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I
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Vo
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3
,
Sep
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b
er
20
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p
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5
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ith
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tim
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Pro
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a
n
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r
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v
eh
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cle
(
UAV)
s
y
s
tem
s
[
1
]
.
Ho
wev
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,
th
e
h
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l
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in
ea
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d
y
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tain
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if
ican
tly
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[
2
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As
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I
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to
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Vo
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.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
2
9
-
5
4
3
530
co
n
d
itio
n
s
.
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p
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in
[
3
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ta
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ties
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4
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e
p
a
r
am
e
ter
m
ain
tain
tr
ac
k
i
n
g
ac
cu
r
a
cy
wh
ile
lo
wer
in
g
co
m
p
u
tatio
n
al
b
u
r
d
e
n
.
T
o
en
s
u
r
e
f
ast
co
n
v
er
g
e
n
ce
an
d
r
o
b
u
s
tn
ess
,
a
f
in
ite
-
tim
e
ad
ap
tiv
e
in
teg
r
al
b
ac
k
s
tep
p
in
g
f
ast
ter
m
in
al
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
is
d
ev
el
o
p
ed
in
[
5
]
.
B
ar
r
ier
L
y
ap
u
n
o
v
–
b
ased
b
ac
k
s
tep
p
in
g
an
d
co
n
s
tr
ain
ed
b
a
ck
s
tep
p
in
g
co
n
tr
o
l
s
tr
ateg
ies
ar
e
also
i
n
v
esti
g
ated
in
[
6
]
t
o
g
u
ar
an
t
ee
s
tab
le
tr
ajec
to
r
y
tr
ac
k
in
g
wh
ile
r
esp
ec
tin
g
p
o
s
itio
n
an
d
attitu
d
e
co
n
s
tr
ai
n
ts
.
A
s
elf
-
tu
n
in
g
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
f
o
r
m
u
ltiro
to
r
d
r
o
n
es
is
p
r
o
p
o
s
ed
,
u
s
in
g
a
n
eu
r
al
n
etwo
r
k
tr
ain
ed
v
ia
m
etah
eu
r
is
tic
-
g
en
er
ate
d
d
ata
to
o
p
tim
ize
en
er
g
y
,
r
is
e
tim
e,
an
d
o
v
e
r
s
h
o
o
t,
o
u
tp
e
r
f
o
r
m
in
g
g
en
et
ic
alg
o
r
ith
m
(
GA)
-
t
u
n
ed
p
r
o
p
o
r
tio
n
al
in
teg
r
al
d
er
iv
ativ
e
(P
ID)
[
7
]
.
I
n
p
ar
allel,
class
ical
an
d
a
d
ap
t
iv
e
PID
-
b
ased
co
n
tr
o
ller
s
r
em
ain
attr
ac
tiv
e
d
u
e
to
th
eir
s
im
p
licity
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
.
A
r
o
b
u
s
t
ad
ap
tiv
e
PID
-
lik
e
co
n
tr
o
ll
er
with
o
n
lin
e
g
ain
ad
ju
s
tm
en
t
,
with
o
u
t
r
eq
u
ir
in
g
an
ac
cu
r
ate
m
o
d
el,
is
p
r
o
p
o
s
ed
in
[
8
]
.
T
r
ajec
to
r
y
tr
ac
k
in
g
c
o
n
tr
o
l
ap
p
r
o
ac
h
c
o
m
b
in
in
g
s
lid
in
g
m
o
d
e
co
n
tr
o
l
with
an
im
p
r
o
v
ed
ex
te
n
d
ed
s
t
ate
o
b
s
er
v
er
(
SMC
-
I
E
SO)
is
p
r
o
p
o
s
ed
in
[
9
]
f
o
r
q
u
a
d
r
o
t
o
r
UAVs.
T
h
e
m
eth
o
d
em
p
lo
y
s
a
h
ier
ar
ch
ical
p
o
s
iti
o
n
–
attitu
d
e
co
n
tr
o
l
s
tr
u
ctu
r
e
an
d
a
d
is
tu
r
b
an
ce
o
b
s
er
v
er
t
o
en
h
an
ce
tr
ac
k
i
n
g
ac
cu
r
ac
y
an
d
d
is
tu
r
b
an
ce
r
ej
ec
tio
n
wh
ile
r
ed
u
cin
g
ch
atter
in
g
.
I
n
[
1
0
]
,
a
g
ain
-
s
ch
ed
u
le
d
f
au
lt
-
to
ler
an
t
PID
co
n
tr
o
l
s
tr
ateg
y
was
p
r
o
p
o
s
e
d
f
o
r
q
u
ad
r
o
to
r
UAVs
to
a
d
d
r
ess
ac
tu
ato
r
f
a
u
lts
.
T
h
e
PI
D
p
ar
am
eter
s
wer
e
o
p
tim
ally
tu
n
ed
u
s
in
g
a
co
m
b
in
atio
n
o
f
g
en
etic
al
g
o
r
it
h
m
(
GA)
an
d
ar
tific
ial
n
e
u
r
al
n
etwo
r
k
s
(
ANN)
,
en
ab
lin
g
im
p
r
o
v
e
d
f
lig
h
t
s
tab
i
lity
an
d
tr
ajec
to
r
y
t
r
ac
k
in
g
u
n
d
er
r
o
to
r
f
ailu
r
e
s
ce
n
a
r
io
s
.
Fu
r
th
er
m
o
r
e
,
a
r
o
b
u
s
t
T
y
p
e
-
2
f
u
zz
y
PID
co
n
tr
o
ller
o
p
tim
ized
v
ia
g
en
etic
alg
o
r
ith
m
s
is
ex
p
er
im
en
tally
v
alid
ated
in
o
u
td
o
o
r
win
d
y
co
n
d
itio
n
s
an
d
s
h
o
wn
to
o
u
t
p
er
f
o
r
m
co
n
v
en
tio
n
al
PID
a
n
d
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
s
in
[
1
1
]
.
T
o
e
n
h
an
ce
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
c
es
an
d
m
o
d
elin
g
u
n
ce
r
tain
ties
,
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
–
b
ased
tech
n
iq
u
es
h
av
e
b
ee
n
wid
ely
ex
p
lo
r
ed
.
A
b
ac
k
s
tep
p
in
g
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
co
m
b
in
ed
with
a
s
u
p
e
r
-
twis
tin
g
o
b
s
er
v
er
is
p
r
o
p
o
s
ed
in
[
1
2
]
to
ac
h
iev
e
ac
cu
r
ate
t
r
ac
k
in
g
u
n
d
er
p
ar
t
ial
-
s
tate
m
ea
s
u
r
em
en
ts
.
I
n
[
1
3
]
,
a
b
ac
k
s
tep
p
i
n
g
–
s
lid
in
g
m
o
d
e
c
o
n
tr
o
ller
en
h
a
n
ce
d
with
a
s
u
p
er
-
twis
tin
g
o
b
s
er
v
er
is
p
r
o
p
o
s
ed
f
o
r
q
u
a
d
r
o
t
o
r
u
n
m
an
n
e
d
ae
r
ial
v
eh
icle
(
QUAV
s
)
,
en
ab
lin
g
r
ea
l
-
tim
e
d
is
tu
r
b
an
ce
esti
m
atio
n
,
im
p
r
o
v
ed
tr
ac
k
i
n
g
,
an
d
r
ed
u
ce
d
ch
atter
i
n
g
u
n
d
er
u
n
ce
r
tain
ties
.
Fix
ed
-
tim
e
s
lid
in
g
m
o
d
e
co
n
tr
o
l
is
in
v
esti
g
ated
in
[
1
4
]
,
en
s
u
r
in
g
f
ast
co
n
v
er
g
e
n
ce
in
d
ep
en
d
en
t
o
f
i
n
itial
co
n
d
itio
n
s
.
Fra
ctio
n
al
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
l
is
d
esig
n
ed
i
n
[
1
5
]
to
s
u
p
p
r
ess
p
ay
lo
ad
o
s
cillatio
n
s
in
s
lu
n
g
-
lo
ad
q
u
a
d
r
o
to
r
s
y
s
tem
s
.
Ad
ap
tiv
e
n
o
n
-
s
in
g
u
lar
ter
m
i
n
al
s
lid
in
g
m
o
d
e
co
n
tr
o
l
with
d
is
tu
r
b
an
ce
o
b
s
er
v
atio
n
i
s
p
r
o
p
o
s
ed
in
[
1
6
]
to
im
p
r
o
v
e
r
o
b
u
s
tn
ess
an
d
d
is
tu
r
b
a
n
ce
r
ej
ec
tio
n
.
Hy
b
r
id
a
n
d
ad
v
an
ce
d
SMC
s
ch
em
es
ar
e
f
u
r
th
er
d
e
v
elo
p
ed
in
[
1
7
]
to
m
itig
ate
ch
atter
in
g
ef
f
ec
ts
,
wh
ile
f
o
r
m
atio
n
an
d
tr
ajec
to
r
y
tr
ac
k
in
g
u
s
in
g
n
o
n
-
s
in
g
u
lar
ter
m
in
al
s
u
p
er
-
twis
tin
g
s
lid
in
g
m
o
d
e
co
n
tr
o
l
ar
e
ad
d
r
ess
ed
in
[
1
8
]
.
