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L
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K
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elec
o
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ica
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m
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lect
ro
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o
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,
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,
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em
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er
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y
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.
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A.
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J
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ttp
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Bila
teral
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ntrol s
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he spa
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e robo
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s
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.
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.
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f
im
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,
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y
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a
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3
,
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a
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.
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a
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p
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ially
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ti
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rticle
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p
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uth
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r
:
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.
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r
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Dep
ar
tm
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t o
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ity
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tian
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an
d
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No
r
way
E
m
ail:
s
k
ad
r
y
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Fu
tu
r
e
s
p
ac
e
ex
p
l
o
r
atio
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ca
n
n
o
t
d
o
with
o
u
t
s
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ial
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is
ted
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tem
s
.
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h
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k
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to
s
p
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u
m
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s
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ct
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ac
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ases
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lar
g
e
d
is
tan
ce
s
f
r
o
m
ea
r
th
.
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f
o
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atel
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h
m
is
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io
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o
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m
u
s
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with
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eter
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is
tic
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en
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wh
ich
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e
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ir
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s
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o
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to
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tly
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a
r
e
n
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et
t
h
at
ca
n
q
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ick
ly
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d
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r
ately
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esp
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to
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ig
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ch
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th
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en
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e
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t,
s
o
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e
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r
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ce
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h
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m
an
o
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er
ato
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in
th
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c
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tr
o
l
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o
p
is
v
er
y
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p
o
r
tan
t.
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n
ad
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itio
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,
wh
en
wo
r
k
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g
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er
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g
d
is
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ce
s
,
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ig
n
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ican
t
d
elay
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th
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tr
an
s
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co
n
tr
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d
f
ee
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k
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ig
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cc
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r
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t
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task
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f
d
ev
elo
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in
g
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b
ilate
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en
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t.
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e
m
aster
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s
lav
e
s
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s
tem
is
m
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s
t
o
f
ten
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ed
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a
s
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s
tem
f
o
r
r
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o
te
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r
o
b
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t.
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h
e
r
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o
te
-
co
n
tr
o
l
s
y
s
tem
h
as
two
s
id
es:
an
o
p
er
ato
r
s
id
e
an
d
a
r
em
o
te
s
id
e
(
Fig
u
r
e
1
)
[
1
]
.
On
th
e
o
p
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ato
r
’
s
s
id
e,
o
r
in
th
e
co
n
tr
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,
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e
a
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m
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r
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a
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r
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b
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ii
)
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d
a
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h
w
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h
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m
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e
ar
e
a
s
lav
e
r
o
b
o
t
iii
)
with
s
en
s
o
r
s
an
d
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v
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n
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y
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tem
in
s
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it,
a
n
d
a
w
o
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in
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en
v
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en
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)
.
Dep
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r
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itectu
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:
d
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t,
co
llab
o
r
ativ
e
an
d
s
u
p
e
r
v
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o
r
y
[
2
]
.
I
f
th
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p
r
o
b
lem
a
r
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es
o
f
m
a
n
ip
u
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t
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r
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b
ac
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r
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b
o
t r
em
o
te
co
n
tr
o
l sy
s
tem
s
ar
e
ca
lled
b
ilater
al
co
n
tr
o
l sy
s
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s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
ila
tera
l c
o
n
tr
o
l sys
tem
o
f th
e
s
p
a
ce
r
o
b
o
t wi
th
la
r
g
e
d
el
a
ys
(
G.
A
lfer
o
v
)
1963
Fig
u
r
e
1
.
T
h
e
m
aster
–
s
lav
e
s
y
s
tem
T
h
e
d
iag
r
am
s
h
o
w
n
in
Fig
u
r
e
2
d
escr
ib
es th
e
co
n
n
ec
tio
n
an
d
in
ter
ac
tio
n
b
etwe
en
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e
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m
en
ts
o
f
th
e
r
o
b
o
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s
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ilater
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o
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tem
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Her
e
ℎ
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,
,
ar
e
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e
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alize
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ates
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n
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o
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en
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esp
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s
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itted
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m
a
n
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d
th
e
en
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ir
o
n
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en
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d
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e
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n
t
r
o
l sig
n
als f
o
r
th
e
s
lav
e
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d
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aste
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o
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o
t.
A
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ig
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ican
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p
r
o
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lem
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th
e
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e
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o
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is
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e
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f
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s
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ilit
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.
R
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ch
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s
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with
v
a
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s
m
eth
o
d
s
,
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d
as
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d
if
f
er
en
t
co
n
tr
o
l
s
ch
em
es
h
av
e
b
ee
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p
r
o
p
o
s
ed
.
Fro
m
th
e
p
r
o
p
o
s
ed
m
eth
o
d
s
,
th
r
ee
m
ain
ca
teg
o
r
ies
ca
n
b
e
d
is
tin
g
u
is
h
ed
:
m
eth
o
d
s
b
ased
o
n
p
ass
iv
ity
,
m
eth
o
d
s
b
ased
o
n
p
r
ed
i
ctiv
e
d
is
p
lay
s
an
d
m
eth
o
d
s
o
f
s
lid
in
g
c
o
n
tr
o
l
m
o
d
e
[
3
]
.
T
h
e
m
et
h
o
d
b
ased
o
n
p
ass
iv
ity
is
th
at
th
e
p
o
wer
d
ev
elo
p
e
d
b
y
t
h
e
wo
r
k
in
g
to
o
l
o
f
th
e
"slav
e"
m
an
ip
u
lato
r
s
h
o
u
l
d
n
o
t
e
x
ce
e
d
th
e
p
o
wer
d
e
v
elo
p
ed
b
y
th
e
h
an
d
o
f
th
e
h
u
m
an
m
o
v
in
g
th
e
to
o
l
o
f
th
e
m
aster
r
o
b
o
t
[
4
]
.
T
h
e
s
ec
o
n
d
ap
p
r
o
ac
h
in
v
o
l
v
es
th
e
u
s
e
o
f
p
r
e
d
ictiv
e
co
n
tr
o
l.
I
t
is
b
ased
o
n
th
e
u
s
e
o
f
co
m
p
u
te
r
m
o
d
els,
wh
ich
ar
e
u
s
ed
to
p
r
ed
ict
th
e
b
eh
a
v
io
r
o
f
th
e
s
lav
e
r
o
b
o
t
a
n
d
its
ex
ter
n
al
en
v
i
r
o
n
m
e
n
t [
5
]
.
T
h
e
th
ir
d
a
p
p
r
o
ac
h
is
b
ased
o
n
th
e
u
s
e
o
f
a
s
lid
in
g
c
o
n
tr
o
l m
o
d
e
[
6
]
.
T
h
e
co
m
p
lex
ity
o
f
t
h
e
p
r
ac
tical
im
p
lem
en
tatio
n
o
f
th
is
ap
p
r
o
ac
h
is
d
u
e
to
th
e
n
ee
d
f
o
r
t
h
e
o
p
e
r
atio
n
o
f
th
e
co
n
tr
o
l
eq
u
ip
m
en
t
an
d
th
e
m
ec
h
an
ical
p
ar
t
o
f
th
e
r
o
b
o
t
in
v
er
y
d
if
f
icu
lt
m
o
d
es
o
f
f
r
e
q
u
en
tly
c
h
an
g
in
g
co
n
t
r
o
l
s
ig
n
.
T
h
is
lead
s
to
th
e
ap
p
ea
r
an
ce
o
f
lar
g
e
ac
ce
ler
ati
o
n
s
o
f
s
tr
u
ctu
r
al
elem
en
ts
an
d
lar
g
e
r
ea
ctiv
e
f
o
r
ce
s
.
T
h
e
a
b
o
v
e
m
e
t
h
o
d
s
c
a
n
e
n
s
u
r
e
t
h
e
s
t
a
b
i
l
it
y
o
f
t
h
e
b
i
l
a
te
r
a
l
s
y
s
t
e
m
wi
t
h
a
ti
m
e
d
e
l
a
y
o
f
n
o
m
o
r
e
t
h
a
n
3
s
e
c
o
n
d
s
[
7
]
,
w
h
i
c
h
s
i
g
n
i
f
i
c
a
n
t
ly
l
i
m
i
t
s
t
h
e
d
is
t
a
n
c
e
a
t
w
h
i
c
h
a
s
p
a
c
e
r
o
b
o
t
c
a
n
b
e
s
e
n
t
.
