Intern
ati
o
n
a
l Jo
urn
a
l
o
f
R
o
botics
a
nd Au
tom
a
tion
(I
JR
A)
V
o
l.
3, N
o
. 3
,
Sep
t
em
b
e
r
2014
, pp
. 21
2
~
22
0
I
S
SN
: 208
9-4
8
5
6
2
12
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
Dynamic Rocker-Bogie: A Stab
ility Enhancement for High-
Speed Traversal
Ho
ng-
a
n Ya
ng
, Luis Ca
rlos V
e
lasco Ro
jas*
,
C
h
a
n
g
k
a
i
X
i
a
,
Qiang Guo
School of Mech
anical
Engin
eering, Northweste
r
n
Poly
technical
Univ
ersity
, Xi’an, Chin
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received J
u
n
9, 2014
Rev
i
sed
Ju
l 9
,
2
014
Accepte
d
J
u
l 25, 2014
The rocker-bogie suspension mechan
ism it’s currently
NASA’s favored
design for wheeled mobile robots
,
main
ly
because it has robust cap
abilities to
deal with obstacles and because it unifo
rmly
distr
i
butes the p
a
y
l
oad over its 6
wheels at all times. Ev
en though
it h
a
s
man
y
ad
vantag
es when d
ealing with
obs
tacl
es
, there
is
one m
a
jor s
h
ortcom
ing which is
its
low average s
p
eed of
operation, making the rock
er-bo
g
ie s
y
st
em
not s
u
itabl
e for s
itu
at
ions
where
high-s
p
eed tr
ave
r
s
a
l over h
a
rd-fl
at s
u
rfac
e
s
is
ne
eded to
cover
la
rge ar
eas
i
n
short periods of time, mainly
du
e to
stability
pro
b
lems.
This paper proposes
to increase the s
t
ability
of the ro
ck
er-bogie s
y
stem by
exp
a
nding
its support
poly
gon
, makin
g
it more stable and
adaptable
while moving at high speed,
but keeping its original robustness
against obstacles:
One rocker-bogie
s
y
stem,
two modes of op
eration.
Keyword:
H
i
gh
sp
eed
Ro
c
k
er
-bo
g
i
e
R
o
l
l
ove
r
Stab
ility m
a
rg
in
Sup
p
o
r
t
po
lygo
n
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
:
Lu
is Carl
o
s
Velasco
Roj
a
s
Sch
ool
o
f
M
e
c
h
ani
cal
E
n
gi
ne
eri
n
g,
Northwestern Polytechnical Uni
v
ersity,
No
1
2
7
Yo
uy
i Xilu, Xi’a
n,
S
h
aa
nxi
Province
, P.
R. C
h
ina.
Em
a
il: v
e
lasco
.
lu
isc@g
m
ail.c
o
m
1.
INTRODUCTION
Th
ere is an
in
creasing
n
e
ed
for m
o
b
ile ro
bo
ts
wh
i
c
h
are ab
le to
o
p
e
rate in un
stru
ctured
envi
ro
nm
ent
s
wi
t
h
hi
ghl
y
u
n
e
ven t
e
rrai
n
. T
h
ese r
o
bot
s a
r
e
m
a
i
n
l
y
used
fo
r t
a
sks
w
h
i
c
h h
u
m
a
ns can
not
do
and
whi
c
h are
not
safe. I
n
o
r
de
r t
o
achi
e
v
e
t
h
ese t
a
sks, any
m
obi
l
e
ro
bot
nee
d
s t
o
h
a
ve a sui
t
a
bl
e m
obi
l
e
syste
m
accordi
n
g to eac
h sit
u
ation.
Am
ong these m
obile
syste
m
s, it’s the roc
k
er-b
ogi
e
sus
p
e
n
sion s
y
ste
m
that was fi
rst u
s
ed f
o
r the M
a
rs Ro
ver
So
jo
ur
ner a
n
d it’s
cur
r
ently
N
A
S
A
’s
fa
vo
red
de
sign
fo
r r
o
ver
wheel
sus
p
ensi
on.
The r
o
c
k
er
-b
o
g
i
e
sus
p
en
si
o
n
i
s
a
m
echani
s
m
t
h
at
, al
ong
wi
t
h
a di
f
f
ere
n
t
i
a
l
,
enabl
e
s a si
x-
wheel
e
d
vehi
cl
e t
o
pas
s
i
v
el
y
kee
p
al
l
si
x
w
h
eels in contact with
a surface
e
v
en
wh
en
d
r
iv
i
ng on
sev
e
r
e
ly un
ev
en
terrain. T
h
ere
are two key advanta
g
es to
this feature. T
h
e first adva
nta
g
e
is that the wheels' press
u
re
on the
g
r
ou
nd
will b
e
eq
u
ilib
rated
.
Th
is is ex
tremely i
m
p
o
r
tan
t
i
n
soft terrain
wh
ere ex
cessive g
r
oun
d
p
r
essu
re can
resu
lt i
n
th
e
v
e
h
i
cle sink
ing
i
n
to
t
h
e
driv
ing surface.
T
h
e
s
econd adva
ntage is t
h
at
whil
e clim
bing
ove
r
hard,
une
ve
n terrai
n
, all six wheels will nom
inall
y
re
m
a
in in
contact with the surface an
d under loa
d
,
helpi
ng t
o
pr
o
p
el
t
h
e veh
i
cl
e over t
h
e t
e
rrai
n
. Ex
pl
o
r
a
t
i
on r
ove
rs t
a
k
e
adva
nt
age
of
t
h
i
s
con
f
i
g
ura
t
i
on by
i
n
t
e
g
r
a
t
i
n
g
each wheel wit
h
a drive
act
uator,
m
a
xi
m
i
z
i
ng
the
vehicle's m
o
t
i
ve force
c
a
pability [1].
