ArticlePDF Available

Stable AGV corridor navigation based on data and control signal fusion

Authors:

Abstract

This work presents a control strategy for mobile robots navigating in corridors, using the fusion of the control signals from two redundant or homogeneous controllers: one based oil optical flow calculation and the other based on the estimates of position of the robot with respect to the centerline of the corridor, which is estimated using data from ultrasonic and vision sensors. Both controllers generate angular velocity commands to keep the robot navigating along the corridor, compensating for the dynamics of the robot. The fusion of both control signals is done through a Decentralized Information Filter. The stability of the resulting control system is analyzed. Experiments oil a laboratory robot are presented to show the feasibility and performance of the proposed control system.
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
6WDEOH$*9&RUULGRU1DYLJDWLRQEDVHGRQ'DWDDQG&RQWURO6LJQDO)XVLRQ
5LFDUGR&DUHOOL&DUORV6RULD(GXDUGR)UHLUH
,QVWLWXWRGH$XWRPiWLFD± 8QLYHUVLGDG1DFLRQDOGH6DQ-XDQ
$Y6DQ0DUWtQ2HVWH6DQ-XDQ$UJHQWLQD
^UFDUHOOLFVRULD`#LQDXWXQVMHGXDU
&HQWURGH&LrQFLDV([DWDVH7HFQRORJLD8QLYHUVLGDGH)HGHUDOGH6HUJLSH
$Y0DUHFKDO5RQGRQ61-DUGLP5RVD(O]H6mR&ULVWRYmR6(%UDVLO
$EVWUDFW7KLV ZRUN SUHVHQWV D FRQWURO VWUDWHJ\ IRU
PRELOHURERWV QDYLJDWLQJLQ FRUULGRUVXVLQJWKHIXVLRQRI
WKH FRQWURO VLJQDOV IURP WZR UHGXQGDQW RU KRPRJHQHRXV
FRQWUROOHUV RQH LV EDVHG RQ WKH RSWLFDO IORZ FDOFXODWLRQ
DQG WKH RWKHU LV EDVHG RQ WKH SRVLWLRQ RI WKH URERW ZLWK
UHVSHFW WR WKH FHQWHUOLQH RI WKH FRUULGRU ZKLFK LV
HVWLPDWHGXVLQJWKHGDWDIXVLRQIURPXOWUDVRQLFDQGYLVLRQ
VHQVRUV  %RWK FRQWUROOHUV JHQHUDWH DQJXODU YHORFLW\
FRPPDQGV WR NHHS WKH URERW QDYLJDWLQJ DORQJ WKH
FRUULGRU DQG FRPSHQVDWH IRU WKH G\QDPLFV RI WKH URERW
7KH IXVLRQ RI ERWK FRQWURO VLJQDOV LV GRQH WKURXJK D
'HFHQWUDOL]HG ,QIRUPDWLRQ )LOWHU 7KH VWDELOLW\ RI WKH
UHVXOWLQJ FRQWURO V\VWHP LV DQDO\]HG ([SHULPHQWV RQ D
ODERUDWRU\URERWDUH SUHVHQWHGWRVKRZWKHIHDVLELOLW\DQG
SHUIRUPDQFHRIWKHSURSRVHGFRQWUROV\VWHP
.H\ZRUGVVHQVRUIXVLRQPRELOH URERWDUWLILFLDO YLVLRQ
QRQOLQHDUFRQWURO
,,1752'8&7,21
$PDLQ FKDUDFWHULVWLFRI$XWRQRPRXV1DYLJDWLRQLV
LWV FDSDELOLW\ RI FDSWXULQJ HQYLURQPHQW LQIRUPDWLRQ
WKURXJK H[WHUQDO VHQVRUV VXFK DV YLVLRQ GLVWDQFH RU
SUR[LPLW\ VHQVRUV $OWKRXJK GLVWDQFH VHQVRUV HJ
XOWUDVRXQG DQG ODVHU W\SHV ZKLFK DOORZ WR GHWHFW
REVWDFOHVDQG PHDVXUHGLVWDQFHVWRZDOOVDQGREVWDFOHV
QHDU WKH URERW DUH WKH PRVW XVXDO VHQVRUV DW SUHVHQW
YLVLRQ VHQVRUV DUH LQFUHDVLQJO\ XVHG EHFDXVH WKH\
UHQGHU D JUDWHU DPRXQW RI LQIRUPDWLRQ IURP YLVXDO
LPDJHV
:KHQ DXWRQRPRXV PRELOH URERWV QDYLJDWH ZLWKLQ
LQGRRU HQYLURQPHQWV HJ SXEOLF EXLOGLQJV RU
LQGXVWULDO IDFLOLWLHV WKH\ VKRXOG EH HQGRZHG WKH
FDSDELOLW\ WR PRYH DORQJ FRUULGRUV WR WXUQ DW FRUQHUV
DQG WR FRPH LQWR URRPV $V UHJDUGV PRWLRQ DORQJ
FRUULGRUVVRPHFRQWURODOJRULWKPVKDYHEHHQ SURSRVHG
LQ YDULRXV ZRUNV ,Q %HPSRUDG HW DO  D
JOREDOO\ VWDEOH FRQWURO DOJRULWKP IRU ZDOOIROORZLQJ
EDVHGRQLQFUHPHQWDO HQFRGHUVDQG RQHVRQDU VHQVRULV
GHYHORSHG,Q9DVDOORHW DO LPDJH SURFHVVLQJ
LVXVHGWRGHWHFWSHUVSHFWLYHOLQHVDQGWRJXLGHWKHURERW
IROORZLQJWKHFRUULGRUFHQWHUOLQH7KLVZRUNDVVXPHVDQ
HOHPHQWDU\ FRQWURO ODZ DQG GRHV QRW SURYH FRQWURO
VWDELOLW\ ,Q <DQJ 7VDL  FHLOLQJ SHUVSHFWLYH
OLQHVDUHHPSOR\HGIRUURERWJXLGDQFHEXWLWDOVRODFNV
DGHPRQVWUDWLRQRQV\VWHPVWDELOLW\2WKHUDXWKRUVKDYH
SURSRVHG WR XVH WKH WHFKQLTXH RI RSWLFDO IORZ IRU
FRUULGRU FHQWHUOLQH JXLGDQFH 6RPH DSSURDFKHV
LQFRUSRUDWHWZRYLGHR FDPHUDV RQWKHURERW VLGHV DQG
WKH RSWLFDO IORZ LV FRPSXWHG WR FRPSDUH WKH DSSDUHQW
YHORFLW\RILPDJH SDWWHUQVIURPERWK FDPHUDV6DQWRV
9LFWRUHWDO  ,Q'HYHW DOD FDPHUD LV
XVHGWRJXLGH D URERWDORQJD FRUULGRU FHQWHUOLQH RUWR
IROORZD ZDOO,Q 6HUYLFHW DO SHUVSHFWLYHOLQHV
DUH XVHG WR ILQG WKH DEVROXWH RULHQWDWLRQ ZLWKLQ D
FRUULGRU ,Q &DUHOOL HW DO  WKH DXWKRUV KDYH
SURSRVHGWKH IXVLRQRIWKHRXWSXWVRIWZRYLVLRQEDVHG
FRQWUROOHUVXVLQJD .DOPDQ)LOWHU LQRUGHUWR JXLGHWKH
URERW DORQJ WKH FHQWHUOLQH RI D FRUULGRU 2QH RI WKH
FRQWUROOHUV LV EDVHG RQ RSWLFDO IORZ DQG WKH RWKHU LV
EDVHG RQ WKH SHUVSHFWLYH OLQHV RI WKH FRUULGRU 7KLV
ZRUN SUHVHQWV D VWDELOLW\ DQDO\VLV IRU WKH SURSRVHG
FRQWUROV\VWHP
,Q JHQHUDO WKH ZRUNV SUHYLRXVO\ FLWHG KDYH QRW
LQFOXGHGD VWDELOLW\DQDO\VLVIRUWKHFRQWUROV\VWHP2Q
WKH RWKHU KDQG WKH SHUIRUPDQFH RI WKH FRQWURO V\VWHP
GHSHQGV RQ  HQYLURQPHQW FRQGLWLRQV VXFK DV
LOOXPLQDWLRQVXUIDFHWH[WXUHVSHUWXUEDWLRQVIURPLPDJH
TXDOLW\ORVV DQGRWKHUIDFWRUVDOORIZKLFKUHVXOWLQJ LQ
WKDW HDFK LQGLYLGXDO FRQWUROOHU GRHV QRW UHDFK
DFFHSWDEOH UREXVWQHVV SURSHUWLHV $ VROXWLRQ IRU WKLV
SUREOHP LV WR FRQVLGHU PXOWLSOH FRQWUROOHUV EDVHG RQ
GLIIHUHQW VHQVLQJ LQIRUPDWLRQ ZKLFK RSHUDWH
VLPXOWDQHRXVO\ $OWKRXJK KDYLQJ WKH VDPH FRQWURO
REMHFWLYHVWKHFRQWUROOHUVFDQEHFRRUGLQDWHGXVLQJWKH
FRQFHSW RI EHKDYLRU FRRUGLQDWLRQ 3LUMDQLDQ 
:LWKWKLVFRQFHSWWKHFRPPDQGIXVLRQVFKHPHVDFFHSW
DVHW RIEHKDYLRU LQVWDQFHVWKDW VKDUHWKH FRQWURORI WKH
HQWLUHV\VWHPDWDOOWLPHV
&RPPDQG IXVLRQ VFKHPHV FDQ EH FODVVLILHG LQWR
IRXU FDWHJRULHV YRWLQJ HJ '$01 5RVHQEODWW
VXSHUSRVLWLRQHJ$X5$$UNLQHWDO
0XOWLSOH 2EMHFWLYH HJ 0XOWLSOH 'HFLVLRQ0DNLQJ
&RQWURO 3LUMDQLDQ  DQG )X]]\ /RJLF HJ
0XOWLYDOXDWHG /RJLF $SSURDFK 6DIILRWWL HW DO 
$QRWKHU H[DPSOH RI D FRPPDQG IXVLRQ VWUDWHJ\ LV WKH
G\QDPLF DSSURDFK WR EHKDYLRUEDVHG URERWLFV %LFKR
 ,Q WKLV SDSHU ZH FRQVLGHU WKH FRPPDQG IXVLRQ
VWUXFWXUHSUHYLRXVO\ SURSRVHGE\WKHDXWKRUVLQ)UHLUH

