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s
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p
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[
2
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[
3
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[
4
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av
e
b
ee
n
alr
ea
d
y
d
o
n
e.
I
n
[
1
7
]
,
a
g
eo
m
et
r
ic
tr
ac
k
i
n
g
co
n
tr
o
l
s
y
s
te
m
o
n
S
O(
3
)
w
a
s
p
r
o
v
id
ed
to
av
o
id
s
in
g
u
lar
iti
es
an
d
a
m
b
i
g
u
itie
s
th
at
ar
e
i
n
h
er
e
n
t
to
o
th
er
att
itu
d
e
r
ep
r
esen
tatio
n
.
T
h
is
p
r
o
p
o
s
ed
tr
ac
k
in
g
co
n
tr
o
l
also
s
h
o
w
its
p
er
f
o
r
m
a
n
ce
to
s
tab
ilize
t
h
e
attit
u
d
e
er
r
o
r
w
it
h
o
u
t
t
h
e
k
n
o
w
led
g
e
o
f
t
h
e
i
n
er
tia
m
atr
i
x
.
I
n
[
1
8
]
,
a
r
o
b
u
s
t
ad
ap
tiv
e
tr
ac
k
i
n
g
co
n
tr
o
l
o
f
th
e
attit
u
d
e
d
y
n
a
m
i
cs
o
f
a
r
ig
id
b
o
d
y
w
a
s
p
r
o
p
o
s
ed
.
T
h
e
co
n
tr
o
ller
m
ad
e
a
tr
ac
k
in
g
f
o
r
an
attit
u
d
e
an
d
an
g
u
lar
v
elo
cit
y
co
m
m
a
n
d
w
it
h
o
u
t
k
n
o
w
led
g
e
o
f
t
h
e
in
er
tia
m
atr
i
x
o
f
a
r
ig
id
b
o
d
y
.
B
o
th
o
f
th
e
s
e
r
esear
ch
es
m
er
el
y
g
i
v
e
th
e
atti
tu
d
e
tr
ac
k
i
n
g
ap
p
r
o
ac
h
w
it
h
o
u
t c
o
n
s
id
er
in
g
th
e
co
n
tr
o
l to
r
q
u
e.
I
n
[
1
9
]
,
th
e
attitu
d
e
co
n
tr
o
lle
r
f
o
r
a
q
u
ad
r
o
to
r
b
ased
o
n
e
x
p
o
n
en
t
ial
co
o
r
d
in
ate
h
ad
b
e
en
alr
ea
d
y
d
o
n
e.
T
h
e
co
n
tr
o
ller
h
as
b
ee
n
d
esig
n
ed
u
s
in
g
T
LC
(
tr
aj
ec
to
r
y
li
n
ea
r
is
a
t
io
n
co
n
tr
o
l)
.
T
h
e
co
n
tr
o
ller
u
s
e
an
ex
p
o
n
en
t
ial
co
o
r
d
in
ates
an
d
an
g
u
lar
v
elo
cit
y
as
an
er
r
o
r
v
ar
iab
le
f
o
r
co
n
tr
o
ller
.
W
h
ile
in
[
1
9
]
u
s
es
a
v
ec
to
r
as
an
e
r
r
o
r
v
ar
iab
le,
a
r
o
tatio
n
m
atr
i
x
er
r
o
r
as
an
er
r
o
r
v
ar
iab
le
is
u
s
ed
as
a
n
in
p
u
t
o
f
t
h
e
co
n
tr
o
ller
in
[
2
0
]
.
I
n
[
2
0
]
,
a
PID
alg
o
r
ith
m
is
u
s
ed
an
d
a
k
n
o
w
led
g
e
o
f
an
g
u
l
ar
v
elo
cit
y
er
r
o
r
as
an
in
p
u
t to
co
n
tr
o
ller
is
n
ee
d
e
d
.
T
h
is
w
o
r
k
is
lo
o
k
li
k
e
f
o
c
u
s
in
r
esp
o
n
s
e
ti
m
e
o
f
t
h
e
r
o
to
r
.
I
n
th
i
s
p
ap
er
,
a
s
im
p
le
P
D
p
lu
s
Feed
f
o
r
w
ar
d
co
n
tr
o
ller
o
n
S
O(
3
)
w
it
h
a
r
o
tatio
n
m
atr
i
x
as
an
er
r
o
r
v
ar
iab
le
f
o
r
t
h
e
s
y
s
te
m
i
s
p
r
o
p
o
s
ed
.
T
h
is
co
n
t
r
o
ller
is
s
i
m
p
ler
t
h
a
n
th
e
co
n
t
r
o
ller
in
[
2
0
]
.
T
h
is
co
n
tr
o
ller
u
s
es
a
p
r
o
p
o
r
tio
n
al
-
d
er
iv
ati
v
e
al
g
o
r
ith
m
an
d
o
n
l
y
r
eq
u
ir
es
th
e
m
ea
s
u
r
e
m
en
ts
o
f
an
g
u
lar
v
elo
cit
y
f
r
o
m
d
y
n
a
m
ic
o
f
q
u
ad
r
o
to
r
to
ca
lcu
late
th
e
attit
u
d
e.
