Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 3,
J
une
2
0
1
4
,
pp
. 32
9~
34
2
I
S
SN
: 208
8-8
7
0
8
3
29
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
/
IJECE
Guided Navigation Control of
an Unmanned Ground Vehicle
using Gl
obal P
o
s
i
tioning Syst
em
s and Inertial Navi
gation
Systems
Pooja Velas
k
ar,
Al
var
o Var
gas
-Cla
r
a
, Os
am
a Jameel,
Sangram
Redkar
* Department of
Engineering
and
Computing S
y
st
em
s
,
Arizona
S
t
ate
Univers
i
t
y
,
United S
t
ates
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 21, 2013
R
e
vi
sed M
a
r
3,
2
0
1
4
Accepted
Mar 27, 2014
This paper d
e
monstrates th
e use of
Global Positioning S
y
stem
(GPS) and
Inertial Nav
i
gation S
y
stem (INS) in
order
to d
e
v
e
lop an
Unmanned Ground
Vehicle (UGV) devised to
perfor
m
a wide
var
i
ety of outdoor tasks. Th
ere
ar
e
man
y
app
licatio
ns for autonomous UGVs
such
as tactical
and
surveillance
applications, ex
ploration
of ar
eas
inaccessible b
y
humans.
Capable to
navigate to
a specif
i
c lo
cation,
and
contro
l their motion depend
ing on their
surroundings without human
in
terven
ti
on. Th
e iner
tial nav
i
gation s
y
stem
m
a
kes
us
e of In
erti
al M
e
as
urem
ent Units
(IM
Us
) to m
eas
ure
th
e
chang
e
to
the UGV'
s positional p
a
rameters, orientatio
n and speed
which are
continuously
monitored and u
pdated
.
With th
e advent of G
PS, and the
positional da
ta
from the iner
tial s
y
s
t
em
the
positional inf
o
rm
ation is
computed leading to
a more accurate
control of
the UGV; which otherwis
e
suffers from
integrat
ion drif
t th
at oc
cu
rs with
t
h
e im
plem
ent
a
ti
on of iner
tia
l
s
y
stems alone.
Autonomous co
ntrol of
the UGV is i
m
plemented b
y
coupling
GPS
sensor and
Mission
Planner, a
tool to map way
p
o
i
nts from Google
Maps. Furtherm
ore, s
y
s
t
em
stabilit
y
and id
eal
PID (Proportional, In
tegr
al
and Derivative)
values are determined
using bicy
cle modeling analy
s
is to
achieve better es
timates
and control
of the
UGV.
Keyword:
Unm
a
nne
d Gr
ou
n
d
Vehi
cl
e
Glob
al Po
sition
i
ng
System
In
ertial Nav
i
g
a
tio
n
System
Ar
du
pi
l
o
t
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
:
Sangram
Redkar,
Depa
rt
m
e
nt
of
En
gi
neeri
n
g
a
n
d C
o
m
put
i
ng
S
y
st
em
s,
Ariz
ona
State
Uni
v
ersity,
7
001
,
E.
William
s
Field
Ro
ad
, Mesa,
AZ-85
2
1
2
,
Unit
ed S
t
ate
s
.
Em
a
il: sred
k
a
r@asu.edu
1.
INTRODUCTION
A U
GV m
o
st
o
f
t
e
n o
p
e
r
at
es w
i
t
hout
a
n
y
o
n
-
b
oar
d
o
p
e
r
at
o
r
o
r
h
u
m
a
n i
n
t
e
rv
ent
i
o
n
.
It
i
s
b
r
o
a
dl
y
use
d
in
task
s
wh
ere
it is al
m
o
st i
m
p
o
s
sib
l
e for a
h
u
m
an
to
b
e
p
r
esen
t.
Naturally, it fin
d
s
app
l
icatio
n
s
in
numero
u
s
fields s
u
c
h
as
military, space
exploration, e
nvi
ronm
en
t sen
s
ing
,
search
an
d rescu
e
. Generally, it is equip
p
e
d
wi
t
h
a cont
rol
l
er an
d on
-
boa
r
d
sens
or
s t
o
o
b
ser
v
e t
h
e en
v
i
ro
nm
ent
and i
t
aut
o
n
o
m
ousl
y
m
a
kes deci
sions
or
pass
o
ff t
h
e i
n
fo
rm
ation
rem
o
tely
to a
n
op
erator
th
r
ough som
e
m
eans
of telecomm
u
n
ication.
Adva
nces i
n
com
put
er p
r
oc
essi
ng
t
ech
ni
q
u
es, m
i
ni
at
uri
zat
i
on, i
m
age pr
ocessi
ng
, an
d c
o
m
m
uni
cati
on t
e
c
hni
que
s
ha
ve
resul
t
e
d
i
n
ra
pi
d
pr
o
g
ress
i
n
t
h
e
fi
el
d
of
aut
o
n
o
m
ous
ve
hi
cl
es. U
G
V
s a
r
e
no
w a
b
l
e
t
o
se
nse t
h
ei
r
w
o
rl
d
us
i
n
g
el
ect
ro-
opt
i
c
a
nd i
n
fra
re
d cam
eras, and a
vari
et
y
of ot
he
r sens
ors
.
The
y
are able to capture, re
prese
n
t and
i
n
t
e
rp
ret
t
h
ei
r envi
ro
nm
ent
and a
u
t
o
nom
ou
sl
y
co
m
b
i
n
e and m
a
ni
pul
at
e t
h
i
s
i
n
fo
rm
at
i
o
n t
h
r
o
ug
h a seri
es
o
f
co
n
t
ro
l action
s
. Ad
d
ition
a
lly, th
e prices of the tech
no
log
i
es h
a
v
e
dropp
ed
co
nsid
erab
ly
su
ch
t
h
at
au
t
o
no
m
o
u
s
syste
m
s are approxim
a
tely
80% chea
pe
r than t
h
ey
we
re
in 1
9
90
[1]
.
Currently, UGVs are
de
ploy
ed for
su
rv
eillan
ce,
min
e
clearan
ce, firefigh
ting
.
Th
is research
d
eals with
i
m
p
l
e
m
en
tin
g
su
ch an
au
ton
o
m
o
u
s UGV
b
y
in
tegrating
t
w
o d
i
fferen
t
sy
ste
m
s, Glob
al
Po
sition
i
ng
Sy
ste
m
(GPS) and
In
ertial Nav
i
g
a
tio
n System
(INS).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
32
9 – 3
4
2
33
0
1.
1
Gl
ob
al
P
o
si
ti
o
n
i
n
g
Sys
t
em
:
The
Global Positioni
ng
Syste
m
as depicted in
Figure
1 is a space-base
d satellite
syste
m
that
pr
o
v
i
d
es
p
o
si
t
i
oni
ng
,
na
vi
gat
i
o
n
,
a
n
d t
i
m
i
n
g
dat
a
t
o
use
r
s
wo
rl
d
w
i
d
e
an
d
has
bec
o
m
e
a key
c
o
m
pone
nt
i
n
eco
no
m
i
c g
r
owth
, transpo
r
tatio
n
safety and
critical n
a
tio
n
a
l in
frast
ru
ct
u
r
e in
th
e
Un
ite
d
States and abroad [2].