7KHSUHVHQWZRUNLVDFRQWLQXDWLRQRI&DUHOOLHWDO
 7KHUH WZR UHGXQGDQW YLVLRQEDVHG FRQWURO
DOJRULWKPV ZHUH XVHG DV PHQWLRQHG EHIRUH RQH RI
WKHP EDVHG RQ RSWLFDO IORZ FDOFXODWLRQ DQG WKH RWKHU
EDVHG RQ WKH SHUVSHFWLYH OLQHV RI WKH FRUULGRU ,Q WKH
SUHVHQW ZRUN WKLV ODVW FRQWUROOHU ZDV UHSODFHG E\
DQRWKHU RQH ZKLFK ILQGV WKH SHUVSHFWLYH OLQHV RI WKH
ZDOOVPHHWLQJ WKHIORRUDQGIXVHVWKLV LQIRUPDWLRQZLWK
WKH GDWD REWDLQHG IURP XOWUDVRQLF VHQVRUV WR HVWLPDWH
ROB_09
945
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
WKHURERWSRVLWLRQZLWK UHVSHFW WR WKHFHQWHUOLQHRI WKH
FRUULGRU%DVHGRQWKLVLQIRUPDWLRQDFRQWUROOHULVXVHG
WRJHQHUDWHWKHDQJXODUYHORFLW\FRPPDQGIRUWKHURERW
7KH OLQHDU YHORFLW\ RI WKH URERW PD\ HLWKHU EH NHSW
FRQVWDQWRU EHFRQWUROOHG LQRUGHU WRDFKLHYH DVPRRWK
DQG FDXWLRXV QDYLJDWLRQ %RWK FRQWUROOHUV DUH
UHGXQGDQW EHFDXVH WKH\ KDYH WKH VDPH FRQWURO
REMHFWLYH 7KH\ DUH EDVHG KRZHYHU RQ GLIIHUHQW
SULQFLSOHVZKLFKWXUQGLIILFXOWWKHLU IXVLRQDWVHQVRULDO
OHYHO+HUHZHSURSRVH D IXVLRQ RI ERWKFRPPDQGV WR
DWWDLQ D FRQWURO VLJQDO WKDW DOORZV D UREXVW QDYLJDWLRQ
DORQJ FRUULGRUV )RU IXVLRQ ZH HPSOR\ D FRQWURO
DUFKLWHFWXUH YLD FRQWURO RXWSXW IXVLRQ DV SURSRVHG LQ
)UHLUHHPSOR\LQJ D 'HFHQWUDOL]HG,QIRUPDWLRQ
)LOWHU±',)±WKDW PLQLPL]HV WKHXQFHUWDLQW\OHYHO LQ
ERWKFRQWUROOHUV7KLVXQFHUWDLQW\LV HYDOXDWHGLQ WHUPV
RIWKH VHQVLQJHUURU DQGWKHHQYLURQPHQWFRQGLWLRQVE\
PHDQV RI D FRYDULDQFH IXQFWLRQ IRU HDFK FRQWUROOHU $
VWDELOLW\ DQDO\VLV RI WKH UHVXOWLQJ FRQWURO V\VWHP LV
SUHVHQWHGDVZHOO7KHZRUNDOVRLQFOXGHV H[SHULPHQWDO
UHVXOWV RQD3LRQHHU '; ODERUDWRU\ URERW QDYLJDWLQJ
WKURXJK WKH FRUULGRUV DW WKH ,QVWLWXWH RI $XWRPDWLFV
1DWLRQDO8QLYHUVLW\RI6DQ-XDQ$UJHQWLQD
,,52%27$1'&$0(5$02'(/6
$5RERW0RGHO
)LJ&RRUGLQDWHV\VWHPV
)LJUHSUHVHQWVWKH FRRUGLQDWH V\VWHPVDVVRFLDWHG
WRWKH URERWDQG WKHHQYLURQPHQW DZRUOG V\VWHP>:@
DV\VWHP>5@IL[HGWR WKHURERW DQGDV\VWHP>&@IL[HG
WRWKHYLVLRQFDPHUD&RQVLGHULQJ)LJWKHNLQHPDWLFV
PRGHO RI D XQLF\FOH W\SH URERW FDQ EH H[SUHVVHG DV
'L[RQHWDO
°
¯
°
®
T
Z
T
T
VLQ
Y
\
Y
[

ZKHUH
Z
LV WKH DQJXODU YHORFLW\ DQG
Y
WKH OLQHDU
YHORFLW\RIWKHURERW
RU
:
[
[
{

RU
:
\
\
{
,Q RUGHU WR FRPSHQVDWH IRU YHKLFOH G\QDPLFV WKH
G\QDPLF PRGHO RI WKH URERW ZDV REWDLQHG
H[SHULPHQWDOO\E\VWHSFRPPDQGUHVSRQVH DQDO\VLV2I
SDUWLFXODU LQWHUHVW LV WKH PRGHO UHODWLQJ
\
5
Z
Z
o

ZKHUH
5
Z
LV WKH UHIHUHQFH DQJXODU YHORFLW\ JHQHUDWHG
E\ WKH FRQWUROOHU DQG VHQW WR WKH URERW DQG
\
Z
LV WKH
PHDVXUHGDQJXODUYHORFLW\RI WKH URERW 7KH LGHQWLILHG
PRGHOLVDSSUR[LPDWHO\UHSUHVHQWHG E\DVHFRQGRUGHU
OLQHDUPRGHO
5
\
D
V
E
V
D
N
Z
Z
Z
Z
Z
Z

ZLWK

Z
N


Z
D


Z
E

)LJ3HUVSHFWLYHSURMHFWLRQFDPHUDPRGHO
%&DPHUD0RGHO
$ SLQKROH PRGHO IRU WKH FDPHUD LV FRQVLGHUHG 7KH
IROORZLQJ UHODWLRQVKLS FDQ EH LPPHGLDWHO\ REWDLQHG
IURP)LJ
]
S
F
S
U
O
D

ZKHUH
U
LV WKH SURMHFWLRQ RI D SRLQW
S
RQ WKH LPDJH
SODQH
O
LVWKH IRFDOOHQJWK RIWKH FDPHUDDQG
D
LVD
VFDOHIDFWRU
&'LIIHUHQWLDO&DPHUD5RERW0RGHO
7KLVVXEVHFWLRQSUHVHQWVWKHNLQHPDWLFVUHODWLRQVKLS
RI WKH FDPHUD PRXQWHG RQ WKH PRYLQJ URERW HYROYLQJ
ZLWK OLQHDU YHORFLW\
Y
DQG DQJXODU YHORFLW\
Z
 7KH
&RULROLVHTXDWLRQUHQGHUV WKH PRWLRQ RIDSRLQW 3LQ D
FRRUGLQDWH V\VWHP ZLWK WUDQVODWLRQDO DQG URWDWLRQDO
PRWLRQ9DQG
:
3
9
3
u
:

%\ WLPHGHULYLQJ  DQG XVLQJ ERWK  DQG  WKH
FRPSRQHQWVRI
U
RQWKHLPDJHSODQHDUHIRXQGDV
\
]
[
\
\
[
[
]
]
[
[
[
U
U
U
U
3
9
U
9
U
Z
O
O
Z
O
Z
O