E
n
h
an
ce
d
r
o
b
u
s
tn
ess
an
d
r
ed
u
ce
d
co
n
tr
o
l
e
f
f
o
r
t
ar
e
ac
h
iev
ed
u
s
in
g
f
u
zz
y
PID
–
b
ased
s
u
p
er
-
twis
tin
g
s
lid
in
g
m
o
d
e
co
n
tr
o
l
in
[
1
9
]
,
an
d
q
u
a
ter
n
io
n
-
b
ased
s
lid
in
g
m
o
d
e
co
n
tr
o
l
is
p
r
o
p
o
s
ed
in
[
2
0
]
to
elim
in
ate
E
u
ler
an
g
le
s
in
g
u
lar
ities
u
n
d
er
s
ev
er
e
win
d
d
is
tu
r
b
an
ce
s
.
Mo
r
e
r
ec
en
tly
,
m
o
d
el
p
r
ed
icti
v
e
co
n
tr
o
l
(
MPC
)
an
d
lear
n
i
n
g
-
b
ased
c
o
n
tr
o
l
ap
p
r
o
ac
h
es
h
av
e
g
ain
e
d
in
cr
ea
s
in
g
atten
tio
n
d
u
e
to
th
e
ir
ab
ilit
y
to
ex
p
licitly
h
an
d
le
co
n
s
tr
ain
ts
an
d
o
p
tim
ize
p
er
f
o
r
m
an
ce
.
No
n
lin
ea
r
MPC
with
co
n
tr
ac
tio
n
-
b
ased
co
s
t
f
u
n
ctio
n
s
is
d
ev
elo
p
e
d
in
[
2
1
]
to
ac
h
iev
e
s
m
o
o
t
h
a
n
d
s
tab
le
tr
ajec
to
r
y
tr
ac
k
in
g
.
A
n
eu
r
al
n
etwo
r
k
-
b
ased
p
ar
allel
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
PMPC
)
ap
p
r
o
ac
h
i
s
p
r
o
p
o
s
ed
[
2
2
]
f
o
r
q
u
ad
r
o
to
r
UAV
tr
ajec
to
r
y
tr
ac
k
in
g
.
T
h
e
m
eth
o
d
r
ec
o
n
s
tr
u
cts
th
e
UAV
d
y
n
am
ics
o
n
li
n
e
u
s
in
g
a
p
ar
allel
n
eu
r
al
n
etwo
r
k
m
o
d
el
an
d
ex
p
er
ien
ce
r
ep
lay
t
o
m
ain
tain
p
r
ed
ictio
n
ac
cu
r
ac
y
in
ch
an
g
in
g
en
v
ir
o
n
m
en
ts
.
I
n
[
2
3
]
,
a
n
in
ter
v
al
ty
p
e
-
2
f
u
zz
y
p
r
e
-
co
m
p
en
s
atio
n
ac
tiv
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
co
n
tr
o
l
(
I
T
2
F
P
-
ADR
C
)
m
eth
o
d
was
p
r
o
p
o
s
ed
to
im
p
r
o
v
e
th
e
tr
ajec
to
r
y
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
o
f
a
q
u
a
d
r
o
to
r
s
lu
n
g
-
lo
ad
s
y
s
tem
u
n
d
er
d
is
tu
r
b
an
ce
s
an
d
u
n
ce
r
tain
ties
.
T
h
e
ap
p
r
o
ac
h
en
h
an
ce
s
d
is
tu
r
b
an
ce
esti
m
atio
n
a
n
d
s
y
s
tem
r
o
b
u
s
tn
ess
u
s
in
g
a
m
o
d
if
ied
ex
te
n
d
ed
s
tate
o
b
s
e
r
v
er
an
d
f
u
zz
y
co
m
p
en
s
atio
n
.
E
f
f
icien
t
r
ea
l
-
tim
e
NM
PC
i
m
p
lem
en
tatio
n
s
o
n
r
eso
u
r
ce
-
lim
ited
em
b
e
d
d
ed
p
latf
o
r
m
s
ar
e
d
em
o
n
s
tr
ated
in
[
2
4
]
u
s
in
g
q
u
ate
r
n
io
n
-
b
a
s
ed
m
o
d
elin
g
an
d
C
/GM
R
E
S
o
p
tim
izatio
n
.
A
co
m
p
r
eh
e
n
s
iv
e
r
ev
iew
in
[
2
5
]
h
ig
h
lig
h
ts
MPC
as
a
p
r
o
m
is
in
g
f
r
am
ewo
r
k
f
o
r
tr
ajec
to
r
y
tr
ac
k
i
n
g
an
d
d
y
n
a
m
ic
o
b
s
tacle
av
o
id
a
n
ce
in
co
m
p
lex
UAV
en
v
ir
o
n
m
en
ts
.
I
n
[
2
6
]
,
a
s
y
s
tem
atic
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
Q
R
)
tu
n
in
g
ap
p
r
o
ac
h
f
o
r
UAV
attitu
d
e
co
n
tr
o
l
is
p
r
o
p
o
s
ed
,
u
s
in
g
m
u
lti
-
o
b
jectiv
e
g
r
ey
wo
lf
o
p
tim
izatio
n
an
d
T
OPSIS
to
s
e
lect
o
p
tim
al
Q
–
R
weig
h
ts
u
n
d
er
v
ar
io
u
s
er
r
o
r
cr
iter
ia.
T
h
e
s
tu
d
y
p
r
esen
ted
in
[
2
7
]
p
r
o
p
o
s
es
a
s
tate
-
f
ee
d
b
ac
k
co
n
tr
o
ller
with
in
teg
r
al
ac
tio
n
f
o
r
3
D
OF
q
u
ad
r
o
t
o
r
h
o
v
er
,
ac
h
iev
in
g
er
r
o
r
-
f
r
ee
,
r
o
b
u
s
t,
an
d
f
au
lt
-
to
ler
a
n
t
attitu
d
e
tr
ac
k
in
g
in
s
im
u
latio
n
s
an
d
ex
p
er
i
m
en
ts
.
A
m
o
d
el
-
f
r
ee
FP
I
D
co
n
tr
o
ller
is
p
r
o
p
o
s
ed
f
o
r
3
-
DOF
q
u
ad
r
o
to
r
attitu
d
e
s
tab
ilizatio
n
,
o
p
tim
ized
v
ia
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
an
d
v
alid
ated
ag
ain
s
t
L
QR
,
PID
,
an
d
b
ac
k
s
tep
p
in
g
with
r
o
b
u
s
t
p
er
f
o
r
m
an
ce
[
2
8
]
.
I
n
ad
d
itio
n
to
i
n
d
iv
id
u
al
q
u
a
d
r
o
t
o
r
co
n
tr
o
l,
co
o
p
er
ativ
e
c
o
n
tr
o
l
s
tr
ateg
ies
h
av
e
also
b
ee
n
ex
p
l
o
r
ed
.
A
f
r
ac
tio
n
al
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
P
r
ec
is
io
n
en
h
a
n
ce
men
t in
d
r
o
n
e
p
o
s
itio
n
c
o
n
tr
o
l b
a
s
ed
o
n
o
p
timiz
ed
P
I
D
… (
I
ma
m
B
a
r
ke
t G
h
ilo
u
b
i
)
531
o
r
d
e
r
PID
c
o
n
tr
o
ller
is
p
r
esen
ted
in
[
2
9
]
to
e
n
h
an
ce
QUAV
s
tr
ajec
to
r
y
tr
ac
k
in
g
,
r
ed
u
ce
o
v
er
s
h
o
o
t,
im
p
r
o
v
e
r
o
b
u
s
tn
ess
,
an
d
e
n
ab
le
s
ca
lab
l
e
s
war
m
o
p
er
atio
n
s
in
co
m
p
le
x
m
is
s
io
n
s
.
Desp
ite
th
e
v
ar
io
u
s
ad
v
a
n
ce
d
co
n
tr
o
l
s
tr
ateg
ies
p
r
o
p
o
s
ed
i
n
th
e
liter
atu
r
e,
P
ID
co
n
tr
o
ller
s
r
em
ain
attr
ac
tiv
e
b
ec
au
s
e
o
f
th
eir
s
i
m
p
licity
,
ea
s
e
o
f
im
p
lem
en
ta
tio
n
,
an
d
p
r
ac
tical
ef
f
ec
tiv
en
ess
.
Ho
wev
er
,
th
eir
p
er
f
o
r
m
an
ce
h
ea
v
ily
d
e
p
en
d
s
o
n
th
e
tu
n
in
g
o
f
co
n
tr
o
ller
g
ain
s
.
C
o
n
v
en
ti
o
n
al
tu
n
i
n
g
m
eth
o
d
s
ar
e
o
f
ten
in
s
u
f
f
icien
t f
o
r
n
o
n
lin
ea
r
s
y
s
tem
s
lik
e
q
u
ad
r
o
to
r
s
,
m
o
tiv
atin
g
th
e
u
s
e
o
f
i
n
tellig
en
t o
p
tim
iza
tio
n
alg
o
r
ith
m
s
.
T
h
is
p
ap
er
f
o
cu
s
es
o
n
o
p
tim
iz
in
g
PID
co
n
tr
o
ller
g
ain
s
u
s
in
g
th
e
p
ar
ticle
s
war
m
o
p
tim
izati
o
n
(
PS
O)
an
d
th
e
f
l
o
wer
p
o
llin
atio
n
alg
o
r
ith
m
(
FP
A)
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
t
h
is
s
tu
d
y
ar
e
s
u
m
m
ar
ized
as f
o
llo
ws:
−
Un
lik
e
co
n
v
en
tio
n
al
I
T
AE
-
b
a
s
ed
tu
n
in
g
,
an
en
h
an
ce
d
o
b
je
ctiv
e
f
u
n
ctio
n
is
p
r
o
p
o
s
ed
b
y
co
m
b
i
n
in
g
th
e
in
teg
r
al
o
f
tim
e
-
weig
h
ted
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
with
an
o
v
er
s
h
o
o
t
p
e
n
aliza
tio
n
ter
m
to
i
m
p
r
o
v
e
tr
an
s
ien
t
r
esp
o
n
s
e
an
d
r
ed
u
ce
o
v
er
s
h
o
o
t,
clea
r
ly
d
is
tin
g
u
is
h
in
g
t
h
is
wo
r
k
f
r
o
m
o
u
r
p
r
ev
io
u
s
s
tu
d
ies.