I
n
t
h
i
s
r
e
g
a
r
d
,
a
n
u
r
g
e
n
t
q
u
e
s
t
i
o
n
a
r
i
s
e
s
o
f
c
o
n
s
t
r
u
c
ti
n
g
s
u
c
h
a
s
t
r
u
c
t
u
r
e
o
f
b
i
l
a
t
e
r
a
l
c
o
n
t
r
o
l
,
w
h
i
c
h
w
o
u
l
d
p
r
o
v
i
d
e
t
h
e
p
o
s
s
i
b
il
i
t
y
o
f
r
e
m
o
t
e
c
o
n
t
r
o
l
o
v
e
r
l
o
n
g
d
i
s
ta
n
c
e
s
.
A
s
a
n
a
p
p
r
o
a
c
h
t
o
s
o
l
v
i
n
g
t
h
i
s
is
s
u
e
,
a
p
r
o
f
e
s
s
o
r
at
S
t
.
P
e
t
e
r
s
b
u
r
g
S
ta
t
e
U
n
i
v
e
r
s
it
y
F
.
K
u
l
a
k
o
v
p
r
o
p
o
s
e
d
a
m
e
t
h
o
d
o
f
r
e
m
o
t
e
c
o
n
t
r
o
l
o
f
a
r
o
b
o
t
b
y
t
e
a
c
h
i
n
g
f
u
t
u
r
e
a
c
t
io
n
s
[
8
]
-
[
1
4
]
.
Fig
u
r
e
2
.
Stru
ctu
r
e
o
f
b
ilater
al
m
aster
–
s
lav
e
s
y
s
tem
2.
M
E
T
H
O
D
I
n
th
is
a
p
p
r
o
ac
h
to
c
o
n
tr
o
l,
th
e
r
em
o
te
wo
r
k
in
g
en
v
ir
o
n
m
e
n
t
is
co
p
ied
in
a
v
ir
tu
al
o
r
f
u
ll
-
s
ca
le
f
o
r
m
in
th
e
co
n
tr
o
l
ce
n
ter
an
d
th
e
h
u
m
an
o
p
er
at
o
r
in
ter
ac
ts
in
t
h
e
n
ec
ess
ar
y
way
with
th
e
o
b
jects
o
f
th
e
m
o
d
el
en
v
ir
o
n
m
en
t,
af
te
r
wh
ich
th
e
s
p
ac
e
r
o
b
o
t
wo
r
k
s
o
u
t
th
e
s
am
e
ac
tio
n
s
at
th
e
o
b
je
cts
o
f
th
e
r
em
o
te
en
v
ir
o
n
m
en
t,
wh
ile
ad
a
p
tin
g
to
its
p
o
s
s
ib
le
ch
an
g
es.
T
h
e
p
r
o
ce
s
s
o
f
co
n
tr
o
l
o
f
a
s
p
ac
e
r
o
b
o
t
u
s
in
g
th
e
teac
h
in
g
m
et
h
o
d
ca
n
b
e
d
i
v
id
e
d
in
to
4
s
tag
es (
Fig
u
r
e
3
)
.
−
Stag
e
1
.
At
th
e
f
ir
s
t
s
tag
e,
th
e
s
p
ac
e
r
o
b
o
t,
u
s
in
g
s
en
s
o
r
s
,
co
llects
th
e
n
ec
ess
ar
y
in
f
o
r
m
atio
n
ab
o
u
t
th
e
wo
r
k
in
g
e
n
v
ir
o
n
m
en
t a
n
d
tr
a
n
s
m
its
it to
th
e
co
n
tr
o
l c
en
ter
.
−
Stag
e
2
.
At
th
e
s
ec
o
n
d
s
tag
e,
a
m
o
d
el
o
f
th
e
r
e
m
o
te
en
v
ir
o
n
m
en
t
is
f
o
r
m
e
d
b
ased
o
n
t
h
e
r
ec
eiv
ed
d
ata.
T
h
e
m
o
d
el
ca
n
b
e
m
ad
e
in
th
e
f
o
r
m
o
f
f
u
ll
-
s
ca
le
m
o
d
els o
r
b
u
ilt o
n
a
co
m
p
u
ter
.
−
Stag
e
3
.
T
h
e
th
ir
d
s
tag
e,
wh
i
ch
tak
es
p
lace
at
t
h
e
co
m
m
a
n
d
ce
n
ter
o
n
ea
r
th
,
ca
n
b
e
p
e
r
f
o
r
m
e
d
in
two
d
if
f
er
en
t
way
s
,
d
e
p
en
d
in
g
o
n
th
e
ty
p
e
o
f
r
em
o
te
en
v
ir
o
n
m
en
t
m
o
d
el.
I
f
th
e
wo
r
k
i
n
g
en
v
ir
o
n
m
en
t
is
p
r
esen
ted
in
th
e
f
o
r
m
o
f
a
f
u
ll
-
s
ca
le
m
o
d
el,
t
h
en
i
n
ter
ac
tio
n
with
it
o
cc
u
r
s
ac
co
r
d
in
g
t
o
th
e
f
o
llo
win
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
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KOM
NI
KA
T
elec
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m
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p
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t E
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tr
o
l
,
Vo
l.
1
9
,
No
.
6
,
Decem
b
e
r
2
0
2
1
:
1
9
6
2
-
1
9
7
4
1964
p
r
in
cip
le:
th
e
h
u
m
a
n
o
p
er
at
o
r
,
in
ter
ac
tin
g
with
th
e
m
aster
r
o
b
o
t,
s
ets th
e
r
eq
u
ir
ed
p
o
s
itio
n
,
an
d
o
r
ien
tatio
n
o
f
th
e
to
o
l,
th
e
in
s
tr
u
m
en
t
o
f
t
h
is
r
o
b
o
t
m
u
s
t
ac
cu
r
ately
in
ter
p
r
et
th
e
in
s
tr
u
m
en
t
o
f
th
e
s
p
a
ce
r
o
b
o
t.
T
h
u
s
,
th
e
o
p
er
ato
r
in
te
r
ac
ts
with
th
e
o
b
jects
o
f
th
e
f
u
ll
-
s
ca
le
m
o
d
el,
a
s
in
th
e
tr
ad
itio
n
al
m
eth
o
d
o
f
b
ilater
al
co
n
tr
o
l.
I
n
s
tr
u
m
e
n
t
m
o
tio
n
s
ar
e
m
em
o
r
ize
d
an
d
tr
a
n
s
m
itted
to
th
e
s
p
ac
e
r
o
b
o
t.
I
f
n
ec
ess
ar
y
,
a
s
p
ac
e
r
o
b
o
t
ca
n
b
e
d
is
p
lay
ed
to
a
h
u
m
a
n
o
p
er
ato
r
in
au
g
m
en
ted
r
ea
lity
g
lass
es.
I
f
i
t is
n
o
t p
o
s
s
ib
le
to
b
u
ild
a
f
u
ll
-
s
ca
l
e
m
o
d
el,
th
e
n
y
o
u
ca
n
u
s
e
th
e
v
ir
tu
al
m
o
d
el
o
f
th
e
w
o
r
k
in
g
e
n
v
ir
o
n
m
en
t.
I
n
th
is
ca
s
e,
at
th
e
th
ir
d
s
tag
e,
th
e
h
u
m
an
o
p
er
ato
r
,
o
b
s
er
v
in
g
t
h
e
v
ir
tu
al
en
v
i
r
o
n
m
e
n
t
th
r
o
u
g
h
au
g
m
en
te
d
r
ea
lity
g
lass
es,
in
ter
ac
ts
with
th
e
o
b
jects
o
f
th
is
en
v
ir
o
n
m
en
t
u
s
in
g
a
r
o
b
o
t
-
g
lo
v
es,
a
n
d
th
er
eb
y
f
u
lf
ills
th
e
n
ec
ess
ar
y
o
p
e
r
atio
n
s
.
