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l J
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An
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1
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Dec
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ter
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th
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ts.
T
h
e
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AU
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to
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o
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a
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d
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a
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e
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ti
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ifi
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d
t
o
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t
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o
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m
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d
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a
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h
m
a
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Th
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K
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s
:
A
*
a
lg
o
r
ith
m
Au
to
n
o
m
o
u
s
u
n
d
er
wate
r
v
eh
icles
E
n
er
g
y
-
o
p
tim
ized
Heu
r
is
tic
s
ea
r
ch
Path
p
lan
n
in
g
T
h
is i
s
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
:
Do
Kh
ac
T
iep
E
lectr
ical
an
d
E
lectr
o
n
ic
E
n
g
i
n
ee
r
in
g
,
Vietn
am
Ma
r
itime
Un
iv
er
s
ity
4
8
4
L
ac
h
T
r
ay
,
L
e
C
h
an
,
Hai
Ph
o
n
g
,
Vietn
am
E
m
ail: d
o
k
h
ac
tiep
@
v
im
ar
u
.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Au
to
n
o
m
o
u
s
u
n
d
e
r
wate
r
v
eh
i
cles
(
AUVs)
ar
e
in
cr
ea
s
in
g
ly
d
ep
lo
y
e
d
in
a
wid
e
r
a
n
g
e
o
f
a
p
p
licatio
n
s
,
in
clu
d
in
g
o
ce
an
o
g
r
ap
h
ic
r
esear
ch
,
en
v
ir
o
n
m
en
tal
m
o
n
ito
r
in
g
,
u
n
d
er
wate
r
i
n
f
r
astru
ctu
r
e
in
s
p
ec
tio
n
,
an
d
m
ilit
ar
y
o
p
e
r
atio
n
s
[
1
]
,
[
2
]
.
A
k
ey
ch
allen
g
e
in
AUV
o
p
e
r
a
tio
n
s
,
p
ar
ticu
lar
l
y
f
o
r
l
o
n
g
-
d
u
r
atio
n
m
is
s
io
n
s
,
is
th
e
lim
ited
o
n
b
o
a
r
d
en
e
r
g
y
c
ap
ac
ity
.
T
h
er
e
f
o
r
e,
e
n
er
g
y
-
ef
f
icien
t
p
ath
p
lan
n
in
g
is
cr
u
ci
al
f
o
r
m
ax
im
izin
g
m
is
s
io
n
r
an
g
e,
en
d
u
r
an
ce
,
an
d
o
v
er
all
ef
f
ec
tiv
en
ess
[
3
]
,
[
4
]
.
T
h
is
is
e
s
p
ec
ially
tr
u
e
in
d
y
n
a
m
ic
en
v
ir
o
n
m
e
n
ts
ch
ar
ac
ter
ized
b
y
s
tr
o
n
g
an
d
tim
e
-
v
ar
y
in
g
o
ce
an
cu
r
r
en
ts
,
wh
er
e
n
aiv
e
p
ath
p
lan
n
in
g
s
tr
ateg
ies
ca
n
lead
to
s
ig
n
if
ican
tly
in
cr
ea
s
ed
en
e
r
g
y
co
n
s
u
m
p
tio
n
an
d
e
v
en
m
is
s
io
n
f
ailu
r
e
[
5
]
,
[
6
]
.
T
r
ad
itio
n
al
p
ath
p
lan
n
i
n
g
alg
o
r
ith
m
s
,
s
u
ch
as
A*
,
Dijk
s
tr
a's
alg
o
r
ith
m
,
an
d
p
o
te
n
tial
f
ield
m
eth
o
d
s
,
h
av
e
b
ee
n
wid
ely
ap
p
lied
to
AUVs
[
7
]
–
[
9
]
.
Ho
wev
er
,
th
es
e
m
eth
o
d
s
o
f
ten
d
o
n
o
t
e
x
p
lic
itly
ac
co
u
n
t
f
o
r
th
e
co
m
p
lex
h
y
d
r
o
d
y
n
am
ic
f
o
r
ce
s
ac
tin
g
o
n
th
e
v
eh
icle
in
a
d
y
n
am
ic
f
lo
w
f
iel
d
.
Simp
ly
f
in
d
in
g
t
h
e
s
h
o
r
test
g
eo
m
etr
ic
p
ath
m
ay
n
o
t
b
e
en
er
g
y
-
ef
f
icien
t
wh
en
s
tr
o
n
g
cu
r
r
en
ts
ar
e
p
r
esen
t
[
1
0
]
.
R
ec
en
t
r
esear
ch
h
as
f
o
cu
s
ed
o
n
d
e
v
elo
p
in
g
en
e
r
g
y
-
awa
r
e
p
ath
p
lan
n
in
g
tec
h
n
i
q
u
es
th
at
in
co
r
p
o
r
ate
f
lo
w
f
i
eld
in
f
o
r
m
atio
n
a
n
d
v
eh
icle
d
y
n
am
ics
[
1
1
]
–
[
1
3
]
.
T
h
ese
ap
p
r
o
ac
h
es
o
f
te
n
in
v
o
lv
e
u
s
in
g
co
m
p
u
tatio
n
al
f
lu
i
d
d
y
n
am
ics
(
C
FD)
s
im
u
latio
n
s
o
r
an
aly
tical
m
o
d
els
to
esti
m
ate
th
e
en
er
g
y
c
o
s
t
o
f
tr
av
e
r
s
in
g
d
if
f
er
en
t
p
at
h
s
[
6
]
,
[
1
4
]
.
Oth
er
ap
p
r
o
ac
h
es in
clu
d
e
th
e
u
s
e
o
f
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
[
1
5
]
,
[
1
6
]
a
n
d
r
ei
n
f
o
r
ce
m
en
t le
ar
n
i
n
g
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
5
3
-
765
754
W
h
ile
s
o
m
e
p
r
o
g
r
ess
h
as
b
ee
n
m
ad
e,
th
er
e
r
e
m
ain
s
a
n
ee
d
f
o
r
c
o
m
p
u
tatio
n
ally
ef
f
icien
t
an
d
p
r
ac
tical
p
ath
p
lan
n
in
g
alg
o
r
ith
m
s
th
at
ca
n
ef
f
ec
tiv
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m
in
im
ize
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er
g
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o
n
s
u
m
p
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-
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o
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n
ea
r
-
r
ea
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tim
e
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o
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er
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s
.
Fu
r
th
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o
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e
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te
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o
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etailed
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n
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m
p
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n
m
o
d
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at
ac
co
u
n
t
f
o
r
a
v
ar
iety
o
f
f
ac
to
r
s
(
e.
g
.
d
r
ag
,
a
d
d
ed
m
ass
,
m
an
eu
v
e
r
i
n
g
)
is
o
f
te
n
co
m
p
u
tatio
n
ally
d
em
an
d
in
g
an
d
m
ay
n
o
t
b
e
s
u
itab
le
f
o
r
r
eso
u
r
ce
-
co
n
s
tr
ain
ed
AUV
p
latf
o
r
m
s
[
1
8
]
,
[
1
9
]
.
So
m
e
r
esear
ch
ad
d
r
ess
es
p
ath
p
lan
n
in
g
in
3
D
en
v
ir
o
n
m
e
n
ts
[
2
0
]
–
[
2
2
]
,
wh
ile
o
th
er
s
tu
d
ies
f
o
cu
s
o
n
m
u
ltip
le
AUV
s
y
s
tem
s
[
2
3
]
.
T
h
er
e
ar
e
also
wo
r
k
s
f
o
cu
s
o
n
t
h
e
u
n
c
er
tain
ty
in
t
h
e
en
v
ir
o
n
m
en
t
[
2
4
]
.
W
h
ile
th
e
ex
is
tin
g
liter
atu
r
e
h
as
m
ad
e
s
ig
n
i
f
ican
t
s
tr
id
es
i
n
en
er
g
y
-
awa
r
e
p
lan
n
in
g
,
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g
ap
r
em
ain
s
f
o
r
a
co
m
p
u
tatio
n
ally
ef
f
icie
n
t
alg
o
r
ith
m
th
at
s
ea
m
less
ly
in
teg
r
ates
a
d
etailed
en
e
r
g
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co
n
s
u
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p
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-
r
ea
l
-
tim
e
a
p
p
licatio
n
.
Pre
v
io
u
s
wo
r
k
s
o
f
ten
tr
ad
e
o
f
f
m
o
d
el
f
id
elity
f
o
r
s
p
ee
d
o
r
v
ice
v
er
s
a.