−
C
o
m
p
r
eh
en
s
iv
e
co
m
p
ar
ativ
e
a
n
aly
s
is
b
etwe
en
FP
A
-
b
ased
an
d
PS
O
-
b
ased
PID
co
n
tr
o
ller
s
u
s
in
g
m
u
ltip
le
s
ce
n
ar
io
s
,
in
clu
d
in
g
s
tep
r
esp
o
n
s
e,
cir
cu
lar
,
an
d
lem
n
is
ca
te
tr
ajec
to
r
ies.
−
Qu
an
titativ
e
ev
alu
atio
n
o
f
tr
a
ck
in
g
p
er
f
o
r
m
a
n
ce
u
s
in
g
d
if
f
er
en
t
er
r
o
r
m
et
r
ics
s
u
ch
as
r
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
,
m
ea
n
ab
s
o
lu
te
er
r
o
r
(
MA
E
)
,
in
teg
r
al
o
f
a
b
s
o
lu
te
er
r
o
r
(
I
AE
)
,
an
d
I
T
AE
.
−
Valid
atio
n
o
n
co
m
p
lex
r
ef
er
e
n
ce
tr
ajec
to
r
ies,
in
clu
d
in
g
lem
n
is
ca
te
p
ath
s
,
is
p
er
f
o
r
m
ed
to
a
s
s
es
s
co
n
tr
o
ller
p
er
f
o
r
m
an
ce
u
n
d
er
m
o
r
e
d
em
an
d
in
g
tr
ac
k
in
g
c
o
n
d
itio
n
s
th
a
n
co
n
v
en
tio
n
al
s
tep
o
r
cir
cu
lar
tr
ajec
to
r
ies.
−
R
o
b
u
s
tn
ess
test
ag
ain
s
t
win
d
d
is
tu
r
b
an
ce
s
is
co
n
d
u
cted
o
n
t
h
e
PID
co
n
tr
o
ller
o
p
tim
ized
u
s
in
g
th
e
s
elec
ted
m
eth
o
d
.
T
h
e
r
e
m
ain
d
er
o
f
th
is
p
ap
er
is
o
r
g
an
ize
d
as
f
o
llo
ws:
Sectio
n
2
p
r
esen
ts
th
e
q
u
a
d
r
o
to
r
m
o
d
elin
g
,
s
ec
tio
n
3
d
escr
ib
es
th
e
co
n
tr
o
l
m
eth
o
d
o
l
o
g
y
,
in
clu
d
in
g
th
e
PID
s
tr
u
ctu
r
e
an
d
o
p
tim
izatio
n
s
tr
ateg
ies,
s
ec
tio
n
4
d
is
cu
s
s
es th
e
s
im
u
latio
n
r
esu
lts
an
d
s
ec
tio
n
5
p
r
ese
n
ts
th
e
co
n
clu
s
io
n
.
2.
Q
UADR
O
T
O
R
M
O
D
E
L
I
N
G
T
h
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
q
u
a
d
r
o
to
r
ca
p
t
u
r
es
th
e
tr
an
s
latio
n
al
m
o
tio
n
alo
n
g
th
e
th
r
ee
ax
es
(
,
,
)
an
d
th
e
r
o
tatio
n
al
d
y
n
am
i
cs
ar
o
u
n
d
r
o
ll,
p
itch
,
an
d
y
aw.
T
h
e
ae
r
o
d
y
n
am
ic
f
o
r
ce
s
an
d
t
o
r
q
u
es
g
en
er
ated
b
y
th
e
f
o
u
r
r
o
t
o
r
s
a
r
e
m
ap
p
e
d
in
to
t
h
e
tr
an
s
latio
n
al
an
d
an
g
u
lar
ac
ce
ler
atio
n
s
o
f
th
e
q
u
a
d
r
o
t
o
r
.
T
o
s
im
p
lify
th
e
m
o
d
elin
g
f
o
r
c
o
n
t
r
o
ller
d
esig
n
,
th
e
f
o
llo
win
g
as
s
u
m
p
tio
n
s
ar
e
m
ad
e:
T
h
e
q
u
a
d
r
o
to
r
is
co
n
s
id
er
e
d
as
a
r
ig
id
b
o
d
y
with
s
y
m
m
et
r
ic
s
tr
u
ctu
r
e
a
n
d
ae
r
o
d
y
n
am
i
c
d
r
ag
f
o
r
ce
s
ar
e
n
eg
lecte
d
co
m
p
ar
ed
to
th
r
u
s
t
f
o
r
ce
s
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
q
u
ad
r
o
to
r
s
tr
u
ctu
r
e
to
g
eth
er
wit
h
its
in
er
tial
an
d
b
o
d
y
-
f
ix
ed
r
ef
er
en
ce
f
r
am
es.
T
h
e
in
er
tial
f
r
am
e
(
,
,
)
i
s
u
s
ed
to
d
escr
ib
e
th
e
tr
an
s
lati
o
n
al
m
o
tio
n
o
f
th
e
v
e
h
icle,
wh
ile
th
e
b
o
d
y
f
r
am
e
is
attac
h
e
d
t
o
th
e
q
u
a
d
r
o
to
r
an
d
d
ef
in
es
its
r
o
tatio
n
al
d
y
n
am
ics.
T
h
e
attitu
d
e
o
f
th
e
q
u
a
d
r
o
to
r
is
r
ep
r
esen
ted
b
y
th
e
r
o
ll
(
)
,
p
itch
(
)
,
an
d
y
aw
(
)
an
g
les.
T
h
e
f
o
u
r
r
o
t
o
r
s
r
o
tate
with
an
g
u
lar
s
p
ee
d
s
[
1
…
4
]
,
g
e
n
er
atin
g
th
r
u
s
t
f
o
r
ce
s
an
d
co
n
tr
o
l
to
r
q
u
es
th
at
allo
w
i
n
d
ep
en
d
en
t
c
o
n
tr
o
l
o
f
altitu
d
e
,
attitu
d
e,
an
d
h
o
r
izo
n
tal
m
o
tio
n
.
Ma
th
em
atica
lly
,
th
e
q
u
a
d
r
o
to
r
ca
n
b
e
m
o
d
eled
b
y
th
e
f
o
llo
w
in
g
n
o
n
lin
ea
r
s
tate
s
p
ac
e
m
o
d
el
[
7
]
:
{
̇
1
=
2
̇
2
=
−
4
6
+
̇
3
=
4
̇
4
=
−
2
6
+
̇
5
=
6
̇
6
=
−
2
4
+
̇
7
=
8
̇
8
=
1
.
3
.
5
+
1
.
5
−
8
+
̇
9
=
10
̇
10
=
1
.
3
.
5
−
1
.
5
−
10
+
̇
11
=
12
̇
12
=
1
.
3
−
12
−
+
(
1
)
w
h
er
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
2
9
-
5
4
3
532
{
1
=
2
=
̇
3
=
4
=
̇
5
=
6
=
̇
7
=
8
=
̇
9
=
10
=
̇
11
=
12
=
̇
(
2
)
an
d
,
,
a
r
e
th
e
ae
r
o
d
y
n
am
ic
f
o
r
ce
s
g
en
er
ated
b
y
win
d
d
is
tu
r
b
an
ce
s
alo
n
g
ea
ch
ax
is
,
g
iv
e
n
b
y
(
3
)
:
{
=
1
2
2
,
=
,
,
(
3
)
an
d
ap
p
lied
in
th
e
last
s
ec
tio
n
o
f
r
esu
lts
to
ev
alu
ate
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
elec
ted
o
p
tim
ized
co
n
tr
o
ller
PID
.
Fig
u
r
e
1
.
Qu
a
d
r
o
to
r
r
ef
e
r
en
ce
f
r
am
es a
n
d
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
T
h
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
q
u
ad
r
o
to
r
u
s
ed
in
th
is
wo
r
k
in
co
r
p
o
r
ates
lin
ea
r
ae
r
o
d
y
n
am
ic
d
r
ag
f
o
r
ce
s
alo
n
g
ea
ch
b
o
d
y
ax
is
,
r
ep
r
esen
ted
b
y
,
an
d
,
to
m
ain
tain
p
h
y
s
ical
co
n
s
is
ten
cy
.
E
x
ter
n
al
d
i
s
tu
r
b
an
ce
s
d
u
e
to
win
d
,
d
en
o
ted
b
y
,
an
d
ar
e
also
e
x
p
licitly
co
n
s
id
er
ed
in
t
h
e
s
im
u
latio
n
s
t
o
ev
al
u
ate
r
o
b
u
s
tn
es
s
u
n
d
er
r
ea
lis
tic
o
p
er
atin
g
c
o
n
d
itio
n
s
.
