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C
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uth
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p
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Dep
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1
2
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I
NT
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UCT
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ety
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d
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in
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v
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o
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co
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ce
r
n
s
o
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h
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last
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e,
an
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ass
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tan
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s
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s
(
ADA
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as
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o
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war
d
[
1
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.
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tech
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ety
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ak
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m
b
in
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s
en
s
o
r
s
,
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er
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d
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ar
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tr
ac
k
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g
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th
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r
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o
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n
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tim
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ac
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to
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atica
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im
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s
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o
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ly
s
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t
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o
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s
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lies
th
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th
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ath
o
f
ADAS.
Sin
ce
v
eh
icle
au
to
m
at
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n
tech
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o
lo
g
y
ad
v
a
n
ce
s
,
it
will
g
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o
n
to
f
u
lly
au
to
n
o
m
o
u
s
s
y
s
tem
s
.
T
h
is
i
s
a
f
o
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n
d
atio
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al
s
tep
in
p
r
o
g
r
ess
iv
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ad
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n
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t
o
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atio
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r
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v
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s
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en
t.
Ma
n
y
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ar
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ased
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o
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o
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v
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ath
o
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tio
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th
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c
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r
r
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n
t
eg
o
-
v
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h
icle
s
tate
o
f
m
o
tio
n
[
2
]
.
T
h
e
eg
o
-
v
eh
icle
p
ath
o
f
m
o
tio
n
is
th
e
p
lan
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e
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o
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tr
ajec
to
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at
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to
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ated
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ex
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w
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r
ea
ch
its
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s
af
el
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an
d
e
f
f
icien
tly
.
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t
co
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s
id
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th
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v
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cu
r
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t
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itio
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,
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p
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u
r
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,
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d
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tacle
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
6
:
427
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4
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428
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e
b
asic
d
r
iv
in
g
s
itu
atio
n
s
wh
er
e
n
o
m
o
r
e
i
n
f
o
r
m
atio
n
r
eg
a
r
d
in
g
th
e
r
o
ad
m
ar
k
er
s
(
lan
es)
o
r
o
th
er
s
p
ec
if
ic
d
r
iv
er
in
p
u
t a
cti
o
n
s
(
lik
e
lan
e
c
h
an
g
es)
ar
e
p
r
o
v
id
ed
[
4
]
.
T
h
e
m
ain
lim
itatio
n
in
th
e
cir
cu
lar
p
r
esen
tatio
n
o
f
th
e
eg
o
-
v
eh
icle
p
ath
is
th
at
it
as
s
u
m
es
th
at
th
e
v
eh
icle
will
co
n
tin
u
e
m
o
v
in
g
with
th
e
s
am
e
cu
r
v
atu
r
e
(
s
am
e
r
ad
iu
s
o
f
r
o
tatio
n
)
,
as
it
co
n
s
id
er
s
o
n
ly
th
e
eg
o
-
m
o
tio
n
i
n
s
tan
tan
eo
u
s
ca
lc
u
latio
n
s
[
5
]
.
On
th
e
o
th
er
h
a
n
d
,
o
th
er
im
p
o
r
tan
t
f
ac
to
r
s
co
u
ld
g
r
ea
tly
af
f
ec
t
th
e
p
r
ed
icted
p
at
h
an
d
wo
r
th
to
b
e
co
n
s
id
er
ed
as
well.
T
h
e
v
eh
icle
m
o
v
in
g
o
n
a
ce
r
tain
lan
e
s
h
o
u
ld
p
r
o
b
ab
l
y
b
e
ex
p
ec
ted
to
c
o
n
tin
u
e
m
o
v
i
n
g
in
th
e
s
am
e
lan
e
in
a
n
o
r
m
al
d
r
iv
in
g
s
itu
atio
n
u
n
less
th
e
d
r
iv
er
s
ets
an
y
o
f
th
e
b
lin
k
er
s
to
in
d
icate
m
o
v
in
g
r
i
g
h
t
o
r
lef
t.
As
a
r
esu
lt,
t
h
e
la
n
es
d
etec
ted
b
y
lo
n
g
-
r
a
n
g
e
s
en
s
o
r
s
(
lik
e
R
ADAR
o
r
L
iDAR
)
s
h
o
u
ld
b
e
co
n
s
id
er
ed
in
th
e
esti
m
atio
n
o
f
th
e
p
r
e
d
icted
p
ath
.
M
o
r
eo
v
er
,
th
e
d
r
i
v
er
in
p
u
t
ac
tio
n
s
to
ch
an
g
e
th
e
cu
r
r
e
n
t
lan
e
s
h
o
u
ld
b
e
co
n
s
id
er
ed
as
well
in
t
h
e
p
r
ed
icted
p
ath
esti
m
atio
n
.
I
t
is
clea
r
th
at
th
e
cir
cu
lar
p
r
esen
tatio
n
o
f
th
e
p
r
ed
icted
p
ath
is
n
o
t
s
u
itab
le
f
o
r
n
o
n
-
cir
cu
lar
r
o
u
n
d
in
g
la
n
e
s
,
as
in
s
n
ak
e
-
lik
e
lan
es,
o
r
f
o
r
lan
e
ch
a
n
g
e
s
ce
n
ar
io
s
wh
er
e
v
eh
icle
m
o
v
es
i
n
S
-
s
h
ap
e
p
ath
.
T
h
u
s
,
th
er
e
i
s
a
n
ee
d
f
o
r
a
m
o
r
e
g
en
er
ic
an
d
r
o
b
u
s
t
ap
p
r
o
ac
h
to
p
r
esen
t
th
e
p
r
ed
icted
eg
o
-
v
eh
icle
p
ath
in
b
o
th
b
asic
d
r
i
v
in
g
s
itu
atio
n
s
an
d
co
m
p
lex
o
n
es r
ath
er
t
h
an
th
e
c
ir
cu
lar
ap
p
r
o
ac
h
.
B
ez
ier
cu
r
v
es
ca
n
b
e
a
p
r
o
p
er
g
en
er
ic
s
o
lu
tio
n
to
s
u
p
p
o
r
t
b
asic
an
d
co
m
p
lex
d
r
iv
in
g
m
a
n
eu
v
er
s
in
p
r
esen
tin
g
p
r
ed
icted
e
g
o
-
v
e
h
i
cle
p
ath
[
6
]
.
B
ez
ier
p
o
ly
n
o
m
i
als,
ac
co
r
d
in
g
t
o
th
eir
o
r
d
er
,
ca
n
g
en
er
ate
p
ath
s
with
v
ar
y
in
g
s
teer
in
g
eith
e
r
n
o
t
co
u
n
te
r
s
teer
in
g
o
r
c
o
u
n
ter
-
s
teer
in
g
,
s
tar
tin
g
f
r
o
m
s
tr
aig
h
t
p
ath
s
th
en
ci
r
cu
lar
o
n
es
an
d
en
d
in
g
with
S
-
s
h
ap
e
s
o
r
d
o
u
b
le
S
-
s
h
ap
e
(
lik
e
tak
e
-
o
v
er
m
an
e
u
v
er
s
)
[
7
]
.
I
n
o
r
d
e
r
n
o
t
to
in
cr
ea
s
e
its
co
m
p
lex
ity
m
u
ch
,
S
-
s
h
ap
e
p
a
th
s
ca
n
b
e
ac
h
iev
ed
b
y
t
h
ir
d
-
o
r
d
er
p
o
ly
n
o
m
ial
B
ez
ier
eq
u
a
tio
n
s
.
B
ez
ier
cu
r
v
es
b
ased
o
n
a
co
m
b
in
atio
n
o
f
two
th
ir
d
-
o
r
d
er
p
o
ly
n
o
m
ials
ca
n
p
r
o
v
i
d
e
cir
cu
lar
p
r
ed
ic
ted
p
ath
s
f
o
r
b
asic
m
an
eu
v
er
s
p
lu
s
S
-
s
h
ap
e
p
ath
s
f
o
r
lan
e
ch
an
g
e
o
r
s
n
a
k
e
-
s
h
a
p
ed
lan
es.
Mo
r
e
o
v
er
,
it
is
ca
p
ab
le
o
f
p
r
esen
tin
g
th
e
C
lo
th
o
id
al
cu
b
ic
p
o
ly
n
o
m
ial
cu
r
v
e
m
o
d
el,
wh
ich
co
u
ld
b
e
e
f
f
icien
t
in
p
r
esen
tin
g
n
o
t
co
u
n
ter
s
teer
in
g
p
ath
s
as
in
[
8
]
,
[
9
]
.
T
h
is
m
ea
n
s
th
at
th
e
C
lo
th
o
id
al
p
ath
p
r
ed
ictio
n
o
n
b
o
th
h
ig
h
wa
y
s
an
d
u
r
b
an
r
o
ad
s
is
a
s
u
b
s
et
o
f
th
e
p
r
o
p
o
s
ed
B
ez
ier
cu
r
v
es
p
ath
p
r
ed
ictio
n
,
wh
er
e
th
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
is
ca
p
ab
le
o
f
co
v
e
r
in
g
cir
cu
lar
m
an
eu
v
er
s
th
at
ar
e
n
o
t
f
u
lly
co
v
er
e
d
b
y
th
e
r
e
g
u
la
r
C
lo
th
o
id
s
.
T
h
u
s
,
th
ir
d
-
o
r
d
er
p
o
ly
n
o
m
ial
B
ez
ier
eq
u
atio
n
s
ca
n
b
e
a
n
ef
f
icien
t,
r
o
b
u
s
t,
an
d
c
h
ea
p
s
o
l
u
tio
n
to
p
r
esen
t
p
r
ed
icted
e
g
o
-
v
eh
icle
p
ath
s
f
o
r
b
o
th
n
o
t
co
u
n
ter
s
teer
in
g
p
ath
s
(
cir
cu
la
r
p
ath
s
an
d
C
lo
th
o
id
s
)
an
d
co
u
n
ter
s
teer
in
g
p
ath
s
(
S
-
s
h
ap
es
)
[
1
0
]
.
I
t
ca
n
b
e
th
e
p
r
o
p
er
s
o
lu
tio
n
f
o
r
p
ath
p
r
ed
i
ctio
n
an
d
p
lan
n
i
n
g
u
s
ed
in
h
i
g
h
-
s
p
ee
d
ADAS
f
ea
tu
r
es
lik
e
AE
B
[
1
1
]
,
lan
e
k
ee
p
ass
is
t (
L
KA)
[
1
2
]
,
a
n
d
lan
e
ch
an
g
e
ass
is
t (
L
C
A)
[
1
3
]
,
an
d
al
s
o
in
lo
w
-
s
p
ee
d
m
a
n
eu
v
er
s
lik
e
p
ar
k
in
g
[
1
4
]
.