T
h
is
co
n
tr
o
ller
ca
n
s
tab
ilize
th
e
attit
u
d
e
o
f
q
u
ad
r
o
to
r
in
h
o
v
er
i
n
g
co
n
d
it
io
n
an
d
m
ak
in
g
a
m
o
tio
n
to
a
d
esire
d
attit
u
d
e.
2.
RE
S
E
ARCH
M
E
T
H
O
D
I
n
th
i
s
s
ec
tio
n
,
s
o
m
e
m
at
h
e
m
atica
l
to
o
ls
w
il
l
b
e
g
iv
e
n
f
o
r
r
o
tatio
n
p
ar
am
etr
izat
io
n
an
d
s
o
m
e
b
asi
c
k
n
o
w
led
g
e
o
f
L
ie
Gr
o
u
p
an
d
L
ie
A
l
g
eb
r
a.
2
.
1
.
M
a
t
he
m
a
t
ics o
f
Ro
t
a
t
i
o
n in SO
(
3
)
R
o
tatio
n
m
atr
i
x
i
s
a
3
x
3
m
atr
i
x
t
h
at
r
ep
r
ese
n
ts
th
e
tr
an
s
f
o
r
m
atio
n
v
ec
to
r
f
r
o
m
a
f
i
x
ed
-
b
o
d
y
f
r
a
m
e
to
an
in
er
tial
f
r
a
m
e.
R
o
tatio
n
m
a
tr
ix
is
a
L
ie
g
r
o
u
p
w
h
ic
h
h
as
an
alg
eb
r
aic
g
r
o
u
p
s
tr
u
ct
u
r
e
b
ased
o
n
m
atr
i
x
m
u
ltip
licatio
n
as
th
e
g
r
o
u
p
o
p
er
atio
n
.
A
cc
o
r
d
in
g
to
t
h
e
E
u
ler
t
h
eo
r
e
m
f
o
r
r
o
tates
b
o
d
y
,
an
y
3
-
d
i
m
e
n
s
io
n
al
r
o
tatio
n
o
f
a
r
i
g
id
b
o
d
y
ca
n
b
e
r
ep
r
esen
ted
b
y
a
r
o
tatio
n
o
f
a
g
iv
e
n
ax
i
s
b
y
an
an
g
le.
S
u
p
p
o
s
e
th
at
is
a
u
n
it
v
ec
to
r
th
at
s
p
ec
i
f
y
in
g
th
e
r
o
tatio
n
a
x
is
o
f
a
r
ig
id
b
o
d
y
,
an
d
is
a
r
o
tatio
n
an
g
le
in
r
ad
i
an
s
.
T
h
e
p
o
s
itio
n
o
f
a
p
o
in
t a
t th
e
r
i
g
id
b
o
d
y
as a
f
u
n
c
tio
n
o
f
ti
m
e
i
s
d
en
o
ted
b
y
q
(
t
)
.
I
f
th
e
b
o
d
y
is
r
o
tated
at
co
n
s
ta
n
t u
n
it
v
elo
cit
y
ab
o
u
t
th
e
ax
i
s
,
th
e
v
elo
cit
y
o
f
th
e
p
o
in
t c
an
b
e
w
r
itte
n
as
̇
̂
(
1
)
T
h
e
h
at
o
p
er
ato
r
m
ap
s
a
v
ec
t
o
r
in
to
a
s
k
e
w
-
s
y
m
m
etr
ic
m
atr
ix
,
d
ef
i
n
ed
as
̂
[
]
(
2
)
T
h
e
in
v
er
s
e
o
p
er
atio
n
o
f
th
e
h
at
o
p
er
ato
r
is
d
en
o
ted
as
a
v
ee
o
p
er
ato
r
,
w
h
ic
h
r
ec
o
v
er
a
v
ec
to
r
f
r
o
m
a
s
k
e
w
-
s
y
m
m
etr
ic
m
atr
i
x
̂
.
T
h
e
s
k
e
w
-
s
y
m
m
etr
ic
m
a
tr
ix
̂
s
atis
f
ie
s
̂
̂
.
A
ll
s
u
c
h
m
atr
ices
f
o
r
m
s
a
v
ec
to
r
s
p
ac
e
d
en
o
ted
as
s
o
(
3
)
:
{
}
(
3
)
T
h
e
ex
p
o
n
en
tial
m
ap
tr
a
n
s
f
o
r
m
s
a
s
k
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w
-
s
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m
m
etr
ic
m
atr
ice
s
in
to
an
o
r
th
o
g
o
n
al
m
atr
ice
s
.
