I
nte
rna
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n (
I
J
R
A)
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
2
0
,
p
p
.
51
~
61
I
SS
N:
2089
-
4
8
5
6
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
r
a
.
v
9
i
1
.
pp
51
-
61
51
J
o
ur
na
l ho
m
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e
:
h
ttp
:
//ij
r
a
.
ia
esco
r
e.
co
m
Discrete
t
i
m
e
rea
ching
law
bas
ed v
a
ria
ble struc
ture
co
ntrol for
fas
t
reachi
ng
w
ith
reduce
d chat
teri
ng
P
o
urna
m
i P
a
d
m
a
la
t
ha
,
Su
s
y
T
ho
m
a
s
Na
ti
o
n
a
l
In
st
it
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te
o
f
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e
c
h
n
o
lo
g
y
Ca
li
c
u
t
Art
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I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
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y:
R
ec
eiv
ed
Au
g
1
9
,
2
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1
9
R
ev
i
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ed
Oct
2
0
,
2
0
1
9
A
cc
ep
ted
No
v
1
5
,
2
0
1
9
In
th
is
p
a
p
e
r,
a
v
a
riab
le
stru
c
tu
r
e
c
o
n
tro
l
law
is
p
ro
p
o
se
d
f
o
r
d
is
c
re
te
ti
m
e
slid
in
g
m
o
d
e
c
o
n
tro
l
so
a
s
to
re
d
u
c
e
b
o
t
h
re
a
c
h
in
g
ti
m
e
a
n
d
q
u
a
si
slid
in
g
m
o
d
e
b
a
n
d
re
d
u
c
ti
o
n
.
T
h
is
n
e
w
law
is
c
o
m
p
o
se
d
o
f
tw
o
d
iff
e
r
e
n
t
slid
i
n
g
v
a
riab
le
d
y
n
a
m
ics
;
o
n
e
to
a
c
h
iev
e
fa
st
re
a
c
h
in
g
a
n
d
th
e
o
t
h
e
r
to
c
o
u
n
ter
it
s
e
ffe
c
t
o
n
w
id
e
n
in
g
th
e
q
u
a
si
sli
d
in
g
m
o
d
e
b
a
n
d
.
T
h
is
is
a
c
c
o
m
p
li
sh
e
d
b
y
in
tro
d
u
c
i
n
g
a
b
o
u
n
d
a
ry
la
y
e
r
a
ro
u
n
d
t
h
e
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d
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g
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rf
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a
b
o
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t
w
h
ich
th
e
tran
sf
o
r
m
a
ti
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n
o
f
th
e
slid
in
g
v
a
riab
le d
y
n
a
m
ics
ta
k
e
s p
lac
e
.
T
h
is
p
r
o
v
id
e
s th
e
f
le
x
ib
il
it
y
to
c
h
o
o
se
t
h
e
in
it
ial
d
y
n
a
m
i
c
s
in
su
c
h
a
w
a
y
a
s
to
sp
e
e
d
u
p
t
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e
re
a
c
h
in
g
p
h
a
se
a
n
d
th
e
n
a
t
th
e
b
o
u
n
d
a
ry
tran
s
f
o
rm
th
is
d
y
n
a
m
ics
to
o
n
e
th
a
t
re
d
u
c
e
s
th
e
q
u
a
si
sli
d
in
g
m
o
d
e
b
a
n
d
.
T
h
u
s,
t
h
e
law
e
ff
e
c
ti
v
e
l
y
c
o
a
les
c
e
s
th
e
a
d
v
a
n
tag
e
o
u
s
tra
it
s
o
f
h
it
h
e
rt
o
p
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o
p
o
se
d
re
a
c
h
in
g
law
s
th
a
t
su
c
c
e
e
d
in
e
i
th
e
r
th
e
re
d
u
c
ti
o
n
o
f
re
a
c
h
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g
p
h
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se
o
r
th
e
e
li
m
in
a
ti
o
n
o
f
q
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a
si
slid
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g
m
o
d
e
b
a
n
d
.
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h
e
e
f
fe
c
ti
v
e
n
e
ss
o
f
th
e
p
ro
p
o
se
d
re
a
c
h
in
g
law
is
v
a
li
d
a
ted
t
h
ro
u
g
h
sim
u
latio
n
s.
K
ey
w
o
r
d
s
:
C
o
n
tr
o
l e
f
f
o
r
t
Dis
cr
ete
-
ti
m
e
s
lid
i
n
g
m
o
d
e
co
n
tr
o
l
Qu
asi
s
lid
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n
g
m
o
d
e
b
an
d
R
ea
ch
i
n
g
la
w
R
ea
ch
i
n
g
ti
m
e
T
h
is
is
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
P
o
u
r
n
a
m
i P
,
E
lectr
ical
E
n
g
i
n
ee
r
i
n
g
Dep
ar
t
m
en
t,
Natio
n
al
I
n
s
tit
u
te
o
f
T
ec
h
n
o
lo
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y
C
alic
u
t,
Ker
ala,
I
n
d
ia
.
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m
ail:
s
u
k
ak
ar
t
h
i
@
g
m
a
il.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Sli
d
in
g
Mo
d
e
C
o
n
tr
o
l
(
SMC
)
,
s
in
ce
it
s
i
n
ce
p
tio
n
i
n
R
u
s
s
ia
in
t
h
e
late
1
9
5
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s
h
a
s
ac
q
u
ir
ed
w
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l
in
th
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ar
ea
o
f
co
n
tr
o
l
en
g
in
ee
r
i
n
g
[
1
-
3
]
,
b
y
v
ir
t
u
e
o
f
th
e
n
u
m
er
o
u
s
ad
v
an
ta
g
e
s
it
o
f
f
er
s
,
t
h
e
m
o
s
t
i
m
p
o
r
tan
t
o
f
w
h
ic
h
i
s
t
h
e
i
n
v
ar
ian
ce
to
ex
ter
n
al
d
i
s
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r
b
a
n
ce
s
a
n
d
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y
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te
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u
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ce
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ap
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d
esig
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.
