turning gait with constant radius of six-legged walking robot

9
!48"!# 2014$% !"#JournalofZhejiangUniversity EngineeringScience Vol.48No.7 Jul.2014 $%&'2013 03 25. ()*""+!"#,-www.journals.zju.edu.cn eng ./01&'()*+,-zVW}*+,-./0151221004 ); 234øÓ*S~./012010R50036 2345O1986- ), F5HJKªNRAM·ËÌ@`M¯4UVW.Email gchen zju.edu.cn XYZ[A-F5`.Email bjin zju.edu.cn DOI 10.3785 j.issn.1008973X.2014.07.020 ýþÿ _> ö ϵ ÿe e :f ge h 23@+ ºmbM[Ú&'øÓó/23 fg 310027 H IUÖ÷(ÖŵT÷ãRAç]É÷(*#o,ÅÖ÷(]É÷(ÿ³$Ç riµT÷ãRAÉ÷(Uø6ªÎfstç]>fU$>¦µT÷ãRAUç] É÷(*#o,Åæçqh>mhU µ T ÷ ãRA¾@É Ö ÌU `$ µ T ÷ ã RAç]É÷(*n¿=h4 É ½P§¨UÉ Ö ÌJ T M RAÉ «d*Ü÷N MATLAB ADAMS{,ÅÖ÷(UµT÷ãRAç]É÷(âã ghgh´óZi#oUÉ÷(ÿ³$UßLqJKLµT÷ãRAç]É÷(Ö÷( MNAOPTP242 QRSTUQVWP1008 973X 2014 07 1278 09 犜狌狉狀犻狀 犵犵 犪犻狋狑犻狋犺犮狅狀狊狋犪狀狋狉犪犱犻狌狊狅犳狊犻狓犾犲 犵犵 犲犱狑犪犾犽犻狀 狉狅犫狅狋 CHENGang JINBo CHENYing 犛狋犪狋犲犓犲 犔犪犫狅狉犪狋狅狉 犉犾狌犻犱犘狅狑犲狉犜狉犪狀狊犿犻狊狊犻狅狀犪狀犱犆狅狀狋狉狅犾 犣犺犲 犻犪狀 犝狀犻狏犲狉狊犻狋 犎犪狀 狕犺狅狌310027 犆犺犻狀犪 犃犫狊狋狉犪犮狋 Thetripodgaitwasusedinturninggaitwithconstantradiusofsixlegged walkingrobot.The planningmethodforturninggaitwithconstantradiusbasedonthetripodgaitwaspresentedwhichsimpli fiestheturninggaitofsixleggedwalkingrobot.Themethodusinglinesegmentstotrackthecircletrajec toryofcenterofgravityofthesixleggedwalkingrobotwasemployedtotheturninggaitwithconstantra dius.Anapproachtocalculatethemaximumturningangleofthesixlegged walkingrobotwasproposed basedonstabilityconstraintand motionconstraint.Differentturningangleswereappliedintheturning gaitwithconstantradiusofthesixleggedwalkingrobottoimprovetheturningabilityineverystepwhen thetwogroupsoflegssupporttherobotrespectively.A simulation wasconducted with MATLABand ADAMStoverifytheturninggaitwithconstantradiusofthesixleggedwalkingrobot.Resultsshowthat theturninggaitwithconstantradiusiscorrect. 犓犲狔狑狅狉犱狊 sixleggedwalkingrobot constantradius turninggait tripodgait T÷ãRA Iu Cþ P Ô ÒVW õãÅÒT÷ãRA K 1 (Äã UVW *ÒT÷ãRA÷(ÿ³*æøÃUVW$ wKalakrishnanÐ 12 {÷ãRAUªã÷ (( É÷([\ ö Ð ÷( âãVWÑ o ( McGheeÐ u µ T ÷ ãRA æ çqO>mqhhP{þè¨ÿ³÷ (.Wettergreen Ð X«(Ä ÷( ³§¨ ç ÷(¯GJ T# 8 µ T ÷ ãRA{ o ( UEÖq.PalÐ P iz $ çR Aæ½Æ U (J Tÿ³µ T ÷ ãR AU÷(³U(Ä ÷(Q ´ ø Å,ÅRA æ çqãÑh ¨ µ T ÷ ãRA _ O u Ù S e Tÿ³ RA ÷

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DESCRIPTION

Cara mengetahui radius belok robot hexapod yaitu dengan mengikuti radius lingkaran yang telah dibuat.