Geo
m
etr
icall
y
,
t
h
e
s
k
e
w
-
s
y
m
m
etr
ic
m
atr
i
x
co
r
r
esp
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n
d
s
to
th
e
ax
is
o
f
r
o
tatio
n
(
v
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th
e
m
ap
p
i
n
g
̂
,
an
d
th
e
ex
p
o
n
en
tial
m
ap
g
en
er
ate
s
th
e
r
o
tatio
n
co
r
r
esp
o
n
d
in
g
to
th
e
r
o
tatio
n
ab
o
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t
th
e
a
x
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b
y
a
s
p
ec
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f
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a
m
o
u
n
t
.
So
th
e
ex
p
o
n
en
t
ial
m
ap
w
ill
m
ap
s
a
s
k
e
w
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y
m
m
etr
ic
m
atr
i
x
̂
to
an
o
r
th
o
g
o
n
al
m
atr
ix
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
5
6
6
–
575
568
(
̂
)
,
th
at
is
̂
̂
̂
̂
(
4
)
w
h
er
e
I
is
a
3
x
3
id
en
t
it
y
m
atr
i
x
,
is
a
r
o
tatio
n
an
g
le,
an
d
is
a
r
o
tatio
n
a
x
is
.
T
h
e
r
o
tatio
n
m
atr
i
x
is
a
th
r
ee
-
d
i
m
e
n
s
io
n
a
l sp
ec
ia
l
o
r
th
o
g
o
n
al
m
atr
ix
t
h
at
s
atis
f
i
es
(
5
)
E
q
u
atio
n
(
4
)
is
an
in
f
i
n
ite
s
e
r
ies
f
o
r
m
u
la.
T
o
o
b
tain
a
clo
s
ed
-
f
o
r
m
ex
p
r
es
s
io
n
f
o
r
̂
,
b
y
r
ef
er
r
ed
to
R
o
d
r
ig
u
es'
Fo
r
m
u
la,
an
e
f
f
ic
ie
n
t
m
e
th
o
d
f
o
r
co
m
p
u
t
in
g
̂
is
s
t
ated
as
̂
̂
̂
(
6
)
w
h
er
e
[
]
,
w
it
h
‖
‖
is
th
e
r
o
tatio
n
ax
is
,
an
d
is
a
r
o
tatio
n
an
g
le.
T
h
e
v
ec
to
r
is
t
h
e
ex
p
o
n
e
n
tial
co
o
r
d
in
ate
s
f
o
r
,
th
er
e
f
o
r
e,
a
r
o
tatio
n
m
at
r
ix
ca
n
b
e
ca
lc
u
lated
b
y
a
n
ex
p
o
n
en
t
ial
m
a
tr
ix
o
f
a
s
k
e
w
-
s
y
m
m
etr
ic
m
a
tr
ix
o
f
e
x
p
o
n
e
n
t
ial
co
o
r
d
in
ate
,
.
(
7
)
T
h
e
in
v
er
s
e
m
ap
p
in
g
f
r
o
m
a
n
o
r
th
o
g
o
n
a
l
m
atr
i
x
S
O(
3
)
to
a
s
k
e
w
-
s
y
m
m
e
tr
ic
m
atr
i
x
s
o
(
3
)
is
d
o
n
e
b
y
th
e
lo
g
ar
it
h
m
ic
m
ap
w
h
ic
h
is
d
e
f
i
n
ed
as
(
8
)
w
h
er
e
is
(
)
an
d
|
|
,
an
d
is
t
h
e
s
u
m
o
f
t
h
e
ele
m
e
n
t
s
o
n
th
e
m
ai
n
d
ia
g
o
n
al
o
f
r
o
tatio
n
m
a
tr
ix
.
I
f
,
th
e
r
o
tatio
n
ax
is
ca
n
b
e
ch
o
s
en
ar
b
itra
r
i
l
y
.
An
d
if
,
th
e
r
o
tatio
n
ax
is
ca
n
b
e
ca
lcu
lated
b
y
,
th
at
is
(
9
)
An
il
lu
s
tr
atio
n
o
f
a
r
o
tatio
n
w
it
h
a
n
a
x
i
s
a
n
d
an
g
le
o
f
r
o
tatio
n
ca
n
b
e
s
ee
n
in
Fig
u
r
e
1
,
w
h
er
e
[
]
is
a
r
ef
er
en
ce
co
n
f
ig
u
r
atio
n
,
a
n
d
[
]
is
a
p
r
ese
n
t
co
n
f
i
g
u
r
atio
n
.
Fro
m
Fig
u
r
e
1
,
a
r
ef
er
en
ce
co
n
f
ig
u
r
atio
n
p
w
ill
b
e
r
o
tated
b
y
a
n
an
g
le
t
o
a
p
r
esen
t
co
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e
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llu
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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SS
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o
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a
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as f
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s
:
[
]
,
(
1
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)
Fig
u
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2
.
