TELKOM
NIKA
, Vol. 11, No. 5, May 2013, pp. 2315 ~
2322
ISSN: 2302-4
046
2315
Re
cei
v
ed
Jan
uary 21, 201
3
;
Revi
sed Fe
brua
ry 27, 20
13; Accepted
March 12, 20
13
Real-time Pose Measurement of Parallel Robot
Based on GRNN
Gao Guo
q
in*
,
Zhang Zhigang, Niu Xue
m
ei
Schoo
l of Elect
r
ical & Informat
i
on En
gin
eer
in
g, Jiangs
u Uni
v
ersit
y
301,
Xuef
u Ro
ad, Z
henj
ia
ng, 212
01
3, Jiangs
u Provinc
e
, P.R.Chin
a, 00
86-
511-
887
91
24
5
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: gqga
o@u
j
s.e
du.cn
A
b
st
r
a
ct
T
he real-ti
m
e pose
me
asure
m
e
n
t of
paral
le
l robot he
lps to
achiev
e the cl
osed l
oop p
o
s
e
contro
l
and i
m
prov
e
th
e
contro
l
a
nd o
perati
ng perfor
m
a
n
ce of
par
al
lel r
obot. But
it is difficu
lt to i
m
ple
m
ent the r
e
al-
time
pos
e
me
asure
m
ent dir
e
ctly. In order to solv
e the p
o
s
e meas
ure
m
e
n
t prob
le
m of
a 6-DOF
par
al
le
l
robot, th
e ki
ne
matics
a
nalys
is
of th
e
para
lle
l
robot
is
made,
and
a
Gen
e
ral
i
z
e
d
Regr
essi
o
n
N
eura
l
Netw
ork
w
h
ich has fast
converg
enc
e
and stro
ng n
o
n
lin
ear
mapp
in
g abi
lity is est
ablis
he
d by se
tting the d
e
sir
e
d
pose
and
its in
verse kin
e
m
ati
cs results as the n
eura
l
netw
o
rk traini
ng sa
mp
les to i
m
ple
m
e
n
t the
map
o
f
para
lle
l robot
from the jo
int
variabl
e spac
e to t
he w
o
rk variabl
e spac
e. F
i
nally, the
real-ti
m
e pos
e
me
asur
e
m
ent
of par
all
e
l ro
bo
t is ach
i
eve
d
b
y
usin
g
the
trai
ned
ne
ural
net
w
o
rk and th
e a
c
tual
moti
on st
at
e
s
of the active jo
ints easily
dete
c
ted.
T
he simu
latio
n
exper
i
m
ent results
sho
w
that
the met
hod of meas
uri
n
g
the par
all
e
l r
o
bot pos
e b
a
se
d on th
e GRN
N
has th
e fa
ster conv
erge
nc
e rate a
nd
hig
her
me
asure
m
en
t
accuracy tha
n
those of the BPNN and RBF
NN methods.
T
he researc
h
establ
ishes the
basis for the direc
t
close
d
control
of paral
lel ro
bo
t pose.
Ke
y
w
ords
: Pa
ralle
l Ro
bot, Pose Meas
ure
m
ent, Kinem
a
tics Analysis, GRNN
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Comp
ared wi
th
the se
rial robot
s
[1, 2],
pa
ra
llel
ro
bo
ts have
the
a
d
vantage
s
of high
er
rigidity, highe
r accu
ra
cy, faster
re
spon
se
spee
d an
d hi
gher l
oad
cap
a
city, and ha
ve dra
w
n g
r
e
a
t
intere
st in both aca
demia a
nd indu
st
ry in
the last few decade
s [3, 4].
The en
d-effe
ctor p
o
se of parall
e
l ro
bot
is t
he impo
rt
ant perfo
rma
n
ce in
dex tha
t
reflects
parall
e
l robo
t motion st
ate and
system perfo
rm
ance. Imple
m
enting th
e
real
-time p
o
se
measurement
of parall
e
l robot is th
e
basi
s
of
the
clo
s
ed
-loo
p
cont
rol of p
a
rallel
rob
o
t. At
pre
s
ent, in t
he a
c
tual pa
rallel robot
system t
he m
o
tion state
s
of servo m
o
tors
are obtai
ned
mainly from
the e
n
code
rs,
but it i
s
difficult to
get
th
e re
al time
p
o
se
directly.
