Computer Animation of Human Walking: a Survey

(1)

HAL Id: inria-00073249

https://hal.inria.fr/inria-00073249

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

Computer Animation of Human Walking: a Survey

Franck Multon, Laure France, Marie-Paule Cani, Gilles Debunne

To cite this version:

Franck Multon, Laure France, Marie-Paule Cani, Gilles Debunne. Computer Animation of Human Walking: a Survey. [Research Report] RR-3441, INRIA. 1998. �inria-00073249�

(2)

ISSN 0249-6399

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Computer Animation of Human Walking: a Survey

Franck Multon, Laure France, Marie-Paule Cani-Gascuel, Gilles Debunne

N ˚ 3441

Juin 1998

TH `EME 3

(3)

(4)

&!'(*)

+-,/.10-24357698;:/<=0?>A@CB*.16-,"DE+-,/.F092GDAHI@J5K.F,MLNDGOPQ.F698NDSRT.10-L;OUV.1W/2X6YDZ8\[I@CUL\8\8\DAW

]^DA_9690-0-DA[

`badc e^fgh ikjXlmf npo4q lsrutvjVadtvewewf xye o4qmazr{jdfv|

r}e ov~f"|zt4jzjd"f"|Fq"t4jzjFovrumovjq"f"

?nmtvf lAi=|1biY|rNVi

ov=t4nslfnsf"qmadf nmqmadfj-g4z(h vzr{jS/h gg(Fov~f"

9 ¡M¢¤£¥4¡G¦ `bazruFov=fnzns§f ¨A©lsadfsf l©tvª9lmfqmajr{«Xf"©zf§f ¬ut4=f"r{j®bt4e!lmf n

nmovar{q"ªNt4nQovjr{e^ovlr{jd~TaXe^ovj¯bov¬{°Xr}jd~±*²Ef³nsl©ªNtAqQt4jlsadff§tv¬{lrut4jª;nmt4e

nmf ¬{¨°Xr{jdf e ovlruq´°Xjdt/¯¬uf~f xyµFo4f"¶ewfladtZz©lmtovznmtGovqmadf"laFovlr}jdq"t4n·tvnpovlsf

z¨XjFove!ruq"Tqt4jdlsnpo¤r{jXlm|tvnTdsfz¨XjFove!ruqTr}e(¬;o¤lsrutvjdlst¸~fjdf npovlsfe^t4lrut4j¹±¸²Ef

¬;o4ls¬{¨ºnmf§Xr{f¯lsafQnmfq"f jAlo4z§vovjdqf"btvj^ewt4lsr{t4j^fzr{lr{jd~z|lsaFovlbfjFo¤µ¬uflsadfQq"t4jXlnmt4¬1t4ª

q"t4e!¬uf¼»ovjr}e ovlrut4j¹µA¨½r}jAlsfnmo4qlr{§f ¬{¨µ¬{fjdZr{jd~©ovjdljr}jd~©¨AjXladflruq*t4n-qMo¤lsnsf"

e^t4lrut4j"±

¾À¿-ÁÂÃ/ÄÁCÅ-ÆÇÂÈÊÉ Ë

ÌCÍ"ÎNÏÐÑ·ÍIÒmÎ;ÓYÎÊÍMÏCÔ4Õ·Ö×*ØIÙIÚÜÛ9Ý/ÞàßáâyÚ\ÞäãÊÖ ÞäâÊá?å/á?æ·ásÖ Ù/çäÞäáÙGÔ¤è"é¼ê ë"ìíÓYáÝIÝ/ásÚYÕ=áå/áî

ï

æ¹Î;ð·ÒmÎ;ñ-ÓÎNÏCÔ4òÎ;Ó9ÍMó·ô;õé éJÖmß áözåIáíç}÷Ñ1ÙIâÊøØvá Ô¤èù èè êCÐøÝ"ãÊúvøÝIÝIø ãYÍMÖ¼ÞûÝ"ãNôuÐÖ âÊã\ÞûÝ

ü

ÞàÐÏYý-ÎÊÍôNý-Ó-ÏAþ-Î;Ó9ÒmÎ;ÐÏYýJÔ¤æ·ðé èIÔMÿzôuèù ê¼ë?ý9âÊáÝ/ø"ú/çäáCÕ=áså/áîê

Unit´e de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) T´el´ephone : 02 99 84 71 00 - International : +33 2 99 84 71 00

T´el´ecopie : 02 99 84 71 71 - International : +33 2 99 84 71 71

(5)

¦ bflovnslruq¬{f½"q nsr{l¬fjsfeºµ¬uff"Qlmf"qmazjru«Gdf©lsr}¬{r{s"fQf j ¨XjXlsac"sf

r}e ov~f"*=t4n¬àovjr}e o¤lsrutvj f½e o¤nmqmadfaXe^ovr{jf""±QtvdQ lsdZrut4jdlst4làovµ·tvnm

¬§tv¬{lrut4j zf!qf"lmfqmajr{«Xf"dovjd¬uflmfe!d|Yzf"e^ lsadtAf½znmf e^f jAl½q r{jd e oIx

lsru«GdfNlsr}¬{r{movjXlf½¬;o q"t4jjdovrumovjdqfºn©¬{f"lsnpoIf"qlst4r{nsf"ovZ»®o¤nmtAqmadfQlmf jFovjXl

q"t4e!lmf©f¬;oºZ¨Ajdovewr{«GdfÊqt4jXlsnmovr{jXlmffltvlsr}¬ubzfr{eº¬;ovlrut4j ±Qt4dz"qnr{§4t4jd

fjdr{lsf¬ufns"qfjXlmfoM§4o¤jdq"f"qt4jdq"f nsjFo¤jAl©¬;oTe^tAzr{³qMovlrut4jfe^t4z§fewfjXls"±©bf"

lmf"qmazjru«Gdf!qt4jdqfnsjfjXl ¬uf^ew¬uovjd~fwfl(¬äo¤lmf e^f jXlTr{jXlmf npo4q lsr{ªzf"(ewt4§f e^f jXlm

¨XjXlsad lsru«Gdf©t4Vo4q«Gru|dfl·f nsewfllmfjXlf½q"tvjAln4¬{fnfovjr{e^ovlrut4jdJq"t4e!¬{f »Zf"±

(6)

1

jr{e^ovlrut4jVt4ªíaXe^ovj®¯bov¬{°Xr{j~^ru©o^qndqruov¬9nst4µ¬{fe r{jSbtvewzlmfnnmovar{q"32

ovjX¨¨XjXlsaflsr{qq"f jdf"r{jX§t4¬}§f§Xr{nlsFov¬·aAze ovj"|ª;nmtve =f"q r;ov¬Üf4·fqlsr}jladf³¬{e

r{jdzlsn¨^lst(§Ar}nslFov¬1nmfMo¤¬{r{l¨^ovjd §Xr{f"tT~Go¤e^f"±A¨XjXlsadfr65r{j~ nsfMov¬}rulsruqaXe^ovje^t¤x

lsrutvjTruCoqmaFov¬}¬ufj~f2Y¯bfovnsftdsfwlmt½f"faAze ovj ¬{tZqt4e^tvlsrutvjºlsadovlC¯bf¯r{¬}¬zjdtvlsruqf

ovjX¨¸ovnslr{ª\o4q l©r}jSladf(ewt4lsr{t4jÜ±87Qt/¯bf §f nM|-¯JfTe oM¨Vµ·f(jdovµ¬uf(lst~4r{§4f ovjSt4µzf"q lsr}§f

nmfMovst4jV¯aA¨o e^tvlsrutvjrujnsfMov¬}rulruqv±J`baf"sf·t4r}jXlmr{jdq nmf"o4sflsafzr:9!q¬}l¨t4ª9ladf

lpo4°=±

`bafTlsz¨ t4ªí¯bov¬{°Xr}jd~^ewt4lsr{t4jdQado4~fjfnpo¤lmf" e(qma r{jXlmf nmf"lr{j tvlsadf n³df¬{

dqmaKo4wµrut4ewf"qmadovjruq^o¤jd nmt4µ=t4lruq"± ikl ov=fMovnsf"7ovµ=t4lw³ª;lmffj¨4fMovnso4~t r}j

bt4ewzlmf n!nmovar{q"|9¯r{la lsadf^³znmlT¯Jt4n° t4j ´k°AjtI¯¬{f"~4f xkµdo4sf¶ ovjr}e ovlrut4jEt4ª

aAze ovj!³d~4znmf"±C`badfr{jXlmf nmf"lJªNtvnlaruovnsfMoaFo4Cjdf§4fnbf"q nmfMovsf"wr{j!lsadf©bt4e!lmf n

Qjr}e ovlrut4j½qt4e!e(jr}l¨|If§4fjTlsat4d~4alsadflpo4°ruÜjdt4l-fMov¨|vr}jdq"fClmfqmajru«Gdf9µFo4f"

t4j °Ar}jdfe^ovlruq"|íz¨XjFove!ruq"|íµrutve^fqmaFovjr{q""|ínst4µ·tvlsruqTovjd f §fj r{~4jFov¬bnmtAq"fsr}jd~

e oM¨^µ=fnmf«Xzr{nmf¹±

`bazruns§4f¨znmt/§Xrufo^q"tvewFo¤npovlr{§fldz¨®tvªínmf §Ar{t4d¯bt4n°r}jlsafTovnmf"o^t4ª

e^t4lrut4jq"t4jXlnmt4¬?r}jEbt4e!lmf nnpovazruq"|·ªNtAqdr{jd~t4j ladfTstv¬{lrut4j f"o4qma¸e^f lsadtA