Fo
r
in
s
tan
ce
,
[
6
]
o
f
f
er
s
h
ig
h
ac
cu
r
ac
y
b
u
t
is
co
m
p
u
tatio
n
ally
p
r
o
h
ib
itiv
e
f
o
r
o
n
lin
e
u
s
e,
wh
ile
[
1
5
]
m
a
y
s
tr
u
g
g
le
with
co
n
v
er
g
e
n
ce
o
r
g
u
ar
an
tee
o
p
tim
ality
.
T
h
is
p
ap
e
r
ad
d
r
ess
es
th
is
g
a
p
b
y
p
r
esen
tin
g
a
n
o
v
el
en
er
g
y
-
o
p
tim
ized
A
alg
o
r
ith
m
*
th
at
is
b
o
th
co
m
p
u
tatio
n
ally
ef
f
i
cien
t
an
d
ef
f
ec
tiv
e
.
Ou
r
k
ey
c
o
n
tr
ib
u
tio
n
s
ar
e:
−
T
ig
h
t
in
teg
r
atio
n
o
f
m
o
d
els:
T
h
e
n
o
v
el
i
n
teg
r
atio
n
o
f
a
co
m
p
u
tatio
n
ally
ef
f
icien
t
f
lo
w
f
i
eld
m
o
d
el
an
d
a
d
etailed
AUV
en
er
g
y
co
n
s
u
m
p
tio
n
m
o
d
el
—
co
n
s
id
er
in
g
d
r
a
g
f
o
r
ce
s
,
r
elativ
e
v
elo
city
,
an
d
m
an
e
u
v
er
i
n
g
co
s
ts
—
d
ir
ec
tly
in
to
th
e
A*
h
eu
r
is
tic
s
ea
r
ch
.
−
C
o
m
p
u
tatio
n
al
ef
f
icien
cy
:
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
m
ain
tain
s
th
e
s
im
p
licity
a
n
d
g
u
ar
a
n
tees
o
f
th
e
A*
alg
o
r
ith
m
wh
ile
s
ig
n
if
ican
tl
y
i
m
p
r
o
v
i
n
g
en
e
r
g
y
ec
o
n
o
m
y
,
m
ak
in
g
it su
itab
le
f
o
r
o
n
lin
e
p
at
h
p
lan
n
i
n
g
.
−
C
o
m
p
r
eh
en
s
iv
e
v
alid
atio
n
:
E
x
ten
s
iv
e
s
im
u
latio
n
ac
r
o
s
s
d
iv
er
s
e
s
ce
n
ar
io
s
(
s
tatic/d
y
n
am
ic
o
b
s
tacle
s
,
wea
k
/s
tr
o
n
g
cu
r
r
en
ts
)
d
e
m
o
n
s
tr
ates
th
e
alg
o
r
ith
m
'
s
r
o
b
u
s
tn
ess
an
d
p
er
f
o
r
m
a
n
ce
,
s
h
o
wi
n
g
u
p
to
a
5
0
%
r
ed
u
ctio
n
i
n
en
er
g
y
c
o
n
s
u
m
p
ti
o
n
co
m
p
ar
ed
t
o
a
s
tan
d
ar
d
A*
im
p
lem
en
tatio
n
.
T
h
e
r
em
ai
n
d
er
o
f
th
is
p
a
p
er
i
s
o
r
g
an
ize
d
as
f
o
llo
ws:
s
ec
tio
n
2
r
ev
iews
r
elate
d
wo
r
k
o
n
AUV
p
ath
p
lan
n
in
g
.
Sectio
n
3
d
escr
ib
es
th
e
p
r
o
p
o
s
ed
en
er
g
y
-
o
p
tim
ized
A*
alg
o
r
ith
m
.
Sectio
n
4
p
r
e
s
en
ts
th
e
s
im
u
latio
n
r
esu
lts
an
d
an
aly
s
is
.
Fin
ally
,
s
ec
tio
n
5
co
n
clu
d
es th
e
p
ap
er
.
2.
M
O
DE
L
I
NG
AP
P
RO
A
CH
E
S
2
.
1
.
AUV
k
inem
a
t
ics mo
del f
o
r
pa
t
h pla
nn
ing
T
o
ac
cu
r
ately
s
im
u
late
th
e
AUV
'
s
tr
ajec
to
r
y
an
d
esti
m
at
e
its
p
o
s
itio
n
o
v
er
tim
e,
we
u
tili
ze
two
co
o
r
d
in
ate
f
r
am
es:
a
n
E
ar
th
-
f
ix
ed
f
r
am
e
(
)
an
d
a
b
o
d
y
-
f
ix
ed
f
r
a
m
e
(
)
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
AUV'
s
m
o
tio
n
is
m
o
d
eled
u
s
in
g
r
ig
i
d
-
b
o
d
y
k
i
n
em
atics,
co
n
s
id
er
in
g
all
s
ix
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
(
6
Do
F).
T
h
ese
in
clu
d
e
s
u
r
g
e,
s
way
,
an
d
h
ea
v
e
f
o
r
tr
an
s
latio
n
al
m
o
tio
n
,
an
d
r
o
ll,
p
itch
,
an
d
y
aw
f
o
r
r
o
tatio
n
al
m
o
tio
n
.
E
q
u
atio
n
(
1
)
d
ef
in
es t
h
ese
k
in
em
atic
r
elatio
n
s
h
ip
s
.
̇
=
=
[
̇
̇
̇
]
=
(
,
,
)
.
[
]
(
1
)
w
h
er
e
p
-
Po
s
itio
n
in
g
l
o
b
al
f
r
a
m
e
(
x
,
y
,
z
)
;
v
-
Velo
city
i
n
g
lo
b
al
f
r
am
e;
R
(
ϕ
,
θ
,
ψ
)
-
R
o
tatio
n
m
atr
ix
f
r
o
m
b
o
d
y
to
g
lo
b
al
f
r
am
e;
u
,
v
,
w
-
Su
r
g
e
,
s
way
,
an
d
h
ea
v
e
v
el
o
cities (
b
o
d
y
f
r
am
e)
.
Fig
u
r
e
1
.
AUV
co
o
r
d
in
ate
s
y
s
tem
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
en
erg
y
-
o
p
timiz
ed
A
*
a
lg
o
r
ith
m
fo
r
p
a
th
p
la
n
n
in
g
o
f
…
(
Do
K
h
a
c
Tiep
)
755
T
h
e
AUV'
s
p
o
s
itio
n
is
u
p
d
ated
b
y
in
teg
r
ati
n
g
th
e
tr
an
s
lat
io
n
al
v
elo
cities
o
v
er
ea
ch
ti
m
e
s
tep
a
s
s
h
o
wn
in
(
2
)
.
+
1
=
+
.
(
2
)
U
p
d
a
t
i
n
g
v
e
l
o
c
it
y
i
s
a
n
i
m
p
o
r
ta
n
t
s
te
p
f
o
r
s
i
m
u
la
t
i
n
g
o
r
p
r
e
d
ic
t
i
n
g
m
o
t
i
o
n
.
I
n
t
h
is
m
et
h
o
d
,
w
e
w
il
l
e
x
a
m
i
n
e
h
o
w
t
o
p
e
r
f
o
r
m
t
h
e
u
p
d
a
t
e
,
w
i
t
h
t
h
e
s
i
m
p
l
i
f
y
i
n
g
as
s
u
m
p
ti
o
n
t
h
a
t
s
p
e
e
d
i
s
k
e
p
t
c
o
n
s
t
a
n
t
i
n
e
a
c
h
c
a
lc
u
l
a
t
i
o
n
s
t
e
p
.
+
1
=
+
.
(
3
)
w
h
er
e
+
1
is
th
e
v
elo
city
v
ec
to
r
a
t
th
e
n
e
x
t
tim
e
s
tep
(
k
+1
)
;
is
th
e
v
elo
city
v
ec
to
r
at
th
e
c
u
r
r
e
n
t
tim
e
s
tep
(
k
)
;
is
th
e
ac
ce
ler
atio
n
v
ec
to
r
at
th
e
cu
r
r
en
t tim
e
s
tep
(
k
)
; Δt
is
th
e
tim
e
s
tep
d
u
r
atio
n
.
B
ased
o
n
th
e
an
g
u
lar
v
elo
city
,
th
e
c
h
an
g
e
i
n
E
u
ler
a
n
g
les ca
n
b
e
ca
lcu
late
d
as p
r
es
en
ted
in
(
4
)
.
+
1
=
+
̇
.