W
h
ile
th
ese
ef
f
ec
ts
a
r
e
in
clu
d
ed
i
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th
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m
o
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p
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th
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en
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atin
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allo
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r
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ess
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o
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th
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n
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h
e
p
a
r
am
eter
s
o
f
th
e
q
u
ad
r
o
to
r
u
s
ed
i
n
th
e
d
y
n
am
ic
m
o
d
el,
i
n
clu
d
in
g
th
e
m
ass
,
g
eo
m
etr
ic
d
im
en
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io
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s
,
g
r
a
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itatio
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al
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tan
t,
an
d
m
o
m
en
ts
o
f
in
er
tia,
ar
e
s
u
m
m
ar
ized
i
n
T
ab
le
1
.
Nu
m
er
ical
s
im
u
latio
n
s
ar
e
ca
r
r
ied
o
u
t
u
s
in
g
a
f
o
u
r
th
-
o
r
d
er
R
u
n
g
e
–
Ku
tta
in
teg
r
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ch
em
e
with
a
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ix
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ize
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f
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ic
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r
o
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g
o
o
d
b
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ce
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etwe
en
c
o
m
p
u
tatio
n
al
ef
f
icien
cy
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ac
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r
ac
y
.
T
ab
le
1
.
Ph
y
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ical
p
ar
a
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o
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ad
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el
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ss t
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2
5
G
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v
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e
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o
n
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.
81
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M
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/
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
P
r
ec
is
io
n
en
h
a
n
ce
men
t in
d
r
o
n
e
p
o
s
itio
n
c
o
n
tr
o
l b
a
s
ed
o
n
o
p
timiz
ed
P
I
D
… (
I
ma
m
B
a
r
ke
t G
h
ilo
u
b
i
)
533
3.
CO
NT
RO
L
M
E
T
H
O
D
3
.
1
.
P
I
D
co
ntr
o
l st
ruct
ure
T
h
e
co
n
tr
o
l
ar
ch
itectu
r
e
is
b
a
s
ed
o
n
a
ca
s
ca
d
e
d
PID
s
ch
em
e.
T
h
e
o
u
ter
lo
o
p
r
eg
u
lates
th
e
p
o
s
itio
n
(
,
)
,
wh
ile
th
e
in
n
er
lo
o
p
co
n
tr
o
ls
th
e
attitu
d
e
an
g
les
(
,
,
)
an
d
altitu
d
e
as sh
o
wn
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
Diag
r
a
m
o
f
th
e
o
p
tim
ized
PID
co
n
tr
o
l a
r
ch
itectu
r
e
T
h
e
d
esire
d
p
o
s
itio
n
r
ef
e
r
en
ce
s
(
,
,
)
ar
e
p
r
o
ce
s
s
ed
b
y
an
o
u
ter
-
lo
o
p
PID
co
n
tr
o
ller
t
h
at
g
en
er
ates
in
ter
m
ed
iate
v
ir
tu
al
co
n
tr
o
l
s
ig
n
als
,
,
an
d
b
ased
o
n
th
e
co
r
r
esp
o
n
d
in
g
p
o
s
itio
n
e
r
r
o
r
s
.
T
h
e
h
o
r
izo
n
tal
v
ir
tu
al
co
n
t
r
o
l
s
ig
n
als
an
d
ar
e
th
en
c
o
n
v
e
r
ted
i
n
to
d
esire
d
r
o
ll
an
d
p
itch
an
g
l
es
an
d
th
r
o
u
g
h
th
e
f
o
llo
win
g
r
elatio
n
s
:
{
=
1
(
−
)
=
1
(
+
)
(
4
)
An
o
u
ter
-
lo
o
p
PID
co
n
tr
o
ller
g
en
er
ates
th
e
v
ir
tu
al
co
n
tr
o
l
in
p
u
ts
an
d
u
s
in
g
th
e
tr
ac
k
in
g
e
r
r
o
r
s
in
p
o
s
itio
n
,
w
h
ile
an
in
n
er
-
l
o
o
p
PID
c
o
n
tr
o
ller
r
eg
u
lates
th
e
attitu
d
e
(
,
,
)
b
ased
o
n
th
e
r
ef
er
en
ce
s
(
,
,
)
.
T
h
e
PID
g
ain
s
o
f
b
o
th
lo
o
p
s
ar
e
o
p
tim
ized
o
f
f
lin
e
u
s
in
g
th
e
FP
A
an
d
PS
O
alg
o
r
ith
m
s
.
T
h
e
o
p
tim
ized
co
n
t
r
o
l
in
p
u
ts
(
,
,
,
)
ar
e
th
en
ap
p
lied
to
th
e
q
u
ad
r
o
t
o
r
d
y
n
am
ic
m
o
d
el,
an
d
t
h
e
m
ea
s
u
r
ed
s
tates a
r
e
f
ed
b
ac
k
to
cl
o
s
e
th
e
co
n
tr
o
l lo
o
p
.
B
ased
o
n
th
e
c
o
n
tr
o
l
s
tr
u
ctu
r
e
illu
s
tr
ated
in
Fig
u
r
e
2
,
th
e
q
u
ad
r
o
to
r
m
o
tio
n
alo
n
g
s
ix
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
-
th
r
ee
tr
an
s
latio
n
al
(
,
,
)
an
d
th
r
ee
r
o
tatio
n
al
(
,
,
)
-
is
r
eg
u
lated
u
s
in
g
a
u
n
if
ied
PID
c
o
n
tr
o
l
law.
Fo
r
ea
ch
co
n
tr
o
lled
v
ar
ia
b
le
,
,
,
,
an
d
,
th
e
co
r
r
esp
o
n
d
in
g
c
o
n
tr
o
l in
p
u
t
is
d
ef
in
ed
as:
=
+
∫
0
+
̇
,
∈
{
,
,
,
,
,
}
(
5
)
wh
er
e
=
−
d
en
o
tes th
e
tr
ac
k
in
g
er
r
o
r
b
etwe
en
t
h
e
d
esire
d
a
n
d
ac
tu
al
s
tates.
T
h
e
p
r
o
p
o
r
tio
n
al,
i
n
teg
r
al,
an
d
d
e
r
iv
ativ
e
g
ai
n
s
,
,
ar
e
tu
n
ed
in
d
e
p
en
d
e
n
tly
f
o
r
ea
ch
d
e
g
r
ee
o
f
f
r
ee
d
o
m
u
s
in
g
th
e
FP
A
an
d
PS
O
o
p
tim
izatio
n
alg
o
r
ith
m
s
.
Fo
r
th
e
tr
a
n
s
latio
n
al
d
y
n
am
ic
s
,
th
e
v
ir
tu
al
co
n
tr
o
l
in
p
u
ts
an
d
ar
e
co
n
v
er
te
d
in
to
th
e
d
e
s
ir
ed
r
o
ll
an
d
p
itc
h
an
g
les
(
,
)
,
wh
ile
d
ir
ec
tly
r
eg
u
lates
th
e
altitu
d
e.
Fo
r
th
e
r
o
tatio
n
al
d
y
n
a
m
ics
:
,
,
co
r
r
esp
o
n
d
d
ir
ec
tly
to
th
e
r
o
ll,
p
itch
,
an
d
y
aw
co
n
tr
o
l to
r
q
u
e
s
ap
p
lied
to
th
e
q
u
ad
r
o
to
r
.
T
h
e
PID
g
ain
s
ar
e
tu
n
ed
b
y
m
i
n
im
izin
g
th
e
f
o
llo
win
g
o
b
jecti
v
e
f
u
n
ctio
n
:
=
∫
(
|
|
+
|
|
+
|
|
)
+
(
+
+
)
0
(
6
)
wh
er
e
,
an
d
d
en
o
te
th
e
in
s
tan
tan
eo
u
s
p
o
s
itio
n
er
r
o
r
s
alo
n
g
ea
ch
ax
is
,
co
m
p
u
ted
as
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
d
esire
d
an
d
ac
tu
a
l
UAV
p
o
s
it
io
n
s
.
,
an
d
r
ep
r
esen
t
th
e
m
ax
im
u
m
o
v
er
s
h
o
o
t
alo
n
g
ea
ch
ax
is
,
d
ef
in
ed
as
th
e
lar
g
est
d
ev
iatio
n
o
f
th
e
UAV
p
o
s
itio
n
f
r
o
m
th
e
r
ef
e
r
en
ce
tr
ajec
to
r
y
d
u
r
in
g
th
e
s
im
u
latio
n
o
r
ex
p
er
im
en
tal
r
u
n
.
T
h
e
in
te
g
r
atio
n
is
p
er
f
o
r
m
e
d
o
v
er
th
e
f
ix
e
d
tim
e
in
ter
v
al
,
co
r
r
esp
o
n
d
in
g
to
th
e
d
u
r
atio
n
o
f
th
e
test
ed
t
r
ajec
to
r
y
,
e
n
s
u
r
in
g
co
n
s
is
ten
cy
an
d
r
e
p
r
o
d
u
cib
ilit
y
o
f
th
e
r
esu
lts
.
T
h
e
weig
h
tin
g
f
ac
to
r
b
alan
ce
s
th
e
tr
ad
e
-
o
f
f
b
etwe
en
m
in
im
izin
g
o
v
er
s
h
o
o
t
an
d
im
p
r
o
v
in
g
tr
ac
k
in
g
ac
cu
r
a
cy
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
2
9
-
5
4
3
534
3
.
2
.
P
I
D
b
a
s
ed
o
n F
P
A
o
pti
m
iza
t
io
n
T
h
e
f
lo
wer
p
o
llin
atio
n
alg
o
r
ith
m
(
FP
A)
is
a
m
etah
eu
r
is
tic
o
p
tim
izatio
n
tec
h
n
iq
u
e
b
as
ed
o
n
th
e
p
o
llin
atio
n
p
r
o
ce
s
s
o
f
f
lo
wer
in
g
p
lan
ts
.