I
t
op
er
ates i
n
all w
eath
e
r
cond
itio
n
s
, an
ywher
e
on
or
near
Earth
where t
h
ere is a
n
u
nobs
t
ructed
line of sight
to
fou
r
of m
o
re GPS
satellites. It is m
a
in
tain
ed
b
y
th
e Un
i
t
ed
States Gov
e
rn
m
e
n
t
an
d
is freely av
ail
a
b
l
e to
anyone
with a
GPS
receive
r. GPS sa
tellites orbit t
h
e ea
rth e
v
ery
12
hou
rs, em
itt
ing c
ontinuous
navi
gation
signals.
With t
h
e prope
r
equi
pm
ent, users c
a
n recei
ve
thes
e signals to ca
lculate tim
e
, lo
cation and
velocity.
The si
gnals a
r
e
so acc
urate, time can be
figured
t
o
with
in
a
mil
lio
n
t
h
o
f
a seco
nd
, v
e
l
o
city with
in a fractio
n of
a
m
i
le and location to within 100
m
e
ters [3]. Also,
the accuracy of the GPS sign
al in space is actually the
sam
e
for both
the civilian GPS serv
ice (SPS) and the
military GPS servic
e (PPS).
Howe
ver, SPS broadcasts
o
n
on
ly
o
n
e
freq
u
e
n
c
y, wh
ile PPS uses two
.
Th
is m
ean
s military u
s
ers can
p
e
rform
io
n
o
sp
heric co
rrect
io
n
,
a
t
echni
q
u
e
t
h
at
re
duce
s
ra
di
o
de
gra
d
at
i
o
n c
a
use
d
by
t
h
e
Eart
h'
s at
m
o
sphere
.
W
i
t
h
l
e
s
s
de
gra
d
at
i
o
n,
PPS
provides
better accuracy th
a
n
the ba
sic SPS [4].
Fig
u
re
1
.
GPS
Satellite an
d
co
n
s
tellatio
n (l
eft).
In
ertial Senso
r
Assem
b
ly (righ
t)
A f
e
w
o
f
i
t
s
do
m
i
nant
feat
u
r
e
s
ha
ve
bee
n
jot
t
ed d
o
w
n
bel
o
w.
-Ex
t
rem
e
ly a
ccu
rate, th
ree-d
i
m
e
n
s
io
n
a
l lo
catio
n informatio
n
(latitu
d
e
, l
o
ng
itud
e
an
d altitu
d
e
),
v
e
lo
city
(spee
d
a
n
d
di
re
ct
i
on)
an
d
pre
c
i
s
e t
i
m
e
.
-A
w
o
rl
dwi
d
e
com
m
on gri
d
t
h
at
i
s
easily conve
rted to a
n
y
local grid.
-All-weathe
r operations
-Su
p
p
o
r
t
s
u
n
l
i
m
i
t
e
d num
ber
of
use
r
s a
n
d a
r
eas.
-Supports t
o
ci
vilians at a
slightly less accurate level.
-Co
n
tinu
o
u
s re
al-tim
e
operati
on
1.
2
Inerti
a
l
N
avi
g
a
ti
on
S
y
s
t
em
:
An
I
n
ert
i
a
l
Na
vi
gat
i
o
n Sy
st
e
m
i
s
a na
vi
gat
i
on t
ool
t
h
at
u
s
es a c
ont
rol
l
e
r, m
o
t
i
on se
ns
ors
,
r
o
t
a
t
i
o
n
sens
ors t
o
co
n
t
i
nuo
usl
y
cal
cul
a
t
e
t
h
e p
o
si
t
i
on,
o
r
i
e
nt
at
i
o
n, a
nd
vel
o
ci
t
y
of a m
ovi
n
g
ob
ject
vi
a a m
e
t
h
o
d
called
d
e
ad
r
e
ck
on
ing
.
Th
e follo
w
i
ng
is a break
dow
n of
a few
ter
m
in
o
l
og
ies p
e
r
t
ain
i
ng
t
o
I
N
S.
Dea
d
Reck
oni
n
g-
T
h
e term
,
dead
reckoning or
de
duce
d
reckoning m
eans the pr
o
cess of esti
m
a
tin
g
th
e v
a
l
u
e
o
f
any v
a
riab
le
qu
an
tity b
y
u
s
ing
an
o
t
h
e
r qu
an
tity an
d add
i
ng
t
o
it wh
atev
er ch
ang
e
s
h
a
v
e
occu
rred
i
n
t
h
e m
eant
i
m
e
. In na
vi
gat
i
on, i
t
i
s
t
h
e p
r
oces
s o
f
cal
cu
l
a
t
i
ng o
n
e’s c
u
rre
nt
p
o
si
t
i
on
by
usi
n
g a p
r
e
v
i
o
usl
y
det
e
rm
i
n
ed p
o
s
i
t
i
on, an
d m
ovi
n
g
t
o
t
h
e
ne
w p
o
si
t
i
on
bas
e
d u
p
on
kn
o
w
n o
r
est
i
m
a
t
e
d speed
o
v
er el
apse
d
t
i
m
e
, and cou
r
se. B
a
si
cal
l
y
, i
t
rel
i
e
s on kn
o
w
i
n
g w
h
er
e y
ou st
art
e
d
fr
om
, pl
us so
m
e
form
of h
eadi
n
g
inform
ation and estim
ate of s
p
eed and tim
e to
d
e
term
in
e th
e d
i
stan
ce travelled
[5
].
Inertial Refer
e
nce
frames-
These are t
h
e
non-rotating a
nd
non-
accelerating coordi
nate fram
es in
wh
ich
Newt
o
n
’s laws of m
o
tio
n are v
a
lid.
Inertial
sens
ors-
T
h
ese a
r
e the
se
nsors that m
easure
in
ertial acceleratio
n
s
and
ro
tation
s
.
Accelerometer
s
m
easure the linear accelera
tion of
the
syste
m
in the inert
i
al
refere
nce fra
m
e
. They are
fixe
d
to
th
e syste
m
an
d
ro
tate with it,
unawa
re o
f
t
h
ei
r o
w
n
ori
e
nt
at
i
on.
G
y
ro
sc
o
p
e
s
m
easure the angular
ve
locity
o
f
a
g
i
v
e
n
syst
e
m
b
y
u
s
i
n
g its orig
in
al
o
r
ien
t
atio
n
as th
e i
n
itial co
nd
itio
n an
d in
tegrating
t
h
e an
gu
lar v
e
l
o
city.