µnsr}jd~lmtladf!ovjr{e^ovlrut4jt4ªbaXe^ovj¸¯*o¤¬{°Xr{jd~z±TQo¤lsadf nlaFovj¸nsf"sf jXlsr{j~onsf¬{¨

arulmt4nruqMo¤¬-nsf§Xruf ¯½|¯Jf q¬uo4sr{ª;¨nmf §Ar{t4d¯Jt4ns°Vr{jXlmtlsaznmf"f(e^ovr}j lnmfMo¤e^|-o¤jd lsns¨

lmtTjdf ns¬}r{jdfladfr{jXlsnr{jdruqo4Z§4o¤jAlmo4~fQo¤jd¬}r{e!r{lmovlsr{t4jdCt4ª-fMo4qmaovnstGo4qma;2

<

?nmtAq"f"Znpov¬=e^f lsadtAµFo4sft4j°Xjdt/¯¬uf~f xyµFo4f" °Xr{jdf e o¤lsruqQovjr}e o¤lsrutvj ovnsf

nmf §Ar{f¯Jf"r{jVZfqlsr{t4j>=Z±

<

`badfwovlslsfe!lmlstr}jdq"t4n·tvnpovlsfTz¨XjFove!ruq"qt4jdlsnpo¤r{jXlm½r{j¸lsaf!~4fjdf npovlrut4jSt4ª

e^tvlsrutvjt4nlmt dfZ¨Ajdovewr{q"r{e(¬uovlsr{t4jovnsfnmfsfjXlsf"Vr}jZf"q lsrutvjgZ±

<@?

o4l¬{¨|ladfovznmtGo4qmaf"fjFovµz¬{r{j~©lsadfr}jAlsfnmo4qlr{§ffzr{lrut4j tvª·f r{lsafnCqMo¤lsnsf"

t4n¨XjXlsaflsr{q¯bov¬}°Ar}jd~(ewt4lsr{t4jdovnsf½flmovr{¬{f" r{jZfqlrut4j±

`baru q¬uo4sr{³dq"ovlsr{t4j q¬{fMovn¬{¨ adt/¯wladff§tv¬{lrut4j lnmfMo¤e t4ªQladf³df¬{¹|br{jdqfladf

³nmlC~4nmt4zwtvª¹ovznmtGovqmadf"í¯Jfnmfe^ovr{jz¬{¨f§4f¬{t4·f!ª;nst4e M)=Qlmt /4BAz|4ladfsf"qt4jd

~4nmt4z ª;nmt4e MVlst /Cz|?ovj lsadf!¬;o4lº~4nst4 ado4QdlTovnrusf j ¯r{lar{jElsadfw¬;o4l

l¯bt ¨f"ovnm±*Zfqlrut4j>D(q"t4jdq ¬{dzf"µA¨^¬{rulsr}jd~(lsadfnst4µ¬{fewblsaFo¤l©o¤nmf½lr{¬{¬·t4=fjovjd

lsaFovl¯r}¬{¬=jdt4zµlmfz¬{¨ r}jdzr{nmfª;zlsnsf½nsf"fMovnsqmar{jladfjdf »AlªNf¯ ¨4fMovns"±

(7)

?w#Yº

"!$#% &'

Qjr}e ovlr{jd~V§fn¨ q"t4e!¬{f » ewtAf¬{Tdqma o4T§Ar}nslFov¬*aXe^ovjdTruTdFov¬}¬{¨ zt4jdfµX¨

f »Alsnmo4qlr{jd~or{e!¬uf nínmf nmfsfjXlmovlsr{t4j^tvª·lsafewtZzf¬k|Xo©´°f ¬uflst4jY¶v|GlaFovlCruovj^ovnslruq¼x

¬;ovlsf"º³~4nmf*e^o4fJt4ªFnsr{~4ru¬{r{jz°Z-q"t4jzjdf"q lmf" µX¨ºar}jd~f"±ít4lsr{t4jTruY³nmlCq"t4e!lsf"

ªNt4n©laru´°4f¬uf lmt4j¶v|¹lsaFo¤lqMovj µ=f(zr{¬uoM¨f" r}jAlsfnmo4qlr{§f ¬{¨4±)(©jdqf(lsadf(ovjr{e^ovlst4nQr{

movlru³f"w¯r}lsawlsadf~4¬utvµFov¬dewt4lsr{t4j!sf"«Gdf jdq"fv|adfe oM¨ q"tvewzlmfaru~4afnJ«Xdov¬{r}l¨(nmf zx

nmf"fjXlpo¤lsrutvjd*t4ªlsaf©e^t/§Xr{j~(qmaFovnmo4qlsfnM|ZµA¨^q"tGo¤lsr{j~ºlsadf©°f ¬uf lmt4j¯r{laf ªNt4nse^ovµ¬{f

nª\o4q"fewtZzf¬{r}jd~º°Xr{j+*ÇMz|Ggz|d)AA|d =-,tvnq¬utvlsadf.*=vZ|Ü =A|dGZ|0/1,Ê±

Z X

X

Z

X Z

Ankle-1D

Foot-1D

Knee-1D Elbow-1D

Waist-3D Shoulder-3D

Z Neck-3D

Hip-3D

Z Wrist-2D

Waist-3D Shoulder-3D X

X Y

Y

Y Y

Y

2-r{~4nsfTB2íQnlsruq ¬;o¤lmf" ³~4nmf¯r}lsalsar}nsl¨zf"~4nsf"f"t4ªYª;nmff"t4eV±

`bazrudov·f nªNtAqsf"ºt4j ewflsatZ½ªNt4n~fjfnpo¤lsr{j~Vlsafwewt4lsr{t4jSt4ª°4f¬{flmtvjd(t4ª

ovnslruqz¬;ovlsf" ³d~4znmf"laFovl¯r{¬}¬·nsfnsf"sf jXlQ§Xr{nlsFo¤¬·aXe^ovjd"±Cjf¼»o¤ew¬{ft4ª-dqma®ovj

ovnslruqz¬;ovlsf"º³d~vnmfru9adt/¯j tvj32Yru~4nsf±?ovlsafe^ovlsr{qMov¬}¬{¨½=fMo¤°Ar}jd~|Glsaf°f ¬uf lmt4j

ru(oazrufnmovnmqmaX¨Et4ª¬utAqMov¬Cª;nmove^f"|íf"o4qma t4ª¯aruqma r{ºqmaFovnmo4qlsfnr5"f µA¨Sr{lsº=tr}lsrutvj

ovjd t4nrufjXlmovlsr{t4j ¯r}lsa nsf"=f"q lTlmtr}lmºdovnmf jAlºª;npovewf4± `bafsfl547698:4<;>=@?A?=>4CBDt4ª

Fovnpo¤e^f lmfnsq"t4nnmf=t4jdzr}jd~ lmt fMovqma f~4nmff¸t4ªª;nsf"ft4e t4ª½ladf ³d~4nsf®ruqMo¤¬{¬uf

lsadf^´lpovlsf §fqlmtvnI¶t4nTlsadf^´~fjdf npov¬}r5f" q"tAt4nszr{jFo¤lmf"M¶ t4ªQladfovnlsruq ¬;o¤lmf" ³~4nmfv±

(8)

A¨XjAladf"r5 r{jd~Se^t4lrut4j t4ª©lsadf°4f¬uf lmt4j lsaXd^qt4jdruls!r}j f ³jr}jd~SatI¯ ladflpo¤lmf

§f"q lmt4nqmaFo¤jd~f"t/§f nQlr{ewf4±

& "!%

fsfMo¤nmqmadf nmr}j¸µrut4ewf"qmadovjruq *àgCZ|í C<,?qmaFovnpovqlmf nsr65"f aAze ovj¸¯bov¬{°Xr}jd~o4lsadf q x

q"f"r{t4j tvªzaFo4sffFo¤npovlsf"¸µA¨ªNtZt4lslnsr{°4f" \ladfTªNtZt4l©rur{j¸qt4jXlpo4q l½¯r{lsa ladf

~4nmt4zjdJo¤jd^lpo¤°f"t 4· \lsaf©ªNtZtvlJ¬{fMoM§fblsadf©~4nmt4zjd ±9ikjlsar{JFov=fn"|A¯Jff ³jdf

1 step

lFS rFS

rTO lTO

= left footstrike = right footstrike

= left takeoff

= right takeoff support

double

supportdouble single

support

single support

rTO rFS lTO

lFS lFS

phases

states (left) (right)

left stance left swing

right swing

0% 50% 100%

right stance

2-r{~4nmf =2JJaFovnpovqlmf nsr{lsr{qaFo4f"t4ª9oT¯bov¬}°Ar}jd~Te^tvlsrutvjÜ±

olsnsr{fQo4bo½q"tvew¬{flsfq ¨Aq¬ufª;nmtve o¬{fª;líªNtAt4lClpov°4f"t4lmtovjdtvlsadf nJ¬{fª;lCªNtZtvlílpov°4f"t4-|

¯ar{¬{fQlsafFovnsltvªYladfq¨Aq ¬ufµ=fl¯Jf"fjVlsadflmov°ft4 t4ªladfl¯btTªNfflrubqMov¬}¬uf"o(lmf Ü±

