Intern
ati
o
n
a
l Jo
urn
a
l
o
f
R
o
botics
a
nd Au
tom
a
tion
(I
JR
A)
Vol.
3, No. 4, Decem
ber
2014, pp. 272~
276
I
S
SN
: 208
9-4
8
5
6
2
72
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRA
Fuzzy Controlled Routing in
a Swarm Robotic Network
N
avy
a Ma
noj
Departem
ent
of
Mechani
cal
Eng
i
neering
,
Nationa
l Institu
te of
Technolog
y
,
Surath
kal, Indi
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 24, 2013
Rev
i
sed
Ju
l 20
,
20
14
Accepted Aug 10, 2014
Swarm
Robotics origina
t
ed
in th
e rese
arch
inspir
ed b
y
bio
l
og
y. I
t
is the
usual
sense of th
e multi-robot s
y
stems wh
ich have been
given
th
e emergin
g
attribu
t
es of swarm
intel
ligen
ce
. In na
ture
, ants
, term
it
es, wasp
s, bees an
d
othe
r soc
i
al insec
t
s ha
ve
inspired su
rprisingly
inspiration of human. These
groups of organisms sho
w
how to inte
r
a
ct with
a larg
e number
of simple
individua
ls and
genera
te th
e co
l
l
ec
tive
inte
llig
en
ce of s
y
s
t
em
s to cope with
complicated tasks. Swarm Rob
o
tics is
a special robot s
y
stem which is
composed of a g
r
oup of indiscriminate r
obots an
d so it is a ty
p
i
cal distributed
s
y
stem. If
a
task
is for only
on
e r
obot
and
the rob
o
t will be v
e
r
y
complex and
expensive in
effi
cien
tl
y. But if it
is
for the swarm
robotics, the com
p
lex task
can be done b
y
man
y
more
simple robots efficiently
.
For the Routing
problem, th
e qu
ality
of
a potential rou
t
e
is de
ter
m
ined b
y
th
e l
e
ngth of th
e
route (i.e. number of links) and the congest
ion along the route. It
is desired to
balan
ce th
e traff
i
c load
am
ong links in the netwo
r
k so
it is desirable to select
routes
with
a lo
w obs
tacl
e ra
te
.
In addi
tion, shorter routes ar
e pr
eferred
over
longer rou
t
es b
e
cause
they
use f
e
wer network
res
ources.
Keyword:
Co
ng
estion
FC-Based Al
gorithm
Fuzzy C
ontrol
R
out
e Le
n
g
t
h
Swarm
Ro
bo
tics
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Navy
a M
a
n
o
j
Dep
a
rtem
en
t o
f
Mech
an
ical En
g
i
n
eeri
n
g,
Natio
n
a
l In
stitu
te
o
f
Techno
log
y
, Surathk
a
l,
India
Em
a
il: lsn
tl@c
c
u
.
ed
u.tw
1.
INTRODUCTION
I
n
an
in
doo
r
sys
t
e
m
w
h
e
r
e
a s
w
ar
m o
f
ro
bo
ts
a
r
e
assigne
d
diffe
re
nt tasks a
n
d are t
o
c
o
mm
unicate
with each
othe
r and divi
de the task am
ong them
se
lves.
T
h
e m
a
in idea in our a
p
proac
h
is to use a routing
alg
o
rith
m
to
se
t u
p
a rou
t
e b
e
t
w
een
t
h
e ev
en
t
an
d
the ro
bo
t th
at wan
t
s to
serv
e it ov
er th
e
n
e
two
r
k
m
a
in
t
a
in
ed
b
e
tween
th
e
rob
o
t
s
u
s
ing
their co
mm
u
n
i
cati
o
n
syste
m
u
s
ing
wh
ich
ro
bo
ts can
calcu
late
relativ
e po
sition
of
each ot
her.
W
e
assum
e
that e
ach eve
n
t is re
prese
n
ted
by
a
robot that
remains static
at the event location and
d
o
e
s all th
e commu
n
i
catio
n
fo
r t
h
e even
t.
Th
is is a realis
tic assu
m
p
tio
n
,
as th
e n
e
ed
t
o
p
e
rform
a task
will b
e
id
en
tified
b
y
on
e o
f
th
e r
obo
ts of
th
e Sw
ar
m
a
n
o
i
d
.