In re
cent ye
a
r
s,
there a
r
e
so
me re
sea
r
ch
es ab
out the
pose
mea
s
u
r
eme
n
t of pa
rallel robot. In [5] a feedb
ack
system of po
se mea
s
u
r
e
m
ent for parallel rob
o
t ba
sed o
n
vision
is desi
gned.
In [6] a immune
evolutiona
ry algorith
m
to
develop
a po
se me
as
ure
m
ent metho
d
for a p
a
rall
e
l
manipul
ator is
prop
osed. In
[7] a multi-se
nso
r
m
e
a
s
urement m
e
tho
d
which i
s
u
s
ed in
the
wh
o
l
e working
sp
ace
of pa
rallel
ma
nipulato
r
i
s
st
udied. In
[8] a
metho
d
b
a
se
d on
dete
c
tin
g
syn
c
h
r
on
ou
sly multi-bea
m
of po
sition
sensitive
dete
c
tor (PSD) i
s
propo
se
d. T
he m
e
a
s
ure
m
ent meth
od
for
pa
rallel
robot
based on the
vision ha
s a good flexibilit
y, but is su
sceptible to noi
se an
d light impact, an
d la
rge
errors will
be
brou
ght in for this re
ason [
9
]. The pa
rall
el rob
o
t po
se
measurement
method b
a
se
d
on immun
e
e
v
olutionary al
gorithm h
a
s
certain robu
st
n
e
ss, but is ea
sy to fall into
local mini
mu
m,
and h
a
s the
low p
r
e
c
isi
o
n [10]. The
parall
e
l ro
bot
pose mea
s
urem
ent met
hod b
a
sed o
n
addition
al se
nso
r
s altho
u
gh
can
be
u
s
ed
in th
e
whole
wo
rki
n
g
sp
ace, but i
t
introdu
ce
s
the
sen
s
o
r
in
stall
a
tion erro
r, the sen
s
o
r
e
rro
r, t
he data a
c
quisitio
n
syst
em error
and
so on [1
1]. The
PSD po
se
m
easure
m
ent
method
for
p
a
rallel
robot
h
a
s fa
st
re
spo
n
se
spee
d a
n
d
hig
h
re
solut
i
on,
but has the n
online
a
r e
rro
r [12].
Acco
rdi
ng to
the p
r
oble
m
s of p
a
rall
el robot
p
o
se m
easure
m
ent
mentione
d a
bove, th
e
method
s b
a
sed o
n
n
eural
netwo
rk
s
are
prop
osed to
i
m
pleme
n
t re
a
l
-time p
o
se m
easure
m
ent
s
of
parall
e
l rob
o
ts witho
u
t increasi
ng the ha
rdware co
sts
of parallel
rob
o
ts. At prese
n
t, the method
s
based
on th
e
BP neu
ral
net
work [13] a
n
d
RBF
neu
ra
l
netwo
rk [14]
have b
een
propo
sed
to
sol
v
e
the probl
em of the pose
measur
ement
of parallel robots. The B
P
neural net
work metho
d
is
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2315 – 232
2
2316
globally
conv
erge
nt, but is easy to fall i
n
to a
lo
cal m
i
nimum, an
d
the sp
eed
of conve
r
ge
nce
is
slo
w
. So it is difficult to meet the requi
reme
nt of the real
-time m
eas
ure
m
ent
and control [
15].
