Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 19
8
~
20
4
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.9
340
1
98
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
A Method for Attitude Control
Based on a Math
ematical M
o
del
for an Inverted Pendulum-Type Mobile Robot
J
i
n-Ho Yoo
n
*, My
ung-J
i
n
C
h
ung**
* Department of
New Technol
og
y
Conv
ergen
c
e,
Korea Poly
techn
i
c Univ
ersity
, K
o
rea
** Departm
e
n
t
o
f
M
echa
t
roni
cs
Engine
ering,
Ko
rea P
o
l
y
t
echn
i
c
Univers
i
t
y
,
Kore
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 21, 2015
Rev
i
sed
No
v
10
, 20
15
Accepted Nov 29, 2015
Amethod for attitude control bas
e
d on a
mathem
atical model for
an inver
t
ed
pendulum-ty
p
e
mobile robot was propos
ed. The inverted pen
dulum-ty
p
e
mobile robot w
a
sdesigned
and
the ma
th
ematical modeli
ng was
conducted.
The param
e
ters
of the m
obile ro
bot were es
tim
at
ed and the s
t
a
t
e-
s
p
ace m
odel
of mobile robot
was obtain
e
d b
y
the s
ubstitution of
the es
timated parameters
into the mathematical model. The tran
sfer fu
nctionof th
e mo
bile robot is
applied to gen
e
rate
the root-
l
ocus di
agram
us
ed for the es
t
i
m
a
tion of th
e
gains of
the PI
D controller
. The a
ttitude
control method
including a PID
controller, non-
linear elements, and
integr
al
saturation prev
ention was
designed and simulated. Th
e experi
ment was conducted b
y
apply
i
ng the
m
e
thod to the m
obile robot. In the attitud
e
control exp
e
rim
e
nt, th
e
perform
ance o
f
atti
tude r
ecov
e
r
y
from
± 12° tilt
e
d
init
ial
stat
ewit
h a set
tling
time of 0.98s
an
d a per
cent over
s
hoot of
40.1%
was obtained
.
F
u
rthermore,
the
attitude main
taining
robustne
ss against d
i
stur
bance wasverif
ied.
Keyword:
Attitu
d
e
con
t
rol
Di
st
ur
ba
nce
I
n
v
e
r
t
ed
p
e
ndulu
m
Mathem
a
tical m
odel
M
obi
l
e
r
o
bot
PID con
t
ro
ller
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
y
ung
-Ji
n
C
h
un
g,
Depa
rt
m
e
nt
of M
echat
ro
ni
cs En
gi
neeri
n
g
,
Korea Po
lytech
n
i
c Un
iv
ersity,
23
7,
Sa
ngi
dae
h
ak
-R
o
,
Si
heu
n
g
-
Si
,
Gy
e
o
n
g
g
i
-
Do
, K
o
rea P
o
l
y
t
echni
c
U
n
i
v
ersi
t
y
, R
e
pu
bl
i
c
of
K
o
rea
.
Em
a
il: m
j
ch
u
n
g
@
kp
u.ac.k
r
1.
INTRODUCTION
In
rece
nt
t
i
m
es, se
veral
pl
at
f
o
rm
s fo
r m
obi
l
e
ro
b
o
t
ha
ve
been
p
r
op
ose
d
by
m
a
ny
m
a
nu
fact
u
r
i
n
g
com
p
anies. The PUMA,
whi
c
h is a vehicle-type m
obile
ro
bo
t fo
r sh
ort d
i
stan
ce tran
spo
r
tation
,
is d
e
velo
p
e
d
by
Se
gway
.