Fo
r t
h
e Rou
ting
prob
lem
,
th
e q
u
a
lity o
f
a
p
o
t
en
tial rou
t
e is d
e
term
in
ed
b
y
th
e len
g
t
h
of the rou
t
e (i.e.
num
ber o
f
l
i
n
k
s
) an
d t
h
e co
n
g
est
i
o
n al
on
g t
h
e ro
ut
e. It
i
s
desi
re
d t
o
bal
a
nce t
h
e t
r
af
fi
c l
o
ad am
ong l
i
nks i
n
th
e n
e
twork
so it is d
e
sirab
l
e
to
select rou
t
es with
a lo
w
o
b
stacle rate. In ad
d
ition
,
sho
r
ter rou
t
es are
preferred
ove
r l
o
n
g
er
r
o
ut
es bec
a
use
t
h
ey
use f
e
we
r
n
e
t
w
o
r
k
res
o
u
r
c
e
s. I
n
ot
he
r
wo
rds
,
t
h
e
p
r
efe
r
r
e
d r
o
ut
e i
s
o
n
e
wi
t
h
a
"s
m
a
ll" ro
u
t
e l
e
n
g
t
h
an
d "ligh
t
" cong
estion
.
Thu
s
, th
e t
w
o fuzzy inp
u
t
variab
les
for the fuzzy con
t
ro
ller are
R
out
e
_
Len
g
t
h
and C
o
n
g
est
i
o
n. The
s
e vari
a
b
l
e
s
m
a
y
be represe
n
t
e
d as c
ont
i
n
u
o
u
s
or di
scret
e
fuzzy
va
ri
abl
e
s
since each input val
u
e is an intege
r. T
h
e
output
variab
le
of the
fuzzy c
o
ntroller is a rat
i
ng
for the
pat
h
. T
h
e
fuzzy out
put
varia
b
le Rating is expres
se
d as a con
tinu
o
u
s
fu
zzy
v
a
riab
le. Bo
t
h
fu
zzy in
pu
t v
a
riab
les,
R
out
e
_
Len
g
t
h
and C
o
n
g
est
i
o
n,
have t
h
ree f
u
zzy
val
u
es
re
sul
t
i
ng i
n
ni
ne
di
ffe
rent
pot
e
n
t
i
a
l
com
b
i
n
at
ions
o
f
in
pu
t v
a
l
u
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJRA Vol. 3, No. 4,
D
ecem
ber 2014:
272 – 276
2
73
2.
PATH NAVIGATION
I
n
an
in
doo
r
sys
t
e
m
w
h
e
r
e
a s
w
ar
m o
f
ro
bo
ts
are
assigne
d
diffe
re
nt tasks a
n
d are t
o
c
o
mm
unicate
with each
othe
r and divi
de the task am
ong them
se
lves.
T
h
e m
a
in idea in our a
p
proac
h
is to use a routing
alg
o
rith
m
to
se
t u
p
a rou
t
e b
e
t
w
een
t
h
e ev
en
t
an
d
the ro
bo
t th
at wan
t
s to
serv
e it ov
er th
e
n
e
two
r
k
m
a
in
t
a
in
ed
b
e
tween
th
e
rob
o
t
s
u
s
ing
their co
mm
u
n
i
cati
o
n
syste
m
u
s
ing
wh
ich
ro
bo
ts can
calcu
late
relativ
e po
sition
of
each ot
her.
W
e
assum
e
that e
ach eve
n
t is re
prese
n
ted
by
a
robot that
remains static
at the event location and
d
o
e
s all th
e commu
n
i
catio
n
fo
r t
h
e even
t.
Th
is is a realis
tic assu
m
p
tio
n
,
as th
e n
e
ed
t
o
p
e
rform
a task
will b
e
id
en
tified
b
y
on
e o
f
th
e r
obo
ts of
th
e Sw
ar
m
a
n
o
i
d
.