The RBF
ne
ural network
method ove
r
co
me
s
t
he
sho
r
tco
m
ing
s
of the BP
neural net
wo
rk
method, but for a co
mplex
parallel robo
t system
with
multi-deg
ree
of freedom, multi-varia
b
le
s,
high no
n-lin
e
a
rity and mu
lti-paramete
r
coupli
ng,
the stru
cture para
m
et
ers
are a
c
qui
re
d
b
y
mean
s of th
e
global
se
arch
to re
ach the
high
re
cog
n
ition a
c
curacy [
16]. And it is
unfavora
b
le f
o
r
the po
se me
a
s
ureme
n
t of p
a
rallel
ro
bot. GRNN
ha
s th
e strong n
onli
near
map
p
ing
ability and th
e
flexible netwo
rk
stru
cture, as
well a
s
th
e high
fault
-
to
leran
c
e and robu
st
ne
ss, can
overco
me the
shortcomings of RBF
neural
network, has go
od approxim
ation capab
ility and fast l
earning
spe
ed, and
can
pro
c
e
ss the unsta
bl
e data.
So
GRNN i
s
more
suitabl
e for the p
o
se
measurement
of parallel ro
bot.
In view of th
e above ana
lysis, for a 6
-
DOF paralle
l robot, a generali
z
e
d
reg
r
essio
n
neural net
work (G
RNN)
wh
ich h
a
s the fa
st co
nverg
e
n
c
e a
nd st
ron
g
nonline
a
r m
a
pping a
b
ility is
establi
s
h
ed
b
a
se
d o
n
the
kinem
atics a
nalysi
s
in
ord
e
r to
solve th
e po
se
me
asurem
ent p
r
ob
lem
of the
6-DOF
parall
e
l
rob
o
t. By setting
th
e de
si
re
d
po
se an
d it
s inve
rse
kinem
atics
re
sults a
s
t
he
neural netwo
rk trai
ning
sa
mples to trai
n the neural
netwo
rk, it can reali
z
e th
e map of parallel
robot
from
th
e joint va
riabl
e spa
c
e to
th
e work
va
riab
le spa
c
e, the
real
-time p
o
se mea
s
u
r
em
ent
of parallel
rob
o
t is
achieve
d
by u
s
in
g th
e train
ed
neu
ral n
e
two
r
k a
nd the
a
c
tual
motion
states of
the active join
ts easily dete
c
ted.
2. Kinematics Anal
y
s
is o
f
Parallel Robot
The pa
rallel
mech
ani
sm
of parall
e
l ro
bot studi
e
d
i
n
this pa
per is of 6-PT
RT type.
Figure.1 sho
w
s
a
sketch
of the pa
rallel
rob
o
t with
a
6-PTRT pa
ral
l
el me
chani
sm studi
ed in t
h
is
pape
r. Each
kinem
atic lim
b con
s
i
s
ts of
a prismatic j
o
int, a hoo
k Hing
e, a rev
o
lute joint an
d a
hoo
k hing
e. The pri
s
m
a
tic joint controll
ed by a moto
r ca
n ma
ke a
one-dimen
s
i
onal tra
n
sl
ational
movement in
a vertical
dire
ction. It is co
mpos
ed of a
AC se
rve mo
tor, a ball screw an
d a g
u
ide
bar. T
he
mov
i
ng pl
atform i
s
inve
rted. T
he
six limb
s
of the m
e
cha
n
ism
are d
r
iv
en by A
C
se
rvo
motors. The movement
s of the sliders drive
the ball screws an
d then make
the links int
o
a
certai
n an
gle
to achieve t
he de
sired m
o
vement
of the moving pl
atform. The
AC se
rvo d
r
ive
system
con
s
i
s
ts of an A
C
servo m
o
tor 500DC2
-T2
A
-B in the serie
s
FAL
D
IC-W GYS a
nd a
servo
amplifi
e
r RY
C5
00D3-VVT2. The
servo
moto
rs a
r
e
adde
d with 17
b
i
ts increm
ent
al
encode
rs to a
c
hieve the
clo
s
ed lo
op cont
rol of the bra
c
hes.
