turning gait with constant radius of six-legged walking robot
DESCRIPTION
Cara mengetahui radius belok robot hexapod yaitu dengan mengikuti radius lingkaran yang telah dibuat.TRANSCRIPT
!48"!7#
2014$7%
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Vol.48No.7Jul.2014
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:www.journals.zju.edu.cn/eng
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DOI:10.3785/j.issn.1008973X.2014.07.020
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:1008 973X(2014)07 1278 09
犜狌狉狀犻狀犵犵犪犻狋狑犻狋犺犮狅狀狊狋犪狀狋狉犪犱犻狌狊狅犳狊犻狓犾犲犵犵犲犱狑犪犾犽犻狀犵狉狅犫狅狋
CHENGang,JINBo,CHENYing(犛狋犪狋犲犓犲狔犔犪犫狅狉犪狋狅狉狔狅犳犉犾狌犻犱犘狅狑犲狉犜狉犪狀狊犿犻狊狊犻狅狀犪狀犱犆狅狀狋狉狅犾,犣犺犲犼犻犪狀犵犝狀犻狏犲狉狊犻狋狔,犎犪狀犵狕犺狅狌310027,犆犺犻狀犪)
犃犫狊狋狉犪犮狋:Thetripodgaitwasusedinturninggaitwithconstantradiusofsixleggedwalkingrobot.The
planningmethodforturninggaitwithconstantradiusbasedonthetripodgaitwaspresentedwhichsimpli
fiestheturninggaitofsixleggedwalkingrobot.Themethodusinglinesegmentstotrackthecircletrajec
toryofcenterofgravityofthesixleggedwalkingrobotwasemployedtotheturninggaitwithconstantra
dius.Anapproachtocalculatethemaximumturningangleofthesixleggedwalkingrobotwasproposed
basedonstabilityconstraintandmotionconstraint.Differentturningangleswereappliedintheturning
gaitwithconstantradiusofthesixleggedwalkingrobottoimprovetheturningabilityineverystepwhen
thetwogroupsoflegssupporttherobotrespectively.AsimulationwasconductedwithMATLABand
ADAMStoverifytheturninggaitwithconstantradiusofthesixleggedwalkingrobot.Resultsshowthat
theturninggaitwithconstantradiusiscorrect.
犓犲狔狑狅狉犱狊:sixleggedwalkingrobot;constantradius;turninggait;tripodgait
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Tab.1 Geometricalparametersofsixleggedrobot m
犔B 犠B 犾2 犾3
0.5952 0.395 0.15 0.1491
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Fig.1 Sixleggedwalkingrobotplatform
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Fig.1 Sketchofsixleggedwalkingrobot
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Fig.5 Turninggaitplanningwithconstantradiusof
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,
�犃1 、犃4 �犃5 U���¿h
:(犠B/2,犔B/2+
犛1)、(-犠B/2,犛1)、(犠B/2,-犔B/2+犛1).�ª
犃1犃4、犃4犃5 U$d�¿h
犔B2犠B
狓-狔+1
4犔B+犛1 =0,
犔B2犠B
狓+狔+1
4犔B-犛1 =0.
a)]羸æç£Oh犕s .
b)�犕I1=犕s,�`犛1 .¦§Ó¦�ªU\û
ýèO¥
犕I1 =
1
4犔B-犛1
犔2B4犠2
B
+槡 1
=犕s,
�
犛1 =1
4犔B-犕s
犔2B4犠2
B
+槡 1.
c)¦§犕s�犛1 ,�`Ⅰn=h4��½U¾
@É�ÖÌ犃S1 .��ø6�£´®Ó犅E1 ÓU�
�h
:(-犚(1-cos犃S1),犚sin犃S1).¦§Ó¦�
ªU\ûýèO¥
犕E1 =
-犔B2犠B
犚(1-cos犃S1)-犚sin犃S1+1
4犔B+犛1
犔2B4犠2
B
+槡 1
.
�犕E1 =犕s,�`¥¦
犃S1 =2arctan2犫+ 4犫2+4(犪
2-犮
2槡 )
2(犪+犮).
è*
:犪=犔B犚,犫=-2犠B犚,
犮=犕s 犔2B+4犠2
槡 B +犔B犚-1
2犠B犔B-2犠B犛1 .
2)Ⅱn�=h4��.u {犅O}hê���[
,
�犃2 、犃3 �犃6 U���¿h
:(-犠B/2,犔B/2+
犛2)、(犠B/2,犛2)、(-犠B/2,-犔B/2+犛2).�ª
犃2犃3 、犃3犃6 U�ª$d�¿h
犔B2犠B
狓+狔-1
4犔B-犛2 =0,
犔B2犠B
狓-狔-1
4犔B+犛2 =0.
a)]羸æç£Oh犕s .
b)�犕I2 =犕s,�`犛2 .
犛2 =1
4犔B-犕s
犔2B4犠2
B
+槡 1.
c)¦§犕s�犛2 ,�`Ⅱn=h4��½U¾
@É�ÖÌ犃S2 .�犕E2 =犕s,�`¥¦
犃S2 =2arctan2犳- 4犳
2+4(犲
2-犵
2槡 )
2(犲+犵).