Fo
r t
h
e Rou
ting
prob
lem
,
th
e q
u
a
lity o
f
a
p
o
t
en
tial rou
t
e is d
e
term
in
ed
b
y
th
e len
g
t
h
of the rou
t
e (i.e.
num
ber o
f
l
i
n
k
s
) an
d t
h
e co
n
g
est
i
o
n al
on
g t
h
e ro
ut
e. It
i
s
desi
re
d t
o
bal
a
nce t
h
e t
r
af
fi
c l
o
ad am
ong l
i
nks i
n
th
e n
e
twork
so it is d
e
sirab
l
e
to
select rou
t
es with
a lo
w
o
b
stacle rate. In ad
d
ition
,
sho
r
ter rou
t
es are
preferred
ove
r l
o
n
g
er
r
o
ut
es bec
a
use
t
h
ey
use f
e
we
r
n
e
t
w
o
r
k
res
o
u
r
c
e
s. I
n
ot
he
r
wo
rds
,
t
h
e
p
r
efe
r
r
e
d r
o
ut
e i
s
o
n
e
wi
t
h
a
"s
m
a
ll" ro
u
t
e l
e
n
g
t
h
an
d "ligh
t
" cong
estion
.
Thu
s
, th
e t
w
o fuzzy inp
u
t
variab
les
for the fuzzy con
t
ro
ller are
R
out
e
_
Len
g
t
h
and C
o
n
g
est
i
o
n. The
s
e vari
a
b
l
e
s
m
a
y
be represe
n
t
e
d as c
ont
i
n
u
o
u
s
or di
scret
e
fuzzy
va
ri
abl
e
s
since each input val
u
e is an intege
r. T
h
e
output
variab
le
of the
fuzzy c
o
ntroller is a rat
i
ng
for the
pat
h
. T
h
e
fuzzy out
put
varia
b
le Rating is expres
se
d as a con
tinu
o
u
s
fu
zzy
v
a
riab
le. Bo
t
h
fu
zzy in
pu
t v
a
riab
les,
R
out
e
_
Len
g
t
h
and C
o
n
g
est
i
o
n,
have t
h
ree f
u
zzy
val
u
es
re
sul
t
i
ng i
n
ni
ne
di
ffe
rent
pot
e
n
t
i
a
l
com
b
i
n
at
ions
o
f
i
n
p
u
t
val
u
es.
T
h
ere
f
o
r
e,
t
h
i
s
f
u
zzy
co
nt
r
o
l
l
e
r
co
nt
ai
ns
ni
ne
f
u
zzy
i
f-t
hen
r
u
l
e
s sh
ow
n i
n
T
a
bl
e 1
.
Thec
onse
q
uent
of each rule is chose
n
to re
flect
the desired route and
wavele
ngt
h prefere
n
ces.
A
di
ag
ram
of t
h
e
pr
o
pose
d
f
u
zzy
co
nt
r
o
l
l
e
r i
s
s
h
o
w
n i
n
Fi
g
u
r
e
1.
Ta
bl
e1. Fuz
z
yIf
-
t
h
en R
u
l
e
s
I
f
R
o
ut
e L
e
ngt
h i
s
s
m
al
l
an
d Co
ng
e
s
t
i
o
n
i
s
l
e
ss t
h
e Rati
ng i
s
e
x
c
e
l
l
e
n
t
I
f
R
o
ut
e L
e
ng t
h
i
s
s
m
al
l
an
d Co
nge
st
i
o
ni
s
m
e
di
u
m
t
h
e Rati
ngi
s g
o
o
d
I
f
R
o
ut
e L
e
ngt
hi
s sm
al
l
a
nd Con
g
e
s
t
i
o
n
i
s
he
av
y
t
h
e
R
a
t
i
ng i
s
po
o
r
I
f
R
o
ut
e L
e
ng t
h
is
m
e
di
u
m
an
d Co
n
g
e
s
t
i
o
n
i
s
le
s
s
t
h
e Ra
t
i
ng i
s
g
o
o
d
I
f
R
o
ut
e L
e
ng t
h
i
s
m
e
di
u
m
an
d Co
nge
st
i
o
n i
s
m
e
di
u
m
the R
a
t
i
ng i
s
av
er
ag
e
I
f
R
o
ut
e L
e
ng t
h
i
s
m
e
di
u
m
an
d Co
n
g
e
s
t
i
o
n
i
s
he
avy
t
h
e
R
a
ti
ngi
s po
o
r
I
f
R
o
ut
e L
e
ngt
h i
s
l
a
r
g
e an
d Co
nge
st
io
n i
s
l
e
s
s
t
h
e R
a
ti
ng i
s
av
e
r
ag
e
I
f
R
o
ut
e L
e
ng t
h
i
s
l
a
r
g
e an
d Co
nge
s
t
io
n i
s
m
e
di
u
m
t
h
e
R
a
t
i
ng i
s
po
o
r
I
f
R
o
ut
e L
e
ngt
hi
s
lar
g
e
a
nd Con
g
e
s
t
i
o
n
i
s
he
av
y
t
h
e R
a
ti
ng i
s
p
o
o
r
Fi
gu
re 1. Fu
zz
y
C
o
nt
rol
l
e
r
3.