I
n
b
o
th
ca
s
es,
if
n
ec
es
s
ar
y
,
th
e
r
esu
lti
n
g
alg
o
r
ith
m
is
test
ed
o
n
a
co
m
p
u
ter
m
o
d
el
o
f
a
s
p
ac
e
r
o
b
o
t
an
d
a
wo
r
k
in
g
m
ed
iu
m
,
with
its
o
b
jects b
ein
g
ar
tific
ially
d
is
p
lace
d
.
I
f
th
e
t
est is
s
u
cc
ess
f
u
l,
th
e
a
lg
o
r
ith
m
is
p
ass
ed
to
th
e
s
lav
e
r
o
b
o
t.
Oth
e
r
wis
e,
th
e
n
e
ce
s
s
ar
y
ch
an
g
es a
r
e
m
a
d
e
to
t
h
e
alg
o
r
ith
m
an
d
t
h
e
test
is
co
n
d
u
cted
a
g
ain
.
−
Stag
e
4
.
At
th
e
las
t
s
tag
e,
th
e
s
p
ac
e
r
o
b
o
t
p
er
f
o
r
m
s
th
e
o
b
t
ain
ed
alg
o
r
ith
m
o
f
ac
tio
n
s
,
wh
ile
ad
ap
tin
g
to
p
o
s
s
ib
le
ch
an
g
es
in
th
e
wo
r
k
i
n
g
en
v
ir
o
n
m
en
t,
a
n
d
s
en
d
s
a
r
ep
o
r
t
o
n
th
e
wo
r
k
d
o
n
e
to
th
e
co
n
tr
o
l
ce
n
ter
.
I
f
th
e
co
n
tr
o
l
ce
n
ter
co
n
f
i
r
m
s
th
e
s
u
cc
ess
an
d
co
m
p
leten
ess
o
f
th
e
m
is
s
io
n
,
th
en
th
e
s
tag
es
ar
e
ter
m
in
ated
.
Oth
er
wis
e,
th
e
cy
cle
is
r
ep
ea
te
d
u
n
til th
e
r
e
q
u
ir
e
d
o
p
e
r
atio
n
i
s
co
m
p
leted
.
Fig
u
r
e
3
.
Pro
ce
s
s
o
f
co
n
tr
o
l sp
ac
e
r
o
b
o
t
b
y
teac
h
i
n
g
m
et
h
o
d
2
.
1
.
M
a
t
hema
t
ica
l
m
o
delin
g
o
f
t
he
ex
ec
utiv
e
s
y
s
t
em
An
y
r
o
b
o
tic
s
y
s
tem
r
eq
u
ir
es
p
r
elim
in
ar
y
m
ath
em
atica
l
m
o
d
elin
g
.
T
h
er
ef
o
r
e,
to
test
th
e
o
p
er
ab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
r
e
m
o
te
-
co
n
tr
o
l
s
y
s
tem
f
o
r
a
s
p
ac
e
r
o
b
o
t,
it
is
n
ec
ess
ar
y
to
s
im
u
late
its
elem
en
ts
an
d
th
eir
in
ter
ac
tio
n
.
T
h
e
s
y
s
tem
u
n
d
er
co
n
s
id
er
atio
n
co
n
s
is
ts
o
f
f
iv
e
k
ey
elem
en
ts
:
a
h
u
m
an
o
p
er
a
to
r
,
a
m
aster
r
o
b
o
t,
a
s
p
ac
e
r
o
b
o
t
m
o
d
el,
a
r
ea
l
s
p
ac
e
r
o
b
o
t,
an
d
a
wo
r
k
in
g
e
n
v
i
r
o
n
m
en
t.
Sin
ce
th
e
m
aster
r
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b
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t
is
an
in
s
tr
u
m
e
n
t
th
at
tr
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m
its
m
o
tio
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d
f
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ce
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ata
b
etwe
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s
p
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m
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el
a
n
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u
m
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o
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ato
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atica
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elin
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o
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o
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ject
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te
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est.
I
n
th
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eg
a
r
d
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t
h
e
s
y
s
tem
"h
u
m
an
o
p
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o
r
-
m
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b
o
t"
will
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e
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esen
ted
as
a
b
lo
ck
with
o
u
tp
u
t
an
d
in
p
u
t
d
ata.
T
h
e
wo
r
k
in
g
en
v
ir
o
n
m
en
t
will
b
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p
r
e
s
en
ted
in
a
s
im
ilar
b
lo
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ce
it
will
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ll
-
s
ca
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an
d
d
ata
ab
o
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t
it
will
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d
d
u
r
in
g
th
e
d
ir
ec
t
d
ev
elo
p
m
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t
o
f
th
e
n
ec
ess
ar
y
o
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atio
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s
.
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h
er
ef
o
r
e,
it
is
n
e
ce
s
s
ar
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b
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ild
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ly
a
m
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el
o
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d
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m
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n
d
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th
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g
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ip
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f
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en
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ical
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ac
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o
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I
n
Fig
u
r
e
4
elem
en
ts
o
f
m
o
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elin
g
wh
ich
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ee
d
to
b
e
p
er
f
o
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m
e
d
ar
e
d
is
p
lay
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d
.
Kin
em
atic
m
o
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elin
g
o
f
r
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b
o
ts
is
n
ec
ess
ar
y
to
d
eter
m
i
n
e
th
eir
k
in
em
atic
ch
ar
ac
ter
is
tics
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v
er
tim
e.
I
n
f
o
r
m
atio
n
ab
o
u
t th
e
p
o
s
itio
n
o
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t
h
e
ch
ar
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ter
is
tic
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o
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ts
o
f
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e
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o
t w
ill b
e
u
s
ef
u
l
f
o
r
g
r
ap
h
ical
d
is
p
lay
o
f
its
m
o
tio
n
.
T
h
e
s
o
lu
tio
n
o
f
th
e
in
v
er
s
e
k
in
em
atics
p
r
o
b
lem
will
m
ak
e
it
p
o
s
s
i
b
le
to
d
eter
m
in
e
th
e
v
alu
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f
th
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er
alize
d
co
o
r
d
in
ates th
at
p
r
o
v
id
e
a
g
iv
en
p
o
s
itio
n
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o
r
ie
n
tatio
n
o
f
th
e
to
o
l in
ab
s
o
lu
te
s
p
ac
e.
An
d
i
n
f
o
r
m
atio
n
ab
o
u
t sp
ee
d
s
is
n
ec
ess
ar
y
wh
en
b
u
ild
i
n
g
a
d
y
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am
ic
m
o
d
el.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
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T
elec
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m
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B
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o
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f th
e
s
p
a
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b
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th
la
r
g
e
d
el
a
ys
(
G.
A
lfer
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v
)
1965
Fig
u
r
e
4
.
E
lem
e
n
ts
o
f
a
r
e
m
o
t
e
-
co
n
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o
l sy
s
tem
f
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s
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teac
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eth
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d
2
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2
.
K
ine
m
a
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chem
es
L
et
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s
b
u
ild
a
k
in
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atic
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iag
r
am
o
f
a
s
p
ac
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r
o
b
o
t,
wh
ich
i
n
g
en
e
r
al
will
b
e
a
b
o
d
y
with
a
-
lin
k
m
an
ip
u
lato
r
in
s
talled
o
n
it
(
Fig
u
r
e
5
)
.
T
h
u
s
,
th
e
r
o
b
o
t
will
co
n
s
is
t
o
f
+
1
s
o
lid
s
.
L
et’
s
ass
o
ciate
a
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r
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esp
o
n
d
in
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co
o
r
d
i
n
ate
s
y
s
tem
with
ea
ch
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en
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o
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th
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r
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b
o
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W
e
will
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m
e
th
at
ea
c
h
lin
k
ca
n
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ly
m
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e
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d
r
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tate
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t
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co
r
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o
n
d
i
n
g
ax
is
with
r
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t
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th
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p
r
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y
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at
is
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h
as
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t
least
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en
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alize
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c
o
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ates
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lin
ea
r
an
d
r
o
tatio
n
al.
