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Motion design of a hybrid wheeled/legged robot for lunar exploration


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M o i n d sg   f a h b i   e l d l g e   o o   o  u a   x o a i n to   e i n o     y r d wh e e / e g d r b tf r l n r e pl r to  
IX io— igl KEI a qn CHEN Xu — n   , T AN  n— an e do g I We g g1 L GO  t n e Wa a ab  
. 。

陈学东,  

田 文罡 ,  

李小清,  

渡边 桂 吾 

( . col f c aia S i c n  n ier g 1 S ho o  hncl ce ea dE gnei ,Huz ogU i ri f c neadT cnlg ,Wu a 30 4, hn ,   Me   n n ah n  nv syo  i c n  eh ooy e t Se h 4 0 7 C ia  n E malc e x e 3 8 s a c r ; . e t f d a c d S s m   o t l n ie r g a a U ie i , a a ) — i: h n u 8 8 @ i . o 2 D p .o A v n e   yt sC nr   g ei ,S g   nv r t J p n   n n   e oE n n s y

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s e s ssx d g e — ffe d m . s s e   i  e e o -r e o   r

o   r tt p si   e l d o  r c   c a im  nd i e - fp o oy e  n wh ee   rta k me h n s a  n l g 
g d m e h n s . Alh u h e   c a im t o g  whe l d e e  m o l r bos a   bi e o t c n

q i k y mo e n t e pln  s f c . Th y c n’  d p   u c l  v  o   h   a e ura e e   a ta a t
t e ev s o h  e te l u e e  g o n h ms le  t t e x r me y n v n r u d. On h    t e

c nrr o ta y,l g e   l i g r bosa e a e t r v lo  h   e g d wa k n  o t  r   bl o ta e  n t e
ir g lr g o n re u a   r u d. Ho v r, t e we e h  m o e n s e d f a v me t p e  o   

lg e   l n  o o  sr ltv l  lw ,a d t   o to   e g d wakig r b ti  ea ie y so n  he c n r l
i  o p ia e sc m lc t d. I   r e  o s l e t e p o lm ,s m e r - n o d rt  ov  h   r b e o  e   s a c e s i r d c d h  c n e t f y rd e r h r  nto u e  t e o c p  o  h b  wh e e / i e ld   lg e   e h ns e g d m c a im  . I  t s a e n hi p p r, a e  n w h b d yr   i

Fi 1 H y i whe l d e ge r bot g.   br d  e e /l g d  o  

wh ee /lg e  me h n s e ld e g d c a im i p o s d o e in n s r po e  t d sg  a  
o n d r ci n l u a  r v r f r h  l a   x lr to   m i ie t a l n r o e   o  t e un r e p o ai n. o

Un i e t e e itn   n s,t   r po e   o o  s s t u   lk  h   xsi g o e he p o s d r b ti  e  p
b     a r e  o o  t  wo a t e d a - e lc se s y a qu d up d r b twi t   c i   u lwh e  a t r  h v e u p d u d r h   o o  d q i pe   n e  t e r b t bo y. T r f r he eo e, t i  o o  hs r b t

c n wak o   h  e te l  ne e   e a n wi   t  e — a   l  n t e x r me y u v n t r i  t is l g  h
gd e  m e h n s , wh r a  i c a im e e s t o e  o  t e ea iey  m v s n h  r l t l  v p a e tran wih iswh ee   c a im . l n  e i  t  t  e l d me h n s  

Fi 2  Le m e hanim   g. g  c s

1 M ECHAN I     SM oF  THE  RoBoT 

2 1 Ga t De i i o   .  i   f t n n i
Fi 1 h ws t   c e a i d a n   f t   y rd g.  s o   he s h m t c r wi g o  he h b i 

wh ee /lg e  o o .Two o i ie to l  c ie d l  e ld e g d rb t   mn d r c ina a tv   ua — wh e c se s e l a tr  a e q i p d n e  t  q a r p d r  e u p e  u d r he u d u e 
m e h n s . Th   wh ee   m e h n s c a im e e ld c a im  c n e t  t e o n cs h  