FUZ
Z
Y
CONTROLLED ROUTING AL
GORITHM
Fu
zzy-con
tro
l
l
e
d
ad
ap
tiv
e R
o
u
ting
al
g
o
rithm
is b
a
sedon
a set of fu
zzyif-th
e
n
ru
les that g
u
i
d
e
s the
selection of
a physical
route eacheve
n
t
requestbased on t
h
e curre
nt state
of
the
network. In a
net
w
ork
with
N
no
des
,
L l
i
n
ks,
and
O
o
b
st
acl
es perl
i
n
k
,
eac
h s
o
u
r
ce
no
des
m
a
i
n
t
a
i
n
si
t
s
ow
n
ro
ut
i
n
g t
a
bl
e R
T
S
(s =
1
,
2..
.
N
)
t
h
at
cont
ai
ns a
l
i
s
t
of al
l
pat
h
s
fr
om
t
h
e sourc
e
no
des t
o
al
l
d
e
st
i
n
at
i
on
no
de
sd
≠
s
.
F
o
r la
rge
r
net
w
o
r
k
s
, the
size
of the
routing table can be
reduce
d by limiting the num
ber of alternat
e routes for each destinati
o
n. For
sim
u
l
a
t
i
on p
u
r
pos
e, l
i
m
i
t
e
d the r
out
i
n
g i
s
l
i
m
i
t
e
d t
o
5 ro
ut
esper
(s,
d)
. Ta
bl
e 2 s
h
o
w
s a
n
exam
pl
e of a r
out
i
n
g
t
a
bl
e f
o
r t
h
e si
m
p
l
e
net
w
or
k
sho
w
n i
n
fi
g
u
r
e
2.
The
net
w
o
r
k maint
a
ins a
L
×
O
l
i
n
k
-
Obs
t
acl
e status matri
x
S
wh
e
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Fu
zzy Con
t
ro
ll
ed
Rou
tin
g in
a S
w
a
r
m Ro
bo
tic Netwo
r
k (Navya
Man
o
j
)
27
4
1
,
if R
o
ut
ewi
s
in
useo
n link
l
,
Sl0 =
0,
ot
h
e
r
w
i
s
e
Tabl
e
2. R
out
i
n
g
Ta
bl
e
De
stina
t
io
n
Route
2
(1
,
2
)
(
1
,6
,5
,2
)
(
1
,6
,5
,4
,3
,
2
)
3
(
1
,2
,3
)
(
1
,6
,5
,2
,
3
)
(
1
,6
,5
,
4
,
3
)
(
1
,
2
,5
,4
,
3
)
4
(
1
,2
,3
,4
)
(
1
,6
,5
,4
)
(
1
,2
,5
,4
)
(
1
,6
,5
,2
,3
,
4
)
5
(
1
,6
,5
)
(
1
,2
,5
)
(
1
,2
,3
,4
,
5
)
6
(1
,
6
)
(
1
,2
,3
,4
,5
,
6
)
Fi
gu
re 2.
N
e
t
w
or
k
Th
is ma
trix
is used
by th
e fuzzy c
o
ntr
o
ller t
o
det
e
r
m
ine th
e n
u
mber o
f
a
v
ail
a
ble wa
v
e
l
e
n
g
th
s
o
n
a
ro
ute
.