(
4
)
w
h
er
e
+
1
is
th
e
s
tate
(
lik
ely
an
g
les,
g
iv
en
th
e
p
r
e
v
io
u
s
p
r
o
m
p
ts
ab
o
u
t
E
u
ler
an
g
les)
at
th
e
n
ex
t
tim
e
s
tep
(
k
+1
)
;
is
th
e
s
tate
at
th
e
c
u
r
r
e
n
t
tim
e
s
tep
(
k
);
̇
is
th
e
r
ate
o
f
ch
an
g
e
o
f
th
e
s
tate
(
a
n
g
u
lar
v
elo
city
)
at
t
h
e
cu
r
r
en
t tim
e
s
tep
(
k
).
T
h
e
in
teg
r
atio
n
o
f
th
e
k
in
em
at
ic
m
o
d
el
with
t
h
e
en
er
g
y
m
o
d
el
is
cr
u
cial.
Velo
city
s
er
v
es
a
s
th
e
lin
k
,
co
n
n
ec
tin
g
k
in
em
atic
asp
ec
ts
with
en
er
g
y
c
o
n
s
u
m
p
ti
o
n
,
as i
n
d
icate
d
in
(
5
)
.
∞
‖
‖
3
=
(
2
+
2
+
2
)
3
/
2
(
5
)
Op
tim
al
p
ath
s
b
alan
ce
k
in
em
a
tic
f
ea
s
ib
ilit
y
(
tu
r
n
r
a
d
ii,
ac
ce
ler
atio
n
)
an
d
en
er
g
y
e
f
f
icien
cy
.
2
.
2
.
E
nerg
y
c
o
ns
um
ptio
n mo
del
f
o
r
AUV
pa
t
h pla
nn
ing
T
h
e
to
tal
en
er
g
y
c
o
n
s
u
m
p
tio
n
(
)
o
f
an
au
to
n
o
m
o
u
s
u
n
d
er
wate
r
v
eh
icle
(
AUV)
is
ty
p
ically
m
o
d
eled
b
y
s
u
m
m
in
g
s
ev
er
al
co
r
e
co
m
p
o
n
en
ts
:
p
r
o
p
u
ls
io
n
en
er
g
y
,
d
r
ag
lo
s
s
in
d
u
ce
d
b
y
cu
r
r
en
ts
,
an
d
th
e
s
tatic
b
ase
lo
ad
o
f
o
n
b
o
ar
d
ele
ctr
o
n
ics
.
F
i
r
s
t
,
p
r
o
p
u
l
s
i
o
n
e
n
e
r
g
y
(
)
r
e
p
r
e
s
e
n
ts
t
h
e
e
n
e
r
g
y
c
o
n
s
u
m
e
d
b
y
t
h
e
p
r
o
p
u
l
s
i
o
n
s
y
s
t
em
t
o
o
v
e
r
c
o
m
e
h
y
d
r
o
d
y
n
a
m
i
c
d
r
a
g
a
n
d
m
a
i
n
t
a
i
n
t
h
e
AU
V'
s
d
e
s
i
r
ed
v
e
l
o
c
i
t
y
(
)
.
T
h
e
p
o
w
e
r
r
e
q
u
i
r
e
d
f
o
r
p
r
o
p
u
l
s
i
o
n
i
s
o
f
t
e
n
m
o
d
e
l
e
d
as
a
f
u
n
c
t
i
o
n
o
f
t
h
e
A
U
V'
s
s
p
e
e
d
(
m
a
g
n
i
t
u
d
e
o
f
v
e
l
o
c
i
t
y
,
|
|
|
|
)
,
as
i
n
d
i
c
at
e
d
in
(
6
)
.
(
)
=
1
3
+
2
2
(
6
)
Her
e,
1
is
a
co
ef
f
icien
t
ass
o
ciat
ed
with
cu
b
ic
d
r
a
g
ef
f
ec
ts
(
w
h
ich
d
o
m
in
ate
at
h
ig
h
e
r
s
p
ee
d
s
)
,
an
d
2
r
elate
s
to
q
u
ad
r
atic
d
r
ag
e
f
f
ec
ts
,
s
u
ch
as
s
k
in
f
r
ictio
n
.
T
h
e
e
n
er
g
y
c
o
n
s
u
m
ed
d
u
r
in
g
a
s
m
all
-
tim
e
s
tep
Δ
t
at
s
tep
is
ca
lcu
lated
as (
7
)
:
,
=
(
1
‖
‖
3
+
2
‖
‖
2
)
(
7
)
Seco
n
d
,
we
ac
c
o
u
n
t
f
o
r
d
r
ag
l
o
s
s
f
r
o
m
cu
r
r
en
ts
(
)
:
T
h
is
co
m
p
o
n
en
t
ac
c
o
u
n
ts
f
o
r
th
e
ad
d
iti
o
n
al
en
er
g
y
ex
p
e
n
d
itu
r
e
d
u
e
to
th
e
p
r
esen
ce
o
f
wate
r
cu
r
r
e
n
ts
.
I
t
d
ep
en
d
s
o
n
th
e
r
elativ
e
v
elo
c
ity
(
)
b
etwe
en
th
e
AUV
(
)
an
d
t
h
e
cu
r
r
en
t (
)
,
d
ef
in
ed
as:
=
−
.
T
h
e
en
er
g
y
ass
o
ciate
d
with
th
i
s
ef
f
ec
t o
v
er
a
tim
e
s
tep
Δ
t a
t step
i
is
m
o
d
eled
as (
8
)
.
,
=
3
‖
,
‖
2
.
(
8
)
wh
er
e
3
is
a
m
o
d
elin
g
co
e
f
f
i
cien
t.
T
h
is
ter
m
s
p
ec
if
ically
r
ep
r
esen
ts
th
e
en
er
g
y
wasted
o
r
a
d
d
itio
n
ally
co
n
s
u
m
ed
wh
e
n
th
e
AUV
is
o
p
er
atin
g
ag
ai
n
s
t o
r
ac
r
o
s
s
cu
r
r
en
ts
.
Fin
ally
,
s
tatic
en
er
g
y
(
)
ac
co
u
n
ts
f
o
r
th
e
co
n
s
tan
t
p
o
wer
d
r
a
w
(
)
o
f
s
en
s
o
r
s
,
n
av
ig
atio
n
s
y
s
tem
s
,
an
d
co
n
tr
o
l
h
ar
d
war
e,
wh
ich
r
em
ain
s
ac
tiv
e
r
eg
ar
d
less
o
f
m
o
tio
n
.
Ov
er
th
e
to
ta
l
m
is
s
io
n
d
u
r
atio
n
t,
th
is
b
ase
lo
ad
is
ca
lcu
lated
as (
9
)
:
=
.
(
9
)
wh
er
e
r
ep
r
esen
ts
th
e
co
n
s
tan
t
s
tatic
p
o
wer
d
r
aw.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
5
3
-
765
756
T
h
e
to
tal
en
er
g
y
co
n
s
u
m
p
tio
n
,
,
is
d
eter
m
in
ed
b
y
s
u
m
m
in
g
th
e
p
r
o
p
u
ls
io
n
en
er
g
y
(
)
an
d
th
e
d
r
ag
l
o
s
s
f
r
o
m
cu
r
r
en
ts
(
)
o
v
er
all
tim
e
s
tep
s
,
an
d
a
d
d
in
g
th
e
to
tal
s
tatic
en
er
g
y
(
)
as (
1
0
)
.
=
,
+
,
+
(
1
0
)
I
n
ad
d
itio
n
t
o
o
th
er
f
ac
t
o
r
s
,
elem
en
ts
s
u
ch
as
h
y
d
r
o
d
y
n
am
ic
m
o
d
elin
g
,
c
u
r
r
en
t
e
f
f
ec
ts
,
an
d
b
atter
y
ef
f
icien
c
y
also
s
ig
n
if
ican
tly
in
f
lu
en
ce
th
e
en
er
g
y
co
n
s
u
m
p
tio
n
o
f
AU
Vs.
3.
P
RO
P
O
SE
D
A*
AL
G
O
RI
T
H
M
3
.
1
.
A
*
a
lg
o
rit
hm
o
v
er
v
iew
T
h
e
A*
(
A
-
s
tar
)
alg
o
r
ith
m
is
a
p
o
wer
f
u
l,
i
n
f
o
r
m
ed
s
ea
r
ch
alg
o
r
ith
m
u
s
ed
to
f
in
d
th
e
o
p
tim
al
p
ath
b
etwe
en
a
s
tar
t a
n
d
g
o
al
n
o
d
e
in
a
g
r
ap
h
.