Inertial
Me
as
urement Uni
t
s (I
MUs
)
–
IMUs include
Inertial Se
nsor
Assemblies
as sh
ow
n i
n
Figure 1
,
whi
c
h are a set
of i
n
ert
i
a
l
sens
or
s
m
ount
ed o
n
a
r
i
gi
d ba
se, a
pr
o
cesso
r an
d
ot
h
e
r su
p
p
o
r
t
el
ect
ro
ni
cs
th
at aid
i
n
calib
rating
and
con
t
ro
l of th
e INS.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Gui
d
ed
N
a
vi
ga
t
i
on C
ont
r
o
l
of
a
n
Un
m
a
n
n
e
d
Gro
u
n
d
Ve
hi
cl
e usi
n
g
Gl
ob
al
Posi
t
i
oni
ng
…
(
S
a
ngr
a
m
Re
d
k
ar)
33
1
Fi
gu
re
2.
Lo
os
el
y
cou
p
l
e
d
G
PS-
IN
S (l
e
f
t
)
.
Ti
ght
l
y
co
u
p
l
e
d
GPS
-
I
N
S
(
r
i
ght
)
1.
3
GPS-INS
In
te
gration
Ine
r
t
i
a
l
Na
vi
ga
t
i
on Sy
st
em
s have
been
used
f
o
r c
o
unt
l
e
ss
navi
gat
i
o
n
a
l
o
p
erat
i
o
ns
f
o
r
t
h
e
past
f
e
w
decade
s
.
Initially, a
m
a
j
o
rity of t
h
ese syste
m
s were ve
ry expe
nsi
v
e
bec
a
use of
c
o
sts of high-quality,
well-
characte
r
ized s
e
ns
ors, and t
h
e
nee
d
fo
r a sta
b
ilized se
nsor
platform
. This
h
i
gh
-co
s
t limit
ed
th
ei
r ap
p
licatio
n
s
to
mili
tary, scien
tific, and
commercial a
i
rcraft. Also
, th
e
use of sta
b
ilized platform
s l
e
d
t
o
IN
S ha
vi
n
g
a si
ze
and
p
o
we
r re
q
u
i
r
em
ent
s
t
oo l
a
rge f
o
r m
a
ny
appl
i
cat
i
ons
.
Ad
van
ces i
n
m
a
t
e
ri
al
proce
ssi
ng
hav
e
m
a
de i
t
pos
si
bl
e t
o
pr
od
uce sm
al
l
,
low
-
c
o
st
i
n
ert
i
a
l
sensor
s [6
]. Ho
wev
e
r, in
ertial syste
m
s s
u
ffer fro
m
a c
e
rtain
phe
n
o
m
e
non
w
h
i
c
h i
s
ex
pl
ai
n
e
d as
f
o
l
l
o
w
s
.
Inte
gra
t
io
n dr
ift-
An
INS is in
itially
g
i
v
e
n
p
o
s
ition
an
d
velo
city in
fo
rm
atio
n
fro
m
an
oth
e
r so
urce,
and the
r
eafter i
t
ge
nerates its
own
update
d
position and
vel
o
city by inte
grating i
n
form
ati
o
n recei
ved from
the
m
o
t
i
o
n
sen
s
ors. So
, an
y s
m
all
errors wh
ich
arise in
th
e
m
e
a
s
urem
ent of ac
celeration and
angular
velocity are
in
teg
r
ated
in
t
o
p
r
og
ressi
v
e
ly larg
e errors. This
dra
w
back of
the INS is
called
in
teg
r
ation
drift.
As these low-cost sens
ors c
a
nnot be e
x
pe
cted
to m
eet
the accuracy and
precisi
on requi
rem
e
nts
of
m
a
ny
navi
gat
i
on
ap
pl
i
cat
i
ons
. The
r
ef
o
r
e,
wi
t
h
GP
S ca
pabi
l
ity fo
r
o
n
-lin
e
calib
ratio
n and erro
r esti
m
a
ti
o
n
, it
i
s
used al
on
g
wi
t
h
IN
S. N
o
w
,
am
ong t
h
e m
o
st
det
r
i
m
ent
a
l fact
ors af
fect
i
ng a GP
S base
d ve
hi
cul
a
r na
vi
gat
i
o
n
syste
m
is th
e ob
stru
ctio
n of t
h
e lin
e
of sigh
t
b
e
tween
v
e
h
i
cle an
d satellite
s. As
u
s
er
s trav
el in
urb
a
n
can
yon
s
and
high
folia
ge areas, the a
b
ility of
GPS
to provide a
n
accurate
pos
ition is c
o
m
p
romised. Although
high
sensitivity GPS (HSGPS) receivers can t
r
ack we
ak si
gnals through fading effe
cts, this
m
a
kes the
m
susce
p
t
i
b
l
e
t
o
m
u
lt
i
p
at
h whi
c
h i
s
t
h
e
phe
n
o
m
e
non
of
rad
i
o si
g
n
al
s reac
hi
n
g
t
h
e a
n
t
e
n
n
a vi
a t
w
o
or
m
o
re
pat
h
s ca
usi
n
g
si
gnal
jam
m
i
ng
[
7
]
.
He
re,
INS
can act
a
s
a sh
ort
-
t
e
rm
fal
l
-
bac
k
wh
en G
PS si
gna
l
s
are
una
vai
l
a
bl
e.
T
hus
, as
GPS
a
n
d
I
N
S
ha
ve
c
o
m
p
l
e
m
e
nt
ary
characte
r
istics, their im
pl
e
m
e
n
tatio
n is co
n
s
id
ered
in an integrate
d
a
p
proach.
Sens
or t
ech
n
o
l
ogy
m
a
de headway
wi
t
h
t
h
e
i
nvent
i
o
ns s
u
ch as st
and
-
al
one
gy
roc
o
m
p
asses (1
9
3
0
)
,
Sch
u
l
e
r t
u
ne
d “Fl
o
at
ed
rat
e
i
n
t
e
g
r
at
i
ng
gy
r
o
devel
ope
d
by
M
I
T, U
S
A
(1
9
5
0
)
,
dy
nam
i
call
y
t
uned
gy
ro
(
1
9
6
0
)
,
fi
ber
opt
i
c
gy
r
o
et
c. M
o
re
o
v
e
r, G
PS was i
n
t
r
o
duce
d
at
t
h
e
end
of t
h
e
20
th
cen
tu
r
y
[8
].
Res
earch proved
that
GPS an
d
INS sh
ortco
m
in
g
s
were nu
llified
with
th
ei
r
in
tegratio
n. GPS-INS arch
itectu
r
es were dev
e
lop
e
d
main
ly as
lo
o
s
ely an
d
tig
h
tly
co
up
led
system
s,
as il
lu
strated
in
Figu
re 2. Th
eir wo
rk
ing is b
r
iefly d
e
p
i
cted
in
t
h
e bl
ock
di
a
g
r
a
m
s
.
Th
e trad
itio
n
a
l
app
r
o
ach to
INS/GPS i
n
teg
r
atio
n
with
Kalman
fi
lters lead
s to a co
n
fi
guratio
n
term
ed
‘l
o
o
sel
y
co
upl
ed’
,
sh
o
w
n i
n
Fi
gu
re
2.
