TELKOM
NIKA
, Vol.13, No
.1, March 2
0
1
5
, pp. 85~9
2
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i1.994
85
Re
cei
v
ed O
c
t
ober 1
7
, 201
4; Revi
se
d Decem
b
e
r
3, 2014; Accepte
d
Jan
uary 4, 2015
Improved Leader Follower Formation Control for
Multiple Quadrotors Based AFSA
Raba
h Abb
a
s*, Qinghe
Wu
Schoo
l of Auto
mation, Bei
jin
g
Institute of
T
e
chno
log
y
, Be
iji
ng 10
00
81, Bei
jing, C
h
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: abbas
_ra
bah
@hotmai
l
.fr
A
b
st
r
a
ct
In this pap
er, formati
on tra
cking i
n
pla
n
e
w
i
th equa
l hei
ght
for all
qua
drotors is
discuss
ed. T
w
o contro
llers
ar
e nec
essary. F
i
rst, PID contro
l
l
er is us
ed to
e
n
sure th
e track
i
ng
of the d
e
sir
e
d
trajectory by the first quadroto
r
named le
a
d
e
r
. T
he
formati
o
n of the quadr
otors in
plane
is achiev
ed
by usin
g the d
i
rected lya
p
u
n
o
v
controll
er. In order to
i
m
pr
ov
e the
contro
ller
performanc
es, the artificial fis
h
sw
arm a
l
g
o
rith
m
is us
ed t
o
ensur
e the
dy
na
mic
opti
m
i
z
ation
of the
p
a
ra
meter c
ontr
o
llers. W
h
en
the
desir
ed sh
ape
formati
on is
ac
hiev
ed, PI
D co
ntroll
er is use
d
agai
n to ens
u
r
e the kee
p
i
n
g
of this formati
o
n
shap
e. F
i
na
lly,
si
mul
a
tio
n
res
u
lts d
e
monstra
t
e the
effective
ness
of the
pr
opos
ed c
ontro
l
l
ers co
mpar
ed
to
the ordi
nary co
ntroll
er and
als
o
co
mpar
ed to
the static opti
m
i
z
at
io
n
by usin
g the sa
me al
g
o
rith
m.
Ke
y
w
ords
:
AFSA (artificial fis
h
sw
arm al
gorit
hm), PID, formation, qu
adr
oto
r
1. Introduc
tion
Quad
roto
rs h
a
ve be
com
e
t
he inte
re
st of
many
researches in th
e
wo
rd [1]-[4]. Q
u
adroto
r
can also
pe
rf
orm solo mission wh
ere
it
can ac
hieve good perfo
rm
ances.
T
h
is chara
c
te
risti
c
will
become m
o
re intere
sting
whe
n
it op
erate in
a coordi
nated fa
shio
n such a
s
form
ation
and
trajec
tory track
i
ng.
In last de
cad
e
, tracking fo
rmation
cont
rol fo
r mult
ipl
e
uav
s h
a
s b
e
com
e
t
he in
t
e
rest
of
many researche
s
i
n
the
word. Ba
sed
on
se
pa
rate
d saturations and
a
multi-agent
co
nse
n
su
s
algorith
m
is
d
e
velope
d to
ensure
the tracking fo
rm
at
ion control
of
mini qu
adrotor [5]. In [6], 3D
path-follo
win
g
of m
u
ltipl
e
qu
adrotors ba
sed
lyap
unov
a
pproa
ch wa
s co
n
s
ide
r
ed.
Inte
gral
backsteppi
ng
co
ntrolle
r i
s
use
d
to m
a
int
a
in a
de
sire
d
formation
tra
c
king
control
for m
u
ltiple u
a
v
s
is presented
in [7]. In [8]
the autho
rs i
n
vestigat
e tracking
cont
ro
ls for a
n
arbi
trary num
ber of
coo
perating
quad
roto
r un
manne
d ae
ri
al vehicle
s
wi
th a suspen
d
ed load. In [9
] Two co
ntroll
ers
based o
n
PID and
sliding
mode
we
re u
s
ed to
en
sure
the trackin
g
formatio
n for
quad
roto
rs
u
a
vs.