Un
lik
e
u
n
in
f
o
r
m
e
d
s
ea
r
ch
es lik
e
B
r
ea
d
th
-
f
ir
s
t se
ar
ch
,
A*
em
p
lo
y
s
a
h
eu
r
is
tic
f
u
n
cti
o
n
,
h
(
n
)
,
t
o
est
im
ate
th
e
r
e
m
ain
in
g
co
s
t
f
r
o
m
a
n
o
d
e
n
to
t
h
e
g
o
al.
T
h
is
h
eu
r
is
tic
g
u
id
es
th
e
s
ea
r
ch
,
p
r
io
r
itizin
g
n
o
d
es th
at
ap
p
ea
r
clo
s
er
to
th
e
s
o
lu
tio
n
.
A*
co
m
b
in
es
asp
ec
ts
o
f
Dijk
s
tr
a'
s
alg
o
r
ith
m
(
wh
ich
co
n
s
id
er
s
th
e
co
s
t
-
so
-
f
ar
)
an
d
Gr
ee
d
y
b
est
-
f
ir
s
t
s
ea
r
ch
(
wh
ich
r
elies
s
o
lely
o
n
th
e
h
eu
r
is
tic)
.
I
t
ac
h
iev
es
th
is
b
y
u
s
in
g
an
e
v
alu
atio
n
f
u
n
ctio
n
,
(
)
,
f
o
r
ea
c
h
n
o
d
e
:
(
)
=
(
)
+
ℎ
(
)
(
1
1
)
wh
er
e
(
)
is
th
e
ac
tu
al
c
o
s
t
o
f
t
h
e
p
ath
f
r
o
m
th
e
s
tar
t
n
o
d
e
to
n
o
d
e
;
ℎ
(
)
is
th
e
esti
m
ated
c
o
s
t
f
r
o
m
n
o
d
e
to
th
e
g
o
al
(
th
e
h
e
u
r
is
tic)
.
T
h
e
A*
alg
o
r
ith
m
ef
f
icien
tly
f
in
d
s
th
e
s
h
o
r
test
p
at
h
b
y
m
ain
tain
in
g
an
OPEN
lis
t
(
p
r
io
r
ity
q
u
eu
e)
o
f
n
o
d
es
to
ex
p
lo
r
e
an
d
a
C
L
OSED
lis
t
o
f
p
r
o
ce
s
s
ed
n
o
d
es.
I
t
iter
ativ
ely
s
elec
ts
th
e
n
o
d
e
with
th
e
lo
west
esti
m
ated
to
tal
co
s
t
(
(
)
=
(
)
+
ℎ
(
)
)
,
ex
p
an
d
in
g
its
n
eig
h
b
o
r
s
an
d
u
p
d
ati
n
g
c
o
s
ts
if
a
b
etter
p
at
h
is
f
o
u
n
d
.
T
h
e
al
g
o
r
ith
m
ter
m
in
a
tes
wh
en
th
e
g
o
al
is
r
ea
ch
ed
,
r
ec
o
n
s
tr
u
ctin
g
t
h
e
p
ath
v
ia
p
ar
en
t
p
o
in
ter
s
,
o
r
wh
en
th
e
OPEN
lis
t
is
em
p
ty
,
in
d
icatin
g
n
o
s
o
lu
tio
n
.
T
h
e
p
er
f
o
r
m
an
ce
r
elies
h
ea
v
ily
o
n
an
ad
m
is
s
ib
le
an
d
co
n
s
is
ten
t h
eu
r
is
tic
f
u
n
ctio
n
,
e
n
s
u
r
in
g
o
p
tim
ality
an
d
co
m
p
le
ten
ess
.
3
.
2
.
E
nerg
y
-
o
ptim
ized
A*
a
l
g
o
rit
hm
f
o
r
AUV
pa
t
h pla
nn
ing
T
h
e
co
r
e
ch
allen
g
e
o
f
p
ath
p
lan
n
in
g
f
o
r
AUVs
in
d
y
n
am
i
c
en
v
ir
o
n
m
en
ts
e
x
ten
d
s
b
ey
o
n
d
m
e
r
ely
f
in
d
in
g
a
c
o
llis
io
n
-
f
r
ee
g
eo
m
e
tr
ic
p
ath
.
T
h
e
p
r
im
ar
y
o
b
jectiv
e
is
to
c
o
m
p
u
te
a
t
r
ajec
to
r
y
t
h
at
is
b
o
th
f
ea
s
ib
le
an
d
en
er
g
y
-
o
p
tim
al,
ac
co
u
n
tin
g
f
o
r
th
e
c
o
m
p
lex
in
ter
p
l
ay
b
etwe
en
th
e
v
eh
icle'
s
k
in
em
atics
an
d
th
e
s
u
r
r
o
u
n
d
in
g
h
y
d
r
o
d
y
n
am
ic
f
o
r
ce
s
ex
er
ted
b
y
o
ce
a
n
cu
r
r
e
n
ts
.
T
r
ad
itio
n
al
s
h
o
r
test
-
p
ath
p
la
n
n
er
s
f
ail
to
ad
d
r
ess
th
is
o
b
jectiv
e,
as
th
ey
d
o
n
o
t
co
n
s
id
er
th
e
s
ig
n
if
ican
t
en
er
g
y
co
s
t
o
f
m
o
v
in
g
ag
ain
s
t
o
r
a
cr
o
s
s
s
tr
o
n
g
f
lo
ws.
T
o
ad
d
r
ess
th
is
lim
itatio
n
,
we
f
o
r
m
u
late
th
e
AUV
p
ath
p
lan
n
in
g
p
r
o
b
lem
as
a
co
n
s
tr
ain
ed
o
p
tim
izatio
n
o
v
er
th
e
s
p
ac
e
o
f
f
ea
s
ib
le
tr
ajec
to
r
ies.
T
h
e
o
b
jectiv
e
is
to
m
in
im
ize
th
e
to
tal
p
r
o
p
u
ls
iv
e
en
er
g
y
co
n
s
u
m
p
tio
n
,
d
er
iv
ed
f
r
o
m
a
d
etailed
v
eh
icl
e
d
y
n
am
ics
an
d
en
er
g
y
m
o
d
el
,
wh
ile
ad
h
er
in
g
to
c
o
n
s
tr
ain
ts
in
clu
d
in
g
o
b
s
tacle
av
o
id
an
ce
,
v
eh
icle
k
i
n
em
atic
co
n
s
tr
ain
ts
,
an
d
th
e
d
y
n
a
m
ic
f
lo
w
f
ield
.
Ou
r
ap
p
r
o
ac
h
b
u
ild
s
u
p
o
n
th
e
class
ic
A
*
alg
o
r
ith
m
d
u
e
to
its
o
p
tim
ality
an
d
c
o
m
p
leten
ess
g
u
ar
an
tees.
T
h
e
k
ey
in
n
o
v
ati
o
n
lies
in
th
e
n
o
v
el
in
teg
r
atio
n
o
f
a
p
h
y
s
ics
-
b
ased
en
er
g
y
co
n
s
u
m
p
tio
n
m
o
d
el
d
ir
ec
tly
in
to
th
e
al
g
o
r
ith
m
'
s
co
r
e
co
s
t
f
u
n
ctio
n
.
T
h
is
tr
an
s
f
o
r
m
s
th
e
s
ea
r
ch
o
b
jectiv
e
f
r
o
m
m
i
n
im
izin
g
g
eo
m
etr
ic
d
is
tan
ce
to
m
in
im
i
zin
g
p
r
e
d
icted
en
e
r
g
y
ex
p
e
n
d
i
tu
r
e.
T
h
e
h
ig
h
-
lev
el
ar
c
h
itectu
r
e
o
f
o
u
r
p
r
o
p
o
s
ed
m
eth
o
d
is
illu
s
tr
ated
in
Fig
u
r
e
2
,
wh
ich
o
u
tlin
es th
e
m
ain
d
a
ta
f
lo
w
an
d
c
o
m
p
u
tatio
n
al
m
o
d
u
les.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
ar
ch
it
ec
tu
r
e
f
o
r
e
n
er
g
y
-
o
p
tim
ized
p
ath
p
lan
n
in
g
c
o
m
p
r
is
es
t
h
r
ee
m
ain
co
m
p
o
n
en
ts
:
in
p
u
t,
p
r
o
ce
s
s
in
g
,
an
d
o
u
tp
u
t.
T
h
e
in
p
u
t
m
o
d
u
le
in
teg
r
ates
th
e
s
tar
t/g
o
al
p
o
s
itio
n
s
,
o
b
s
tacle
m
ap
,
f
lo
w
f
ield
d
ata,
an
d
AUV
m
o
d
el
p
ar
am
ete
r
s
in
clu
d
in
g
d
y
n
a
m
ics
an
d
d
r
a
g
co
ef
f
icien
ts
.