The
TB
ot
,
de
vel
o
ped
by
I
H
M
C
, i
s
a
n
i
nve
rt
ed
pe
nd
ul
um
-
typ
e
m
o
b
ilerobo
t fo
r
mil
itary
ap
p
lication
s
an
d is a reconfigu
r
ab
le ro
bot th
at can
s
w
i
t
ch bet
w
een a
four-w
heele
d
and a two-wheeled
co
nf
igu
r
ation. A
s
an
indu
str
i
al ser
v
ice ro
bot, th
e EMI
E
W
1
, h
a
v
i
n
g
a human
o
i
d-
typ
e
up
p
e
r
bod
y an
d a tw
o-
wheel
-type lower
body, and the EMIE
W2
havi
ng a hum
a
noi
d-type
body ar
e propose
d by Hitac
h
i. In recent
t
i
m
e
s, num
erous resea
r
ches
has bei
n
g co
n
duct
e
d o
n
i
n
v
e
rt
ed pe
n
dul
u
m
-ty
p
e t
w
o-
w
h
eel
ed m
obi
l
e
rob
o
t
s
because of the
i
r adva
ntages
suc
h
as low powe
r cons
um
ption, light wei
ght, sim
p
le
confi
g
uration, excellent
ex
p
a
nd
ab
ility, an
d
a wi
d
e
area o
f
app
licatio
n
s
[1
], [2
],
[3
], [4
], [5
]. Since th
e in
v
e
rted
pen
d
u
l
u
m
-typ
e m
o
b
i
l
e
robo
t h
a
s un
stab
le ch
aracteristics in
th
e sy
ste
m
co
n
f
ig
u
r
atio
n
,
h
i
g
h
techn
o
l
o
g
i
es su
ch
as p
r
ecision
attitu
de
sen
s
ing
and
con
t
ro
l alg
o
r
it
h
m
are requ
ired
fo
r rob
u
s
t attitu
d
e
b
a
lan
c
e [6
], [7
], [8
]. Fu
rt
herm
o
r
e, a co
mb
in
ed
desig
n
i
n
clu
d
in
g the
m
echanism
,
hard
ware,
a
n
d
so
ftwa
re is
req
u
ire
d
[9]
.
In
this study, an attitude cont
rol m
e
thod
bas
e
d on
a m
a
them
atical m
odel fo
r an inve
rted pendul
um
-
t
y
pe m
obi
l
e
ro
bot
i
s
p
r
o
p
o
se
d.
The
i
n
vert
e
d
pen
d
u
l
u
m
-
t
ype m
obi
l
e
r
o
b
o
t
was
desi
g
n
e
d
an
d
param
e
t
e
rs we
re
estim
a
ted by
mathe
m
atica
l
m
odeling. The state-
space m
odel for mobile robot was obtaine
d by the
su
bstitu
tio
n
of
th
e estim
a
t
ed
param
e
ters in
to
th
e m
a
th
e
m
at
ic
al
m
o
d
e
l. Th
e t
r
an
sfer fu
n
c
ti
on
o
f
m
o
b
ile rob
o
t
is
appl
i
e
d t
o
gen
e
rat
e
t
h
e ro
ot
-l
ocu
s
di
ag
ram
use
d
fo
r t
h
e est
i
m
a
ti
on of t
h
e gai
n
s o
f
t
h
e PID c
ont
rol
l
e
r
.
The
attitu
d
e
con
t
rol
m
e
th
o
d
in
clud
ing
a PID con
t
ro
ller,
no
n-lin
ear elem
en
ts, and
i
n
teg
r
al
satu
ration
p
r
even
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
19
8 – 20
4
19
9
wasd
esi
g
ned
a
n
d
si
m
u
l
a
t
e
d. The e
x
p
e
ri
m
e
nt
was c
o
n
d
u
ct
ed
by
ap
pl
y
i
ng
t
h
e m
e
t
hod t
o
t
h
e m
obi
l
e
ro
b
o
t
.
I
n
th
e attitu
d
e
con
t
ro
l exp
e
rim
e
n
t
, th
e
p
e
rfo
rman
ce o
f
attitu
d
e
reco
v
e
ry fro
m
±1
2° tilted
in
itial state an
d
t
h
e
attitu
d
e
m
a
in
ta
in
in
g rob
u
s
t
n
ess of th
e rob
o
t
ag
ain
s
t
d
i
sturb
a
n
ce
was
v
e
ri
fied
.