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Page 1: Turning Gait With Constant Radius of Six-legged Walking Robot

!48"!7#

2014$7%

! " # $ $ %

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)JournalofZhejiangUniversity(EngineeringScience)

Vol.48No.7Jul.2014

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:2013 03 25. ()*""+

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),-

:www.journals.zju.edu.cn/eng

./01

:&'()*+,-�zVW}�*+,-./01

(51221004);234øÓ*S�zÑ~^³./01

(2010R50036).

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、M·ËÌ

、@`�M¯4UVW.Email:gchen@zju.edu.cn

XYZ[A

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,5`.Email:bjin@zju.edu.cn

DOI:10.3785/j.issn.1008973X.2014.07.020

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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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Page 2: Turning Gait With Constant Radius of Six-legged Walking Robot

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Page 3: Turning Gait With Constant Radius of Six-legged Walking Robot

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Page 4: Turning Gait With Constant Radius of Six-legged Walking Robot

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犔B2犠B

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a)]羸æç£Oh犕s .

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4犔B-犕s

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+槡 1.

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@É�ÖÌ犃S1 .��ø6�£´®Ó犅E1 ÓU�

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: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 .

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�犃2 、犃3 �犃6 U���¿h

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犔B2犠B

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4犔B+犛2 =0.

a)]羸æç£Oh犕s .

b)�犕I2 =犕s,�`犛2 .

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4犔B-犕s

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+槡 1.

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@É�ÖÌ犃S2 .�犕E2 =犕s,�`¥¦

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2+4(犲

2-犵

2槡 )

2(犲+犵).

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: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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���[

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Page 5: Turning Gait With Constant Radius of Six-legged Walking Robot

N6 ⅠxⅡ�/A62ù78/d?9*µ$Ëp¯°N

Fig.6 Maximumturninganglewithrobotsupportedby

legsinⅠandⅡgrouprespectively

[

{犅}þ¨.íî�ç]�É�÷(Ü÷¸I½U

�4��UeT�

{犅I}*U78

: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

2犃( )M1

2犚sin1

2犃( )M1 cos

2犃( )M1

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

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

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

-犔B1

2犔B+( )犛 ,

犽=-2犚+1

2犠( )B

-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

-犔B1

2犔B+( )犛 ,

犽=-2犚-1

2犠( )B

-犔B1

2犔B+( )犛 -犛2-

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犻=-2犛1

2犠B+( )犚 ,

犼=-2犚+1

2犠( )B

犽=-2犚+1

2犠( )B

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2+(犾2+犾3)

2 ;

{�4,

犻=-2犛 -1

2犠B+( )犚 ,犼=-2犚-

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犽=-2犚-1

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2 ;

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犻=-2犛1

2犠B+( )犚 ,

犼=-2犚+1

2犠( )B

+犔B -1

2犔B+( )犛 ,

犽=-2犚+1

2犠( )B

+犔B -1

2犔B+( )犛 -

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Page 6: Turning Gait With Constant Radius of Six-legged Walking Robot

犛2-犎2+(犾2+犾3)

2;

{�6,

犻=-2犛 -1

2犠B+( )犚 ,

犼=-2犚-1

2犠( )B

+犔B -1

2犔B+( )犛 ,

犽=-2犚-1

2犠( )B

+犔B -1

2犔B+( )犛 -犛2

-犎2+(犾2+犾3)

2.

  ¦§3.1�3.2­U��Oî

,ÛⅠn�h4

��½ç]�É�÷(U¾@É�ÖÌh

:犃mt1 =

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]� É � ÷ ( U ¾ @ É � Ö Ì h

:犃mt2 =

min犃S2,犃M2,犃M3,犃( )M6 .é§DE"�`U¾

@É�ÖÌ

,�µT÷ã�RAç]�É�÷(ÿ

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4 ç]�É�÷(óZ��

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÷ã�RAç]�É�÷(âãghóZ.ghê

ëõµ2"j

,ghóZºdõi7"j.