Mo
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t
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o
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r
esp
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f
q
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10
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ca
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w
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as
[
]
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1
1
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T
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in
p
u
ts
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ad
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's
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y
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ts
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en
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y
[
]
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h
e
r
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t
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r
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en
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ate
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to
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e
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]
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r
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s
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T
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to
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d
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ated
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ip
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ad
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to
r
ar
e
g
iv
e
n
b
y
̇
̂
(
1
3
)
̇
,
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
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lec
&
C
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p
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g
,
Vo
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1
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Feb
r
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ar
y
2
0
1
8
:
5
6
6
–
575
570
w
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th
e
in
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tia
m
atr
i
x
i
n
th
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b
o
d
y
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ed
f
r
a
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;
,
is
th
e
an
g
u
lar
v
elo
cit
y
i
n
th
e
b
o
d
y
f
r
a
m
e;
,
is
th
e
r
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tatio
n
m
atr
i
x
as
a
tr
an
s
f
o
r
m
f
r
o
m
th
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b
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d
y
f
r
a
m
e
to
th
e
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er
tial
f
r
a
m
e
;
,
is
th
e
co
n
tr
o
l
to
r
q
u
e
g
e
n
er
ated
b
y
t
h
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ac
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r
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f
t
h
e
r
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b
o
t.
T
h
e
d
y
n
a
m
ics
o
f
q
u
ad
r
o
to
r
in
(
1
4
)
ca
n
b
e
r
e
w
r
itte
n
as
̇
,
(
1
5
)
an
d
t
h
e
q
u
ad
r
o
to
r
'
s
k
in
e
m
atic
s
i
n
(
1
3
)
,
r
ef
er
r
ed
f
r
o
m
[
2
1
]
,
th
is
d
if
f
er
en
tial
eq
u
atio
n
ca
n
b
e
r
e
w
r
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ten
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ter
m
s
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th
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n
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le
as
̇
(
̂
(
‖
‖
)
̂
‖
‖
)
(
1
6
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w
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⁄
⁄
is
a
b
o
d
y
a
n
g
u
lar
v
elo
cit
y
,
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d
is
an
ex
p
o
n
e
n
tial
co
o
r
d
in
ate
o
f
r
o
tatio
n
m
atr
ix
.
T
h
er
ef
o
r
e,
th
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s
ec
o
n
d
o
r
d
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s
y
s
te
m
o
f
q
u
ad
r
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to
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UA
V
i
n
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O(
3
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s
d
ef
i
n
ed
as
̇
(
̂
(
‖
‖
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‖
‖
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̇
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(
1
7
)
2
.
3
.
P
D
P
lus
F
ee
d
-
f
o
r
w
a
rd
C
o
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n SO
(
3
)
B
ased
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n
th
e
w
o
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k
s
o
f
B
u
llo
in
[
2
2
]
,
f
o
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s
im
p
le
f
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o
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s
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O(
3
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d
y
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m
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y
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m
w
it
h
s
tate
ev
o
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g
̇
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(
1
8
)
w
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G
is
a
L
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Gr
o
u
p
m
a
tr
ix
,
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th
e
co
n
f
i
g
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r
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n
o
f
s
y
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te
m
,
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d
is
th
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o
d
y
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el
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cit
y
.
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s
s
u
m
e
th
at
t
h
e
q
u
a
n
tit
y
o
f
ca
n
b
e
d
ir
ec
tly
co
n
tr
o
lled
to
an
y
d
esire
d
v
al
u
e
(
i.e
.
th
e
s
y
s
te
m
i
s
f
u
ll
y
ac
t
u
ated
)
.
T
h
en
th
e
p
r
o
p
o
r
tio
n
al
co
n
tr
o
l a
ctio
n
is
.
(
1
9
)
No
w
,
co
n
s
id
er
t
h
e
s
tab
ilizati
o
n
p
r
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b
lem
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ec
o
n
d
o
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s
y
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m
s
,
th
at
is
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o
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t
h
e
s
y
s
t
e
m
w
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er
e
h
av
e
f
u
ll
co
n
tr
o
l o
v
er
f
o
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ce
s
(
ac
ce
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atio
n
s
)
r
ath
er
th
a
n
v
e
lo
cities.
A
s
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o
n
d
o
r
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y
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te
m
o
n
S
O
(
3
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h
as t
h
e
f
o
r
m
̇
̇
,
(2
0)
w
h
er
e
is
t
h
e
co
n
f
ig
u
r
atio
n
o
f
t
h
e
s
y
s
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m
,
is
t
h
e
i
n
ter
n
al
d
r
if
t,
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n
d
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th
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co
n
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p
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t.
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o
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eg
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tit
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atr
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x
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p
r
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o
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tio
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al
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tio
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w
il
l
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e
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u
p
led
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it
h
a
d
er
iv
ativ
e
ter
m
,
i.e
.
w
it
h
a
ter
m
p
r
o
p
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tio
n
al
to
th
e
v
elo
cit
y
.
L
et
an
d
b
e
s
y
m
m
etr
ic,
p
o
s
itiv
e
d
e
f
in
ite
g
ain
s
.
T
h
en
t
h
e
co
n
tr
o
l la
w
is
,
(
2
1
)
ex
p
o
n
en
t
ia
ll
y
s
tab
ilize
s
th
e
s
t
ate
g
at
f
r
o
m
a
n
y
in
i
tial
co
n
d
itio
n
(
)
an
d
f
o
r
all
an
d
s
u
c
h
th
at
‖
‖
‖
‖
,
(
2
2
)
w
h
er
e
is
th
e
m
i
n
i
m
u
m
ei
g
e
n
v
alu
e
o
f
.