In [10], the synch
r
oni
ze
d p
o
sition trackin
g
cont
rolle
r
is inco
rpo
r
ated
in formation f
light cont
rol for
multiple uav
s. In [11] base
d
on line
a
r P
D
and
slid
i
n
g
mode
control
l
er, flight form
ation co
ntrol f
o
r
leade
r follower qua
drotor i
s
pre
s
e
n
ted,
It is tested in real appli
c
atio
n.
Motivated by the different
advantag
es
of
the qua
dro
t
or, the prese
n
t pape
r stu
d
i
es the
probl
em of leader follo
we
r formation con
t
rol for multiple quad
rotors.
The pre
s
ent
work is mai
n
l
y
based o
n
[11
], the control
strategy i
s
di
vided on
t
w
o
part
s
such a
s
the trackin
g
and fo
rmati
o
n
tracking
cont
rol. In th
e first pa
rt, PID
controlle
r
i
s
use
d
to
en
su
re th
e tra
c
kin
g
of the
de
si
red
trajecto
ry by t
he first qu
ad
rotor n
a
me
d l
eade
r. Thi
s
controlle
r i
s
al
so
used to
en
sure the
keep
ing
formation by the followe
rs.
The second
part
is devote
d
for the formation trackin
g
in
plane
with equ
al hei
ght (
) for all quadrotors.
In order to
achieve a
go
od
perfo
rman
ce
of ti
me
conve
r
gen
ce
of th
e
co
ntrolle
r
propo
sed,
Artificial Fish
swarm Al
go
rithm is
used
in th
is p
ape
r. AFSA wa
s prop
osed in
2002 [1
2], it is
inspi
r
ed by th
e natural
so
ci
al behavio
r of fish scho
o
li
ng and swa
r
m intelligen
ce. This algo
ri
th
m
can
achieve f
a
ster co
nver
g
ence spee
d a
nd re
qui
re fe
w pa
ram
e
te
rs to be adj
uste
d. In literature,
many wo
rks about optimi
z
ation we
re prese
n
ted [13]-[15]; howeve
r
the tune of param
eters is
static. Differe
nt to the existing works in liter
ature, the present p
aper
use AFSA to tune the
controlle
r parameters dyna
mically.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 85 – 92
86
2. Quadro
tor
D
y
namic Model
The motion of
quadrotor i
s
controlled by
varyi
ng the ro
tation spe
ed
of the four rot
o
rs to
cha
nge the th
rust an
d the torqu
e
produ
ced by each o
ne (Fig
ure 1
)
.
Figure 1. Qua
d
roto
r Co
nfig
uration
In this pa
pe
r, we con
s
ide
r
the mo
del
dynamic
ba
sed Newto
n
-E
uler a
p
p
r
oa
ch. The
dynamic m
o
d
e
l is pre
s
e
n
te
d as [16],[17]:
(1)
,
,
Corre
s
p
ond to the relative position of the mass cent
re of the quadroto
r
with re
spe
c
t to
an inertial
co
ordin
a
te fram
e,
is the gra
v
itational acceleratio
n
.
is the length fro
m
the mass
centre to the rotor,
,
,
denot
es the thre
e Euler angl
es
that
represe
n
t
the attitude
of the
quad
roto
r, namely roll-pit
c
h-ya
w of the quadrotor.
is the thrust force vect
or in the body
sy
st
em.
,
and
corre
sp
ond to the
control input
s of roll, pitch and yaw moments,
r
e
spec
tively.
3. Contr
o
ller Design
In this
se
ctio
n, two
co
ntrol
l
ers a
r
e
desi
g
ned
to
en
su
re the trackin
g
and
the fo
rm
ation for
multiple quadrotors.
3.1. Tracking
controller
A simple PID is de
sign
ed
to ensure th
e tracki
n
g
of
the de
sire
d
trajecto
ry by
the first
quad
roto
r na
med lea
d
e
r
. It is also u
s
e
d
to en
su
re t
he keepi
ng o
f
formation in
x-y plane. T
h
e
controlle
r ca
n
be expre
s
se
d as:
(2)
With
and
are the error an
d the derivati
on of error in
i-
dire
ction. T
he error i
s
de
fined as:
,
,
,
,
,
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Improv
ed Leader Follower
Formation Control for Multiple
Quadrotors
Bas
e
d .... (
R
abah Abbas)
87
3.2.