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R
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ased
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,
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e
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d
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o
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o
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s
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it
ca
n
p
r
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ib
e
th
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r
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ch
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n
g
d
y
n
a
m
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s
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.
th
e
m
an
n
er
i
n
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ich
t
h
e
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y
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te
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tr
aj
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to
r
y
m
o
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t
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e
s
lid
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u
r
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e.
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r
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g
la
w
ap
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h
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s
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ir
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t
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p
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s
ed
f
o
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co
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tin
u
o
u
s
s
y
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te
m
s
[
2
,
3
]
,
b
u
t
w
i
th
t
h
e
wid
esp
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ea
d
u
s
e
o
f
co
m
p
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ter
s
i
n
co
n
tr
o
l
tech
n
iq
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it
w
as
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n
l
y
n
a
tu
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al
t
h
at
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C
b
e
ex
ten
d
ed
to
d
is
cr
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e
s
y
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te
m
s
[
4
]
.
T
h
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R
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g
la
w
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y
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n
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Ho
m
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if
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[
5
]
.
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n
th
is
p
ap
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th
is
R
L
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s
r
ef
er
r
ed
to
as
Gao
’
s
Di
s
cr
ete
R
ea
ch
in
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L
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w
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GDR
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.
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ak
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e
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ev
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r
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ar
d
m
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if
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r
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la
w
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[7
-
1
1
]
th
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u
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[
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1
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[
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W
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I
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I
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,
Vo
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9
,
No
.
1
,
Ma
r
ch
2
0
2
0
:
51
–
61
5
2
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m
e
s
in
t
o
p
lay
d
ep
en
d
in
g
o
n
th
e
v
alu
e
o
f
th
e
s
lid
i
n
g
v
ar
iab
le.
T
h
is
is
ac
co
m
p
li
s
h
ed
b
y
th
e
co
n
ce
p
t
o
f
a
b
o
u
n
d
ar
y
la
y
er
ar
o
u
n
d
th
e
s
lid
in
g
s
u
r
f
ac
e
w
h
er
e
th
e
R
L
u
n
d
er
g
o
es
a
tr
an
s
f
o
r
m
atio
n
f
r
o
m
t
h
e
f
ast
p
ac
ed
r
ea
ch
in
g
p
r
o
v
id
ed
b
y
th
e
R
L
i
n
[
1
1
]
(
r
ef
er
r
ed
as
No
v
el
E
x
p
o
n
e
n
tia
l
R
ea
c
h
i
n
g
L
a
w
(
NE
R
L
)
)
to
an
as
y
m
p
to
tic
co
n
v
er
g
en
ce
o
f
t
h
e
s
lid
in
g
v
ar
iab
le
to
th
e
s
li
d
in
g
s
u
r
f
ac
e
as
p
er
[
1
0
]
(
b
e
in
g
r
e
f
er
r
ed
to
as
B
ar
to
s
ze
w
icz
L
ato
s
i
´
n
s
k
i D
is
c
r
ete
-
ti
m
e
R
ea
c
h
i
n
g
L
a
w
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B
L
D
R
L
)
i
n
t
h
is
p
ap
er
)
.
T
h
is
p
ap
er
is
s
t
r
u
ct
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r
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as
f
o
llo
w
s
.
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n
s
ec
t
io
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2
,
a
b
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ief
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ie
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o
f
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an
d
B
L
DR
L
i
s
g
iv
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a
n
d
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ased
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n
th
ese,
th
e
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r
o
p
o
s
e
d
R
L
is
f
o
r
m
u
lated
f
o
r
n
o
m
i
n
al
an
d
p
er
tu
r
b
ed
s
y
s
te
m
s
.
I
n
s
ec
tio
n
3
,
th
e
s
i
m
u
lat
io
n
r
es
u
lt
s
o
b
tai
n
ed
f
o
r
th
e
p
r
o
p
o
s
ed
R
L
la
w
ar
e
g
i
v
e
n
to
g
e
th
er
w
it
h
a
co
m
p
ar
is
o
n
b
et
w
ee
n
t
h
e
v
ar
io
u
s
r
ea
c
h
in
g
la
w
s
,
v
iz.
,
G
DR
L
,
NE
R
L
an
d
B
L
DR
L
.
C
o
n
clu
d
i
n
g
r
e
m
ar
k
s
ar
e
g
i
v
en
i
n
Sectio
n
4
.
2.
P
RO
P
O
SE
D
CO
NT
RO
L
S
T
RAT
E
G
Y
2
.
1
.
B
rief
re
v
ie
w
o
f
NE
RL
a
nd
B
L
DR
L
C
o
n
s
id
er
th
e
f
o
llo
w
i
n
g
d
i
s
cr
ete
lin
ea
r
s
y
s
te
m
:
(
)
(
)
(
)
(
1
)
w
h
er
e
is
an
m
atr
i
x
,
(
)
is
th
e
s
tate
v
ec
to
r
,
is
th
e
in
p
u
t
v
ec
to
r
an
d
(
)
is
th
e
s
ca
lar
co
n
tr
o
l
s
ig
n
al.
T
h
e
s
lid
in
g
s
u
r
f
ac
e
i
s
d
ef
i
n
ed
as:
(
)
(
)
(
2
)
w
h
er
e
(
)
(
)
(
)
is
t
h
e
er
r
o
r
v
ec
to
r
an
d
is
th
e
s
lid
in
g
co
ef
f
icie
n
t
v
ec
t
o
r
th
at
is
s
o
d
esi
g
n
ed
to
y
ield
s
tab
le
d
y
n
a
m
ics
w
h
e
n
t
h
e
s
y
s
te
m
is
i
n
Sl
id
in
g
Mo
d
e
Mo
tio
n
(
SMM
)
.
(
)
is
t
h
e
d
esire
d
v
alu
e
o
f
th
e
s
tate
v
ec
to
r
.
T
h
e
s
e
m
in
a
l R
L
p
r
o
p
o
s
ed
b
y
Gao
et
al.
in
1
9
9
5
[
5
]
tak
es th
e
f
o
llo
w
in
g
f
o
r
m
:
(
)
(
)
(
)
,
(
)
-
(
3
)
w
h
er
e
is
th
e
p
r
o
p
o
r
tio
n
al
ter
m
,
is
th
e
co
n
s
tan
t
ter
m
w
it
h
an
d
an
d
is
th
e
s
a
m
p
li
n
g
p
er
io
d
.