No
w
,
i
f
t
h
e
s
y
s
te
m
is
as
s
u
m
ed
as
a
q
u
ad
r
o
to
r
.
An
d
th
a
n
,
f
r
o
m
t
h
e
f
o
r
m
u
latio
n
ab
o
v
e,
i
f
is
r
ep
lace
d
w
ith
,
w
it
h
,
an
d
w
it
h
,
th
en
t
h
e
co
n
tr
o
l la
w
f
o
r
q
u
ad
r
o
to
r
is
,
(
2
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
ttit
u
d
e
C
o
n
tr
o
l o
f Q
u
a
d
r
o
to
r
Usi
n
g
P
D
P
lu
s
F
ee
d
fo
r
w
a
r
d
….
(
A
lmid
o
H
Gin
tin
g
)
571
Fig
u
r
e
3
.
B
lo
ck
Diag
r
a
m
w
h
er
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is
an
attit
u
d
e
o
f
q
u
ad
r
o
to
r
,
is
a
n
g
u
lar
v
elo
cit
y
i
n
b
o
d
y
f
r
a
m
e,
J
is
m
o
m
e
n
t
in
er
t
ia
o
f
q
u
ad
r
o
to
r
an
d
is
t
h
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co
n
tr
o
l
to
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q
u
e.
Usu
al
l
y
,
P
D
co
n
tr
o
l
u
s
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p
r
o
p
o
r
tio
n
al
an
d
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ati
v
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er
r
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ter
m
.
Fo
r
ex
a
m
p
le,
i
f
t
h
e
o
b
j
ec
tiv
e
is
t
o
co
n
tr
o
l
a
v
ar
iab
le
to
m
a
tc
h
th
e
co
n
s
ta
n
t
s
e
t
p
o
in
t
w
it
h
P
D
co
n
tr
o
l,
th
e
co
n
tr
o
l la
w
w
o
u
ld
b
e
̇
,
(
2
4
)
w
h
er
e
an
d
ar
e
p
r
o
p
o
r
tio
n
al
an
d
d
er
iv
ati
v
e
co
n
s
tan
t,
r
e
s
p
ec
tiv
el
y
.
W
ith
t
h
i
s
er
r
o
r
ter
m
,
if
th
e
is
ex
p
o
n
en
t
ial
co
o
r
d
in
ate
o
f
a
r
o
tatio
n
m
atr
i
x
,
th
e
E
q
u
atio
n
(
2
4
)
s
h
o
u
ld
b
e
w
r
it
ten
a
s
(
2
5
)
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
t
h
is
co
n
tr
o
ller
is
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
F
r
o
m
t
h
e
b
lo
ck
d
ia
g
r
a
m
o
f
co
n
t
r
o
ller
,
th
e
d
if
f
er
e
n
ce
b
et
w
ee
n
r
o
tatio
n
tar
g
et
m
atr
i
x
an
d
cu
r
r
en
t
r
o
tatio
n
m
atr
ix
w
il
l
b
e
ca
lcu
lated
in
m
u
ltip
licatio
n
o
f
m
atr
i
x
to
g
et
an
er
r
o
r
r
o
tatio
n
m
a
tr
ix
.
W
ith
t
h
is
m
u
ltip
l
y
o
p
er
atio
n
,
th
e
r
esu
lt
i
s
s
till
i
n
th
e
f
o
r
m
o
f
a
r
o
tatio
n
m
atr
i
x
,
w
h
ic
h
s
ati
s
f
y
an
d
.
T
h
e
r
o
tatio
n
cu
r
r
en
t
m
atr
ix
i
s
ca
lcu
lated
w
it
h
th
e
g
iv
e
n
a
n
g
u
lar
v
elo
cit
y
f
r
o
m
d
y
n
a
m
ic
m
o
d
el.
Fro
m
[
2
1
]
,
g
i
v
en
b
o
d
y
a
n
g
u
lar
v
elo
cit
y
,
th
e
w
h
ic
h
co
n
s
is
t o
f
ex
p
o
n
e
n
tial c
o
o
r
d
in
at
e
o
f
r
o
tatio
n
m
atr
i
x
ca
n
b
e
ca
lcu
lated
u
s
i
n
g
(
7
).
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
Her
e,
th
e
co
n
tr
o
ller
w
as
s
i
m
u
lated
i
n
3
ca
s
es.
I
n
th
e
f
ir
s
t
ca
s
e,
th
e
co
n
tr
o
ller
is
u
s
ed
t
o
d
r
iv
e
th
e
attitu
d
e
f
r
o
m
a
n
attit
u
d
e
co
n
d
i
tio
n
to
h
o
v
er
i
n
g
co
n
d
itio
n
.