2FtvnJªNtAt4lslsnr{°4f©ovj^lpov°4f"t4Vf§4fjXlmtAq"q n*Znsr}jd~(olsnruf 29¬uf ª;lJlmov°ft4 \¬ |G¬uf ª;l

ªNtZt4lslnsr{°4f \¬ |¹nru~4aXllmov°ft4 \n |ovj¸nru~4aXlªNtAt4lmlsnr{°f\n ¼± `baru¬{fMo4zlmt

lsadf½qmaFovnmo4qlsfnr5Mo¤lsrutvjt4ª-l¯Jtwewt4lrut4j zaFo4sfªNtvnfMo4qma¬uf~ \sff)2-r{~4nsf= 2

±lsadf=fnrutAt4ª9=t4nsl¯ar{qmaVr{*nmf ªNfnsnsf"lmtwo4*lsaf |

=Z±lsadf=fnrutAt4ª-jt4jzx=t4nsl¯ar{qmaVr{*°Xjdt/¯j o4*ladf ' |

ewt4nsf o4q"q npovlsfwzf"sq nsr}lsr{t4j tvªJladf!¯bov¬}°Ar}jd~aFo4f"½runstI§Xr{f"¸µX¨ r{¬{st4j f l

ov¬k± *gBC<,Ê±-`badf¨½dfbf »Alsfjdrut4j(ovjdf »Arut4jlsfdYªNt4nYf³zjr{jd~¬utAq"tve^t4lrut4jµzxkq¨Aq¬{f"

o4stZq r;ovlsf" ¯r{lsawfMovqmaovnslruq ¬;ovlrut4j¹±-Co4qma^f »Almf jdr{t4jf »Arut4j lmf ^r{qmadovnpo4q lmf nsr5f"

µA¨¸r}lm¬;ovq"f r{jSlsadf ¯*o¤¬{°Xr{jd~q¨Aq ¬uf4|Yr{lszznpovlrut4jÜ|-ovjdSlsadfwo4stAqr;o¤lmf"S¬ut/¯Jfnºovjd

(9)

C

=fnovjd~4¬{f¸µ=t4j §vov¬{f""± r{¬{st4jKflov¬k±lsz¨7adt/¯ lsadfsfS§4o¤¬{dfVqmaFo¤jd~f

o4q"qt4nmzr}jd~©lstlsadf*§4f¬utAqr}l¨ºtvª1¯bov¬}°Ar}jd~±²adfj ladf*§f ¬utAqr{l¨r{jqnmf"o4sf"|ladfznmovlsr{t4j

t4ªlsadfVt4µz¬uf=t4nsl lpo¤lmf®fqnsfMo4f"t/¯jlmt 5"fnst|¯aruqmaewfMo¤jdwlaFovl^ladf

¯*ov¬}°f nado4¯r{lsqmadf"ª;nmt4e¯*o¤¬{°^lst!njÜ±

(©jdfznmt4µ¬{fer{j¨XjXlsaf"r65r}jd~!nsfMov¬}rulsruq¯*o¤¬{°Xr{jd~(ewt4lrut4j r{*lsadf=fjflsnmovlsr{t4jt4ª

lsadf½ªNf"f lr}jXlmt lsadf~4nmtvjd¹±jdf nQladf½aA¨X=t4lsaf"r{laFovllsafªNfflQt!jt4l©¬{r{f4|zladf

r{jdf«Xdov¬{r}l¨¸q"t4jdlsnmovr{jXlmº=f"qr}ª;¨Xr{jd~laFovl(ladf^ªNfflTadt4¬{ lmo/¨ ovµ=t/§f lsaf ~4nmtvjd

e oM¨Tµ=fQqt4jX§fnlmf r{jXlmtf"«GFov¬}r{l¨ q"tvjdlnpovr}jAlsat4¬uzr}jd~znsr}jd~½lsadfQ=t4nlJado4sf"±

VtZzf¬{r}jd~ tvµ¬ufº=t4nlruo^nst4µ¬{fer{jq"fTq"tvewzlmfnovjr{e^ovlrut4j®ov¬u~tvnsr{laew"|

lsaFovlQfMovr{¬}¨q"tv·f½¯r{la®t4=fjqmaFovr{j"|FaFoM§f(zr:9!q¬}l¨aFovjdz¬}r{jd~ q ¬utf"¬{tZt4"±`bar{

rut4jdf½t4ª-lsadf½nmf"o4st4j¯aX¨¯*o¤¬{°Xr{jd~Tewt4lsr{t4jdovnsfadovnmf nlmt e^tAf¬ÜlaFovjnsjzjr{jd~z|

ªNt4n¯aruqmalsafnmfr{*jdtwzt4µ¬{f=t4nlM±

`baf«Gdflrut4jt4ªAaFovjdz¬}r{jd~*r}jXlmfnmo4qlrut4j·¯r{laladfC~4nmtvjd¬uf"o4¹dÜlmtolnpovlsf"~4r{q

«Xf"lrut4j 2adt4¬{¯Jf½dsf½aX¨Aruq"ov¬{¬}¨GxkµFo4f"r}e(¬;o¤lsrutvj lmtTadf ¬{Vq"t4e!lsf½nsfMov¬}rulsruq

e^t4lrut4j `badf ovjd¯Jfnºruzjdq¬{fMovn"± 2-r}nmlM|-ladfwdovnsl¬;oM¨4f" µX¨ Z¨Ajdovewr{q"½ru½¬ufs

r{e!·t4nlpovjXlr{jo¯*ov¬}°Xr{jd~ºewt4lrut4jwlsaFovj^r{jt4ladfnbaAze ovjewt4lrut4jdqmaovbnsjzjr{jd~z|

ewzr{jd~!t4nZr{§Xr{jd~ *&=vg<,y±Zf"qt4jd¹|=lsadfº¯boM¨t4ewfµ=tZz¨¯bov¬{°A©lsf¬}¬ud©e(dqma ewt4nsf

t4j aru¤adfnT=fnsst4jdov¬{r}l¨ ovjd ewtZtA¹|?¯ar{qma ¯r}¬{¬Jµ·f µX¨ fssf jdq"f§f ns¨ zr:9wq ¬{lºlmt

f§vov¬{dovlmfQovjd^lstewtZzf¬k± 7©ov¬}ª¹t4ª·lsadf©ewtAf¬{Cznmf"fjXlmfr{j^laruCFov=fnJdsfQz¨XjFove x

ruq"|=¯ar}¬uf½lsadfºt4lsadf n©aFo¤¬{ªCt^jt4lM±Qikj lsadfº³znmlqMo4f4|Üo^~4tZtAr{e(¬uovlmtvnznmt/§Xruzr}jd~

o4q"q npovlsfe^tAf ¬{¬{r}jd~ºtvª9qt4jXlpo4q lm Iª;nsruq lsr{t4j¯r{lalsadf½~4nst4jd¯r{¬}¬·µ=fnmf«Xzr{nmf¹±`badf

e ovr}j nmt4µz¬ufe ¯r{¬{¬zµ·flmt½³jd!Fovnpo¤e^f lmfnr5f"!q"t4jXlsnst4¬{¬{fnsClaFovl~f jdfnmovlmfe(dq¬uovn

o4qlrut4jdt/§fnºlsr{ewf4±V`badfsfo4q lsrutvjdºadt4¬{ e o¤°fwladf^aXe^ovj ewtZzf¬C¯*o¤¬{°S¯ar{¬{f

e ovr}jXlpovr}jr{jd~!r{ls½µdov¬;ovjq"f4±,7Qf nmfv|Ylsf"qmajr{«Gdf"f§4f¬utv·fEr{j¸ladf!nst4µ=t4lsr{q"q"tvewe(Zx

jr{l¨EªNt4nTlsadfqt4jXlsnmtv¬t4ªQµzr{=f" nmt4µ=t4ls(e oM¨ adf ¬{ \¯Jf¯r{¬}¬o4znsf" laruTr{sfr}j

Zf"q lsrutvjg ±Cikªío(°Xr{jdf e o¤lsruq½o¤jr{e^ovlsr{t4j^ewfladtAr{qmadtsf jÜ|dlsadfewtZzf¬¹¯r}¬{¬¹ewtl¬{¨

nmf¬}¨½t4j(zf"sq nsr}lsr{t4jdt4ª¯bov¬{°Xr}jd~ewt4lrut4jdÜdqma!o4lsadt4sfJznmt/§Xrufr{jµr{t4e^fqmaFovjr{q"±

" ½

`badfí³nml9flYt4ªAlmtAt4¬uÜf §f ¬ut4=f"½ªNt4nÜewt4lsr{t4j½=f"q r{³dq"ovlsr{t4j½r{jºbt4e!lmf nQjr}e o¤lsrutvj

ruµdo4sf t4j zr}nmf"q lTovj r{jX§f nmsf °Xr}jdfe^ovlsr{q"±²Ef^³nsl(nsf"fjXlTlsadfsf lstZt4¬{"|9ovjd

lsadf jV¬{tZt4°^ovlladf¯*oM¨lsaf¨¯Jfnmfovz¬{r{f"lmtTlsaf~4fjdf npovlrut4jt4ªYaXe o¤j¯bov¬}°Ar}jd~±

(10)