B
ez
ier
cu
r
v
es
h
as
p
r
o
v
en
h
ig
h
ef
f
icien
cy
in
p
ath
p
lan
n
i
n
g
eith
er
at
th
e
lev
el
o
f
lo
n
g
-
r
a
n
g
e
r
o
u
te
p
lan
n
in
g
[
1
5
]
o
r
s
h
o
r
t
-
r
an
g
e
m
an
eu
v
er
s
p
la
n
n
in
g
lik
e
at
in
ter
s
ec
tio
n
s
in
r
o
u
n
d
ab
o
u
ts
[
1
6
]
.
I
t
ca
n
co
n
n
ec
t
ef
f
icien
tly
an
d
s
m
o
o
th
ly
b
etwe
en
in
ter
s
ec
tio
n
p
o
i
n
ts
wh
ile
g
u
ar
an
teein
g
co
n
tin
u
o
u
s
cu
r
v
atu
r
e
an
d
s
teer
in
g
.
W
h
ile
B
ez
ier
cu
r
v
es
ar
e
co
m
m
o
n
ly
u
s
ed
f
o
r
s
m
o
o
t
h
tr
ajec
to
r
y
g
e
n
er
atio
n
,
alter
n
ativ
es
s
u
ch
as
B
-
s
p
lin
es
an
d
NUR
B
S
also
o
f
f
er
s
tr
o
n
g
co
n
tin
u
ity
an
d
f
lex
i
b
ilit
y
in
t
r
ajec
to
r
y
d
esig
n
,
as
d
etailed
in
th
e
s
em
in
al
wo
r
k
b
y
Pieg
l
an
d
T
iller
[
1
7
]
.
T
h
e
o
r
d
er
o
f
th
e
B
ez
ier
cu
r
v
e
a
n
d
its
co
m
p
lex
ity
s
h
all
in
cr
ea
s
e
wit
h
th
e
in
cr
ea
s
e
in
t
h
e
co
n
n
ec
ted
i
n
ter
s
ec
tio
n
p
o
i
n
ts
th
at
s
h
all
b
e
p
r
o
v
id
ed
b
ased
o
n
g
iv
e
n
m
ap
n
o
d
es.
B
ased
o
n
its
ef
f
icien
cy
in
p
ath
p
lan
n
i
n
g
,
th
e
B
ez
ier
cu
r
v
es
ca
n
b
e
u
s
ed
ef
f
icien
tly
as
well
in
p
ath
p
r
ed
ictio
n
.
T
h
e
n
u
m
b
er
o
f
co
n
n
ec
ted
p
o
in
ts
o
r
f
r
am
es
i
n
p
at
h
p
r
ed
i
ctio
n
s
h
all
b
e
v
er
y
lim
ited
c
o
m
p
ar
ed
to
p
ath
p
la
n
n
in
g
,
wh
e
r
e
a
f
r
am
e
is
d
ef
in
ed
b
y
a
lo
ca
tio
n
p
o
in
t
a
n
d
o
r
ie
n
tatio
n
an
g
le.
T
h
is
is
b
ec
a
u
s
e
t
h
e
p
at
h
p
r
ed
ictio
n
co
v
er
s
a
lim
ited
s
p
ac
e,
as
it
is
m
ain
ly
b
ased
o
n
th
e
in
s
tan
ta
n
eo
u
s
eg
o
-
v
e
h
icle
m
o
tio
n
s
tate
an
d
p
er
ce
p
tio
n
in
f
o
r
m
atio
n
o
f
t
h
e
s
u
r
r
o
u
n
d
in
g
en
v
ir
o
n
m
en
t.
C
o
n
s
eq
u
en
tly
,
t
h
er
e
is
a
s
tr
o
n
g
d
e
m
an
d
f
o
r
e
n
h
an
cin
g
p
ath
p
r
e
d
ictio
n
tech
n
iq
u
es
to
b
e
r
o
b
u
s
t,
ef
f
icien
t,
an
d
d
e
p
lo
y
a
b
le
o
n
lo
w
-
p
o
wer
a
u
to
m
o
tiv
e
-
g
r
ad
e
h
a
r
d
war
e.
Su
c
h
a
s
o
lu
tio
n
s
h
all
b
e
b
ased
o
n
B
ez
ier
cu
r
v
es
an
d
ca
p
a
b
le
o
f
r
u
n
n
in
g
p
er
f
ec
tly
o
n
d
if
f
e
r
en
t
au
to
m
o
tiv
e
co
n
tr
o
ller
s
in
clu
d
in
g
lo
w
co
m
p
u
tin
g
p
o
we
r
o
n
es
with
o
th
er
co
m
p
le
x
ap
p
licatio
n
s
an
d
b
asic
co
m
p
o
n
e
n
ts
o
n
th
e
au
to
m
o
tiv
e
s
o
f
twar
e
s
tack
r
u
n
n
in
g
in
p
ar
allel.
W
h
ile
B
ez
ier
cu
r
v
es
ar
e
wid
el
y
u
s
ed
f
o
r
tr
ajec
to
r
y
g
en
er
atio
n
,
th
eir
d
ir
ec
t
ap
p
licatio
n
to
e
g
o
-
v
e
h
icle
p
ath
p
r
e
d
ictio
n
f
ac
es
ch
allen
g
es:
i)
co
n
tr
o
l
p
o
in
ts
ar
e
o
f
ten
s
elec
ted
h
eu
r
is
tically
,
lead
in
g
to
c
u
r
v
atu
r
e
d
is
co
n
tin
u
ities
d
u
r
in
g
d
y
n
am
ic
m
an
eu
v
er
s
;
ii)
h
ig
h
-
o
r
d
er
B
ez
ier
cu
r
v
es
im
p
r
o
v
e
ac
c
u
r
ac
y
b
u
t
in
cr
ea
s
e
co
m
p
u
tatio
n
al
co
s
t,
m
ak
in
g
t
h
em
u
n
s
u
itab
le
f
o
r
r
ea
l
-
tim
e
ADAS
[
1
8
]
;
a
n
d
iii)
m
o
s
t
im
p
lem
en
tatio
n
s
f
o
cu
s
o
n
g
lo
b
al
p
ath
p
lan
n
in
g
r
ath
e
r
th
an
k
in
em
atic
-
awa
r
e
lo
ca
l
p
r
ed
ictio
n
[
1
9
]
.
T
h
u
s
,
th
e
p
r
o
b
lem
tack
led
in
th
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
R
o
b
u
s
t e
fficien
t e
g
o
-
ve
h
icle
p
a
th
p
r
ed
ictio
n
b
a
s
ed
o
n
B
ezier
cu
r
ve
s
fo
r
…
(
Ha
n
a
n
H.
H
u
s
s
ein
)
429
p
ap
er
is
h
o
w
to
u
s
e
th
e
B
ez
ier
cu
r
v
es
ef
f
icien
tly
in
eg
o
-
v
eh
icle
p
ath
p
r
e
d
ictio
n
.
T
h
e
ef
f
icien
cy
is
in
ten
d
ed
b
ased
o
n
th
e
d
if
f
e
r
en
t a
s
p
ec
ts
o
f
ac
cu
r
ac
y
,
r
o
b
u
s
tn
ess
,
an
d
c
o
s
t.
B
ec
au
s
e
o
f
th
eir
s
m
o
o
th
n
ess
ch
ar
ac
ter
is
tics
an
d
co
m
p
u
t
atio
n
al
ef
f
icien
cy
,
B
ez
ier
cu
r
v
es
h
av
e
b
ec
o
m
e
a
b
asic
to
o
l
in
au
to
n
o
m
o
u
s
v
eh
icle
tr
ajec
to
r
y
g
en
er
atio
n
.
T
h
ir
d
-
o
r
d
e
r
B
ez
ier
cu
r
v
es
h
av
e
lately
b
ee
n
in
v
esti
g
ated
f
o
r
s
ev
er
al
u
s
es
in
p
ath
p
lan
n
i
n
g
a
n
d
c
o
n
tr
o
l.
Usi
n
g
N
-
o
r
d
er
p
o
l
y
n
o
m
ial
s
ea
r
ch
with
b
o
u
n
d
ar
y
co
n
d
itio
n
s
,
Vin
ay
ak
et
a
l.
[
1
6
]
p
r
esen
te
d
a
n
ew
B
ez
ier
cu
r
v
e
co
n
tr
o
l
p
o
in
t
s
ea
r
ch
al
g
o
r
ith
m
f
o
r
a
u
to
n
o
m
o
u
s
n
av
ig
atio
n
.
Alth
o
u
g
h
th
eir
a
p
p
r
o
ac
h
s
h
o
ws
g
o
o
d
p
ath
g
en
er
atio
n
,
it
is
less
ap
p
r
o
p
r
iate
f
o
r
r
ea
l
-
tim
e
eg
o
-
v
eh
icle
p
ath
p
r
e
d
ictio
n
s
in
c
e
it
co
n
ce
n
tr
ates
m
o
s
tly
o
n
g
lo
b
al
r
o
u
te
p
lan
n
in
g
an
d
r
eq
u
ir
es
p
r
ed
ef
in
e
d
g
eo
m
etr
ic
co
n
s
tr
ain
ts
.
Ar
s
lan
an
d
T
iem
ess
en
[
1
8
]
d
ev
el
o
p
ed
an
ad
a
p
tiv
e
B
ez
ier
d
eg
r
ee
r
ed
u
ctio
n
an
d
s
p
litt
in
g
m
eth
o
d
f
o
r
co
m
p
u
tatio
n
ally
ef
f
ec
tiv
e
m
o
tio
n
p
lan
n
i
n
g
in
th
e
f
r
am
ewo
r
k
o
f
v
eh
icl
e
m
o
tio
n
p
lan
n
in
g
.
T
h
eir
wo
r
k
m
ain
tain
s
a
f
o
cu
s
o
n
o
f
f
lin
e
p
ath
s
m
o
o
th
in
g
r
ath
er
th
an
d
y
n
am
ic
p
r
ed
ictio
n
b
ased
o
n
v
e
h
icle
k
in
em
atics,
ev
en
wh
ile
it
g
r
e
atly
ad
v
an
ce
s
th
e
f
ield
b
y
o
p
t
im
izin
g
cu
r
v
e
co
m
p
lex
ity
.
Si
m
ilar
ly
,
Din
g
et
a
l.
[
1
4
]
u
s
ed
B
ez
ier
cu
r
v
es
m
im
i
ck
in
g
C
lo
th
o
id
s
f
o
r
p
e
r
p
en
d
icu
lar
p
ar
k
in
g
m
o
v
es
to
p
r
o
d
u
c
e
s
m
o
o
th
lo
w
-
s
p
ee
d
p
ath
s
.