2.
CO
NFIG
U
R
A
TIO
N
O
F
I
NVE
RTED
P
E
ND
ULU
M
T
Y
PE
MOBIL
E
ROBOT
The c
o
n
f
i
g
urat
i
on
of a
n
i
n
ve
rt
ed p
e
n
d
u
l
u
m
-
t
y
pe
m
o
b
ile ro
bo
tis as fo
llows: (Fi
g
ure 1), a sen
s
i
n
g
m
odulefor the
sensing t
h
e attitude
of t
h
e
body, a m
oving m
odule for m
ovi
ng the
body and
ge
nerati
ng the
inertia force
,
a control m
odule fo
r controlling the attitude
bala
nce,
and a c
o
m
m
u
n
ication m
o
dule for
tran
sferring
th
e d
a
ta
b
e
tween
t
h
e m
o
b
ile ro
bot an
d th
e m
a
in
com
puter.
(a)
(
b
)
Fi
gu
re
1.
C
o
nfi
g
u
r
at
i
o
n
of a
n
i
nve
rt
ed
pe
n
dul
um
-t
y
p
e
m
obi
l
e
r
o
b
o
t
;
(a
) c
o
n
t
rol
di
agram
,
(
b
)
r
o
b
o
t
pl
at
fo
r
m
3.
MAT
H
EM
AT
ICAL
M
O
DE
L
The m
a
t
h
em
atical
m
odel
of t
h
e i
n
v
e
rt
ed
pe
nd
ul
um
-t
y
p
e m
obi
l
e
robot
i
s
obt
ai
ne
d as t
h
e st
at
e-spac
e
m
odel
wi
t
h
t
w
o
deg
r
ees
o
f
f
r
eedom
usi
n
g t
h
e free
-
bo
dy
a
n
d t
h
e
ki
nem
a
t
i
c di
ag
ram
as sho
w
n i
n
Fi
g
u
r
e
2.
(a)
(
b
)
Fig
u
r
e
2
.
Fr
ee-b
od
y an
d k
i
n
e
matic d
i
ag
r
a
m
o
f
inv
e
r
t
ed p
e
nd
u
l
u
m
-
t
yp
e
m
o
b
ile ro
bo
t; (
a
)
w
h
eel, (b
) body
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Metho
d fo
r
Attitu
d
e
Con
t
ro
l Ba
sed on
a
Ma
th
ema
tica
l
Mod
e
l fo
r
an
In
verted …
(Myu
ng-
Jin
C
h
ung)
20
0
Fro
m
Figu
re 2(a), th
e equ
a
tion
for t
h
e m
o
tio
n
o
f
th
e wh
eel
is ob
tain
ed
u
s
in
g th
e
ho
rizon
t
al and
t
h
e
rot
a
t
i
o
nal
com
p
o
n
e
n
t
s
as
des
c
ri
be
d i
n
eq
uat
i
on
(
1
)
[
8
]
.
r
R
T
)
I
mr
(
H
2
2
2
(
1
)
Wh
ere, m
is th
e
m
a
ss, r is th
erad
i
u
s, I
w
is the
m
a
ss
m
o
m
e
n
t
o
f
in
ertia, and
θ
is th
e ang
l
e o
f
ro
tation
of t
h
e
wheel, respectively. T
w
is th
e t
o
rq
u
e
gen
e
rated
b
y
the wh
eel m
o
to
r
an
d R
H
is th
e su
m
o
f
th
e ho
ri
zo
n
t
al
com
pone
nts of
the reaction
force betwee
n the two wheels a
n
d the
body.
It
is
assum
e
d tha
t
the wheel
has
only
a ro
tatio
n
a
l m
o
tio
n
with
ou
t a
slid
in
g m
o
tio
n
.