One
of t
h
e m
a
jo
r s
h
o
r
t
c
om
i
ngs o
f
c
u
r
r
ent
r
o
cke
r
-
b
ogi
e
ro
vers i
s
t
h
at
t
h
e
y
are sl
ow
. I
n
or
der t
o
be
ab
le to
ov
ercome sig
n
i
fican
tly ro
ugh
terrai
n
(i.e.,
o
b
s
tacl
es
m
o
re
than
a fe
w
pe
rcent of wheel
ra
dius
)
wi
thout
si
gni
fi
ca
nt
ri
sk
of fl
i
p
pi
n
g
t
h
e
vehi
cl
e o
r
da
m
a
gi
ng t
h
e s
u
s
p
en
si
o
n
, t
h
ese
ro
b
o
t
s
m
ove sl
owl
y
an
d cl
im
b o
v
e
r
the obstacles by having
whee
ls lift each
pie
ce of t
h
e s
u
spe
n
sion
ove
r the
obstacle
one
portion at a time [2].
Wh
ile p
e
rforman
ce on
rou
g
h
terrain
o
b
s
tacl
es is i
m
p
o
r
tan
t
, it sh
ou
ld
b
e
also
con
s
id
ered
situ
atio
n
s
wh
ere th
e
surface is
flat or it
has alm
o
st im
pe
rceptibl
e
obstacles, where t
h
e rover sh
oul
d inc
r
ea
se its spee
d to arri
ve
fast
er
fr
om
poi
nt
A
t
o
p
o
i
n
t
B
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
21
2 – 22
0
2
13
In t
h
i
s
pa
pe
r,
t
h
e aut
h
o
r
s
pr
o
pose m
odi
f
i
cat
i
ons i
n
t
h
e st
ruct
ure
of
t
h
e r
o
c
k
er
-b
ogi
e sy
st
em
in
creasing
t
h
e
sp
an
of t
h
e sup
port po
lygo
n
in
pursu
an
ce
of ach
i
ev
ing
a
g
r
eater stab
ility
m
a
rg
in
ov
er h
i
gh-
sp
eed
trav
ersal
witho
u
t
l
o
sing th
e
o
r
i
g
in
al con
f
i
g
uratio
n.
2.
R
E
SEARC
H M
ETHOD
NA
SA '
s
m
o
st
m
odern
ro
ve
r
,
t
h
e M
a
r
s
R
o
ver C
u
ri
osi
t
y
(
M
R
C
)
, gi
ves
us
pr
o
v
en i
n
f
o
rm
ati
on t
h
at
dem
onstrates the efficiency
of
roc
k
e
r
-
b
o
g
i
e
sy
st
em
s deal
i
ng
wi
t
h
obst
a
cl
es the size of the
diam
eter
of its
wh
eels, bu
t
mo
v
i
n
g
at an
averag
e sp
eed
b
e
lo
w 2
cm
/s to
en
su
re stab
ility ag
ain
s
t o
v
e
rt
u
r
n
i
ng
du
e to
su
dd
en
ch
ang
e
s i
n
th
e p
o
s
ition
o
f
the cen
ter
o
f
g
r
av
ity. Si
m
ilarl
y, stu
d
i
es
o
b
t
ain
e
d
with
th
e
MRC sh
ow that th
e
max
i
m
u
m
sp
eed
on
h
a
rd
, flat g
r
oun
d
is 4
c
m
/s, also
h
a
vin
g
as m
a
in
li
mit
i
n
g
cond
itio
n
t
h
e po
sition
of th
e
Co
G
and
its influ
e
n
ce
on
the stab
ility
m
a
rg
in
of th
e system
[3
].
Th
is is wh
ere
th
e qu
estion
th
at m
o
tiv
ates
th
is re
searc
h
a
r
ises: what ca
n be
done t
o
increase t
h
e
stab
ility o
f
th
e ro
ck
er-bog
ie syste
m
in
situ
atio
n
s
re
q
u
i
ring tran
sfers at h
i
g
h
sp
eed
?
Th
e p
r
op
o
s
ed
so
lu
t
i
o
n
is
th
e resu
lt fro
m
a p
r
ev
iou
s
stud
y o
f
th
e fact
ors th
at ru
le th
e stab
ility
o
f
an n
wh
eels v
e
h
i
cle, co
n
c
lud
i
ng
th
at
the area of the vehicle (wheel
s) that is in contact with
the ground has
gre
a
t influe
nce
on the displacement
of
th
e CoG and
therefo
r
e on
t
h
e
stab
ility
m
a
rg
in
o
f
th
e
v
e
h
i
cle.
In o
r
der t
o
p
r
e
s
ent
and a
n
al
y
ze t
h
e pro
p
o
se
d dy
na
m
i
c rocker-bogie syste
m
,
the criteria used and a
seri
es
of e
x
peri
m
e
nt
s an
d si
m
u
l
a
t
i
ons
are
p
r
esent
e
d
i
n
t
h
e
f
o
l
l
o
wi
ng
pa
rt
s
of
t
h
i
s
doc
um
ent
.
2
.
1
.
Sta
b
ility Ma
rg
in
Ap
pl
i
cat
i
ons
o
f
hi
g
h
-
s
pee
d
r
o
b
o
t
s
co
ver e
xpl
orat
i
o
n,
rec
o
n
n
ai
ssa
nce, a
nd m
a
t
e
ri
al
del
i
v
ery
,
b
o
t
h
mil
itary an
d
civ
ilian
.
Th
ese syste
m
s are d
e
sig
n
e
d
to
o
p
e
rate o
n
natu
ral
terrain th
at m
a
y b
e
sl
o
p
e
d
,
sl
ip
p
e
ry,
deform
able,
uneve
n
, flat
or hard. Un
fort
unately, these syste
m
s are susc
ep
tib
le to
ro
llov
e
r
wh
ile
m
o
vin
g
at
hi
g
h
spee
d o
r
per
f
o
r
m
i
ng severe m
a
neuve
r
s
, especi
al
l
y
in t
h
e r
o
ck
er
-b
ogi
e sy
st
em
,
whe
r
e i
t
s
desi
gn
wa
s
m
e
rely focuse
d on slow spee
d trave
r
sal ove
r
obstacles. De
spite the fact
t
h
at
m
a
ny
sy
st
em
s are desi
gne
d wi
t
h
rugged cha
ssis
(and s
o
m
e
ar
e designe
d to
be inve
rtible
), rollove
r accidents or a
b
r
upt
perturbations
in the
t
r
ans
f
er l
o
ad
o
f
t
e
n di
sa
bl
e t
h
e
ro
b
o
t
an
d/
o
r
da
m
a
ge i
t
s
pay
l
o
a
d
[4]
.