[
]
\
[
\
\
[
]
]
\
\
\
U
U
U
U
3
9
U
9
U
Z
O
Z
O
O
Z
O

)RU WKH FDPHUD PRXQWHG RQ WKH URERW¶V FHQWHU DQG
SRLQWLQJIRUZDUG
\
[
9
9
DQG
]
[
Z
Z
%HVLGHV
E\ FDOOLQJ
]
9Y

\
Z
Z
  DQG  FDQ EH ZULWWHQ
DV
O
O
Z
[
]
F
[
[
U
S
Y
U
U
\
[
\
]
F
\
\
U
U
S
Y
U
U
O
Z

ZKLFK UHSUHVHQW WKH GLIIHUHQWLDO NLQHPDWLFV HTXDWLRQV
IRUWKHFDPHUDPRXQWHGRQWKHURERW
'0RGHOIRUWKHSHUVSHFWLYHOLQHV
7KH SRVLWLRQ DQG RULHQWDWLRQ RI WKH URERW FDQ EH
REWDLQHGIURPWKHSURMHFWLRQRI WKHSHUVSHFWLYHOLQHVLQ
ROB_09
946
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
WKH FRUULGRU RQ WKH LPDJH SODQH 7KH SDUDOOHO OLQHV
UHVXOWLQJ IURP WKH LQWHUVHFWLRQ RI FRUULGRU ZDOOV DQG
IORRU DUH SURMHFWHG RQWR WKH LPDJH SODQH DV WZR OLQHV
LQWHUVHFWLQJDWWKHVRFDOOHGYDQLVKLQJSRLQW
$ SRLQW
S
LQ WKH JOREDO IUDPH >:@ FDQ EH
H[SUHVVHG LQ WKH FDPHUD IUDPH >&@ DV
RF
5
5
&
RU
:
:
:
&
&
S
5
S
S
5
S
ZKHUH
»
»
»
¼
º
«
«
«
¬
ª
VLQ
FRV
FRV
VLQ
J
J
J
J
5
&
5
DQG
VLQ
FRV
FRV
FRV
VLQ
FRV
VLQ
FRV
VLQ
VLQ
VLQ
FRV
»
»
¼
º
«
«
¬
ª
J
J
T
J
T
J
J
T
J
T
T
T
:
&
5
ZLWK
J
WKHFDPHUDWLOWDQJOHDQG
T
WKHURERWKHDGLQJ
&RQVLGHULQJ WKH FRPSRQHQWZLVH H[SUHVVLRQV IRU
WKHSLQKROHFDPHUDPRGHO
]
&
\
&
\
\
]
&
[
&
[
[
S
S
U
S
S
U
O
D
O
D

DQ\SRLQWLQWKHJOREDOFRRUGLQDWHV\VWHPLVUHSUHVHQWHG
LQ WKH LPDJH SODQH DV D SURMHFWLRQ SRLQW ZLWK
FRRUGLQDWHV
K
S
S
S
S
S
S
S
S
U
\RU
:
\
:
\RU
:
\
:
[RU
:
[
:
[RU
:
[
:
[
[
VLQ

VLQ
FRV

VLQ

FRV
VLQ

FRV
J
J
T
T
J
T
T
O
D

K
S
S
K
S
S
S
S
S
S
U
\RU
:
\
:
\RU
:
\
:
[RU
:
[
:
[RU
:
[
:
\
\
VLQ

VLQ
FRV
FRV

VLQ
FRV

FRV
VLQ

VLQ
VLQ
J
J
T
J
J
T
J
T
J
T
O
D

)LJ*XLGHOLQHVLQWKHFRUULGRU
1RZ FRQVLGHU WKH SRLQWV
>
@
7
X

>
@
7
X

>
@
7
G
X
>
@
7
G
X
WKDW
GHILQHWKHLQWHUVHFWLRQ OLQHV
X
X
U
DQG
X
X
U
EHWZHHQ FRUULGRU ZDOOV DQG IORRU DV LOOXVWUDWHG LQ )LJ
 %DVHG RQ  DQG  WKH IROORZLQJ UHODWLRQVKLSV
DUH REWDLQHG IRU WKHVORSH RI WKHSHUVSHFWLYHOLQHV WKH
YDQLVKLQJSRLQWFRRUGLQDWHVDQGWKHLQWHUVHFWLRQRIERWK
OLQHVZLWKWKHKRUL]RQWDOD[LVLQWKHLPDJHSODQH)LJ
VLQ
VLQ
FRV
FRV
K
S
K
P
[RU
:
[
\
J
T
J
T
D
D

VLQ
VLQ

FRV
FRV
K
G
S
K
P
[RU
:
[
\
J
T
J
T
D
D

FRV
WDQ
J
T
O
D
[
Y
[

WDQ
J
O
D
\
Y
\

FRV

VLQ
FRV
VLQ
T
J
J
T
O
D
K
S
K
P
E
[RU
:
[

FRV
FRV
VLQ
VLQ
T
J
T
J
O
D
K
K
S
G
P
E
[RU
:
[

,,,'$7$)86,21
$'DWDIURP8OWUDVRQLF6HQVRUV
7KH FRQWUROOHU EDVHG RQ WKH SRVLWLRQ RI WKH URERW
ZLWKUHVSHFWWRWKHFHQWHUOLQH RIWKHFRUULGRULVUHTXLUHG
WREHEDFNIHGZLWKWKHYDOXHVRIVWDWHV
a
W[
DQG
W
T
DWHDFKLQVWDQW7KHVHYDOXHVFDQDOVREHREWDLQHGIURP
VRQDU PHDVXUHPHQWV )LJ  VKRZV D W\SLFDO VLWXDWLRQ
ZKHUHODWHUDOVRQDUVHQVRUV666DQG6DUHXVHG
)RUWKLVFDVHWKHIROORZLQJHTXDWLRQVDOORZFDOFXODWLQJ
WKHVWDWHYDULDEOHV

6
6
6
6
\
\
GULJKW
\
\
GOHIW


6
6
6
6
\
\
\
\
GLII

a
VLQ
GOHIW
GULJKW
[
G
GLII
¸
¹
·
¨
©
§
T

6RQDU PHDVXUHPHQWV PD\ GHWHULRUDWH RU EH
LPSRVVLEOHWRREWDLQXQGHUFHUWDLQFLUFXPVWDQFHVOLNH
IRU H[DPSOH ZKHQ WKH URERW LV WUDYHOLQJ E\ DQ RSHQ
GRRULQWKHFRUULGRURUZKHQWKHURERWKDVDVLJQLILFDQW
DQJOH RI GHYLDWLRQ IURP WKH FRUULGRU D[LV 7KH ODWWHU
FRQGLWLRQ RULJLQDWHV IURP WKH IDFW WKDW D VRQDU VHQVRU
FROOHFWVXVHIXOGDWD RQO\ ZKHQLWVGLUHFWLRQ RUWKRJRQDO
WRWKHUHIOHFWLQJVXUIDFH OLHV ZLWKLQWKHEHDP ZLGWK RI
)LJ&DOFXODWLRQRIVWDWHYDULDEOHVIURPGLVWDQFHPHDVXUHPHQWV
ROB_09
947
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
WKHUHFHLYHUWKXVDOORZLQJIRUZDOOGHWHFWLRQRQO\IRUD
UHVWULFWHG KHDGLQJ UDQJH %HPSRUDG HW DO  7KH
UDQJH IRU WKLV DQJOH LV DSSUR[LPDWHO\