Formati
on Con
t
rolle
r Design
The formatio
n control by kee
p
ing a fixed dista
n
ce
and a fixed deviation
∆
betwee
n
the leade
r an
d the
i-
th follower quadrotors
(Figure 2).
No
w, we
co
n
s
ide
r
quad
ro
tors. In o
u
r
st
udy we
assu
med that the
quad
roto
rs
h
a
s the
same tran
slat
ional dynami
c
model in
pla
ne as give
n b
y
the followin
g
system [11]
:
Figure 2. Position and ori
e
ntation of
the leade
r and fol
l
owe
r
qua
drot
ors in
plane [11]
cos
sin
sin
cos
(4)
Whe
r
e:
and
are th
e velo
city com
pon
e
n
t in the
an
d
directio
ns.
is the
ang
ular
velocity for the yaw angl
e
and
,
for the leader a
nd the
followe
r qua
d
r
otors.
3.3. Distan
ce
and angle c
ontroller
Let
,
be the
x and y
coo
r
dinate
s
of the
vector
drawn
from the
ma
ss ce
nter
of the
leade
r to the
one of the foll
owe
r
, in the l
eade
r’s
body fixed
frame.
T
hese
two coo
r
dinate
s
can be
given by:
cos
sin
s
i
n
cos
(5)
We con
s
ide
r
the orie
ntation
and the form
ation errors d
e
fined a
s
:
(6)
After s
o
me
s
i
mplific
ations
, we obtain [11]:
cos
sin
sin
cos
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 85 – 92
88
In matrix form, (05) can be
written as
:
(8)
With
,
,
co
s
s
i
n
0
sin
c
o
s
0
00
1
and
We choo
se th
e lyapunov candid
a
te function as:
(9)
Differentiating
with res
p
ect to time
and con
s
id
erin
g Equation (09
)
we have:
X
X
(10)
To sati
sfy the Lyapunov st
ability conditi
on, it is obvious to ch
oo
se
as
follows
:
(11)
Whe
r
e
is a
diago
nal po
si
tive matrix.
,
,
. Then
< 0 i
s
negative
definite.
3.4. Optimization
In orde
r to i
m
prove th
e
controlle
r pro
posed in
(11
)
, AFSA is
applie
d to tu
ne the
c
ontroller
parameters
(
,
,
) fo
r better time
conve
r
ge
nce
of the forma
t
ion co
ntrol e
rro
rs.
For this we defined
(fitn
e
ss function
) as conve
r
ge
nce cr
iteri
on to evaluate the co
st of th
e
prop
osed al
g
o
rithm. In thi
s
context the fitness fu
n
c
tion of the
artificial fishe
s
is
define
d
as
follows:
∆
(12)
with:
And
∆
are the di
stan
ce an
d the orie
ntatio
n error
betwe
en th
e
lead
er and
followe
r. Th
e
be
st fit
ness is th
e
small
e
st fitne
s
s value
amon
g
the
artificial fish
e
s
whi
c
h
corre
s
po
nd to the best value
s
o
f
,
.
3.4.1. Artifici
al Fish s
w
a
r
m Algorithm
The a
r
tificial
fish individ
ual state
ca
n be exp
r
e
s
sed
as
n
di
mensi
on ve
ctor.
,
…
. Each artificial fish represents a solutio
n
to the optimization p
r
ob
lem. In our case
this solutio
n
given by AF represents a set
of controlle
r para
m
eters whi
c
h can ma
ke
the
function mini
mal. This alg
o
rithm can be
presented a
s
follow:
The be
hav
i
o
r
of s
ear
chin
g food
(pr
e
y
):
We as
sum
e
,
the a
c
tual
state an
d the
next state
of AF, respe
c
tively. This new state is gi
ven by this equation:
.
,
with
is
the visual
di
stan
ce fo
r th
e AF. The
moving of A
F
from
t
o
will
be taken pl
ace if the
corre
s
p
ondin
g
con
c
entration food (
) at
state
is more important than the food con
c
e
n
tratio
n
(
) at state
. This step
can b
e
expre
s
sed
by:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Improv
ed Leader Follower
Formation Control for Multiple
Quadrotors
Bas
e
d .... (
R
abah Abbas)
89
.
.
(13
)
The beh
a
v
i
o
r
of s
w
a
r
m:
We
ass
u
me
as the
nu
mber
of the
neigh
bors
within the visua
l
distan
ce of th
e AF
.