I
n
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
,
ea
ch
ca
n
d
id
ate
s
o
lu
tio
n
is
r
ep
r
esen
ted
b
y
a
d
ec
is
io
n
v
ec
to
r
:
=
[
]
(
7
)
wh
ich
co
n
tain
s
th
e
p
r
o
p
o
r
tio
n
al,
in
teg
r
al,
an
d
d
er
i
v
ativ
e
g
ain
s
o
f
th
e
PID
co
n
tr
o
ller
.
T
h
e
o
b
jectiv
e
o
f
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
is
to
d
ete
r
m
in
e
th
e
o
p
tim
al
PID
p
a
r
am
e
ter
s
th
at
m
in
im
ize
th
e
p
er
f
o
r
m
an
ce
in
d
ex
.
FP
A
alter
n
ates
b
etwe
en
g
lo
b
al
an
d
lo
ca
l
p
o
llin
atio
n
m
ec
h
a
n
is
m
s
.
Glo
b
al
p
o
llin
atio
n
m
o
d
els
cr
o
s
s
-
p
o
llin
atio
n
an
d
is
p
er
f
o
r
m
e
d
u
s
in
g
L
e
v
y
f
lig
h
ts
,
wh
ich
en
ab
le
lo
n
g
-
d
is
tan
ce
ex
p
lo
r
atio
n
to
war
d
th
e
cu
r
r
e
n
t
b
est
s
o
lu
tio
n
∗
.
T
h
e
g
lo
b
al
p
o
llin
atio
n
u
p
d
ate
r
u
le
is
g
iv
en
b
y
:
+
1
=
+
(
−
∗
)
(
8
)
wh
er
e
d
en
o
tes
th
e
PID
g
ain
v
ec
to
r
o
f
t
h
e
ℎ
ca
n
d
id
ate
s
o
lu
tio
n
at
iter
atio
n
,
∗
r
ep
r
esen
ts
th
e
b
est
PID
g
ain
v
ec
to
r
f
o
u
n
d
s
o
f
ar
,
a
n
d
is
th
e
L
ev
y
f
lig
h
t
s
tep
s
ize
f
o
llo
win
g
a
h
ea
v
y
-
tailed
p
r
o
b
ab
il
ity
d
is
tr
ib
u
tio
n
as
s
h
o
wn
in
T
ab
le
2
.
T
ab
le
2
.
Op
tim
izatio
n
p
ar
am
et
er
s
f
o
r
PS
O
an
d
FP
A
alg
o
r
ith
m
s
P
a
r
a
me
t
e
r
FPA
PSO
P
o
p
u
l
a
t
i
o
n
s
i
z
e
2
0
0
2
0
0
N
u
mb
e
r
o
f
i
t
e
r
a
t
i
o
n
s
3
0
0
3
0
0
G
l
o
b
a
l
p
o
l
l
i
n
a
t
i
o
n
p
r
o
b
a
b
i
l
i
t
y
0
.
8
/
Lé
v
y
f
l
i
g
h
t
s
t
e
p
1
.
5
/
A
c
c
e
l
e
r
a
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
1
/
1
.
7
A
c
c
e
l
e
r
a
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
2
/
1
.
5
I
n
e
r
t
i
a
w
e
i
g
h
t
/
0
.
7
S
e
a
r
c
h
s
p
a
c
e
g
a
i
n
b
o
u
n
d
s f
o
r
[
]
:
(
L
o
w
e
r
b
o
u
n
d
s:
[
0
,
0
,
0
]
;
u
p
p
e
r
b
o
u
n
d
s
a
s s
p
e
c
i
f
i
e
d
b
e
l
o
w
)
P
o
si
t
i
o
n
,
[
8
,
4
,
3
]
[
8
,
4
,
3
]
P
o
si
t
i
o
n
[
1
2
,
4
,
5
]
[
1
2
,
4
,
5
]
A
n
g
l
e
s
,
[
3
,
2
,
3
]
[
3
,
2
,
3
]
A
n
g
l
e
[
4
,
2
,
2
]
[
4
,
2
,
2
]
L
o
ca
l
p
o
llin
atio
n
r
ep
r
esen
ts
s
e
lf
-
p
o
llin
atio
n
with
in
a
lo
ca
l
n
e
ig
h
b
o
r
h
o
o
d
,
allo
win
g
f
in
e
-
t
u
n
in
g
o
f
t
h
e
PID
g
ain
s
b
y
ex
ch
an
g
in
g
i
n
f
o
r
m
atio
n
b
etwe
en
r
a
n
d
o
m
ly
s
elec
ted
ca
n
d
i
d
ate
s
o
lu
ti
o
n
s
.
A
s
witch
in
g
p
r
o
b
a
b
ilit
y
co
n
tr
o
ls
th
e
tr
an
s
itio
n
b
etwe
en
g
lo
b
al
an
d
lo
ca
l
p
o
llin
atio
n
.
At
ea
ch
iter
atio
n
,
th
e
f
itn
ess
o
f
ea
ch
ca
n
d
id
ate
s
o
lu
tio
n
is
ev
alu
ate
d
u
s
in
g
th
e
o
b
jectiv
e
f
u
n
ctio
n
,
wh
ich
co
m
b
in
es
th
e
I
T
AE
an
d
an
o
v
e
r
s
h
o
o
t
p
en
alty
.
Ov
er
s
u
cc
ess
iv
e
g
en
e
r
atio
n
s
,
th
e
FP
A
co
n
v
er
g
es
to
war
d
th
e
o
p
tim
al
s
et
o
f
PID
g
ain
s
th
at
m
in
im
izes
[
3
0
]
.
3
.
3
.
P
I
D
ba
s
ed
o
n P
SO
o
pti
m
iza
t
io
n
Par
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
is
a
p
o
p
u
latio
n
-
b
ased
s
to
ch
asti
c
o
p
tim
izatio
n
alg
o
r
ith
m
in
s
p
ir
ed
b
y
th
e
co
llectiv
e
b
eh
a
v
io
r
o
f
b
ir
d
f
lo
c
k
s
an
d
f
is
h
s
ch
o
o
ls
.
Si
m
ilar
to
t
h
e
FP
A
-
b
ased
a
p
p
r
o
ac
h
d
escr
ib
e
d
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
,
ea
ch
p
ar
tic
le
is
ass
o
ciate
d
with
a
PID
g
ain
v
ec
to
r
d
ef
i
n
ed
in
(
7
)
,
wh
ich
r
ep
r
esen
ts
a
ca
n
d
id
ate
s
o
lu
tio
n
i
n
th
e
s
ea
r
c
h
s
p
ac
e.
T
h
e
d
y
n
am
ic
ev
o
l
u
tio
n
o
f
ea
c
h
p
ar
ticle
is
g
o
v
e
r
n
ed
b
y
its
v
e
lo
city
an
d
p
o
s
itio
n
u
p
d
ate
eq
u
atio
n
s
:
{
+
1
=
+
1
1
(
−
)
+
2
2
(
−
)
+
1
=
+
+
1
(
9
)
wh
er
e
an
d
d
en
o
te
th
e
p
o
s
itio
n
(
PID
g
ain
s
)
an
d
v
elo
city
o
f
th
e
ℎ
p
ar
ticle
at
iter
atio
n
,
r
esp
ec
tiv
ely
.
T
h
e
ter
m
r
ep
r
esen
ts
th
e
p
er
s
o
n
al
b
est
PID
g
ain
v
ec
to
r
ac
h
ie
v
ed
b
y
t
h
e
p
ar
ticle,
wh
ile
d
en
o
tes
th
e
g
lo
b
al
b
est
s
o
lu
tio
n
f
o
u
n
d
b
y
th
e
s
war
m
.
T
h
e
p
ar
a
m
eter
s
,
1
,
an
d
2
ar
e
th
e
in
er
tia
weig
h
t
an
d
ac
ce
ler
atio
n
co
ef
f
icien
ts
co
n
tr
o
llin
g
th
e
tr
ad
e
-
o
f
f
b
etwe
en
e
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
,
a
n
d
1
,
2
ar
e
r
an
d
o
m
n
u
m
b
er
s
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
in
[
0
,
1
]
as sh
o
wn
in
T
ab
le
2
.
T
h
r
o
u
g
h
iter
ativ
e
u
p
d
ates,
p
ar
ticles
m
o
v
e
to
war
d
r
eg
io
n
s
o
f
th
e
s
ea
r
ch
s
p
ac
e
ass
o
ciate
d
with
lo
wer
co
s
t
v
alu
es.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
co
n
tin
u
es
u
n
til
co
n
v
e
r
g
en
ce
cr
iter
ia
ar
e
m
et,
r
esu
ltin
g
in
an
o
p
tim
al
o
r
n
ea
r
-
o
p
tim
al
s
et
o
f
PID
g
ain
s
th
at
m
in
im
izes th
e
o
b
jectiv
e
f
u
n
ctio
n
[
3
0
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
P
r
ec
is
io
n
en
h
a
n
ce
men
t in
d
r
o
n
e
p
o
s
itio
n
c
o
n
tr
o
l b
a
s
ed
o
n
o
p
timiz
ed
P
I
D
… (
I
ma
m
B
a
r
ke
t G
h
ilo
u
b
i
)
535
I
n
th
is
wo
r
k
,
FP
A
an
d
PS
O
ar
e
em
p
lo
y
e
d
as
o
p
tim
izatio
n
tech
n
iq
u
es
to
d
eter
m
in
e
s
u
itab
le
PID
co
n
tr
o
ller
g
ain
s
th
at
m
in
im
ize
th
e
d
e
f
in
ed
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
ese
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
d
o
n
o
t
m
o
d
if
y
th
e
s
tr
u
ctu
r
e
o
f
th
e
c
o
n
tr
o
l
l
aw
b
u
t
in
s
tead
s
ea
r
ch
f
o
r
a
p
p
r
o
p
r
iate
p
ar
am
eter
v
alu
es
w
ith
in
th
e
p
r
e
d
ef
in
e
d
b
o
u
n
d
s
.