M
IRU WKH
HOHFWURVWDWLF VHQVRUV LQ WKH URERW XVHG LQ WKH
H[SHULHQFHV2QWKLVDFFRXQWLWLVLPSRUWDQWWRFRQVLGHU
RWKHUPHDVXUHPHQWVDVZHOOVXFKDVWKHRGRPHWULFGDWD
SURYLGHG E\ WKH URERW 7KH IXVLRQ RI WKHVH GDWD XVLQJ
RSWLPDO ILOWHUV SURGXFHV RSWLPDO HVWLPDWLRQV RI WKH
URERW VWDWHV WKXV PLQLPL]LQJ WKH XQFHUWDLQW\ LQ WKH
VHQVRU PHDVXUHPHQWV 6RPH DXWKRUV HJ 6DVLDGHN HW
DO KDYHIXVHG WKHRGRPHWULFDQGVRQDUGDWD,Q
WKLV ZRUN ZH IXVH WKH VRQDU GDWD ZLWK WKH YLVLRQ GDWD
GHVFULEHGLQ WKHQH[WVHFWLRQ+HUHZHSURSRVHWR IXVH
WKH VRQDU PHDVXUHPHQWV
a
T
[
DQG WKH YLVLRQ
PHDVXUHPHQWV
a
T
[
 E\ XVLQJ D GLVWULEXWHG
LQIRUPDWLRQILOWHU',)
%'DWDIURP9LVLRQ6HQVRU
,W LV LPSRUWDQW WR H[SUHVV WKH FRQWURO REMHFWLYH RI
QDYLJDWLQJDORQJ WKHFRUULGRU FHQWHUOLQHLQ WHUPVRIWKH
LPDJH IHDWXUHV IURP SHUVSHFWLYH OLQHV 7KH URERW LV
IROORZLQJWKH FHQWHUOLQHRI WKHFRUULGRU ZKHQWKHVORSH
RI ERWK SHUVSHFWLYH OLQHV EHFRPH HTXDO WKDW LV ZKHQ
Y
[
WKH YDQLVKLQJ SRLQWDQG
[
G
WKH PLGGOH SRLQW
EHWZHHQWKHLQWHUVHFWLRQRIERWK SHUVSHFWLYHOLQHVZLWK
WKH KRUL]RQWDO D[LVDUH HTXDO WR ]HUR )LJ  ,Q WKH
ZRUNVSDFHRULHQWDWLRQURERWHUURU
T
DQGSRVLWLRQURERW
HUURUUHODWLYHWRWKHFHQWHURIWKHFRUULGRU
a
G
[RU
:
S
[
DUHGHILQHG7KHVH HUURUVFDQEH H[SUHVVHGLQWHUPV RI
WKH LPDJH IHDWXUHV
Y
[
DQG
[
G
 (TXDWLRQ  FDQ EH
ZULWWHQDV
FRV

J
O
D
T
[
Y
.
WDQ
.
[
IURPZKLFK
¸
¸
¹
·
¨
¨
©
§
.
[
DUFWDQ
Y
T

%HVLGHV
¸
¸
¹
·
¨
¨
©
§
P
E
P
E
[
G
%\VXEVWLWXWLQJDQG
FRV

FRV
T
J
J
T
O
D
G
K
G
[RU
S
:
VLQ
KVLQ
[
[
DQG UHFDOOLQJ WKDW
a
G
[RU
:
S
[

[
a
FDQ EH H[SOLFLWO\
H[SUHVVHGDV
FRV
a
T
G
T
WDQ
.
.
[
[

ZKHUH
K
VLQ
.
[
J
O
D

FRV
J
O
D
[
.
(TVDQGUHQGHUWKHRULHQWDWLRQDQG
SRVLWLRQHUURUVDVDIXQFWLRQRI
Y
[
DQG
[
G
)LJ3HUVSHFWLYHOLQHV
&'HFHQWUDOL]HG,QIRUPDWLRQ)LOWHU
7KH VWDWH YDULDEOHV
a
W[
DQG
W
T
REWDLQHG XVLQJ
WKH GDWD IURP WKH XOWUDVRQLF DQG YLVLRQ VHQVRUV DUH
IXVHGXVLQJD GHFHQWUDOL]HG LQIRUPDWLRQILOWHU',) DV
SUHVHQWHGLQ)LJ
/RFDO)LOWHU
/RFDO)LOWHU
8OWUDVRQLF
6HQVRUV
9LVL RQ
6HQVRU
*OREDO
)LOWHU
[
a
T
[
a
T
[
a
T
'HFHQWUDOL]HG,QIRUPDWLRQ)L OWHU
<
\
<
\
<\
[
a
T
[
a
T
H
H
)LJ'HFHQWUDOL]HG,QIRUPDWLRQ)LOWHU
7KHYDULDEOHV \DQG<WKDW DSSHDUVLQ WKHILJXUHDUH
UHVSHFWLYHO\WKHLQIRUPDWLRQYHFWRUDQGWKHLQIRUPDWLRQ
PDWUL[ 7KH LQIRUPDWLRQ PDWUL[ LV WKH LQYHUVH RI WKH
FRYDULDQFHPDWUL[3RIWKH.DOPDQILOWHUDQGWKHYHFWRU
RI LQIRUPDWLRQ LV REWDLQHG E\ PXOWLSO\LQJ WKH
LQIRUPDWLRQ PDWUL[ E\ WKH VWDWH YHFWRU 0RUH
LQIRUPDWLRQ DERXW WKLV IXVLRQ E\ ',)  LV JLYHQ LQ
)UHLUH
,,,&21752//(56
$&RQWUROOHU%DVHGRQWKH2SWLFDO)ORZ
2QH RI WKH FRQWURO SURSRVDOV IRU QDYLJDWLRQ DORQJ
WKHFRUULGRULV EDVHGRQWKH FDOFXODWLRQ RIRSWLFDOIORZ
%DUURQ HW DO  LQ WZR V\PPHWULF ODWHUDO UHJLRQV
RQ WKH LPDJH SODQH
[
[
U
U
 )LJ  )URP  WKH
KRUL]RQWDORSWLFDOIORZLQWKHVHSRLQWVLVJLYHQE\
O
O
Z
O
O
Z
[
]
[
[
[
]
[
[
U
3
Y
U
U
U
3
Y
U
U

7R QDYLJDWH DORQJ WKH FRUULGRU FHQWHUOLQH WKH
FRQWURO REMHFWLYH RQ WKH LPDJH SODQH LV WR HTXDWH WKH
ODWHUDORSWLFDOIORZV
[
[
U
U
7KHQIURP
O
O
Z
[
]
F
]
F
[
U
S
S
Y
U

ROB_09
948
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
[
U
[
U
S
F
[
F
S
=
F
]
F
S
]
F
S
[
F
S
S
F
)LJ6FKHPDWLFVRIWKHFRQWUROSURSRVDO
,Q DGGLWLRQ LI URERW URWDWLRQ
Z

WKHQ
]
F
]
F
S
S
 ZKLFK PHDQV WKDW WKH URERW LV
QDYLJDWLQJDORQJWKHFRUULGRUFHQWHUOLQH)URPWKH
YLVLRQ PRGHO IRU WKH ODWHUDO RSWLFDO IORZ PHDVXUHG DW
[
[
U
U
LV
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
¸
¸
¸
¸
¸
¹
·
¨
¨
¨
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
Z
Z
O
O
O
O
Y
-
Y
U
S
U
U
S
U
U
U
[
]
F
[
[
]
F
[
[
[

ZKHUH
-
LV FDOOHG WKH -DFRELDQ RI WKH URERWFDPHUD
V\VWHP
1RZ E\ FRQVLGHULQJ WKH G\QDPLF PRGHO RI WKH
URERW
5
D
N
D
E
Z
Z
Z
Z
Z
Z
Z
Z

DQLQYHUVHG\QDPLFVFRQWUROODZLVUHJDUGHG
^
`
Z
Z
K
Z
Z
Z
Z
Z
D
E
D
N
5

ZKHUH
K
LVDYDULDEOHGHILQHGDV
Z
Z
Z
Z
Z
K
Z
Z
G
G
G
S
G
N
N

,Q 
G
Z
LV LQWHUSUHWHG DV WKH GHVLUHG DQJXODU
YHORFLW\ ZKLFK LV VHW WR ]HUR LQ RUGHU WR FRPSO\ ZLWK
WKHFRQWUROREMHFWLYHRIPDLQWDLQLQJDVWDEOHQDYLJDWLRQ
DORQJWKH FRUULGRU%HVLGHV
Z
Z
G
S
N
N
DUH GHVLJQJDLQV
,Q RUGHU WR LQFOXGH WKH H[WHURFHSWLYH LQIRUPDWLRQ RI
RSWLFDOIORZWKHLQYHUVHRIUHODWLRQ
^
`


U
M
U
M
M
-
U
-
Y
M
L
»
¼
º
«
¬
ª
Z
Z

LV VXEVWLWXWHG LQ WKH WHUP RI DQJXODU YHORFLW\ HUURU LQ

@
>


Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
D
E
N
U
M
U
M
N
D
N
G
S
5

%\FRPELQLQJDQGWKHFORVHGORRSHTXDWLRQLV
REWDLQHGDV
Z
Z
Z
Z
Z
S
G
N
N
ZKLFK LPSOLHV
o
W
Z
DV
f
o
W
 )URP  ZLWK
Z

[
[
U
U
7KHQWKHXQLTXHQDYLJDWLRQFRQGLWLRQ
LVYHULILHGDWWKHFHQWHUOLQHRIWKHFRUULGRU
% &RQWUROOHU %DVHG RQ WKH 5RERW 3RVWXUH ZLWK
5HVSHFWWRWKH&HQWHUOLQHRIWKH&RUULGRU
,QWKLVVHFRQGFRQWUROSURSRVDOWKHGHVLJQREMHFWLYH
LV WR REWDLQ D FRQWUROOHU ZKLFK EDVHG RQ HVWLPDWHG
YDOXHV RI WKH VWDWH YDULDEOHV
T
DQG
[
a
REWDLQHG IURP
GDWDIXVLRQDWWDLQV
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
³
f
o
a
\
GW
Y
W
\
W
[
OLP
W
WKDW LV WKH FRQWURO QDYLJDWLRQ REMHFWLYH LV
DV\PSWRWLFDOO\ REWDLQHG 7R WKLV DLP WKH IROORZLQJ
FRQWUROODZLVSURSRVHG
FRQVWDQW
VLQ
a
a
a
Y
Y
[
[
.
.
[
V
V
U
T
T
T
T
Z
T