Th
er
e is tw
o ty
pes o
f
r
e
quest
s used in
t
h
e alg
o
r
ith
m. C
o
n
n
ect
i
o
n r
e
que
sts ar
riv
e
a
t
indiv
i
dual n
o
d
e
s an
d
co
nta
i
n the s
o
u
r
ce n
o
des
,
destinatio
n n
o
de
d,
and h
o
ldin
g tim
e h fo
r the c
o
n
n
ecti
o
n
.
Te
r
m
inati
o
n reque
sts are
set
up by each
no
d
e
o
n
ce a
p
a
th
h
a
s bee
n
e
s
tab
lish
e
d.
Algorithm
:
F
C
- based Routing algorithm
Initialize: RTs=[empty table] for s=1,…, N.
S=L*O zero matrix.
T=[empty table].
While (termination criterion not fulfilled)
Wait for a request to arrive (connection or termination).
If request is a connection request (s, d, h)
Let Rsd be the set of routes in routing table RTs to destination d.
For each route ri
∈
Rsd, i=1,….,| Rsd|
Let Li be the set of links that compose route ri.
Let Routelength*=| Li|.
Let Congestion*=| Oi |.
Invoke fuzzy controller
For each fuzzy rule
Fuzzify Route Length* and Congestion* from the membership function
after fuzzification
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJRA Vol. 3, No. 4,
D
ecem
ber 2014:
272 – 276
2
75
End
For each fuzzy rule
Calculate fuzzy output from Mamdani’s rule
End
Aggregate the fuzzy outputs
Defuzzify to yield a crisp rating
Let Rating; be the output of the fuzzy controller for
routeri
Exit fuzzy controller.
End
Let i* be the index of the route with the highest rating.
If Oi * is full
request is blocked.
Else
Set Li *=L
Route request on route ri*.
Update T by adding termination request (L*,t + h)
End
Else
If request is a termination request (L*,O*)
End
End
End
4.
R
E
SU
LTS AN
D ANA
LY
SIS
The
Per
f
o
r
m
a
nces i
s
eval
ua
t
e
d f
o
r t
h
e
F
C
-base
d
r
out
i
n
g
al
g
o
ri
t
h
m
on
t
h
e
net
w
o
r
k s
h
ow
n i
n
Fi
gu
re 2
.
A t
r
affi
c m
odel
i
n
whi
c
h co
n
n
ec
t
i
on re
q
u
est
s
arri
ve at
eac
h n
ode acc
o
r
di
ng
t
o
a Poi
s
s
o
n p
r
oce
s
s
wi
t
h
net
w
or
k-
wi
de a
rri
val
ra
t
e
λ
is used fo
r sim
u
lat
i
o
n
s
.
An arriv
i
ng
sessio
n
is eq
u
a
ll
y lik
ely to
b
e
d
e
stin
ed
t
o
any
no
de i
n
t
h
e net
w
o
r
k
.
T
h
e sessi
on
h
o
l
d
i
ng t
i
m
e i
s
expone
nt
i
a
l
l
y
di
st
ri
but
ed
wi
t
h
m
ean 1/
μ
. T
h
e l
o
a
d
pe
r
so
urce d
e
stinatio
n
nod
e p
a
ir
is
λ
/
N
(N-
1
) µ
A no
de m
a
y
enga
ge i
n
m
u
lt
i
p
l
e
sessi
ons
and
paral
l
e
l
sessi
ons
may be conducted betwee
n
a source-destination
node.
In each case FC-Based algo
rith
m
is found to be
sup
e
ri
o
r
com
p
ared t
o
Fi
xed
-
SP an
d Al
t
e
r
n
a
t
e R
out
i
ng m
e
tho
d
s. Ta
bl
e 3 s
h
o
w
s t
h
e av
era
g
e bl
oc
ki
n
g
rat
e
ove
r
all network l
o
a
d
s for each al
gorithm
.
It is observe
d th
at a
v
e
r
age Blocki
ng
Rate decrease
d
by usi
ng
FC-Based
al
go
ri
t
h
m
.
The
Tabl
e
3 s
h
ow
t
h
e A
v
e
r
age
bl
ocki
ng
rat
e
of
al
l
3 r
o
ut
i
n
g
m
e
t
h
o
d
s.