From
Fi
gu
re
2
(
b
)
, t
h
e e
quat
i
on
f
o
r t
h
e m
o
t
i
on
of
t
h
e
b
o
d
y
i
s
obt
ai
ne
d
u
s
i
ng t
h
e
ho
ri
zo
nt
al
an
d t
h
e
rot
a
t
i
o
nal
com
p
o
n
e
n
t
s
as
des
c
ri
be
d i
n
eq
uat
i
on
(
2
).
T
sin
MgL
cos
MrL
)
ML
I
(
p
2
2
(
2
)
Whe
r
e, I
p
is th
e
m
a
ss
m
o
m
e
n
t
o
f
in
ertia, M is th
e
m
a
ss, and
φ
is th
e ang
l
e o
f
ro
tation
of
th
e bo
d
y
,
respectively. L
is the
distanc
e
betwee
n t
h
e
center
of
ma
s
s
of
th
e wh
e
e
l
s (
A
)
and
th
e ce
n
t
e
r
o
f
ma
s
s
o
f
th
e
bo
dy
(G
).
From
Fi
gu
re
2
(
a) a
n
d
2(
b)
, R
H
i
s
obt
ai
ned
u
s
i
ng t
h
e
ho
ri
zo
nt
al
an
d r
o
t
a
t
i
onal
m
o
t
i
on
o
f
t
h
e
wheel
and
b
o
d
y
as
de
scri
be
d i
n
eq
ua
t
i
on
(3
).
2
sin
ML
cos
ML
Mr
R
H
(
3
)
By su
b
s
titu
tin
g th
e eq
u
a
tion
(3
) in
eq
u
a
ti
o
n
s
(1
) and
(2
), and
lin
earizing
at th
e eq
u
ilibrium p
o
i
n
t
φ
=
0, t
h
e e
quat
i
on
s o
f
m
o
t
i
on
fo
r
t
h
e
wheel
a
n
d
the body are
sim
p
lified as
foll
ows:
T
MrL
)]
I
r
)
M
m
[(
2
2
2
2
(
4
)
T
MgL
MrL
)
ML
I
(
p
2
2
(
5
)
In eq
uat
i
o
n (
4
)
and (
5
),
wheel
t
o
rq
ue (T
w
) ca
n be desc
ri
be
d usi
n
g t
h
e eq
ui
val
e
nt
ci
rcui
t
o
f
t
h
e whee
l
m
o
to
r
as sh
own
in Figur
e
3
.
Fi
gu
re
3.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
t
h
e
DC
m
o
t
o
r
B
y
i
gnori
n
g i
n
duct
a
nce an
d t
h
e coe
ffi
ci
ent
of f
r
i
c
t
i
on
of t
h
e m
o
t
o
r, ap
pl
y
i
ng Ki
rc
h
h
o
f
f
'
s vol
t
a
ge
law, an
d using
th
e equ
a
tion
for th
e m
o
m
e
n
t
at th
e ax
is of
t
h
e m
o
to
r, th
e load
torq
u
e
is cal
cu
lated
as fo
llows:
m
m
a
a
T
m
a
b
T
L
J
V
R
K
R
K
K
T
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
19
8 – 20
4
20
1
Whe
r
e,
K
T
i
s
t
h
e t
o
r
que
co
ns
t
a
nt
, K
b
is
the
back em
f const
a
nt, R
a
is t
h
e resistance,
V
a
is th
e ap
p
lied
vol
t
a
ge
, a
n
d
J
m
is th
e m
o
m
e
n
t
of in
ertia of the m
o
to
r.
Wh
en
th
e
g
e
ar ratio
is
n
,
t
h
e wh
eel torqu
e
(T
w
) an
d t
h
e loa
d
to
rq
u
e
(T
L
) a
r
e rel
a
ted by
the
equat
i
o
nT
w
=nT
L
. T
h
e a
n
gula
r
displacem
ent of the
m
o
tor
(
θ
m
) and the a
n
gula
r
displace
ment of the
wheel (
θ
)
are related
b
y
th
e equ
a
tion
θ
=
(
θ
m
/n
) +
φ
, wh
ere th
e i
n
itial an
gu
lar
d
i
splace
m
e
n
t
is
φ
.