The Nat
i
o
nal
Hi
g
h
way
Tra
f
f
i
c Safet
y
Adm
i
ni
st
rat
i
on
(N
H
T
SA
) of t
h
e
D
e
part
m
e
nt
of Trans
p
ort
a
t
i
o
n
of
t
h
e
U
n
i
t
e
d
St
at
es g
ove
rn
m
e
nt
has
use
d
vari
ous
m
e
t
r
i
c
s an
d
dri
v
i
n
g
m
a
neuve
rs t
o
c
h
aract
eri
z
e
t
h
e
r
o
l
l
o
v
e
r
resistance
of vehicles in
parti
c
ular situations. Metr
i
c
s are
usu
a
l
l
y
m
easurem
ent
s
of
di
m
e
nsi
onal
,
m
a
ss an
d
in
ertial p
r
o
p
e
rties o
f
v
e
h
i
cles o
r
calcu
lation
s
co
m
b
in
ing th
ese p
r
o
p
e
rt
ies in
ways in
tend
ed
to
rep
r
esen
t
rol
l
o
ver
resi
st
a
n
ce. Ea
ch
o
f
t
h
ese i
ndi
cat
ors
of
r
o
l
l
ove
r
resi
st
ance ha
s
bot
h
ad
vant
a
g
es a
n
d
di
sad
v
ant
a
ge
s, an
d
several
would be acceptable
candi
dates for com
p
arative
sc
ientific inform
ation. Th
e
agency fa
vors static
stability factor because it is applicab
le t
o
both induced and accidental ro
llover. The causal
basis for its
good
correlation t
o
crash
outcomes is clear. It is rela
t
i
v
el
y
sim
p
l
e
t
o
un
de
rst
a
n
d
a
nd ca
n
be m
easur
e
d
in
exp
e
nsiv
ely with
g
ood
accuracy
and
rep
e
atab
ility
[5
].
The
Static Stability Factor
(SSF) of a
ve
hicle is
one
hal
f
the
track wi
dth,
T
W
,
divi
ded by
h, the
h
e
igh
t
o
f
th
e cen
ter of g
r
avity
ab
ov
e
th
e ro
ad
.
Th
e
in
e
r
tial force
whic
h ca
uses
a
ve
hicle to
sway
on its
su
sp
en
si
on
(
a
nd
ro
ll ov
er
in
extrem
e cases) in re
sponse t
o
c
o
rneri
n
g,
ra
pid
stee
rin
g
re
versals o
r
stri
k
i
ng
a
trip
p
i
n
g
m
ech
an
ism
,
lik
e a curb,
wh
en slid
ing
laterally m
a
y
b
e
tho
ugh
t
o
f
as a
force acti
n
g
at t
h
e C
o
G t
o
pu
l
l
t
h
e ve
hi
cl
e bo
dy
l
a
t
e
ral
l
y
. A red
u
ct
i
on i
n
C
o
G
hei
g
ht
increases th
e lateral in
ertia
l force necessa
ry to caus
e
rol
l
o
ver
by
red
u
ci
n
g
i
t
s
l
e
ver
a
ge, an
d t
h
e a
dva
nt
age i
s
re
prese
n
ted
by an increase i
n
the com
puted
value of
SSF.
A wi
der track wi
dth a
l
so increase
s
the lateral fo
rc
e necessary to cause rollove
r by increa
sing the
l
e
vera
ge o
f
t
h
e
ve
hi
cl
e'
s wei
ght
i
n
resi
st
i
n
g
r
o
l
l
ove
r, a
n
d t
h
at
adva
nt
age
al
so i
n
c
r
eases t
h
e com
put
ed
va
l
u
e o
f
SSF. T
h
e factor of two in the
com
putation "T
W
over
2h"
m
a
kes SSF equal to the lateral acceleration in g'
s
(g
-f
orce
) at
w
h
i
c
h r
o
l
l
o
ver
be
gi
ns
i
n
t
h
e m
o
st
sim
p
l
i
f
i
e
d r
o
l
l
over
anal
y
s
i
s
of
a
vehi
cl
e
re
prese
n
t
e
d
by
a
ri
gi
d
bo
dy
wi
t
h
o
u
t
s
u
sp
ensi
on
m
ovem
e
nt
or
t
i
r
e
d
e
fl
ect
i
ons
[
5
]
.
Th
is ap
pro
ach
will b
e
u
s
ed
to
p
e
rform
th
e stab
ility an
alysis o
f
th
e
p
r
op
osed
system
later i
n
Section 3
of
t
h
i
s
doc
um
ent
.
2.
2. Desi
gn M
o
di
fi
c
a
ti
o
n
s
In orde
r t
o
a
n
a
l
yze the proposed i
d
eas, the
Mars Ro
ve
r C
u
ri
osi
t
y
i
s
use
d
as
a
ge
om
et
r
i
cal
m
odel
t
o
desi
g
n
t
h
e s
u
g
g
est
e
d
dy
nam
i
c roc
k
er
-b
o
g
i
e
sy
st
em
. For sim
u
l
a
t
i
on pu
rp
oses t
h
e
di
m
e
nsi
o
ns o
f
t
h
e s
t
udi
e
d
ro
ver a
r
e desc
r
i
bed i
n
Fi
g
u
r
e 1. T
h
e l
a
t
e
ral
vi
ew s
h
o
w
s i
n
(a) an
d (
b
) t
h
e l
e
ngt
hs a
nd
hei
g
ht
s of t
h
e m
odel
,
wh
ile th
e top
view in
(c) sh
ows th
e ho
rizontal an
d
v
e
r
tical
distances bet
w
een the
wh
eels co
n
t
acts po
in
ts. All
the dim
e
nsions are expresse
d in centim
ete
r
s (cm
)
. Fi
nal
l
y
, an i
s
om
et
ric vi
ew o
f
t
h
e
3D C
A
D m
odel
i
s
showe
d
i
n
(d).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Dynamic Ro
cker-Bo
g
i
e: A
S
t
a
b
ility Enha
n
c
emen
t f
o
r
High-Sp
eed
Tra
versa
l (Ho
n
g
-
an
Ya
ng
)
21
4
(a)
(b
)
(c)
(d
)
Fi
gu
re
1.