I
n
th
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ca
s
e,
th
e
r
o
b
o
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av
e
(
2
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)
-
th
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er
alize
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co
o
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ates.
T
h
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f
ir
s
t
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ix
co
o
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ates
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r
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o
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ates
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r
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ib
l
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th
e
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o
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o
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n
o
f
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lin
k
o
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th
e
m
a
n
ip
u
l
ato
r
.
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alize
d
co
o
r
d
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ates
1
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2
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3
d
eter
m
in
e
th
e
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o
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y
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ax
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0
0
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0
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d
0
0
,
r
esp
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tiv
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an
d
4
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5
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ar
e
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m
o
v
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g
t
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ce
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ter
o
f
m
ass
o
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b
o
d
y
alo
n
g
th
e
s
am
e
ax
es.
C
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o
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ate
6
+
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r
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o
n
d
s
to
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o
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k
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6
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to
its
lin
ea
r
m
o
v
e
m
en
t.
T
h
e
r
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tatio
n
an
d
m
o
v
em
en
t
o
f
th
e
th
lin
k
ca
n
o
cc
u
r
alo
n
g
a
n
y
o
f
th
e
t
h
r
ee
ax
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o
f
its
co
o
r
d
in
ate
s
y
s
tem
,
o
r
.
I
f
th
e
r
o
b
o
t
is
in
ten
d
ed
to
ca
r
r
y
o
u
t
wo
r
k
in
th
e
o
r
b
it
o
f
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c
elestial
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o
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y
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en
th
e
b
o
d
y
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f
th
e
r
o
b
o
t
will
b
e
f
r
ee
an
d
all
its
g
e
n
er
alize
d
co
o
r
d
in
ates
will
tak
e
p
lace
.
I
f
th
e
r
o
b
o
t
o
p
er
ate
s
o
n
th
e
s
u
r
f
ac
e
o
f
a
ce
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ial
b
o
d
y
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th
e
n
th
e
g
en
er
alize
d
co
o
r
d
in
ates
1
,
2
an
d
6
will
b
e
co
n
s
tan
t.
L
et
u
s
m
o
v
e
o
n
to
b
u
ild
in
g
a
k
in
em
atic
s
ch
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o
f
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g
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n
d
r
o
b
o
t,
th
e
in
s
tr
u
m
en
t
o
f
wh
ich
will
d
is
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e
in
s
tr
u
m
en
t
o
f
th
e
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p
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ce
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o
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A
s
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a
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u
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o
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m
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l
(
F
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)
M
2
0
-
i
A
[
1
5
]
,
[
1
6
]
,
wh
ich
is
ac
tiv
ely
u
s
ed
at
th
e
Facu
lty
o
f
Ap
p
lied
Ma
th
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atics
-
C
o
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o
l
Pro
ce
s
s
es
o
f
St
.
Peter
s
b
u
r
g
State
Un
iv
er
s
ity
.
L
et
u
s
ass
o
ciate
a
co
r
r
esp
o
n
d
in
g
c
o
o
r
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ate
s
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with
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ch
m
an
ip
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lato
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o
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y
a
n
d
d
e
n
o
t
e
g
en
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alize
d
co
o
r
d
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ates
(
Fig
u
r
e
6
)
.
B
ased
o
n
th
e
co
n
s
tr
u
ct
ed
s
ch
em
es,
it
is
p
o
s
s
ib
le
to
s
o
lv
e
f
o
r
war
d
an
d
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k
in
em
atics
p
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s
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f
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d
in
s
tan
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k
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m
atics
p
r
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p
r
esen
tin
g
r
o
b
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ts
as
a
s
e
t
o
f
in
ter
co
n
n
ec
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co
o
r
d
in
ate
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y
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tem
s
.
Fig
u
r
e
5
.
Gen
e
r
alize
d
k
in
e
m
atic
s
ch
em
e
o
f
a
s
p
ac
e
r
o
b
o
t
Fig
u
r
e
6
.
Kin
em
atic
s
ch
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o
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m
an
ip
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lato
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FANUC
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.
3
.
F
o
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t
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T
o
b
u
ild
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d
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am
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m
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o
f
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r
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o
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it
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ar
y
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ir
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o
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e
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ce
o
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th
e
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ea
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cities
o
f
th
e
lin
k
s
o
n
th
e
g
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alize
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v
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o
cities.
T
h
e
s
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r
ch
will
b
e
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r
r
ied
o
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t
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s
in
g
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ec
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r
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r
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ted
in
[
1
7
]
.
L
e
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s
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o
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h
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f
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d
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o
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a
s
p
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r
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g
r
o
b
o
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T
h
e
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g
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lar
v
elo
city
o
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a
r
i
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o
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y
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ir
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ted
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o
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a
x
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o
f
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o
tatio
n
.
T
h
e
d
ir
ec
tio
n
o
f
th
e
an
g
u
lar
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
1
6
9
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6
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3
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T
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Decem
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ip
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[
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[
]
=
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,
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r
o
b
o
t
b
o
d
y
d
o
n
o
t
d
ep
e
n
d
o
n
th
e
an
g
u
lar
v
elo
cities
o
f
its
lin
k
s
.
C
o
n
s
eq
u
en
tly
,
in
th
e
a
b
s
o
lu
te
co
o
r
d
i
n
ate
s
y
s
tem
,
th
e
an
g
u
lar
v
elo
city
o
f
th
e
b
o
d
y
will
b
e
ex
p
r
ess
e
d
th
r
o
u
g
h
th
e
v
ec
to
r
o
f
g
en
er
alize
d
v
elo
cities
as
f
o
llo
ws
;
[
]
0
=
0
⋅
[
̇
1
̇
2
̇
3
]
,
0
=
[
2
3
−
2
1
3
3
2
+
3
1
2
1
2
−
3
2
−
3
1
2
−
2
3
+
2
1
3
1
2
3
1
−
3
1
1
]
,
in
th
is
ca
s
e
0
Ω
=
[
2
3
−
2
1
3
3
2
+
3
1
2
1
2
0
0
0
0
0
0
−
3
2
−
3
1
2
−
2
3
+
2
1
3
1
2
0
0
0
0
0
0
3
1
−
3
1
1
0
0
0
0
0
0
]
T
h
en
f
o
r
th
e
1
s
t lin
k
th
e
an
g
u
l
ar
v
elo
city
will b
e
eq
u
al
to
[
]
1
=
[
0
1
⋅
0
Ω
+
1
]
⋅
[
̇
1
,
̇
2
,
…
,
̇
9
]
,
h
er
e
0
1
=
[
1
0
0
0
7
−
7
0
7
7
]
,
1
=
[
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
]
.
th
en
1
Ω
=
[
1
11
1
12
1
13
0
0
0
1
0
0
1
21
1
22
1
23
0
0
0
0
0
0
1
31
1
32
1
33
0
0
0
0
0
0
]
,
1
11
=
2
3
,
1
12
=
−
1
3
−
3
1
2
,
1
13
=
1
3
−
1
3
2
,
1
21
=
2
7
3
−
2
7
,
1
22
=
7
(
1
3
−
1
2
3
)
−
2
1
7
,
1
23
=
−
7
(
3
1
+
1
2
3
)
−
1
2
7
,
1
31
=
7
2
+
2
3
7
,
1
32
=
7
(
1
3
−
1
2
3
)
+
2
7
1
,
1
33
=
1
2
7
−
7
(
3
1
+
1
2
3
)
.
2
Ω
=
[
2
11
2
12
2
13
0
0
0
8
0
0
2
21
2
22
2
23
0
0
0
8
0
0
2
31
2
32
2
33
0
0
0
0
1
0
]
,
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
ila
tera
l c
o
n
tr
o
l sys
tem
o
f th
e
s
p
a
ce
r
o
b
o
t wi
th
la
r
g
e
d
el
a
ys
(
G.
A
lfer
o
v
)
1967
3
Ω
=
[
3
11
3
12
3
13
0
0
0
8
9
−
9
0
3
21
3
22
3
23
0
0
0
8
0
1
3
31
3
32
3
33
0
0
0
8
9
9
0
]
.