C
en
tr
al
to
th
e
p
r
o
ce
s
s
in
g
m
o
d
u
le
is
th
e
en
er
g
y
-
o
p
tim
ized
A*
alg
o
r
it
h
m
,
wh
ich
i
n
co
r
p
o
r
ates
a
s
p
ec
ialized
en
er
g
y
co
n
s
u
m
p
tio
n
m
o
d
el
an
d
co
s
t
f
u
n
ctio
n
(
)
=
(
)
+
ℎ
(
)
to
ev
alu
ate
p
ath
s
b
ased
o
n
en
er
g
y
ex
p
en
d
itu
r
e
r
ath
er
th
a
n
m
er
e
d
is
tan
ce
.
T
h
e
o
u
tp
u
t
g
en
er
ates
an
en
er
g
y
-
o
p
tim
al
p
at
h
alo
n
g
s
id
e
its
to
tal
en
er
g
y
co
n
s
u
m
p
tio
n
esti
m
ate,
co
m
p
l
etin
g
an
in
teg
r
ated
p
lan
n
i
n
g
f
r
am
ewo
r
k
th
at
ex
p
licitly
co
n
s
id
er
s
h
y
d
r
o
d
y
n
am
ic
in
f
lu
en
ce
s
o
n
AUV
n
av
ig
atio
n
ef
f
icien
cy
.
W
e
f
o
r
m
u
late
th
e
AUV
p
ath
p
lan
n
in
g
p
r
o
b
lem
as
a
co
n
s
tr
ain
ed
o
p
tim
izatio
n
o
v
er
th
e
s
p
ac
e
o
f
f
ea
s
ib
le
tr
ajec
to
r
ies,
with
th
e
o
b
jectiv
e
o
f
m
in
im
izin
g
to
ta
l
en
er
g
y
c
o
n
s
u
m
p
tio
n
wh
ile
r
esp
ec
tin
g
d
y
n
a
m
ic
an
d
en
v
ir
o
n
m
en
tal
c
o
n
s
tr
ain
ts
.
I
n
p
lan
n
in
g
al
g
o
r
ith
m
s
lik
e
A*
,
ea
ch
n
o
d
e
in
th
e
s
ea
r
c
h
s
p
ac
e
is
p
r
ec
is
ely
a
p
o
in
t
in
t
h
e
AUV'
s
s
tate
s
p
ac
e.
Def
in
in
g
th
is
s
tate
s
p
ac
e
is
th
e
f
ir
s
t
s
tep
in
m
o
d
elin
g
th
e
p
r
o
b
lem
.
L
et
th
e
AUV
s
tate
at
tim
e
s
tep
i
b
e
d
ef
in
ed
as:
=
(
,
,
)
.
W
h
er
e
∈
3
is
p
o
s
itio
n
(
x,
y,
d
ep
t
h
)
;
∈
3
is
v
elo
city
v
ec
to
r
;
is
tim
e
s
tam
p
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
en
erg
y
-
o
p
timiz
ed
A
*
a
lg
o
r
ith
m
fo
r
p
a
th
p
la
n
n
in
g
o
f
…
(
Do
K
h
a
c
Tiep
)
757
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
th
e
en
er
g
y
-
o
p
tim
al
p
ath
p
lan
n
in
g
s
y
s
tem
f
o
r
an
AUV
T
h
e
to
tal
en
er
g
y
(
)
f
o
r
a
p
at
h
=
(
0
,
.
.
.
,
)
co
m
b
in
es
en
er
g
y
co
s
ts
ac
r
o
s
s
all
s
eg
m
en
ts
(
→
+
1
)
,
as (
1
2
)
:
(
)
=
∑
[
1
2
.
.
‖
,
−
,
‖
3
.
‖
,
‖
+
|
ℎ
|
]
−
1
=
0
(
1
2
)
w
h
e
r
e
ρ
i
s
w
a
t
e
r
d
e
n
s
i
t
y
(
k
g
/
m
³
)
;
i
s
d
r
a
g
c
o
e
f
f
i
c
i
e
n
t
;
,
i
s
g
r
o
u
n
d
v
e
l
o
c
i
t
y
v
e
c
t
o
r
o
f
t
h
e
A
U
V
i
n
s
e
g
m
e
n
t
j
(
m
/
s
)
;
,
i
s
o
c
e
a
n
c
u
r
r
e
n
t
v
e
l
o
c
i
ty
v
e
c
t
o
r
i
n
s
e
g
m
e
n
t
j
(
m
/
s
)
;
is
l
e
n
g
t
h
o
f
s
e
g
m
e
n
t
j
(
m
)
;
m
is
m
a
s
s
o
f
t
h
e
A
U
V
(
k
g
)
;
g
i
s
g
r
a
v
i
t
a
t
i
o
n
al
a
c
c
e
l
e
r
a
ti
o
n
(
9
.
8
1
m
/
s
²
)
;
ℎ
i
s
d
e
p
t
h
c
h
a
n
g
e
i
n
s
e
g
m
e
n
t
,
ℎ
=
ℎ
(
+
1
)
−
ℎ
(
)
;
η
i
s
t
h
r
u
s
t
e
r
e
f
f
i
c
i
e
n
c
y
(
0
<
η
≤
1
).
T
h
e
en
e
r
g
y
co
n
s
u
m
ed
b
y
th
e
p
r
o
p
u
ls
io
n
s
y
s
tem
(
p
r
o
p
u
ls
io
n
en
er
g
y
)
is
m
o
d
eled
b
ased
o
n
th
e
o
b
s
er
v
atio
n
th
at
th
e
p
r
o
p
u
ls
i
o
n
p
o
wer
is
ap
p
r
o
x
im
ately
p
r
o
p
o
r
tio
n
al
to
th
e
cu
b
e
o
f
th
e
r
elativ
e
s
p
ee
d
(
th
e
AUV
'
s
s
p
ee
d
r
elativ
e
to
th
e
wate
r
)
,
as d
escr
ib
ed
b
y
(
1
3
)
.
,
=
1
‖
‖
3
(
1
3
)
T
h
e
h
y
d
r
o
d
y
n
am
ic
d
r
ag
f
o
r
ce
(
d
r
ag
lo
s
s
)
ac
tin
g
o
n
th
e
v
eh
i
cle
is
m
o
d
eled
as
b
ein
g
q
u
ad
r
atica
lly
d
ep
en
d
en
t
o
n
its
r
elativ
e
v
elo
city
in
th
e
wate
r
,
as d
escr
ib
ed
in
(
1
4
)
.
,
=
2
‖
−
u
rr
(
)
‖
2
(
1
4
)
T
o
en
s
u
r
e
th
e
tr
ajec
to
r
y
e
n
d
s
p
r
o
p
er
l
y
at
th
e
d
esire
d
d
esti
n
atio
n
,
a
ter
m
i
n
al
co
s
t,
o
r
'
g
o
al
p
en
alty
,
'
is
in
clu
d
ed
in
th
e
co
s
t f
u
n
ctio
n
as sh
o
wn
i
n
(
1
5
)
.
(
)
=
{
0
=
∞
ℎ
(
1
5
)
T
h
e
t
o
t
al
e
n
e
r
g
y
c
o
n
s
u
m
ed
b
y
t
h
e
v
e
h
ic
le
d
u
r
i
n
g
t
h
e
t
r
a
ject
o
r
y
is
c
alc
u
l
ate
d
b
y
a
g
g
r
eg
ati
n
g
t
h
e
e
n
er
g
y
co
m
p
o
n
e
n
ts
d
is
c
u
s
s
ed
e
ar
lie
r
,
in
c
lu
d
i
n
g
p
r
o
p
u
ls
io
n
e
n
e
r
g
y
a
n
d
o
t
h
e
r
e
n
e
r
g
y
c
h
a
n
g
es
,
as
s
h
o
w
n
in
(
1
6
)
.
(
)
=
∑
(
ro
p
,i
+
−
1
=
0
dr
,i
)
+
(
)
(
1
6
)
T
h
e
o
p
tim
izatio
n
p
r
o
b
lem
ai
m
s
to
f
i
n
d
t
h
e
o
p
tim
al
tr
ajec
t
o
r
y
π*
t
h
at
m
in
im
izes
t
o
tal
e
n
er
g
y
co
n
s
u
m
p
tio
n
s
u
b
ject
to
all
g
iv
en
c
o
n
s
tr
ain
ts
.
T
h
is
o
p
tim
al
tr
ajec
to
r
y
is
p
r
e
s
en
ted
in
(
1
7
)
.