ZKHUH
T
T
V
.
DQG
a
a
[
.
[
V
DUH YDULDEOHV GHVLJQHG WR
DYRLG VDWXUDWLRQ RI FRQWURO VLJQDOV DV LW ZLOO EH
H[SODLQHGODWHU
%\FRQVLGHULQJ DQG ZLWK VWDWH YDULDEOHV
T
DQG
[
a
WKHXQLTXH HTXLOLEULXPSRLQWRIWKHFORVHGORRS
HTXDWLRQLV DW
>
@
7
$V\PSWRWLFVWDELOLW\RIWKHFRQWURO
V\VWHP FDQ EH SURYHG E\ UHJDUGLQJ WKH IROORZLQJ
/\DSXQRYIXQFWLRQ
K
K
T
T
G
.
[
9
[
[
V
³
a
a
a
DQG E\ DSSO\LQJ WKH .UDVRYVNLL/DVDOOH WKHRUHP
.KDOLO
6DWXUDWLRQ JDLQV LQ  FDQ EH GHILQHG DV IROORZV
&DUHOOL)UHLUH
T
T
T
D
.
.
V
V
 ZKHUH
!
V
.
DQG
!
D
 LQ RUGHU
WR REWDLQ D SRVLWLYH GHILQLWH IXQFWLRQ 'RLQJ OLNHZLVH
ZLWK
[
D
.
[
.
V
[
V
a
a
a
ZLWK
!
V
.

!
D
7KH FRQVWDQWV DUH VHOHFWHG VXFK WKDW WKH WHUPV LQ
GRQRWSURGXFHVDWXUDWLRQRIWKHFRQWUROVLJQDO
U
Z

)LQDOO\DQLQYHUVHG\QDPLFVFRQWUROOHULVUHJDUGHGOLNH
WKDWRIDQGZLWK
5
Z
VWDWHGE\
,9)86,212)&21752/6,*1$/6
7KH FRQWUROOHUV GHVFULEHG LQ 6HFWLRQ  DUH
UHGXQGDQW EHFDXVH WKH\ KDYH WKH VDPH FRQWURO
REMHFWLYH WR JXLGH WKH URERW DORQJ WKH FRUULGRU
FHQWHUOLQH 7KH\ DUH EDVHG KRZHYHU RQ GLIIHUHQW
SULQFLSOHV ZKLFK WXUQ GLIILFXOW WKHLU IXVLRQ DW WKH
VHQVRULDO OHYHO +HUH WKH IXVLRQ RI ERWK FRQWURO
FRPPDQGV LV SURSRVHG LQ RUGHU WR DWWDLQ D FRQWURO
VLJQDO WKDW DOORZV D UREXVW QDYLJDWLRQ DORQJ WKH
FRUULGRU 7KH IXVLRQ LV PDGH E\ XVLQJ D GLVWULEXWHG
LQIRUPDWLRQ ILOWHU ',) WKXV PLQLPL]LQJ WKH
ROB_09
949
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
XQFHUWDLQW\ RQ FDOFXODWLQJ ERWK FRQWURO VLJQDOV 7KLV
XQFHUWDLQW\ LV HYDOXDWHG LQ WHUPV RI WKH VHQVLQJ HUURU
DQGWKHHQYLURQPHQWFRQGLWLRQVE\ LQWURGXFLQJD WLPH
YDU\LQJFRYDULDQFH IXQFWLRQIRUHDFKFRQWUROOHU)UHLUH

$6WDELOLW\RIWKH&RQWURO6\VWHP
/HW XV FRQVLGHU WKDW OLNH LQ )LJ  QFRQWUROOHUV
ZLWK WKH VDPH FRQWURO REMHFWLYH DUH XVHG 7KHQ WKH
IROORZLQJ VHW RI FRQWURO VLJQDOV IURP WKH LQYHUVH
G\QDPLFVFRQWUROOHUVDUHREWDLQHG
Z
Z
K
Z
Z
Z
K
Z
Z
Z
K
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
D
E
ND
D
E
ND
D
E
ND
Q
UQ
U
U
7KHIXVHGFRQWUROVLJQDOFDQEHUHSUHVHQWHGDV
Ö
Ö
Z
Z
K
Z
Z
Z
Z
D
E
N
U

/RFDO)LOWHU
/RFDO)LOWHU
*OREDO
)LOWHU
'HFHQWU DOL]HG,QIRUPDWLRQ)LOWHU
<
\
<
\
/RFDO)LOWHU
<
\
<\
)LJ2XWSXWIXVLRQIURPGLIIHUHQWFRQWUROOHUV
)RUDQLGHDOFRQWUROFRPPDQGZGZGL'ZGL LW
FRUUHVSRQGVDQLGHDOKVXFKWKDW
Q
Q
K
K
K
K
K
K
K
K
K
'
'
'
RULQWHUPVRIWKHIXVHGVLJQDO
K
Ö
K
K
K
Ö
Ö
'

%\ HTXDWLQJ  DQG  DQG WDNLQJ  LQWR
DFFRXQW
Z
K
K
K
'
Ö
Ö

)URPDQGLWLVQRZSRVVLEOHWRZULWHWKH
IROORZLQJG\QDPLFVIRUWKHDQJXODUYHORFLW\HUURU
K
Z
Z
Z
Z
Z
Ö
a
a
a
'
S
G
N
N

'HILQLQJWKHVWDWHYHFWRU
>
@
7
[
Z
Z
a
a
HTXDWLRQ
FDQEHZULWWHQDV
[
/
$[
[

ZKHUH
¸
¸
¹
·
¨
¨
©
§
'
¸
¸
¹
·
¨
¨
©
§
K
Z
Z
Ö
/
[
N
N
$
G
S
,WFDQEHSURYHG WKDW WKH V\VWHP GHVFULEHGE\
KDVDQXOWLPDWHO\ERXQGHGVROXWLRQ.KDOLO7KLV
PHDQV WKDW WKHUH H[LVW E F! VXFK WKDW IRU HDFK D
F WKHUH LV D SRVLWLYH FRQVWDQW 7 7DVR WKDW
D
D
7
W
W
E
W
[
W
[
t
d
 ZKHUH ELV WKH
XOWLPDWH ERXQG %\ UHJDUGLQJ WKH IROORZLQJ /\DSXQRY
FDQGLGDWH
!
7
7
3
3[3
[
9
LWVWLPHGHULYDWLYHLV
[
3
/
[
4[
[
9
7
7

ZKHUH
4
3$
3
$
7
%HVLGHVFRQVLGHULQJERXQGVRQ
ERWKWHUPVRI
[
[
3
[
4
9
PD[
PLQ
G
d

)URP
K
Ö
'
d
[
/
%\UHJDUGLQJ
û
[
3
[
4
[
4
9
PD[
PLQ
PLQ
Ö
d
T
T
ZLWK
T)LQDOO\LWUHVXOWV
4
û
3
[
[
4
9
PLQ
PD[
PLQ
Ö
t
d
O
T
VRWKDWWKHXOWLPDWHERXQGLV
û
3
3
4
3
E
PLQ
PD[
PLQ
PD[
Ö
6LQFH D',) LV EHLQJ XVHG WR IXVH WKH FRQWURO
VLJQDOVWKHXOWLPDWHERXQGRQWKHVWDQGDUGGHYLDWLRQRI
XOWLPDWHHUURU LVVPDOOHUWKDQ WKDWFRUUHVSRQGLQJ WRWKH
HUURUVSURGXFHGE\HDFKFRQWUROOHU
9(;3(5,0(17$/5(68/76
,Q RUGHU WR HYDOXDWH WKH SHUIRUPDQFH RI WKH
SURSRVHG FRQWURO V\VWHP VHYHUDO H[SHULHQFHV ZHUH
GRQHRQ D3LRQHHU';PRELOHURERWZLWKDQRQERDUG
6RQ\37=&&'FDPHUD7KHLPDJHVDUHWUDQVPLWWHGYLD
5) WR WKH LPDJH SURFHVVLQJ XQLWV RQH 3& IRU RSWLFDO
IORZ FDOFXODWLRQ DQG D VHFRQG RQH IRU WKH FRUULGRU
SHUVSHFWLYH OLQHV FDOFXODWLRQ $ WKLUG 3& LV XVHG WR
SURFHVV WKH XOWUDVRQLF GDWD WR FDOFXODWH WKH FRQWURO
DFWLRQV DQG WR SHUIRUP WKHLU IXVLRQ $OO 3&V DUH
FRQQHFWHG YLD 7&3,3 7KH UHVXOWLQJ FRQWURO DFWLRQ LV
VHQWWRWKHURERWYLD5)
7KHRSWLFDOIORZ FDOFXODWLRQZDV UHDOL]HGXVLQJWKH
/HDVW0HDQ6TXDUH 0HWKRG 'HY HW DO  7KH
FRUULGRU SHUVSHFWLYH OLQHV DUH FDOFXODWHG XVLQJ +RXJK
WUDQVIRUPV7KH LQIRUPDWLRQRIWKHLPDJHSURFHVVLQJ LV
XSGDWHGHYHU\ PVHF 7KHFDPHUDFRQVWDQWVYDOXHV
DUH
[
D