The swarming of AF from
t
o
will b
e
taken pl
ace
if the corre
spondi
ng
con
c
e
n
tration
food (
) at state c is more
important
than the food
con
c
e
n
tration
(
) at state
and the swa
r
m is not crowd (
). Otherwi
se AF choose
s
to search food behavio
r.
This step ca
n
be sum
m
ari
z
ed by:
|
|
.
.
(14)
The beh
a
v
i
o
r
of follo
w
:
In this beh
avior, The AF
swarm from hi
s a
c
tual state
to the large
s
t
food con
c
e
n
tration if the
conce
n
tration of
food (
y
>
y
) is
more imp
o
rta
n
t and the swarm is not
cro
w
d. Oth
e
rwise AF cho
o
s
e
s
to sea
r
ch
f
ood behavio
r. This ste
p
can be summa
rize
d by:
|
|
.
.
(15)
Finally, the best fitness an
d the best fish co
rre
s
p
ond
to this best fu
nction a
r
e sel
e
cted.
3.4.2.
Static Optim
i
za
tion
In this techni
que, for N ite
r
ation
s
of alg
o
ri
thm on
e b
e
st fitness function i
s
ch
o
s
en. Thi
s
function corresponds to the best
controll
er
parameters. These pa
rameters will be
inj
e
cted
in
the
contr
o
lle
r (11
)
.
3.4.3.
D
y
namic Optim
i
zati
on
In this te
chni
que a
nd diffe
rent to the
st
atic techniq
u
e
, for ea
ch it
eration
of alg
o
rithm a
best fun
c
tion
is sele
cted a
nd a best co
ntrolle
r par
a
m
eters co
rre
s
po
nd to th
is function are also
sele
cted a
nd online inje
cte
d
in the controller (
11). Th
e same p
r
o
c
e
dure
will be repeate
d
until the
n-th
iteratio
n.
4. Results a
nd Analy
s
is
The propo
se
d formation
control ha
s b
e
en sim
u
lated
for the ca
se
of three qua
droto
r
s
(one
lead
er
a
nd two
followers). Th
e
co
ntrolle
rs’
obje
c
tives a
r
e: Fi
rst: The tracki
ng of traj
ecto
ry
by the quadrotor leade
r d
e
scrib
ed by:
,
s
i
n
,
5
0
. Second: The
formation a
n
d
the ke
epin
g
of formatio
n by the
follo
wers d
e
scri
b
ed by the de
sire
d di
stan
ce and
deviation an
g
l
e to the lead
er are given b
y
:
Firs
t follower
2
meters and
∆
0
and for the se
con
d
followe
r
4
meters
and
∆
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 85 – 92
90
Figure
3.
T
r
aje
c
tories of lea
d
e
r
and foll
o
w
er
qua
drotors i
n
directi
on bef
ore optimiz
ation
Figure
4.
T
r
aje
c
tories of lea
d
e
r
and foll
o
w
er
qua
drotors i
n
plane before optimization
F
i
gure 5. Distance err
o
r bet
w
e
e
n
lea
der a
nd
follo
w
e
r qu
adr
otors before
op
timizatio
n
F
i
gure 6. Ya
w
ang
le error b
e
t
w
e
e
n
lea
der a
nd
follo
w
e
r
qua
dr
otors before
op
timizatio
n
F
i
gure 7. T
r
ajectories of lea
d
e
r
and foll
o
w
er
qua
drotors in
pla
ne b
y
static
optimiz
ation
F
i
gure 1
0
.
T
r
ajectories of le
ad
er and fol
l
o
w
e
r
qua
drotors in
pla
ne b
y
d
y
n
a
mic optimizati
o
n
0
5
10
15
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
t
(
se
c)
z(
m
)
Lead
er
Fo
llo
w
e
r
1
Fo
llo
w
e
r
2
-5
0
5
10
15
20
-2
-1
0
1
2
3
4
5
x(
m
)
y(
m
)
L
eader
Fo
llo
w
e
r
1
Fo
llo
w
e
r
2
0
5
10
15
-3
-2.
5
-2
-1.
5
-1
-0.
5
0
0.
5
1
1.