∗
=
(
)
(
1
7
)
Fo
r
th
e
A*
s
ea
r
ch
im
p
lem
en
t
atio
n
,
th
e
AUV'
s
wo
r
k
s
p
ac
e
is
m
o
d
eled
as
a
g
r
ap
h
wh
er
e
n
o
d
es
ar
e
d
is
cr
ete
s
tates
s
ᵢ
an
d
ed
g
es
ar
e
tr
an
s
itio
n
s
b
etwe
en
ad
jace
n
t
s
tates.
T
h
e
co
s
t
a
s
s
o
ciat
ed
with
ea
ch
ed
g
e
tr
an
s
itio
n
is
ca
lcu
lated
b
ased
o
n
th
e
en
er
g
y
e
x
p
en
d
itu
r
e
f
o
r
th
at
s
eg
m
en
t,
in
clu
d
in
g
p
r
o
p
u
ls
io
n
en
er
g
y
an
d
d
r
ag
lo
s
s
es
,
.
T
h
is
v
alu
e
r
ep
r
e
s
en
ts
th
e
in
cr
em
en
tal
p
ath
co
s
t
(
)
=
(
0
→
)
ac
cu
m
u
lated
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
5
3
-
765
758
th
e
alg
o
r
ith
m
.
T
h
e
o
v
er
all
A*
co
s
t
f
u
n
ctio
n
th
en
co
m
b
in
es
t
h
is
p
ath
c
o
s
t
with
a
h
eu
r
is
tic
to
ef
f
icien
tly
g
u
id
e
th
e
s
ea
r
ch
to
war
d
s
th
e
g
o
al.
T
h
e
h
e
u
r
is
tic
f
u
n
ctio
n
h
(
n
)
,
p
r
esen
ted
in
(
1
8
)
,
is
u
s
ed
t
o
es
tim
ate
th
e
o
p
tim
al
co
s
t
f
r
o
m
t
h
e
cu
r
r
en
t
s
tate
to
th
e
g
o
al,
th
e
r
eb
y
ac
ce
ler
atin
g
th
e
s
ea
r
ch
p
r
o
ce
s
s
.
ℎ
(
)
=
1
3
+
2
−
2
.
‖
−
‖
(
1
8
)
I
n
o
r
d
er
to
m
a
k
e
a
tr
an
s
itio
n
,
th
e
r
e
q
u
ir
e
d
r
elativ
e
v
elo
cit
y
m
u
s
t
s
atis
f
y
≤
,
wh
er
e
r
ep
r
esen
ts
th
e
m
ax
im
u
m
s
p
ee
d
o
f
th
e
AUV.
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
4
.
1
.
Sim
ula
t
i
o
n
s
et
up
T
h
e
s
im
u
latio
n
is
co
n
d
u
cted
i
n
an
AUV
wo
r
k
in
g
en
v
ir
o
n
m
en
t
wh
ich
is
a
2
D
g
r
id
m
ap
s
ized
5
0
×
50
ce
lls
,
r
ep
r
esen
tin
g
an
u
n
d
e
r
w
ater
o
p
er
atio
n
al
ar
ea
with
r
es
o
lu
tio
n
co
r
r
esp
o
n
d
in
g
t
o
th
e
g
r
id
ce
ll
s
ize,
an
d
co
n
tain
in
g
s
tatic
o
b
s
tacle
s
at
s
p
ec
if
ic
co
o
r
d
in
ates
an
d
a
n
o
n
-
u
n
if
o
r
m
o
ce
a
n
cu
r
r
en
t
f
ield
m
o
d
eled
as
a
co
m
p
lex
v
o
r
tex
f
lo
w.
T
h
e
s
im
u
latio
n
p
ar
am
ete
r
s
ar
e
lis
ted
in
T
ab
le
1.
Tab
le 1
.
S
imu
lati
o
n
p
a
ra
m
e
ters
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
U
n
i
t
M
a
ss
o
f
A
U
V
m
1
0
0
kg
Le
n
g
t
h
o
f
A
U
V
L
1
.
5
m
D
i
a
me
t
e
r
o
f
A
U
V
D
0
.
3
m
AUV
sp
e
e
d
v
2
m
/
s
W
a
t
e
r
d
e
n
s
i
t
y
ρ
1
0
2
5
k
g
/
m
3
D
r
a
g
c
o
e
f
f
i
c
i
e
n
t
Cd
0
.
1
5
Th
r
u
s
t
e
r
e
f
f
i
c
i
e
n
c
y
η
0
.
5
4
.
2
.
Resul
t
s
Scen
ar
io
1
:
Simu
latin
g
th
e
s
ce
n
ar
io
with
n
o
o
b
s
tacle
s
an
d
n
o
cu
r
r
en
t.
Fig
u
r
e
3
illu
s
tr
ates
th
e
r
esu
lts
o
f
th
e
A*
p
ath
f
in
d
in
g
alg
o
r
ith
m
in
a
s
im
p
lifie
d
s
ce
n
ar
i
o
,
with
o
u
t
o
b
s
tacle
s
o
r
f
lo
w.
T
h
e
id
en
tif
ied
o
p
tim
al
p
ath
(
b
lu
e
lin
e)
r
e
p
r
esen
ts
th
e
s
h
o
r
test
r
o
u
te
b
et
wee
n
th
e
s
tar
t
an
d
g
o
al
p
o
in
ts
,
m
a
r
k
ed
b
y
g
r
ee
n
an
d
r
ed
n
o
d
es,
r
esp
ec
tiv
ely
.
T
h
e
o
b
tain
ed
p
ar
am
eter
s
,
i
n
clu
d
in
g
a
p
ath
le
n
g
th
o
f
5
6
.
5
7
m
eter
s
a
n
d
a
to
tal
e
n
er
g
y
co
n
s
u
m
p
tio
n
o
f
2
2
6
2
.
7
4
J
o
u
les,
d
em
o
n
s
tr
ate
th
e
alg
o
r
it
h
m
'
s
ef
f
icien
cy
in
m
in
im
izin
g
b
o
th
d
is
tan
ce
an
d
en
er
g
y
co
s
ts
.
T
h
e
r
esu
lts
s
h
o
wca
s
e
th
e
ca
p
ab
ilit
y
o
f
th
e
A*
alg
o
r
ith
m
in
d
eter
m
in
in
g
e
f
f
ec
tiv
e
r
o
u
tes i
n
an
u
n
o
b
s
tr
u
cte
d
en
v
ir
o
n
m
e
n
t.
Fig
u
r
e
3
.
Simu
latin
g
th
e
s
ce
n
a
r
io
with
n
o
o
b
s
tacle
s
an
d
ze
r
o
f
lo
w
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
en
erg
y
-
o
p
timiz
ed
A
*
a
lg
o
r
ith
m
fo
r
p
a
th
p
la
n
n
in
g
o
f
…
(
Do
K
h
a
c
Tiep
)
759
Scen
ar
io
2
:
Simu
latin
g
th
e
s
ce
n
ar
io
with
o
b
s
tacle
s
an
d
n
o
c
u
r
r
en
t
.
Fig
u
r
e
4
p
r
esen
ts
th
e
r
esu
lts
o
f
ap
p
ly
in
g
th
e
A*
p
ath
f
in
d
in
g
alg
o
r
ith
m
in
a
m
o
r
e
co
m
p
lex
s
ce
n
ar
io
,
with
th
e
p
r
esen
ce
o
f
o
b
s
tacle
s
.
T
h
e
o
p
tim
ized
p
ath
,
d
e
p
icted
b
y
th
e
b
l
u
e
lin
e,
is
s
u
cc
ess
f
u
lly
d
eter
m
in
ed
t
o
co
n
n
ec
t
t
h
e
s
tar
t
p
o
in
t
(
g
r
ee
n
n
o
d
e)
an
d
th
e
g
o
al
p
o
i
n
t
(
r
e
d
n
o
d
e)
with
o
u
t
co
llid
in
g
wit
h
th
e
o
b
s
tacle
s
(
r
e
d
o
b
jects).
T
h
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r
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clu
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n
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m
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.
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4
J
o
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o
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ate
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o
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ith
m
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to
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ef
f
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e
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o
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tio
n
s
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a
m
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in
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icate
en
v
ir
o
n
m
e
n
t c
o
m
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ar
e
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to
th
e
o
b
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r
ee
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s
e.
T
h
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ath
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eter
m
in
atio
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s
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o
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o
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p
ath
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n
in
g
with
in
ch
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g
in
g
e
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ir
o
n
m
en
ts
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Fig
u
r
e
4
.