\
D
 SL[HOVP
O
P
J

K
P 7KH URERW QDYLJDWHV ZLWK OLQHDU
YHORFLW\
Y
PV7KHFRQWUROOHUVGHVLJQSDUDPHWHUV
IRU WKH RSWLFDO IORZ FRQWUROOHU DUH VHW WR

Z
S
N

Z
G
N
DQGIRU WKH FRQWUROOHUEDVHGRQ WKH SRVLWLRQRI
WKHURERWZLWK UHVSHFWWR WKHFHQWHUOLQHRIWKHFRUULGRU
WKH SDUDPHWHUV DUH VHW WR

Z
S
N

Z
G
N


V
.
UDGV

V
.
UP
D
UDG
D
P
)LJ  VKRZV WKH WUDMHFWRU\ RI WKH URERW QDYLJDWLQJ
DORQJDFRUULGRUDWWKH,QVWLWXWHRI$XWRPDWLFV1DWLRQDO
8QLYHUVLW\ RI 6DQ -XDQ $UJHQWLQD 7KH H[SHULPHQW LV
GHVLJQHGLQDZD\WKDWWKHURERWILQGVGLIIHUHQWVHQVLQJ
DQG HQYLURQPHQW FRQGLWLRQV GXULQJ QDYLJDWLRQ 7KLV
ROB_09
950
;,5HXQLyQGH7UDEDMRHQ3URFHVDPLHQWRGHOD,QIRUPDFLyQ \&RQWURODOGHVHSWLHPEUHGH
YDU\LQJFRQGLWLRQSURGXFHVFKDQJHV LQ WKHYDULDQFHRI
WKHFRQWURODFWLRQIRUHDFKFRQWUROOHU7KHHYROXWLRQRI
WKHVH YDULDQFHV LV VKRZQ LQ )LJ  7KH GDWD IXVLRQ
REWDLQHG IURP XOWUDVRQLF VHQVRUV DQG SHUVSHFWLYH OLQHV
LVVKRZQLQ)LJ  )LJGHSLFWVWKH FRQWURO DFWLRQ
REWDLQHG IURP WKH IXVLRQ RI ERWK FRQWUROOHUV 7KH
H[SHULPHQW VKRZV D JRRG SHUIRUPDQFH RI WKH URERW
HYROXWLRQ ZKHQ QDYLJDWLQJ DORQJ WKH FRUULGRU
FHQWHUOLQH LQGHSHQGHQWO\ RI WKH YDU\LQJ HQYLURQPHQW
FRQGLWLRQV
9,&21&/86,216
7KLV ZRUN KDV SUHVHQWHG D FRQWURO VWUDWHJ\ IRU
PRELOHURERWVQDYLJDWLQJ LQFRUULGRUVXVLQJ WKHIXVLRQ
RIFRQWUROVLJQDOVIURPYLVLRQEDVHGFRQWUROOHUV7RWKLV
DLPWZRFRQWUROOHUVKDYHEHHQ SURSRVHGRQHEDVHG RQ
WKHRSWLFDOIORZFDOFXODWLRQDQG WKHRWKHUEDVHG RQWKH
SHUVSHFWLYH OLQHV LQ WKH FRUULGRU %RWK FRQWUROOHUV
JHQHUDWH DQJXODUYHORFLW\ FRPPDQGV WRNHHSWKH URERW
QDYLJDWLQJDORQJ WKHFRUULGRU DQGWKH\FRPSHQVDWHIRU
WKH G\QDPLFV RI WKH URERW 7KH IXVLRQ RI ERWK FRQWURO
VLJQDOVZDVUHDOL]HGE\XVLQJDGLVWULEXWHG LQIRUPDWLRQ
ILOWHU',)6WDELOLW\RIWKHUHVXOWLQJFRQWUROV\VWHPZDV
DQDO\]HG DQG H[SHULPHQWV RQ D ODERUDWRU\ URERW ZHUH
SUHVHQWHG VKRZLQJ WKH SHUIRUPDQFH RI WKH SURSRVHG
FRQWUROV\VWHP
0 2 4 6 8 10 12
−1
0
1Mobile Robot Trajectory
X [m]
Y [m]
)LJ0RELOHURERWWUDMHFWRU\
0 10 20 30 40 50 60 70
0
5
10
15
Seconds
Variance of W (Lines)
0 10 20 30 40 50 60 70
0
2
4
6
8
10
12
Seconds
Variance of W (Flow)
)LJ9DULDQFHVIURP/LQHDQG2SWLFDO)ORZFRQWUROOHUV
0 10 20 30 40 50 60 70
−0.3
−0.2
−0.1
0
0.1
0.2
Seconds
[m]
Xtilde (Fusion)
0 10 20 30 40 50 60 70
−10
−5
0
5
10
Seconds
[deg]
Theta (Fusion)
)LJ;WLOGHDQG7KHWDIURPGDWDIXVLRQ
0 10 20 30 40 50 60 70
−8
−6
−4
−2
0
2
4
6
8
[deg/s]
Seconds
W (Fusion)
)LJ&RQWURODFWLRQ
9,$&.12:/('*(0(176
7KH DXWKRUV JUDWHIXOO\ DFNQRZOHGJH 6(7&,3 DQG
&21,&(7 $UJHQWLQD DQG WKH 8QLYHUVLGDGH )HGHUDO
GH6HUJLSH %UD]LOIRUSDUWLDOO\IXQGLQJWKLVUHVHDUFK
9,,5()(5(1&(6
$UNLQ5DQG7%DOFK$X5$SULQFLSOHVDQGSUDFWLFHLQUHYLHZ
([SHULPHQWDODQG7KHRUHWLFDO$UWLILFLDO,QWHOOLJHQFHSS

%DUURQ-/ '- )OHHW6 6%HDXFKHPLQ3HUIRUPDQFH RIRSWLFDO
IORZWHFKQLTXHV,-9&SS 
%HPSRUDG0'L0DUFRDQG$7HVL:DOO±IROORZLQJFRQWUROOHUVIRU
VRQDU±EDVHG PRELOH URERWV 3URF WK ,((( &RQI RQ
'HFLVLRQDQG&RQWURO6DQ'LHJR
%LFKR ( 7KH G\QDPLF DSSURDFK WR EHKDYLRUEDVHG URERWLFV3K'
7KHVLV8QLYHUVLW\RI0LQKR3RUWXJDO
&DUHOOL 5 DQG ( )UHLUH &RUULGRU 1DYLJDWLRQ DQG :DOO)ROORZLQJ
6WDEOH&RQWUROIRU 6RQDU%DVHG0RELOH 5RERWV5RERWLFV$QG
$XWRQRPRXV6\VWHPVYS 
&DUHOOL 5 & 6RULD 2 1DVLVL DQG ( )UHLUH6WDEOH $*9 &RUULGRU
1DYLJDWLRQ ZLWK )XVHG 9LVLRQ%DVHG &RQWURO 6LJQDOV ,Q
,(&21 ± R$QQXDO &RQIHUHQFH RI WKH ,((( ,QGXVWULDO
(OHFWURQLFV6RFLHW\6HYLOODSS
'HY$%.U|VHDQG)*URHQ1DYLJDWLRQ RIDPRELOHURERWRQWKH
WHPSRUDO GHYHORSPHQW RI WKH RSWLF IORZ 3URF 2I WKH
,(((56-*, ,QW &RQI 2Q ,QWHOOLJHQW 5RERWV DQG 6\VWHPV
,526*UHQREOHSS
'HY $ % - $ .U|VH ) & $ *URHQ &RQILGHQFH PHDVXUHV IRU
LPDJHPRWLRQHVWLPDWLRQ5:&36\PSRVLXP7RNLR
'L[RQ : ' 'DZVRQ ( =HUJHURJOX DQG $ %HKDO 1RQOLQHDU
&RQWURORIZKHHOHGPRELOHURERWV6SULQJHU9HUODJ 
)UHLUH(7%DVWRV)LOKR06DUFLQHOOL)LOKRDQG5 &DUHOOL$1HZ
0RELOH 5RERW &RQWURO $UFKLWHFWXUH )XVLRQ RI WKH 2XWSXW RI
'LVWLQFW &RQWUROOHUV,((( 7UDQVDFWLRQV RQ 6\VWHPV 0DQ DQG
&\EHUQHWLFV 3DUW %&\EHUQHWLFV Y  Q  S  