B
u
t
th
eir
m
eth
o
d
ig
n
o
r
es
th
e
d
if
f
icu
lties
o
f
h
ig
h
-
s
p
e
ed
p
ath
p
r
e
d
ictio
n
an
d
o
n
l
y
c
o
n
s
id
er
s
o
r
g
a
n
ized
p
ar
k
in
g
s
itu
atio
n
s
.
I
n
teg
r
atio
n
o
f
B
ez
ier
cu
r
v
es
with
lear
n
in
g
-
b
ased
m
eth
o
d
s
h
as
b
ee
n
tr
ied
b
y
s
ev
er
al
r
ese
ar
ch
er
s
.
Fo
r
r
is
k
ass
es
s
m
en
t
in
v
eh
icle
m
o
tio
n
p
lan
n
i
n
g
,
W
an
g
et
a
l.
[
3
]
co
u
p
led
lo
n
g
s
h
o
r
t
-
ter
m
m
e
m
o
r
y
(
L
STM
)
n
etwo
r
k
s
with
B
ez
ier
p
ar
am
eter
p
r
ed
ictio
n
.
Alth
o
u
g
h
cr
ea
tiv
e,
s
u
c
h
h
y
b
r
id
tech
n
iq
u
es
b
r
in
g
co
m
p
u
tatio
n
al
co
m
p
lex
ity
an
d
lo
wer
ed
in
ter
p
r
etab
ilit
y
th
a
t
m
ig
h
t
n
o
t
s
atis
f
y
th
e
s
tr
ict
cr
iter
ia
o
f
s
af
ety
-
cr
itical
ADAS
f
u
n
ctio
n
s
.
Mo
r
eo
v
er
,
s
u
ch
lear
n
in
g
-
b
ased
m
e
th
o
d
s
d
ep
en
d
o
n
h
eu
r
is
tic
co
n
tr
o
l
p
o
i
n
t
s
elec
tio
n
th
at
m
ay
r
esu
lt
in
cu
r
v
atu
r
e
d
is
co
n
tin
u
ities
d
u
r
in
g
d
y
n
am
ic
m
an
eu
v
er
s
.
E
x
is
tin
g
ap
p
r
o
ac
h
es
f
o
r
eg
o
-
v
eh
icle
p
ath
p
r
ed
ictio
n
in
ADAS
p
r
i
m
ar
ily
r
ely
o
n
g
eo
m
etr
ic
m
o
d
els
s
u
ch
as
C
lo
th
o
id
cu
r
v
es,
p
o
ly
n
o
m
ial
f
itti
n
g
,
o
r
d
ata
-
d
r
iv
e
n
tech
n
iq
u
es
in
[
1
9
]
.
T
h
ey
p
r
esen
t
lear
n
in
g
-
b
ased
m
eth
o
d
s
th
at
d
ep
e
n
d
s
o
n
lar
g
e
d
atasets
to
p
r
ed
ict
tr
ajec
to
r
ies.
Un
f
o
r
t
u
n
ately
,
it
r
eq
u
i
r
es
h
ig
h
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
a
n
d
m
ay
n
o
t
p
r
e
d
ict
well
to
u
n
s
ee
n
s
ce
n
ar
io
s
.
Gao
et
a
l.
[
2
0
]
i
n
tr
o
d
u
ce
d
a
s
elf
-
s
u
p
er
v
is
ed
d
ee
p
lear
n
in
g
f
r
am
ewo
r
k
t
h
at
o
p
tim
izes
d
e
p
th
an
d
e
g
o
-
m
o
tio
n
esti
m
atio
n
.
T
h
ei
r
n
o
v
e
lty
lies
in
th
e
in
tr
o
d
u
ctio
n
o
f
a
f
ea
tu
r
e
q
u
ad
tr
ee
lo
s
s
,
wh
ich
r
ep
lace
s
tr
ad
itio
n
al
p
h
o
to
m
etr
ic
lo
s
s
to
b
etter
ca
p
tu
r
e
d
etails.
Ho
wev
e
r
,
c
o
m
p
ar
ed
to
o
u
r
p
r
o
p
o
s
ed
B
ez
ier
-
b
as
ed
p
ath
p
r
ed
ictio
n
,
th
eir
m
eth
o
d
p
r
esen
ts
s
ig
n
if
ican
t
d
is
ad
v
an
tag
es
in
ter
m
s
o
f
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
an
d
ar
ch
itectu
r
al
co
m
p
lex
ity
.
Fu
r
th
er
m
o
r
e,
t
h
ey
f
o
cu
s
o
n
v
is
u
al
p
e
r
c
ep
tio
n
,
o
u
r
a
p
p
r
o
ac
h
p
r
o
v
i
d
es
a
co
n
tin
u
o
u
s
,
k
in
em
atica
lly
-
f
ea
s
ib
le
p
ath
r
e
p
r
esen
tatio
n
th
at
is
s
p
ec
if
icall
y
o
p
tim
ized
f
o
r
ac
tiv
e
s
af
ety
f
u
n
ctio
n
s
lik
e
AE
B
,
p
ar
ticu
lar
ly
in
c
o
m
p
lex
S
-
s
h
ap
ed
an
d
cir
cu
lar
m
an
eu
v
er
s
wh
er
e
v
is
u
al
-
o
n
l
y
p
o
s
e
esti
m
atio
n
m
ay
e
n
co
u
n
ter
d
r
if
t.
Pen
g
et
a
l.
[
2
1
]
p
r
o
p
o
s
ed
a
f
ix
ed
d
u
al
th
ir
d
-
o
r
d
e
r
B
éz
ier
cu
r
v
e
ar
ch
itectu
r
e
th
at
d
ir
ec
tly
m
ap
s
in
s
tan
tan
eo
u
s
eg
o
-
v
e
h
icle
m
o
tio
n
s
tates
to
a
co
n
tin
u
o
u
s
p
a
th
r
ep
r
esen
tatio
n
.
Un
lik
e
co
n
v
en
tio
n
al
m
eth
o
d
s
th
at
d
ep
en
d
o
n
iter
ativ
e
f
itti
n
g
,
v
ar
ia
b
le
m
o
d
el
s
tr
u
ctu
r
es,
o
r
d
ata
-
d
r
iv
en
tr
ain
in
g
p
r
o
ce
s
s
es,
th
e
p
r
o
p
o
s
ed
f
o
r
m
u
latio
n
p
r
o
v
id
es
a
d
eter
m
in
is
tic
an
d
clo
s
ed
-
f
o
r
m
s
o
l
u
tio
n
with
lo
w
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
.
T
h
is
en
ab
les
co
n
s
is
ten
t
m
o
d
ellin
g
o
f
b
o
th
cir
cu
lar
a
n
d
S
-
s
h
ap
e
d
tr
ajec
to
r
ies
with
in
a
u
n
if
ie
d
f
r
am
ewo
r
k
,
wh
ile
m
ain
tain
in
g
r
ea
l
-
tim
e
p
e
r
f
o
r
m
an
ce
s
u
itab
le
f
o
r
em
b
ed
d
ed
au
to
m
o
tiv
e
s
y
s
tem
s
.
Ho
wev
er
,
Mo
r
e
o
v
er
,
th
eir
s
y
s
tem
is
b
u
ilt
b
ased
o
n
ca
lcu
latio
n
ex
ec
u
te
d
o
n
s
o
cial
p
o
o
l
in
g
n
etwo
r
k
i
n
f
r
astru
ctu
r
e
as
t
h
ey
n
ee
d
t
o
co
llect
d
ata
f
r
o
m
th
e
v
e
h
icle
its
elf
an
d
th
e
s
u
r
r
o
u
n
d
in
g
e
n
v
ir
o
n
m
en
t.
T
h
e
ex
is
tin
g
r
esear
c
h
s
u
f
f
e
r
s
f
r
o
m
t
h
r
ee
m
ain
co
n
s
tr
a
in
ts
:
First,
f
ew
tech
n
iq
u
es
s
o
lv
e
th
e
co
m
p
u
tatio
n
al
c
o
n
s
tr
ain
ts
o
f
au
to
m
o
tiv
e
-
g
r
ad
e
h
ar
d
war
e
.
Seco
n
d
,
m
o
s
t
B
ez
ier
im
p
lem
en
tatio
n
s
co
n
ce
n
tr
ate
o
n
p
ath
p
lan
n
in
g
r
ath
er
th
a
n
r
ea
l
-
tim
e
p
r
ed
ictio
n
.
T
h
ir
d
,
c
o
n
tr
o
l
p
o
in
ts
ar
e
u
s
u
ally
d
eter
m
in
ed
g
eo
m
etr
ically
r
ath
er
th
an
f
r
o
m
v
eh
icle
k
in
e
m
atics.
B
y
m
ea
n
s
o
f
a
k
in
em
atic
-
awa
r
e
B
ez
ier
f
o
r
m
u
latio
n
esp
ec
ially
in
ten
d
e
d
f
o
r
eg
o
-
v
eh
icle
p
ath
p
r
ed
ictio
n
in
ADAS
ap
p
licatio
n
s
,
th
e
k
in
em
atic
co
n
s
tr
ain
ts
o
f
th
e
v
eh
icle
m
o
tio
n
,
lik
e
m
ax
im
u
m
later
al
ac
ce
ler
atio
n
an
d
m
ax
im
u
m
s
teer
in
g
,
ca
n
b
e
ap
p
r
o
p
r
iately
co
n
s
id
er
ed
.
Un
lik
e
th
ese
p
r
ev
io
u
s
ef
f
o
r
ts
,
o
u
r
wo
r
k
s
u
g
g
ests
a
n
ew
ap
p
r
o
ac
h
th
at
co
m
b
in
es
two
th
ir
d
-
o
r
d
er
B
ez
ier
cu
r
v
es
f
o
r
r
ea
l
-
tim
e
e
g
o
-
v
e
h
icle
p
ath
p
r
ed
ictio
n
.
W
e
d
er
iv
e
th
e
co
n
tr
o
l
p
o
in
ts
a
n
aly
tically
b
ased
o
n
th
e
in
s
tan
tan
eo
u
s
v
eh
icle
s
ta
te
(
y
aw
r
ate,
s
p
ee
d
,
an
d
o
r
i
en
tatio
n
)
,
w
h
ich
allo
ws
f
o
r
h
ig
h
-
ac
cu
r
ac
y
p
ath
ap
p
r
o
x
im
atio
n
with
m
in
im
al
c
o
m
p
u
tatio
n
al
o
v
er
h
ea
d
,
in
co
n
tr
ast to
ex
is
tin
g
m
eth
o
d
s
th
at
e
ith
er
ass
u
m
e
h
ig
h
-
o
r
d
er
cu
r
v
e
f
its
o
r
r
ely
o
n
n
u
m
er
ical
o
p
tim
izatio
n
.