Dy
na
m
i
c rocke
r
-
b
og
i
e
sim
u
l
a
t
i
on
m
odel
dim
e
nsi
ons
2.
2.
1.
D
y
n
a
mi
c B
o
gi
e M
o
di
f
i
cati
o
n
s
Ackno
wled
g
i
ng
th
at
on
e
way to
in
crease t
h
e stab
ility
m
a
rg
in
o
f
a rov
e
r
wi
th
ro
ck
er-bog
ie syste
m
is
to expand the
area in contact
with
th
e gro
u
n
d
(Su
ppo
rt Po
lyg
on), it's
necessary to anal
yze how to m
a
ke this
p
o
s
sib
l
e
with
ou
t co
m
p
letely alterin
g
t
h
e
o
r
i
g
in
al
o
p
e
ration sch
e
m
e
o
f
t
h
e
ro
ck
er-b
og
ie su
spen
si
o
n
.
As m
e
ntioned in Section 2.
1,
a sim
p
le but useful m
e
tric is
the Static Stabil
ity Factor (SSF), which i
s
co
m
p
u
t
ed
as the ratio
of th
e lateral po
sitio
n
o
f
th
e
v
e
h
i
cle
Co
G to
t
h
e
v
e
rtical p
o
s
itio
n (see Figu
re
2
)
.
Larg
er
values
of SSF
indicate greate
r
stability
. Phy
s
ically, the SSF corres
p
onds
to th
e lateral a
cceleration i
n
g’s t
h
at
causes
wheel lift-off for a
rigi
d
vehi
cle tr
av
er
sing
f
l
at g
r
oun
d [4
].
Fig
u
re
2
.
Static Stab
ility Factor
d
i
ag
ram
SSF =
T
W
/
2h
E
quation
1.
Sev
e
ral
m
e
tric
s
b
a
sed
on
g
e
o
m
etric
p
r
in
ci
p
l
es h
a
v
e
b
e
en
d
e
v
e
l
o
p
e
d
fo
r stab
ility
measu
r
em
en
t.
Research
ers in
m
o
b
ile rob
o
t
i
c
s h
a
v
e
reco
gn
ized
th
at th
e
lo
catio
n
o
f
t
h
e Co
G relativ
e to
th
e wh
eel–
t
errai
n
co
n
t
act po
in
ts
is critical to
v
e
h
i
cle stab
ility
[1
]. Th
e su
ppo
rt po
lygon
is d
e
fi
n
e
d
as t
h
e co
nv
ex
hu
ll o
f
the
p
o
l
ygon
fo
r
m
ed
b
y
w
h
eel
–
t
er
r
a
in
con
t
act p
o
i
n
t
s pr
oj
ected
on
to
a
hor
izon
tal p
l
an
e. A
n
ear
l
y g
e
ometr
i
c
m
easure de
fi
n
e
d st
abl
e
ve
hi
cl
e confi
g
u
r
at
i
ons as t
h
os
e where
the horiz
ontal
proj
ection of the ve
hicle CoG
lies with
in
th
is p
o
l
ygo
n. A stab
ility
marg
in
was th
en
defin
e
d
b
a
sed
o
n
th
e sh
ortest d
i
stan
ce from th
e
p
r
oj
ected
C
o
G
to
a si
d
e
o
f
t
h
e
p
o
l
ygon
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
21
2 – 22
0
2
15
Fi
gu
re
3.
S
u
p
p
o
rt
p
o
l
y
go
n
fo
r
a ge
ne
ral
r
o
b
o
t
In
th
is
app
r
o
a
ch
,
t
h
e robo
t’s n
wh
eel-terrain
co
n
t
act po
in
ts p
i
, i={1,…,l}
are
num
bere
d i
n
asce
nding
or
der
i
n
a cl
oc
kwi
s
e m
a
nne
r
whe
n
vi
ewe
d
f
r
om
abo
v
e, as
sho
w
n i
n
Fi
g
u
r
e
3. T
h
ese
p
o
i
n
t
s
f
o
rm
t
h
e n
ode
s o
f
a th
r
e
e-d
i
m
e
n
s
io
n
a
l sup
por
t
p
o
l
ygon
.
Th
e
lin
es jo
in
i
n
g t
h
e
w
h
eel
-
t
er
r
a
in
con
t
act
p
o
i
n
t
s ar
e r
e
f
e
rr
ed
to as
t
i
pove
r a
x
es a
n
d a
r
e
den
o
t
e
d
r
i
[4]
.
After an
an
aly
s
is, th
e au
tho
r
s in
trod
u
ce a
p
o
s
sib
l
e so
l
u
tio
n
th
at m
eets
th
e co
nd
ition
s
laid
d
o
w
n,
whi
c
h i
s
base
d
on a
ddi
ng a
ro
t
a
t
i
on axi
s
o
v
e
r
t
h
e Y
-
pl
a
n
e o
f
t
h
e b
o
g
i
e
sy
st
em
, vary
i
ng t
h
e y
a
w ori
e
nt
at
i
on
of
th
e bo
g
i
e, t
h
ereb
y alterin
g
t
h
e p
o
s
ition
of the o
u
t
er supp
ort p
o
l
ygon
po
in
t
s
an
d
i
n
creasi
n
g
th
e size of the area
in contact wit
h
the
ground
(Fi
g
ure
4).
(a)
(b
)
Fi
gu
re
4.
Dy
na
m
i
c bogi
e m
o
d
i
fi
cat
i
ons:
(a
)
R
o
cke
r
-
b
ogi
e
r
e
gul
a
r
c
o
n
f
i
g
ur
at
i
on,
(b
) R
o
cke
r
-
d
y
n
a
m
i
c bogi
e
hi
g
h
s
p
ee
d c
o
n
f
i
g
urat
i
o
n
The proposed
syste
m
include
s rotation m
o
tors for each
wheel that are in
charge
of the translation of
the rove
r, also, it uses an e
x
tra m
o
tor on
each wheel
to change its orientation and t
h
ere
f
ore c
h
ange the
o
r
ien
t
atio
n
o
f
th
e ro
v
e
r. In
ad
d
ition
it co
n
t
ro
ls th
e ad
d
e
d b
o
g
i
e ro
tatio
n ax
is with
a mo
tor th
at allo
ws the
m
ovem
e
nt
of e
ach
bo
gi
e
whe
n
i
t
’
s
nee
d
ed
.