.KDOLO + . 1RQOLQHDU V\VWHPV 6HFRQG (GLWLRQ 3UHQWLFH+DOO

3LUMDQLDQ30XOWLSOHREMHFWLYHEHKDYLRUEDVHGFRQWURO5RERWLFVDQG
$XWRQRPRXV6\VWHPVSS
5RVHQEODWW - '$01 $ GLVWULEXWHG DUFKLWHFWXUH IRU PRELOH
QDYLJDWLRQ´ 3K' 7KHVLV &DUQHJLH 0HORQ 8QLYHUVLW\ 86$

6DIILRWWL $ . .RQROLJH DQG ( 5XVSLQL $ PXOWLYDOXDWHG ORJLF
DSSURDFK WR LQWHJUDWLQJ SODQQLQJ DQG FRQWURO $UWLILFLDO
,QWHOOLJHQFHSS 
6DQWRV9LFWRU- *6DQGLQL)&XURWWRDQG 6*DULEDOGL 'LYHUJHQW
VWHUHR LQ DXWRQRPRXV QDYLJDWLRQ IURP EHHV WR URERWV ,QW
-RXUQDORI&RPSXWHUV9LVLRQ
6DVLDGHN - = 3 +DUWDQD  2GRPHWU\ DQG VRQDU GDWD IXVLRQ IRU
PRELOH URERW QDYLJDWLRQ WK ,)$& 6\PSRVLXP RQ 5RERW
&RQWURO 6<52&2 9LHQQD $XVWULD 3UHSULQWV 9RO,,
SS
6HUYLF6 DQG6 5LEDULF'HWHUPLQLQJ WKH$EVROXWH 2ULHQWDWLRQLQ D
&RUULGRUXVLQJ3URMHFWLYH *HRPHWU\DQG$FWLYH 9LVLRQ ,(((
7UDQVRQ,QGXVWULDO(OHFWURQLFVYRO1R
9DVVDOOR 5 + - 6FKQHHEHOL DQG - 6DQWRV±9LFWRU 9LVXDO
QDYLJDWLRQ FRPELQLQJ YLVXDO VHUYRLQJ DQG DSSHDUDQFH EDVHG
PHWKRGV 6,56 ,QW 6\PS RQ ,QWHOOLJHQW 5RERWLF 6\VWHPV
(GLQEXUJK6FRWDOQG 
<DQJ= DQG:7VDL 9LHZLQJFRUULGRUVDV ULJKWSDUDOOHOHSLSHGV IRU
YLVLRQEDVHG YHKLFOH ORFDOL]DWLRQ ,((( 7UDQV RQ ,QGXVWULDO
(OHFWURQLFVYRO1R
ROB_09
951
... To circumvent this problem, the fusion was implemented using a Correlated Extended Kalman Filter [31]. In Carvalho et al. [32], and Carelli et al. [33], Decentralized Information Filters are used to perform information fusion and pose estimation for a mobile robot operating in internal environments. By their turn, Inoue et al., used approaches based on the Robust Kalman Filters to perform robot localization in internal environments and inertial navigation, respectively [34][35][36]. ...
... Stochastic approaches were used in modeling and to performing output control fusion. In [33] and [55], a Decentralized Information Filter was used to fuse output control signals provided by two redundant controllers designed to follow corridors. In [56] an Extended Kalman Filter was used in the calculation process of the inverse kinematics model of a quadruped robot. ...
... In the other applications mentioned in this work, the evolution of the tools used in the state estimation has followed the same pattern. The Particle Filter has been replacing the Kalman Filter in situations where the disturbances are multimodal, or when there are very Decentralized Information Filter [16], [17] Information Filter / α-β Filter [14] Extended Kalman Filter [18] Other Sensing Tasks Descriptor Kalman Filter [19], [21] Extended Kalman Filter [20] Pose Tracking Extended Kalman Filter222324252627, [30] Unscented Kalman Filter [28], [29] Information Filter / α-β Filter [32] Decentralized Information Filter [33] Descriptor Kalman Filter [34], [35] Global Localization Monte Carlo Filter373839404142 Monte Carlo Filter (parallel implementation) [43] Markov Localization [44] SLAM MAP estimate525354 Extended Kalman Filter45464748495051 Fusion of output control signals Decentralized Information Filter [33], [55] Modeling Extended Kalman Filter [56], [57] expressive nonlinearities. However, the Kalman Filter is still the most widely used for tasks in which such conditions do not occur, given its lower computational cost. ...
Conference Paper
Full-text available
Stochastic approaches have become increasingly common in robotics. Techniques that consider the uncertainties of sensors and models are being adopted in various applications. In this context, state estimation techniques play an important role, since they deal directly with these uncertainties, making systems more reliable. This paper aims to survey the state of the art of application of stochastic approaches in robotics in the context of the work developed in Brazil. At the end, the main applications that use stochastic approaches in robotics are summarized, and the main tools used in each case are suggested. Moreover, the main outstanding issues, which should be the focus of further research, are indicated. Thus, this paper is intended to be a useful tool for new researchers in this booming research area.
... So, the output of the fusion scheme tends to the output of the controller with the smallest variance. The stability of a control system based on the fusion of control signals from homogeneous or redundant controllers using Kalman and Information filter was analyzed in Carelli et al (2002) and Soria et al (2006), respectively. It was found that such systems are ultimately bounded, which means that the ultimate bound on the standard deviation of the error is smaller than that corresponding to errors produced by each controller. ...
... The fusion of both control signals is made using a Decentralized Information Filter. The resultant control system is ultimately bounded (Khalil, 1996), as shown in Soria et al (2006). Experiments on a laboratory robot have been presented that show the good performance of the proposed controller. ...
Article
Full-text available
This work presents a control strategy for mobile robots navigating in corridors, using the fusion of the control signals from two instances of the same controller: one is based on the perspective lines of the corridor (the projection of lines formed by the intersection of the walls and the floor) and the other is based on distance measurements performed by ultrasonic sensors. Both controllers generate angular velocity commands to keep the robot navigating along the corridor, and compensate for the dynamics of the robot. The fusion of both control signals is made using a Decentralized Information Filter -DIF. Experiments on a labora-tory robot are presented to show the feasibility and performance of the proposed controller.
... For this purpose, two data fusion strategies are proposed, Variance Weighted Average (VWA) and Decentralized Kalman Filter (DKF) [6], by means of an arrangement of redundant potentials, that is, combining the EMG signals from two or more acquisition channels in such a way that after the fusion stage, the algorithms provide a more reliable signal to be applied to the control system. Data fusion techniques are frequently implemented in robotic control, where the information is redundant and/ or of diverse nature [7,8] . When the data sensors are similar , fusion is applied over the signals, but when the data sensors are of different nature, fusion takes place on the control signals [8] . ...
Article
Full-text available
Myoelectric control of a robotic manipulator may be disturbed by failures due to disconnected electrodes, interface impedance changes caused by movements, problems in the recording channel and other various noise sources. To correct these problems, this paper presents two fusing techniques, Variance Weighted Average (VWA) and Decentralized Kalman Filter (DKF), both based on the myoelectric signal variance as selecting criterion. Tested in five volunteers, a redundant arrangement was obtained with two pairs of electrodes for each recording channel. The myoelectric signals were electronically amplified, filtered and digitalized, while the processing, fusion algorithms and control were implemented in a personal computer under MATLAB environment and in a Digital Signal Processor (DSP). The experiments used an industrial robotic manipulator BOSCH SR-800, type SCARA, with four degrees of freedom; however, only the first joint was used to move the end effector to a desired position, the latter obtained as proportional to the EMG amplitude. Several trials, including disconnecting and reconnecting one electrode and disturbing the signal with synthetic noise, were performed to test the fusion techniques. The results given by VWA and DKF were transformed into joint coordinates and used as command signals to the robotic arm. Even though the resultant signal was not exact, the failure was ignored and the joint reference signal never exceeded the workspace limits. The fault robustness and safety characteristics of a myoelectric controlled manipulator system were substantially improved. The proposed scheme prevents potential risks for the operator, the equipment and the environment. Both algorithms showed efficient behavior. This outline could be applied to myoelectric control of prosthesis, or assistive manipulators to better assure the system functionality when electrode faults or noisy environment are present.
... In [5] and [6], a camera is used to guide the robot along the corridor's centerline, or parallel to a wall. A control algorithm which combines vision based perspective lines and optical flow is presented in [7], including the stability proof of the control system. In [8], perspective lines are used to determine the absolute orientation of the robot within the corridor. ...
Conference Paper
Full-text available
This work presents a control strategy that allows a follower robot to track a target vehicle moving along an unknown trajectory with unknown velocity. It uses only artificial vision to establish both the robot's position and orientation relative to the target, so as to maintain a specified formation at a given distance. The control system is proved to be asymptotically stable at the equilibrium point, which corresponds to the navigation objective. Experimental results with two robots, a leader and a follower, are included to show the performance of the proposed vision-based tracking control system
Article
In this work, a vision-based control interface for commanding a robotic wheelchair is presented. The interface estimates the orientation angles of the user's head and it translates these parameters in command of maneuvers for different devices. The performance of the proposed interface is evaluated both in static experiments as well as when it is applied in commanding the robotic wheelchair. The interface calculates the orientation angles and it translates the parameters as the reference inputs to the robotic wheelchair. Control architecture based on the dynamic model of the wheelchair is implemented in order to achieve safety navigation. Experimental results of the interface performance and the wheelchair navigation are presented.
Article
