime. We use a cons an eloci y model o
compu e hose u u e p edic ions, al hough mo e complex mod-
els could be used oo. Mo eo e , al e na i e geome ical ep e-
sen a ions could be used o he obs acles i mo e in o ma ion
abou hei shape we e known. Fo ins ance, 3D ellipsoids wi h
h ee di e en axis leng hs a e used in [4]. In ou con ex , we
do no o esee UAVs ge ing so close o a ge s so ha i s geo-
me ical shape eally ma e s, and hence, we p e e ed sphe ical
shapes ha ease ma hema ical o mula ion.
Obs acle de ec ion is ou o he scope o his pape , so we
assume ha he e is a pe cep ion module p o iding an es i-
ma ion o he obs acle 3D posi ions and eloci ies ( o mo ion
p edic ion). In p ac ice, we used in ou expe imen s dynamic
obs acles whose posi ions could be measu ed wi h a GPS and
communica ed, i.e., o he UAV eamma es and he ilmed a -
ge . None heless, his in o ma ion could be ob ained by al-
go i hms p ocessing measu emen s om poin cloud-based sen-
so s on boa d he UAVs, such as 3D LIDARs o RGB-D cam-
e as. In ha case, al e na i e obs acle ep esen a ions based
on dis ance o he poin s (e.g., o he cen oid o o he clos-
es poin ) wi hin he co esponding poin clouds could be used,
as i is done by he au ho s in [16].
4. Sys em A chi ec u e
In his sec ion, we p esen ou sys em a chi ec u e, desc ib-
ing he di e en so wa e componen s equi ed o ajec o y
planning and hei in e connec ion. Besides, we in oduce
b ie ly he o e all a chi ec u e o ou comple e sys em o cine-
ma og aphy wi h mul iple UAVs, which was p esen ed in [34].
Ou sys em coun s on a G ound S a ion whe e he compo-
nen s ela ed wi h mission design and planning a e execu ed.
We assume ha he e is a cinema og aphy di ec o who is in
cha ge o desc ibing he desi ed sho s om a high-le el pe -
spec i e. We c ea ed a g aphical ool and a no el cinema og-
aphy language [6] o suppo he di ec o h ough his ask.
Once he mission is speci ied, he sys em has planning com-
ponen s [7] ha compu e easible plans o he mission, assign-
ing sho s o he a ailable UAVs acco ding o sho du a ion and
emaining UAV ligh ime. The mission execu ion is also mon-
i o ed in he G ound S a ion, in o de o calcula e new plans in
case o unexpec ed e en s like UAV ailu es.
The componen s dedica ed o sho execu ion un on boa d
each UAV. Those componen s a e depic ed in Figu e 4. Each
UAV has a Schedule module ha ecei es sho assignmen s
om he G ound S a ion and indica es when a new sho should
be s a ed. Then, he Sho Execu o is in cha ge o planning and
8
UAV 2
Ta ge
T acke
Gimbal
Con olle
T ajec o y
Planne
T ajec o y
Followe UAL
Gimbal
UAV n
UAV 1 Sho Execu o
Schedule
pD
D
pT
T
Figu e 4: Sys em a chi ec u e on boa d each UAV. A Schedule ini ia es he sho and upda es con inuously he desi ed s a e o ajec o y planning, whe eas he Sho
Execu o plans op imal ajec o ies o pe o m he sho . UAVs exchange hei plans o coo dina ion.
execu ing op imal ajec o ies o pe o m each sho , implemen -
ing he me hod desc ibed in Sec ion 3. As inpu , he Sho Ex-
ecu o ecei es he u u e desi ed 3D posi ion pDand eloci y
D o he UAV, which is upda ed con inuously by he Sched-
ule depending on he sho pa ame e s and he a ge posi ion.
Fo ins ance, in a la e al sho , he dynamic model o he a ge
is used o p edic i s posi ion by he end o he ho izon ime
and hen place he UAV desi ed posi ion a he la e al dis ance
indica ed by he sho pa ame e s.
Addi ionally, he a ge posi ioning p o ided by he Ta ge
T acke is equi ed by he Sho Execu o o poin he gimbal
and place he UAV adequa ely. In o de o alle ia e he e ec
o noisy measu emen s when con olling he gimbal and o p o-
ide a ge es ima ions a high equency, he Ta ge T acke im-
plemen s a Kalman Fil e in eg a ing all ecei ed obse a ions.