By su
b
s
titu
ting th
ese
rel
a
t
i
ons i
n
e
q
uat
i
o
n
(
6
)
,
t
h
e
wheel
t
o
r
q
ue i
s
desc
ri
be
d
by
t
h
e
fol
l
o
wi
n
g
e
quat
i
o
n:
2
2
2
2
n
J
n
J
V
R
K
n
n
R
K
K
n
R
K
K
T
m
m
a
a
T
a
b
T
a
b
T
(
7
)
By su
b
s
titu
ting th
e equ
a
tion
(7
) i
n
equ
a
tion
s
(4) and
(5), the eq
u
a
ti
o
n
s
o
f
m
o
t
i
o
n
are com
p
le
ted
.
Th
e
state-space m
odel is obtaine
d
by a
pplying t
h
e system
parameters, which
are calcula
ted and
m
easured [7],
a
s
descri
bed
i
n
e
q
uat
i
o
n
(
8
)
.
.
V
u
,
X
,
CX
Y
,
Bu
AX
X
a
T
(
8
)
Whe
r
e we ha
v
e
:
45
4
82
50
45
4
0
1
0
0
0
41
13
63
46
41
13
0
0
0
1
0
.
.
.
.
.
.
A
,
69
4
0
14
14
0
.
.
B
, a
n
d
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
C
.
4.
CO
NTR
O
L METHO
D
A
N
D
E
X
PE
RI
MENT
Although the
s
t
ate-space m
o
del has
t
w
o de
grees
of freedom
, the st
ate-space equation is
conve
rted
t
o
t
h
e t
r
a
n
s
f
er
f
unct
i
o
n a
s
gi
ve
n i
n
eq
uat
i
o
n
(
9
)
,
a
nd t
h
e
gai
n
s
of
t
h
e
PI
D c
ont
rol
l
e
r ca
n
b
e
est
i
m
a
t
e
d usi
n
g
t
h
e
ro
ot
-l
oc
us
di
a
g
ram
generat
e
d
fr
om
t
h
i
s
t
r
ans
f
er
f
unct
i
o
n.
2
889
82
50
86
17
69
4
2
3
.
s
.
s
.
s
s
.
)
s
(
V
)
s
(
)
s
(
G
a
(
9
)
The m
obile robotis unsta
b
le because it has
the poles
on the right plane
as
shown in
Figure 4(a).
Using
t
h
e
roo
t
-lo
c
u
s
d
i
agram
,
th
e rang
e
o
f
th
e
propo
rt
io
n
a
l
g
a
in fo
r th
e stab
ility o
f
th
e
syste
m
can b
e
esti
m
a
ted
in
the d
i
fferen
t cas
es
wh
ere
th
e PI o
r
th
e PID
co
n
t
ro
lleris u
s
ed
(Fig
ure 4
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Metho
d fo
r
Attitu
d
e
Con
t
ro
l Ba
sed on
a
Ma
th
ema
tica
l
Mod
e
l fo
r
an
In
verted …
(Myu
ng-
Jin
C
h
ung)
20
2
(a)
(
b
)
(c)
Figure 4.
Root-locus
dia
g
ram
for the
m
obile robot accordi
n
g to the
type
of controller use
d
; (a
) P control
l
er,
(b
) P
I
c
o
ntrolle
r,
(c)
PI
D c
o
ntr
o
ller
R
oot
-l
ocu
s
di
a
g
ram
of t
h
e m
obi
l
e
r
o
bot
ca
n be
cha
n
ged
by
ad
de
d zer
o
s
an
d p
o
l
e
s
us
i
ng t
h
e PI
o
r
PID
co
nt
r
o
l
l
e
r
as sh
o
w
n i
n
F
i
gu
res 4
(
b) a
n
d 4
(
c)
. E
quat
i
o
n
s (
1
0) a
n
d (
1
1)
desc
ri
be t
h
e
t
r
ans
f
er
fu
nct
i
on
o
f
the PI and PID controller. Fr
om these equations
, the positions
of t
h
e zer
os can
b
e
determin
ed
b
y
th
e gain
of
th
e con
t
ro
ller.