In
t
h
i
s
st
ruct
ure
a GPS
fi
lter (g
en
erally EKF
o
r
Least-sq
u
a
res
recu
rsi
o
n)
pr
o
cesses t
h
e GP
S si
gnal
s
a
nd
out
put
s t
h
ree
di
m
e
nsi
onal
p
o
si
t
i
on
(an
d
p
o
ssi
bl
y
vel
o
ci
t
y
) i
n
t
h
e
st
anda
rd
GP
S
Eart
h C
e
nt
ere
d
Eart
h
Fi
xe
d (
E
C
E
F)
refe
ren
ce fram
e
. The
desi
g
n
of t
h
e
GPS sy
st
em
requi
res
fou
r
satellites t
o
b
e
t
r
ack
ed
i
n
o
r
d
e
r t
o
so
lv
e for three
d
i
m
e
n
s
ion
a
l po
sition
(a
fourth
time u
n
c
ertain
ty is also
so
lv
ed
).
Wh
en less th
an
fou
r
satelli
tes are
v
i
sib
l
e,
stand
-
alo
n
e
three d
i
men
s
ion
a
l GPS p
o
s
ition
i
ng
can
n
o
t
be
accom
p
lished. Loosely c
o
upled con
fi
gu
rati
o
n
s
em
p
l
o
y
a
secon
d
, m
a
ster Kalm
an
Filter to pred
ict i
n
ertia
l
sens
or e
r
r
o
rs
f
r
om
t
h
e equat
i
ons
o
f
i
n
ert
i
a
l
navi
gat
i
o
n
.
T
h
e
fi
l
t
e
r i
s
up
da
t
e
d wi
t
h
di
rect
obse
r
vat
i
o
n
s
of t
h
e
p
o
s
ition
erro
r
form
ed
fro
m
t
h
e
o
u
t
p
u
t
s of
th
e in
ertial u
n
i
t an
d th
e
GPS
fi
lter.
Th
e stan
d
a
rd
Kalm
an
fi
lter
equat
i
o
ns a
r
e
opt
i
m
al
when
sens
or
obs
er
va
t
i
ons are
un
bi
ased wi
t
h
w
h
i
t
e
noi
se. B
y
fi
l
t
eri
ng t
h
e
GP
S dat
a
twice th
is
op
timali
t
y co
n
s
trai
n
t
is e
ff
ectiv
el
y ab
an
don
ed [9
].
G
P
S r
a
ng
in
g
sign
als
are fu
sed
d
i
rectly in
the
update stage of the Kalm
an
fi
lter. Th
e m
o
re satelli
tes u
s
ed
in
th
e ran
g
i
ng
p
r
o
cess the m
o
re in
fo
rm
ati
o
n
the
fi
lter h
a
s to
con
s
train th
e i
n
ertial n
a
v
i
g
a
tion
so
lu
tion
.
In
a situ
ation
of d
e
grad
ed
G
P
S av
ailab
ility, a ‘tig
h
tly coupled
’ co
n
fi
g
u
r
at
i
on i
s
ca
pa
bl
e
of
u
pdat
i
n
g
th
e
fi
lter with
o
n
l
y on
e
v
i
sible satelli
te. This co
nfigu
r
ation
is illu
strated in
Figu
re
2
.
In
add
ition
,
a t
i
g
h
tly
coupled
fi
lter p
r
o
cesses t
h
e GPS si
g
n
a
ls
directly. In
a we
ll designe
d s
y
ste
m
this increases the c
h
a
n
ce of
o
p
tim
al
fi
l
t
e
r perf
orm
a
nce [9]
.
Kal
m
an Fi
lt
er Sm
oot
heni
ng
al
gori
t
h
m
was devel
o
pe
d t
o
post
p
r
ocess t
h
e dat
a
to
ob
tain
po
sitio
n
so
l
u
tion
when
n
o
t
d
i
rectly av
ailab
l
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
32
9 – 3
4
2
33
2
R
e
search re
ga
r
d
i
n
g t
h
i
s
w
o
r
k
i
s
di
scusse
d be
l
o
w. I
n
2
0
0
6
,
Go
d
h
a di
sc
uss
e
d t
h
e use
of
M
E
M
S
IM
Us
fo
r vehi
c
u
l
a
r n
a
vi
gat
i
o
n,
i
n
cl
udi
ng
t
h
e use
of hei
ght
a
n
d no
n
-
h
o
l
o
n
o
m
i
c
vel
o
ci
t
y
c
onst
r
ai
nt
s. Ot
he
r re
search
in
th
e sa
m
e
ar
ea in
clu
d
e
s: Salych
ev
et al.
(200
0), Ma
th
ur an
d
Grass (20
00), Kealy et al. (2
00
1). M
c
Millan
incorporate
d
t
w
o
IMUs i
n
a Kalm
an filter for m
a
rin
e
ap
p
lication
s
. Th
e system
,
called
Du
al
In
ertial
Navi
gat
i
o
n
Sy
st
em
(DI
N
S
)
u
s
ed a
re
fere
nc
e sy
st
em
t
o
t
e
st
ot
he
r
navi
gat
i
on
sy
st
em
s, e.
g.
Sche
rzi
n
ge
r
et
al
.
(199
6
& 19
97). Wh
ile
it p
r
o
v
i
d
e
d
fau
lt
detectio
n
o
n
IMU
m
easu
r
emen
ts,
its
m
a
i
n
fo
cu
s was
to
p
r
ov
id
e
redun
d
a
n
c
y in case o
f
sing
le IMU failure.
Brand
and
Ph
ilip
s (20
03) in
trodu
ced
th
e
u
s
e o
f
two
IMUs for
pede
strian
na
vi
gation using
MEMS IMUs. Their m
e
thod
us
e
d
a
dditiona
l RF obse
rva
b
l
e
s to
directly observe
the distance between IM
Us. Petovello
et
al
. (20
0
5
) u
s
e
d
a dual
GP
S/
INS m
e
t
hod
ol
ogy
t
o
q
u
ant
i
f
y
shi
p
flex
ure i
n
airc
raft car
riers
.
T
w
o
sets o
f
I
N
S we
re
u
s
ed
t
o
d
e
term
in
e th
e relativ
e po
si
tio
n
of each
i
n
ertial
syste
m
and each INS
was provi
ded
GPS observa
b
les th
rough the use of a
GPS a
n
tenna a
n
d receiver [7]
.
Ran
d
l
e and
Horton
d
e
scri
b
e
d
in
th
eir
wo
rk
s
th
e in
tegration o
f
GPS/INS
usin
g
a low co
st IMU con
s
istin
g of
m
i
cro-m
achi
n
ed sens
ors a
nd
on
-
boa
rd cal
i
b
r
a
t
i
on. Si
m
u
l
a
t
i
ons
have
been
do
ne f
o
r b
o
t
h
f
l
i
ght
and a
u
t
o
m
o
ti
ve
navi
gat
i
o
n
.