% ' % '

Qr{nsf"ql-°Xr{jdf e ovlruq9q"tvjdr{lm-r{j(·fqr}ª;¨Ar}jd~©ladf*lmovlmfJ§f"q lmt4n?t4ª1ovj!ovnlsruq ¬;o¤lmf"½³d~4znmf

tI§4fnlsr}e^fv±^`bar{½=f"qr}³dqMo¤lsrutvjEr{½Fov¬}¬{¨ zt4jdf ªNt4noe ov¬}¬ísf lºtvª´°4f¨Gxkª;nmovewf"/¶¤|

¯ar{¬{f©r{jXlmf ns=t4¬;o¤lsrutvj^lmfqmajr{«Xf"Qovnmf©sf"lmt ~f jdfnmovlmfr}jzxkµ=fl¯Jf"f jV=tr{lsr{t4jd±í`badf

e ovr}jwznmt4µ¬{fewbo¤nmfQladffr{~4jt4ªÜqt4jX§f jruf jAl°4f¨Gxkª;nmovewf""|zovjd ladf©qmadtvruq"fQt4ªYo4f¼x

«Xdovlmf©r}jXlmfn·tv¬;ovlrut4j!lmfqmajru«Gdf"±J`badf¬;o¤lslmf nbnst4µ¬{feV|zovj r{j Fo¤nslsr{q¬uovnlsadf¯boM¨

t4nsr{fjXlpovlrut4jJq"ovj µ=fQnmf nmfsf jAlsf"Vovjd^r}jXlmfn·tv¬;ovlsf"wado4Jµ=f"f j¯ruf ¬{¨!ldzruf *G<,Ê±

©f"ru~4jr}jd~½°f¨ =tr}lsr{t4jdíruídFov¬{¬}¨(¬uf ª;lt4jXlmtladfQovjr{e^ovlst4níaFovjd¹|Zovjd!lsadf«GFov¬Çx

r{l¨ tvª-nsf"z¬{lsr}jd~Te^tvlsrutvjd*ff¬}¨f=fjQtvjazru°Xr{¬}¬u±?ikjVe^ovjX¨ q"o4sf"|1oM§vovr{¬uovµ¬uf

aX¨Zruq"ov¬-ovjdVµzrut4ewf"qmaFo¤jruq"ov¬Ü°Xjdt/¯¬uf"z~fdqmaSo4lsadfqmaFovnmo4qlsfnr5Mo¤lsrutvjt4ª-e^tvlsrutvj

aFo4f"fsqnr{µ=f"®r}j¸Zfqlsr{t4j ±&=!ªNt4nQaAze ovj¯*ov¬}°Xr{jd~|1qMo¤j adf¬}®lsadf(ovjr{e^ovlst4nlmt

qnmf"ovlmfnsf¬uf §vovjXl°f¨Gxyª;npovewf"±

`baff »Zq¬}dr}§fdsftvª-Zr{nmfql°Xr{jfe^ovlsr{q"Je^ov°4f"*r{lbzr69!q ¬{l*lst o4q"tvjdlnpovr}jAls

lmtladfQewt4lrut4jÜ|Xdqmao4Jladtf©=f"q r{ª;¨Xr{j~lsadovlbladfQªNffl*adt4¬{^jdt4l=fjdf lsnpo¤lmf©r}jAlst

lsadf~vnmt4jznsr}jd~ºladfz·t4nl*aFovsf"±b`baf"sfqt4jdlsnpo¤r{jXlm*e^oM¨!µ=fstv¬{§f dr}jd~

r{jX§f nmsf°Xr}jdfe^ovlsr{qov¬{~t4nr{lsaze^± 7Qf nmfv|ze^tvlsrutvjt4ªÜlsadff jd¬{r}j°!t4ª-o(qmaFovr{j Nrufv±

oªNtAt4l ¹ruY=f"q r{³df(µA¨lsaf*ovjr}e o¤lmt4nÜr}jº¯Jt4ns¬{(q"tAt4nmZr{jFovlsf"±9`badfb¨Alsfeq"t4e!lsf"

lsadf§vovnsruovlsr{t4j 4t4ª¹ladfQlpovlsfQ§4f"qlst4n Nrufv±9lsadfQt4nsr{fjXlpo¤lsrutvjdíµ·f l¯bffjr{jXlsfnsewf"Zr;ovlsf

¬{r{jz°ZYlsadovl?¯r{¬}¬Zewf"f lílsadfqt4jdlsnpo¤r{jXlM±9`badfnmf¬uovlsr{t4j(µ=fl¯Jf"f jwladfJ´e^ovr{jºlpo4°¹¶

ovjdlsadfovj~4¬;o¤nzru¬;o4qfewfjXlm54(lpo¤°f"lsaf½ªNtvnse 2

654

¯adfnsfVr{Jlsafo4qt4µr;o¤j e o¤lsnsrÇ» t4ªÜladf©¨Zlmf e *G<,Ê±ruCjdt4lbzr{nsf"q ls¬{¨ r}jA§4fnlsr{µz¬uf4|

zdf½lmtwladfzr64=fnsfjXl©Zr{ewfjdrut4jdtvª o¤jd 4 \r{f4±Jladfnsfr{Qo¤jr{jz³jr{l¨ t4ªíovj~4¬;o¤n

·tr{lrut4jdo¤lCtvr{jXlm*laFovl¬ufMovlst!ladfmovewf*ovnslsf"ruovj·tr{lrut4jt4ª?o ªNtAt4l ¼±JZt!ladf

e^tlª;nmf«XfjXls¬}¨ dsft4¬{lrut4jr{ 2

54 68 ! D"$# =

¯adfnsf

rulsadfdsf dtvxyr{jX§f nmsfºt4ª?lsafTo4qt4µr;o¤je^ovlsnr}»%-| ruQo!=fjFo¤¬{l¨q"tvjzx

lpo¤jAl"|&^rulsafr{fjXlsr}l¨ e^ovlsnr}»=|dovjd'$#!ruo q"t4jlsnmovr{jXllmt ewr}jr{e!r 5f4|AqMov¬}¬ufladf

sf"qt4jddo¤ns¨ lmo4°1±`baruf"qt4jddovn¨ lpov°^r{*fjzªNt4nmqf"t4jlsadfjX¬}¬¹do4q"f½t4ªlsaf½e^ovr}j

lpo4°=±C`baXd|zlsaf©sfq"t4j lmfne tZfbjdt4lbo 4=f"q lblsafo4qmar{f§f e^f jXl*t4ªÜladfQe^ovr{j!lpov°1|

¯aFovlmf §f nladfsfq"t4jdovns¨lmo4°($# r{"±fjdf npov¬}¬{¨|)$# r{*dsflmt!o4q"qt4jXlªNt4n9t4r}jXl

ovjd~4¬uovn*¬}r{e!r{lmt4nlmtTe!r{jr}ewr65"fst4ewffjfnm~4flsr{q½qnsr}lmf nsr;oZ±

(11)

% " #% & "!%

Vtl t4ª½lsadf°Xr}jdfe^ovlsr{q®ovznmtGovqmadf" df"ªNt4n~4fjdf npovlr{jd~ ¨XjAladflruq aXe^ovj ¬ut¤x

q"t4ewt4lsr{t4j nmf ¬{¨ tvj µr{t4ewf"qmaFovjzruqMo¤¬*°Xjdt/¯¬uf"z~f4|o¤jd qt4e(µr}jdfzr{nsf"q l^o¤jd r}jX§fnssf

°Ar}jdfe^ovlruq"JªNt4nq"t4e!lr{jd~(ewt4lrut4jd±

ikj^lsadfQfru~vaAlruf"|Xe^f lsadtAJ¯Jfnsff §f¬{t4=f" lmtºovlst4e o¤lsruq"ov¬{¬}¨(~f jdfnmovlmfª\ove!r{¬{r{f"

t4ª-°4f¨Gxkª;nmovewf"ª;nmt4eµrut4ewf"qmadovjruq"ov¬¹r}jªNt4nse^ovlrut4jd|AlaXdznmt/§Xruzr}jd~TfMo4¨lsjzr{jd~ t4ª

lsadfnmf¬}lsr}jd~®e^tvlsrutvjÜ± `bar{TruTt4jf lsanst4d~4a ³jr}lmflmovlmfe^o4qmar}jdf"Tqt4jXlsnmtv¬{¬uf

µA¨ azru~4a ¬uf §f ¬dovnpovewflsfns!dqmaovwlmf ¬uf jd~4lsa ovj lmf ª;nmf«Xfjdq ¨±`badf³nsl

ovnstGo4qmaVt4ª9laFovlq¬uo4sruf ³jdf"µX¨·f ¬{l 5"fn *D4gz| D¤ ,y±Jiklfe(µ=f"µr{t4e^fqmaFovjr{qMov¬

°AjtI¯¬{f"~4f t4ª½¬utAq"t4ewt4lsr{t4j r{jXlmt ar{fnmovnmqmar{qMov¬©q"t4jqnnmfjXllmovlmf®e^o4qmar}jdf"w¯aruqma

q"t4jXlsnst4¬Clsadfw~Govr}ltvªoV¨XjAladflruq °f ¬uflst4jÜ± °f¨Gxy·tlsnsf^ruo4stAqr;o¤lmf"SlmtVfMo4qma

lpo¤lmf4±`badfsf½·t4lsznmf"ovnsf¬{r{jfMovn¬{¨ r{jXlmf ns=t4¬;o¤lmf"lst znmtAzdq"fr}jzxkµ=fl¯Jf"f j®ovj~4¬;o¤n