5
2
t
(
se
c)
ED
(
m
)
Di
s
t
an
c
e
E
rror Le
ader-F
ol
l
o
wer 1
Di
s
t
an
c
e
E
rror Le
ader-F
ol
l
o
wer 2
0
5
10
15
-0.
8
-0.
6
-0.
4
-0.
2
0
0.
2
0.
4
0.
6
t
(
se
c)
E
A
(ra
d
)
A
n
g
l
e E
rror Le
ader-F
ol
l
o
wer 1
A
n
g
l
e E
rror Le
ader-F
ol
l
o
wer 2
-5
0
5
10
15
20
-2
-1
0
1
2
3
4
x(
m
)
y(
m
)
L
eader
F
o
l
l
ow
er
1
F
o
l
l
ow
er
2
-4
-2
0
2
4
6
8
10
12
14
16
-2
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
x(
m
)
y(
m
)
L
eader
Fo
llo
w
e
r
1
Fo
llo
w
e
r
2
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Improv
ed Leader Follower
Formation Control for Multiple
Quadrotors
Bas
e
d .... (
R
abah Abbas)
91
F
i
gure 8. Dista
nce error b
e
t
w
een l
e
a
der an
d
follo
w
e
r qu
adr
otors b
y
us
in
g static optimizat
ion
F
i
gure 1
1
. Distance err
o
r bet
w
e
e
n
lea
der a
nd
follo
w
e
r qu
adr
otors b
y
usin
g d
y
nam
ic optimi
z
ation
F
i
gure 9. Ang
l
e
error bet
w
e
en
lea
der an
d foll
o
w
er
qua
drotors b
y
usin
g
static opt
imizatio
n
F
i
gure 1
2
. Angl
e error bet
w
e
e
n
lea
der a
nd fo
llo
w
e
r
qua
drotors b
y
usin
g d
y
n
a
mic optimiz
ation
Figure 3 depi
cts the traje
c
torie
s
of the p
o
sition
for
the leader an
d also the follo
wer
quad
roto
rs. The traje
c
tori
es of the leader and follo
wer qu
ad
roto
rs in
plane (De
s
i
r
ed
formation
)
a
r
e de
picte
d
in
Figu
re
4, while
the
dista
n
ce
an
d an
gl
e erro
rs bet
ween l
eade
r
a
nd
followe
r qua
droto
r
s by u
s
ing the con
t
roller
(11) a
r
e depi
cted
in Figure 5
and Figu
re
6,
r
e
spec
tively.
By using stat
ic optimi
z
atio
n as sho
w
n i
n
Fi
gures 7,
8 and 9, the
results a
r
e i
m
prove
d
comp
aratively to the Figures 4, 5 and 6
.
From
Figure
s
10, 11 and
12, It is shown the results
are
con
s
id
ere
d
p
e
rfect i
n
term
of erro
r con
v
ergen
ce
(b
o
t
h distan
ce
a
nd e
rro
r b
e
tween le
ade
r a
nd
followe
r qua
droto
r
s), this can be expl
ain by the
fact that in dynamic o
p
timi
zation
ca
se, the
para
m
eters
are
sel
e
cte
d
dynami
c
ally
whi
c
h
en
su
re th
at the
d
i
stan
ce
and
angle
erro
rs are
minimal for
e
a
ch ite
r
ration
of the pro
p
o
s
ed alg
o
ri
thm. Comp
ared
to the
static opti
m
ization ca
se
,
only one fitness functio
n
is sel
e
cte
d
, this fun
c
tion i
s
not ne
ce
ssary
co
rre
sp
o
nd to the go
od
para
m
eters for the
iteration of the algori
t
hm.
5. Conclusio
n
This
pap
er
a
ddre
s
sed
the
pro
b
lem
of leade
r follo
wer fo
rmation
tracking
cont
rol for
multiple
quad
rotors. PID
controlle
r i
s
used to
tra
c
k
th
e de
si
red
traj
ectory
by the
leade
r, by
usi
n
g
0
5
10
15
-3
-2
.
5
-2
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
t(
s
e
c
)
ED
(
m
)
D
i
s
t
an
c
e
E
r
r
o
r
Leader
-
F
ol
l
o
w
e
r
1
D
i
s
t
an
c
e
E
r
r
o
r
Leader
-
F
ol
l
o
w
e
r
2
0
5
10
15
-3
-2
.