W
h
ile
th
is
R
L
r
e
m
ain
s
p
o
p
u
lar
to
th
is
d
ate,
th
i
s
la
w
ca
u
s
e
s
t
h
e
s
y
s
te
m
r
ep
r
ese
n
tati
v
e
p
o
in
t
(
tip
o
f
t
h
e
sy
s
te
m
tr
aj
ec
to
r
y
an
d
/o
r
s
lid
i
n
g
v
ar
iab
le)
to
cr
o
s
s
th
e
s
l
id
in
g
s
u
r
f
ac
e
at
s
o
m
e
f
i
n
ite
ti
m
e
an
d
t
h
e
n
m
o
v
e
i
n
a
p
er
p
etu
all
y
zi
g
za
g
m
a
n
n
er
ar
o
u
n
d
th
e
s
u
r
f
ac
e.
T
h
is
m
o
tio
n
,
in
co
n
tr
ast
to
th
e
id
ea
l
SMM
,
w
as
co
i
n
ed
as
t
h
e
Qu
asi
S
lid
in
g
Mo
d
e
(
QSM)
m
o
tio
n
ar
o
u
n
d
t
h
e
s
lid
in
g
s
u
r
f
ac
e
[
5
]
.
Du
e
to
th
e
QSM,
m
o
r
e
co
n
tr
o
l
ef
f
o
r
t
is
ex
p
en
d
ed
in
th
e
s
lid
i
n
g
m
o
d
e.
Hen
ce
,
it
is
d
esira
b
le
to
k
ee
p
th
e
w
id
th
o
f
t
h
e
QSMB
as
m
i
n
i
m
u
m
as
p
o
s
s
ib
le.
T
h
e
w
id
th
o
f
QSMB
is
d
ir
ec
t
l
y
af
f
ec
ted
b
y
th
e
co
n
s
tan
t
ter
m
in
(
3
)
an
d
it
ca
n
b
e
r
e
d
u
ce
d
b
y
th
e
u
s
e
o
f
a
s
m
al
ler
v
alu
e
o
f
.
Ho
w
e
v
er
,
th
is
w
ill
i
n
tu
r
n
r
ed
u
ce
th
e
r
ate
o
f
ch
an
g
e
o
f
th
e
s
lid
i
n
g
v
ar
iab
le
lead
in
g
to
in
cr
ea
s
ed
r
ea
ch
i
n
g
p
h
a
s
e.
Si
n
ce
it
is
t
h
e
SMM
th
a
t
o
f
f
er
s
r
o
b
u
s
tn
es
s
to
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
,
in
cr
ea
s
ed
r
ea
ch
in
g
p
h
ase
i
s
u
n
d
e
s
ir
ab
le.
On
th
e
o
th
er
h
a
n
d
,
if
th
e
ter
m
,
th
at
af
f
ec
t
s
th
e
r
ea
ch
i
n
g
ti
m
e,
is
in
cr
ea
s
ed
,
th
e
r
ea
c
h
i
n
g
ti
m
e
i
s
r
ed
u
ce
d
,
b
u
t
ca
u
s
es
a
n
i
n
cr
ea
s
e
in
t
h
e
w
id
t
h
o
f
t
h
e
QSMB
d
u
e
to
t
h
e
in
cr
ea
s
ed
r
ate
o
f
ch
an
g
e
o
f
t
h
e
s
l
id
in
g
v
ar
iab
le
n
ea
r
t
h
e
s
l
id
in
g
s
u
r
f
ac
e.
I
n
o
r
d
er
to
s
o
lv
e
t
h
is
d
ile
m
m
a,
s
ev
er
al
n
e
w
R
L
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
th
at
u
s
e
co
n
tr
o
ller
g
ai
n
s
th
at
ad
ap
t
to
th
e
v
a
r
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n
s
i
n
t
h
e
s
lid
i
n
g
v
ar
iab
le
.
NE
R
L
,
p
r
o
p
o
s
ed
b
y
Ma
e
t
al.
s
tr
i
v
es
to
s
o
lv
e
t
h
is
d
ile
m
m
a
b
y
i
n
co
r
p
o
r
atin
g
an
ex
p
o
n
e
n
tial
ter
m
[
1
1
]
in
(
3
)
.
T
h
e
NE
R
L
f
o
r
a
n
o
m
i
n
al
s
y
s
te
m
i
s
d
ef
i
n
ed
as:
(
)
(
)
(
)
(
)
(
)
(
(
)
)
(
4
)
w
h
er
e
(
)
(
)
|
(
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|
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
Dis
crete
ti
me
r
ea
ch
in
g
la
w
b
a
s
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va
r
ia
b
le
s
tr
u
ctu
r
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co
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tr
o
l fo
r
fa
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ch
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g
... (
P
o
u
r
n
a
mi
P
a
d
ma
la
th
a
)
53
{
(
6
)
Fro
m
(
5
)
,
it
is
s
ee
n
t
h
at
t
h
e
v
alu
e
o
f
(
)
is
f
o
r
lar
g
e
v
al
u
es
o
f
th
e
s
lid
in
g
v
ar
iab
le,
i.e
.
w
h
en
th
e
s
y
s
te
m
s
tates
ar
e
f
ar
a
w
a
y
f
r
o
m
t
h
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s
lid
in
g
s
u
r
f
ac
e
a
n
d
it
tak
e
s
th
e
v
alu
e
o
n
e
w
h
e
n
s
y
s
te
m
s
s
tat
es
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clo
s
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to
th
e
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in
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in
ce
is
a
p
o
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itiv
e
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less
t
h
a
n
o
n
e,
th
e
f
i
r
s
t
ter
m
b
ec
o
m
es
(
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w
h
ic
h
is
le
s
s
er
th
an
(
)
an
d
th
e
s
ec
o
n
d
ter
m
b
ec
o
m
e
s
w
h
ich
is
h
ig
h
er
t
h
an
.
T
h
is
ca
u
s
e
s
a
f
a
s
ter
r
ate
o
f
ch
a
n
g
e
o
f
th
e
s
l
id
in
g
v
ar
iab
le
at
th
e
b
eg
in
n
i
n
g
a
s
co
m
p
ar
ed
to
(
3
)
(
=1
s
ec
is
a
s
s
u
m
ed
)
.