2
.
4
.
L
inea
r
v
elo
cit
ies o
f
t
he
s
pa
ce
ro
bo
t
L
et
u
s
f
in
d
th
e
d
ep
en
d
en
ce
o
f
th
e
lin
ea
r
v
elo
cities
o
f
th
e
ch
ar
ac
ter
is
tic
p
o
in
ts
o
f
th
e
r
o
b
o
t
o
n
th
e
v
ec
to
r
o
f
g
en
er
alize
d
v
el
o
cities.
T
h
e
g
en
er
alize
d
co
o
r
d
in
ates
4
,
5
an
d
6
o
f
its
b
o
d
y
ar
e
r
esp
o
n
s
ib
le
f
o
r
th
e
lin
ea
r
m
o
v
em
en
ts
o
f
th
e
r
o
b
o
t
.
I
n
ad
d
itio
n
,
wh
en
th
e
lin
k
s
a
n
d
th
e
b
ase
o
f
th
e
r
o
b
o
t
r
o
tate
,
th
e
ch
ar
ac
ter
is
tic
p
o
in
ts
will
h
av
e
lin
ea
r
v
elo
cit
ies
p
er
p
en
d
ic
u
lar
to
t
h
e
d
ir
ec
t
io
n
o
f
th
e
a
n
g
u
lar
v
elo
city
v
e
cto
r
an
d
ca
lcu
lated
b
y
th
e
E
u
ler
f
o
r
m
u
la.
T
h
e
r
e
latio
n
s
h
ip
b
etwe
en
lin
ea
r
an
d
g
en
er
alize
d
v
el
o
cities,
with
r
esp
ec
t
to
th
e
-
th
ch
ar
ac
ter
is
tic
p
o
in
t
(
“0
”
-
ce
n
te
r
o
f
m
ass
o
f
t
h
e
b
o
d
y
,
“
1
,
2
,
3
”
—
b
eg
in
n
in
g
o
f
1
,
2
,
3
lin
k
s
,
“4
”
—
ch
ar
ac
ter
is
tic
p
o
in
t
o
f
th
e
t
o
o
l)
,
is
d
eter
m
in
ed
in
th
e
f
o
llo
win
g
f
o
r
m
(
u
s
in
g
th
e
t
h
eo
r
em
o
n
th
e
a
d
d
itio
n
o
f
v
elo
cities
in
a
co
m
p
lex
m
o
tio
n
a
n
d
th
e
f
o
r
m
u
la
f
o
r
t
h
e
d
is
tr
ib
u
tio
n
o
f
v
elo
cities in
a
s
o
lid
[
1
9
]
,
[
2
0
]
)
:
[
]
=
⋅
[
̇
1
,
̇
2
,
…
,
̇
9
]
,
wh
er
e
=
−
1
⋅
−
1
+
−
1
⋅
−
1
⋅
−
1
Ω
,
h
er
e
th
e
s
k
ew
-
s
y
m
m
etr
ic
m
at
r
ix
−
1
d
eter
m
in
es
th
e
d
is
tan
ce
f
r
o
m
th
e
-
t
h
p
o
in
t
to
th
e
a
x
is
o
f
r
o
tatio
n
o
f
th
e
p
r
ev
io
u
s
b
o
d
y
.
W
ith
r
esp
ec
t to
th
e
0
th
ch
a
r
ac
t
er
is
tic
p
o
in
t:
[
]
0
=
0
⋅
[
̇
4
̇
5
̇
6
]
.
T
h
er
ef
o
r
e
0
=
[
0
0
0
2
3
−
2
1
3
3
2
+
3
1
2
1
2
0
0
0
0
0
0
−
3
2
−
3
1
2
−
2
3
+
2
1
3
1
2
0
0
0
0
0
0
3
1
−
3
1
1
0
0
0
]
.
f
o
r
th
e
1
s
t c
h
ar
ac
ter
is
tic
p
o
in
t:
1
=
0
1
⋅
0
+
0
1
⋅
0
⋅
0
Ω
,
0
1
=
[
1
0
0
0
7
−
7
0
7
7
]
,
0
=
[
0
−
1
1
1
0
0
−
1
0
0
]
.
s
im
ilar
ly
f
o
r
th
e
2
n
d
,
3
r
d
an
d
4
th
ch
ar
ac
ter
is
tic
p
o
i
n
ts
:
2
=
1
2
⋅
1
+
1
2
⋅
1
⋅
1
Ω
,
1
2
=
[
8
−
8
0
8
8
0
0
0
1
]
,
1
=
[
0
0
1
0
0
0
−
1
0
0
]
,
3
=
2
3
⋅
2
+
2
3
⋅
2
⋅
2
Ω
,
2
3
=
[
9
0
9
0
1
0
−
9
0
9
]
,
2
=
[
0
0
2
0
0
0
−
2
0
0
]
,
4
=
3
+
2
3
⋅
3
⋅
3
Ω
,
3
=
[
0
0
3
0
0
0
−
3
0
0
]
.
2
.
5
.
F
o
rwa
rd
dy
na
m
ics pro
blem
Fo
r
f
u
r
th
er
in
v
esti
g
atio
n
o
f
th
e
o
p
e
r
ab
ilit
y
o
f
t
h
e
s
y
s
te
m
o
f
b
ilater
al
c
o
n
tr
o
l
b
y
th
e
teac
h
in
g
m
eth
o
d
,
it
is
n
ec
ess
ar
y
to
co
n
s
tr
u
ct
a
d
y
n
am
ic
m
o
d
el
o
f
a
s
p
ac
e
f
r
ee
-
f
ly
i
n
g
r
o
b
o
t
an
d
a
g
r
o
u
n
d
m
an
ip
u
lato
r
FANUC
[
1
9
]
,
[
2
0
]
.
T
h
e
f
o
r
wa
r
d
d
y
n
am
ics p
r
o
b
lem
is
t
o
s
ea
r
ch
f
o
r
f
o
r
ce
s
an
d
m
o
m
en
ts
f
o
r
a
g
iv
en
m
o
tio
n
o
f
th
e
s
y
s
tem
an
d
th
e
m
ass
–
in
er
t
ial
ch
ar
ac
ter
is
tics
o
f
its
elem
e
n
ts
.
L
et
u
s
s
o
l
v
e
th
e
f
o
r
war
d
d
y
n
am
ics
p
r
o
b
lem
f
o
r
s
p
ac
e
a
n
d
g
r
o
u
n
d
r
o
b
o
ts
.
T
h
e
eq
u
atio
n
s
o
f
m
o
tio
n
f
o
r
r
o
b
o
ts
will
b
e
s
o
u
g
h
t
in
t
h
e
f
o
r
m
o
f
t
h
e
L
ag
r
an
g
e
eq
u
atio
n
o
f
th
e
s
ec
o
n
d
k
i
n
d
.
̇
−
=
Q
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
1
9
,
No
.
6
,
Decem
b
e
r
2
0
2
1
:
1
9
6
2
-
1
9
7
4
1968
T
h
e
k
in
etic
en
er
g
y
o
f
t
h
e
s
y
s
tem
is
eq
u
al
to
th
e
s
u
m
o
f
th
e
k
in
etic
en
er
g
ies
o
f
its
elem
en
ts
.
L
et’
s
f
in
d
t
h
e
k
in
etic
en
e
r
g
y
f
o
r
a
s
p
ac
e
f
r
ee
-
f
ly
in
g
r
o
b
o
t
(
Fig
u
r
e
7
)
.
T
h
e
r
o
b
o
t
co
n
s
is
ts
o
f
f
o
u
r
b
o
d
ies
-
a
b
o
d
y
an
d
th
r
ee
lin
k
s
,
th
er
e
f
o
r
e,
h
av
in
g
c
alcu
lated
th
e
v
alu
e
o
f
t
h
e
k
in
e
tic
en
er
g
y
f
o
r
ea
c
h
b
o
d
y
,
we
will
f
in
d
th
e
k
in
etic
en
er
g
y
o
f
th
e
en
tire
s
y
s
tem
.