C
o
n
s
eq
u
en
tly
,
t
h
e
s
tab
ilit
y
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
d
ep
en
d
s
o
n
th
e
PID
c
o
n
tr
o
ller
d
esig
n
an
d
t
h
e
q
u
ad
r
o
to
r
d
y
n
am
ic
m
o
d
el,
wh
ile
th
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
ac
t
s
o
lely
as
to
o
ls
f
o
r
p
a
r
am
eter
tu
n
in
g
.
All
s
im
u
latio
n
s
s
tar
t
f
r
o
m
ze
r
o
in
itial
co
n
d
itio
n
s
f
o
r
p
o
s
itio
n
,
v
elo
city
,
an
d
attitu
d
e
s
tates.
T
h
e
m
ain
p
a
r
am
eter
s
u
s
ed
f
o
r
t
h
e
PID
o
p
tim
izatio
n
with
th
e
FP
A
an
d
PS
O
ar
e
s
u
m
m
ar
ized
in
T
a
b
le
2.
T
ab
le
2
p
r
o
v
id
es
d
etailed
s
etti
n
g
s
f
o
r
b
o
t
h
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
in
clu
d
in
g
PID
g
ain
s
ea
r
ch
s
p
ac
e,
p
o
p
u
latio
n
s
ize,
n
u
m
b
er
o
f
iter
atio
n
s
,
an
d
alg
o
r
ith
m
-
s
p
ec
if
ic
p
ar
am
eter
s
s
u
ch
as
p
o
llin
atio
n
p
r
o
b
ab
ilit
y
,
L
e
v
y
ex
p
o
n
e
n
t
f
o
r
FP
A,
an
d
in
e
r
tia
weig
h
t
an
d
ac
ce
ler
atio
n
co
ef
f
icien
ts
f
o
r
PS
O.
T
h
e
s
e
s
ettin
g
s
en
s
u
r
e
r
ep
r
o
d
u
cib
ilit
y
o
f
th
e
s
tu
d
y
an
d
a
f
air
c
o
m
p
ar
is
o
n
b
etwe
en
t
h
e
two
ap
p
r
o
ac
h
es.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
ev
alu
ate
th
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
o
p
tim
ized
PID
co
n
tr
o
ller
s
,
th
r
ee
r
e
f
er
en
ce
s
ce
n
ar
io
s
:
Step
r
esp
o
n
s
e,
cir
c
u
lar
a
n
d
le
m
n
is
ca
te
tr
ajec
to
r
ies
wer
e
s
im
u
la
ted
,
f
o
llo
wed
b
y
a
r
o
b
u
s
tn
es
s
test
o
f
th
e
b
est
-
p
er
f
o
r
m
in
g
c
o
n
tr
o
ller
.
4
.
1
.
F
irst
s
ce
na
rio
:
Ste
p r
es
po
ns
e
A
s
tep
test
is
ca
r
r
ied
o
u
t w
ith
d
esire
d
v
alu
es o
f
:
{
=
1
=
0
.
5
=
1
(
1
0
)
Fig
u
r
e
3
illu
s
tr
ates
th
e
s
tep
r
esp
o
n
s
e
p
er
f
o
r
m
an
ce
o
f
th
e
q
u
ad
r
o
to
r
u
n
d
er
b
o
th
PID
-
FP
A
an
d
PID
-
PS
O
co
n
tr
o
ller
s
.
T
h
e
tim
e
-
r
e
s
p
o
n
s
es
f
o
r
th
e
,
,
an
d
p
o
s
itio
n
s
clea
r
ly
s
h
o
w
th
at
th
e
PID
-
PS
O
ex
h
ib
its
n
o
ticea
b
le
o
v
er
s
h
o
o
t
in
all
th
r
ee
ax
es,
wh
ile
th
e
PID
-
FP
A
ef
f
ec
tiv
ely
elim
in
ates
o
v
er
s
h
o
o
t.
Mo
r
eo
v
er
,
th
e
PID
-
FP
A
ac
h
iev
es
f
as
ter
co
n
v
er
g
en
ce
,
p
ar
ticu
lar
ly
in
th
e
x
an
d
z
r
esp
o
n
s
es,
in
d
icatin
g
s
u
p
er
io
r
tr
an
s
ien
t
b
eh
av
io
r
as
s
h
o
wn
in
Fig
u
r
e
3
(
a)
.
T
h
e
3
D
tr
ajec
to
r
y
in
F
ig
u
r
e
3
(
b
)
r
e
p
r
esen
tatio
n
f
u
r
t
h
er
co
n
f
ir
m
s
th
ese
o
b
s
er
v
atio
n
s
,
h
ig
h
lig
h
tin
g
th
e
ab
ilit
y
o
f
t
h
e
PID
-
FP
A
t
o
p
r
o
v
id
e
m
o
r
e
ac
c
u
r
ate
a
n
d
s
tab
le
t
r
ac
k
in
g
p
er
f
o
r
m
an
ce
co
m
p
ar
e
d
to
th
e
PID
-
PS
O.
Fig
u
r
e
3
.
Step
r
esp
o
n
s
e:
(a
)
3
D
m
o
tio
n
an
d
(
b
)
x
,
y
,
z
p
o
s
itio
n
s
v
er
s
u
s
tim
e
T
ab
le
3
c
o
m
p
a
r
es
th
e
p
e
r
f
o
r
m
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ce
o
f
th
e
q
u
ad
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o
to
r
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tem
u
n
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er
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n
t
r
o
ller
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o
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iz
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O
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o
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ith
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s
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o
th
m
eth
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d
s
ac
h
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e
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ze
r
o
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y
-
s
tate
er
r
o
r
,
in
d
icatin
g
ac
cu
r
at
e
tr
ac
k
in
g
in
s
tead
y
s
tate.
Ho
wev
er
,
clea
r
d
if
f
e
r
en
ce
s
ap
p
ea
r
in
th
e
tr
an
s
ien
t r
es
p
o
n
s
e.
Fo
r
th
e
x
-
a
x
is
,
th
e
PID
-
FP
A
co
n
tr
o
ller
ac
h
iev
es
a
f
aster
s
ettlin
g
tim
e
c
o
m
p
ar
e
d
with
PI
D
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PS
O
an
d
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ig
n
if
ican
tly
r
ed
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ce
s
th
e
o
v
e
r
s
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o
o
t
f
r
o
m
4
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%
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.
3
%.
A
lo
n
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th
e
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a
x
is
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o
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h
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n
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o
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er
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it
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ilar
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t
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e
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ased
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n
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o
ller
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o
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ch
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r
th
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e
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r
o
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e
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t
r
e
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ar
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ettlin
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e
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ed
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ce
d
f
r
o
m
3
.
6
to
1
s
an
d
t
h
e
o
v
er
s
h
o
o
t
co
m
p
letely
elim
in
ated
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
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I
n
t
J
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&
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to
m
,
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l
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1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
2
9
-
5
4
3
536
T
ab
le
3
.
Per
f
o
r
m
an
ce
co
m
p
a
r
is
o
n
o
f
PID
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n
tr
o
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ia
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d
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izatio
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e
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t
r
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l
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r
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e
t
t
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i
me
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e
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o
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t
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o
si
t
i
o
n
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P
I
D
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2
.
2
43
P
I
D
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FPA
1
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1
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.
3
P
o
si
t
i
o
n
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I
D
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3
3
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D
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2
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l
t
i
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d
e
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I
D
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6
2
8
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6
P
I
D
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FPA
1
0
4
.
2
.
Seco
nd
s
ce
na
rio
:
Circ
ula
r
t
ra
j
ec
t
o
ry
I
n
th
is
ca
s
e,
a
cir
cu
lar
tr
ajec
to
r
y
with
a
r
a
d
iu
s
o
f
1
m
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d
alt
itu
d
e
o
f
1
m
is
co
n
s
id
er
e
d
:
{
=
1
0
.
5
=
1
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5
=
1
(
1
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)
Fig
u
r
e
4
p
r
esen
ts
th
e
q
u
ad
r
o
to
r
p
er
f
o
r
m
a
n
ce
wh
e
n
tr
ac
k
in
g
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ci
r
cu
lar
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r
ajec
to
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y
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o
u
g
h
b
o
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h
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d
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ap
p
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h
es
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en
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all
y
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e
t
o
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d
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e
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A
d
em
o
n
s
tr
ates
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u
p
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io
r
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ilit
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d
ac
cu
r
ac
y
d
u
r
in
g
th
e
in
itial
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ac
k
in
g
p
h
ase.
I
n
co
n
tr
ast,
th
e
PID
-
PS
O
in
Fig
u
r
e
4
(
a)
s
h
o
ws
less
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r
ec
is
e
co
n
v
er
g
e
n
ce
at
th
e
s
tar
t.
T
h
ese
d
if
f
e
r
en
ce
s
ar
e
m
o
r
e
ev
id
en
t
in
th
e
3
D
tr
ajec
to
r
y
p
lo
t,
s
h
o
w
n
in
Fig
u
r
e
4
(
b
)
wh
er
e
th
e
PID
-
FP
A
m
ain
tain
s
a
s
m
o
o
th
er
an
d
clo
s
er
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ath
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e
r
ef
er
en
ce
cir
cle
c
o
m
p
a
r
ed
to
t
h
e
PID
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PS
O.