B
u
t,
as
th
e
s
y
s
te
m
r
ep
r
esen
ta
tiv
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p
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ts
(
R
P
)
m
o
v
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clo
s
er
to
t
h
e
s
lid
i
n
g
s
u
r
f
ac
e
th
e
r
ea
ch
in
g
la
w
(
4
)
tr
an
s
f
o
r
m
s
i
n
to
GD
R
L
a
s
in
(
3
)
.
T
h
u
s
,
th
e
w
id
t
h
o
f
t
h
e
QSMB
is
b
o
u
n
d
to
r
e
m
ai
n
t
h
e
s
a
m
e
a
s
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at
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u
t
t
h
e
r
ea
ch
i
n
g
ti
m
e
is
r
ed
u
ce
d
.
B
L
DR
L
i
n
[
1
0
]
o
f
f
er
ed
r
ed
u
ce
d
QSMB
o
w
i
n
g
to
a
b
o
u
n
d
ed
r
ate
o
f
co
n
v
er
g
en
ce
o
f
t
h
e
s
lid
in
g
v
ar
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le
to
ze
r
o
.
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h
is
R
L
ac
t
s
as
a
co
m
p
r
o
m
is
e
b
et
w
ee
n
th
e
s
w
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tch
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t
y
p
e
R
L
s
,
w
h
e
r
e
s
lid
in
g
v
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iab
le
cr
o
s
s
es
th
e
s
lid
in
g
s
u
r
f
ac
e
in
e
ac
h
d
is
cr
ete
in
s
ta
n
t
in
t
h
e
QS
M,
an
d
th
e
n
o
n
s
w
itc
h
i
n
g
t
y
p
e
R
L
s
th
a
t
r
etain
t
h
e
s
lid
in
g
v
ar
iab
le
in
a
s
p
ec
i
f
ied
b
an
d
ar
o
u
n
d
th
e
s
lid
in
g
s
u
r
f
a
ce
[
1
0
]
.
W
h
eth
er
th
e
s
lid
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v
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cr
o
s
s
es
th
e
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lid
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f
ac
e
o
r
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s
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e,
t
h
e
d
is
tan
ce
o
f
th
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s
y
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m
R
P
f
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o
m
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r
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h
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w
h
en
t
h
e
s
y
s
te
m
is
in
QSM,
m
ak
in
g
it
t
h
e
id
ea
l
r
ea
c
h
in
g
la
w
n
ea
r
.
T
h
e
B
L
DR
L
i
s
g
i
v
e
n
b
y
:
(
)
,
(
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-
(
(
)
,
(
)
-
)
(
7
)
w
h
er
e
,
(
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-
*
,
(
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-
+
is
a
p
o
s
itiv
e
r
ea
l
n
u
m
b
er
an
d
.
T
h
e
v
alu
e
o
f
f
o
r
lar
g
e
v
alu
es
o
f
(
)
is
o
n
e,
th
er
eb
y
ca
u
s
i
n
g
th
e
th
e
s
lid
i
n
g
v
ar
iab
le
to
d
ec
r
ea
s
e
at
an
al
m
o
s
t
co
n
s
ta
n
t
r
ate,
.
B
u
t,
clo
s
er
to
th
e
s
lid
in
g
s
u
r
f
a
ce
th
e
v
al
u
e
o
f
d
ec
r
ea
s
es
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d
ten
d
s
to
ze
r
o
asy
m
p
to
tical
l
y
.
A
s
a
r
es
u
lt,
ar
o
u
n
d
th
e
s
lid
i
n
g
s
u
r
f
ac
e,
if
(
)
r
ea
ch
es
e
x
ac
tl
y
o
n
th
e
s
u
r
f
ac
e
(
)
,
it
w
i
ll
r
e
m
ai
n
th
er
e
f
r
o
m
t
h
en
o
n
.
Ot
h
er
w
is
e,
th
e
v
al
u
e
o
f
(
)
k
ee
p
s
d
ec
r
ea
s
in
g
w
it
h
ea
ch
s
tep
.
T
h
u
s
,
th
e
co
n
tr
o
l
e
f
f
o
r
t
d
u
r
i
n
g
s
lid
i
n
g
m
o
d
e
is
g
r
ea
tl
y
r
ed
u
ce
d
as
co
m
p
ar
ed
to
NE
R
L
a
n
d
GD
R
L
.
Ho
w
e
v
er
,
th
e
r
ea
ch
i
n
g
ti
m
e
i
s
m
o
r
e
th
a
n
th
a
t
p
r
o
v
id
ed
b
y
th
e
m
o
d
i
f
ied
co
n
s
ta
n
t
ter
m
in
(
4
)
.
T
h
e
p
r
o
p
o
s
ed
R
L
s
u
cc
e
s
s
f
u
ll
y
u
ti
lizes t
h
e
af
o
r
em
e
n
tio
n
ed
m
er
its
o
f
b
o
th
NE
R
L
an
d
B
L
D
R
L
.
2
.
2
.
P
ro
po
s
ed
re
a
ching
la
w
f
o
r
no
m
i
na
l sy
s
t
e
m
s
Kee
p
in
g
i
n
co
n
s
id
er
atio
n
b
o
th
r
ed
u
ce
d
r
ea
ch
in
g
ti
m
e
an
d
r
ed
u
ce
d
QSMB
w
i
d
t
h
,
it
is
d
esi
r
ab
le
th
at
NE
R
L
b
e
u
s
ed
f
o
r
lar
g
e
v
alu
e
s
o
f
th
e
s
lid
in
g
v
ar
iab
le
(
in
it
i
al
p
h
ase
o
f
r
ea
ch
in
g
)
,
th
er
eb
y
p
r
o
v
id
in
g
f
ast
r
ate
o
f
ch
a
n
g
e
o
f
s
lid
i
n
g
v
ar
iab
le
at
th
e
b
eg
i
n
n
i
n
g
a
n
d
B
L
D
R
L
b
e
u
s
ed
as
th
e
s
y
s
te
m
R
P
in
ch
e
s
clo
s
er
to
th
e
s
lid
in
g
s
u
r
f
ac
e,
r
es
u
lti
n
g
i
n
s
m
aller
Q
SMB
.