Simu
latin
g
th
e
s
ce
n
a
r
io
with
o
b
s
tacle
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an
d
n
o
cu
r
r
en
t
Scen
ar
io
3
:
Simu
latin
g
th
e
s
ce
n
ar
io
c
o
m
p
lex
o
b
s
tacle
s
p
r
esen
t a
n
d
n
o
cu
r
r
en
t
.
Fig
u
r
e
5
d
em
o
n
s
tr
ates
th
e
A*
alg
o
r
ith
m
'
s
p
ath
f
in
d
in
g
with
in
a
ch
allen
g
i
n
g
s
ce
n
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io
in
v
o
lv
in
g
a
s
u
b
s
tan
tial
r
ec
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g
u
lar
o
b
s
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T
h
e
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g
o
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ith
m
y
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s
an
o
p
tim
ized
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ajec
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y
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,
lin
k
in
g
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e
o
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ig
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n
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d
esti
n
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n
p
o
i
n
ts
with
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u
t
en
co
u
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ter
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g
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e
o
b
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Ke
y
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o
r
m
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n
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icato
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s
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e
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ically
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ce
o
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7
4
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7
3
m
eter
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er
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y
ex
p
en
d
itu
r
e
o
f
2
9
8
9
.
1
2
J
o
u
les,
q
u
an
tify
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e
alg
o
r
ith
m
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er
f
o
r
m
an
ce
u
n
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er
th
ese
co
n
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itio
n
s
.
Fig
u
r
e
5
.
Simu
latin
g
th
e
s
ce
n
a
r
io
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co
m
p
le
x
o
b
s
tacle
s
an
d
n
o
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u
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Scen
ar
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4
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r
r
en
t p
r
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t (
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ak
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lo
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o
o
b
s
tacle
s
.
Fig
u
r
e
6
illu
s
tr
ates
th
e
p
at
h
f
in
d
in
g
r
esu
lts
o
f
th
e
A*
alg
o
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it
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m
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e
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ir
o
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en
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ch
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ized
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y
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d
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m
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ar
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g
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o
th
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o
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ash
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lin
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u
p
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e)
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ath
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h
ile
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o
th
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ath
s
ex
h
ib
it
an
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u
al
len
g
th
o
f
5
6
.
1
5
m
eter
s
,
th
e
en
er
g
y
co
s
ts
v
ar
y
,
h
ig
h
lig
h
tin
g
th
e
im
p
ac
t
o
f
f
lo
w
o
n
n
av
ig
atio
n
.
T
h
is
d
if
f
e
r
en
ce
in
e
n
er
g
y
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n
s
u
m
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n
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7
0
1
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0
7
J
f
o
r
d
o
wn
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tr
ea
m
a
n
d
2
6
3
5
.
1
7
J
f
o
r
u
p
s
tr
ea
m
)
em
p
h
asizes
th
e
s
ig
n
if
ican
ce
o
f
co
n
s
id
er
in
g
f
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w
d
y
n
a
m
ics
wh
en
p
lan
n
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g
r
o
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tes
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ea
l
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wo
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en
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ir
o
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en
ts
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ly
wh
er
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e
n
er
g
y
o
p
tim
iza
tio
n
is
a
p
r
im
ar
y
co
n
ce
r
n
.
Fig
u
r
e
6
.
Simu
latin
g
th
e
s
ce
n
a
r
io
with
c
u
r
r
e
n
t p
r
esen
t
(
wea
k
f
lo
w)
,
n
o
o
b
s
tacle
s
Scen
ar
io
5
:
Simu
latin
g
th
e
s
ce
n
ar
io
with
c
u
r
r
en
t p
r
esen
t (
s
tr
o
n
g
f
l
o
w)
,
n
o
o
b
s
tacle
s
.
Fig
u
r
e
7
illu
s
tr
ates
th
e
p
ath
f
in
d
in
g
r
esu
lts
o
f
th
e
A*
alg
o
r
ith
m
in
an
en
v
ir
o
n
m
en
t
with
a
s
tr
o
n
g
f
lo
w
b
u
t
with
o
u
t
o
b
s
tacle
s
.
T
h
e
c
o
m
p
ar
is
o
n
b
etwe
en
th
e
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ea
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ath
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e
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ash
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lin
e)
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d
t
h
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u
p
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m
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ath
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e
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n
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n
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d
if
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e
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ce
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e
n
er
g
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s
t
s
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7
2
7
3
.
8
4
J
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er
s
u
s
5
7
6
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0
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J
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d
esp
ite
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e
p
ath
len
g
th
s
b
ein
g
n
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r
l
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en
tical
(
5
6
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1
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er
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s
5
6
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1
1
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.
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h
is
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h
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e
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b
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im
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t
o
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s
tr
o
n
g
f
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n
tr
a
v
el
co
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ts
.
Fig
u
r
e
7
.
Simu
latin
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th
e
s
ce
n
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r
io
with
c
u
r
r
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t p
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t
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s
tacle
s
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&
C
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A
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761
Scen
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6
:
Simu
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e
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ce
n
ar
io
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o
b
s
tacle
s
p
r
esen
t,
cu
r
r
en
t
p
r
esen
t (
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k
f
lo
w)
.
Fig
u
r
e
8
illu
s
tr
ates
th
e
A*
p
ath
f
in
d
in
g
alg
o
r
ith
m
in
a
n
en
v
ir
o
n
m
en
t
with
o
b
s
tacle
s
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d
a
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k
f
lo
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m
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ar
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g
th
e
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o
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tr
ea
m
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ath
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ash
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d
t
h
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u
p
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ath
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ath
s
h
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g
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g
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5
6
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4
m
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e
e
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er
g
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o
n
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u
m
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if
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er
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ig
n
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ican
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5
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J
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o
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ea
m
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d
3
9
9
7
.
6
6
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u
p
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m
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,
r
e
f
lectin
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th
e
im
p
ac
t
o
f
f
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n
d
o
b
s
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s
o
n
tr
av
el
en
er
g
y
e
f
f
icien
c
y
.
Fig
u
r
e
8
.
Simu
latin
g
th
e
s
ce
n
a
r
io
with
o
b
s
tacle
s
p
r
esen
t,
cu
r
r
en
t p
r
esen
t (
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k
f
lo
w)
Scen
ar
io
7
:
Simu
latin
g
th
e
s
ce
n
ar
io
with
o
b
s
tacle
s
p
r
esen
t,
cu
r
r
en
t
p
r
esen
t (
s
tr
o
n
g
f
lo
w)
.
Fig
u
r
e
9
illu
s
tr
ates
th
e
r
esu
lts
o
f
th
e
A*
p
ath
f
in
d
i
n
g
alg
o
r
ith
m
in
an
en
v
ir
o
n
m
e
n
t
with
o
b
s
tacle
s
an
d
a
s
tr
o
n
g
f
lo
w.
No
tab
l
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er
e
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s
ig
n
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ican
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d
if
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e
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ce
in
e
n
er
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ts
b
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en
th
e
d
o
w
n
s
tr
ea
m
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ath
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at
4
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1
7
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9
9
J
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d
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ath
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at
8
2
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6
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3
9
J
,
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e
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ath
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th
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r
ly
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7
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e
r
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s
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.
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h
is
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ig
h
lig
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ts
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e
s
u
b
s
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ts
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tr
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t twic
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ten
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v
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as d
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wn
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tr
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m
tr
a
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el.
Fig
u
r
e
9
.
Simu
latin
g
th
e
s
ce
n
a
r
io
with
o
b
s
tacle
s
p
r
esen
t,
cu
r
r
en
t p
r
esen
t (
s
tr
o
n
g
f
l
o
w)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
7
0
8
I
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t J E
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&
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m
p
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n
g
,
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l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
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5
3
-
765
762
Scen
ar
io
8
:
Simu
latin
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t
h
e
s
ce
n
ar
io
with
n
o
p
o
s
s
ib
le
p
at
h
e
x
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ts
(
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o
al
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u
r
r
o
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n
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e
d
b
y
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b
s
tacle
s
)
.
T
h
is
is
a
test
ca
s
e
f
o
r
alg
o
r
ith
m
co
r
r
ec
tn
ess
/r
o
b
u
s
tn
ess
.
Fig
u
r
e
1
0
d
ep
icts
a
s
p
ec
ial
ca
s
e
o
f
th
e
A*
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o
r
ith
m
wh
er
e
n
o
f
ea
s
ib
le
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ath
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ts
b
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e
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e
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t
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ts
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u
e
to
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m
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te
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e
b
y
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b
s
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.