A sces ep r r a c 1t ps igae dp t  uc si   e om n e(i  — n h a —u  v f fu w
d wn)frfu   g fteq a r p drb ti d f e  s o o  o r e so    u d e  o o    e n d a  l h u s i
a g i  y l . F g 3 s o  he s he ai  a ng o      atc c e i .   h ws t   c m tc dr wi   f a

g n r l e   a tc c e,i   e eai d g i y l z   n whih t e do d  ie r p e  c   h   ue l   e r — n s n s t e nta p su e f t e o b t e t  h  i i l o t r  o   h  r o .wh l t e s ld i ie h   o i   ln   e oe  h   e t i ii   su e a tr a g i c c e  i e d n ts t e n x  n t po t r   f     a t y l . l a e  

q a rp drb t i  eo t jit i.2pee t a u du e  oo  t rv l e ons g  rsns   wh u   .F  
l g me h n s o he q a r p d r b t e   c a im  ft   u d u e   o o ,wh c   a  hr e ih h s t e  

a t e iit.T e iitb t e  h  e   n  h  o ti  ci  ons h  on  ewe n te lg a d te fo s v
s h rc o e s  h tt e b d   ft e qu d p d r b tp — p e   n   o t a h   o y o  h   a r e   o o   o   i u

T e mo e n ( rn lt n n   tt n) o  e r — h   v me t ta sai  a d r ai o o o f t   o  h
b t b d   n a g i  y l  s d fn d a   e srd   f t e o   o y i     atc ce i  e e   t   ti e o     i s h h

Re e v d 2 o c ie   0 3—0 —0 . 6 3 

S osrdb   -ehR sac  dD vl m n Porm fC i ( rn  . 0   4 2 8 ) pnoe yHi c  eerha   eeo e t rga o hn G at T n p   a No201 2 30   AA

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Jun lfHabnIstt o eho g Nw Srs ,V11 N . , 0 3 ora  o ri  tuefTcnl y( e ei ) o.0, o3 20  ni   o e
”P   =【 ( + )  。m    
y  


凡 。 一。 一 】 ,       ‘  

【  . . s s .】     s  , :
= 1,i fi= 3 o   h e     r4,t n

whe e,i i= 2 o     e  l = 1;i r f   r4 t n h f/= 1o   h e     r3,t n
= 一

1;i i= 1 o   h e   f   r2,t n




1 Z( .。   i=1 2 3 4 e o s en x f tod a / , , , )d n t    e toh l  et h  

h ih   ft e l g o   e u e e   r un   u f c e g to h  e   n t   n v n go d s ra e.I o — h tfl 
lwst a  o   t h O p似 = O + 足0 p    +R~ ‘ p  .  

2 3 De e m i io o   qu nc   fSwi .  t r nat n  fSe e e o   ng  g Le   Th  ee t n o   es q nc   fs n  e  sb s d  e s l c i   ft  e ue e o  wi g lg i  a e o h

o  es t  t it  ayi i.  hw   epoe— nt  t i s blya l s g 4so s  r c  h a c a i n s .F h t j
to   ft e qu dr e r b t i h rz n a   ln   , , in o  h   a up d  o   n o o t l pa e Ai Aj  o i

A adA , e rsn  epo ci so  tod fte   n   rpee tt   rj t n ff h lso    z h e o o h

o o,w i     h   r et n fcne? - ai   f rbt hl ci tep jc o so etr f rvt o  e s o i og y
D 

t e r b t L n igAi n   A a d c AIa d c A   d c h  o o . ikn   dc,   a n  ,     ,z n n a   
wih sr i h  i e t   tag tln s,r s c ie y,t e e sr ihtln s a e e pe tv l h s   ta g  i e   l   d fn d a  he b u d r  i s u h t   u da y l s e e  st   o n ay l i ne .S c  wo b n r  i   o ne c nsi t  n a e   i h i  e ne   o b   h   t tc ly o tt e a   r a wh c  s d f d t  e t e s i a l  u i a sa l  r a.Th   e ue c   fs n  e   ft e r b tC l  t e ae b e s q n e o  wig l g o h   o   al o b   e e i e   y u i g t e sa i  t b lt  ay i  . e d tr n d b   sn     t tc sa iiy a lss   m h n

F g 3 A  a tc c e o  h   u d u e   e h n s i.   g i  y l   f t e q a r p d m c a im 

rbt h   oind s n( at e eai )o  el - o o.T em t   ei o g gig n rt n fh   g    o t e
g d r b tme n  o dee mi e t e fo h l   o ii n   n   e   o o  a st  t r n  h  o t o d p sto sa d
s q n e o  wig l g i     a tc ce  e ue c   fs n  e  n a g i y l .  