I
n
teg
r
at
io
n
with
a
co
llis
io
n
esti
m
atio
n
m
o
d
u
le
f
o
r
AE
B
v
alid
ates
o
u
r
ap
p
r
o
ac
h
,
wh
ich
is
esp
ec
ially
we
ll
s
u
ited
to
s
af
ety
-
cr
itical
ADAS
ap
p
licati
o
n
s
.
T
o
th
e
b
est
o
f
o
u
r
k
n
o
wled
g
e,
th
is
is
th
e
f
ir
s
t
wo
r
k
th
at
u
s
es
a
f
ix
ed
d
u
al
t
h
ir
d
-
o
r
d
er
B
ez
ier
cu
r
v
e
ar
c
h
itectu
r
e
f
o
r
e
m
b
ed
d
ed
p
r
ed
ictiv
e
s
af
ety
f
u
n
ctio
n
s
t
o
p
r
ed
ict
p
ath
s
f
r
o
m
i
n
s
tan
tan
eo
u
s
m
o
tio
n
s
tates.
I
t
s
h
al
l
b
e
n
o
ted
th
at
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
is
v
alid
ated
with
test
ca
s
es
o
f
r
ec
o
r
d
e
d
v
e
h
icle
test
tr
ac
es,
in
cl
u
d
in
g
r
ea
l
s
ig
n
als
o
f
v
e
h
icle
s
p
ee
d
an
d
y
aw
r
ate.
Ho
wev
e
r
,
th
e
p
r
e
p
r
o
ce
s
s
in
g
o
f
s
u
ch
s
i
g
n
als
b
ef
o
r
e
b
ein
g
f
ed
t
o
o
u
r
s
o
lu
tio
n
is
b
ey
o
n
d
th
e
s
co
p
e
o
f
th
e
p
a
p
er
,
w
h
ich
f
o
cu
s
es
o
n
p
r
o
v
in
g
th
e
alg
o
r
ith
m
ic
co
n
ce
p
t.
Mo
d
ellin
g
u
n
ce
r
tain
ties
in
th
e
in
p
u
t
s
ig
n
als
a
n
d
p
r
o
p
ag
atin
g
th
em
in
t
h
e
p
ath
p
r
ed
ictio
n
to
h
av
e
th
e
g
en
er
ate
d
p
at
h
with
ac
co
m
p
an
ied
u
n
ce
r
tain
ty
c
o
u
ld
b
e
m
o
r
e
ef
f
i
cien
t in
th
e
co
llis
io
n
esti
m
atio
n
f
o
r
AE
B
with
ac
co
m
p
an
ied
u
n
ce
r
tain
ty
as we
ll.
Ho
wev
er
,
th
is
p
r
in
ci
p
le
s
h
all
b
e
ex
ten
d
e
d
to
o
u
r
f
u
tu
r
e
w
o
r
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
427
-
4
4
4
430
T
h
e
m
ain
co
n
tr
ib
u
tio
n
in
th
is
p
ap
er
,
wh
ich
is
th
e
s
u
b
ject
o
f
th
e
g
r
an
ted
p
aten
t
[
1
1
]
,
lies
in
s
o
lv
in
g
th
e
tack
led
p
r
o
b
lem
th
r
o
u
g
h
t
h
e
f
o
r
m
u
latio
n
o
f
a
n
ew
r
ep
r
esen
tatio
n
o
f
th
e
p
r
e
d
icted
eg
o
-
v
eh
icle
p
ath
.
T
h
e
p
r
o
p
o
s
ed
n
ew
r
e
p
r
esen
tatio
n
b
ased
o
n
th
ir
d
-
o
r
d
er
p
o
ly
n
o
m
ial
B
ez
ier
eq
u
atio
n
s
h
as
th
e
f
o
llo
win
g
ch
ar
ac
ter
is
tics
th
at
ar
e
h
ig
h
ly
i
m
p
o
r
tan
t
f
o
r
p
r
o
p
er
an
d
ef
f
ici
en
t e
n
d
-
u
s
er
f
u
n
ctio
n
s
o
f
AD
AS.
−
Acc
u
r
ac
y
:
T
h
e
p
r
o
p
o
s
ed
s
o
l
u
tio
n
ac
h
iev
es
h
ig
h
er
ac
c
u
r
a
cy
with
less
er
r
o
r
(
m
o
r
e
th
a
n
9
0
%
in
s
o
m
e
s
ce
n
ar
io
s
)
th
an
th
e
r
eg
u
lar
C
lo
th
o
id
s
wh
en
test
ed
o
n
cir
cu
lar
m
an
eu
v
er
s
as ju
s
tifie
d
in
s
im
u
latio
n
r
esu
lts
.
−
R
o
b
u
s
tn
ess
:
T
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
is
ca
p
ab
le
o
f
co
v
er
in
g
th
e
d
if
f
er
en
t
b
asic
m
an
eu
v
er
s
s
tar
tin
g
f
r
o
m
s
im
p
le
s
tr
aig
h
t
an
d
cir
cu
lar
,
a
n
d
en
d
i
n
g
with
s
in
u
s
o
id
al
o
r
S
-
s
h
ap
e
m
an
eu
v
e
r
s
.
Mo
r
eo
v
e
r
,
it
is
b
ased
o
n
th
e
in
p
u
t
in
s
tan
tan
eo
u
s
s
p
ee
d
an
d
y
aw
r
ate,
wh
ich
ca
n
b
e
p
r
o
v
id
ed
f
o
r
an
y
v
e
h
icle
ty
p
e
(
ca
r
,
b
u
s
,
tr
u
ck
,
v
an
,
an
d
m
o
t
o
r
cy
cle)
.
−
C
h
ea
p
n
ess
:
T
h
e
s
o
lu
tio
n
as
p
r
esen
ted
in
th
e
f
o
r
m
u
late
d
alg
o
r
ith
m
(
Alg
o
r
ith
m
1
in
s
ec
tio
n
3
)
h
as
lo
w
co
m
p
lex
ity
(
O(
n
)
,
wh
e
r
e
n
p
r
esen
ts
th
e
n
u
m
b
er
o
f
way
p
o
in
ts
f
o
r
m
in
g
t
h
e
g
en
er
ated
p
at
h
)
th
at
m
ak
es
it
ca
p
ab
le
o
f
r
u
n
n
in
g
o
n
c
h
ea
p
t
ar
g
ets.
I
n
th
e
n
ex
t
s
ec
tio
n
s
o
f
th
e
p
a
p
er
,
we
will
s
h
o
w
h
o
w
th
e
B
ez
ier
cu
r
v
es
ca
n
b
e
ea
s
ily
an
d
ef
f
icien
tly
u
s
ed
to
p
r
esen
t
th
e
p
r
e
d
icted
e
g
o
-
v
e
h
icle
p
ath
.
C
o
m
p
ar
is
o
n
p
lo
ts
o
f
s
ce
n
ar
io
s
ar
e
p
r
esen
te
d
f
o
r
th
e
g
en
er
ated
B
ez
ier
p
ath
v
er
s
u
s
th
e
o
n
e
o
b
t
ain
ed
f
r
o
m
C
lo
th
o
i
d
s
ag
ain
s
t
th
e
g
r
o
u
n
d
tr
u
th
r
ef
er
e
n
ce
r
o
a
d
o
n
C
ar
Ma
k
er
f
o
r
cir
cu
lar
p
ath
s
.
Sectio
n
2
clar
if
ies
th
e
p
ath
p
r
ed
ictio
n
f
r
a
m
e
wo
r
k
.
I
t
in
tr
o
d
u
ce
s
th
e
m
ath
e
m
atica
l
b
ac
k
g
r
o
u
n
d
f
o
r
th
e
th
ir
d
o
r
d
er
p
o
ly
n
o
m
ia
l
B
ez
ier
eq
u
atio
n
s
,
th
e
B
ez
ier
cu
r
v
es
o
b
tain
ed
f
r
o
m
th
e
c
o
m
b
in
atio
n
o
f
two
B
ez
ier
eq
u
atio
n
s
,
an
d
h
o
w
t
o
g
en
er
ate
a
B
ez
ier
p
ath
,
wh
ic
h
is
th
e
clo
s
est
to
a
cir
cu
lar
ar
c
with
a
s
p
ec
if
ic
g
iv
en
r
ad
i
u
s
o
f
r
o
tatio
n
.
I
n
s
ec
tio
n
3
,
we
s
h
o
w
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
f
o
r
eg
o
-
v
e
h
icle
p
r
ed
icted
p
at
h
g
en
er
atio
n
.
Simu
latio
n
r
esu
lts
ar
e
p
r
esen
ted
in
s
ec
tio
n
4
.
C
o
m
p
ar
is
o
n
p
lo
ts
o
f
p
ath
p
r
e
d
ictio
n
with
B
ez
ier
cu
r
v
e
v
e
r
s
u
s
C
lo
th
o
id
al
p
o
ly
n
o
m
ial
ag
ain
s
t
C
ar
Ma
k
er
g
r
o
u
n
d
tr
u
th
an
d
ca
lc
u
latio
n
o
f
B
ez
ier
p
ath
co
llis
io
n
p
o
in
ts
f
o
r
AE
B
ar
e
p
r
esen
ted
.
Fin
ally
,
th
e
p
ap
er
is
co
n
clu
d
e
d
in
s
ec
tio
n
5
s
u
p
p
o
r
ted
with
f
u
tu
r
e
wo
r
k
.
2.
P
AT
H
P
RE
D
I
CT
I
O
N
F
RA
M
E
WO
RK
Ou
r
p
r
o
p
o
s
ed
s
o
lu
tio
n
co
n
s
id
er
s
o
n
ly
th
e
in
p
u
t
m
o
tio
n
s
tate
o
f
th
e
eg
o
-
v
eh
icle,
s
p
ec
if
icall
y
its
s
p
ee
d
an
d
y
aw
r
ate
(
w
h
ich
r
e
p
r
esen
t
th
e
in
s
tan
tan
eo
u
s
r
ad
iu
s
o
f
r
o
tatio
n
o
r
c
u
r
v
atu
r
e)
.
As
a
r
esu
lt,
th
e
p
r
e
d
icted
p
ath
s
h
all
b
e
a
cir
cu
lar
m
an
eu
v
er
b
ased
o
n
t
h
e
in
s
tan
tan
eo
u
s
in
p
u
t
cu
r
v
atu
r
e.
As
m
e
n
tio
n
ed
b
ef
o
r
e,
t
h
e
p
r
o
p
o
s
ed
th
ir
d
-
o
r
d
er
p
o
ly
n
o
m
ial
B
ez
ier
eq
u
atio
n
s
ar
e
ca
p
ab
le
o
f
co
v
e
r
in
g
m
o
r
e
co
m
p
lex
m
an
eu
v
er
s
lik
e
S
-
s
h
ap
es.