I
n
th
e
s
ec
o
n
d
ca
s
e,
th
e
co
n
tr
o
ller
is
u
s
ed
to
co
n
tr
o
l
th
e
attit
u
d
e
f
r
o
m
h
o
v
er
i
n
g
co
n
d
itio
n
to
a
d
esire
d
attitu
d
e.
An
d
in
th
e
last
ca
s
e,
t
h
e
s
i
m
u
latio
n
s
h
o
w
s
t
h
e
ab
ilit
y
o
f
t
h
e
co
n
tr
o
ller
to
co
m
p
en
s
ate
an
at
tit
u
d
e
d
is
tu
r
b
an
c
e.
T
h
e
in
itial
an
d
tar
g
et
o
f
r
o
tatio
n
m
atr
i
x
ca
n
b
e
an
an
y
3x3
m
atr
i
x
,
w
h
er
e
th
e
m
a
tr
ix
s
atis
f
ies
th
e
co
n
d
itio
n
in
(
5
).
T
h
e
co
n
tr
o
lle
r
w
as
s
i
m
u
lated
in
6
DOF
eu
l
er
an
g
les
w
i
th
m
o
d
el
p
ar
a
m
et
er
o
f
q
u
ad
r
o
to
r
ar
e
cr
ea
ted
b
y
C
o
r
k
e
in
[
2
3
]
,
i.e
.
.
3
.
1
.
Ca
s
e
1
I
n
th
is
ca
s
e,
th
e
s
i
m
u
latio
n
will
s
h
o
w
t
h
e
p
er
f
o
r
m
an
ce
o
f
c
o
n
tr
o
ller
to
d
r
iv
e
an
attit
u
d
e
to
w
ar
d
a
h
o
v
er
i
n
g
co
n
d
itio
n
(
)
.
I
n
h
o
v
e
r
in
g
co
n
d
itio
n
,
w
ill
b
e
a
id
en
tit
y
m
atr
i
x
.
I
n
t
h
i
s
ca
s
e,
th
e
i
n
itial
attitu
d
e
o
f
q
u
ad
r
o
to
r
is
[
]
.
T
h
e
er
r
o
r
o
f
attitu
d
e
ca
n
b
e
ca
lcu
lated
b
y
m
u
ltip
l
y
in
g
t
h
e
tr
an
s
p
o
s
e
m
a
tr
ix
o
f
d
esire
d
attitu
d
e
w
it
h
t
h
e
in
itial a
tti
tu
d
e
o
f
q
u
ad
r
o
to
r
,
th
at
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
5
6
6
–
575
572
[
]
[
]
[
]
T
h
e
ex
p
o
n
en
t
ial
co
o
r
d
in
ates
o
f
th
e
er
r
o
r
o
f
attit
u
d
e
b
ec
o
m
e
an
in
p
u
t
to
th
e
co
n
tr
o
lle
r
,
to
ca
lcu
late
th
e
r
eq
u
ir
ed
to
r
q
u
e
f
o
r
th
e
s
y
s
te
m
to
ac
h
ie
v
e
t
h
e
d
esire
d
atti
tu
d
e.
T
h
e
r
esu
lt
o
f
t
h
e
s
i
m
u
l
atio
n
is
s
h
o
w
n
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
Si
m
u
latio
n
r
esu
l
t o
f
ca
s
e
1
I
n
Fig
u
r
e
4b
,
th
e
ex
p
o
n
e
n
ti
al
co
o
r
d
in
ate
o
f
th
is
ca
s
e
b
ec
o
m
e
s
[
]
w
h
e
n
t
h
e
s
y
s
te
m
i
s
co
n
v
er
g
e
n
t.
T
h
is
ex
p
o
n
e
n
tial
co
o
r
d
in
ates
v
ec
to
r
w
ill
b
e
tr
an
s
f
o
r
m
ed
in
to
a
s
k
e
w
-
s
y
m
m
etr
ic
m
atr
i
x
b
y
o
p
er
ato
r
,
an
d
th
e
attit
u
d
e
o
f
t
h
is
co
n
d
it
io
n
ca
n
b
e
ca
lcu
late
d
b
y
ex
p
o
n
e
n
tial
m
atr
i
x
o
f
t
h
e
s
k
e
w
-
s
y
m
m
etr
ic
m
atr
i
x
o
f
ex
p
o
n
e
n
tial c
o
o
r
d
in
ates a
s
s
h
o
w
n
i
n
(
7
).
[
]
[
]
.
T
h
e
co
n
d
itio
n
d
escr
ib
es
t
h
at
t
h
e
q
u
ad
r
o
to
r
h
a
s
n
o
r
o
tatio
n
o
r
in
h
o
v
er
i
n
g
co
n
d
itio
n
,
t
h
e
s
a
m
e
as
th
e
r
o
tatio
n
tar
g
et
in
th
i
s
ca
s
e.
T
h
e
r
o
tatio
n
an
g
le
is
0
r
ad
as
s
h
o
w
n
i
n
Fi
g
u
r
e
4a
.