This il e is able o accep wo kinds o measu emen s: 3D
global posi ions coming om a GPS ecei e on boa d he a -
ge , and 2D posi ions on he image ob ained by a ision-based
de ec o [8]. In pa icula , in he expe imen al se up o his pa-
pe , we used a GPS ecei e on boa d a human a ge commu-
nica ing measu emen s o he Ta ge T acke . Communica ion
la ency and lowe GPS a es a e add essed by he Kalman Fil e
o p o ide a eliable a ge es ima ion a high a e.
The Sho Execu o , as i was explained in Sec ion 3, consis s
o h ee submodules: he T ajec o y Planne , he T ajec o y
Followe and he Gimbal Con olle . The T ajec o y Planne
compu es op imal ajec o ies o he UAV sol ing he p oblem
in (12) in a eceding ashion, ying o each he desi ed s a e
indica ed by he Schedule . The T ajec o y Followe calcula es
3D eloci y commands a highe a e so ha he UAV ollows
he op imal e e ence ajec o y, which is upda ed any ime he
Planne gene a es a new solu ion. The Gimbal Con olle gen-
e a es commands o he gimbal mo o s in he o m o angula
a es in o de o keep he came a poin ing owa ds he a ge .
The UAV Abs ac ion Laye (UAL) is a so wa e componen
de eloped by ou lab [35] o in e ace wi h he posi ion and e-
loci y con olle s o he UAV au opilo . I p o ides a common
in e ace abs ac ing he use om he p o ocol o each speci ic
ha dwa e. Finally, ecall ha each UAV has a communica ion
link wi h o he eamma es in o de o sha e hei cu en com-
pu ed ajec o ies, which a e used o mul i-UAV coo dina ion
by he T ajec o y Planne .
4.1. Cinema og aphy sho s
In ou p e ious wo k [34], ollowing ecommenda ions om
cinema og aphy expe s, we selec ed a se ies o canonical sho
ypes o ou au onomous mul i-UAV sys em. Each sho has a
ype, a ime du a ion and a se o geome ic pa ame e s ha a e
used by he sys em o compu e he desi ed came a posi ion wi h
espec o he a ge . The ep esen a i e sho s used in his wo k
o e alua ion a e he ollowing:
•Chase/lead: The UAV chases a a ge om behind o leads
i in he on a a ce ain dis ance and wi h a cons an al i-
ude.
•La e al: The UAV lies beside a a ge wi h cons an dis-
ance and al i ude as he came a acks i .
•Flyby: The UAV lies o e aking a a ge wi h a cons an
al i ude as he came a acks i . The ini ial dis ance be-
hind he a ge and inal dis ance in on o i a e also sho
pa ame e s.
•O bi : The UAV lies wi h a cons an al i ude o bi ing
a ound he a ge om a ce ain dis ance, as he came a
acks i .
E en hough ou comple e sys em [34] implemen s addi-
ional sho s, such as s a ic, ele a o , e c., hey ollow simila
beha io s o a e no ele an o ajec o y planning e alua ion.
Pa icula ly, we dis inguish be ween wo g oups o sho s o
assessing he pe o mance o he ajec o y planne : (i) sho s
whe e he ela i e dis ance be ween UAV and a ge is cons an
(e.g., chase, lead o la e al), deno ed as Type I sho s; and (ii)
sho s whe e his ela i e dis ance a ies h oughou he sho
(e.g., lyby o o bi ), deno ed as Type II sho s. No e ha an o -
bi sho can be buil wi h wo consecu i e lyby sho s. In Type I
sho s, he ela i e mo ion o he gimbal wi h espec o he UAV
is qui e limi ed, and he desi ed came a posi ion does no a y
wi h he sho phase, i.e., i is always a he same dis ance o he
a ge . In Type II sho s hough, he e is a signi ican ela i e
mo ion o he gimbal wi h espec o he UAV, and he desi ed
came a posi ion depends on he sho phase, e.g., i ansi ions
om behind o he on h oughou a lyby sho . These wo
kinds o pa e ns will esul in di e en beha io s o ou ajec-
o y planne , so o a p ope e alua ion, we es i wi h sho s
om bo h g oups.
9
17 (1984) 1603–1608. URL: h ps://www.sciencedi ec .
com/science/a icle/pii/S1474667017612059. doi:h ps:
//doi.o g/10.1016/S1474-6670(17)61205-9, 9 h IFAC Wo ld
Cong ess: A B idge Be ween Con ol Science and Technology, Budapes ,
Hunga y, 2-6 July 1984.
16