§4o¤¬{df"±

³nsl½ewflsatZ®ªNt4n½f jdznsr{j~jdtvjzxk=fjdf lsnmovlsr{t4j ¯r{laSladf ~4nmtvjd¸¯ar{¬{fºdr}jd~

zr{nsf"ql°Xr{jdf e o¤lsruqQqt4jdrulsQr}jqmaFo¤jd~4r{j~^lsadf½nmtAt4l¬{r}e(µt4ª?lsafº°4f¬{flmtvj ¯adfj®ladf

=t4nlªNtAt4lqmadovjd~f 2ovl½fMo4qmaEªNtZtvlxlsnr{°fv|¹lsadfTjdf ¯=t4nsl½ªNtAt4lµ=f"q"tve^f½ladf

nmtAt4lM|?r}lm=tr{lsr{t4j µ=fr}jd~®³z»Zf" r{j ¯Jt4n¬u q"tAt4nszr{jFo¤lmf"±S`baru(ewfladtZEruºdf" µX¨

Jnsdzfns¬}r{jVovjd®*ov¬{§4fnl)*/1,Ê|d¯adtwr{e(z¬;ovlsf½ovjVr}jX§fnlmf·f jdz¬}e ªNt4nqt4ewzlsr}jd~

nmfMo¤¬{rulsr{q(e^t4lrut4j ªNtvnladfwlpovjq"f xy¬uf~± ikj laFovl½Fov=fn"|9t4jz¬{¨ t4jf½t4r}jXltvªblsaf^zzx

·t4nl©¬{f"~^ewt/§f"ovlo ~4r}§f j lsr{ewf4|F¯ar{qma e oM¨¬uf"o4lmt¬{r{~4aXls¬{¨o¤nslsr}³dqruov¬Üewt4lsr{t4jd"±

Jnsdzfns¬}r{j ovjd*ov¬}§f nsl*<,1r{e!nmt/§flsadfQlmf"qmazjru«GdfµX¨wr{eº¬{lmovjdf"tvd¬}¨ r{eº¬;ovlr{jd~

ov¬{¬lsaff~4nmff"t4ªª;nsf"ft4eV|*¬ufMovzr{jd~SlmtEewtZt4laovj Fovnmove^f lmf nsr5"ovµ¬{f¯bov¬{°Xr}jd~

~Govr{ls"±Qt4lsf laFovlladfTmovewf(°Xr{jd¸t4ªbovznmtGo4qmaSaFo4ewt4nsf(nmf"qfjXls¬}¨®µ=f"fjSdf"¸ªNt4n

lsadfovjr}e o¤lsrutvj t4ªYaXe o¤jVnjjr}jd~ *à<,Ê±

jdt4ladfn¯*oM¨¸lmte o¤r{jXlpovr}j¸f »AlsnmoVqt4jdlnpovr}jXlmt4j ladf!ªNtAt4l½=tr}lsrutvjSr{lmtVsf

r{jX§f nmsfw°Ar}jdfe^ovlruq!ov¬u~4t4nsr}lsaew5*=Az|| C1,Ê±btv¬{r{q!f l(o¤¬k±*1,J³znmldsf^oVlpovjdovnm

zr{nsf"ql°Xr}jdfe^ovlsr{q"ovznmtGovqmaÜ|F~fjdf npovlr{jd~T°4f¨Gxk=tr}lsr{t4jd*lsadovlQovnmfr{jXlsfns=t4¬uovlmf¹±í

´¬uf~vxqt4nsnsf"q lsrutvjY¶wnmtAq"fs!ru lsadf j df" lstSewtZZr{ª;¨ r}jA§vov¬}ru r}jzxkµ=fl¯Jf"f j ·t4lsznmf"32

r{ªJo ªNtZt4l=fjflsnmovlmflsadf ~4nst4jd¹|Yovj¸r}jA§4fnssf °Ar}jdfe^ovlruqTov¬{~t4nr{lsaze r{½ov¬}ruf®lmt

e^tAzr{ª;¨ºr{lm·t4r{lrut4j¹|XlaXdbewtZf ¬{r}jd~½q"t4jXlpovql*¯r}lsa ladf©~4nst4jd \sff 2-ru~vnmfQg ±9©

adt/¯j r{j *D1,y|?ladfsfq"t4jdovns¨Elpo4° nst/§Ar{f" µX¨ r}jX§fnssf °Xr{jfe^ovlsr{q ovznmtGo4qmaf"

e oM¨^µ=fdsfVlst e^ovr}jAlmovr{j^lsadf½qmaFovnmo4qlsfn àµFov¬uovjdq"fv±

(12)

Leg Correction Prediction

kinematic param.

constraints success/failure

High-level Parameters Handling

2Yru~4nsf½g 2A¨Xjdt4rut4ª9bt4z¬{ruq à*¬{tZqt4ewt4lsr{t4j ¨Zlmf e±

% ' ' '

bt4ewdovnmf lmtladfzr{nsf"q lTf"ru~4j tvª°f¨Gxyª;npovewf"|Cladf °Xr{jdf e o¤lsruq lmfqmajr{«Xf"Tnmf¼x

sfjXlsf" ovµ=t/§f¸nmf ¬{¨7t4j o qfnslmovr{jKjdzfnmlpovjzr{jd~ t4ªºladf¸µFo4r{q ¯*ov¬}°Xr{jd~ e^tvlsrutvj

e^fqmaFovjr{ew"|Üovl©¬ufMovlª;nst4e o^znmf¬}¨zf"sq nsr}lsr}§fT·tvr{jXlt4ªC§Xruf ¯½±(`badf «GFov¬}r{l¨t4ª

lsadfe^t4lrut4j laAbnmf ¬{rufJtvj^lsaf©«GFov¬}r{l¨ t4ª¹ladfQewtAf¬\r{f4±Ylsadf³jr{lsfQlpovlsfQe^o4qmar}jdf

lsaFovlC¨XjAladf"r 5f"Jladfe^tvlsrutvj |¤npovladfnClsadovj!t4j o¤j^o¤nslsr{l àí°Ar}¬{¬{"± (©jdft4ª1lsafe^ovr}j

o4z§vovjXlpo4~4f"!t4ªQladf"fVewtZzf¬u(r{Tlsadfar{~4a ¬{f§4f¬Fovnmove^f lmf nmTlsadf ¨ nmt/§Xruzf \dqma

o4§4f¬{tZq r{l¨|1lsf ¬{fjd~4laÜ|Fflsq |1¬uf"o4zr{j~ lst^lsafº~f jdfnmovlsr{t4jtvª?ª\ove!r{¬{r{f"t4ª?zr64=fnsfjXl

~Govr{ls"±SQjdtvlsadf n!o4z§vovjXlpo4~4f ruºladf¬ut/¯ q"tl t4ª©qt4e!lpo¤lsrutvjd"±E`badfq"t4e!¬{f »Ar{l¨

t4ª9r}jA§4fnssf°Xr}jdfe^ovlsr{q½ov¬u~4t4nsr}lsaewbru 8 Db¯r}lsanmf"·fqlQlmtwladf½jAze(µ·f n©tvª=t4r}jAls

Êzdf½lmt lsafr}jA§4fnsrutvjt4ª-lsadfºo4qt4µr;o¤jVe^ovlsnr}» |ZµlQr{jq"flsadfov¬{~t4nsr}lsaerudzx

ov¬{¬}¨ dsf ªNt4n©tvjdfº¬uf~|Flsar{©tAf"©jt4l©aFoM§4fTovj®r}ew=t4nslmovjXl©f4·fqltvj®lsadff39!qr{fjdq ¨

t4ª9qt4e!lpo¤lsrutvjd"±

tlTadt4nlmq"tvewr}jd~ºqt4ewfwª;nmtve ladf ~ft4ewflsnruq!r{jXlmf ns=t4¬;ovlrut4jSnstZqf"s¯aruqma

rudf"EªNtvn½~fjdf npovlr{jd~r}jAlsfne^fzr;ovlsfºª;npo¤e^f 2½ovjd~v¬;ovnlnpo¤fqlst4nsr{f"½ovnsf r}jdf ·f jzx

fjXls¬}¨ qt4ewzlmf ªNt4nTfMovqmaSt4r}jXlM|Cov¬}lsadt4~4a lsafnmfadt4¬{ µ·fo lsnmtvjd~ q"t4z¬{r}jd~

µ·f l¯bffj t4r}jXle^t4lrut4j"± Vt4nsf"t/§f nM|ladfSr}jXlmfn·tv¬;ovlrut4j znmtAq"f"e^oM¨ ³¬}lmfnladf

r{jXlsnr{jdruq®z¨XjFo¤ewr{q"t4ªlsadf ¬utAq"tve^t4lrut4j¹|*¬ufMovzr{jd~ lst o ¬{tst4ªnmf"ov¬{r{eV±

?

o4l¬{¨4|

ov¬{ladt4d~4a ewtlTlmfnnpovr}jd!ovnmfjdtvlFovlM|Clsafnmfru(jtEf"o4¨ ¯boM¨ lmt¸~fjfnpo¤lmf¯*o¤¬{°Gx

r{jd~!e^t4lrut4jt4j¸ownst4d~4a lsfnnpovr}jª;nmtveladf"fTovnstGo4qmadf"±`badfTovdovlmovlsr{t4j®t4ªíladf