Tabl
e 3. A
v
era
g
e
B
l
oc
ki
n
g
R
a
t
e
R
o
ut
i
ng
Meth
o
d
Rou
t
e
A
s
s
ig
n
m
en
t
P
olicy
Ave
r
ag
e Bl
oc
ki
ngR
at
e
L
e
as
t-
Use
d
M
o
st
-
U
s
e
d
E
xha
us
t
i
v
e
R
a
n
dom
FC
0.
0039
0.
0031
0.
0038
0.
0023
Fi
xe
d 0.
2827
0.
2763
0.
2850
0.
2740
Al
t
e
r
n
a
t
e 0.
2600
0.
2542
0.
2605
0.
2596
5.
CO
NCL
USI
O
N
Insp
i
r
ed
by swar
m
int
e
lligen
ce, we ha
v
e
i
n
tro
d
uced
an
altern
a
tive app
r
o
a
ch
t
o
s
o
l
v
in
g
t
h
e mult
ica
s
t
ro
u
ting
pro
b
lem
in
m
o
bilead
hoc
net
w
o
r
k
s
.
M
u
lticas
ting
wi
th
mult
iple c
o
res b
y
ad
o
p
tin
g
swar
m
inte
lli
gen
ceis
an
o
ndemand multicas
t ro
uting
pr
o
t
o
c
o
l
tha
t
c
r
eat
es a
multicas
t
mesh s
h
ar
ed
b
y
a
l
l
th
e
me
m
b
ers
with in
each
gro
u
p
with
o
t
h
e
r members. Ant agen
ts are us
ed
t
o
se
l
ect
multiple co
r
e
s and
th
e seco
r
e
s use ant ag
en
ts t
o
e
s
t
a
b
l
i
s
h
c
o
n
n
e
c
t
i
v
i
t
y
w
i
t
h
group m
e
m
b
e
r
s
.
M
u
lticas
t
with
multipl
e
c
o
res
will su
p
p
o
r
t th
e lar
g
e scal
e
D
i
strib
u
te
d
Vi
rtu
a
l e
n
v
i
ro
n
m
en
t (
DVE) ap
p
licatio
ns used
with
i
n
mo
bil
e
ad
h
o
c netw
o
r
k
s
. M
u
lticas
ting
wi
th
m
u
l
t
i
p
l
e
c
o
r
e
s
b
y
u
s
i
n
g
s
w
a
r
m
in
tellig
ence
c
a
n
b
e
ap
pl
i
e
d w
i
t
h
ot
h
e
r
ob
j
e
c
t
i
v
e
s
s
u
c
h
a
s
l
o
a
d
b
a
l
a
n
c
i
n
g
,
energy c
o
nser
vati
o
n
, a
nd s
ecurit
y
as futu
re
wo
r
k
.
ACKNOWLE
DGE
M
ENTS
I wo
u
l
d
lik
e to
th
ank
all th
e staff and
Departm
e
n
t
of Mechanical Engi
neerin
g f
o
r thei
r su
pp
o
r
t. I
wou
l
d also like to
t
h
ank
Tech
yog
i an
d Sh
ru
th
i so
lu
tion
s
an
d Gad
e
Au
ton
o
m
o
u
s
system
s Ltd
for th
ei
r su
ppo
rt
i
n
t
h
i
s
pr
o
j
ect
.
I
wo
ul
d
al
so l
i
ke t
o
ac
kn
owl
e
dge
m
y
presen
t
wo
r
k
i
n
g c
o
m
p
any
Ha
ppi
est
M
i
nds
Pvt
.
Li
m
i
t
e
d
fo
r all the l
o
ve
and
s
u
p
p
o
rt.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Fu
zzy Con
t
ro
ll
ed
Rou
tin
g in
a S
w
a
r
m Ro
bo
tic Netwo
r
k (Navya
Man
o
j
)
27
6
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BI
O
G
R
A
P
HY
OF
A
U
T
HO
R
Nav
y
a Manoj b
o
rn on May
10
1989 in Shinoga, Ka
rnatak
a,
India. Studied M.tech (R) in
M
echatron
i
cs
at NITK
and
pres
e
n
tl
y
workin
g
in
Happiest Minds
Pvt. Ltd in
Bang
alore.
Evaluation Warning : The document was created with Spire.PDF for Python.