Fig
u
r
e
4
.
C
ir
cu
lar
tr
ajec
to
r
y
tr
ac
k
in
g
:
(
a)
3
D
m
o
tio
n
an
d
(
b
)
x
,
y
,
z
p
o
s
itio
n
s
v
er
s
u
s
tim
e
4
.
3
.
T
hird s
ce
na
rio
:
L
em
nis
ca
t
e
(
∞)
t
r
a
j
ec
t
o
r
y
T
o
f
u
r
t
h
er
ev
al
u
ate
p
er
f
o
r
m
an
ce
,
a
lem
n
is
ca
te
tr
ajec
to
r
y
wit
h
a
r
ad
iu
s
o
f
1
m
an
d
altitu
d
e
o
f
1
m
is
ap
p
lied
as a
d
esire
d
tr
ajec
to
r
y
:
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=
1
0
.
25
1
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0
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)
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0
.
25
)
1
+
2
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0
.
25
)
=
1
(
1
2
)
Fig
u
r
e
5
s
h
o
ws
th
e
q
u
a
d
r
o
t
o
r
tr
ac
k
in
g
p
e
r
f
o
r
m
an
ce
f
o
r
a
l
em
n
is
ca
te
(
∞
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s
h
ap
ed
)
tr
ajec
to
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y
o
f
1
m
r
ad
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s
at
1
m
altitu
d
e.
T
h
is
tr
a
jecto
r
y
is
m
o
r
e
co
m
p
lex
an
d
r
eq
u
ir
es
h
ig
h
er
t
r
ac
k
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g
ac
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u
r
a
cy
co
m
p
ar
e
d
to
th
e
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cu
lar
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ath
.
T
h
e
r
esu
lts
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ig
h
lig
h
t
th
at
th
e
PID
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FP
A
p
r
o
v
i
d
es
s
m
o
o
th
er
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d
m
o
r
e
s
tab
le
tr
ac
k
in
g
alo
n
g
th
e
en
tire
tr
ajec
to
r
y
,
m
ain
tain
in
g
clo
s
er
ad
h
er
en
ce
to
th
e
d
esire
d
p
ath
,
as
s
h
o
wn
in
Fig
u
r
e
5
(
a)
.
I
n
c
o
n
tr
ast,
th
e
PID
-
PS
O
ex
h
ib
its
n
o
ticea
b
l
e
d
ev
iatio
n
s
,
p
ar
ticu
la
r
ly
i
n
th
e
c
u
r
v
e
d
s
ec
tio
n
s
,
co
n
f
i
r
m
in
g
th
e
s
u
p
e
r
io
r
r
o
b
u
s
tn
ess
an
d
p
r
ec
is
io
n
o
f
th
e
PID
-
FP
A
in
h
an
d
lin
g
c
o
m
p
l
ex
m
an
eu
v
er
s
as sh
o
wn
in
Fig
u
r
e
5
(
b
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
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P
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n
en
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n
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t in
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o
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itio
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D
… (
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ma
m
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r
ke
t G
h
ilo
u
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i
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537
Fig
u
r
e
5
.
L
e
m
n
is
ca
te
tr
ajec
to
r
y
tr
ac
k
in
g
:
(
a)
3
D
m
o
tio
n
a
n
d
(
b
)
x
,
y
,
z
p
o
s
itio
n
s
v
er
s
u
s
tim
e
4
.
4
.
Q
ua
ntit
a
t
iv
e
c
o
m
pa
riso
n o
f
t
ra
j
ec
t
o
ry
t
ra
c
k
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o
rm
a
nce
I
n
o
r
d
e
r
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r
o
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id
e
a
n
o
b
jecti
v
e
an
d
q
u
an
titativ
e
ev
alu
atio
n
o
f
th
e
tr
ajec
to
r
y
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
,
ad
d
itio
n
al
er
r
o
r
-
b
ased
m
etr
ics
ar
e
co
n
s
id
er
ed
to
co
m
p
lem
e
n
t
th
e
tim
e
-
d
o
m
ain
r
esp
o
n
s
es
an
d
q
u
alitativ
e
p
lo
ts
p
r
esen
ted
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th
e
p
r
ev
io
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s
s
u
b
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n
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T
h
ese
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etr
ics
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d
ir
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t
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m
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r
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o
n
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etwe
e
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th
e
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ized
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d
th
e
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A
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ized
P
I
D
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n
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o
ller
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u
n
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er
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tical
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im
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n
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n
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itio
n
s
.
L
et
th
e
p
o
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itio
n
tr
ac
k
i
n
g
er
r
o
r
v
ec
to
r
b
e
d
ef
in
e
d
as:
[
]
=
[
(
)
−
(
)
(
)
−
(
)
(
)
−
(
)
]
(
1
3
)
wh
er
e
(
,
,
)
an
d
(
,
,
)
d
en
o
te
th
e
d
esire
d
an
d
ac
tu
al
q
u
ad
r
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to
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o
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n
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r
esp
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ely
.
T
h
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win
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q
u
a
n
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e
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er
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m
an
ce
in
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ices a
r
e
em
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lo
y
e
d
to
ev
alu
ate
t
h
e
3
D
tr
ajec
to
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y
tr
ac
k
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g
(
,
,
)
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
.
−
R
o
o
t
m
ea
n
s
q
u
ar
e
e
r
r
o
r
(
R
MSE
)
:
=
√
1
∫
(
)
2
0
(
1
4
)
wh
ich
m
ea
s
u
r
es
t
h
e
o
v
er
all
t
r
ac
k
in
g
ac
cu
r
ac
y
o
v
er
th
e
en
tire
tr
ajec
to
r
y
an
d
is
s
en
s
itiv
e
to
lar
g
e
t
r
an
s
ien
t
er
r
o
r
s
.
−
Me
an
ab
s
o
lu
te
er
r
o
r
(
MA
E
)
:
=
1
∫
|
(
)
|
0
(
1
5
)
wh
ich
p
r
o
v
id
es a
n
av
er
ag
e
m
e
asu
r
e
o
f
th
e
a
b
s
o
lu
te
tr
ac
k
in
g
er
r
o
r
o
v
er
t
h
e
f
u
ll si
m
u
latio
n
h
o
r
izo
n
.
−
I
n
teg
r
al
o
f
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
:
=
∫
|
(
)
|
0
(
1
6
)
wh
ich
q
u
an
tifie
s
th
e
c
u
m
u
lati
v
e
tr
ac
k
in
g
er
r
o
r
an
d
r
ef
lects th
e
o
v
er
all
d
ev
iatio
n
f
r
o
m
t
h
e
r
ef
er
en
ce
tr
ajec
to
r
y
.
−
I
n
teg
r
al
o
f
tim
e
-
weig
h
ted
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
:
=
∫
|
(
)
|
0
(
1
7
)
wh
ich
p
e
n
alize
s
p
er
s
is
ten
t
tr
a
ck
in
g
e
r
r
o
r
s
o
cc
u
r
r
in
g
at
later
tim
e
in
s
tan
ts
an
d
is
co
n
s
is
ten
t
with
th
e
o
b
jectiv
e
f
u
n
ctio
n
u
s
ed
d
u
r
in
g
t
h
e
PID
tu
n
in
g
p
r
o
ce
s
s
.
wh
er
e
:
(
)
=
√
2
+
2
+
2
d
en
o
tes
t
h
e
E
u
cli
d
e
an
n
o
r
m
o
f
th
e
3
D
p
o
s
itio
n
tr
ac
k
in
g
er
r
o
r
,
an
d
r
ep
r
esen
ts
th
e
to
tal
s
im
u
latio
n
tim
e
with
∈
[
0
,
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
2
9
-
5
4
3
538
All
m
etr
ics
ar
e
co
m
p
u
ted
f
o
r
ea
ch
tr
ajec
to
r
y
s
ce
n
ar
i
o
an
d
s
u
m
m
ar
ized
in
T
ab
le
4
.
T
h
e
ta
b
le
p
r
esen
ts
th
e
q
u
a
n
titativ
e
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
m
etr
ics
o
b
tain
e
d
f
o
r
th
e
cir
c
u
lar
a
n
d
lem
n
is
ca
te
tr
ajec
to
r
ies
u
s
in
g
th
e
PID
co
n
tr
o
ller
s
t
u
n
ed
v
ia
FP
A
an
d
PS
O.
Fo
r
b
o
th
t
r
ajec
to
r
ies,
th
e
PID
-
FP
A
co
n
tr
o
ller
c
o
n
s
is
ten
tly
ac
h
iev
es
lo
wer
R
MSE
an
d
MA
E
v
alu
es
co
m
p
ar
ed
to
PID
-
PS
O,
in
d
icatin
g
im
p
r
o
v
e
d
o
v
er
all
tr
a
ck
in
g
ac
c
u
r
ac
y
an
d
r
ed
u
ce
d
av
e
r
ag
e
er
r
o
r
m
ag
n
it
u
d
e.
I
n
p
ar
tic
u
lar
,
f
o
r
th
e
lem
n
is
ca
te
tr
ajec
to
r
y
,
PID
-
FP
A
e
x
h
ib
its
a
n
o
ticea
b
le
r
ed
u
ctio
n
in
R
MSE
(
0
.
1
3
7
2
0
4
v
s
0
.
1
4
7
1
3
6
)
an
d
MA
E
(
0
.