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h
is
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in
d
icate
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y
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e
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ath
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g
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g
0
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0
0
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eter
s
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d
th
e
en
er
g
y
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n
s
u
m
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tio
n
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ein
g
in
f
in
ity
(
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n
f
J
)
,
d
em
o
n
s
tr
atin
g
th
at
th
e
alg
o
r
ith
m
h
as
d
eter
m
in
ed
n
o
p
o
s
s
ib
le
r
o
u
te.
Fig
u
r
e
1
0
.
Simu
latin
g
th
e
s
ce
n
ar
io
with
n
o
p
o
s
s
ib
le
p
ath
ex
is
ts
4
.
3
.
Dis
cus
s
io
n
T
h
e
s
im
u
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
th
e
u
n
eq
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iv
o
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l
s
u
p
er
io
r
ity
o
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e
e
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g
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o
p
tim
ized
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o
r
ith
m
o
v
er
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e
s
tan
d
ar
d
g
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m
etr
ic
A*
f
o
r
m
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im
izin
g
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er
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n
s
u
m
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tio
n
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y
n
a
m
ic
f
lo
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ield
s
.
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h
e
m
o
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t
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ig
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ican
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f
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d
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th
e
s
u
b
s
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er
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y
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ctio
n
o
f
u
p
to
5
0
%
in
s
ce
n
ar
io
s
with
s
tr
o
n
g
cu
r
r
en
ts
(
Scen
ar
io
7
)
.
T
h
is
im
p
r
o
v
em
en
t
d
ir
ec
tly
v
alid
ates
o
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r
c
o
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n
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ti
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e
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atio
n
o
f
a
p
h
y
s
ics
-
b
ased
en
er
g
y
m
o
d
el
in
t
o
th
e
p
at
h
co
s
t c
alcu
latio
n
.
A
co
m
p
r
e
h
en
s
iv
e
co
m
p
ar
is
o
n
b
etwe
en
t
h
e
p
r
o
p
o
s
ed
en
e
r
g
y
-
o
p
tim
ized
A
a
n
d
t
h
e
s
tan
d
ar
d
A*
alg
o
r
ith
m
,
b
ased
o
n
k
ey
p
er
f
o
r
m
an
ce
in
d
icato
r
s
,
is
s
u
m
m
ar
ized
in
T
ab
le
2
.
T
h
e
r
esu
lts
h
ig
h
lig
h
t
a
cr
itical
p
er
f
o
r
m
an
ce
tr
ad
e
-
o
f
f
:
o
u
r
alg
o
r
ith
m
e
x
p
licitly
s
ac
r
if
ices
p
ath
len
g
th
o
p
tim
ality
to
ac
h
iev
e
a
p
ar
a
m
o
u
n
t
r
ed
u
ctio
n
i
n
en
er
g
y
co
n
s
u
m
p
tio
n
.
Fu
r
th
er
m
o
r
e,
a
c
o
m
p
u
tatio
n
al
tr
ad
e
-
o
f
f
is
o
b
s
er
v
e
d
.
W
h
ile
th
e
p
er
-
n
o
d
e
co
m
p
u
tatio
n
co
s
t
is
h
ig
h
e
r
d
u
e
to
t
h
e
s
o
p
h
is
ticated
en
er
g
y
m
o
d
el,
th
e
o
v
er
all
co
m
p
u
tatio
n
al
ef
f
icien
c
y
o
f
th
e
A*
f
r
am
ewo
r
k
is
m
ain
tain
ed
,
m
ak
in
g
o
u
r
m
et
h
o
d
f
ea
s
ib
le
f
o
r
o
n
lin
e
p
ath
p
lan
n
in
g
.
T
h
is
q
u
an
titativ
e
an
aly
s
is
u
n
d
er
s
co
r
es
th
at
o
u
r
m
eth
o
d
ac
h
i
ev
es
its
p
r
im
ar
y
g
o
al
o
f
m
ass
iv
e
en
e
r
g
y
s
av
in
g
s
wh
ile
m
ain
tain
in
g
th
e
co
m
p
u
tatio
n
al
p
r
ac
ticality
n
ec
ess
ar
y
f
o
r
d
e
p
lo
y
m
e
n
t
o
n
co
n
s
tr
ain
ed
AUV
p
latf
o
r
m
s
.
Ou
r
a
p
p
r
o
ac
h
o
cc
u
p
ies
a
cr
u
cial
n
ich
e
b
etwe
e
n
co
m
p
u
tatio
n
al
co
m
p
lex
ity
an
d
m
o
d
el
f
id
elity
.
C
o
m
p
ar
ed
to
m
eth
o
d
s
r
ely
in
g
o
n
h
i
g
h
-
f
i
d
elity
C
FD
m
o
d
els
[
1
4
]
o
r
lev
el
s
et
eq
u
atio
n
s
f
o
r
o
p
tim
al
co
n
t
r
o
l
[
6
]
o
u
r
al
g
o
r
ith
m
is
f
ar
less
co
m
p
u
tatio
n
ally
i
n
ten
s
iv
e,
m
ak
in
g
it
s
u
itab
le
f
o
r
o
n
lin
e,
r
ea
ctiv
e
p
ath
p
la
n
n
in
g
o
n
r
eso
u
r
ce
-
co
n
s
tr
ain
ed
AUV
h
ar
d
war
e.
T
h
is
d
ir
ec
tly
ad
d
r
e
s
s
es
th
e
lim
itatio
n
o
f
co
m
p
u
tatio
n
al
tr
ac
tab
ilit
y
r
aised
in
[
1
8
]
,
[
1
9
]
.
C
o
n
v
er
s
ely
,
co
m
p
ar
ed
to
o
th
er
h
eu
r
i
s
tic
o
r
lear
n
in
g
-
b
ased
ap
p
r
o
a
ch
es
lik
e
p
o
te
n
tial
f
ield
s
[
9
]
o
r
r
ein
f
o
r
ce
m
en
t
le
ar
n
in
g
[
1
7
]
,
o
u
r
m
eth
o
d
p
r
o
v
id
es
d
eter
m
in
is
tic
p
er
f
o
r
m
a
n
ce
an
d
g
u
ar
an
teed
o
p
tim
ality
with
in
th
e
d
is
cr
ete
s
ea
r
ch
s
p
ac
e,
a
s
ig
n
if
ican
t a
d
v
an
tag
e
f
o
r
s
af
ety
-
cr
itical
m
is
s
io
n
s
.
T
h
e
p
r
ac
tical
im
p
licatio
n
is
th
at
AUVs
ca
n
ac
h
iev
e
s
ig
n
if
ican
tly
lo
n
g
er
m
is
s
io
n
d
u
r
a
tio
n
s
an
d
o
p
er
atio
n
al
r
an
g
es
in
c
u
r
r
en
t
-
p
r
o
n
e
en
v
ir
o
n
m
en
ts
with
o
u
t
h
ar
d
war
e
m
o
d
if
icatio
n
s
.
T
h
is
en
h
an
ce
s
th
e
f
ea
s
ib
ilit
y
o
f
lo
n
g
-
ter
m
au
to
n
o
m
o
u
s
m
o
n
ito
r
in
g
an
d
in
s
p
ec
tio
n
m
is
s
io
n
s
.
Ou
r
m
eth
o
d
p
r
o
v
id
es
a
r
o
b
u
s
t,
p
r
ac
tical,
an
d
c
o
m
p
u
tatio
n
ally
f
ea
s
ib
le
s
o
lu
tio
n
f
o
r
o
n
lin
e
en
er
g
y
-
o
p
tim
ized
p
at
h
p
lan
n
in
g
.
T
h
is
s
tu
d
y
h
as
lim
itatio
n
s
th
at
p
o
in
t
to
war
d
v
alu
a
b
le
f
u
t
u
r
e
r
esear
c
h
.
First,
o
u
r
m
o
d
el
ass
u
m
es
p
er
f
ec
t
k
n
o
wled
g
e
o
f
th
e
f
lo
w
f
ield
,
wh
ich
is
o
f
ten
u
n
ce
r
tain
in
r
ea
l
o
ce
an
s
.
Fu
tu
r
e
wo
r
k
will
in
teg
r
ate
p
r
o
b
a
b
ilis
tic
cu
r
r
en
t
f
o
r
ec
asts
[
2
4
]
an
d
r
o
b
u
s
t
p
lan
n
i
n
g
tech
n
iq
u
es.
Seco
n
d
,
th
e
k
i
n
em
atic
m
o
d
el
is
s
im
p
lifie
d
;
in
teg
r
atin
g
f
u
ll
6
-
DOF
d
y
n
am
ics
wo
u
ld
in
c
r
ea
s
e
f
id
elity
.
T
h
ir
d
,
th
e
co
m
p
u
t
atio
n
al
co
s
t,
wh
ile
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