s
)
K
K
s
(
K
)
s
(
G
p
i
p
PI
(
1
0
)
s
)
K
K
s
K
K
s
(
K
)
s
(
G
d
i
d
p
d
PID
2
(
1
1
)
Whe
r
e,
K
p
is th
e
p
r
op
o
tion
a
l
g
a
in
, K
i
is th
e in
tegral g
a
i
n
, an
d K
d
is th
e
d
e
riv
a
tiv
e
g
a
in.
A tran
sfer functio
n
m
o
d
e
l can
n
o
t
reflect t
h
e in
itial state o
f
th
e tilted
bo
d
y
. By ap
p
l
yin
g
th
e state-
space m
odel a
n
d the
fee
dbac
k
from
the state va
riables,
the
attitude c
ontrol syste
m
including a
PID cont
roller,
no
n
-
l
i
n
ear el
e
m
ent
s
, an
d i
n
t
e
gral
sat
u
rat
i
o
n
pre
v
e
n
t
i
o
n
i
s
c
onst
r
uct
e
d i
n
t
h
e Si
m
u
l
i
nk as
sh
ow
n i
n
Fi
g
u
r
e
5.
Fig
u
re
5
.
Attitu
d
e
con
t
ro
l syste
m
co
n
s
tru
c
ted
in th
e
Sim
u
li
n
k
In
Figu
re
4
,
the p
r
op
ortion
a
l
g
a
in
is estim
at
ed
to
be
2
00
f
o
r a
perce
n
t
o
v
e
r
sh
o
o
t
o
f
30%
.
The i
n
t
e
g
r
al
and
deri
vat
i
v
e
gai
n
s are d
e
t
e
rm
i
n
ed by
t
h
e sim
u
l
a
t
i
on of t
h
e ro
ot
-l
ocu
s
di
agram
based o
n
t
h
e est
i
m
at
ed
p
r
op
ortio
n
a
l
gain
. Usi
n
g
th
e esti
m
a
ted
g
a
in
p
a
ram
e
ters, th
e p
e
rfo
r
m
a
n
ce o
f
t
h
e attit
u
d
e
con
t
ro
l syste
m
is
si
m
u
lated
with and
with
ou
t the ado
p
tion
of t
h
e
n
on-
lin
ear
ele
m
en
ts as show
n in
Figu
r
e
6.
-2
0
-1
5
-1
0
-5
0
5
10
-4
0
-3
0
-2
0
-1
0
0
10
20
30
40
0.
1
0.2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
0.
1
0.2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
10
20
30
10
20
30
P
Re
a
l
A
x
i
s
I
m
a
g
in
a
r
y
Ax
is
-2
0
-1
5
-1
0
-5
0
5
10
-4
0
-3
0
-2
0
-1
0
0
10
20
30
40
0.
1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.
1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
10
20
30
10
20
30
PI
Re
a
l
A
x
i
s
I
m
a
g
in
a
r
y
Ax
is
-2
0
-1
5
-1
0
-5
0
5
10
-4
0
-3
0
-2
0
-1
0
0
10
20
30
40
0.1
0.
2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.
2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
10
20
30
10
20
30
PI
D
Re
a
l
A
x
i
s
I
m
a
g
in
a
r
y
Ax
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
19
8 – 20
4
20
3
Fig
u
re
6
.