Figure 1. The
parallel m
e
chani
sm of a 6-DOF pa
rallel
robot
In ord
e
r to m
a
ke th
e ki
ne
matics analy
s
is of the p
a
ra
llel rob
o
t me
chani
sm, the
dynamic
and stati
c
two
-
co
ordinate
s
are e
s
tabli
s
h
ed, as sho
w
n
in Figure 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Real
-tim
e Pose Mea
s
u
r
em
ent of Parallel
Robot Based
on GRNN
(G
ao Guo
q
in)
2317
4
B
3
B
2
B
1
B
6
B
5
B
Z
O
Y
X
Z
O
X
Y
Figure 2. The
coordinate
s
of the 6-DOF parall
e
l rob
o
t
For a point
P
in the
dynami
c
coo
r
di
nate,
whe
n
the
dyn
a
mic coordin
a
te
O-XYZ
trans
lates
p
x
、
p
y
、
p
z
re
spe
c
tively along t
h
e
static
co
ordi
nate, and
the
n
rotate
s the
angle
, the a
ngl
e
, the angle
re
spe
c
tively arou
nd the
X
axis, the
Y
axis, the
Z
axis, its h
o
moge
neo
u
s
c
o
or
d
i
na
te
s
'
P
in the static coordi
nate can
be cal
c
ulate
d
by the following Eq. (1
)
'
PT
P
(1)
whe
r
e
T
de
no
tes the dire
cti
onal cosi
ne
matrix of the moving platfo
rm po
se.
T
ca
n be introd
uced
as
cc
c
s
s
ss
c
c
s
c
c
s
s
s
s
c
ss
c
s
c
c
s
s
s
c
cc
00
0
1
P
P
P
x
y
z
T
(2)
whe
r
e
cc
o
s
,
ss
i
n
,
cc
o
s
,
ss
i
n
,
cc
o
s
,
ss
i
n
.
Since th
e lin
k len
g
ths
of the 6
-
PTRT
p
a
rallel
me
cha
n
ism
are fixe
d, in the mov
e
ment,
only the
Z
co
ordin
a
te of th
e hinge
point
i
B
cha
nge
s, wh
ile the
X, Y
coordi
nate
s
do
not ch
ange,
it is obtained
as
''
'
22
2
2
2
2
()
(
)
(
)
(
)
(
)
()
ii
i
i
i
i
i
i
i
ii
i
BP
B
P
B
P
B
B
B
PP
P
x
xy
y
z
z
x
x
y
y
z
z
(3)
Acco
rdi
ng to Eqs. (1
) and (2), the co
ordi
nate of
Bi
z
is arri
ved. The disp
lacem
ent of the
sc
re
w is
i
Bi
Bi
hz
z
(4)
The Eq. (4) i
s
the pose inv
e
rse kin
e
mati
cs of the 6
-
DOF parallel ro
bot mech
ani
sm. The
motor rotation angle
can b
e
further o
b
ta
ined by the scre
w pitch.
3. Building of GRNN
The topol
ogy
stru
cture of
GRNN
i
s
sho
w
n in Fi
gure
3, whi
c
h in
cl
ude
s the inp
u
t layer,
the pattern
layer, the
sum
m
ation
layer a
n
d
output lay
e
r. Th
e inp
u
t of GRNN is
12
[,
,
]
T
n
X
xx
x
(n=
6
),
X
d
e
n
o
tes the
mov
i
ng di
spla
ce
ment vecto
r
of the six d
r
i
v
e rod
s
, an
d
the output
12
[,
,
]
T
m
Yy
y
y
(m
=6) d
enote
s
the po
se of the parall
e
l rob
o
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2315 – 232
2
2318
Figure 3. The
topology of GRNN
(1) Inp
u
t laye
r. The unit n
u
mbe
r
of inp
u
t layer is e
q
ual to the di
mensi
on n of
the input
vector. Eve
r
y unit di
re
ctly passe
s t
h
e ele
m
ent
s
of the in
put
vecto
r
to t
he p
a
ttern
l
a
yer
r
e
spec
tively.
(2) Pattern layer. The ne
uron
s nu
mbe
r
of the pattern laye
r is
equal that of
learnin
g
sampl
e
s m. T
he tran
sfer fu
nction of ne
uron is a
s
follo
ws
2
exp
2
T
ii
i
XX
XX
P
(5)
whe
r
e
X
den
otes the inp
u
t variable of the netwo
rk,
X
i
denote
s
the l
earni
ng samp
le of neuro
n
i
.