2.   De e m i t蚰 2 t r na i

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I  i. , 。 O Z) e rsns h  ol ori nFg 3 ∑ ( XY rpeet tew r cod—   d  
n t f me w i ∑ (xz d n t   h   oria   ae r , hl   cy ) e oe te codnt   a e s e

f mef e t h o o b d .   i= 12, , )i te r   xda terbt o y A ( a i     , 34 sh   
c re t f o od o iin , whi   u r n   o t l  p sto h l A e
。  

d n t s h  ne t e oe  t e x 

fo o d p st n at rag i c ce.Th   t d   ft e r — o t l  o ii   fe     at y l h o   e sr e o  h  o   i
h t i    atc c e i  x r s e   yS wih c mpo e t    o  n a g i  y l s e p e s d b     t  o n n sS

i  一 ie to n d r c i n,S n Y d r c i n,S: nz die to  i   — ie to i — r c i n,a d n  a tr n a l    u nig—nge . As u   h t h  sa t g o iin s me t a t e t ri  p sto   n a dR。 n    ,i  i— swrt  a d o e t to   ft  o o  r   x r se   y n   r n a in o  he r b ta e e p e s d b   i t e o  he r b ti  te  ie,de o e   y ur  ft   o  n dot d ln o n td b  

wi  e p c o∑。 e p ciey h s h  nt lp s  t rs e tt h ,rs e t l .T u ,te iia  o — v i

ro o — i o cs   s a   n  0 。 ] x  , c

0 

_ L % l 【     ,    
0   0   0   1j   
wh r  0 rpr s n st e sa tn   re t t n a g e o  h   e e   e e e t h   tri g o n a i   n l  ft e i o

rb twi  e p c o∑。i h   atc ce o o  t rs e tt h n t e g i y l.Ea i   s y,w   l e
o ti   e n x n ta  o t r   ft e r b ta trt   at b an t   e ti iilp su e o  h   o o  e  he g i  h f

T ef todp s ini   cy ) a    a ua— h   oh l oio  o   t n∑ (xz Cl b cll t l e c   e codn     ejitp s i s h e poef n  f d acrigt t  o   oio .T   r c o so  oh n tn j i t e fo h l s n 一 p a h   o t o d  i  y l ne o ∑ (x z r  eoe   y f   cy )a d ntd b   e (  Y  ,  ,   , 戈 Y ,  , ) h eeoe   。 。 ( Ⅱ, ) (  , ) ( Y .T rfr, , ) Y


c c e,d n t d b   yl e oe   y T‘,a  ol ws sf l o  

t e b u d r  l   r u h A a d c a d t e o u d r   h   o n ay i t o g   ne h n    n    b n a y h l     n    a   e e p e s d b i Aia d c c b   x r s e   y,r s e tv l   ne n e p c i ey,
,  
’  

z =  p】 ’ = 0 1  } 【   , L J  
wh r  ee

,  
。  

rO( o   ) 一s ( o   ) 0  CS +   i   +   n 7

Th , t  sa ia l sa l a e  c ns t t d b   t e us he t tc y t e r a o t u e   y h   l b i b u da  i e  s fr u a e   y o n r ln s i o y m ltd b  
≤ y≤ 
X a  /

R lna+ ) c(0  ) 0   :  (0    o  + L   s i s   I .
0   0   1l -  
F o Fi. r m  g 3,we a s   bti  h  o lwi g r l t n—   o o an t e f l l o n   ea i   o s is hp   O p 
O p 

.  