è*
:犲=犔B犚,犳=2犠B犚,
犵=犔B犚+1
2犠B犔B+2犠B犛2-犕s 犔2B+4犠
2槡 B .
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:犅I犘犃1,
犅I犘犃
2,犅I犘犃
3,犅I犘犃
4,犅I犘犃
5,犅I犘犃
6,̈
½íî¦�
k Ó �
{犅I}�
{犅E}* U 7 8 þ ¨
:犅犘犗01,
犅犘犗02,犅犘犗0
3,犅犘犗0
4,犅犘犗0
5,犅犘犗0
6.
ujI����[
{犅I}hê���[
,ç
]�É�÷(Ü÷>m*��ø6JjIÓ¦´®
ÓU>mwOh
犕犞G =
-2犚sin1
2犃( )M1 sin
1
2犃( )M1
2犚sin1
2犃( )M1 cos
1
2犃( )M1
熿
燀
燄
燅0
,
��4��UeT�
{犅E}*U78h
犅E犘犃犻 =
犅E犅I犚(犅I犘犃犻 -犕犞G)=(
犅I犅E犚)T(犅I犘犃犻 -犕犞G).
è*
:
犅I犅E犚=
cos犃M1 -sin犃M1 0
sin犃M1 cos犃M1 0
熿
燀
燄
燅0 0 1
,
犃MC1 hÜ÷>m*��U(wÖ
,efïSÓ�R
A��no¤A½UÉ�çè
,�.¥¦Öβ=0,
§¨Öγ=0.
�1、�2、�3、�4、�5ö�6U>mh�
$dh
犅E犘犃
u-犅E犘犗0狌 ≤犾2+犾3;狌=1,2,3,4,5,6.
Û§Ðè$dåÐŽÉ�ÖÌ奾@¬
,�
`O¥
犃Mu=
min(狀1,狀2),狀1 ≥0,狀2 ≥0;
狀1,狀1 >0,狀2 <0;
狀2,狀1 <0,狀2 >0;
/`
,狀1 <0,狀2 <0
烅
烄
烆 .
è*
:
狌=1,2,3,4,5,6,
狀1 =2tan2犻+ 4犻2-4(犽
2-犼
2槡 )
2(犽+犼),
狀2 =2tan2犻- 4犻2-4(犽
2-犼
2槡 )
2(犽+犼).
{�1,
犻=-2犛1
2犠B+( )犚 ,
犼=-2犚+1
2犠( )B
2
-犔B1
2犔B+( )犛 ,
犽=-2犚+1
2犠( )B
2
-犔B1
2犔B+( )犛 -犛2-
犎2+(犾2+犾3)
2;
{�2,
犻=-2犛 -1
2犠犅+( )犚 ,
犼=-2犚-1
2犠( )犅
2
-犔B1
2犔B+( )犛 ,
犽=-2犚-1
2犠( )B
2
-犔B1
2犔B+( )犛 -犛2-
犎2+(犾2+犾3)2;
{�3,
犻=-2犛1
2犠B+( )犚 ,
犼=-2犚+1
2犠( )B
2
,
犽=-2犚+1
2犠( )B
2
-犛2-犎
2+(犾2+犾3)
2 ;
{�4,
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2犠( )B
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,
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-犛2-犎
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犻=-2犛1
2犠B+( )犚 ,
犼=-2犚+1
2犠( )B
2
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2犔B+( )犛 ,
犽=-2犚+1
2犠( )B
2
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2犔B+( )犛 -
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2.
¦§3.1�3.2U��Oî
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Fig.7 Verificationflowchartofturninggaitwithconstantradiusofsixleggedwalkingrobot
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Tab.2 Simulationparametersofturninggaitwithconstant
radiusofsix-leggedwalkingrobot
êë êë¬ êë êë¬
犕s/mm 25 犃t1/(°) 14
犚/mm 800 犃t2/(°) 16
犛1/mm 117 β 0.5
犛2/mm 117 犺/mm 250
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Fig.11 Deviationbetweenactualandidealpositionsof
centerofgravityofsixleggedwalkingrobot
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Fig.12 Yawangleofsixleggedwalkingrobotduringturning
�RAç]�É�÷(ßL��.
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]yQR
(犚犲犳犲狉犲狀犮犲狊):
[1]KALAKRISHNANM,BUCHLIJ,PASTORP,etal.
Learning,planning,andcontrolforquadrupedlocomo
tionoverchallengingterrain[J].犜犺犲犐狀狋犲狉狀犪狋犻狅狀犪犾犑狅狌狉
狀犪犾狅犳犚狅犫狅狋犻犮狊犚犲狊犲犪狉犮犺,2011,30(2):236 258.
[2]ESTREMERAJ,DESANTOSPG.Freegaitsfor
quadrupedrobotsoverirregularterrain[J].犜犺犲犐狀狋犲狉
狀犪狋犻狅狀犪犾犑狅狌狉狀犪犾狅犳犚狅犫狅狋犻犮狊犚犲狊犲犪狉犮犺,2002,21(2):
115 130.