Sim
u
latio
n
resu
lt
o
f
attitu
d
e
con
t
ro
l sy
ste
m
with
an
d withou
t th
e
n
on-lin
ear elemen
ts
Th
e exp
e
rim
e
n
t
is co
n
d
u
c
ted
b
y
ap
p
l
ying
the d
e
v
e
l
o
p
e
d
attitu
d
e
con
t
ro
l syste
m
h
a
v
i
n
g
t
h
e esti
m
a
ted
co
n
t
ro
l
g
a
in to
th
e m
o
b
ile robo
t. Th
e i
n
itial state o
f
t
h
e m
o
bile rob
o
t
is tilted
b
y
±12
°
and
th
e ang
l
e is
redu
ced
an
d m
a
in
tain
e
d
at zero
b
y
attitu
d
e
co
n
t
ro
l.
Fig
u
re
7
sh
ows th
e
p
e
rform
a
n
ce
o
f
attitu
d
e
co
n
t
ro
l
u
s
ing
t
h
e PID
gai
n
s
obt
ai
ned
by
sim
u
l
a
t
i
on i
n
cl
u
d
i
n
g t
h
e c
o
m
p
ensat
i
o
n
f
o
r
di
st
u
r
ba
nce
.
The g
a
i
n
s
of
K
p
, K
i
, a
nd
K
d
are 1.1,
1
7
, an
d 0.01
resp
ectiv
ely. Tab
l
e 1 lists th
e
p
e
rform
a
n
ce of attitu
d
e
con
t
ro
l d
e
term
in
ed
fro
m
th
e ex
p
e
ri
m
e
n
t
an
d sim
u
latio
n
.
Fig
u
re
7
.
Attitu
d
e
con
t
ro
l
p
e
rform
a
n
ce u
s
in
g
th
e PID g
a
i
n
so
b
t
ai
n
e
d fro
m
sim
u
lat
i
o
n
Tab
l
e
1
.
Performan
ce of attitu
d
e
co
n
t
ro
l
Variable
Rising Ti
m
e
(s
)
%OS (%
)
Settling Ti
m
e
(s
)
Steady St
ate
Error
(deg)
E
xper
i
m
e
nt 0.
14
40.
1
0.
98
±0.
3
Sim
u
lation 0.
13
37.
0
0.
83
±0.
1
5.
CO
NCL
USI
O
N
The attitude c
o
ntrol m
e
thod
based
on a m
a
them
atical
m
odel for an i
nve
rt
ed pe
ndul
um
-type m
obile
ro
b
o
t
was
p
r
o
p
o
se
d. T
h
e i
nve
rt
ed
pe
nd
ul
um
-t
y
p
e m
obi
l
e
r
o
b
o
t
was
desi
g
n
ed
an
d t
h
e m
a
t
h
em
ati
cal
m
odel
i
n
g
was conducte
d. The
param
e
ters of m
obile robot were
est
i
m
a
ted and the
state-sp
ace model
of m
obile robot
was ob
tain
ed
b
y
th
e su
b
s
titu
tio
n
o
f
th
e esti
m
a
ted
p
a
rameters in
to
th
e
m
a
th
e
m
a
tica
l
m
o
d
e
l. Th
e tran
sfer
fu
nct
i
o
n o
f
m
obi
l
e
ro
b
o
t
i
s
ap
pl
i
e
d t
o
ge
nera
t
e
t
h
e ro
ot
-l
oc
us
di
agr
a
m
used f
o
r
t
h
e est
i
m
at
i
on
of t
h
e gai
n
s
of
th
e PID con
t
roller. Th
e attitud
e
con
t
ro
l m
e
t
h
od
in
cl
u
d
i
n
g
a PID con
t
ro
ller,
n
o
n
-
lin
ear
ele
m
en
ts, an
d
i
n
tegral
sat
u
rat
i
o
n p
r
e
v
ent
i
on
was
des
i
gne
d an
d si
m
u
l
a
t
e
d. T
h
e e
x
peri
m
e
nt
was con
d
u
ct
ed
by
appl
y
i
n
g
t
h
e sy
s
t
em
t
o
0
.
0
0
.2
0.4
0
.6
0.8
1
.0
1
.
2
1
.4
1
.
6
1
.8
2
.