T
h
us, t
h
e resea
r
c
h
o
n
GPS
-
I
N
S
i
n
t
e
grat
i
o
n c
o
nt
i
nue
s t
o
foc
u
s
on ac
hi
evi
n
g hi
gh
pe
rf
or
m
a
nce
p
o
s
ition
i
ng
for growing
app
licatio
n
s
and
areas.
1.
4
Descripti
o
n and
Sc
ope
:
Th
is research
is d
i
v
i
d
e
d
in
to
two
p
a
rts, i) Bu
ild
ing
a UGV (n
am
ed
Ardu
rov
e
r as it is
b
u
ilt u
s
in
g
Ard
u
p
ilo
t Mega) with in
tegrated
GPS an
d INS and
ii) Bi
cycle
m
odel analysis. The
pra
c
tical aspect of this
researc
h
l
i
m
it
s i
t
s
el
f t
o
t
h
e
ope
rat
i
o
n
of t
h
e
Ar
d
u
r
ove
r
i
n
m
a
nual
m
ode a
n
d
f
o
l
l
o
w
i
ng t
h
ree
di
ff
erent
waypo
in
t co
urses in
au
to
m
o
d
e
.
Wh
ile th
e t
h
eory asp
e
ct deals with
th
e
dev
e
lop
m
en
t o
f
a b
i
cycle
m
o
d
e
l u
s
ing
t
h
e pa
ram
e
t
e
rs of
t
h
e i
m
pl
em
ent
e
d A
r
d
u
r
ove
r t
o
ge
ne
ra
t
e
a set
of
PI
D
val
u
es
fo
r
o
p
t
i
m
u
m
cont
r
o
l
of t
h
e
UG
V.
2.
R
E
SEARC
H M
ETHOD
Th
is
p
a
rt
o
f
t
h
e work
d
eals
with
m
o
d
e
lin
g th
e v
e
h
i
cle to stu
d
y
th
e p
a
t
h
track
i
ng
an
d stab
ility o
f
m
o
ti
on o
f
t
h
e
UG
V t
o
na
vi
g
a
t
e
freel
y
i
n
u
n
k
n
o
w
n
e
nvi
ro
nm
ent
s
. The m
odel
i
n
g t
ech
ni
que
use
d
h
e
re,
i
s
t
h
e
three degree-of-free
dom
bicycle modeling,
whi
c
h i
s
a c
o
m
m
on ap
pr
oxi
m
a
t
i
on use
d
f
o
r m
o
t
i
on
pl
a
nni
ng
,
sim
p
le vehicle analysis and de
riving
intuitive
control algorith
m
.
This is done by the assum
p
tion of com
b
ini
ng
th
e left an
d
righ
t sid
e
o
f
th
e
wh
eel of
a car into a single in-line pair of wh
eel
s. The
pat
h
-t
racki
ng c
ont
r
o
l
of a
n
autonom
ous
vehicle is one of the m
o
st difficult auto
m
a
t
i
on c
h
allenges
because of constraints
on mobility,
sp
eed
o
f
m
o
tio
n,
u
ndu
latin
g terrain etc. Th
e
v
e
h
i
cle c
o
n
t
rol
ca
n
be se
parat
e
d i
n
t
o
lateral and
long
itu
d
i
n
a
l
co
n
t
ro
ls. Here, we
fo
cu
s on
t
h
e lateral con
t
rol to
fo
llo
w a t
r
aject
o
r
y
i
n
t
e
r
m
s of hea
d
i
n
g
and
pat
h
c
ont
r
o
l
.
Fi
gu
re
3.
B
i
cy
cl
e M
odel
[1
0]
Bicycle Model
Thi
s
si
m
p
l
e
bicy
cl
e
m
odel
can be
use
d
t
o
de
ri
ve co
nt
r
o
l
l
a
ws (e
q
u
at
i
ons
of m
o
t
i
on)
by
assum
i
ng t
h
e
four-wheele
d
vehicle as a t
w
o-wheeled
bicyc
l
e
m
odel. T
h
e
two
de
grees
of free
d
om
are lateral (vehicle
fixe
d
y
)
and y
a
w
(he
a
di
n
g
)
.
The e
x
t
e
rnal
f
o
rces a
nd t
o
r
ques act
i
ng
on t
h
e ve
hi
cl
e are t
w
o m
a
i
n
t
y
pes:
t
i
r
e cont
act
fo
rces a
n
d ae
r
ody
nam
i
c forc
es. T
h
e
ve
hi
cl
e m
o
t
i
on deal
t
i
n
t
h
i
s
p
r
oject
i
s
m
a
i
n
l
y
gener
a
t
e
d by
t
h
e t
i
r
e
f
o
rces
alone
assum
i
ng that
aerodyna
m
i
c forces
ac
ting
on a city
r
o
ad
ar
e
min
i
ma
l.
T
h
r
e
e
forces act upon t
h
e tire,
nam
e
ly
l
ongi
t
u
di
nal
fo
rce, l
a
t
e
ral
f
o
rce
an
d
vert
i
cal
f
o
rce
.
The e
ffect
of
t
h
e l
o
n
g
i
t
udi
nal
fo
rce ca
uses
v
e
hi
cl
e
traction a
n
d braking. T
h
e e
ffe
ct of t
h
e
vertic
al force is
g
ood a
dhesi
on of t
h
e
vehicle to the roa
d
[8]. The
effect
of t
h
e lateral
force is
to m
a
ke the
vehicle t
u
rn as
we
ll as
p
u
s
h
it si
d
e
ways. Th
is
proj
ect d
eals with only th
is
lateral
fo
rce. Th
e wh
eels o
f
th
e
v
e
h
i
cle are affected
by the slip angle
at the tires. The slip a
ngle
for a
n
i
ndi
vi
dual
t
i
r
e
i
s
defi
ned
as t
h
e di
rect
i
o
n t
h
at
t
h
e
wheel
is
po
in
ting
to th
e
directio
n
t
h
at the cen
ter of th
e
wh
eel
i
s
m
ovi
n
g
. Sl
i
p
an
gl
es c
o
n
f
orm
t
o
t
h
e si
gn c
o
nve
nt
i
o
n
s
defi
ned
f
o
r
t
h
e b
ody
fi
xe
d co
o
r
di
nat
e
s
y
st
em
;
clo
c
kwise ro
tatio
n
is d
e
fin
e
d
as p
o
s
itiv
e. A
p
o
s
itiv
e steeri
n
g
ang
l
e p
r
od
u
c
es at a rig
h
t
tu
rn
, bu
t slip
ang
l
es are
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Gui
d
ed
N
a
vi
ga
t
i
on C
ont
r
o
l
of
a
n
Un
m
a
n
n
e
d
Gro
u
n
d
Ve
hi
cl
e usi
n
g
Gl
ob
al
Posi
t
i
oni
ng
…
(
S
a
ngr
a
m
Re
d
k
ar)
33
3
n
e
g
a
tiv
e
[10
]
. To
lin
earize th
e syste
m
,
we assu
m
e
th
at th
e v
e
h
i
cle is d
i
stu
r
bed
merely b
y
th
e s
m
al
l
p
e
rt
u
r
b
a
tio
n
in th
e eq
u
ilib
ri
um p
o
i
n
t
, th
at is, sm
a
ll an
g
l
e
ap
pro
x
i
m
a
tio
n
is u
s
ed
. Figu
re 3
sh
ows th
e
b
i
cycle
m
o
d
e
l sh
owing
v
e
lo
cities at
th
e tires
for a
righ
t tu
rn
w
ith n
e
g
a
tiv
e slip
an
g
l
es. Th
e imp
o
rtan
t
v
a
riab
l
e
s are:
is steerin
g
an
gle (Po
s
itiv
e CW
i
n
to
p
v
i
ew),
x
V
i
s
for
w
ar
d (l
o
ngi
t
u
di
nal
)
spe
e
d,
F
is fro
n
t
tire slip
an
g
l
e,
R
is rear tire slip angle,
a
i
s
di
st
ance f
r
om
C
G
(C
ent
e
r
of
gra
v
i
t
y
) t
o
fr
ont
axl
e
,
b
is distance from
C
G
(Cen
ter
o
f
g
r
av
ity) to
rear ax
le,
y
is lateral s
p
eed
(po
s
itiv
e
u
p
), an
d
is yawin
g
sp
eed
(p
o
s
itiv
e CW
in
t
op
vi
ew
).