I
n
t
h
is
co
n
d
itio
n
,
w
h
ile
t
h
e
attit
u
d
e
,
th
e
r
o
tatio
n
a
x
is
ca
n
b
e
ch
o
s
en
ar
b
itra
r
il
y
.
W
h
en
th
e
s
y
s
te
m
m
ee
t
s
co
n
v
er
g
e
n
ce
,
t
h
e
an
g
u
la
r
v
elo
cit
y
f
o
r
all
ax
is
ar
e
[
]
as
s
h
o
w
n
in
Fi
g
u
r
e
4c
.
T
h
e
s
tead
y
s
tate
in
th
i
s
s
y
s
te
m
i
s
r
ea
ch
e
d
in
3
s
ec
w
it
h
t
h
e
r
is
e
ti
m
e
is
ab
o
u
t 1
s
e
c.
3
.
2
.
Ca
s
e
2
I
n
t
h
e
s
ec
o
n
d
ca
s
e,
t
h
e
s
i
m
u
la
tio
n
w
i
ll
s
h
o
w
t
h
e
p
er
f
o
r
m
a
n
c
e
o
f
co
n
tr
o
ller
to
co
n
tr
o
l
th
e
q
u
ad
r
o
to
r
’
s
attitu
d
e
f
r
o
m
h
o
v
er
in
g
co
n
d
iti
o
n
to
a
d
esire
d
attitu
d
e.
I
n
th
is
ca
s
e,
th
e
in
itial
attit
u
d
e
is
a
id
en
tit
y
m
atr
i
x
an
d
th
e
d
esire
d
attit
u
d
e
is
[
]
T
h
e
er
r
o
r
o
f
attitu
d
e
in
th
is
s
ec
o
n
d
ca
s
e
ca
n
b
e
ca
lcu
lated
b
y
m
u
l
tip
l
y
i
n
g
th
e
tr
an
s
p
o
s
e
m
atr
i
x
o
f
d
esire
d
attitu
d
e
w
i
th
t
h
e
i
n
itia
l a
ttit
u
d
e
o
f
q
u
ad
r
o
to
r
,
th
at
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
ttit
u
d
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C
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tr
o
l o
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u
a
d
r
o
to
r
Usi
n
g
P
D
P
lu
s
F
ee
d
fo
r
w
a
r
d
….
(
A
lmid
o
H
Gin
tin
g
)
573
[
]
[
]
[
]
.
T
h
e
r
esu
lt
o
f
t
h
e
s
ec
o
n
d
ca
s
e
is
s
h
o
w
n
i
n
Fig
u
r
e
5
.
W
h
e
n
t
h
e
s
y
s
te
m
i
s
co
n
v
er
g
e
n
t,
th
e
v
alu
e
o
f
e
x
p
o
n
en
tial
co
o
r
d
in
ate
ar
e
[
]
as
s
h
o
w
n
i
n
F
ig
u
r
e
5b
,
an
d
t
h
e
attit
u
d
e
ca
n
b
e
ca
lcu
lated
b
y
t
h
e
s
a
m
e
w
a
y
as s
h
o
w
n
in
C
ase
1
,
th
at
is
[
]
[
]
.
Fig
u
r
e
5
.
Si
m
u
latio
n
r
esu
l
t o
f
ca
s
e
2
As
s
h
o
w
n
i
n
Fi
g
u
r
e
5a
an
d
t
h
e
v
alu
e
o
f
,
th
e
r
o
tatio
n
a
x
i
s
ca
n
b
e
ca
lcu
lated
b
y
(
9
)
,
t
h
at
i
s
[
]
.
T
h
is
m
ea
n
s
t
h
at
t
h
e
q
u
ad
r
o
t
o
r
is
r
o
tated
w
it
h
t
h
is
r
o
tatio
n
ax
is
,
a
n
d
r
o
tates
ab
o
u
t
1
.
2
8
7
r
a
d
(
7
3
.
4
d
eg
r
ee
)
.
T
h
e
v
alu
e
o
f
an
g
u
lar
v
e
lo
cit
y
in
Fi
g
u
r
e
5
c
in
d
icate
s
t
h
at
t
h
er
e
is
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o
alter
atio
n
o
f
r
o
tatio
n
an
g
le
w
h
e
n
t
h
e
s
y
s
te
m
is
co
n
v
er
g
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
5
6
6
–
575
574
3
.
3
.
Ca
s
e
3
I
n
th
e
th
ir
d
ca
s
e,
th
e
s
i
m
u
lati
o
n
is
d
o
n
e
to
test
th
e
co
n
tr
o
ll
er
'
s
ab
ili
t
y
to
co
m
p
en
s
ate
t
h
e
d
is
tu
r
b
an
ce
o
f
th
e
s
y
s
te
m
.
T
h
e
co
n
tr
o
ller
is
s
i
m
u
la
ted
w
i
th
d
is
t
u
r
b
an
ce
b
y
[
]
in
attit
u
d
e
cu
r
r
en
t
,
w
it
h
t
h
e
in
itial
a
n
d
tar
g
et
o
f
attit
u
d
e
is
th
e
s
a
m
e
a
s
in
C
a
s
e
2
.