Usi
n
g E
quat
i
o
n 1
,
di
f
f
ere
n
t
rot
a
t
i
o
n an
gl
es
abo
u
t the ne
w axis are a
n
alyzed, seeki
n
g to fi
nd a
sui
t
a
bl
e val
u
e
i
n
w
h
i
c
h t
h
e s
u
sp
ensi
on
p
r
o
v
i
d
e
d
by
t
h
e r
o
cke
r
-
b
ogi
e sy
st
em
i
s
not
co
m
p
rom
i
sed an
d t
h
e
expa
nsi
o
n of t
h
e c
ontact
polygon is
expa
nde
d ac
hieving
an
optim
al SSF (s
ee Table
1).
Tab
l
e 1
.
Static
Stab
ility
Facto
r
v
a
riatio
n
du
e to
in
crease o
f
su
ppo
rt po
lyg
on
area
Ro
ta
tio
n
deg
ree
TW [c
m]
h [c
m]
SSF
1 10.
0
295.
5
110.
0
1.
34
2 20.
0
309.
0
110.
0
1.
40
3 35.
0
338.
5
110.
0
1.
54
4 45.
0
340.
0
110.
0
1.
55
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Dynamic Ro
cker-Bo
g
i
e: A
S
t
a
b
ility Enha
n
c
emen
t f
o
r
High-Sp
eed
Tra
versa
l (Ho
n
g
-
an
Ya
ng
)
21
6
At first
glance
we ass
u
m
e
45 degrees as t
h
e
op
t
i
m
al
rot
a
t
i
on fact
or
i
n
t
h
e dy
nam
i
c
bo
gi
e
desi
g
n
because the c
r
iteria in Equation
1 s
h
ows
a favora
ble incr
e
a
se in the
SSF, conside
r
ing t
h
is rotation a
n
gle a
s
th
e
m
a
x
i
m
u
m
p
o
s
sib
l
e withou
t alterin
g
th
e
o
r
i
g
in
al rock
er-bog
ie p
e
rforman
ce. Th
ese v
a
lu
es will b
e
p
r
o
v
e
n
efficien
t later i
n
Section
3
of t
h
is
p
a
p
e
r.
Th
e
p
r
opo
sed Dyn
a
m
i
c rock
er-bog
ie (DRB) h
a
s a t
r
ad
itio
n
a
l con
f
ig
uratio
n with a rob
u
st
perform
a
nce when m
ovi
ng t
h
rough surf
aces with
obstacles, and
it also
ha
s the ability to
increase its c
o
ntact
poi
nts polygon whe
n
e
v
er
high-s
pee
d
tr
avers
a
l is needed. T
h
is cha
nge i
n
c
o
nfiguration
is accom
p
lished after
a
t
r
ans
f
o
r
m
a
ti
on
usi
ng t
h
e
dy
n
a
m
i
c bogi
e, achi
e
vi
n
g
a hi
g
h
-
spee
d m
ode:
One ro
cke
r
-
b
ogi
e sy
st
em
,
t
w
o m
odes
of
o
p
erat
i
o
n.
Fi
gu
re
5.
Dy
na
m
i
c rocke
r
-
b
og
i
e
t
r
ans
f
o
r
m
a
t
i
on
se
que
nce
Th
e tran
sfo
r
m
a
tio
n
sequ
en
ce th
at allo
ws th
e
DRB to switch
fro
m
a trad
itio
n
a
l
ro
ck
er-bog
ie
co
nf
igu
r
ation
t
o
th
e pr
opo
sed h
i
gh
-sp
e
ed
m
o
d
e
is d
e
scr
i
bed
in Figu
r
e
5,
w
h
er
e t
h
e ord
e
r
of
t
h
e seq
u
e
nce is
defi
ned
by
t
h
e
num
bers
sh
o
w
ed i
n
t
h
e
b
ody
of
t
h
e
ro
ve
r.
Th
e fi
rst step
in
th
e seq
u
e
n
c
e is to
stop
the fro
n
t
wh
eels lo
ck
i
n
g
t
h
e ro
v
e
r’s po
sition in
ord
e
r t
o
pr
ocee
d wi
t
h
t
h
e t
r
a
n
sf
orm
a
t
i
on st
e
p
s.
Ne
xt
t
h
e m
i
ddl
e an
d
rear
wheel
s
ro
t
a
t
e
90 d
e
g
r
ees
swi
n
gi
n
g
out
fr
om
t
h
e o
r
i
g
i
n
al
po
si
t
i
on.
Aft
e
r t
h
i
s
, t
h
e ex
pa
nsi
on
o
f
t
h
e
pol
y
g
o
n
s
u
pp
ort
be
gi
ns
by
spi
nni
ng t
h
e m
i
ddl
e wheel
s
to
ward
s th
e exterio
r
of th
e rov
e
r and
th
e rear wh
eels toward
s th
e in
teri
o
r
of it, at th
e
sam
e
t
i
m
e
th
e
m
o
to
rs
th
at co
n
t
ro
l th
e b
o
g
i
e ro
tation ax
is d
e
tect th
e ap
p
lied
fo
rce
b
y
th
e ro
tation o
f
wh
eels and start ro
tatin
g
th
e 45
degrees calc
u
l
a
ted in
Table
1.
Once the
45 de
grees
rotatio
n of t
h
e
bogi
e is com
p
leted, the
wheels re
turn t
o
th
eir
o
r
ig
i
n
al
po
sitio
n faci
n
g
fo
rward
,
and
t
h
e ro
v
e
r
is
ready to
start its
h
i
g
h
-sp
eed m
o
d
e
trav
ersal.
2.
2.
2.
Sup
por
t
Pol
y
gon
Exp
a
nsion
As it was ex
plain
e
d
befo
re i
n
th
is
p
a
p
e
r, t
h
e au
t
h
ors ai
m to
in
crease
th
e stab
ility
marg
i
n
of th
e
r
o
ck
er-b
og
ie syste
m
b
y
ex
p
a
n
d
i
n
g
its sup
p
o
r
t
p
o
l
ygon
con
s
id
er
ing
th
at’s i
m
p
o
r
tan
t
to p
r
eserv
e
th
e
n
a
tiv
e
sus
p
ensi
on perform
a
nce
o
f
the orig
in
al
d
e
si
g
n
of t
h
is system
.