[3]MCGHEERB,ISWANDHIGI.Adaptivelocomotion
ofamultileggedrobotoverroughterrain [J].犐犈犈犈
犜狉犪狀狊犪犮狋犻狅狀狊狅狀犛狔狊狋犲犿狊,犕犪狀犪狀犱犆狔犫犲狉狀犲狋犻犮狊,1979,
9(4):176 182.
[4]WETTERGREEND,THORPEC.Developingplanning
andreactivecontrolforahexapodrobot[C]∥犐犈犈犈
犐狀狋犲狉狀犪狋犻狅狀犪犾犆狅狀犳犲狉犲狀犮犲狅狀 犚狅犫狅狋犻犮狊犪狀犱 犃狌狋狅犿犪狋犻狅狀.
[S.l.]:IEEE,1996:2718 2723.
[5]PALPK,KARDC.Gaitoptimizationthroughsearch
[J].犜犺犲犐狀狋犲狉狀犪狋犻狅狀犪犾犑狅狌狉狀犪犾狅犳犚狅犫狅狋犻犮狊犚犲狊犲犪狉犮犺,
2000,19(4):394 408.
[6]�ý
,O+�
,̧f¹.µT÷ã�RA^$7÷(UV
W
[J].�ÿbMc
,2004(3):48 52.
SUJun,CHENXuedong,TIAN Wengang.Astudy
5821&7'
��
,+
:�����4��������
oftheomnidirectionalgaitforahexapodwalkingrobot
[J].犕犪犮犺犻狀犲狉狔犪狀犱犈犾犲犮狋狉狅狀犻犮狊,2004(3):48 52.
[7]MIAOS,HOWARDD.Optimaltripodturninggait
generationforhexapodwalkingmachines[J].犚狅犫狅狋犻
犮犪,2000,18(6):639 649.
[8]BOJ,CHENGC,WEIL,etal.Designandconfigura
tionofahexapodwalkingrobot[C]∥犘狉狅犮犲犲犱犻狀犵狊狅犳犐犆
犕犜犕犃.Shanghai:IEEE,2011:863 866.
[9]�¸º
,]&ß
,»&+.ÎzµTgI�RAö÷�Ö
÷(UVW
[J].]+!Ë>d
,2002,10(4):392 396.
XU Xiaoyun, YAN Guozheng, DING Guoqing.
Researchonminiaturehexapodbiorobotanditstripod
gait [J].犗狆狋犻犮狊犪狀犱 犘狉犲犮犻狊犻狅狀 犈狀犵犻狀犲犲狉犻狀犵,2002,
10(4):392 396.
[10]GONZALEZDESANTOSP,GARCIAE,ESTREM
ERAJ.Improvingwalkingrobotperformancesbyop
timizingleg distribution [J].犃狌狋狅狀狅犿狅狌狊 犚狅犫狅狋狊,
2007,23(4):247 258.
[11]ý¼½
,ý¾.^$7¾T÷ã�RAJTUWM—IIÉ
�÷(ËÌUVW
[J].D`�X@++ú
,1995,
29(5):87 92.
MAPeisun,MALie.Astudyofturninggaitcontrol
forquadrupedwalkingvehicle[J].犑狅狌狉狀犪犾狅犳犛犺犪狀犵犺犪犻
犑犻犪狅狋狅狀犵犝狀犻狏犲狉狊犻狋狔,1995,29(5):87 92.
[12]\òn
,}5
,u�..¾TgI�RAæçq�ç$
�
[J].¿ÀÁ>�@++ú
,2008,40(7):1063 1066.
WANGPengfei,HUANGBo,SUNLining.Stability
judgingmethodforquadrupedbionicrobot[J].犑狅狌狉狀犪犾
狅犳犎犪狉犫犻狀犐狀狊狋犻狋狌狋犲狅犳犜犲犮犺狀狅犾狅犵狔,2008,40(7):1063
1066.
[13]OÂ.Æ�]ªzT3UµT�RA÷(IÏ�NØ
:rVW
[D].fg
:23@+
,2012:30 31.
CHENCheng.Gaitgenerationandpowerconsumption
optimizaionofhexapodwalkingrobotwithsemiround
rigidfeet[D].Hangzhou:ZhejiangUniversity,2012:
30 31.
[14]ASIFU,IQBALJ.Anapproachtostablewalking
overuneventerrainusingareflexbasedadaptivegait
[J].犑狅狌狉狀犪犾狅犳犆狅狀狋狉狅犾犛犮犻犲狀犮犲犪狀犱犈狀犵犻狀犲犲狉犻狀犵,2011,
2011:1 12.
[15]GUARDABRAZOTA,JIMENEZMA,GONZALEZ
DESANTOSP.Analysingandsolvingbodymisplace
mentproblemsinwalkingrobotswithroundrigidfeet
[J].犚狅犫狅狋犻犮狊犪狀犱犃狌狋狅狀狅犿狅狌狊犛狔狊狋犲犿狊,2006,54(3):
檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾檾
256 264.
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