Mo
r
eo
v
er
,
p
r
ed
ictio
n
o
f
S
-
s
h
a
p
e
o
r
s
im
ilar
m
a
n
eu
v
er
s
r
e
q
u
ir
e
m
o
r
e
in
p
u
t
i
n
f
o
r
m
atio
n
o
f
f
u
ll
p
er
ce
p
tio
n
o
f
th
e
lan
es,
s
tatu
s
o
f
th
e
b
lin
k
er
s
,
an
d
p
r
ed
eter
m
in
atio
n
o
f
th
e
r
o
u
te
an
d
u
p
d
at
ed
m
ap
o
f
th
e
r
o
a
d
as
in
[
1
5
]
.
Ho
wev
e
r
,
th
is
co
u
l
d
n
o
t
b
e
e
n
o
u
g
h
to
p
r
e
d
ict
s
n
ak
e
m
an
e
u
v
er
s
as
f
o
r
a
n
y
r
ea
s
o
n
th
e
d
r
iv
e
r
co
u
ld
ch
an
g
e
h
is
d
ec
is
io
n
b
y
n
o
t
f
o
llo
win
g
th
e
r
o
u
te,
o
r
n
o
t
ch
a
n
g
in
g
t
h
e
lan
e
af
ter
to
g
g
lin
g
th
e
b
lin
k
er
,
o
r
c
h
an
g
e
m
o
r
e
th
a
n
o
n
e
lan
e
in
s
tead
o
f
o
n
e.
T
h
e
r
e
s
h
all
b
e
s
o
lid
cr
it
er
ia
an
d
clea
r
r
eq
u
i
r
em
en
ts
d
ef
in
ed
to
co
v
er
th
e
s
y
s
tem
b
eh
av
io
r
f
o
r
s
u
ch
s
ev
er
al
u
s
e
ca
s
es.
T
h
e
e
n
d
-
u
s
er
f
u
n
ctio
n
u
n
d
e
r
s
tu
d
y
in
o
u
r
s
ce
n
ar
io
is
AE
B
,
wh
ic
h
is
a
h
ig
h
ly
s
af
ety
cr
itical
f
ea
t
u
r
e
ac
co
r
d
in
g
to
th
e
n
ew
ca
r
ass
es
s
m
en
t
p
r
o
g
r
am
(
NC
AP)
s
tan
d
ar
d
s
an
d
test
p
r
o
to
co
ls
[
2
2
]
.
T
h
u
s
,
th
e
eg
o
-
v
eh
icle
p
ath
p
r
ed
ictio
n
p
r
o
p
o
s
ed
in
th
is
p
ap
er
s
er
v
in
g
A
E
B
f
u
n
ctio
n
ality
is
b
ased
o
n
l
y
o
n
th
e
in
p
u
t
in
s
t
an
tan
eo
u
s
c
u
r
r
en
t
v
e
h
icle
s
tate,
an
d
it
p
r
o
v
id
es
o
n
ly
p
r
e
d
icted
cir
cu
lar
an
d
s
tr
aig
h
t
m
an
eu
v
er
s
.
Mo
r
e
co
m
p
lex
m
an
eu
v
er
s
s
h
all
b
e
co
n
s
id
er
ed
as
f
u
tu
r
e
wo
r
k
f
o
r
p
ath
p
lan
n
in
g
r
ath
e
r
th
an
p
ath
p
r
e
d
ictio
n
,
wh
er
e
t
h
e
g
en
e
r
ated
p
ath
s
h
all
b
e
f
o
llo
wed
b
y
th
e
a
u
to
m
atic
co
n
t
r
o
l
s
y
s
tem
to
s
er
v
e
o
th
er
f
u
n
ctio
n
alities
lik
e
L
C
A
with
clea
r
r
eq
u
ir
em
e
n
ts
an
d
s
tan
d
ar
d
s
d
ef
in
ed
t
o
co
v
er
its
d
if
f
er
en
t
u
s
e
ca
s
es
[
2
3
]
.
T
h
is
s
ec
tio
n
clar
if
ies
th
e
in
f
o
r
m
atio
n
r
elate
d
to
th
e
tr
ajec
to
r
y
p
lan
n
in
g
m
eth
o
d
o
lo
g
y
u
tili
zin
g
r
ea
l
-
tim
e
p
ar
am
etr
ic
B
ez
ier
cu
r
v
es.
T
h
ese
cu
r
v
es
o
b
tain
ed
f
r
o
m
two
th
ir
d
o
r
d
er
p
o
ly
n
o
m
ial
B
ez
ier
eq
u
atio
n
s
.
T
h
e
ap
p
r
o
ac
h
will
c
o
n
ce
n
tr
ate
o
n
em
p
lo
y
in
g
th
ese
cu
r
v
es
f
o
r
p
a
th
p
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e
d
ictio
n
in
h
ig
h
way
an
d
u
r
b
an
en
v
ir
o
n
m
en
ts
,
in
clu
d
in
g
in
ter
s
ec
tio
n
s
,
r
o
u
n
d
ab
o
u
ts
,
an
d
la
n
e
ch
a
n
g
es,
as
well
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f
o
r
s
p
ee
d
p
lan
n
in
g
t
o
en
s
u
r
e
co
m
f
o
r
t
an
d
s
af
ety
.
T
h
e
ex
p
lan
atio
n
o
f
th
e
p
lan
n
in
g
f
r
am
ewo
r
k
will
b
e
s
ep
ar
ated
in
t
o
th
r
ee
s
u
b
-
s
ec
t
io
n
s
:
i
)
th
e
g
en
e
r
ic
th
ir
d
o
r
d
er
B
ez
ier
eq
u
atio
n
,
i
)
h
o
w
th
e
B
ez
ier
cu
r
v
e
ca
n
b
e
o
b
tain
e
d
f
r
o
m
co
m
b
in
in
g
two
t
h
ir
d
o
r
d
er
p
o
ly
n
o
m
ial
eq
u
atio
n
s
.
iii
)
B
ez
ier
cu
r
v
e
p
r
esen
tatio
n
f
o
r
cir
c
u
lar
ar
c.
2
.
1
.
T
hird
o
rder
po
ly
no
m
ia
l
B
ez
ier
equa
t
io
n
T
h
e
cu
b
ic
(
th
ir
d
o
r
d
er
)
B
ez
ier
eq
u
atio
n
r
(
t
)
ca
n
b
e
wr
itten
i
n
its
g
en
er
ic
f
o
r
m
as f
o
llo
ws:
(
)
=
(
1
−
)
3
0
+
3
(
1
−
)
2
1
+
3
(
1
−
)
2
2
+
3
3
(
1
)
T
h
e
in
d
ep
en
d
en
t
p
ar
am
eter
is
in
t
h
e
r
a
n
g
e
[
0
,
1
]
.
0
an
d
3
ar
e
t
h
e
v
alu
es
o
f
(
=
0
)
an
d
(
=
1
)
,
r
esp
ec
tiv
ely
.
1
an
d
2
ar
e
th
e
c
o
n
tr
o
l
p
o
in
ts
with
th
e
v
al
u
es
o
f
[
̇
(
=
0
)
3
+
(
=
0
)
]
an
d
[
(
=
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
R
o
b
u
s
t e
fficien
t e
g
o
-
ve
h
icle
p
a
th
p
r
ed
ictio
n
b
a
s
ed
o
n
B
ezier
cu
r
ve
s
fo
r
…
(
Ha
n
a
n
H.
H
u
s
s
ein
)
431
1
)
−
̇
(
=
1
)
3
]
,
r
esp
ec
tiv
ely
.
As
s
h
o
w
n
in
Fi
g
u
r
e
1
,
th
e
b
lu
e
p
o
in
ts
(
0
an
d
3
)
ar
e
th
e
in
itial
an
d
f
i
n
al
v
alu
es o
f
th
e
r
ed
B
ez
ier
cu
r
v
e.
T
h
e
g
r
ee
n
p
o
in
ts
(
1
an
d
2
)
ar
e
th
e
co
n
tr
o
l
p
o
in
ts
at
=
1
/
3
an
d
=
2
/
3
,
r
esp
ec
tiv
ely
.
T
h
e
g
r
ee
n
co
n
tr
o
l
p
o
in
ts
o
b
tain
ed
f
r
o
m
th
e
d
er
iv
ativ
es
o
f
th
e
B
ez
ier
c
u
r
v
e
at
its
b
o
u
n
d
a
r
ies
(
=
0
an
d
=
1
)
co
n
tr
o
ls
th
e
s
h
ap
e
o
f
t
h
e
B
ez
ier
cu
r
v
e
(
)
.
T
ab
le
A.
1
lis
ts
th
e
m
ath
em
atica
l
s
y
m
b
o
ls
u
s
ed
in
th
e
B
ez
ier
p
o
ly
n
o
m
ial
eq
u
a
tio
n
s
,
its
d
ef
in
itio
n
s
,
an
d
its
ev
alu
atio
n
in
Ap
p
en
d
ix
A.
Fig
u
r
e
1
.
Plo
t o
f
th
ir
d
o
r
d
e
r
B
ez
ier
eq
u
atio
n
2
.
2
.
B
ez
ier
c
urv
e
o
bt
a
ined f
ro
m
t
he
co
m
bin
a
t
io
n o
f
t
wo
t
hird o
rder
po
ly
no
m
ia
l Bezier
equa
t
io
ns
A
c
c
o
r
d
i
n
g
t
o
(
1
)
,
t
h
e
t
h
i
r
d
o
r
d
e
r
p
o
l
y
n
o
m
i
a
l
B
e
z
i
e
r
e
q
u
a
t
i
o
n
s
f
o
r
t
h
e
t
w
o
c
o
o
r
d
i
n
a
t
e
v
a
r
i
a
b
l
e
s
(
)
a
n
d
(
)
c
a
n
b
e
a
s
f
o
l
l
o
w
s
.
(
)
=
(
1
−
)
3
0
+
3
(
1
−
)
2
1
+
3
(
1
−
)
2
2
+
3
3
(
2
)
(
)
=
(
1
−
)
3
0
+
3
(
1
−
)
2
1
+
3
(
1
−
)
2
2
+
3
3
(
3
)
T
h
e
co
o
r
d
in
ates
,
s
et
as
th
e
lo
c
al
co
o
r
d
in
ates
f
o
r
th
e
B
ez
ier
c
u
r
v
e
g
en
er
atio
n
ar
e
ch
ar
ac
te
r
ized
b
y
th
e
f
o
llo
win
g
b
o
u
n
d
ar
y
co
n
d
itio
n
s
as sh
o
wn
in
Fig
u
r
e
2
.