A.
Dyn
a
m
i
cal Eq
u
a
tio
ns
o
f
m
o
tio
n fo
r lateral an
d yaw
d
y
n
a
m
i
cs:
From
t
h
e a
b
o
v
e
fi
g
u
re
, t
h
e
f
r
ont
a
n
d
rear
sl
i
p
a
ngles
are
re
prese
n
ted in t
h
e followi
ng equations:
11
ta
n
,
t
a
n
FR
x
xx
x
x
x
yy
y
y
aa
b
b
VV
V
V
V
V
(1
)
A li
near const
itutive equation is
us
e
d
for the tires to calcu
l
a
te the lateral
force
generated
by the tires
as a function
of slip a
n
gle. T
h
e c
o
rr
esponding force
s
are
t
h
e
tire cornering stif
fnesses
m
u
l
tiplied by t
h
e slip
angle.
**
,
*
*
yF
F
y
R
R
FF
F
F
R
R
R
x
xx
x
yy
a
FC
C
C
C
F
C
C
C
VV
b
VV
(2
)
Whe
r
e,
F
C
= Front tire cornering stif
fness (always
positive)
R
C
= Rear tire cornering
sti
ffness (al
w
ays positive)
The t
o
tal lateral acceleration is the ce
ntri
petal acceler
ation plus
the direct lateral
acceleration (ÿ), a
s
give
n belo
w.
y
x
V
ÿ
a
(3
)
Expressi
ng the centri
p
etal a
cceleration as
x
V
produces the correct si
gn (d
irection) for the cent
r
ipet
a
l
acceleration.
Ap
p
l
ying
Newton
’
s
2
nd
law
yields:
FR
F
F
F
R
R
x
x
xx
x
VF
F
C
C
C
C
C
VV
V
V
ya
y
b
ÿm
(4
)
The tire for
c
e
s
also pr
od
uc
e a
m
o
m
e
nt
acting o
n
the
vehicle and
applicatio
n of
the angula
r
m
o
m
e
ntum
principle y
i
elds:
22
zF
R
F
F
F
R
R
x
xx
x
IF
a
F
b
C
a
C
C
a
C
b
C
VV
V
ya
y
b
V
(5
)
R
earra
ngi
ng e
quatio
ns (
4
) a
nd (
5
), we get
the fi
nal dy
na
m
i
c equations
go
ve
rni
ng lateral and y
a
w
m
o
tion:
FR
F
R
F
x
xx
C
C
Ca
Cb
C
V
mV
m
V
m
ÿy
(6
)
22
FR
F
R
F
zz
z
xx
C
a
Cb
Ca
Cb
I
y
Ca
IV
V
I
(7
)
B.
Param
e
ter Identification for UGV:
The ab
ove
dif
f
ere
n
tial equations can
be u
s
ed to
m
odel
any vehicle after choosing a
p
propriate
param
e
ters. Som
e
param
e
ters can
be
directl
y
m
easured
o
r
calculated a
n
d s
o
m
e
have t
o
be estim
ated
usin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 4, No
. 3,
J
u
ne 2
0
1
4
:
32
9 – 3
4
2
33
4
kn
o
w
n in
f
o
rm
ation. T
h
e acc
uracy
o
f
suc
h
param
e
ters is
li
kely low. The followi
ng ar
e the param
e
ters, their SI
units,
an
d t
h
eir
co
rres
p
on
din
g
m
e
thod
o
f
m
easurem
ent/estim
ation.
1.
m
(Mass of t
h
e
Ve
hicle)-
Dire
ctly
m
easured i
n
kilogram
s.
2.
a (Distance
from
CG to front
axle
)- Di
rectly m
easured in m
e
ters
3.
b
(Distance from
CG to rear axle
)- Di
rectly m
easured in m
e
ters
4.
x
V
(Longitudi
nal velocity)- The set
ve
locity of
Ardurover i
n
m/sec
5.
F
C
(Front tire corneri
ng stiffne
s
s) &
R
C
(Rear tire corneri
ng
stiffne
ss)- Estim
ated base
d
on
available
data
on
R
C
car
JAC
2
1
6
4
Pin
k
Se
d
a
n
[1
1]
.
6.
z
I
(Ya
w
m
o
m
e
nt
of
Ine
r
tia)- T
h
e Ar
du
r
ove
r w
a
s treated as a rectan
gula
r
b
o
x
an
d its lengt
h a
n
d
width
we
re m
easure
d
.
T
h
e m
o
m
e
nt of i
n
erti
a was
f
o
u
n
d
ou
t by
the
f
o
rm
ula:
22
12
z
wl
Im
The values
for the
above para
m
e
te
rs fo
r
UG
V a
r
e f
o
un
d
o
u
t
to be:
m
= 0
.
92
7 kg
,
a =
0
.
20
32
m
,
b
=
0
.
15
24
m
,
x
V
= 1m
/s, 3m
/s, 6m
/s, 1
0
m
/
s
F
C
=
30
.2
N
/
r
a
d
,
R
C
=
21
.0
N
/
r
a
d
,
z
I
= 0.
122
1 kg*m
2
Headi
n
g c
o
n
t
r
o
l
:
For
hea
d
i
ng c
ont
rol,
the
o
b
jectiv
e is to m
ove
alo
n
g
a
d
e
sired
hea
d
in
g
.