(3) Sum
m
atio
n layer. The
way to sum i
s
sele
cted a
s
2
exp
2
T
ii
i
XX
XX
Y
(6)
The wei
ghted
summation
of all the outputs of
the pattern layer n
euro
n
s i
s
cal
c
ulate
d
.
The co
nne
ction weig
ht
be
tween
the
i
th
neu
ron
of th
e patte
rn l
a
yer
and
the
j
t
h
ne
uro
n
of th
e
summ
ation la
yer is the
j
th element of
Y
i
. The tran
sfer
function i
s
as
follows
1,
2
,
Nj
i
j
i
Sy
P
j
m
(7)
(4) O
u
tput la
yer. The neu
ron n
u
mbe
r
i
n
the
output l
a
yer is e
qual
to the domin
ion n of
the output vector of the lea
r
ning
sam
p
le.
/1
,
2
,
.
.
.
,
jN
j
D
yS
S
j
m
(8)
For th
e G
RNN, on
ce
the training
sampl
e
s i
s
determi
ned, the
n
the
network
stru
cture
an
d
the co
nne
cti
on weight
be
tween
neu
ro
ns a
r
e
dete
r
mined, the f
a
ctor that
aff
e
cts the n
e
twork
outputs i
s
the
smooth pa
ra
meter
σ
, so the GRNN lea
r
ning d
epe
nd
s entirely on t
he sam
p
le da
ta.
The real
-time
pose mea
s
u
r
eme
n
t of parallel robot
is
reali
z
ed b
a
se
d on the GRNN which is off-
line train
ed,
whi
c
h
can im
prove the
wo
rkin
g a
c
curacy of parallel
robot
without
increa
sing t
h
e
co
sts of pa
ral
l
el robot sy
stem.
4. Pose Mea
s
uremen
t of
the Parallel Robo
t and Analy
s
is of Ex
periment
4.1. Pose Me
asureme
nt o
f
the Par
a
llel Robot
The procedu
re of real-time
pose mea
s
u
r
em
ent of parallel rob
o
t is as follo
ws.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Real
-tim
e Pose Mea
s
u
r
em
ent of Parallel
Robot Based
on GRNN
(G
ao Guo
q
in)
2319
(1) Acco
rdin
g to the measu
r
em
ent requireme
nt, the initial an
d terminal p
o
se
s are
determi
ned,
and the
n
the
parallel
rob
o
t movement
traje
c
tory pl
annin
g
of th
e end
-effe
cto
r
is
made.
(2) Ta
ke
m
grou
ps of
da
ta point
s
{,
,
,
,
,
}
pp
p
p
p
p
xy
z
(p=
1
，，
2
3
…m
) from
the
plann
ed trajecto
ry, a
nd obtai
n
the correspon
ding
six screw di
spl
a
cements
1
,
2,
3
,
4,
5
,
6
{}
p
pp
p
p
p
hh
h
h
h
h
(p=1
，，
2
3
…
m
) of the parallel rob
o
t by
the inverse ki
nematics.
(3) T
a
ke the
other n
gro
u
p
s
from th
e pl
anne
d traje
c
t
o
ry and
obtai
n the co
rresp
ondin
g
n
grou
ps di
spl
a
ceme
nts in th
e same m
e
th
od, whi
c
h are
used a
s
the testing
sampl
e
s.
(4) The
m
group
s of i
nput
and
output
d
a
ta no
rmali
z
e
d
are u
s
e
d
a
s
the
trai
ning
sampl
e
s
to build the GRNN.
(5) Afte
r obt
aining th
e
co
rre
sp
ondi
ng
actual
po
se
s of the n
group
s sampl
e
s by the
GRNN,
comp
are the
actu
al
poses
with th
e de
sire
d po
ses a
nd
cal
c
ul
ate the erro
rs betwe
en the
m
in orde
r to examine the effectivene
ss an
d accu
racy of
the parallel
robot po
se me
asu
r
em
ent.