There
f
ore,
onc
e t
h
e sy
st
em
has
rot
a
t
e
d i
t
s
b
ogi
es
4
5
de
grees
t
o
t
h
e
r
e
qui
red
hi
gh
-s
peed
m
ode
p
o
s
ition
,
th
e
rov
e
r’s sup
port po
lyg
o
n
is exp
a
n
d
e
d
reach
i
ng
a b
i
gg
er co
n
t
act area
as
showed
in Figure
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
21
2 – 22
0
2
17
(a)
(b
)
Fig
u
r
e
6
.
D
R
B
Supp
or
t
p
o
l
ygo
n exp
a
n
s
ion
:
(
a
)
R
o
ck
er-
bogie tr
ad
itio
n
a
l
ro
bu
st
ob
stacle tr
av
erse
co
nfigu
r
ation,
(b) R
o
ck
er-bo
g
ie h
i
gh
-
s
p
e
ed
t
r
av
er
sal co
nf
igu
r
ation
This expa
nsion of the conta
c
t area size sets the
ro
ve
r’s
C
o
G i
n
si
de a
bi
g
g
er t
r
ac
k b
a
se, m
a
ki
ng i
t
m
o
re rob
u
s
t again
s
t lo
ad transfers
du
e to
t
h
e in
teraction
of internal and
external fo
rces
suc
h
as
g-forc
es a
nd
in
ertia m
o
m
e
n
t
s.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
In
t
h
is section
o
f
t
h
e
do
cu
m
e
n
t
, th
e resu
lts
of th
e an
alysis
perfo
r
m
e
d
u
s
i
n
g th
e Static Stabilit
y Facto
r
(SSF) m
e
tric in
tro
d
u
c
ed
in [5
] are
presen
ted
,
showing
th
e stab
ility
m
a
rg
in
im
p
r
o
v
e
m
e
n
t
of t
h
e
h
i
gh
-sp
eed
m
o
d
e
co
m
p
ared
with
th
e trad
itio
n
a
l config
ur
at
i
on of
t
h
e r
o
c
k
er
-b
o
g
i
e
sy
st
em
.
Al
so, a m
odel
of t
h
e pr
o
p
o
s
ed sy
st
em
was devel
o
pe
d i
n
Sol
i
d
wo
rk
s,
and usi
ng i
t
s
m
u
l
t
i
body
dy
nam
i
c
m
o
t
i
on a
n
al
y
s
i
s
i
t
w
a
s p
o
ssi
bl
e t
o
a
p
p
r
eci
at
e t
h
e
p
e
rf
orm
a
nce o
f
bot
h m
odes
of
t
h
e dy
nam
i
c rocker
-
b
o
g
i
e system
, t
h
u
s
data ob
tained
o
f
th
is sim
u
latio
n
s
will b
e
co
n
t
rasted
with th
e SM
m
e
tric
resu
lts.
3
.
1
.
Sta
b
ility Moment
As explaine
d i
n
Section 2.2.1, the
propose
d syst
em
has two
operating
m
odes, each
with di
ffe
rent
SSF
values. The traditional
rocker-bogie
configuration
has
a narrowe
r
spa
n
in
its polygon support (see
Figure
7)
.
Fi
gu
re
7.
Dy
na
m
i
c rocke
r
-
b
og
i
e
t
r
adi
t
i
onal
r
o
b
u
st
ob
stacles trav
erse con
f
i
g
uration
So
lidworks m
o
d
e
l
The SSF calculation for the Dynam
i
c rocker-bogie tr
aditional robust obstacle
traverse configurati
on
was do
ne
as fo
l
l
o
ws:
T
W
=
285 cm
.
h
=
11
0 cm
.
SSF =
T
W
/
2h = 285 /
(2*110) =
1.
295.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Dynamic Ro
cker-Bo
g
i
e: A
S
t
a
b
ility Enha
n
c
emen
t f
o
r
High-Sp
eed
Tra
versa
l (Ho
n
g
-
an
Ya
ng
)
21
8
Fi
gu
re
8.
Dy
na
m
i
c rocke
r
-
b
og
i
e
hi
g
h
-s
pee
d
t
r
ave
r
sal
c
o
n
f
i
g
urat
i
o
n
Sol
i
d
w
o
r
k
s m
odel
Fo
llowing
th
e
sam
e
criteria, t
h
e
R
o
c
k
er
-
b
o
g
i
e hi
gh
-s
pee
d
t
r
ave
r
sal
co
n
f
i
g
urat
i
o
n (
s
ee Fi
gu
re
8)
was
subjecte
d
to the sam
e
SSF analysis:
T
W
=
340 cm
.
h
=
11
0 cm
.
SSF =
T
W
/
2h = 340 /
(2*110) =
1.
545.
These
res
u
lts s
h
ow t
h
at like e
xpect
e
d
, the
DRB design i
n
creases the
st
ab
il
ity
m
a
rg
in
o
f
t
h
e rov
e
r, b
y
a 16.
2% f
o
r t
h
e gi
ve
n di
m
e
nsi
o
ns o
f
t
h
e st
udi
e
d
m
odel
.
Thi
s
i
n
crease
can be det
e
r
m
i
n
ant
i
f
t
h
e
ro
ver i
s
m
ovi
ng at
hi
g
h
spee
d a
n
d i
t
e
n
co
u
n
t
e
rs a
n
o
b
st
acl
e t
o
o cl
o
s
e t
o
be a
v
oi
de
d.
3.2. Dynamic Roc
k
er-B
ogie Simulati
ons
As m
e
nt
i
oned
i
n
Sect
i
o
n 2
,
t
h
e M
a
rs R
o
ver
C
u
ri
o
s
ity has a
n
ave
r
a
g
e top s
p
eed
of 4
cm
/s
, which t
h
e
authors
consider not fa
st enough
whe
n
a
flat-ha
r
de
ne
d s
u
rface is
prese
n
t and the
rover nee
d
s t
o
re
ach
a
d
e
stin
ation
with
ou
t d
ealing
with
an
y sign
ifican
t ob
stacl
e, thus
, for the
realized sim
u
lations a highe
r
spee
d
co
nsid
ered
a feasib
le app
r
o
a
ch
to th
e
situ
atio
n of “h
igh
-
speed
trav
ersal” is u
s
ed
:
2
6
2
cm
/s.