(
=
0
)
=
0
=
0
(
=
1
)
=
3
=
(
=
0
)
=
0
=
0
(
=
1
)
=
3
=
0
As a
r
esu
lt,
(
2
)
an
d
(
3
)
ca
n
b
e
s
im
p
lifie
d
to
b
e
as f
o
llo
ws.
(
)
=
3
1
(
1
−
)
2
+
3
2
(
1
−
)
2
+
3
(
4
)
(
)
=
3
1
(
1
−
)
2
+
3
2
(
1
−
)
2
(
5
)
{
1
,
2
}
an
d
{
1
,
2
}
ar
e
th
e
co
n
tr
o
l p
o
in
ts
o
f
(
)
an
d
(
)
,
r
esp
ec
tiv
ely
.
T
h
u
s
,
th
ey
ar
e
ch
ar
ac
ter
ized
b
y
th
e
f
o
llo
win
g
e
q
u
atio
n
s
.
1
=
(
=
0
)
+
̇
(
=
0
)
3
=
1
3
̇
(
=
0
)
1
=
(
=
0
)
+
̇
(
=
0
)
3
=
1
3
̇
(
=
0
)
2
=
(
=
1
)
−
̇
(
=
1
)
3
=
−
1
3
̇
(
=
1
)
2
=
(
=
1
)
−
̇
(
=
1
)
3
=
−
1
3
̇
(
=
1
)
T
h
u
s
,
th
e
d
e
r
iv
ativ
es a
t th
e
b
o
u
n
d
ar
ies ca
n
b
e
d
e
d
u
ce
d
as f
o
l
lo
ws.
̇
(
=
0
)
=
3
1
(
6
)
̇
(
=
0
)
=
3
1
(
7
)
̇
(
=
1
)
=
3
(
−
2
)
(
8
)
̇
(
=
1
)
=
−
3
2
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
427
-
4
4
4
432
T
h
e
o
r
ien
tatio
n
o
f
th
e
v
eh
icl
e
in
t
h
e
d
ef
in
ed
lo
ca
l
B
ez
ier
C
o
o
r
d
in
ates
(
,
)
is
p
r
esen
te
d
with
.
T
h
e
tan
g
en
t o
f
th
e
o
r
ien
tatio
n
o
f
th
e
v
eh
icle
ca
n
b
e
d
ef
i
n
ed
as f
o
l
lo
ws.
(
)
=
∆
∆
=
̇
̇
(
1
0
)
B
ased
o
n
(
6
)
–
(
1
0
)
,
we
ca
n
d
ed
u
ce
th
e
r
elatio
n
b
etwe
en
th
e
co
n
tr
o
l p
o
in
ts
o
f
th
e
B
ez
ier
eq
u
atio
n
s
in
th
e
two
d
ef
in
e
d
co
o
r
d
in
ates.
ta
n
(
0
)
=
0
=
̇
(
=
0
)
̇
(
=
0
)
=
1
1
1
=
0
1
(
1
1
)
ta
n
(
)
=
=
̇
(
=
1
)
̇
(
=
1
)
=
−
2
−
2
2
=
−
(
−
2
)
(
1
2
)
B
y
s
u
b
s
titu
tin
g
(
1
1
)
a
n
d
(
1
2
)
in
(
5
)
,
th
e
B
ez
ier
eq
u
atio
n
in
th
e
lo
ca
l c
o
o
r
d
in
ates (
,
)
b
ec
o
m
e
s
as
:
(
)
=
3
0
1
(
1
−
)
2
−
3
(
−
2
)
(
1
−
)
2
(
1
3
)
wh
er
e
(
)
an
d
(
)
ar
e
as
p
r
esen
ted
i
n
(
4
)
an
d
(
1
3
)
,
r
esp
ec
tiv
el
y
.
T
h
ey
s
h
o
w
th
at
t
h
e
B
ez
ier
cu
r
v
e
to
b
e
g
en
er
ated
b
etwe
en
two
in
p
u
t
f
r
am
es
with
d
ef
in
ed
0
an
d
is
m
ain
ly
a
f
u
n
ctio
n
in
th
e
p
lace
s
o
f
th
e
co
n
tr
o
l
p
o
in
ts
1
an
d
2
.
I
n
o
r
d
e
r
to
s
i
m
p
lify
th
e
v
alu
es
o
f
th
e
two
co
n
tr
o
l
p
o
in
ts
b
y
c
o
m
b
in
in
g
th
em
in
o
n
e
v
ar
iab
le
with
th
eir
f
u
n
ctio
n
a
lity
alm
o
s
t
p
r
eser
v
ed
,
th
ey
ca
n
b
e
ass
u
m
ed
to
b
e
eq
u
ally
p
lace
d
f
r
o
m
th
e
b
o
u
n
d
ar
ies
with
a
d
is
tan
ce
.
T
h
en
,
th
e
v
alu
es
o
f
1
an
d
2
ca
n
b
e
ass
u
m
ed
to
b
e
(
)
an
d
(
1
−
)
,
r
esp
ec
tiv
ely
.
T
h
e
r
a
n
g
e
o
f
is
[
0
,
0
.
5
]
.
As
a
r
esu
lt,
t
h
e
g
e
n
er
ated
B
ez
ier
cu
r
v
e
ca
n
b
e
f
in
ally
p
r
e
s
en
ted
as
a
f
u
n
ctio
n
d
ep
en
d
in
g
o
n
as
:
(
)
=
(
3
)
+
3
(
1
−
3
)
2
−
2
(
1
−
3
)
3
(
1
4
)
(
)
=
(
3
0
)
−
3
(
+
2
0
)
2
+
3
(
+
0
)
3
(
1
5
)
Fig
u
r
e
2
s
h
o
ws
a
g
en
er
al
p
lo
t
o
f
th
e
B
ez
ier
c
u
r
v
e
g
en
er
ate
d
f
r
o
m
th
e
c
o
m
b
in
atio
n
o
f
th
e
two
th
ir
d
o
r
d
er
p
o
ly
n
o
m
ial
B
ez
ier
(
1
4
)
an
d
(
1
5
)
.
T
h
e
ch
allen
g
e
af
ter
war
d
s
is
to
lo
o
k
f
o
r
th
e
b
est
v
alu
e
o
f
th
at
co
u
ld
s
er
v
e
a
s
p
ec
if
ied
f
u
n
ctio
n
ality
b
y
th
e
g
en
er
ated
B
ez
ier
p
a
th
.
R
o
u
g
h
l
y
,
th
e
s
ettin
g
o
f
with
1
/
3
co
u
ld
b
e
m
o
s
tly
s
u
f
f
icien
t
to
h
a
v
e
r
ea
s
o
n
ab
le
B
ez
ier
p
ath
s
co
n
n
ec
tin
g
a
s
p
ec
if
ic
in
itial
f
r
am
e
(
0
,
0
,
0
)
with
a
s
p
ec
if
ic
tar
g
et
o
n
e
(
,
0
,
)
in
th
e
lo
ca
l
B
ez
ier
co
o
r
d
in
ates
(
,
)
.
Settin
g
(
)
with
(
1
/
3
)
s
h
all
b
e
ca
p
ab
le
o
f
p
r
esen
tin
g
c
u
b
ic
cl
o
th
o
id
al
p
o
ly
n
o
m
ial,
wh
er
e
(
)
=
is
lin
ea
r
,
an
d
(
)
=
(
0
)
−
(
+
2
0
)
2
+
(
+
0
)
3
is
a
th
ir
d
-
o
r
d
er
p
o
ly
n
o
m
ial.
Ho
wev
er
,
f
o
r
s
p
ec
if
ic
d
esire
d
p
ath
s
,
wh
ich
we
ca
n
en
clo
s
e
m
ain
ly
in
cir
cu
lar
p
ath
s
an
d
S
-
s
h
ap
e
o
n
es,
th
e
v
alu
e
o
f
n
ee
d
s
to
b
e
f
u
r
th
er
in
v
es
tig
ated
to
h
av
e
th
e
b
est
o
u
tco
m
e
f
r
o
m
t
h
e
g
en
e
r
a
ted
B
ez
ier
p
ath
to
f
it
with
th
e
d
esire
d
f
u
n
ctio
n
ality
.
T
h
e
n
e
x
t
s
ec
tio
n
ex
p
lain
s
h
o
w
th
e
v
alu
e
o
f
ca
n
b
e
co
m
p
u
ted
to
h
av
e
th
e
B
ez
ier
p
a
th
as
clo
s
e
a
s
p
o
s
s
ib
le
to
a
c
i
r
cle
with
s
p
ec
if
ic
g
iv
en
r
a
d
iu
s
o
f
r
o
tatio
n
.
Fig
u
r
e
2
.
Plo
t o
f
B
ez
ier
cu
r
v
e
f
r
o
m
c
o
m
b
in
atio
n
o
f
two
th
ir
d
o
r
d
er
B
ez
ier
e
q
u
atio
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
R
o
b
u
s
t e
fficien
t e
g
o
-
ve
h
icle
p
a
th
p
r
ed
ictio
n
b
a
s
ed
o
n
B
ezier
cu
r
ve
s
fo
r
…
(
Ha
n
a
n
H.
H
u
s
s
ein
)
433
2
.
3
.
B
ez
ier
curv
e
presenta
t
i
o
n f
o
r
circ
ula
r
pa
t
h
Acc
o
r
d
in
g
to
t
h
e
p
a
r
am
etr
ic
t
h
ir
d
o
r
d
er
p
o
ly
n
o
m
ial
in
(
4
)
an
d
(
5
)
,
th
e
c
o
n
tr
o
l
p
o
i
n
ts
ar
e
d
ed
u
ce
d
f
r
o
m
th
e
g
eo
m
etr
y
o
f
Fig
u
r
e
3
s
im
ilar
to
[
2
4
]
as f
o
llo
ws.
T
h
e
r
ed
p
o
in
ts
in
th
e
f
ig
u
r
e
co
r
r
e
s
p
o
n
d
to
in
itial a
n
d
g
o
al
f
r
am
es
(
b
o
u
n
d
ar
y
p
o
i
n
ts
(
0
,
0
)
an
d
(
3
,
3
)
)
,
w
h
ile
th
e
g
r
ee
n
p
o
in
ts
co
r
r
esp
o
n
d
to
th
e
c
o
n
tr
o
l
p
o
i
n
ts
(
1
,
1
)
an
d
(
2
,
2
)
.
T
h
e
b
lu
e
s
tar
is
th
e
ce
n
ter
o
f
r
o
tatio
n
o
f
th
e
ci
r
cu
l
ar
ar
c.
0
=
0
1
=
c
os
(
∗
)
2
=
−
c
os
(
∗
)
3
=
0
=
0
1
=
s
in
(
∗
)
2
=
s
in
(
∗
)
3
=
0
wh
er
e
(
)
is
th
e
r
ad
iu
s
o
f
th
e
t
ar
g
et
cir
cle
th
at
B
ez
ier
cu
r
v
e
is
in
ten
d
ed
to
b
e
as
clo
s
e
as
p
o
s
s
ib
le.