In the end
-effector
of pa
ral
l
el rob
o
t, the angul
ar di
spl
a
cem
ent si
gn
als of the m
o
tors a
r
e
measured
by
the en
co
ders.
Wh
en th
e
rot
a
tion a
ngle
s
of the m
o
tors are o
b
tained
, sup
p
o
s
ing
the
scre
w pitch to
be 5mm, the displ
a
cem
ent
s of the scre
ws a
r
e a
s
follows
5
2
ii
l
(9)
Usi
ng the a
b
o
ve scre
w di
spla
cem
ents
as t
he in
put vector of the
trained G
R
NN, the
output vector
is the po
se of
the par
allel
robot in the cu
rre
nt state.
4.2. Experimental Analy
s
is
Experiment 1
:
the movement of end-effe
ctor i
s
a strai
ght line, and
α
=
β
=
γ
=0.
For the
strai
g
ht moving, se
t the start lo
cation a
s
(0, 0
,
0, 0, 0, 0), the termi
nal l
o
catio
n
as (45.55, 4
5
.
55, -45.55, 0
,
0, 0). From t
he stra
ight trajecto
ry, sele
ct 250
point
s as the i
nput a
n
d
output sampl
e
s. After the
neural net
wo
rk is
esta
b
lish
ed, 80 p
o
ints
are
sele
cted f
r
om the
de
sired
straig
ht-lin
e t
r
aje
c
tory
and
used
as th
e test
in
g
sa
mples.
The
moving di
spl
a
cem
ents of
the
s
c
r
e
w
s
a
r
e
so
lve
d
b
y
th
e
in
ve
r
s
e
k
i
n
e
m
a
t
ic
s
,
an
d
th
en
th
e
d
a
t
a is
n
o
r
ma
lize
d
as
th
e
inp
u
t
and
output of the
trained
G
R
NN. The
erro
r
curve
s
wh
en
the end
-effe
ctor move
s in
a line a
r
e
sh
o
w
n
in Figure 4. The erro
r ra
nge of the curves
refl
e
c
ts the measu
r
ement ac
cu
racy of the neural
netwo
rk.
0
0.
5
1
1.
5
2
2.
5
-1
-0
.
5
0
0.
5
1
x 1
0
-3
T
i
m
e
t/s
△
P
o
s
i
t
i
o
n
erro
r
x
/
m
m
X
0
0.
5
1
1.
5
2
2.
5
-1
-0
.
5
0
0.
5
1
x 1
0
-3
Ti
m
e
t
/
s
△
P
o
s
i
t
i
on er
ror
y
/
m
m
Y
0
0.
5
1
1.
5
2
2.
5
-1
-0
.
5
0
0.
5
1
x 1
0
-3
T
i
m
e
t/s
△
Po
s
i
t
i
o
n
e
r
r
o
r
y
/
mm
Y
(a) T
he er
ro
r curv
e in x
-
ax
is
(b) The
erro
r c
u
rv
e i
n
y
-
ax
is (
c
) Th
e er
ro
r c
u
rv
e in z
-
ax
is
Figure 4. The
erro
r curve
s
whe
n
the end
-effecto
r
mov
e
s in a line
Experiment 2
:
the end-effe
ctor of the pa
ra
llel robot m
a
ke
s a move
ment in an arc.
For the a
r
c m
o
vement, set
the start lo
cat
i
on is (0
, 0, 0, 0, 0, 0), the terminal lo
ca
tion is
(45.55, 45.5
5
,
-45.55, 0, 0, 0.18°). T
he e
rro
r cu
rve
s
are sho
w
n in Fi
gure 5.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2315 – 232
2
2320
0
1
2
3
-1
-0.
5
0
0.
5
1
x 1
0
-3
T
i
m
e
t/s
△
P
o
s
i
t
i
o
n
e
rro
r
x
/
m
m
X
0
1
2
3
-1
-0.
5
0
0.