5
-2
-1
.
5
-1
-0
.
5
0
0.
5
t(
s
e
c
)
ED
(
m
)
D
i
s
t
anc
e E
r
r
o
r
Lea
der
-
F
ol
l
o
w
e
r
1
D
i
s
t
anc
e E
r
r
o
r
Lea
der
-
F
ol
l
o
w
e
r
2
0
5
10
15
-0
.
8
-0
.
7
-0
.
6
-0
.
5
-0
.
4
-0
.
3
-0
.
2
-0
.
1
0
0.
1
0.
2
t(
s
e
c
)
E
A
(
r
ad)
A
ngl
e E
r
r
o
r
Lead
er
-
F
ol
l
o
w
e
r
1
A
ngl
e E
r
r
o
r
Lead
er
-
F
ol
l
o
w
e
r
2
0
5
10
15
-1
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
t(
s
e
c
)
E
A
(ra
d
)
A
n
g
l
e E
r
r
o
r
Leader
-
F
ol
l
o
w
e
r
1
A
n
g
l
e E
r
r
o
r
Leader
-
F
ol
l
o
w
e
r
2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 85 – 92
92
a direct lyapu
nov method a new controller is pr
op
ose
d
to ensure the formation tracking in
plane with e
q
ual height (
) for all quad
rot
o
rs, an
d then
PID is used
again to en
su
re the kee
p
ing
of formation b
y
the followers.
Simulation
res
u
lts
demonstrate
that
the prop
osed AF
SA algorithm
is an effectiv
e tuning
strategy
of L
y
apunov-ba
s
ed controller’
s pa
ram
e
ter
controls. AFS
A
algorith
m
l
ead
s to
satisf
ying
and effici
ent formation tra
cki
ng pe
rfo
r
mances i
n
te
rms
of the speed of
con
v
ergen
ce
of the
tracking e
r
rors and time a
c
hievin
g of the desi
r
ed formation by tuning the co
ntrolle
r parame
t
ers
dynamically.
Referen
ces
[1]
A T
a
y
e
bi, S Mc
Gilvray
.
Attitude st
abiliz
ation
of a vtol
quadr
otor
aircraft.
IEEE Transactions on Control
Systems T
e
ch
nol
ogy
. 20
06; 14(3): 56
2-5
7
1
.
[2]
T
Madani, A
Benal
leg
ue.
Control of a quadrot
or
m
i
ni-helicopter via full st
ate
backstepping
techni
qu
e
. 45th IEEE Confer
ence o
n
Dec
i
si
on an
d Co
ntrol
.
San Dieg
o
, CA. 2006; 15
15-
152
0.
[3]
L D
e
rafa, A B
e
nall
e
g
ue,
L F
r
i
d
man. S
u
p
e
r tw
i
s
ting
control algorithm
fo
r the attitude trac
k
i
ng
of a
fou
r
rotors UAV.
Journa
l of the F
r
anklin Institute
.
201
2; 349(
2): 685-6
99.
[4]
K Hic
ham. R
o
bust co
ntrol
al
gorithm
cons
id
erin
g th
e
actu
ator fau
l
ts for
attitude tr
ackin
g
of
an
U
A
V
Quadrotor Airc
raft.
Internation
a
l Jour
nal of C
ontrol a
nd Auto
mati
on
. 20
12;
5(4): 55-6
6
.
[5]
Jose AG, Pedr
o CSS, Rog
e
li
o L. Mini rot
o
rc
raft flight forma
tion co
ntrol usi
ng b
oun
de
d in
puts.
J Intell
Robot Syst
. 2012; 65(1-
4): 17
5–1
86.
[6]
Vena
nzio
C, Isaac K, Enric
X, Vla
d
imir
D, Naira H, A P
edro A, Anto
ni
o MP.
A Lyap
unov-
base
d
appr
oach f
o
r T
i
me-coor
di
nate
d
3D
path-
fol
l
o
w
ing of
multi
p
l
e
Quadr
otors
. 51st IEEE Conference
on
Decisi
on a
nd C
ontrol. USA. 20
12: 177
6-1
781.
[7]
Lon D, Nad
a
v B, Shai A.
For
m
a
tion flight using
m
u
ltiple
integral backste
pping controllers.