0
-1
2
-1
0
-8
-6
-4
-2
0
2
4
6
R
o
tat
i
onal angle of
bod
y
(
deg)
Time
(
s
e
c
)
L
i
ne
ar
No
nl
i
n
ear
0.
0
0
.2
0.
4
0
.6
0.8
1
.
0
1.2
1
.
4
1.
6
1
.8
2.
0
-12
-10
-8
-6
-4
-2
0
2
4
6
Rota
ti
onal angle
of
body (deg)
Ti
me (
s
ec
)
Ex
peri
m
en
t
Si
m
u
l
a
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Metho
d fo
r
Attitu
d
e
Con
t
ro
l Ba
sed on
a
Ma
th
ema
tica
l
Mod
e
l fo
r
an
In
verted …
(Myu
ng-
Jin
C
h
ung)
20
4
th
e m
o
b
ile ro
bo
t. In
th
e attitu
d
e
con
t
ro
l exp
e
rim
e
n
t
, th
e
p
e
rform
a
n
ce of attitu
d
e
recov
e
ry fro
m
±1
2° tilted
in
itial sta
t
e wi
th
a settlin
g
ti
me o
f
0
.
9
8
s
an
d
a p
e
rcen
t ov
ersho
o
t
of 40.1
%
was ob
tain
ed. Furth
e
rmo
r
e, th
e
attitu
d
e
m
a
in
ta
in
in
g rob
u
s
t
n
ess ag
ai
n
s
t d
i
st
u
r
b
a
n
c
e was
v
e
ri
fied
.
ACKNOWLE
DGE
M
ENTS
Thi
s
w
o
r
k
wa
s sup
p
o
rt
e
d
b
y
t
h
e Nat
i
onal
R
e
search F
o
un
dat
i
o
n o
f
K
o
rea
Gra
n
t
fu
nde
d by
t
h
e
K
o
r
e
an
G
o
v
e
rn
m
e
n
t
(
3
1
Z
201
300
129
87)
.
REFERE
NC
ES
[1]
F.
Gra
sse
r
,
et al, "JOE:
A Mobil
e
, Inverted Pendulum",
IEEE T
r
ansactions on In
dustrial Elec
tronics,
vol. 49, p
p
.
107-114, 2002
.
[2]
T.S. Jin
,
"Command Fusion for
Navi
gation of M
obile Robo
ts in
D
y
na
m
i
c
Enviro
nm
ents
with Obj
ects
"
,
Journal of
information
and
communication
convergen
c
e
eng
i
neering
,
vol. 11
, pp
. 24-29
, 201
3.
[3]
D.
L.
Nguy
en and M.
E.
Lee,
"OSEK/VDX Portin
g to the
Two-Wheel Mobile Robot Base
d onthe Differential Drive
Method",
Journal of information
and communi
ca
tion convergenc
e eng
i
neering,
v
o
l. 10
, pp
. 372-3
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2.
BIOGRAP
HI
ES OF
AUTH
ORS
Jin-Ho Yoon received h
i
s B.S.
in
mechatron
i
cs
engineer
ing (201
4) from the Kor
ea Poly
techn
i
c
University
in Korea, wher
e heis currently
pur
suing the M.S. in new
technolo
g
y
conv
ergence
engineering
M
y
ung-Jin Chu
ng received his
M.S. in production
engineering (
1991) and a Ph
D in mechanical
engineering
(20
02) from
the Korea Advan
ced
In
stitute Sci
e
nce and Technolog
y
(
KAIST). Now
he is
a prof
es
s
o
r in
the
m
e
c
h
atroni
cs
engin
eering
dep
a
rtm
e
nt of
th
e Kor
ea P
o
l
y
t
echn
i
c
Univers
i
t
y
in K
o
rea. His
curr
en
t res
ear
ch int
e
re
s
t
s
include th
e c
ontrol of quadc
opter,
invert
ed
pendulum
-t
y
p
e m
obile robot
s, high-precis
io
n positioning
s
y
stem
s, and
sem
i
conductor
manufacturing
s
y
stems.
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