¯*ov¬}°(lmtqma lmf nsnpo¤r{jd?¯Jt4¬{waFoM§flmt½µ=ff¼»A¬{r{qr{l¬{¨ºf"qnsr}µ·fw¯ar}¬uffr{~4jr{j~½ladf

e^tAf¬y±

(13)

A

)^

`badfJzf"~4nsf"fbtvªznmf"ov¬{r{e tvªdo¯*ov¬}°Xr{jd~e^tvlsrutvjr{ÜadfMoM§Xr{¬}¨f=fjdovjXl?t4ªZlsadfCnmf=f"q l?t4ª

aX¨Zruq"ov¬d¬;oM¯"±!Q¨XjFove!ruq"Co¤nmto4qmadf"íe^oM¨ºµ=fsf"!fr}lsadf níªNt4no4Zr{jd~½q"tvjdlnpovr}jAls

lsaFovlC~vFovnpo¤jAlsf"fQoq"fnlpovr}j nmfMo¤¬{rue lstºonsf"f ³jdf"we^t4lrut4j¹|t4níªNt4nCzr}nmfqls¬}¨(¨AjXladf x

r5 r{jd~(ladf¯*o¤¬{°1±í©r{jladfnmf §Ar{t4dsfqlrut4jÜ|¯Jf³nml~4r{§4f½o adt4nlQ~v¬ut4µFo¤¬·nmf §Xruf¯

t4ªQladfz¨XjFove!ruq"Tr{e(z¬;ovlrut4j lsf"qmajr{«Gdf" µ·f ªNt4nmffsq nsr{µzr{jd~¸lsadfovz¬{r{qMovlrut4jdlmt

aAze ovj¯bov¬{°Xr}jd~±

' & '

Qf¯lst4j ¬uoM¯Jo¤nmf°Xjdt/¯jo4ílsafª;zjddovewfjXlpo¤¬dnsr}jdqr}¬uf*tvª·z¨XjFo¤ewr{q""±?`badf¨T¬}r{j°

lsadfªNt4nsq"f" \nsf"Ü±?lmt4ns«Gdf"CªNt4nCnmt4lmovlsr{t4jd-lmt½lsadfnmf¬}lsr}jd~ewt4lrut4j Nnmf"Ü±?nmtvlpovlrut4j

ª;nmt4elsadf½f"«GFo¤lsrutvj;2

6 ?

Êg

¯adfnsf nmf nmfsfjXlsJlsafªNtvnmq"fovz¬{r{f"Tlmtovjwt4µzf"q lM| r}lm?e^o4sovjd

ladfsf"qt4jd

fnr{§vovlsr}§f(¯r}lsaSnmf"·fqllmtlsr}e^fTt4ªlsaf!=tr}lsr{t4j §fqlmtvn

±^`badfwf«GFovlsr{t4jS¬utAt4°A

r{e!r{¬uovnªNt4nnmt4lmovlsr{t4jd|Z¯adf nmf½lmt4ns«Xf"Qovjdovjd~4z¬;ovn=tr}lsr{t4jdovnsf¬{r}j°fµX¨ 2

6 ?444 \

¯adfnsf

r{ ladflmt4ns«Xf4|½lsadfr{jdf nslr;o®e o¤lsnsrÇ»=|4 ru lsadfVovjd~v¬;ovnT§4f¬{tZq r{l¨ ovjd 4

lsadf!ovjd~v¬;ovnovq"q"f ¬uf npovlrut4jÜ±¢Z¥4¡! #"£ ¥G r{lsadfwov¬}ruq"ovlsr{t4j t4ªJlsadfsf ¬;oM¯

¯aruqma qMov¬{q¬uovlmf ladfe^tvlsrutvj ~fjdf npovlsf" µX¨ oS~4r}§f j ªNt4nsq"fv± btvjA§4fns¬{¨4|"$%A¢¤ &

# #"£ ¥G e^f lsadtAq"ov¬uq ¬;ovlsflsadfªNt4nsq"flaFovl¯Jt4¬{V~f jdfnmovlmfoT~4r}§fjewt4lsr{t4jÜ±

`baff«GFovlsr{t4jdo¤µ·t/§fadtv¬u ªNt4no(r{jd~v¬uft4¬{r{¹±CA=f"q r{³dqewfladtZz *&=DZ|=Z|·/Z|¹ ,

aFoM§fTµ·ffjSdsfSlstov¬}¨lsaf"sf f«Xdovlsr{t4jdlmtovjEovnlsr{q¬uovlmf °f ¬uf lmt4jÜ|ÜewtZzf¬uf

o4ºoaruf npovnsqmaX¨¸t4ª*nsr{~4ru¸t4¬{r{ \jFovewf¬}¨®lsafw¬{r}e(µd©q"t4jjf"qlsf" µX¨t4r}jAls"± ª;¬{¬

f"qnsr}lsr{t4j t4ªlsadfsfe^f lsadtA(r{(µ·f ¨t4jd lsafq"t4=ft4ªlsar{(Fov=fnM± ²Efµnsr{f ¨

f"qnsr}µ·fladfl¯bt µFo4ruq½ovznmtGo4qmaf""±

`baf^³nmlºewfladtZE¯*o4r{jXlsnstZzq"f"EµA¨Sisoo4q"(ovjd bt4afj *=BD1,bovjd nsf¬{r{f"t4j

o ?

o4~4npo¤jd~4r;o¤j ªNt4ne ov¬}rue± Qr{jd~ ~4fjdf npov¬}r 5"f q"tAt4nszr{jFo¤lmf" Êf"o4qma7¬{r{eºµ ovj~4¬;o¤n

·tr{lrut4j ru f¼»Zznmf"sf7r}j r}lm ª\ovlsafn ¬utAqMov¬qtZt4nszr{jdovlmf¨Almfe |*o ´~4fjdf npov¬}r 5"f

e o4Je^ovlsnr}»')( qMovjµ=fqt4ewzlmf¹±bt4e!lsr}jd~ewt4lrut4jwlsadf jewfMo¤jdbt4¬{§Xr{j~Tovj

(14)

f"«GFovlrut4jt4ªílsadfªNt4nse 2 6 ( ? |1¯afnmf jdt/¯ nsfnsf"sf jXlmow~f jdfnmov¬{r65"fªNt4nmqf

§f"q lmt4n \q"t4jrulsr}jd~t4ª=ov¬{¬Alsafzr64=fnsfjXl?ªNt4nsq"f"Co¤¬{r{f"Tt4j f"o4qma!st4¬}ru(tvª1ladf¨Almfe

ovjd ruÜladfJ~4fjdf npov¬}r5"fºqtZt4nszr{jdovlmf?§4f"qlst4nM±íAr{jdqfladfCe ovlnsrÇ» ( zf=fjd9t4jladf

fMo4qma!lsr}e^f*lmf Ü±?ikjX§f nmsfQz¨XjFove!ruqíqMovjwfMo4r{¬}¨µ=fq"t4eºµr{jdfT¯r{lsa!zr}nmfqlCz¨XjFove!ruq

dr}jd~laruewflsatZ 2o§vov¬{dfír{-~4r}§f jºlmtstve^ft4ªzladfJzj°Xjdt/¯jd ¯ar{¬{flmo4~~4r}jd~o4

j°Xjdt/¯j stve^fq"t4e!=t4jdfjXlsQt4ª!±`bazru¬ufMovlst^o¤jr{e^ovlsr{t4jdb¯afnmflsadf½e^tvlsrutvj

ovnmf½ovzlmt4e^ovlsr{qMov¬}¬{¨ qt4ewzlmfª;nst4e ovz¬{r{f"ªNt4nmqf"±

jdt4ladfno¤nmto4qmalsaFo¤loM§t4r{JlaruJf »A=fjdr{§fe^ovlsnr}» qt4e!lpo¤lsrutvj^¯bo4b³nsl

r{jXlsnstZzq"f" µX¨S*ovn 5"f ¬ovjdS*ovnn$*&=1,Ê±!Co4qma t4¬{r{®rur}jdf=fjfjXls¬}¨ r}e(¬uovlmf¸ovl

fMo4qmaElsr{ewf(lmf¹± 9»AlsnpoªNt4nmqf"ovnsf ladfj q"t4e!lsf"¸lmt~4FovnmovjXlmffwqt4jdlnpovr}jXlm½t4j

t4r{jXlm±`badf"f ªNtvnmq"fnmf"lmt4nsf(lsadft4r{jXlqt4jdlnpovr}jXlm"|o¤jd®lsadf(jf »Allsr}e^flmf q"ovj

lsadf jµ=fr{e(¬uovlmf¹±bQzr}jd~!r}jX§fnssfz¨XjFove!ruq"ruov¬{st!lnpovr{~4aXlsªNt4n¯*ovns¯r}lsalsar{

e^f lsadtA 2íoewt4lrut4jwrub·fqr}³df" ªNt4nJFovnlm*t4ªt4¬{r{"±?`badft4lsafnmJªNt4nb¯ar{qmae^tvlsrutvj