T
h
e
ter
m
(
)
p
r
esen
ts
th
e
f
ac
to
r
o
f
t
h
e
r
ad
iu
s
b
y
wh
ich
th
e
tan
g
e
n
tial
d
is
tan
ce
f
r
o
m
th
e
in
itial
an
d
g
o
al
p
o
s
itio
n
s
ar
e
co
n
s
id
er
ed
t
o
ca
lcu
late
th
e
co
n
tr
o
l
p
o
in
ts
.
T
h
e
an
g
le
(
∗
)
is
b
o
th
th
e
i
n
itial
an
d
g
o
al
o
r
ien
ta
tio
n
an
g
les
in
th
e
lo
ca
l
co
o
r
d
in
ates
ac
co
r
d
in
g
t
o
th
e
ch
ar
ac
ter
is
tics
o
f
a
cir
c
u
lar
ar
c
as
s
h
o
wn
(
0
=
−
=
∗
)
.
T
h
u
s
,
t
h
e
tar
g
et
co
n
n
ec
tio
n
ar
c
h
as
n
et
an
g
le
(
2
∗
)
.
B
y
s
u
b
s
titu
tio
n
in
(
4
)
an
d
(
5
)
,
with
th
e
co
r
r
esp
o
n
d
in
g
v
al
u
es
o
f
co
n
tr
o
l p
o
in
ts
,
th
e
f
o
llo
win
g
e
q
u
atio
n
s
ca
n
b
e
o
b
tain
e
d
.
(
)
=
3
c
os
(
∗
)
(
1
−
)
2
+
3
(
−
c
os
(
∗
)
)
(
1
−
)
2
+
3
(
)
=
3
s
in
(
∗
)
(
1
−
)
2
+
3
s
in
(
∗
)
(
1
−
)
2
∵
=
2
s
in
(
∗
)
∴
(
)
=
3
c
os
(
∗
)
[
−
2
2
+
3
]
+
3
(
2
s
in
(
∗
)
−
c
os
(
∗
)
)
[
2
−
3
]
+
2
s
in
(
∗
)
3
(
)
=
[
3
(
∗
)
]
+
[
6
(
∗
)
−
9
(
∗
)
]
2
+
[
6
(
∗
)
−
4
(
∗
)
]
3
(
1
6
)
(
)
=
3
(
∗
)
[
−
2
]
(
1
7
)
Fig
u
r
e
3
.
C
ir
cu
lar
B
ez
ier
d
e
r
iv
atio
n
I
n
o
r
d
er
to
h
a
v
e
th
e
B
ez
ier
p
at
h
as
clo
s
e
as
p
o
s
s
ib
le
to
th
e
cir
cu
lar
p
ath
,
t
h
e
m
id
d
le
p
o
in
t
(
at
=
0
.
5
)
is
s
elec
ted
s
o
th
at
th
e
B
ez
ier
v
alu
es
ar
e
o
n
th
e
cir
cu
lar
p
at
h
.
Su
ch
a
s
im
p
lifie
d
a
p
p
r
o
ac
h
is
v
er
y
cl
o
s
e
to
th
e
o
p
tim
ized
a
p
p
r
o
ac
h
d
er
iv
e
d
i
n
Ap
p
en
d
ix
B
.
Ho
wev
er
,
it
is
g
r
ea
tly
m
o
r
e
e
f
f
icien
t f
o
r
r
ea
liz
atio
n
o
n
em
b
ed
d
ed
tar
g
ets
with
r
estricte
d
r
eso
u
r
c
es
an
d
r
ea
l
tim
e
co
n
s
tr
ain
ts
th
an
th
e
o
p
tim
ized
ap
p
r
o
ac
h
wh
ich
n
ee
d
s
n
u
m
er
ical
in
teg
r
atio
n
co
m
p
u
tin
g
as p
r
o
v
ed
in
th
e
Ap
p
en
d
i
x
B
to
b
e
p
e
r
f
o
r
m
e
d
ev
er
y
p
r
o
ce
s
s
in
g
cy
cl
e.
(
=
0
.
5
)
=
[
3
2
−
9
4
+
6
8
]
c
os
(
∗
)
+
[
6
4
−
4
8
]
s
in
(
∗
)
=
s
in
(
∗
)
=
2
(
=
0
.
5
)
=
3
4
s
in
(
∗
)
=
−
c
os
(
∗
)
∴
=
4
3
[
1
−
c
os
(
∗
)
s
in
(
∗
)
]
As
m
e
n
ti
o
n
e
d
in
t
h
e
p
r
e
v
i
o
u
s
s
ec
ti
o
n
,
t
h
e
c
o
n
t
r
o
l
p
o
i
n
ts
(
1
)
a
n
d
(
2
)
ar
e
ass
u
m
e
d
at
(
)
a
n
d
(
(
1
−
)
)
,
r
es
p
e
cti
v
e
ly
.
T
h
e
ter
m
,
wh
ic
h
is
n
ec
ess
ar
y
to
co
m
p
u
te
th
e
lo
ca
tio
n
o
f
t
h
e
co
n
tr
o
l
p
o
in
ts
,
ca
n
b
e
co
m
p
u
ted
b
y
s
u
b
s
titu
tio
n
in
(
1
4
)
an
d
(
1
5
)
with
(
=
−
0
)
an
d
(
0
=
ta
n
(
0
)
=
ta
n
(
∗
)
)
,
th
en
co
m
p
ar
i
n
g
ag
ain
s
t
(
1
6
)
an
d
(
1
7
)
,
r
esp
ec
tiv
ely
.
S
am
e
co
n
cl
u
s
io
n
ca
n
b
e
s
im
p
l
y
o
b
tain
ed
b
y
eq
u
atin
g
th
e
t
wo
v
alu
es
o
f
c
o
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
427
-
4
4
4
434
p
o
in
t
(
1
=
=
c
os
(
∗
)
)
.
∴
=
c
os
(
∗
)
=
2
ta
n
(
∗
)
=
2
3
[
c
os
(
∗
)
−
c
os
2
(
∗
)
s
in
2
(
∗
)
]
Sin
ce
th
e
an
g
le
(
∗
)
is
h
alf
th
e
d
i
f
f
er
en
ce
b
etwe
en
th
e
in
itial
f
r
am
e
o
r
ien
tatio
n
a
n
g
le
(
0
)
an
d
g
o
al
f
r
am
e
o
r
ien
tatio
n
an
g
le
(
)
in
th
e
g
lo
b
al
co
o
r
d
in
ates
(
eg
o
-
v
e
h
icle
co
o
r
d
in
ates
to
b
e
in
tr
o
d
u
ce
d
in
th
e
n
ex
t
s
ec
tio
n
)
,
th
en
ca
lcu
latio
n
o
f
(
)
f
o
r
cir
cu
lar
B
ez
ier
ca
n
b
e
s
im
p
lifie
d
in
th
e
f
o
llo
win
g
two
e
q
u
atio
n
s
.
∆
=
|
−
0
|
(
1
8
)
=
2
3
[
(
∆
2
)
−
2
(
∆
2
)
2
(
∆
2
)
]
(
1
9
)
3.
T
H
E
P
RO
P
O
SE
D
AP
P
RO
A
CH
F
O
R
E
G
O
-
VE
H
I
CL
E
P
RE
DI
CT
E
D
P
AT
H
G
E
NE
R
AT
I
O
N
T
h
is
s
ec
tio
n
d
etails
th
e
g
e
n
er
a
tio
n
o
f
th
e
cir
c
u
lar
p
r
ed
icted
e
g
o
-
v
e
h
icle
p
ath
with
B
ez
ier
c
u
r
v
e
b
ased
o
n
th
e
d
er
iv
e
d
in
(
1
8
)
an
d
(
1
9
)
to
co
m
p
u
te
th
e
co
n
tr
o
l
p
o
i
n
ts
.
T
h
e
p
r
ed
icted
p
ath
is
g
e
n
er
ated
in
th
e
eg
o
-
v
eh
icle
(
g
lo
b
al)
co
o
r
d
in
ates
(
,
)
as
s
h
o
wn
in
Fig
u
r
e
4
.
T
h
e
co
o
r
d
in
ate
(
)
p
r
esen
ts
th
e
lo
n
g
itu
d
in
al
ax
is
o
f
th
e
eg
o
-
v
eh
icle,
wh
ile
t
h
e
co
o
r
d
in
ate
(
)
p
r
esen
ts
th
e
later
al
ax
is
.
Giv
en
a
s
p
ec
if
ic
i
n
s
tan
tan
eo
u
s
r
a
d
iu
s
o
f
r
o
tatio
n
o
f
t
h
e
v
e
h
icle
(
)
,
a
s
p
ec
if
ic
cir
cu
lar
p
ath
ca
n
b
e
d
ef
in
ed
with
its
ce
n
ter
o
f
r
o
tatio
n
as
th
e
p
o
in
t
o
f
in
ter
s
ec
tio
n
o
f
th
e
p
er
p
e
n
d
icu
l
ar
lin
es to
th
e
f
o
u
r
wh
ee
ls
d
ir
e
ctio
n
s
(
b
lu
e
s
tar
in
Fig
u
r
e
4
)
.
Fig
u
r
e
4
.
C
ir
cu
lar
p
r
ed
icted
e
g
o
-
v
e
h
icle
p
ath
p
r
esen
ted
with
B
ez
ier
cu
r
v
e
A
g
o
al
f
r
am
e
p
o
s
itio
n
ca
n
b
e
d
ef
in
e
d
b
y
th
e
in
ter
s
ec
tio
n
o
f
th
e
cir
cu
lar
p
ath
with
h
o
r
iz
o
n
tal
lin
e
p
ar
allel
to
th
e
eg
o
-
v
eh
icle
late
r
al
ax
is
an
d
lo
ca
ted
at
a
d
ef
in
ed
m
ax
im
u
m
d
is
tan
ce
f
r
o
m
th
e
eg
o
-
v
e
h
icle
ce
n
ter
o
f
th
e
r
ea
r
a
x
le.
Su
ch
m
ax
im
u
m
d
is
tan
ce
is
d
ef
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ed
as
th
e
r
a
n
g
e
lim
it
o
f
eg
o
-
v
eh
icle
p
at
h
p
r
ed
ictio
n
(
)
.
T
h
e
in
itial
eg
o
-
v
eh
icle
f
r
am
e
i
s
in
b
lu
e
in
Fig
u
r
e
4
,
wh
ile
th
e
tar
g
et
cir
cu
lar
B
ez
ier
p
ath
is
in
o
r
an
g
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d
th
e
g
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al
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r
am
e
o
b
tain
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f
r
o
m
t
h
e
in
ter
s
ec
tio
n
is
in
r
ed
.