T
h
is
is
ac
co
m
p
lis
h
ed
b
y
i
n
tr
o
d
u
cin
g
a
b
o
u
n
d
ar
y
la
y
er
ar
o
u
n
d
t
h
e
s
lid
in
g
s
u
r
f
ac
e,
s
a
y
(
)
,
w
h
er
e
is
a
s
m
all
p
o
s
iti
v
e
v
al
u
e
less
er
th
an
t
h
e
in
itia
l
v
al
u
e
o
f
th
e
s
lid
in
g
v
ar
iab
le.
Fo
r
v
al
u
es
o
f
|
(
)
|
,
th
e
co
n
tr
o
ller
ev
o
lv
i
n
g
f
r
o
m
NE
R
L
is
e
m
p
lo
y
ed
a
n
d
f
o
r
|
(
)
|
,
B
L
DR
L
's
co
n
tr
o
ller
is
u
s
ed
.
Hen
ce
,
it
is
e
s
s
e
n
tial
to
h
av
e
a
R
L
t
h
at
w
i
ll
as
s
u
m
e
t
h
e
f
o
r
m
i
n
(
4
)
u
n
til
(
)
an
d
b
ey
o
n
d
th
at
it
s
h
o
u
ld
tr
an
s
f
o
r
m
to
(
7
)
.
T
h
is
is
ac
h
ie
v
ed
b
y
t
h
e
p
r
o
p
o
s
ed
R
L
w
it
h
th
e
s
tr
u
ctu
r
e:
(
)
,
(
)
-
(
(
)
,
(
)
-
)
,
(
)
-
(
(
)
(
)
(
)
(
)
,
(
)
-
)
,
(
)
-
(
8
)
w
h
er
e
,
(
)
-
(
,
(
)
-
(
,
(
)
-
,
(
)
-
)
)
,
(
)
-
(
,
(
)
-
(
,
(
)
-
,
(
)
-
)
)
Fro
m
th
e
ab
o
v
e
ex
p
r
es
s
io
n
s
,
it
ca
n
b
e
s
ee
n
t
h
at
f
o
r
v
al
u
es
o
f
|
(
)
|
,
is
ze
r
o
an
d
is
o
n
e
an
d
(
8
)
tr
an
s
f
o
r
m
s
i
n
to
NE
R
L
g
i
v
en
b
y
(
4
)
.
I
n
a
s
im
ilar
m
an
n
er
,
f
o
r
|
(
)
|
,
b
ec
o
m
es
o
n
e
an
d
is
eq
u
al
t
o
ze
r
o
,
th
u
s
ca
u
s
in
g
(
8
)
to
m
eta
m
o
r
p
h
o
s
e
in
to
(
7
)
.
T
h
u
s
,
in
i
ti
all
y
f
o
r
lar
g
e
v
al
u
e
s
o
f
s
lid
i
n
g
v
ar
iab
le,
f
aster
r
ate
o
f
ch
a
n
g
e
i
s
o
b
tain
ed
an
d
n
e
ar
th
e
s
lid
in
g
s
u
r
f
ac
e,
a
co
n
s
tan
t
r
ate
o
f
ch
a
n
g
e
f
o
llo
w
ed
b
y
a
n
as
y
m
p
to
tic
co
n
v
er
g
e
n
ce
is
ac
h
ie
v
ed
.
T
h
i
s
r
es
u
lts
i
n
m
u
ch
f
aster
r
ea
c
h
in
g
as
co
m
p
ar
ed
to
GD
R
L
an
d
B
L
D
R
L
.
T
h
e
r
ea
ch
in
g
ti
m
e
i
s
co
m
p
ar
ab
le
to
th
at
o
f
NE
R
L
,
b
u
t
t
h
e
Q
SMB
is
r
ed
u
ce
d
to
a
g
r
ea
t
e
x
ten
t
w
h
ich
i
s
n
o
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
2
0
:
51
–
61
54
p
o
s
s
ib
le
w
ith
NE
R
L
.
I
n
s
h
o
r
t,
it
co
m
b
in
e
s
t
h
e
b
en
e
f
it
s
o
f
N
E
R
L
a
n
d
B
L
D
R
L
,
g
iv
in
g
a
r
e
ac
h
in
g
la
w
th
a
t
ca
n
s
u
cc
e
s
s
f
u
ll
y
tac
k
le
t
h
e
r
ea
ch
i
n
g
ti
m
e/QSMB
d
ile
m
m
a
m
e
n
ti
o
n
ed
ea
r
lier
.
2
.
2
.
1
.
Rea
cha
bil
it
y
o
f
t
he
pro
po
s
ed
re
a
ching
la
w
Ass
u
m
e
th
at
(
)
w
i
th
(
)
.
Fro
m
(
8
)
,
w
e
ca
n
w
r
ite:
(
)
(
)
(
)
(
)
(
)
(
9
)
w
h
ic
h
ca
n
b
e
r
e
w
r
it
ten
a
s
:
(
)
(
)
(
)
(
)
(
)
(
1
0
)
W
e
h
av
e
,
an
d
(
)
.
T
h
u
s
,
t
h
e
R
HS
o
f
(
1
0
)
is
n
e
g
ati
v
e
w
h
er
eb
y
w
it
h
(
)
,
it
f
o
llo
ws
th
at
(
)
(
)
.
Si
m
ilar
l
y
,
i
t
ca
n
b
e
s
ee
n
th
at
f
o
r
(
)
an
d
(
)
,
th
e
s
lid
in
g
v
ar
iab
le
v
al
u
e
d
ec
r
ea
s
es
in
ea
ch
d
is
cr
ete
s
te
p
.
I
t
ca
n
t
h
u
s
b
e
co
n
cl
u
d
ed
t
h
at
o
u
ts
id
e
t
h
e
b
o
u
n
d
ar
y
la
y
e
r
,
(
)
(
)
.
On
ce
t
h
e
s
lid
in
g
v
ar
iab
le
e
n
te
r
s
th
e
b
o
u
n
d
ar
y
la
y
er
,
(
)
an
d
(
)
o
r
(
)
an
d
(
)
.