" ' "' "'0 "$ ' " "

aFoM§Ar}jd~®lmt ·fqr}ª;¨ lsaf ªNt4nmqf"(lsadovl qnsfMovlsf lsadf ewt4lsr{t4j r{ºlmt dfz¨XjFove!ruqTo4 o

q"t4jdlsnmovr{jXlM± t4lsr{t4j ru(³nsl!q"t4e!lsf" o lpo¤jddovns °Xr{jfe^ovlsr{q^e^tAf ¬k± =tlx

`baf¨Zlmf e t4ªtwo¤jd®*ovz¬uf n)*=CA| = /-, Êf"f³d~4nsf bdf"r{jX§f nmfºz¨XjFove!ruq

§4o¤¬{ruZr{l¨ Êtladf¨e^ovr}jAlmovr{jQµFov¬uovjdq"fCo¤jd½q"t4e!ªNt4nsl^tlsadf ¨°fft4r{jXlÜlsnsf"sjdzfn

o½lanmfadt4¬{ ±Ct4lsr{t4j ruCq"t4nnmfqlmfwr}ª=jdff"f¹|X¯r{lsa!aFovjZxkljdf"wq"tAf39!qr{fjXlmClsadovl

r{jdlpovjdqf4|zladf¨AjXladflruqo4qlst4novzlmt4e^ovlsr{qMov¬}¬{¨(o4vdlm*ar{b·t4lsznmfµX¨^µ=fjdZr{jd~(ar{

·f ¬{§Xrur{ª*adfwruºadtv¬uzr}jd~oafMoM§X¨ ¯Jfru~vaAl"± Qnr{jd~ o¯bov¬}°Ar}jd~q ¨Aq¬ufv|ílsadf^r}ewdo4qls

¯r{lsa!lsafQ~4nst4jd!e o¤°fr{lzr69!q ¬{lClmtq"tvewzlmflsadff"«Gr}§4o¤¬ufjXlCªNt4nsq"f"bovjd!lmt4ns«Xf"

ovlTq"tvjAlmo4qlTlr{ewf4±tEo¤jd *o4z¬{fnTr{e!¬{r}ª;¨¸lsadf nst4µ¬{fe µA¨ o4sewr}jd~¸o¬{r}jdfMo¤n

zru¬;o4qfewfjXlt4ªAlsadfCqt4jXlpo4q lY=t4r}jAltvjladfíªNtZt4lZnsr}jd~lsadfCz·tvnslaFo4f4±- ewt4nsf

nmfqrufst4¬}lsr{t4jÜ|9µdo4sf tvj ovj r{jXlmf npo4q lsr{t4j ewtZf ¬ *À-/1,J¯aruqma r}jdq¬}df"ºq"t4¬}¬{rurut4j

flsf"qlrut4jEovj bt4z¬ut4e(µ ª;nruq lsrutvj ¯r{lsa¸ladf ~4nmt4zjdSr{dsfSµX¨ 2FovnsfTflov¬y±*À/<,Ê|

(15)

=

Generation Kinematic locomotion

Motion modification

Inverse Dynamic Balance Control Comfort Control

2Yru~4nsf 2A¨Xjdt4rut4ªYlsaf½¬{tZqt4ewt4lsr{t4j ¨Zlmf e ª;nst4e t!ovjdV*o4Z¬ufn"±

¯aruqmanstI§Xr{flsadflst4nm«Gdfq ns§4f"lsaFo¤lq"t4nnmf=t4jdlmt oºª\ove!r{¬}¨ t4ªFovnpo¤e^f lmfnr5f"

Qzr}jd~ z¨XjFove!ruq"qt4jdlsnpo¤r{jXlm*lst °Xr}jdfe^ovlsr{qMov¬}¬{¨ qt4ewzlmfewt4lrut4j nsf"¬{lsr}j

o½~4tZtA(q"tvewnst4e!rusfJµ·f l¯bffj^nsfMov¬}rueovj!qt4jXlsnst4¬k|r{jdqfr{l?adf ¬{d?ladfovjr}e o¤lmt4n-lmt

f"ru~4j!e^tvnmf*nmf"ov¬{r{lruqbewt4lsr{t4jd?¯r}lsadt4zlCqmaFovjd~4r}jd~½aruí¯bo/¨ tvª·r{jXlsfnpovqlsr}jd~¯r{la!ladf

¨AlsfeV± 7Qt/¯bf §f nM|ztvj¬{¨ o¬{r}ewr}lmf(sf lbt4ª·z¨XjFove!ruqqt4jdlsnpo¤r{jXlmCqMo¤j^µ=fQovf"!lsar{

¯*oM¨ \ªNt4nr{jdlpovjq"f4|Ylsadfwf34=f"q lm(t4ª*~4npoM§Xr{l¨¸ªNt4nnsjzjr{jd~Vt4n~fllsr{j~ ovjd t/¯j

lpo¤r{nmQ¯bt4z¬u µ·fTZr69!q¬}llmt µ=f(lpo¤°fjSr{jXlsto4q"qt4jXl ¼± Vt4nsf"t/§f nM|lsadf(l¯Jtvxlpo4~4f"

nmtAq"fsnmtAzdqf"f »AlnpoTq"t4e!lmovlsr{t4jdo¤jdtZf*jdt4l~4dovnpovjXlsf"flsafq"t4jX§f nm~f jdq"f

t4ªlsadf!nmtAq"fs32^oVjXeºµ·f nTt4ªlsfdºq"t4¬{ µ=fwjdff"f µ=fªNtvnmfwladf qt4nsnsf"qlrut4jºt4ª

lsadf°Xr{jdf e o¤lsruqe^tAf ¬¹¬uf"o4lmt!o(aX¨Zruq"ov¬{¬}¨^§vov¬{r{^ewt4lsr{t4j \r}e o4~vr{jdfªNt4n*r{jlpo¤jdq"fo

§Ar}nslFov¬íovqlmtvnlsn¨Ar}jd~ lmtqt4jXlsnst4¬?µFov¬uovjdqfTovlf"o4qma¸lsr{ewfºlmf E¯ar}¬uf¯*ov¬}°Xr{jd~t/¯j

lpo¤r{nm ±² fCjdt/¯ nsf"sf jXl?lmfqmajru«Gdf-laFovl-zr{nsf"ql¬{¨nstZZdq"fCnmf"ov¬{r{lsr{q Êz¨XjFo¤ewr{qMov¬}¬{¨

st4jbe^t4lrut4j"±

' " '

`badfwqt4e(µr}jFovlrut4j tvª*zr}nmf"q lovjd¸r{jX§f nmsf °Xr{jdf e o¤lsruq½ov¬{¬{t/¯Fovnsls½t4ª*o¤nslsr{q¬uovlmf

adf¬} ªNt4nf ³jr}jd~ lsadfsf(lnpo¤fqlmtvnsruf"±²r{l°Xr{j¸ovj ovs5*DZ ,-nmt4=tfTo^jdf¯%ªNt4nx

e(¬;o¤lsrutvj t4ªbladfTnmtvµ¬uf e|Üq"ov¬{¬{f"´Fo4q"f lsr}e^f q"tvjdlnpovr}jAls/¶ 2ladfTµFo4r{qTruf"or{lmt

ovjr{e^ovlrut4jf"«Gdf jdq"fºr}jdlsfMo4t4ª9t4r{j~!r}lsf"«Gdf jXlsr;o¤¬{¬{¨^r{jlsr{ewf4±`badfzr{sqnsflsf§vov¬Çx

(16)

df"t4ªCªNt4nsq"f"|¹§f ¬utAqr}lsrufovj®·tr{lrut4jdQt/§fnlr{ewf(ovnsf(sf lr{jSo^§4fns¨¬;ovns~f§4f"qlst4n

r{jdq ¬{df 2

<

lsr{f""|Zlsanst4d~4a¯aruqmalsaf½sfnqt4jXlsnmtv¬u*lsaf½ewt4lrut4j

<

q"t4jlsnmovr{jXlsºlsaFo¤lº¬{r}ewr}le(dq¬uovn(ªNt4nsq"f"|ít4nºlaFovl(ewtAf¬Jq"t4jXlmo4ql(¯r}lsa ladf

~4nmtvjd

<

lsadf Qf ¯lmt4jzr;ovj aX¨Aruq"ov¬¬;oM¯TlsaFovl!nstI§Xr{fo¸q"tvjdlnpovr}jAl!µ=fl¯Jf"fj ªNt4nmqf"

ovjd ·t4r{lrut4jCovlCl¯btq"t4jdf"q lsr}§fQlr{ewflsfd±J`bazruCq"t4jlsnmovr{jXlCruo4zf"!ªNt4n

fMo4qmar{jlpo¤jAlr}jlsr{ewf4±

`badf§f"q lmt4nJt4ª1j°Xjdt/¯jdCruíqt4ewzlmfwzznsr{j~½ovjwr}lmf npovlr{§fbq"t4jdlsnmovr{jdfwtvlsr}ewr65Mo¤x

lsrutvj nmtAq"fs"±!`bar{rut4jf µX¨ ·fqr}ª;¨Ar}jd~oq"tlª;zjdqlrut4jÜ|¹¯azruqmaSrulsafjSewr}jr}x

ewr65"f"·±½`baruª;jqlsr{t4j®r{t4ª;lmf j¸sf llmt lsafTe t4ªs«GFovnsf" e(dq¬uovnªNt4nsq"f"t/§4fn