Ba e  o  t e pr p s d o ua i n, a e a —i   s d n h   o o e  fr lto m  r ltme
:O p  +   一  P 
=  + o     ,  

,  

o e a in o  e e tn   e s q n e o  w n  e   alb   p r to   fs l ci g t   e ue c   fs g lg C l  h i e i e n   c o d n   o t e f l wi g r l s:fr t t e mplme t a c r i g t    ol n   u e i s , h   h o
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J un lfHabnIs tt o  eh ooy( e   e e) o. 0 o 3 2 0   or   ao ri  tue f Tcn l ni   g N w Sr s ,V 11 ,N . , 0 3 i
r b tm u tb   t tc l   tb e;s c n l e c  e   ny o o  s  e sa ia l sa l y e o d y, a h l g o l 

T =[ 2   
, ,  

,  

2 h ; = [    ] Y 七

咖].   

wo ksa  he s ng l g o e a g i c ce;a d t id y, r   st   wi  e   nc     at y l   n  hrl  
t   e   te c   o s n t e c e   t  l wa e o r a h he lg sr th d e   o   x e d is a l o nc  t  e c   t e de ie  o to d. h   sr d f oh l  

3   M o  o N  n DES G N  I oF W HEELED M[ ECHA?   NI SM   3.   M o i   od lofAc l e Dua ? he lCase   1 ton M e    tv   lW e  tr Fi . 5 h ws h   d l f a   c ie u lwhe l g  s o  t e mo e o  n a t  d a — v e 

cs r o I rpee t te f c  oria   yt   at . n  e rsns h  o e codnt ss m e j   r e e i da te s e n   e t   f h  at ,i hc    f e  t h  t r g c ne o te cs r n w ih x x   ei r   e   f
h s t   a e d r c in a  he f r r   f t   a t r  a  he s m   ie to   s t  o wa d o  he c se .

d n ts山e die to   n l  ft e c se ,F,a     e   e oe   r ci n a g e o  h   a t r nd Flr — p e e t山 e a t a i n f r e o  h   a t r tflo  h t rs n   cu to   c   ft e c se .i o l ws t a  o  
D 


【 _ 麓 c  
,   =  ̄

( 1 )  
一  

F g 6 M o lo i.   de  fwh e e   o o   e ld r b t

: 

+ 

— m 。  

b(  F
 


)争。 一  ,  

A crigt E s ( )a d( ) ifl w   a codn     q . 1 n 2 , tol st t o   o h  


whe e m。i h   a s o  h   u lwh e  a t r 。i h   r  s t e m s   ft e d a — e lc se ;, s t e mo e   fi ri  r un  he c n e   fr tto   x s o   m nto  ne t a o d t   e t r o  o ai n a i  f a t e c se h   a tr;sa     r  h   tu t a  a a tr .   nd ba e t e sr cur lp r me e s  wh r  ee A =  

Ax + BT, Y = Cx,  



≥】 =  ,   。  

y 

C =  

1    1 r 000     0      0  1
【  0 1 0 0 0        

I  n whih A。a d B。a e 3 ×3 wh l  c  n  r    ie C。i  ×4 c e l  s3   of— l
c e   a rx  intm t . i

4 S耵 ULATI0     oN 
C 

T ec r so dn   c a i  aa t sae矛V h o ep n igmeh ns p rme r r m e  —  
e  s n a :m = 1 0 m m ,n = 2 0 m m ,u0 = 25   0  0  2 mm ,  

M : 2   g,m 2k

= 6 5 g,I = 3 4 g ?m ,I = .  k .  k 。  

0 1 g?   L =00 1 .2k m , .0 
D 

?n , I c=l5k I2s 2 _  g?n/ ,  

r= 5   0 mm .s = 75 mm ,b = 1 0 mm 。L = 3 0    5  5 mm.  
Fi .   D ua - g5 lwhe lm e han s   e  c im

As u  h tt e i i a  o i o   o r i ae   f fu  e t s me t a  h  n t l st n c o d n t s o   r f e  i p i o

a dC G o 山erb t r    l w 1 n : l 一3 2  n   0  f  o o ae f l s( l ) A ( 5 ,   a oo s n
3 2 Con r lM O lOft e W he l d  e h im   .  to  de   h   ee n c an s
Fi 6 s o  h   c e ai  r wi g o  h   e l d g.   h wst e s h m tc d a n   ft e wh ee  