The
co
ntr
o
l
varia
b
le is
steer
in
g an
d ou
tpu
t
var
i
ab
le
is h
e
ad
in
g
(y
aw),
whic
h is c
ont
rolled
to
steer to
war
d
a
wa
y
point.
E
quati
ons
(
6
)
and (7) can be
written i
n
te
rm
s of constants such as:
¨
,
ÿy
A
B
C
F
yD
E
(8
)
Whe
r
e t
h
e c
o
n
s
tants are
de
fin
e
d
by
:
A =
F
R
x
CC
mV
, B
=
FR
x
x
Ca
Cb
V
mV
, C
=
F
C
m
, D
=
FR
z
x
Ca
Cb
IV
, E
=
22
FR
z
x
Ca
C
b
I
V
F =
F
z
Ca
I
Taking the La
place transform
and so
lving for the ope
n
lo
op transfe
r
function
from
s
t
eering angle
to heading angle
yield
s
:
32
()
()
(
)
Fs
FA
C
D
s
s
sA
E
A
E
B
D
s
s
(9
)
A P
I
D
co
ntr
o
l
logic is em
plo
y
e
d:
()
I
P
D
K
s
KK
s
es
s
(1
0)
W
h
er
e
e(
s
)
is
th
e
er
ro
r
b
e
twee
n
th
e h
e
ad
ing (
)
an
d
t
h
e desired hea
d
in
g (
d
).
The c
o
rres
p
on
din
g
closed transfe
r
function si
m
p
li
fied
using Maple is:
32
43
2
()
(
)
()
(
)
(
)
(
)
DD
D
P
p
p
I
I
i
D
DP
D
P
I
p
I
I
d
FK
s
s
A
F
K
C
DK
F
K
s
AFK
CDK
F
K
AFK
C
D
K
s
s
s
F
K
A
E
s
AF
K
K
F
A
E
C
D
K
B
D
s
A
F
K
AF
K
C
D
K
AF
K
C
D
s
K
(1
1)
A.
3D
pl
ot f
o
r
sta
b
le val
u
es
of
K
p
,
Ki,
K
d
:
Equation (11)
is substituted
with values of A, B,
C, D, E, F and not the va
lues of Kp, Ki and Kd.
The resulting
equation’s characteristic
equation is used
to find stable
values
for
Kp,
Ki and Kd. The
characte
r
istic equatio
n
f
o
r t
h
e
closed
-lo
o
p
tra
n
sfe
r
fu
nctio
n i
s
f
o
u
n
d
out t
o
be:
s
4
+s
3
(
5
0
2
.
59Kd
+
197
.3
0)
+s
2
(1
992
4.
73Kd
+
50
2.
59Kp
+
73
25.
71
)
+
s(
2775
.0
8Ki+19
924
.7
Kp)
+
199
24
.73
K
i =0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Gui
d
ed
N
a
vi
ga
tion C
ontr
o
l of
a
n
Un
m
a
n
n
e
d
Gro
u
n
d
Ve
hicle usi
n
g
Gl
ob
al
Positioni
ng
…
(
S
a
ngr
a
m
Re
d
k
ar)
33
5
The val
u
es of A,B,C,D,E,F
and
Kp, Ki,
Kd
(u
sed for Ardurove
r) are substituted in the above
equatio
n a
n
d
u
s
ing
M
A
TLA
B
,
the
ro
ot lo
ci are
plotted
f
o
r
x
V
=1 m
/
s, 3m
/s, 5m
/s and
10m
/s.
B.
R
e
sulting plots
f
o
r hea
d
in
g
c
o
ntr
o
l:
This sectio
n d
e
picts the
out
com
e
of the
h
eadin
g c
ontr
o
l
bicy
cle
m
ode
ling a
n
aly
s
is in term
s of
gra
p
hin
g
stable
K
p
,
Ki,
K
d
va
lues a
n
d
r
oot l
o
cu
s
plots.
1.
3D Surface
plots for sta
b
le PID
values:
The
following
are the
3D surface
plots for PID
values for ra
nge
s
x
V
=1 m
/
s and
3 m
/
s
a)
x
V
=1 m
/
s
b)
x
V
=3
m/s
Fig
u
r
e
4
.
Kp
,
Ki,
an
d Kd
fo
r
r
a
ng
es
-5
to 5 (f
or
x
V
=1 m
/
s), an
d
fo
r
ran
g
es
-
1
0 to
1
0
(
x
V
=3m
/
s
)
2.
Roo
t
lo
cu
s:
Th
e fo
llowing
ar
e th
e d
i
g
ital
r
o
o
t
lo
ci p
l
o
t
fo
r
v
a
r
y
ing
v
e
l
o
cities an
d
Kp, Ki, Kd
set as 0
.
9
0
0
,
0
.
020
an
d 0.
040
r
e
spectiv
ely.
Figu
re
5.
R
o
ot
locu
s
of
hea
d
ing
co
ntr
o
l f
o
r
x
V
= 1m
/s (left), and
x
V
=3 m
/
s (rig
h
t).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 4, No
. 3,
J
u
ne 2
0
1
4
:
32
9 – 3
4
2
33
6
Figu
re
6.
R
o
ot
locu
s
of
Hea
d
ing
co
ntr
o
l f
o
r
x
V
= 6 m
/
s (left),
and
x
V
=10 m
/
s (r
ight)
The
ro
ot loci a
r
e o
b
taine
d
by
vary
in
g
pr
o
p
o
r
tional ga
in
Kp
.
W
h
e
n
th
e
g
a
i
n
i
s
sm
a
ll, the poles start at
the poles
of th
e transfe
r
f
unc
tion an
d as ga
in becom
e
s highe
r,
poles an
d zer
o tend to
ove
rlap. Eac
h
locu
s
starts at a pole and ends at a zero.
Here, as roots lie on t
h
e unit circle, th
e syste
m
is
marginally sta
b
le. In
cases whe
r
e som
e
of t
h
e loci
end at zero l
o
c
a
ted infin
itely
far
fr
om
poles.
This
ha
p
p
ens
whe
n
t
h
e sy
ste
m
has
m
o
re poles t
h
a
n
ze
ros.
Path c
o
n
t
rol:
Path co
ntr
o
l is anot
her c
ontr
o
l ap
pr
oach t
h
at is us
eful in
mini
mizing the late
ral displacem
e
nt of the
vehicle f
r
om
the straig
ht line path bet
w
ee
n two
way
p
o
i
n
ts. To com
p
ly with a Lin
ear Tim
e
Inva
riant (LT
I
)
sy
stem
, a fe
w
chan
ges
are
m
a
de.