Als
o
,
in
Fig
u
r
e
4
,
th
e
lo
ca
l
B
ez
ier
co
o
r
d
in
ates
(
,
)
ar
e
in
g
r
ee
n
,
wh
ile
th
e
g
l
o
b
al
eg
o
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v
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co
o
r
d
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ates
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,
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ar
e
in
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lu
e.
T
h
e
a
n
g
le
(
)
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th
e
r
o
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d
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ates.
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h
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e
r
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ce
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t
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am
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as in
[
2
4
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Acc
o
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d
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g
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o
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etr
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cir
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lar
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in
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u
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4
,
it is
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r
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at
(
=
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2
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.
I
t
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wo
r
th
m
en
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e
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Su
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ld
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e
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o
r
e
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u
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ate
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ig
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ican
t
s
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ee
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n
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ially
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ee
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s
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At
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ee
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wh
er
e
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ate
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e
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u
ld
b
e
b
etter
to
ca
lcu
late
th
e
eg
o
-
v
eh
icle
r
ad
iu
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o
f
r
o
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th
e
r
atio
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etwe
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th
e
w
h
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ase
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d
th
e
ta
n
g
en
t
o
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th
e
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r
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n
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wh
ee
l
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ass
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th
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r
wh
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o
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teer
ab
le
as
r
ev
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led
in
t
h
e
k
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em
atics
m
o
d
el
in
[
2
5
]
.
T
h
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ca
lcu
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ased
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n
ac
c
u
r
ate
esti
m
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th
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r
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n
t w
h
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n
t
h
e
m
ea
s
u
r
ed
s
teer
in
g
wh
ee
l a
n
g
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
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I
n
t
J
R
o
b
&
A
u
to
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I
SS
N:
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-
2
5
8
6
R
o
b
u
s
t e
fficien
t e
g
o
-
ve
h
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p
a
th
p
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ed
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a
s
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n
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ezier
cu
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ve
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r
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(
Ha
n
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n
H.
H
u
s
s
ein
)
435
B
ased
o
n
th
e
g
eo
m
etr
y
in
Fig
u
r
e
4
an
d
th
e
r
ea
ch
ed
f
o
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m
u
l
as
in
p
r
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ez
ier
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ath
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v
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ath
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n
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al
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o
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ates
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,
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ca
n
b
e
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o
llo
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an
d
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R
eg
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ath
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la
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th
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ar
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ic
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m
ial
e
q
u
ati
o
n
s
o
f
th
e
B
ez
ier
cu
r
v
e
in
(
1
4
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1
5
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s
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f
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icien
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to
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en
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ate
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ab
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ath
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ic
in
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=
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T
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is
s
h
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asic
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er
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o
ly
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ials
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le
d
in
[
8
]
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d
[
9
]
.
Ho
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f
o
r
S
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ased
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ials
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ig
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ath
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ee
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s
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I
t
s
h
all
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e
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in
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h
e
v
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o
f
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(
m
o
v
in
g
th
e
co
n
tr
o
l
p
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ts
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th
e
m
id
d
le)
lead
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o
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v
in
g
th
e
s
t
ee
r
in
g
ac
tio
n
s
m
o
r
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at
th
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id
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th
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ath
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ile
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f
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m
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tr
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l
p
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ts
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e
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n
d
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ies)
lead
s
to
h
av
e
t
h
e
s
teer
in
g
m
o
r
e
at
th
e
s
tar
t a
n
d
en
d
o
f
th
e
p
ath
.
As
th
e
p
ath
p
r
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n
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b
ase
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o
n
th
e
c
u
r
r
e
n
t
in
s
tan
tan
eo
u
s
eg
o
-
v
e
h
icle
m
o
tio
n
s
tate
o
f
s
p
ee
d
an
d
y
aw
r
ate
co
v
er
in
g
o
n
ly
cir
cu
l
ar
m
an
eu
v
e
r
s
,
th
en
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
ca
n
b
e
f
o
r
m
u
lated
in
th
e
f
o
llo
win
g
Alg
o
r
ith
m
1
.
T
h
e
alg
o
r
ith
m
e
x
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ts
as
in
p
u
t
th
e
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n
s
tan
tan
e
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s
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d
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al
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ee
d
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y
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w
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ate
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th
e
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o
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icle,
a
n
d
p
r
o
v
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es
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a
n
o
u
tp
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t
th
e
g
e
n
er
ated
p
r
e
d
icted
p
ath
p
r
esen
ted
with
(
,
)
p
o
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ts
d
ef
in
ed
in
th
e
lo
ca
l
C
ar
tesi
an
co
o
r
d
in
ates
o
f
th
e
eg
o
-
v
e
h
icle
s
h
o
wn
in
Fig
u
r
e
4
.
T
h
e
g
en
e
r
ated
p
o
in
ts
p
r
esen
tin
g
th
e
p
r
ed
icted
p
ath
(
(
)
,
(
)
)
ar
e
f
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n
ctio
n
o
n
th
e
in
d
ep
e
n
d
en
t p
ar
am
eter
(
)
,
wh
ich
v
ar
ies
f
r
o
m
0
to
1
with
s
tep
(
∆
)
d
ef
in
ed
ac
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r
d
in
g
to
t
h
e
d
is
tan
ce
r
eso
lu
tio
n
f
o
r
p
ath
g
e
n
er
atio
n
(
∆
)
.
Su
ch
d
is
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ce
r
eso
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tio
n
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d
r
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lim
it
(
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s
h
all
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e
co
n
s
id
er
e
d
as
in
p
u
t
to
th
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alg
o
r
ith
m
as
well.
A
n
ew
p
ar
am
eter
(
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is
ad
d
ed
p
r
esen
tin
g
th
e
m
ax
im
u
m
lim
it
o
f
later
al
ac
ce
ler
atio
n
f
o
r
a
n
o
r
m
al
d
r
i
v
in
g
s
ce
n
ar
i
o
with
n
o
s
ig
n
if
ican
t
later
al
s
lip
p
in
g
to
lim
it
th
e
p
ath
p
r
e
d
ictio
n
er
r
o
r
th
at
ass
u
m
es
p
u
r
e
cir
cu
lar
m
o
tio
n
.
Fin
ally
,
a
cu
r
v
atu
r
e
th
r
esh
o
l
d
(
ℎ
)
s
h
all
b
e
d
ef
in
ed
to
d
if
f
e
r
en
ti
ate
b
etwe
en
th
e
s
tr
aig
h
t
a
n
d
c
ir
cu
lar
p
at
h
g
e
n
er
atio
n
s
,
wh
ic
h
co
u
l
d
b
e
an
in
p
u
t
to
th
e
alg
o
r
ith
m
.
I
f
th
e
cu
r
r
en
t
cu
r
v
atu
r
e
is
g
r
ea
ter
th
an
th
e
d
ef
in
ed
th
r
esh
o
ld
th
e
n
th
e
m
an
eu
v
er
is
cir
cu
lar
,
o
th
er
wis
e
it
is
s
tr
aig
h
t.
I
t
is
clea
r
f
r
o
m
th
e
alg
o
r
ith
m
f
o
r
m
u
lated
as
f
o
llo
ws
th
at
its
co
m
p
lex
ity
i
s
(
)
,
w
h
e
r
e
(
)
p
r
e
s
e
n
t
s
t
h
e
n
u
m
b
e
r
o
f
w
a
y
p
o
i
n
t
s
f
o
r
m
i
n
g
t
h
e
g
e
n
e
r
a
t
e
d
p
a
t
h
(
=
1
∆
+
1
)
.
R
o
u
g
h
l
y
,
(
ℎ
)
ca
n
b
e
ass
u
m
ed
as
(
1
/
[
4
∗
]
)
s
o
th
at
th
e
g
en
er
ated
p
ath
is
alm
o
s
t
s
tr
aig
h
t
at
s
u
ch
c
u
r
v
at
u
r
e
th
r
esh
o
ld
an
d
b
elo
w.
Alg
o
r
ith
m
1
.
E
g
o
-
v
eh
icle
p
r
ed
icted
p
ath
g
e
n
er
atio
n
1:
[
(
)
,
(
)
]
=
ℎ
(
,
̇
,
∆
,
,
,
ℎ
)
2:
=
̇
3:
(
<
)
4:
∆
=
∆
/
5:
=
̇
/
6:
(
|
|
>
ℎ
)
7:
∆
=
si
n
−
1
(
×
)
8:
=
2
si
n
(
∆
2
)
/
9:
=
2
3
[
co
s
(
∆
2
)
−
co
s
2
(
∆
2
)
s
in
2
(
∆
2
)
]
10:
0
=
−
tan
(
∆
2
)
11:
(
=
0
∶
∆
∶
1
)
12:
(
)
=
(
3
)
+
3
(
1
−
3
)
2
−
2
(
1
−
3
)
3
13:
(
)
=
(
3
0
)
(
1
−
)
14:
(
)
=
(
)
cos
(
∆
2
)
−
(
)
si
n
(
∆
2
)
15:
(
)
=
(
)
si
n
(
∆
2
)
+
(
)
cos
(
∆
2
)
16:
17:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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2
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20
2
6
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4
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18:
(
=
0
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22:
23:
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4
.
1
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pr
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(
1
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(
1
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t
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r
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at
h
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n
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lo
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2
D
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ar
tesi
an
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r
d
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ates
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s
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th
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ce
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tain
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in
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e
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u
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r
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it
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r
r
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in
g
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e
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ce
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ac
cu
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r
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r
a
g
ain
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th
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d
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lated
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r
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at
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ly
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Fig
u
r
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5
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ch
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ed
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ly
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lu
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d
in
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‘
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h
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m
e
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in
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p
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ed
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n
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w
h
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b
e
ex
p
r
ess
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with
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h
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p
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ce
n
tag
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d
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s
e
in
th
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er
r
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r
.
F
o
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test
ca
s
es
1
,
2
,
3
,
an
d
4
f
o
r
d
if
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er
e
n
t
r
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an
d
s
h
ar
p
cir
cu
lar
m
an
eu
v
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s
,
th
e
ac
cu
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ac
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was
en
h
an
ce
d
a
b
o
u
t
9
5
%
o
r
m
o
r
e.
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r
test
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s
e
5
f
o
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s
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tly
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t m
an
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v
er
,
th
e
ac
c
u
r
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d
ab
o
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t 5
0
%.
Fig
u
r
e
5
.
C
o
m
p
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r
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n
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r
test
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s
e
1
Fig
u
r
e
6
.
C
o
m
p
a
r
is
o
n
p
lo
t
f
o
r
test
ca
s
e
2
Evaluation Warning : The document was created with Spire.PDF for Python.