I
n
th
i
s
ca
s
e,
th
is
co
n
tr
o
ller
ca
n
p
r
eser
v
e
th
e
v
al
u
e
o
f
attitu
d
e
cu
r
r
e
n
t in
3
.
0
3
s
ec
as sh
o
w
n
in
F
ig
u
r
e
6a
.
W
h
en
a
d
is
t
u
r
b
an
ce
is
ad
d
ed
to
th
e
s
y
s
te
m
,
th
e
r
o
tatio
n
er
r
o
r
r
aises
b
y
0
.
0
6
p
o
in
t
in
x
-
a
x
is
a
n
d
th
e
co
n
tr
o
ller
d
r
iv
es
th
e
s
y
s
t
e
m
t
o
m
a
k
e
t
h
e
er
r
o
r
o
f
attit
u
d
e
b
ec
o
m
e
ze
r
o
in
3
.
0
3
s
ec
a
s
s
h
o
w
n
i
n
F
ig
u
r
e
6b
.
As
lo
n
g
as
t
h
e
s
y
s
te
m
i
s
ad
d
ed
b
y
a
d
is
t
u
r
b
an
ce
,
t
h
e
co
n
tr
o
ller
p
r
eser
v
es
er
r
o
r
in
ze
r
o
p
o
in
t.
W
h
e
n
t
h
e
d
is
tu
r
b
an
ce
i
s
eli
m
i
n
ated
f
r
o
m
t
h
e
s
y
s
te
m
,
r
o
tatio
n
er
r
o
r
in
t
h
is
s
y
s
t
e
m
is
r
ed
u
ce
d
f
r
o
m
ze
r
o
p
o
in
t
to
p
o
in
t
-
0
.
0
6
.
I
n
ab
o
u
t
3
s
ec
,
t
h
e
co
n
tr
o
ller
ca
n
d
r
iv
e
th
e
t
h
e
s
y
s
te
m
to
th
e
d
esire
d
attit
u
d
e,
an
d
th
e
r
o
tatio
n
er
r
o
r
b
ec
o
m
es
ze
r
o
w
h
e
n
th
e
s
y
s
te
m
m
ee
t
s
co
n
v
er
g
en
ce
.
B
ased
o
n
all
o
f
th
e
ca
s
e
s
,
r
o
tatio
n
er
r
o
r
m
atr
ix
i
s
a
3
x
3
id
en
tit
y
m
atr
i
x
w
h
e
n
t
h
e
s
y
s
te
m
is
co
n
v
er
g
e
n
t.
T
h
e
s
tead
y
s
tate
ti
m
e
i
s
ab
o
u
t
3
s
ec
an
d
th
e
r
is
e
ti
m
e
i
s
ab
o
u
t 1
s
ec
f
o
r
all
ca
s
es.
6a
6b
Fig
u
r
e
6
.
Si
m
u
latio
n
r
esu
l
t o
f
ca
s
e
3
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2012
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l.
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2
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p
.
1
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2
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4
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p
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5
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3
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4
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ss
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n
,
M
.
Ottes
tad
,
a
n
d
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.
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v
lan
d
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m
,
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2013
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ter
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l
Co
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ma
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ms
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p
p
.
4
8
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-
4
8
5
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2
0
1
3
.
[1
5
]
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F
re
sk
a
n
d
G
.
Nik
o
lak
o
p
o
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l
o
s
,
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u
ll
Qu
a
tern
i
o
n
Ba
se
d
A
tt
it
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d
e
Co
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Qu
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ro
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o
r
,
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2
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1
3
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ro
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e
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e
(
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p
p
.
3
8
6
4
-
3
8
6
9
,
2
0
1
3
.
[1
6
]
K.
D.
Do
, "
G
lo
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a
l
T
ra
c
k
in
g
Co
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tro
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d
ro
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e
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m
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n
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l
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p
a
c
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201
5
In
ter
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J
o
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rn
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f
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b
o
ti
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n
d
Au
t
o
ma
ti
o
n
(
IJ
CRA
)
,
v
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l.
3
,
N
o
.
1
,
p
p
.
13
-
29
,
2
0
1
5
.
[1
7
]
T
.
L
e
e
,
"
Ge
o
m
e
tri
c
T
ra
c
k
in
g
Co
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o
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A
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it
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m
i
c
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o
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Rig
id
Bo
d
y
o
n
S
o
(3
)
,
"
201
1
A
me
ric
a
n
Co
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tro
l
Co
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fer
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e
,
p
p
.
1
2
0
0
-
1
2
0
5
,
2
0
11.
[1
8
]
T
.
Lee
,
"
Ro
b
u
st
A
d
a
p
ti
v
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tt
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tu
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ra
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d
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r
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V
,
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ra
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c
ti
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l
S
y
ste
ms
T
e
c
h
n
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y
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l.
2
1
,
No
.
5
,
p
p
.
1
9
2
4
-
1
9
3
0
,
2
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