¬{r{lls¬{fºfjfnm~v¨So4·tr}µ¬uf(~vr{§f jEladfTdsf nxkf³jf" ~tov¬u±Tl¨AzruqMo¤¬ovnstGo4qmaSªNt4n

jXlsr{¬·lsadfovjr}e o¤lmt4nJrumo¤lsru³df"·±

7t/¯bf §fn"|lsar{!ewfladtZ 4·f nmwª;nst4e sf §f npov¬¬{r}ewr}lpovlrut4jd± 2-r{nsl¬{¨|ClsafVar{~4a

¬{r{e!r{lslsadf^¬{fjd~vlsa t4ªQovjr}e o¤lsrutvj f"«Gdfjq"f"± `badf·fqr{³qMovlrut4j o¤jd lsadf^jXewfnx

ruqMo¤¬*r{jXlmf~4npo¤lsrutvj lmf dwovnmfjdt4jZxkr{jXlsfnpovqlsr}§fv|¯ar{qma e^ov°fTr{l zr:9wq ¬{lTlstEf e(µ=f"

lsadfsf*lmfqmajr{«Xf"ír{j o¤j!ovjr{e^ovlrut4jf"ru~4j ¨Almf e±?bf"q"ovdsfqt4jdlnpovr}jXlmíovjT~tGov¬{

e oM¨ µ=fjt4jzxk¬}r{jdf"ovnM|Alsadf½dfnrujdt4lQ~4FovnmovjXlmff"VlaFovllsafjXewfnruqMo¤¬ÜnmtAq"fs¯r{¬{¬

q"t4jX§f nm~flmtSovj o4q"qflmovµ¬{fVt4¬{lrut4j¹± Zf"qt4jd¹|*r{jdqfVZ¨Ajdovewr{q"Tru(lnmf"ovlmf o4!o

q"t4jdlsnmovr{jXlµ·f l¯bffj j°Xjdt/¯jd|ÜovjdVr}jdq"f½lsadf¨Alsfeq"t4e!nst4ewr{sfµ=fl¯Jf"f jSov¬{¬

q"t4jdlsnmovr{jXlmlstVµ=fwo¤µ¬ufTlmt³jd ot4¬{zlsrutvjÜ|z¨XjFove!ruq"¬uo/¯e^oM¨®jdt4lµ·f f jAlr{nsf¬{¨

ovjr{e^ovlst4n¹ruzlY¬utAt4°Xr{jd~*ªNt4n§XruFov¬GnsfMov¬}rue ±

?

o4ls¬}¨|¤r{jq"ff§f ns¨q"tvjdlnpovr}jAlr}jladf

ovjr{e^ovlrut4je(dlíµ=f=f"q r{³dfV¶"onsr{t4nsr¶v|4qt4¬{¬}rur{t4jd-ovjd q"tvjAlmo4qlsíµ·f l¯bffj tvµzf"q lm

ovnmf(ewtZzf¬uf®µX¨ q"t4jlsnmovr{jXlst4jE=tr{lsr{t4jdlsaFovlat4¬u¸znr{jd~·fqr}³dqTlsr{ewfºr}jAlsfnx

(17)

M

§4o¤¬u"±w`bar{½znmf§4fjXlmlsadfTdf^t4ªbovj ovlmtve ovlruqTqt4¬{¬}rur{t4j f lmfqlsr{t4j ovjd¸nmf"·tvjdsf

e^tAz¬{fznr{jd~Tlsafo¤jr{e^ovlsr{t4jÜ±

btvadfj *Ç DC,Tnmfsf jAlsf" o¤jr}ewnst/§f" ewfladtZ ªNt4nSt4¬{§Xr{j~Fo4qf xylsr{ewf q"tvjzx

lsnmovr{jXls"± ikl!nmf ¬{r{f" t4j ´do4q"f lsr{ewf¯r{jdztI¯M¶¯ar{qmaovnsff"ru~4jdf r}jAlsfnmo4qlr{§f ¬{¨4|

ovjd®f jFovµ¬{fºlsadfºst4¬}lsr{t4j®t4ªow~4r{§4fj FovnlM|1r{j Fo4q"f o¤jd®lsr}e^fv|=t4ªíladfTovjzr{e^ovlsr{t4jÜ±

t4ªQlr{ewf4±EQj r{lsfnpo¤lsr{§4ft4lr{e!r 5Mo¤lsrutvj nstZqf"s fMovnsqmadf" ªNt4nTª;jdq lsr{t4jdTfsqnr{µr}jd~

lsadf^ewt4lrut4jEt4ªfMo4qma zf"~4nsf"ft4ªª;nsf"f"zt4e r}j lsaf^¯r{jdztI¯½|?laFovlewr}jr{e!r5f"o~tGo¤¬

st4¬}lsr{t4jÜ|¹qt4jXlsr{jXdtvdr{jSFovq"f!ovjd¸lsr}e^fv|·rut4µzlpovr}jdf" µX¨¸q"t4eºµr{jr}jd~^ladfTFovnslr;ov¬

¯r{jdt/¯ít4¬{lrut4j"± Qdflmt§XruFov¬Fo¤jd(jXe^f nsr{qMov¬ZªNf"f"ZµFo4qm° t4jTladf*nmt4~4nmfsr{t4j t4ª

ovjr{e^ovlrut4jÜ|lsadfJovjr}e ovlst4nÜq"ovjTo4zjdf ¯ q"t4jlsnmovr{jXls"|Ir{jdq nmfMovsft4nYf"q nmfMovsfJznmf§Xr{t4d

q"t4jdlsnmovr{jXl9¯Jfr{~4aXlm|Gt4n?ewtZzr}ª;¨r{jXlmf nsewf"zruovns¨½t4¬{zlsrutvjd"±9`badfovjr}e o¤lmt4nYlsaXd?r}jAlsfnx

o4qlsJo¤jd^~4zrufCladft4lsr}ewr65Movlrut4jr{jwt4nmzfnClmt½e o¤°fr{lq"tvjA§4fns~fQlsto¤jo4qq"fzlpovµ¬{f

st4¬}lsr{t4jÜ±

Af§f npov¬tvlsadf nr{e!nmt/§f e^f jXlm*aFoM§f½µ=f"fjnst4=tsfVdqma®ov*lsadfnmf ªNt4nseº¬;ovlrut4j

t4ªClsadf f§4t4¬{zlsrutvj¸t4ªJladfTf~4nmff"½t4ªª;nmf"ft4e r}j aruf npovnsqmaruq"ov¬9¯boM§f ¬uflnmf nmfsf jAlmo¤x

lsrutvj *g)=-,Ê±`bar{nsfnsf"sf jXlpovlrut4j ov¬{¬{tI¯ladfwru~4jzr{³dq"ovjXlnsf"zqlsr{t4j tvªblsaf^q"tvewZx

lpovlrut4jFo¤¬íq"tlM± Qf§4fnlsadf ¬uf""|íoe oIt4n½znpoM¯µFovqm°Etvª*do4q"f¼xklsr}e^fTqt4jdlsnpo¤r{jXlmlr{¬{¬

e ovlruq"ov¬{¬}¨±Ü`badf ¨(o¤nmfr{e!¬}¨q"t4jruzfnmf o4Yq"t4jXlpovql?qt4jdlsnpo¤r{jXlm|vlsadovlíovnsfJ·fqr}³df"

jdt4lTµ=f"fj zr{nsf"q ls¬{¨ ov¬}ruf lst aAze ovj ¯bov¬{°Xr{j~¸¨4fl"± Q¬}¬*lsafVo¤µ·t/§fVovznmtGo4qmaf"

lmfj^lmtt4·f nJladfo¤jr{e^ovlmtvnolmtAt4¬dlmtr{jXlmf npo4q lsr{§4f¬}¨Te^tAzr{ª;¨lsadfnmtAq"fs*tvª¹e^tvlsrutvj

q"t4e!lmovlsr{t4jÜ±ikj¸qt4jXlsnpovlM|=lsadfºjf »AlovnstGo4qmadflsaFo¤l¯bf(¯r}¬{¬Yfsqnr{µ=f(nmtv·tf

$.

½ewtZzf¬uTtvªQaXe^ovj ¬utAq"t4ewt4lrut4jElsaFovl zfMov¬¯r}lsa lsadfr}jAlnsr}jdr{q z¨Gx

jFove!ruq"9t4ª=aXe^ovj!e^tvlsrutvjÜ±-bt4jXlsnmtv¬{¬uf nm?e^ov°f*r}lí·t4sr}µ¬uf*lst½znsr}§f*lsaf"sfz¨XjFove!ruq

¯ar{¬{fo4q"qt4jXlsr}jd~ ªNt4nfe!r{nruq"ov¬¹o¤jdµzrut4ewf"qmaFo¤jruq"ov¬·°Xjdt/¯¬uf~ft4jaXe o¤jV~ovr{l"±

7# ' !! '

`badfºo¤r{e tvª9lsafdftvª?q"tvjAlnmt4¬}¬uf nm*rulstôvjzr{eôvlmf½o ¨XjXlsadf lsr{qaXeôvj³~4nmf¯r}lsa

zr{nsf"qlCZÄjdovewr{q"|¯aruqmaôv¬{¬{t/¯9dílmtovlst4eôvlsr{qMov¬}¬{¨lmov°fr{jXlstovq"q"tvjXlladff34=f"q lm