5
1
x 1
0
-3
Ti
m
e
t
/
s
△
P
o
s
i
t
i
on
e
r
ror
x
/
m
m
X
(a) The error c
u
rve in x-axis
(b) The error
c
u
rve in y-axis
0
1
2
3
-1
-0.
5
0
0.
5
1
x 1
0
-3
T
i
m
e
t/s
△
P
o
s
i
t
i
o
n
e
rro
r
z
/
m
m
z
0
1
2
3
-1
-0
.
5
0
0.
5
1
x 1
0
-3
T
i
m
e
t/
s
△
P
o
s
i
ti
o
n
e
r
r
o
r
z
/
m
m
z
(c) The error
c
u
rve in
z
-
axis
(d) The error
curve of
γ
Figure 5. The
erro
r curve
s
whe
n
the end
-effecto
r
mov
e
s in an a
r
c
In Figure 4,
whe
n
the end
-effecto
r
moves in a li
ne, the ab
solute value of the errors in x,
y and z axis is less than
1×1
0
-3
mm. It
can b
e
see
n
from Figu
re 5 that, when the end-effector
moves in
an
arc, the
ab
sol
u
te value of the er
ro
rs in x
,
y and z axis is less tha
n
1×1
0
-3
mm, and
the absolute
value of the erro
r of
γ
is le
ss than 4
×
10
-1
7
rad.
4.3. Experimental Compa
r
ison
w
i
th BP and RBF
Neural Ne
t
w
o
r
k Detec
t
ion
BP neural
ne
twork is
a m
u
lti-layer fee
d
-
forwar
d net
work, an
d its stru
cture is
sho
w
n in
Figure 6, wh
ere,
X
=[
x
1
,x
2
,…,
x
n
]
T
and
Y
=[
y
1
,y
2
,…,
y
m
]
T
are the in
pu
t and output
vectors of th
e
netwo
rk resp
ectively,
X
de
notes the m
o
ving di
spla
ce
ment vecto
r
o
f
the six
drive
rod
s
,
Y
de
no
tes
the pose of the parall
e
l rob
o
t end-effe
cto
r
.
Figure 6. BP
neural network
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Real
-tim
e Pose Mea
s
u
r
em
ent of Parallel
Robot Based
on GRNN
(G
ao Guo
q
in)
2321
The RBF ne
ural net
wo
rk
is a three
-
lay
e
r f
eed
-forwa
rd network which
con
s
i
s
ts of the
input laye
r, t
he hi
dde
n la
yer, an
d the
output laye
r.
Its structu
r
e
i
s
sho
w
n
in
F
i
gure
7,
wh
ere
X
=[
x
1
,x
2
,…,x
n
]
T
and
Y
=[
y
1
,y
2
,…,y
m
]
T
are the input an
d output vecto
r
s of the network
re
spe
c
tively,
X
denote
s
the moving displacement ve
ctor of the si
x drive rod
s
,
Y
denotes t
he po
se of the
parall
e
l rob
o
t.
Figure 7. RBF neural network
Usi
ng the
sa
me test samp
les to trai
n th
e BP, RBF and G
R
NN, the co
nverg
e
n
c
e time of
the BP, RBF
and G
R
NN is sho
w
n in Ta
ble 1.
Table 1. The
conve
r
ge
nce ti
me of the BP, RBF and GRNN
BP RBF
G
R
NN
convergence time (s)
1.582
0.012
0.010
With the sa
m
e
test sam
p
le
s, the errors
of the BP, RBF and G
R
NN
method
s are sho
w
n
in Figure 8.
0
0.
5
1
1.
5
2
2.
5
-2
-1
0
1
2
3
x 1
0
-3
T
i
m
e
t/s
△
P
o
si
ti
o
n
e
r
r
o
r
x/
m
m
:B
P
:R
B
F
:
G
RNN
0
0.
5
1
1.
5
2
2.
5
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
2.
5
x 1
0
-3
T
i
m
e
t/
s
△
P
o
s
i
t
i
on
error
y
/
m
m
:B
P
:R
BF
:
G
RNN
0
0.
5
1
1.