L
et
u
s
f
ir
s
t c
o
n
s
id
er
th
e
ca
s
e
w
h
e
n
(
)
an
d
(
)
.
Fro
m
(
8
)
,
(
)
,
(
)
-
(
(
)
)
(
1
1
)
T
h
e
s
lid
in
g
s
u
r
f
ac
e
is
cr
o
s
s
ed
w
h
e
n
(
)
.
T
h
u
s
,
,
(
)
-
(
(
)
)
(
1
2
)
Sin
ce
,
(
)
-
is
al
w
a
y
s
p
o
s
itiv
e,
(
)
(
1
3
)
Fro
m
(
1
3
)
,
it
ca
n
b
e
co
n
clu
d
e
d
th
at
th
e
s
lid
i
n
g
s
u
r
f
ac
e
w
il
l
b
e
cr
o
s
s
ed
w
h
e
n
(
)
b
ec
o
m
e
s
les
s
th
a
n
.
I
n
a
s
i
m
ilar
m
a
n
n
er
,
th
is
ca
n
b
e
p
r
o
v
ed
f
o
r
th
e
ca
s
e
w
h
e
n
(
)
.
I
n
g
en
er
al,
w
e
ca
n
w
r
i
te
if
|
(
)
|
,
th
en
,
(
)
-
,
(
)
-
.
On
th
e
o
th
er
h
an
d
,
if
|
(
)
|
,
(
)
(
)
.
T
h
u
s
,
w
e
ca
n
co
n
clu
d
e
t
h
at
t
h
e
v
alu
e
o
f
t
h
e
s
lid
i
n
g
v
ar
iab
le
k
ee
p
s
d
ec
r
ea
s
in
g
o
u
ts
id
e
th
e
b
o
u
n
d
ar
y
as
w
ell
a
s
i
n
s
id
e
t
h
e
b
o
u
n
d
ar
y
.
On
ce
th
e
v
al
u
e
o
f
(
)
b
ec
o
m
e
s
les
s
th
a
n
,
it
cr
o
s
s
es
th
e
s
l
id
in
g
s
u
r
f
ac
e.
T
h
is
is
e
n
s
u
r
ed
d
u
e
to
th
e
s
tead
y
d
ec
r
ea
s
e
in
t
h
e
v
a
lu
e
o
f
s
lid
i
n
g
v
ar
iab
le
b
ec
au
s
e
o
f
w
h
ic
h
at
s
o
m
e
p
o
in
t
(
)
.
T
h
u
s
,
it
is
en
s
u
r
ed
th
at
t
h
e
s
lid
i
n
g
s
u
r
f
ac
e
is
r
ea
ch
ed
in
f
in
ite
ti
m
e.
2
.
2
.
2
.
Q
ua
s
i
-
s
lid
i
ng
m
o
de
o
f
t
he
pro
po
s
ed
re
a
ching
la
w
On
ce
th
e
s
lid
in
g
v
ar
iab
le
r
e
ac
h
es
t
h
e
v
ici
n
it
y
o
f
t
h
e
s
li
d
in
g
s
u
r
f
ac
e
(
)
,
th
e
f
u
n
ctio
n
b
eg
in
s
to
d
r
o
p
.
A
s
a
r
es
u
lt,
in
th
e
q
u
a
s
i
s
lid
in
g
m
o
d
e
b
an
d
,
in
s
tead
o
f
m
ain
tain
in
g
t
h
e
s
a
m
e
v
alu
e
as
i
s
s
ee
n
w
it
h
NE
R
L
an
d
GD
R
L
,
t
h
e
s
l
i
d
in
g
v
ar
iab
le
v
al
u
e
d
r
o
p
s
in
ea
ch
s
u
b
s
eq
u
e
n
t d
is
cr
ete
in
s
ta
n
t.
(
)
,
(
)
-
(
(
)
)
(
1
4
)
w
h
er
e
in
th
e
n
ea
r
v
ic
in
it
y
o
f
(
)
.
W
h
eth
er
t
h
e
s
lid
i
n
g
v
ar
iab
le
s
w
itc
h
es
i
n
ev
er
y
i
n
s
ta
n
t
o
r
n
o
t,
it
is
ass
u
r
ed
th
at
th
e
v
al
u
e
o
f
(
)
r
ed
u
ce
s
in
ea
ch
s
a
m
p
lin
g
ti
m
e
in
QSM.
T
h
u
s
,
it
r
ed
u
ce
s
th
e
w
id
th
o
f
th
e
QSMB
to
a
n
eg
li
g
ib
l
y
s
m
all
v
alu
e.
2
.
3
.
P
ro
po
s
ed
re
a
ching
la
w
f
o
r
pert
urbed sy
s
t
e
m
s
C
o
n
s
id
er
th
e
f
o
llo
w
i
n
g
p
er
t
u
r
b
ed
s
y
s
te
m
:
(
)
(
)
(
)
(
)
(
1
5
)
w
h
er
e
is
t
h
e
s
tate
v
ec
to
r
,
is
an
m
a
tr
ix
a
n
d
is
t
h
e
i
n
p
u
t
v
ec
to
r
.
(
)
is
th
e
p
er
tu
r
b
atio
n
te
r
m
,
w
h
o
s
e
u
p
p
er
an
d
lo
w
er
b
o
u
n
d
s
ar
e
ass
u
m
ed
to
b
e
k
n
o
w
n
.
I
n
o
r
d
e
r
to
s
atis
f
y
t
h
e
m
atc
h
i
n
g
co
n
d
itio
n
s
,
w
e
ca
n
w
r
ite
̃
[
5
]
.