In
t
h
is section
,
th
e resu
lts
o
f
th
e realized
si
m
u
l
a
t
i
ons are
pre
s
ent
e
d, a
n
al
y
z
i
ng an
d c
o
m
p
ari
ng t
h
e
disturba
nces i
n
the rover’s
Center of Gra
v
ity position
in each
of t
h
e two
operating
m
odes, cont
rasting the
resp
o
n
se o
f
t
h
e
s
e t
w
o di
f
f
ere
n
t
confi
g
uratio
ns o
f
th
e ro
ck
er-bog
ie syste
m
ag
ain
s
t triv
ial o
b
s
tacles th
at can
be
prese
n
t along t
h
e hi
gh-s
peed
traversa
l surfa
ce. The test track use
d
for
these expe
rim
e
nts is a 10x30
m
e
ters
p
l
atform
with
two
cylin
drical b
u
m
p
e
rs
with th
e h
e
igh
t
of
h
a
lf th
e
wh
eel’s. Th
e sim
u
la
ted
rov
e
r h
a
s
a to
tal
m
a
ss of 305
Kg.
Fi
gu
re
9.
Dy
na
m
i
c rocke
r
-
b
og
i
e
t
r
adi
t
i
onal
r
o
b
u
st
o
b
stacles trav
erse con
f
i
g
uration
So
lidworks sim
u
lati
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
21
2 – 22
0
2
19
Th
e first set o
f
ob
tain
ed
resu
lts sh
ows ho
w th
e rov
e
r’s Co
G ch
an
g
e
s p
o
s
ition
co
nstan
tly an
d
v
i
o
l
en
tly,
h
a
v
i
n
g
a t
o
ugh
im
p
act in
th
e
p
a
ylo
a
d an
d in
creasin
g
th
e po
ssi
bilit
ies o
f
h
a
v
i
ng
a ro
ll ov
er si
tu
atio
n
whi
l
e
m
ovi
ng
at
hi
gh
-s
peeds
and e
n
co
u
n
t
e
ri
n
g
a com
m
o
n
obstacle (rock, slope,
etc.) u
s
ing
th
e traditio
n
a
l
ro
ck
er-b
og
ie co
nfigu
r
ation
.
(See Figure
9
)
.
Fig
u
r
e
10
. D
yna
m
i
c
r
o
ck
er
-bog
ie
h
i
g
h
-
s
p
eed
trav
ersal con
f
i
g
uration
So
lidworks sim
u
lati
o
n
On
t
h
e
ot
her
si
de, t
h
e
resul
t
s of
t
h
e
hi
gh
-spee
d
t
r
ave
r
s
a
l
co
nfi
g
u
r
at
i
o
n s
h
ow
t
h
at
,
even
t
h
o
u
g
h
th
ere’s still co
n
s
tan
t
ch
ang
e
s in
th
e ro
v
e
r’s
Co
G
p
o
sitio
n
,
th
e i
m
p
act o
n
t
h
e p
a
ylo
a
d
it’s
m
o
re equ
a
lized
ov
er
ti
m
e
, n
o
t
h
a
v
i
n
g
th
e t
o
ugh
im
p
act seen
in
th
e trad
itio
n
a
l
ro
ck
er-bog
ie co
nfigu
r
ation, th
u
s
m
a
k
i
n
g
it
m
o
re
st
abl
e
i
f
i
t
e
n
c
o
u
n
t
e
rs
a c
o
m
m
on ob
st
acl
e (
r
oc
k,
sl
o
p
e,
et
c.)
w
h
i
l
e
m
ovi
ng
at
hi
g
h
-s
pe
ed
ove
r a
ha
r
d
-fl
at
t
e
n
surface.
W
i
t
h
the realized sim
u
lations,
the authors
are convi
nced that th
e pro
p
o
se
d
m
odi
fi
cat
i
ons o
n
t
h
e
trad
itio
n
a
l ro
ck
er-bog
ie d
e
si
g
n
m
a
k
e
a sig
n
ifican
t in
creas
e in
th
e rov
e
r’s
stab
ility in
situ
atio
n
s
wh
ere it n
eeds
to
m
o
v
e
thr
ough
d
i
stan
ces
ov
er
u
n
i
for
m
su
r
f
a
ces and
f
acing
tr
av
ersab
l
e
ob
stacles at an
y g
i
v
e
n ti
m
e
.
4.
CO
NCL
USI
O
N
Th
e p
r
esen
t p
a
p
e
r propo
sed
a
n
o
v
e
l d
e
sign
i
n
pursu
e of in
creasing
th
e
ro
ck
er-bog
ie m
o
b
ilit
y syste
m
beha
vior
whe
n
high-s
pee
d
tra
v
ersal is re
quired. T
h
is
situation was faced prese
n
ting
two
m
odes of ope
ration
un
de
r t
h
e
sam
e
w
o
r
k
i
n
g
pri
n
ci
pl
e,
a r
o
c
k
e
r
-
b
o
g
i
e
sy
st
em
with
a robust obstacles
tra
v
erse
features a
n
d a
n
ex
p
a
nd
ed
suppo
r
t
p
o
l
ygon
ach
i
ev
ed
b
y
r
o
tatin
g
th
e
b
o
g
i
es o
f
each
sid
e
o
f
t
h
e v
e
h
i
cle. Th
is in
cr
ease
in
th
e
stability
margin was prove
d
cont
rasting the
SSF m
e
tric w
ith the 3D m
odel sim
u
lations done in Soli
dworks
,
sh
owing
t
h
at at h
i
gh
-sp
e
ed
s t
h
e exp
a
nd
ed
sup
port po
l
ygo
n
eq
u
a
lizes t
h
e
paylo
a
d
tran
sfer stab
ilizin
g
it ag
ain
s
t
fi
erce c
h
a
nges
i
n
t
h
e
r
ove
r’s
c
e
nt
er
of
g
r
a
v
i
t
y
.