Fig
u
r
e
7
.
Sear
ch
f
o
r
ch
ar
ac
ter
i
s
tic
p
o
in
ts
o
f
th
e
en
v
ir
o
n
m
en
t
u
s
in
g
laser
r
an
g
e
f
in
d
er
s
=
∑
3
=
0
.
T
h
e
k
in
etic
en
e
r
g
y
o
f
a
r
ig
id
b
o
d
y
in
t
h
e
g
e
n
er
al
ca
s
e
o
f
m
o
t
io
n
is
eq
u
al
to
:
=
̇
̇
,
(
1
)
wh
er
e
̇
is
th
e
Plü
ck
er
co
o
r
d
in
ates
[
2
1
]
o
f
th
e
v
elo
city
o
f
th
e
b
o
d
y
(
1
)
,
a
n
d
th
e
m
at
r
ix
ch
ar
ac
ter
izes
th
e
m
ass
–
in
er
tial
ch
ar
ac
ter
is
tics
.
Ma
tr
ices
f
o
r
r
i
g
id
b
o
d
ies
o
f
a
s
p
ac
e
r
o
b
o
t
will
h
av
e
th
e
f
o
llo
win
g
f
o
r
m
(
we
n
eg
lect
th
e
m
o
m
en
ts
o
f
in
e
r
tia
with
r
esp
ec
t
to
th
e
ax
es o
f
th
e
lin
k
s
)
:
0
=
[
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
]
,
=
[
1
0
0
0
0
0
0
0
0
0
0
0
0
3
−
0
0
0
0
−
0
0
0
0
0
0
0
0
0
0
0
]
,
=
1
,
2
,
3
,
h
er
e
is
th
e
c
o
o
r
d
in
ate
o
f
t
h
e
ce
n
ter
o
f
m
ass
o
f
th
e
lin
k
alo
n
g
th
e
ax
is
(
in
th
e
co
o
r
d
in
ate
s
y
s
tem
o
f
th
e
–
th
lin
k
)
.
I
n
t
h
is
ca
s
e,
th
e
k
in
e
tic
en
er
g
y
o
f
th
e
e
n
tire
s
p
ac
e
r
o
b
o
t w
ill b
e
f
o
u
n
d
b
y
th
e
f
o
r
m
u
la
:
=
̇
̇
,
wh
er
e
=
[
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
]
.
Fo
r
a
g
r
o
u
n
d
r
o
b
o
t,
th
e
m
atr
ic
es
will h
av
e
th
e
f
o
llo
win
g
f
o
r
m
:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
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KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
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tr
o
l
B
ila
tera
l c
o
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tr
o
l sys
tem
o
f th
e
s
p
a
ce
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b
o
t wi
th
la
r
g
e
d
el
a
ys
(
G.
A
lfer
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v
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1969
=
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1
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ate
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k
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alize
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v
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cities
in
to
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e
L
ag
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an
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eq
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atio
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ac
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f
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m
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,
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,
T
h
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th
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eq
u
atio
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s
o
f
m
o
tio
n
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g
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er
al
f
o
r
m
ca
n
b
e
wr
itten
as
f
o
llo
ws
(
f
o
r
a
g
r
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n
d
r
o
b
o
t,
in
s
tead
o
f
9
th
e
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e
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(
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.
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,
(
q
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=
1
2
(
+
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,
wh
er
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a
u
n
it v
ec
to
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a
co
l
u
m
n
wh
o
s
e
u
n
it is
in
th
e
-
th
r
o
w.
Su
b
s
titu
tin
g
in
to
(
2
)
th
e
d
esire
d
law
o
f
v
ar
iatio
n
o
f
g
e
n
er
alize
d
co
o
r
d
in
ates,
we
f
in
d
g
en
er
alize
d
f
o
r
ce
s
th
at
p
r
o
v
id
e
t
h
e
d
esir
ed
m
o
tio
n
o
f
t
h
e
r
o
b
o
t.
Hen
ce
,
(
2
)
is
th
e
s
o
lu
ti
o
n
to
t
h
e
f
o
r
war
d
d
y
n
am
ics
p
r
o
b
lem
.
3.
ADAP
T
I
NG
T
O
E
N
VIRO
N
M
E
N
T
A
L
CH
ANG
E
S
Fo
r
th
e
r
o
b
o
t’
s
wo
r
k
in
g
t
o
o
l
t
o
s
u
cc
ess
f
u
lly
p
er
f
o
r
m
a
n
o
p
e
r
atio
n
with
an
o
b
ject,
it
is
n
ec
ess
ar
y
th
at
in
th
e
p
r
o
ce
s
s
o
f
im
p
lem
en
tin
g
th
e
o
p
e
r
atio
n
th
e
p
o
s
itio
n
o
f
th
e
o
b
ject
r
elativ
e
to
th
e
wo
r
k
in
g
t
o
o
l,
u
n
iq
u
ely
d
eter
m
in
ed
b
y
th
e
p
o
s
itio
n
o
f
its
ch
ar
ac
ter
is
tic
p
o
in
ts
,
as
well
as
th
e
m
ag
n
itu
d
e
o
f
th
e
f
o
r
ce
o
f
in
ter
ac
tio
n
b
etwe
en
th
e
to
o
l
an
d
th
e
o
b
j
ec
t,
ar
e
id
en
tical
to
th
e
f
o
r
ce
s
an
d
p
o
s
itio
n
o
f
th
eir
m
o
d
el
s
in
th
e
p
r
o
ce
s
s
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
1
9
,
No
.
6
,
Decem
b
e
r
2
0
2
1
:
1
9
6
2
-
1
9
7
4
1970
s
tu
d
y
in
g
.
L
et
u
s
c
o
n
s
id
er
an
a
d
ap
tatio
n
m
eth
o
d
b
ased
o
n
th
e
s
ea
r
ch
f
o
r
ch
ar
ac
ter
is
tic
p
o
in
ts
o
f
o
b
jects
u
s
in
g
laser
r
an
g
ef
in
d
er
s
,
wh
ich
ar
e
n
ec
ess
ar
y
to
ca
lcu
late
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
r
ea
l
p
o
s
itio
n
an
d
r
o
tatio
n
o
f
th
e
b
o
d
y
f
r
o
m
its
m
o
d
el
p
o
s
itio
n
.
T
h
e
r
a
n
g
e
f
in
d
e
r
s
will
b
e
in
s
talled
at
th
e
en
d
o
f
t
h
e
last
lin
k
o
f
th
e
m
an
ip
u
lato
r
,
r
ig
id
ly
c
o
n
n
ec
te
d
to
th
e
b
o
d
y
o
f
th
e
wr
is
t
f
o
r
c
e
-
to
r
q
u
e
s
en
s
o
r
(
Fig
u
r
e
7
)
.
T
h
e
m
o
v
a
b
le
p
ar
t
o
f
th
e
s
en
s
o
r
s
tr
u
ctu
r
e
is
u
s
u
ally
f
asten
ed
t
o
th
e
wo
r
k
i
n
g
to
o
l
o
f
th
e
m
an
ip
u
lato
r
,
wh
ich
allo
ws
th
e
g
r
ip
p
er
t
o
s
lig
h
tly
d
is
p
lace
r
elativ
e
to
th
e
last
lin
k
d
u
e
to
d
ef
o
r
m
atio
n
o
f
t
h
e
elastic
s
tr
u
ctu
r
e
o
f
th
e
s
en
s
o
r
u
n
d
er
t
h
e
ac
tio
n
o
f
th
e
f
o
r
ce
ap
p
lied
to
t
h
e
g
r
ip
p
e
r
wh
en
it
in
ter
ac
ts
with
en
v
ir
o
n
m
en
tal
o
b
jects.