E
q
u
atio
n
(
9
)
b
ec
o
m
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
Dis
crete
ti
me
r
ea
ch
in
g
la
w
b
a
s
ed
va
r
ia
b
le
s
tr
u
ctu
r
e
co
n
tr
o
l fo
r
fa
s
t rea
ch
in
g
... (
P
o
u
r
n
a
mi
P
a
d
ma
la
th
a
)
55
(
)
(
)
(
(
)
̃
(
)
)
(
1
6
)
No
w
,
as
s
u
m
i
n
g
th
e
co
n
tr
o
l la
w
to
b
e
g
e
n
er
ated
f
r
o
m
t
h
e
s
a
m
e
R
L
(
8
)
f
o
r
th
e
s
y
s
te
m
(
1
6
)
,
w
e
o
b
tain
(
)
as:
(
)
(
)
{
,
(
)
-
(
(
)
,
(
)
-
)
(
(
)
)
(
(
)
(
)
(
)
(
)
,
(
)
-
)
(
(
)
)
(
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̃
(
)
}
(
1
7
)
Sin
ce
̃
(
)
is
n
o
t
u
s
u
a
ll
y
k
n
o
w
n
,
th
is
ter
m
h
as
to
b
e
ad
eq
u
ately
d
ea
lt
w
it
h
.
T
h
is
ter
m
is
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e
n
ce
r
ep
lace
d
b
y
an
o
th
er
ter
m
(
)
in
s
u
c
h
a
w
a
y
s
o
th
at
th
e
r
ea
c
h
i
n
g
co
n
d
itio
n
s
a
r
e
s
till
s
ati
s
f
ied
[
5
]
.
(
)
(
)
{
,
(
)
-
(
(
)
,
(
)
-
)
(
(
)
)
(
(
)
(
)
(
)
(
)
,
(
)
-
)
(
(
)
)
(
)
(
)
}
(
1
8
)
W
ith
th
e
co
n
tr
o
l la
w
a
s
in
(
1
8
)
,
R
L
i
n
(
8
)
b
ec
o
m
es:
(
)
,
(
)
-
(
(
)
,
(
)
-
)
(
(
)
)
(
(
)
(
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(
)
(
)
,
(
)
-
)
(
(
)
)
(
̃
(
)
)
(
1
9
)
L
et
(
̃
(
)
)
̃
.
R
e
w
r
it
in
g
(
1
9
)
,
(
)
,
(
)
-
(
(
)
,
(
)
-
)
(
(
)
)
(
(
)
(
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(
)
(
)
,
(
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-
)
(
(
)
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(
̃
)
(2
0
)
Sin
ce
,
i
t
is
as
s
u
m
ed
t
h
e
u
p
p
er
an
d
lo
w
er
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o
u
n
d
s
o
f
(
)
ar
e
k
n
o
w
n
,
i
t
f
o
llo
w
s
t
h
at
̃
is
also
b
o
u
n
d
ed
b
y
k
n
o
w
n
v
al
u
es,
s
a
y
an
d
.
I
n
(
2
9
)
,
s
h
o
u
ld
b
e
s
o
c
h
o
s
e
n
t
h
a
t
th
e
r
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ch
i
n
g
co
n
d
itio
n
s
ar
e
s
atis
f
ied
[
5
]
.
T
h
er
ef
o
r
e,
is
tak
e
n
as:
,
(
)
-
w
h
er
e
an
d
.
T
h
e
p
r
o
p
o
s
e
d
r
ea
ch
in
g
la
w
f
o
r
p
er
tu
r
b
ed
s
y
s
te
m
s
ca
n
h
e
n
ce
b
e
f
o
r
m
u
lated
as:
(
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,
(
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-
(
(
)
,
(
)
-
)
(
(
)
)
(
(
)
(
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(
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(
)
,
(
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-
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(
(
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(
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,
(
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-
(
2
1
)
I
n
th
e
n
e
x
t
s
ec
tio
n
,
th
e
p
r
o
p
o
s
ed
R
L
s
as
in
(
8
)
an
d
(
1
9)
ar
e
s
i
m
u
lated
o
n
th
e
s
a
m
e
s
y
s
te
m
o
n
w
h
ich
B
ar
to
s
e
w
icz
et
al.
v
er
i
f
ied
B
L
DR
L
[
1
0
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
2
0
:
51
–
61
56
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
3
.
1
.
No
m
i
na
l
s
y
s
t
e
m
s
T
h
e
s
y
s
te
m
as
in
[
1
0
]
is
b
ein
g
co
n
s
id
er
ed
f
o
r
s
i
m
u
lati
n
g
th
e
p
er
f
o
r
m
a
n
ce
w
h
e
n
t
h
e
s
y
s
te
m
is
co
n
tr
o
lled
b
y
t
h
e
p
r
o
p
o
s
ed
R
L
s
.
T
h
e
m
a
tr
ices/
v
ec
to
r
s
f
o
r
t
h
e
s
y
s
te
m
(
1
)
an
d
th
e
in
itial
s
tates
a
s
i
n
[
1
0
]
ar
e
g
iv
e
n
b
y
:
[
]
,
-
an
d
,
-
.
T
h
e
in
itial
v
alu
e
o
f
s
t
ates
ar
e
also
tak
en
as
in
[
1
0
]
,
w
ith
,
-
an
d
,
-
.
T
h
e
co
n
tr
o
l in
p
u
t,
(
)
f
o
r
s
y
s
te
m
(
1
)
w
ith
t
h
e
s
lid
in
g
s
u
r
f
ac
e
(
2
)
u
s
i
n
g
GD
R
L
(
3
)
ca
n
b
e
d
er
iv
ed
as
[
5
]
:
(
)
(
)
{
(
)
(
)
(
)
(
(
)
)
(
)
}
(2
2
)
W
ith
NE
R
L
(
4
)
(
)
tu
r
n
s
o
u
t to
b
e
[
1
1
]
:
(
)
(
)
{
(
)
(
)
(
)
(
)
(
(
)
)
(
)
}
(2
3
)
an
d
w
ith
B
L
DR
L
(
7
)
,
(
)
is
[
1
0
]
:
(
)
(
)
*
,
(
)
-
(
(
)
,
(
)
-
)
(
)
+
(2
4
)
W
ith
th
e
p
r
o
p
o
s
ed
R
L
i
n
(
8
)
,
t
h
e
co
n
tr
o
l in
p
u
t
(
)
is
d
er
iv
ed
as:
(
)
(
)
{
,
(
)
-
(
(
)
,
(
)
-
)
(
(
)
)
(
(
)
(
)
(
)
(
)
,
(
)
-
)
(
(
)
)
(
)
}
(2
5
)
T
h
e
v
alu
es
o
f
t
h
e
v
ar
io
u
s
p
ar
am
eter
s
ar
e
tak
e
n
as
=
0
.