0
3
2
7
9
4
v
s
0
.
0
4
3
1
1
6
)
,
h
ig
h
lig
h
tin
g
its
s
u
p
er
io
r
ab
ilit
y
to
h
an
d
le
m
o
r
e
co
m
p
le
x
an
d
h
ig
h
l
y
n
o
n
lin
ea
r
r
ef
er
e
n
ce
p
ath
s
.
Fu
r
t
h
er
m
o
r
e,
th
e
i
n
teg
r
al
p
er
f
o
r
m
an
ce
in
d
ices
(
I
AE
an
d
I
T
AE
)
r
ep
o
r
ted
in
T
a
b
le
4
c
o
n
f
ir
m
th
e
a
d
v
an
tag
e
o
f
t
h
e
FP
A
-
b
ased
t
u
n
in
g
s
tr
ateg
y
.
T
h
e
PID
-
FP
A
co
n
tr
o
ller
y
ield
s
l
o
wer
I
AE
v
al
u
es
f
o
r
b
o
th
cir
c
u
lar
an
d
lem
n
is
ca
te
tr
ajec
to
r
ies
,
r
ef
lectin
g
r
ed
u
ce
d
cu
m
u
lativ
e
tr
ac
k
in
g
er
r
o
r
o
v
er
th
e
f
u
ll
s
im
u
latio
n
h
o
r
izo
n
.
Mo
r
e
im
p
o
r
tan
tly
,
th
e
I
T
AE
m
etr
ic,
wh
ich
p
en
alize
s
p
er
s
is
ten
t
er
r
o
r
s
a
t
later
tim
e
in
s
tan
ts
an
d
is
co
n
s
is
ten
t
with
th
e
o
p
tim
i
za
tio
n
o
b
jectiv
e,
is
s
ig
n
if
ican
tly
s
m
aller
f
o
r
PID
-
FP
A,
p
ar
ticu
lar
ly
in
th
e
lem
n
is
ca
te
ca
s
e
(
5
.
3
6
3
8
4
7
v
s
6
.
1
8
3
6
8
3
)
.
T
h
is
in
d
icate
s
f
aster
er
r
o
r
atten
u
atio
n
a
n
d
im
p
r
o
v
e
d
s
tead
y
-
s
tate
tr
ac
k
in
g
p
er
f
o
r
m
a
n
ce
.
Ov
er
all,
t
h
e
r
esu
l
ts
d
em
o
n
s
tr
ate
th
at
th
e
FP
A
-
b
ased
PID
co
n
tr
o
ller
p
r
o
v
id
es
m
o
r
e
ac
cu
r
ate
an
d
ef
f
icien
t
3
D
tr
ajec
to
r
y
tr
ac
k
in
g
t
h
an
its
PS
O
-
b
ased
co
u
n
ter
p
a
r
t,
esp
ec
ially
f
o
r
tr
aj
ec
to
r
ies
with
h
ig
h
e
r
cu
r
v
atu
r
e
an
d
d
y
n
am
ic
co
m
p
lex
ity
.
Ov
er
all,
th
e
PID
-
FP
A
co
n
tr
o
ller
ac
h
iev
es
f
aster
co
n
v
er
g
en
ce
,
s
m
o
o
th
er
r
esp
o
n
s
es,
an
d
im
p
r
o
v
e
d
d
am
p
i
n
g
ch
ar
a
cter
is
tics
co
m
p
ar
ed
to
PID
-
PS
O,
wh
ich
is
co
n
s
is
ten
t
with
th
e
s
u
p
er
io
r
q
u
an
tit
ativ
e
tr
ac
k
in
g
m
etr
ics
an
d
co
n
f
ir
m
s
th
e
h
ig
h
er
ef
f
icien
cy
o
f
th
e
f
l
o
wer
p
o
llin
atio
n
alg
o
r
ith
m
f
o
r
PID
g
ain
o
p
tim
izatio
n
.
T
ab
le
4
.
Qu
a
n
titativ
e
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
m
etr
ics
M
e
t
h
o
d
Tr
a
j
e
c
t
o
r
y
R
M
S
E
M
A
E
I
A
E
I
TA
E
P
I
D
-
FPA
C
i
r
c
u
l
a
r
0
.
1
4
3
8
6
5
0
.
0
5
0
9
8
3
1
.
5
2
2
9
3
4
1
2
.
7
0
0
3
4
4
Le
mn
i
sc
a
t
e
0
.
1
3
7
2
0
4
0
.
0
3
2
7
9
4
0
.
9
7
7
1
5
4
5
.
3
6
3
8
4
7
P
I
D
-
PSO
C
i
r
c
u
l
a
r
0
.
1
4
9
2
9
4
0
.
0
5
8
1
7
2
1
.
7
3
8
6
5
3
1
2
.
9
3
7
6
5
1
Le
mn
i
sc
a
t
e
0
.
1
4
7
1
3
6
0
.
0
4
3
1
1
6
1
.
2
8
6
9
0
9
6
.
1
8
3
6
8
3
Fro
m
a
co
m
p
u
tatio
n
al
p
er
s
p
e
ctiv
e,
b
o
th
PS
O
an
d
FP
A
b
elo
n
g
to
p
o
p
u
latio
n
-
b
ased
m
et
ah
eu
r
is
tic
o
p
tim
izatio
n
alg
o
r
it
h
m
s
.
PS
O
u
p
d
ates
p
ar
ticle
v
elo
cities
an
d
p
o
s
itio
n
s
u
s
in
g
lo
ca
l
an
d
g
l
o
b
al
b
est
s
o
lu
tio
n
s
,
wh
ile
FP
A
r
elies
o
n
g
lo
b
al
p
o
llin
atio
n
b
ased
o
n
L
év
y
f
lig
h
ts
an
d
lo
ca
l
p
o
llin
atio
n
m
ec
h
an
is
m
s
.
Alth
o
u
g
h
b
o
th
al
g
o
r
ith
m
s
h
av
e
co
m
p
a
r
ab
le
co
m
p
u
tatio
n
al
co
m
p
lex
ity
d
ep
e
n
d
in
g
o
n
p
o
p
u
latio
n
s
ize
an
d
iter
atio
n
n
u
m
b
er
,
FP
A
o
f
ten
r
eq
u
ir
es
f
ewe
r
iter
atio
n
s
to
co
n
v
er
g
e
to
war
d
h
ig
h
-
q
u
ality
s
o
lu
tio
n
s
d
u
e
to
its
b
alan
ce
b
etwe
en
g
lo
b
al
e
x
p
lo
r
atio
n
an
d
lo
ca
l e
x
p
l
o
itatio
n
.
4
.
5
.
Ro
bu
s
t
nes
s
t
est
un
der
wind
di
s
t
urba
nce
s
A
win
d
p
r
o
f
ile
is
i
n
tr
o
d
u
ce
d
as
an
ex
ter
n
al
d
is
tu
r
b
an
ce
t
o
ass
ess
th
e
r
o
b
u
s
tn
ess
o
f
th
e
q
u
a
d
r
o
to
r
co
n
tr
o
l
s
y
s
tem
.
I
n
ac
c
o
r
d
an
ce
with
th
e
r
esu
lts
o
f
th
e
p
r
ev
io
u
s
s
u
b
s
ec
tio
n
,
wh
er
e
t
h
e
FP
A
-
tu
n
ed
PID
co
n
tr
o
ller
was
s
elec
ted
d
u
e
to
its
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
to
th
e
PS
O
-
b
ased
ap
p
r
o
ac
h
,
th
e
r
o
b
u
s
tn
ess
an
aly
s
is
is
co
n
d
u
cte
d
u
s
in
g
t
h
e
FP
A
-
PID
co
n
tr
o
ller
.
T
h
e
o
b
jectiv
e
is
to
ev
alu
ate
its
ca
p
ab
ilit
y
to
m
ain
tain
ac
cu
r
ate
tr
ajec
to
r
y
tr
ac
k
in
g
u
n
d
er
en
v
i
r
o
n
m
e
n
tal
p
er
tu
r
b
atio
n
s
.
T
h
e
win
d
v
el
o
city
co
m
p
o
n
e
n
ts
alo
n
g
th
e
h
o
r
izo
n
tal
ax
es a
r
e
d
ef
in
ed
as:
{
(
)
=
[
1
+
(
0
.
7
)
+
0
.
5
(
0
.
5
)
]
+
(
)
(
)
=
[
1
+
1
.
2
(
0
.
7
+
/
3
)
]
+
(
)
(
1
8
)
T
h
e
tu
r
b
u
len
t c
o
m
p
o
n
e
n
ts
ev
o
lv
e
ac
co
r
d
in
g
to
th
e
f
o
llo
win
g
s
to
ch
asti
c
d
if
f
er
en
ce
eq
u
atio
n
s
:
{
(
)
=
(
−
)
+
√
1
−
²
(
)
,
=
−
(
)
=
(
−
)
+
√
1
−
²
(
)
,
=
−
(
1
9
)
T
h
e
ef
f
ec
t
o
f
win
d
o
n
t
h
e
q
u
a
d
r
o
to
r
is
th
en
m
o
d
eled
t
h
r
o
u
g
h
ae
r
o
d
y
n
am
ic
d
r
ag
f
o
r
ce
s
ac
tin
g
alo
n
g
ea
c
h
ax
is
,
ex
p
r
ess
ed
u
s
in
g
th
e
class
ical
q
u
ad
r
atic
d
r
a
g
f
o
r
m
u
latio
n
:
{
=
1
2
2
=
1
2
2
(
2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.