5
2
2.
5
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
x 1
0
-3
T
i
m
e
t/s
△
P
o
s
i
t
i
on
er
r
o
r
z
/
m
m
:B
P
:R
B
F
:
G
RNN
(a)
T
he e
rro
r c
o
mpa
r
is
on in
X (b)The er
ror
comp
ari
s
o
n
in Y (c)Th
e
erro
r c
o
mpa
r
ison in Z
Figure 8. The
erro
r compa
r
ison of G
R
NN, BP and RBF when the
end-effecto
r
moves in a lin
e
In Figure 8, when the end
-effector move
s in a li
ne, the absol
ute values of the errors in x,
y and z
axis
of the BPNN
me
thod a
r
e l
e
ss than
2.5×10
-3
mm, the
absolute valu
es of the
erro
rs i
n
x, y and
z ax
is of th
e
RBF
N
N metho
d
a
r
e le
ss tha
n
1.5×1
0
-3
mm,
and th
ose of
GRNN metho
d
are le
ss than
1×1
0
-3
mm. Table 1 sho
w
s that the conv
erge
nce time of the GRNN
method i
s
less
than that of t
he BPNN a
n
d
RBF
N
N me
thods with
th
e sa
me traini
ng sampl
e
s.
So the real-ti
m
e
pose meas
urement
of Parallel robot
bas
e
d on th
e GRNN
has
the fas
t
er
c
onvergenc
e
rate
and
highe
r mea
s
u
r
eme
n
t accuracy.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2315 – 232
2
2322
5. Conclusio
n
The real-tim
e
,
pre
c
ise
po
se mea
s
u
r
eme
n
t of parallel robot may b
e
use
d
for
reali
z
ing th
e
full
clo
s
e
d
-lo
op cont
rol o
f
parallel ro
bot
in
order
to
e
nhan
ce
its co
ntrol and ope
ratio
n
perfo
rman
ce.
For a 6-DO
F parallel ro
bot, based o
n
the kinem
atics an
alysi
s
, a generali
z
ed
reg
r
e
ssi
on n
eural
network which
ha
s the stro
ng
nonlin
ear m
a
pping a
b
ility and the flexi
b
le
netwo
rk
stru
cture, a
s
well
as th
e hi
gh fa
ult-to
leran
c
e
and
rob
u
stn
e
s
s is e
s
tabli
s
hed to
solve t
h
e
pose mea
s
u
r
ement proble
m
of the 6-DOF parallel
robot. The ex
perim
ent re
sults sh
ow th
a
t
the
pose mea
s
u
r
ement of the
parall
e
l rob
o
t
based
on
th
e GRNN
ha
s the faster
co
nverge
nce ra
te
and hi
ghe
r m
easure
m
ent a
c
cura
cy tha
n
those
of
the
BPNN a
nd
RBFNN metho
d
s. Th
e resea
r
ch
establi
s
h
e
s th
e basi
s
for th
e dire
ct full close
d
-lo
op co
ntrol of parall
e
l robot.
Ackn
o
w
l
e
dg
ements
This work
wa
s fina
nci
a
lly suppo
rted
by t
he Pri
o
rity Academi
c
P
r
og
ram
Develop
m
ent of
Jian
gsu Hig
h
e
r Edu
c
ation
Institutions
(NO. 6,
201
1),
Zhenjia
ng M
unici
pal Key Tech
nolo
g
y R&D
Program (G
rant No. NY2
0110
13) a
n
d
the Postgr
a
duate Research an
d Innovation Prog
ra
m of
Jian
gsu High
er Edu
c
ation
Institutions
(1
2211
4004
6).
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udi
n, Mo
hamma
d, Moh
a
med, Z
a
haru
ddi
n,
Hus
a
in,
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l R
a
shi
d
.
D
y
namic
Mo
d
e
l a
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d
Ro
bus
t
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l
exibl
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Li
nk R
obot Man
i
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zz
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han
g
Shup
in
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on Pos
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a
s
ureme
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Parall
el R
obot
Based o
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C
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m
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t
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