2
,
=
0
.
6
,
=
0
.
6
,
=
5
,
=
1
0
,
=
1
a
n
d
=
2
.
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
(
u
s
in
g
s
a
m
e
v
al
u
e
s
f
o
r
th
e
co
m
m
o
n
R
L
p
ar
a
m
eter
s
)
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
s
1
-
8.
Fig
u
r
e
1
d
ep
icts
th
e
s
lid
in
g
v
ar
iab
le
o
f
th
e
p
r
o
p
o
s
ed
R
L
an
d
Fig
u
r
e
2
g
iv
es
t
h
e
s
lid
in
g
v
ar
iab
les
f
o
r
NE
R
L
,
B
L
DR
L
an
d
GD
R
L
.
Fi
g
u
r
e
4
(
a)
an
d
Fig
u
r
e
6
(
a)
h
i
g
h
li
g
h
t
th
e
QSMB
in
GDR
L
an
d
NE
R
L
r
esp
ec
ti
v
el
y
a
n
d
Fig
u
r
e
4
(
b
)
an
d
Fig
u
r
e
6
(
b
)
r
ev
ea
l
th
e
n
eg
l
ig
ib
le
Q
SMB
o
f
B
L
DR
L
a
n
d
th
e
p
r
o
p
o
s
e
d
R
L
.
Fro
m
t
h
es
e
f
i
g
u
r
es,
it
i
s
e
v
id
en
t
t
h
at
t
h
e
p
r
o
p
o
s
ed
R
L
ac
h
iev
e
s
t
h
e
b
es
t
r
ea
ch
in
g
w
h
ile
it
e
m
b
r
ac
es
t
h
e
n
e
g
li
g
ib
le
Q
S
MB
o
f
B
L
DR
L
.
T
h
e
zo
o
m
ed
v
ie
ws
ar
e
in
co
r
p
o
r
ated
in
Fig
u
r
e
s
4
an
d
6
to
h
ig
h
li
g
h
t
t
h
e
QSM
B
w
id
t
h
o
f
th
e
f
o
u
r
R
L
s
.
C
o
m
p
ar
i
n
g
t
h
e
co
n
tr
o
l
i
n
p
u
t
s
s
h
o
w
n
i
n
Fi
g
u
r
e
5
(
a)
an
d
5
(
b
)
,
it
is
n
o
ted
t
h
at
t
h
e
p
r
o
p
o
s
ed
R
L
ac
h
iev
e
s
f
aster
r
ea
ch
in
g
w
it
h
a
n
in
p
u
t
co
m
p
ar
ab
le
to
th
at
o
f
NE
R
L
.
An
y
at
te
m
p
t
to
i
n
cr
ea
s
e
t
h
e
r
ea
ch
in
g
s
p
ee
d
o
f
GDR
L
b
y
p
r
o
v
id
in
g
m
o
r
e
co
n
tr
o
l
ef
f
o
r
t
(
th
r
o
u
g
h
its
R
L
p
ar
a
m
eter
s
)
w
i
ll
lead
to
w
id
er
QSMB
an
d
m
a
k
i
n
g
th
is
e
f
f
o
r
t
o
n
B
L
DR
L
w
il
l
n
o
t
y
ield
p
o
s
itiv
e
r
es
u
lts
i
n
ter
m
s
o
f
r
ea
ch
i
n
g
ti
m
e
b
ec
au
s
e
it
s
i
n
h
er
e
n
t
s
tr
u
c
tu
r
e
f
o
cu
s
es
o
n
Q
SMB
r
ed
u
ctio
n
p
r
ev
en
ti
n
g
f
ast
r
ea
ch
i
n
g
.
T
ab
l
e
1
h
a
s
t
h
e
f
i
g
u
r
e
o
f
m
er
it
s
i
n
ter
m
s
o
f
w
id
th
o
f
QSMB
an
d
p
er
f
o
r
m
an
ce
s
p
e
ed
.
W
ith
NE
R
L
,
th
e
s
lid
i
n
g
v
ar
iab
le
en
ter
s
Q
SM
at
7
s
e
c
(
s
ee
Fi
g
u
r
e
6
(
a)
)
,
w
h
er
e
th
e
Q
SM
is
d
ef
in
ed
as [
5
]
:
*
|
(
)
+
I
n
th
e
p
r
o
p
o
s
ed
r
ea
ch
in
g
la
w
,
th
e
s
y
s
te
m
R
P
r
ea
ch
e
s
t
h
e
s
li
d
in
g
s
u
r
f
ac
e
(
(
)
)
at
5
s
ec
,
w
h
ic
h
is
t
h
e
n
r
etai
n
ed
as
i
n
B
L
DR
L
.
Ho
w
ev
er
,
i
n
B
L
D
R
L
,
t
h
e
r
ea
ch
in
g
p
h
ase
is
lo
n
g
er
.
T
h
e
f
as
ter
r
ea
ch
i
n
g
o
f
th
e
p
r
o
p
o
s
ed
R
L
an
d
NE
R
L
d
e
m
a
n
d
s
g
r
ea
ter
co
n
tr
o
l e
f
f
o
r
t i
n
t
h
e
r
ea
ch
in
g
p
h
ase.
Ho
w
ev
er
,
i
n
NE
R
L
,
d
u
e
to
t
h
e
lar
g
er
QSMB
,
e
x
ce
s
s
iv
e
co
n
tr
o
l e
f
f
o
r
t is d
is
s
ip
ated
i
n
t
h
e
s
li
d
in
g
p
h
ase.
T
h
e
p
r
o
p
o
s
ed
R
L
e
m
u
lates B
L
D
R
L
'
s
tr
ait
o
f
r
etain
i
n
g
th
e
Q
SMB
,
th
u
s
en
s
u
r
i
n
g
th
a
t
u
n
n
ec
ess
ar
y
d
is
s
ip
atio
n
o
f
co
n
tr
o
l
en
er
g
y
in
s
lid
i
n
g
p
h
ase
i
s
av
o
id
ed
.
Fig
u
r
e
s
7
an
d
8
d
ep
ict
th
e
d
y
n
a
m
ics
o
f
t
h
e
s
tate
s
o
f
t
h
e
s
y
s
te
m
.
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