In this paper, wide-field integration methods, which are inspired by the spatial decompositions of wide-field patterns of optic flow in the insect visuomotor system, are explored as an efficient means to extract visual cues for guidance and navigation. A control-theoretic framework is developed and used to quantitatively link weighting functions to behaviorally-relevant interpretations such as relative orientation, position, and speed in a corridor environment. It is shown through analysis and demonstration on a ground vehicle that the proposed sensorimotor architecture gives rise to navigational heuristics, namely, centering and speed regulation, which are observed in natural systems.
Article
Full-text available
While different optical flow techniques continue to appear, there has been a lack of quantitative evaluation of existing methods. For a common set of real and synthetic image sequences, we report the results of a number of regularly cited optical flow techniques, including instances of differential, matching, energy-based, and phase-based methods. Our comparisons are primarily empirical, and concentrate on the accuracy, reliability, and density of the velocity measurements; they show that performance can differ significantly among the techniques we implemented.
Article
Full-text available
This article presents some experiments of a real-time navigation system driven by two cameras pointing laterally to the navigation direction (Divergent Stereo). Similarly to what has been proposed in (Franceschini et al. 1991; Coombs and Roberts 1992), our approach (Sandini et al. 1992; Santos-Victor et al. 1993) assumes that, for navigation purposes, the driving information is not distance (as it is obtainable by a stereo setup) but motion and, more precisely, by the use of qualitative optical-flow information computed over nonoverlapping areas of the visual field of two cameras. Following this idea, a mobile vehicle has been equipped with a pair of cameras looking laterally (much like honeybees) and a controller based on fast, real-time computation of optical flow has been implemented. The control of the mobile robot (Robee) is based on the comparison between the apparent image velocity of the left and the right cameras. The solution adopted is derived from recent studies (Srinivasan 1991) describing the behavior of freely flying honeybees and the mechanisms they use to perceive range. This qualitative information (no explicit measure of depth is performed) is used in many experiments to show the robustness of the approach, and a detailed description of the control structure is presented to demonstrate the feasibility of the approach in driving the mobile robot within a cluttered environment. A discussion about the potentialities of the approach and the implications in terms of sensor structure is also presented.
Article
Full-text available
This paper proposes an alternative approach to address the problem of coordinating behaviors in mobile robot navigation: fusion of control signals. Such approach is based on a set of two decentralized information filters, which accomplish the data fusion involved. Besides these two fusion engines, control architectures designed according to this approach also embed a set of different controllers that generate reference signals for the robot linear and angular speeds. Such signals are delivered to the two decentralized information filters, which estimate suitable overall reference signals for the robot linear and angular speeds, respectively. Thus, the background for designing such control architectures is provided by the nonlinear systems theory, which makes this approach different from any other yet proposed. This background also allows checking control architectures designed according to the proposed approach for stability. Such analysis is carried out in the paper, and shows that the robot always reaches its final destination, in spite of either obstacles along its path or the environment layout. As an example, a control architecture is designed to guide a mobile robot in an experiment, whose results allows checking the good performance of the control architecture and validating the design approach proposed as well.
Conference Paper
Full-text available
The robot navigation task presented in this paper is to drive through the center of a corridor, based on a sequence of images from an on-board camera. Our measurements of the system state the distance to the wall and orientation of the wall, are derived from the optic flow. Whereas the structure of the environment is usually computed from the spatial derivatives of the optic flow, we used the structure contained in the temporal derivatives of the optic flow to compare the environment structure and hence the system state. The algorithm is used to control a `remote brain' robot and results on the accuracy of the state estimates are presented
Article
Full-text available
The capability of a mobile robot to determine its position in the environment (self-localization) is a prerequisite for achieving autonomous navigation. An approach is proposed for determining the absolute orientation of an autonomous robot in a system of corridors, based on the projective geometry and active computer vision. In the proposed approach, the common direction of longitudinal corridor edges is inferred by detecting the vanishing point of the corresponding straight line segments in the image. It is assumed that the knowledge about the vertical direction in the scene is available, so that the image coordinates of these vanishing points are considerably constrained. However, longitudinal corridor edges are not visible in images acquired for many viewing directions, so that the processing in a localization procedure has to be performed on a sequence of images acquired from the given position, for regularly arranged orientations of the camera. Extensive experimentation was performed on real scenes and the obtained results are provided
Article
Full-text available
This paper reviews key concepts of the Autonomous Robot Architecture (AuRA). Its structure, strengths, and roots in biology are presented. AuRA is a hybrid deliberative/reactive robotic architecture that has been developed and refined over the past decade. In this article, particular focus is placed on the reactive behavioral component of this hybrid architecture. Various real world robots that have been implemented using this architectural paradigm are discussed, including a case study of a multiagent robotic team that competed and won the 1994 AAAI Mobile Robot Competition. 1 Introduction The Autonomous Robot Architecture (AuRA) was developed in the mid-1980's as a hybrid approach to robotic navigation [6]. Hybridization arises from the presence of two distinct components: a deliberative or hierarchical planner, based on traditional artificial intelligence techniques; and a reactive controller, based upon schema theory [2]. It was the first robot navigational system to be pres...
Article
To solve the problems in guidance, navigation, and control for an autonomous robot, its accurate positioning and localization are needed. Two or more different sensors are often used to obtain reliable data useful for control system. Extended Kalman Filter (EKF) is widely used to fuse those data to obtain one optimal result. The signals used during navigation cannot be always considered as white noise signals. On the other hand, colored signals will cause the EKF to diverge. This paper presents the data fusion system for mobile robot navigation. Odometry and sonar signals are fused using Extended Kalman Filter (EKF) and Adaptive Fuzzy Logic System (AFLS). The AFLS was used to adapt the gain and therefore prevent the Kalman filter divergence. The fused signal is more accurate than any of the original signals considered separately. The enhanced, more accurate signal is used to guide and navigate the robot.
Article
In this paper, a mobile robot control law for corridor navigation and wall-following, based on sonar and odometric sensorial information is proposed. The control law allows for stable navigation avoiding actuator saturation. The posture information of the robot travelling through the corridor is estimated by using odometric and sonar sensing. The control system is theoretically proved to be asymptotically stable. Obstacle avoidance capability is added to the control system as a perturbation signal. A state variables estimation structure is proposed that fuses the sonar and odometric information. Experimental results are presented to show the performance of the proposed control system.
Article
elligent agents embedded in a dynamic, uncertain environment should incorporate capabilities for both planned and reactive behavior. Many current solutions to this dual need focus on one aspect, and treat the other one as secondary. We propose an approach for integrating planning and control based on behavior schemas, which link physical movements to abstract action descriptions. Behavior schemas describe behaviors of an agent, expressed as trajectories of control actions in an environment, and goals can be defined as predicates on these trajectories. Goals and behaviors can be combined to produce conjoint goals and complex controls. The ability of multivalued logics to represent graded preferences allows us to formulate tradeoffs in the combination. Two composition theorems relate complex controls to complex goals, and provide the key to using standard knowledge-based deliberation techniques to generate complex controllers. We report experiments in planning and execution on a mobile robot platform, Flakey.
Article
The notion of optimality and its feasibility are revisited in the context of behavior-based control. It is argued that optimal behavior is not feasible for real-world applications. As an alternative to optimality I promote Pareto-optimal and satisficing solutions which correspond to efficient and “good enough” behavior. It is then demonstrated that multiple objective decision theory provides a suitable framework for formulating behavior-based controllers that generate Pareto-optimal and satisficing behavior. A set of simulated and real-world experiments are reported that support this view.