T
h
u
s
,
th
e
p
o
s
itio
n
s
o
f
th
e
ch
ar
ac
ter
is
tic
p
o
i
n
ts
o
f
e
n
v
ir
o
n
m
e
n
tal
o
b
jects
p
r
esen
ted
in
th
e
co
o
r
d
in
ate
s
y
s
tem
o
f
t
h
e
last
lin
k
(
s
en
s
o
r
b
o
d
y
)
s
lig
h
tly
d
if
f
e
r
f
r
o
m
th
ei
r
p
o
s
itio
n
in
th
e
g
r
ip
p
er
co
o
r
d
in
ate
s
y
s
tem
an
d
co
i
n
cid
e
wit
h
it
in
th
e
ab
s
en
ce
o
f
elastic
d
ef
o
r
m
atio
n
o
f
th
e
s
en
s
o
r
,
th
at
is
,
in
th
e
a
b
s
en
ce
o
f
i
n
ter
ac
tio
n
o
f
th
e
g
r
ip
p
e
r
with
o
b
jects
o
f
th
e
ex
ter
n
al
en
v
i
r
o
n
m
e
n
t.
W
h
en
u
s
in
g
laser
r
an
g
e
f
in
d
er
s
,
th
e
c
h
ar
ac
ter
is
tic
p
o
in
ts
ar
e
th
e
p
o
in
ts
o
f
r
ef
lectio
n
o
f
th
e
laser
b
ea
m
f
r
o
m
th
e
s
u
r
f
a
ce
o
f
th
e
m
o
d
els
o
f
en
v
ir
o
n
m
en
tal
o
b
jects
o
b
tain
ed
d
u
r
in
g
t
h
e
tr
ain
in
g
p
r
o
ce
s
s
,
an
d
th
e
p
o
in
ts
o
f
r
ef
lectio
n
o
f
th
e
b
ea
m
f
r
o
m
r
ea
l
o
b
jects
o
b
tain
ed
d
u
r
in
g
th
e
im
p
lem
en
ta
t
io
n
o
f
th
e
r
eq
u
ir
ed
ac
tio
n
.
E
ac
h
p
o
in
t
co
r
r
esp
o
n
d
s
to
th
r
ee
co
m
p
o
n
en
ts
o
f
th
e
p
o
s
itio
n
v
ec
to
r
in
th
e
co
o
r
d
in
at
e
s
y
s
tem
o
f
th
e
las
t
lin
k
o
f
th
e
m
an
ip
u
lato
r
.
T
h
e
m
o
s
t
co
m
m
o
n
d
if
f
er
e
n
ce
b
etw
ee
n
th
e
r
ea
l
e
x
ter
n
al
e
n
v
ir
o
n
m
en
t
an
d
its
m
o
d
el
is
n
o
t
th
e
d
if
f
er
en
c
e
in
s
p
atial
co
n
f
ig
u
r
atio
n
s
o
f
o
b
jects,
b
u
t
b
asically
o
n
ly
in
th
e
r
elativ
e
d
is
p
lace
m
en
t
an
d
r
o
tatio
n
r
elativ
e
to
ea
ch
o
th
e
r
.
T
h
er
ef
o
r
e
,
to
ac
h
iev
e
th
e
p
o
s
i
tio
n
o
f
th
e
wo
r
k
in
g
to
o
l
r
elati
v
e
to
th
e
s
u
r
f
ac
e
o
f
th
e
ex
ter
n
al
en
v
ir
o
n
m
en
t,
id
e
n
tical
to
th
eir
r
ela
tiv
e
m
o
d
el
p
o
s
itio
n
,
it
is
n
ec
es
s
ar
y
to
r
o
tate
an
d
s
h
if
t
th
e
g
r
ip
p
er
ac
c
o
r
d
in
g
ly
.
Fig
u
r
e
7
ex
p
lain
s
th
is
.
On
it,
f
o
r
co
n
v
e
n
ien
ce
o
f
p
er
ce
p
tio
n
,
n
o
t
a
th
r
ee
-
d
im
en
s
io
n
al,
b
u
t
a
two
-
d
im
en
s
io
n
al
ca
s
e
o
f
th
e
ex
ter
n
al
en
v
ir
o
n
m
en
t
is
p
r
esen
ted
.
Fo
r
th
e
p
o
s
itio
n
o
f
th
e
g
r
ip
p
er
r
elativ
e
to
th
e
r
ea
l
s
u
r
f
ac
e
t
o
b
e
i
d
en
tica
l
to
th
e
p
o
s
itio
n
o
f
its
m
o
d
el
r
elativ
e
to
th
e
m
o
d
el
s
u
r
f
ac
e,
it
is
n
ec
ess
ar
y
th
at
th
e
p
o
s
itio
n
v
ec
to
r
s
o
f
at
l
ea
s
t
two
p
o
in
ts
ar
e
eq
u
al,
t
h
at
is
,
X
=
X
,
=
1
,
2
,
3
,
…
.
Fo
r
th
e
p
r
a
ctica
l
im
p
lem
en
tati
o
n
o
f
th
e
e
f
f
ec
t
o
f
co
m
b
in
i
n
g
ch
ar
ac
te
r
is
tic
p
o
in
ts
co
r
r
esp
o
n
d
in
g
to
ea
ch
o
th
er
in
th
e
co
n
tr
o
l
p
r
o
ce
s
s
,
it
is
ad
v
is
ab
le
to
u
s
e
in
th
e
co
n
tr
o
l
law
f
o
r
t
h
e
lo
ca
l
co
n
tr
o
l
s
y
s
tem
o
f
a
s
p
ac
e
r
o
b
o
t
a
ter
m
th
at
is
a
f
u
n
ctio
n
o
f
th
e
v
al
u
e
o
f
th
e
m
is
m
atch
b
etwe
en
t
h
e
d
esire
d
X
an
d
th
e
cu
r
r
e
n
t
X
v
ec
to
r
s
o
f
p
o
s
itio
n
o
f
ch
ar
ac
ter
is
tic
p
o
in
ts
o
f
th
e
ex
ter
n
al
en
v
ir
o
n
m
en
t.
An
d
to
m
ain
tain
th
e
v
ec
to
r
o
f
f
o
r
ce
o
f
in
ter
ac
tio
n
o
f
th
e
wo
r
k
in
g
t
o
o
l
with
o
b
jects
o
f
t
h
e
ex
ter
n
al
e
n
v
ir
o
n
m
en
t
Q
clo
s
e
to
th
e
d
esire
d
Q
o
b
tain
e
d
d
u
r
i
n
g
tr
ain
in
g
,
it
is
n
ec
ess
ar
y
to
u
s
e
in
t
h
e
co
n
tr
o
l
law,
in
ad
d
itio
n
to
th
e
ab
o
v
e
,
th
e
ter
m
t
h
at
is
a
f
u
n
ctio
n
th
e
m
ag
n
itu
d
e
o
f
th
e
m
is
m
atch
b
etwe
en
th
e
v
ec
t
o
r
s
Q
an
d
Q
.
T
h
e
law
is
as f
o
llo
ws
:
=
1
∑
=
1
(
)
(
X
−
X
)
+
(
Q
−
Q
)
,
wh
er
e
Q
an
d
Q
ar
e
v
ec
to
r
s
o
f
th
e
d
esire
d
an
d
cu
r
r
en
t
v
alu
es
o
f
th
e
f
o
r
ce
s
o
f
in
ter
ac
tio
n
o
f
th
e
g
r
ip
p
er
with
th
e
o
b
ject
o
f
th
e
ex
ter
n
al
en
v
i
r
o
n
m
en
t.
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
o
v
er
if
y
th
e
r
esu
lts
,
we
will
ca
r
r
y
o
u
t
co
m
p
u
ter
m
o
d
elin
g
in
th
e
Ma
tlab
k
in
em
at
ics
p
ac
k
ag
e.
T
h
e
p
ac
k
ag
e
is
b
r
o
k
en
u
p
i
n
to
f
u
n
ctio
n
s
th
at
d
ea
l
p
r
im
a
r
ily
with
h
o
m
o
g
en
e
o
u
s
tr
an
s
f
o
r
m
s
an
d
th
eir
L
ie
alg
e
b
r
a,
an
d
a
s
et
o
f
f
u
n
ctio
n
s
f
o
r
in
te
r
ac
tin
g
with
s
er
ial
lin
k
k
in
em
at
ic
s
tr
u
ctu
r
es.