Ev
en
th
ou
gh
th
e r
obu
stn
e
ss ag
ai
nst
o
b
st
acl
es whi
l
e
m
ovi
ng at
hi
g
h
-sp
e
ed
s was sligh
tly in
creased,
the aut
h
ors s
u
gge
st furthe
r
research analyz
ing t
h
e
dy
nam
i
c beha
vi
o
r
of
every
m
e
m
b
er o
f
t
h
e
sy
st
em
t
o
co
n
tinu
e
rov
i
ng
th
e eff
i
cien
cy o
f
th
e pr
oposed
D
y
n
a
m
i
c
Ro
ck
er
-bo
g
i
e
syste
m
. A
l
so
, f
i
eld
exp
e
r
i
m
e
n
t
atio
n
u
s
ing
a pro
t
o
t
yp
e is
h
i
gh
ly sugg
ested in ord
e
r t
o
an
al
yze th
e
resu
lt
s ob
tain
ed
i
n
th
e calcu
lations and
sim
u
l
a
t
i
ons, a
n
d t
h
e
be
ha
vi
o
r
of
a real
m
odel
.
ACKNOWLE
DGE
M
ENTS
Th
e au
tho
r
s
wo
u
l
d
lik
e to
t
h
an
k all th
e st
ud
en
ts fro
m
th
e Schoo
l of Mech
an
ics th
at sup
ported
i
n
di
ffe
re
nt
way
s
t
o
t
h
e
de
vel
o
p
m
ent
of
t
h
i
s
pr
oject
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Dynamic Ro
cker-Bo
g
i
e: A
S
t
a
b
ility Enha
n
c
emen
t f
o
r
High-Sp
eed
Tra
versa
l (Ho
n
g
-
an
Ya
ng
)
22
0
REFERE
NC
ES
[1]
T. Thüer
,
Mobility eva
luation of
wheeled all-terrain robots
. Eidg
enössische Tech
nische Hochsch
u
le Zürich, Zur
i
ch
2009.
[2]
D. M
ill
er,
T.
L
ee,
High-Speed
Traversal of Ro
ugh Terrain
Using a
Rocker-Bogi
e Mob
ility S
y
stem
. Schoo
l o
f
Aerospace & M
echan
ical
Engin
eering
,
Univ
ersity
of Oklahoma,
USA 2001.
[3]
Jet Propultion
Laborator
y
,
NASA. URL:
http:/
/m
ars.jp
l
.
nasa.gov/m
s
l/m
ultim
edia/int
e
ract
ives/learncur
iosi
t
y
/
Visited on
April
2014.
[4]
S.
Pe
te
rs,
K.
Ia
gne
mma
,
An Anal
y
s
is of Rollov
e
r S
t
abili
ty M
e
as
urement for High-S
p
eed Mobile Ro
bots.
Departmen
t
of Mechan
ical
Engineer
ing,
Massachusetts Institute of
Technolo
g
y
, Cambridg
e 2
006.
[5]
National Highway
Traf
fic Safe
ty Admi
ni
st
ra
t
i
o
n. URL
:
http://www.nhtsa.gov/cars/rules/rulings/Rollo
v
e
r
/
Chapt05
.
html V
i
sited
on April 2
014.
BIOGRAP
HI
ES OF
AUTH
ORS
Hong-an Yang,
Ph.D, is an Associate Professor
in
the Schoo
l of
Mechanical En
gineer
ing at the
Northwestern Pol
y
te
chnic
a
l Universit
y
. He r
e
c
e
ived his
P
h
.D.
with a m
a
jor in M
echani
cal
Manufactur
ing and Autom
a
tion in 2004. He was
a vis
iting scholar in the Universi
t
y
of Tex
a
s at
San Antonio, U
S
A from Feb 20
10 to Feb 2011
. Dr.
Yang specializes in
the stu
d
y
of
stochastic
simulation op
timization prob
lems
, mobile robotic
ve
hicles and
job
shop scheduling
problems.
Luis Carlos Vel
a
sco Rojas, M.Sc, is an El
ect
ron
i
c Engin
eer grad
uated from
the Militar
y
Schoo
l
of Engin
eering
in L
a
Paz
,
Bo
li
via.
His rese
arc
h
fie
l
d is b
i
om
im
etics with
a s
p
eci
ali
zat
ion in
swarm robotics and unmanned vehicl
es. Mobile r
obotics has alway
s
been h
i
s passion, and this is
wh
y
he’s
curre
ntl
y
cours
i
ng a
M
a
s
t
ers
Degree program
in the field of M
ech
atroni
cs
at the
Northwestern Pol
y
technical Uni
v
ersit
y
,
res
ear
ch
ing innovative
m
obilit
y
s
y
st
em
s for unm
anned
vehicles and
swarm behavior
alg
o
rithms for multirobot s
y
s
t
ems.
Changkai
Xia, M.Sc, comes
fro
m Mechanical and
Electronic
Eng
i
neer
ing, Northwestern
P
o
l
y
t
echni
ca
l
Univers
i
t
y
,
Chi
n
a. His
a
r
eas
of res
ear
ch in
t
e
res
t
are robo
t
i
cs
,
autom
a
tion
manufacturing
,
and stochastic
sim
u
lation o
p
tim
izat
ion.He
hol
ds
a bach
el
or's
degr
ee in
Mechanism design, manufactur
ing and automati
zation. Durin
g
his undergraduate, he also
finishes some se
condar
y
dev
e
lop
m
ents to 3D de
sign software. Recently
, h
e
works on a variety
of
control of robo
tics and p
r
ojects,
which ar
e
closel
y
rel
a
ted
to
stoc
hastic
sim
u
lation
optim
iz
ation
.
Qiang Guo, M
.
S
c
.
,
com
e
s
fr
om
M
echanic
al
and El
ec
troni
c Engin
eering
,
Northwes
tern
P
o
l
y
t
echni
ca
l
Univers
i
t
y
,
Chi
n
a. His
a
r
eas
of res
ear
ch in
t
e
res
t
are robo
t
i
cs
,
autom
a
tion
manufacturing
,
and
stochastic
simulation op
timization.
He holds a bachelor
'
s
degree in Mechanical
engineer
ing and
automation
.
He is working on
design of mechanical structur
e, robot control,
and a variety
of simu
lation optimizations From
undergraduate to
now.
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