The
strai
g
ht
path
betwee
n way
p
o
ints
ha
s
a glo
b
al h
eading
angle. The
path
is
rotated
by this angle to that it is parallel wit
h
the earth-fi
xed X-axis. It is then transl
ate
d
so that the previous
waypoint is at
ori
g
in. T
hus,
the eart
h
-fixe
d
Y
displacem
e
n
t is the
path
error. T
o
linea
rize the syste
m
, the
headi
n
g
a
ngle
is assum
e
d to
be sm
all. No
w,
integrating equation (7) yields
heading
(
). Using
t
h
is heading
angle, the linear vel
o
cities are transf
orm
e
d into the eart
h
fixed coordinat
e
syste
m
. The
kinem
a
tic coordinat
e
transform
a
tions are:
Ẋ
earth
=
)s
i
n
(
)
cos(
x
Vy
(1
2)
Ẏ
earth
=
si
n
)c
o
s
(
)
(
x
y
V
(1
3)
If
is assu
m
e
d to be sm
a
ll, th
en equation
(13)
re
d
u
ces to the foll
owi
ng e
quatio
n,
whe
r
e
y
is the
lateral velocity and
x
V
is the l
o
ngitudi
nal velocity.
Ẏ
earth
=
x
Vy
=
ė
(1
4)
The
ope
n l
o
op trans
f
er
functi
on use
s
steering a
ngl
e as a
n
i
n
put a
nd t
h
e
perpe
n
dicular
di
splacem
ent
in the
Y
earth
direction, a
n
d (e
)
as an
out
put
. T
hus
, a
relations
hip
betwee
n la
te
ral displacem
ent (y) a
n
d ste
e
ring
angle
is
neede
d
to
m
a
ke Eq
u
a
tion
(1
4)
int
o
the required tr
ansfe
r
fu
nctio
n
.
T
h
e
tra
n
s
f
er f
unctio
n bet
w
ee
n
yaw
and steering
angle was found
in
Equati
on (9) and
is rewritten
here.
32
()
()
(
)
Fs
FA
C
D
s
ss
A
E
s
A
E
B
D
s
(1
5)
Si
m
ilarly, the transfer
functi
on
bet
w
een la
teral displace
m
e
nt and
steerin
g an
gle is
f
o
u
n
d
out
by
solvi
n
g equations
(8)
for lateral disp
lacem
ent instead
of ya
w a
ngle a
n
d is,
32
()
()
(
)
()
Cs
CE
B
F
s
ss
A
E
s
E
A
B
ys
D
(1
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Gui
d
ed
N
a
vi
ga
tion C
ontr
o
l of
a
n
Un
m
a
n
n
e
d
Gro
u
n
d
Ve
hicle usi
n
g
Gl
ob
al
Positioni
ng
…
(
S
a
ngr
a
m
Re
d
k
ar)
33
7
The La
place transform
of e
quation (14)
cont
ains bot
h
s
and
y(s):
s Y
earth
(s
) =
()
(
)
x
V
s
sy
s
(1
7)
Solvi
n
g
eq
uati
ons
(
1
5-
17
)
f
o
r
the tra
n
s
f
er
f
u
nction
eart
h
Ys
s
yields:
eart
h
Ys
s
=
2
43
2
()
(
)
()
(
)
xx
s
Cs
V
F
C
E
B
F
V
F
A
C
D
ss
A
E
s
E
A
B
D
(1
8)
The cl
osed
-lo
o
p
fu
nctio
n
whe
n
c
o
m
b
ined
with a P
I
D c
ontr
o
ller y
i
elds the
f
o
llowi
ng
eq
uat
i
on:
eart
h
Ys
s
=
43
2
54
3
((
)
)
(
(
)
(
)
)
.
.
.
()
(
(
)
)
.
.
.
xx
x
x
DP
P
I
D
x
DP
D
CK
s
s
Kd
B
F
CE
F
V
CK
s
K
B
F
CE
F
V
C
K
K
A
F
V
CD
V
C
s
s
A
E
A
E
C
K
s
C
K
K
BF
C
E
F
V
AE
BD
2
...
(
(
)
(
)
)
(
)
.
.
.
((
)
(
)
)
((
)
(
)
(
)
xx
x
x
PI
I
xx
x
x
x
PI
D
P
I
I
s
K
AFV
C
D
V
K
BF
C
E
FV
K
V
AF
C
D
s
K
B
F
C
E
F
V
C
K
K
AFv
C
D
V
s
K
AFV
C
D
K
B
F
C
E
F
V
K
V
A
F
C
D
(1
9)
Usin
g the a
b
ov
e closed l
o
o
p
t
r
ans
f
er
f
unctio
n,
parts
1 an
d
2 de
scribe
d in
headi
ng c
o
ntr
o
l are rep
eated t
o
plot the 3D
plot of stable
values of
Kp,
Ki,
Kd and root locus
for stability
analysis.
A.
R
e
sulting plots
f
o
r Path
c
o
ntr
o
l:
1.
3D Surface
plots for sta
b
le PID
values:
The
following
are the
3D s
u
rface pl
ots
of sta
b
le PID val
u
es
for
x
V
= 1 m
/
s and
x
V
= 3 m
/
s
b)
x
V
=1 m
/
s
b)
x
V
=3
m
/
s
Fig
u
r
e
7
.
Kp
,
K
i
,
an
d Kd
fo
r
x
V
=1 m
/
s, and K
p
,
K
d
a
n
d Ki
f
o
r
x
V
=3 m
/
s
2.
R
oot l
o
cus:
Th
e fo
llowing
ar
e th
e an
al
o
g
r
o
o
t
lo
ci p
l
o
t
fo
r
v
a
r
y
ing
v
e
l
o
cities an
d
Kp, Ki, Kd
set as 0
.
9
0
0
,
0
.
020
an
d 0.040
r
e
spectiv
ely.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 4, No
. 3,
J
u
ne 2
0
1
4
:
32
9 – 3
4
2
33
8
Figu
re
8.
R
o
ot
locu
s
of
path
c
ont
rol
fo
r
x
V
= 1
m/s (left), a
n
d
x
V
=3 m
/
s (rig
h
t)
Figu
re 9.
R
o
ot locus
o
f
path
c
ont
rol fo
r
x
V
=6 m/s
For,
x
V
= 1
m
/
s, the system
is highly unstable a
s
the poles lie outsi
de the uni
t
circle. For,
x
V
= 3 m
/
s
,
all poles lie inside the
unit circle render
i
ng the system
stable. T
h
e syst
e
m
with
x
V
= 6
m/s is
m
a
rginall
y
stable.
The
vehicle
being m
odeled and an
alyzed for the various PID pa
rameters and
vel
o
cities, the
Ardurover
was put into action.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
The
Ardurover was
tested i
n
an
em
pty lot in
AS
U’s
P
o
ly
technic cam
pus.
Fig
u
re
1
0
depicts t
h
e
Ar
du
r
ove
r set up a
nd the m
i
ssions
were c
o
n
ducte
d o
n
c
oncrete lots. Figure 10 sh
ows the UGV connec
t
ed t
o
the ground station
wirelessly t
h
rough telem
e
t
r
y.
Figu
re 1
0
. Ar
d
u
r
o
ver setu
p o
n
field
(le
f
t),
a
n
d
PI
D
pa
ram
e
ters (
r
ig
ht)
Evaluation Warning : The document was created with Spire.PDF for Python.