T
h
er
e
ar
e
also
q
u
ite
a
f
ew
f
u
n
ctio
n
s
f
o
r
g
en
e
r
atin
g
n
i
ce
p
lo
ts
an
d
an
im
atio
n
s
o
f
th
e
r
esu
lts
.
I
n
cl
u
d
ed
is
an
h
tm
l
d
o
c
u
m
en
tatio
n
p
ag
e
th
at
lis
ts
all
th
e
f
u
n
ctio
n
s
,
an
d
ea
c
h
f
u
n
cti
o
n
p
r
o
v
i
d
es
its
o
wn
d
o
cu
m
e
n
tatio
n
.
First,
we
will
m
o
d
el
t
h
e
Kin
em
atic
o
f
a
f
r
ee
-
f
ly
in
g
s
p
ac
e
r
o
b
o
t,
th
en
a
f
ter
we
will
m
o
d
el
th
e
d
y
n
am
i
c
wh
er
e
we
r
ep
r
esen
t
th
e
s
o
lu
t
io
n
o
f
th
e
f
o
r
war
d
d
y
n
am
ics p
r
o
b
lem
.
4
.
1
.
K
ine
m
a
t
ic
m
o
delin
g
L
et
th
e
f
o
llo
win
g
in
itial
an
d
f
in
al
v
alu
es
o
f
th
e
g
e
n
er
ali
ze
d
co
o
r
d
in
ates
o
f
a
f
r
ee
-
f
ly
in
g
s
p
ac
e
r
o
b
o
t [
2
2
]
,
[
2
3
]
b
e
g
iv
en
(
Fig
u
r
e
7
)
:
q
0
=
[
0
0
−
/
2
0
2
1
0
0
0
]
,
q
=
[
−
/
6
0
/
4
0
−
2
5
2
/
3
−
/
2
0
]
let
u
s
in
tr
o
d
u
ce
t
h
e
f
o
llo
win
g
d
ep
en
d
e
n
ce
o
f
th
e
ch
a
n
g
e
in
t
h
e
g
en
er
alize
d
co
o
r
d
in
ates o
n
tim
e
̇
(
)
=
̇
(
)
(
1
−
0
)
,
=
1
,
…
,
9
,
wh
er
e
∫
1
0
̇
(
)
=
1
,
L
et
u
s
̇
(
)
=
1
th
en
we
g
et
th
e
f
o
llo
win
g
m
o
t
io
n
o
f
a
f
r
ee
-
f
ly
in
g
s
p
ac
e
r
o
b
o
t (
Fig
u
r
e
8)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
ila
tera
l c
o
n
tr
o
l sys
tem
o
f th
e
s
p
a
ce
r
o
b
o
t wi
th
la
r
g
e
d
el
a
ys
(
G.
A
lfer
o
v
)
1971
L
et
u
s
p
r
esen
t
a
co
m
p
u
ter
s
im
u
latio
n
o
f
th
e
f
o
r
war
d
k
in
e
m
atics
p
r
o
b
lem
f
o
r
th
e
FANUC
g
r
o
u
n
d
m
an
ip
u
lato
r
[
2
4
]
,
[
2
5
]
.
T
ak
e
t
h
e
f
o
llo
win
g
co
o
r
d
in
ates a
s
th
e
in
itial a
n
d
f
in
al
v
alu
es:
q
0
=
0
,
q
=
[
3
/
2
−
/
8
/
3
/
6
−
/
2
/
4
]
th
e
d
ep
e
n
d
en
ce
o
f
th
e
g
e
n
er
ali
ze
d
co
o
r
d
in
ates
o
n
tim
e
will
b
e
s
im
ilar
.
I
n
t
h
is
ca
s
e,
th
e
m
o
t
io
n
o
f
th
e
FANUC
m
an
ip
u
lato
r
(
Fig
u
r
e
6
)
is
s
h
o
wn
in
Fig
u
r
e
9
.
W
e
will
s
o
lv
e
th
e
in
v
er
s
e
k
i
n
em
atics
p
r
o
b
lem
s
im
u
ltan
eo
u
s
ly
f
o
r
b
o
th
g
r
o
u
n
d
an
d
s
p
ac
e
r
o
b
o
ts
,
s
in
ce
th
eir
to
o
ls
m
u
s
t
b
e
t
h
e
s
am
e
f
o
r
b
ilater
al
co
n
tr
o
l.
T
h
e
s
p
ac
e
r
o
b
o
t
will
b
e
v
ir
tu
al,
s
o
it
will
b
e
s
h
o
wn
with
a
d
ash
ed
lin
e.
As
in
p
u
t
d
ata,
we
tak
e
two
p
o
s
itio
n
s
o
f
t
h
e
to
o
l,
in
to
wh
ich
th
e
r
o
b
o
ts
s
h
o
u
ld
co
m
e
f
r
o
m
th
eir
in
itial st
ate:
1
=
[
1
.
5
2
3
/
3
0
/
12
]
,
2
=
[
−
1
−
1
4
/
3
0
−
/
12
]
,
h
er
e
th
e
f
ir
s
t
th
r
ee
co
m
p
o
n
e
n
ts
o
f
th
e
v
ec
to
r
ar
e
r
esp
o
n
s
ib
le
f
o
r
th
e
co
o
r
d
i
n
ates
o
f
th
e
ch
ar
ac
ter
is
tic
p
o
in
t
o
f
th
e
to
o
l
in
ab
s
o
lu
te
s
p
ac
e,
a
n
d
th
e
last
th
r
ee
f
o
r
th
e
o
r
ien
t
atio
n
o
f
th
e
to
o
l.
T
h
e
m
o
tio
n
o
f
r
o
b
o
ts
,
as
in
t
h
e
ca
s
e
o
f
th
e
f
o
r
war
d
k
i
n
em
atics
p
r
o
b
lem
,
will
also
b
e
u
n
if
o
r
m
.
Fig
u
r
e
1
0
illu
s
tr
ates
th
e
p
o
s
itio
n
s
o
f
th
e
r
o
b
o
ts
at
th
e
in
itial m
o
m
en
t o
f
tim
e,
as we
ll a
s
in
th
e
g
iv
en
p
o
s
itio
n
s
o
f
th
e
to
o
l.
Fig
u
r
e
8
.
So
lu
tio
n
o
f
th
e
f
o
r
w
ar
d
k
in
em
atics
p
r
o
b
lem
f
o
r
t
h
e
s
p
ac
e
r
o
b
o
t
Fig
u
r
e
9
.
So
lu
tio
n
o
f
th
e
f
o
r
w
ar
d
k
in
em
atics p
r
o
b
lem
f
o
r
th
e
g
r
o
u
n
d
r
o
b
o
t
Fig
u
r
e
1
0
.
So
lu
tio
n
o
f
th
e
i
n
v
e
r
s
e
k
in
em
atics p
r
o
b
lem
f
o
r
th
e
s
p
ac
e
an
d
g
r
o
u
n
d
r
o
b
o
t
4
.
2
.
Dy
na
m
ic
m
o
delin
g
W
e
r
ep
r
esen
t
th
e
s
o
lu
tio
n
o
f
th
e
f
o
r
war
d
d
y
n
am
ics
p
r
o
b
le
m
.
T
h
e
task
is
to
s
ea
r
ch
f
o
r
g
en
er
alize
d
f
o
r
ce
s
th
at
p
r
o
v
id
e
a
g
iv
en
la
w
o
f
ch
an
g
e
o
f
g
en
er
alize
d
co
o
r
d
in
ates.
L
et
u
s
g
iv
e
a
s
o
lu
tio
n
to
th
e
p
r
o
b
lem
f
o
r
th
e
f
r
ee
-
f
l
y
in
g
s
p
ac
e
r
o
b
o
t.
L
e
t u
s
s
et
th
e
f
o
llo
win
g
law
o
f
c
h
an
g
e
o
f
g
e
n
er
alize
d
co
o
r
d
in
a
tes:
Evaluation Warning : The document was created with Spire.PDF for Python.