IEEE. 5th
Internatio
na
l C
onfere
n
ce o
n
C
y
ber
netics an
d Inte
lli
ge
nt S
y
stems (CIS).
C
h
in
a. 201
1: 31
7-32
2.
[8]
T
aeyou
ng
L, K
oush
il S, Vi
ja
y K.
Geo
m
etric
control
of co
o
perati
ng
multip
le q
u
a
d
rotor
U
AVs w
i
th a
suspe
n
d
ed pay
loa
d
. 52n
d IEEE Confere
n
ce
on Dec
i
sio
n
an
d Contro
l. Ital
y
.
2013: 5
510-
55
15.
[9]
Mohamm
ad F
Bin Abas, D
w
i
P, Syaril A, Md. Ali,
D KeI
w
a
k
ura, Yuze S, Kenzo N,
Da
ig
o F
.
Circular
lea
der-fol
lo
w
e
r
formation co
n
t
rol of qua
d-ro
tor aeria
l veh
i
cles.
Auton
o
m
ous Co
ntrol S
ystems a
nd
Vehic
l
es Intell
i
gent Syste
m
s, Contro
l
and A
u
tomati
on: Scie
nce an
d Eng
i
n
eeri
n
g
. 20
13; 6
5
: 109-1
32.
[10]
Norman HML,
Hugh HT
L.
F
o
rmati
on U
AV flight co
n
t
rol us
in
g virt
ual structur
e and
motio
n
synchroni
z
a
tion
. American C
ontrol C
onfere
n
ce. USA. 200
8: 1782-
17
87.
[11]
DA Merca
do,
R Castro, R
Lo
zano.
Qua
d
rot
o
rs flig
ht forma
tion co
ntrol us
i
ng l
ead
er-foll
o
w
e
r appro
a
ch.
Europ
e
a
n
cont
rol confer
ence.
Z
u
rich. 2013: 385
8-38
63.
[12]
Li
XL, Sh
ao Z
,
Qian J. An o
p
t
imizing m
e
tho
d
bas
ed o
n
a
u
t
onomo
u
s a
n
i
m
als: fish s
w
ar
m algor
ithm.
Systems En
gin
eeri
ng T
h
e
o
ry and Practic
e
. 2
002; 22(
11): 32
-38.
[13]
F
Yacef, O Bo
uha
li, M H
a
me
rlain, A
Rez
o
u
g
.
PSO optim
i
z
ation
of Integr
al
backstepping controller
for
qua
drotor attitude stab
ili
z
a
t
i
o
n
. Proceed
in
g
s
of the 3rd Internat
io
na
l
Co
n
f
e
r
en
ce
on
Sy
ste
m
s and
Contro
l, Algeri
a
. 2013: 4
62-4
66.
[14]
Karim B, Z
hu Q.
Genetic fuzz
y
lo
gic co
ntrol
techniq
ue for
a Mobi
le Ro
bo
t tracking a movin
g
target.
IJCSI Internationa
l Journ
a
l
of
Computer Sci
ence Issues
. 2
013; 10(
1): 607
-613.
[15]
W
ael MK, Hassen T
D
, Hassan ME.
Bacterial fora
gi
ng
orie
nted by
p
a
rticle sw
arm
opti
m
i
z
at
ion
strategy for PID tunin
g
. 8th IEEE internati
o
nal co
nferenc
e
on Co
mput
ati
ona
l intel
lig
enc
e in robotic
s
and a
u
tomati
o
n
. USA. 2009:
445-
450.
[16]
Dae
w
o
n
L, H
Jin K, Sh
ank
ar S. F
eed
bac
k
lin
eariz
atio
n
vs ad
aptive
slidi
ng m
o
d
e
control for
a
qua
drotor H
e
lic
opter.
Internati
ona
l Journ
a
l of
Control, Auto
mati
on a
nd Sy
stems
. 20
09; 7
(
3): 419-4
28.
[17]
Ming
u K, Yo
u
dan
K, Jai
ung
J.
Adaptiv
e slidi
ng mod
e
control usi
ng slack
var
i
ab
le
s
for
affin
e
underactuated system
s
. 51st IEEE Confere
n
c
e on Dec
i
sio
n
and
Co
ntrol. U
SA. 2012: 60
9
0
-60
95.
Evaluation Warning : The document was created with Spire.PDF for Python.