N7 ýþÿ!_>"ö#ϵ$ÿe�:u�N

Fig.7 Verificationflowchartofturninggaitwithconstantradiusofsixleggedwalkingrobot

  1)¦§µ1UµT÷ã�RA��êë

,µ2

U¾¸æç£OöÉ�]�

,Ä MATLAB^¨µ

T÷ã�RAç]�É�÷(*UÜw[÷\û�

¾@É�ÖÌ.^¨�´õ�

:Üw[÷\ûh

117.4987mm,¾@É�ÖÌ�¿h15.4561°、

19.7624°,¾´gh*Uxåêëõµ2"j.µ

*

,犚hÉ�]�

,βhÛM[ë

,犺h��8Ì.

\2 ýþÿ!_>"ö#ϵ$ÿe;<]^

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

  2)¦§÷�1)U^¨�´ö2©�ŵT÷

ã�RAç]�É�÷(Uÿ³$�

,{�RA÷

(âãÿ³.

3)¦§ÿ³]ÏUµT÷ã�RAç]�É�÷

(

,��MATLAB��¦§�RA¤>m+^¨µT

÷ã�RAÆ��­U�­ÖÌα,õi8"j.

4)�� ADAMS����µT÷ã�RA�

z

,hiËé�RAªzT3��{�RAÉ�!

ÌU£¤

,�z*��þ¨AJU«0T3bðª

N8 ýþÿ!_>"-=J>?J>Ëp

Fig.8 Jointanglesofsixleggedwalkingrobot

3821&7'

��

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Page 7: Turning Gait With Constant Radius of Six-legged Walking Robot

zT3

[1315];)»¦§÷�3)¥¦U�RAÆ��

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ãgh

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õi9"jhµT÷ã�RAç]�É�÷(

ADAMSghi.i9²EiµT÷ã�RA¤½

bÉ�«d*7Å8�ùz78½Ugh�´

,ù

z7 8 � ¿ h ç ] � > � f U 0°、45°、90°、

135°、180°、225°、270°、315°78.õi10"j

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LAB*^¨¥¦U�RAÆ��­U�­ÖÌh

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ë

,�ADAMS{�RAÉ�÷(gh*�RAÆ

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ã�RA>m«d*�RA�{¬øzÐ��.Ä

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,DE1)、2)、3)

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,¬ÏÆ��¯Gþy¢�ö°±

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f.îgh*µT÷ã�RAç]�É�«dh¸

oËÌ

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m�fbÿ³ôR�f�IUuûG9K§�²¥

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,)T¾@uûG9¸Å25mm,�³´,�

á.õi12~14"j�¿h� ADAMS*âãÉ

�÷(gh*�RA��U(wÖ犢aw、¥¦Ö狉oll

�§¨Ö狆itchUørçè.�÷(ÿ³*

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RAç]�É�÷(ÿ³$�_ßL

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Fig.9 SnapshotsinADAMSsimulationforturninggaitwithconstantradiusofsixleggedwalkingrobot

5 � Ó

(1)efX«���Ö÷(UpÓ

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Page 8: Turning Gait With Constant Radius of Six-legged Walking Robot

N10 ýþÿ!_>"_â'¼+,Ç�Å�?Ç�

Fig.10 Idealandactualpositionsofcenterofgravityof

sixleggedwalkingrobot

N11 ýþÿ!_>"_â'¼�?Ç�C+,Ç�

?@AÒÑ

Fig.11 Deviationbetweenactualandidealpositionsof

centerofgravityofsixleggedwalkingrobot

N12 ýþÿ!_>"µ$��M?B¿Ë

Fig.12 Yawangleofsixleggedwalkingrobotduringturning

�RAç]�É�÷(ßL��.

�»5VW*U)efVWÏ´Ö�ŵT÷

ã�RAA�*

,X«�óâæ÷óZ,Å�Ö÷

(UµT÷ã�RAç]�É�÷(U��q.e

fgh�´µ¶

,̧oËÌçè��RAÉ�«d

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¤�RAUã�!Ì

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�RAã�!Ì

,JTvwÄÅG9§�Ö@T¬

N13 ýþÿ!_>"µ$��M?CDË

Fig.13 Rollangleofsixleggedwalkingrobotduringturning

N14 ýþÿ!_>"µ$��M?EFË

Fig.14 Pitchangleofsixleggedwalkingrobotduringturning

Ï�RA�p>m�fYøuûÿ³�f.

]yQR

(犚犲犳犲狉犲狀犮犲狊):

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