2 0 0)A ( 5 2 0, ) A (一 3 2 一 2 0, )  0 , , 2 3 2,0 0 , 3 5, 0 0 , A ( 5 ,一2 0, ) c 0 0,3 ,/ = 0 43 2 0 0 ,( , 2 6) o 0 .卟 e rb t  oo 
c a s f r a d n u h  d r c in 山 a r wl  w r  i s c  a ie to o t山 e a g e e —   n l b   t e  h   r ci n a d X  i s4  .The srd   f山 e we n t e die to   n   a si  5o x   ti e o  
r b ti  h sg i c ce i  5   o o  n t i  a t y l  s2 7 mm . T e n x  iht  f   h   e thes so   t e fo h l   r  0 m m ,1   m 。一2 mm 。一2 mm 。 h  o t odsa e 1   0m 0  0   

me h n s ,i  c a im n whih o i  h   e t ro   r vt  ft e c     s t e c n e   fg a i o  h   y
wh e e   c a im , wh l  。 a d o6 r  t  c n e t e ld me h n s ie o n    a e he o n c 

ji sb tenteb d n   oat ed a— h e cs   on  e e    o ya dt  ci  u l el at t w h w v w   —
e s r s e tv l . r , e p c i ey  i  t e d r c in a l  o   t e s h   ie t   nge f h   o wh ee   c a im ., , , Fh a   a e t   c u — e ld me h n s   F  ,  nd Fh r  hea t a  to  o c s o  h   o r s o d n   e l. Th r f r   i n fr e   ft e c re p n i g wh e s e eo e,


r s e t ey.T e eo e.t   t d   f山e r b t n 山i  ep ci l h rfr v he sr e o i   o o i s g i  y l s a  o lws atc c e i  sf lo   S = S,   ,= 1 2 mm ,S,= 0 mm , 8      = 0。  . Usn  he p o s d me h d,h n e,t e n x o t  i g t   r po e   t o e c h   e tfo —
h l   r   t r i e  o b   ods a e dee m n d t  e

F  + Fh ,  



My = F 、 。 +F   h, () 2  L    ̄,   一F cs  o F   )一   (   一Fx , F b) 


wh r    e eM i s山 e ma s o  h   e ld me h n s :Ii  h     s  f te wh ee   c a im  s te
mo n   f ie i  r u d te c n e  fg a i me to  n r a ao n   h   e tr o   rv t t y;L i  h    s te

A1 一10,8 ,0 , 2( 3 3 3 1 )  " ( 7 3 3 1 ) A   5 4,8 ,0 , A  一1 0 3( 7 ,一1 9,一2 ) A  5 4,一1 ,一2 ) 0 ,4( 3 9 0.  
An   lo,t e s q n e o   wig lg o   e r b t d as h   e ue c   f s n   e   f t   o o  h i  h sg i c ce i  ee i e   o b   _ —4 —  . n t i  a t y l  s d t r n d t  e 3 ÷1   m  

ds neb ten 。 n  6 = [ Y 咖 5   ia c e e  ado. t w o     g 'y
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J un l fH ri Is tt o  eh ooy( e   e e) o. 0 o 3 2 0   o ra  abn ntue f Tc n l o   i   g N w Sr s ,V 11 ,N . , 0 3 i
Si l t n tme o   to   o to   f t   e l d mu a i   i   f mo in c n r l o  he wh ee   o me h nim  s 2  S; s mp i g p ro  i 1  ms;k : c a s i  0 a ln   e d s 5 i  
1 0: t e ni a v l e f t e t t v ra l i  . h  i t l au  o   h  sa e a b e S i i =  

i  t wh ee   c a im  n   n t e e t me y u e e   n i   e l d me h n s a d o  h   x r s e l  n v n
tr an i  t  e g d me h n s . e i  n isl g e   c a im   Re e e e   f r nc s:

[   0 0 0 0 0】 0          ;a dteii a  o tr  f a h n  h  nt l s eo  c   i p u e
d 1wh e  a t ri n z r   o i o ua . e lc se  S i  e o p st n. He e.P . a t o   i r I g isf r e c   eo i   r   s u e  o b a h v lct a e a s m d t  e:k = 2 ,  = 20,   y   0 k k


1 0, k  

= 3 . Th   r f r n e v c o   i Y = 0 e ee e c   e t r S ,  

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