Straight Leg ged Walking of a Biped Robot

Sraigh Leg ged Walking of a Biped Robo Ryo Kurazume, Shunaro Tanaka, Masahiro Yamashia Tsuomu Hasegawa Kyushu Universiy 6-10-1, Hakozaki, Higashi-ku, Fukuoka, Japan Email: kurazume @ is.kyushu-u.ac.jp Kan Yoneda Tokyo Insiue of Technology 2-12-1, Ookayama, Meguro-ku, Tokyo, Japan Email: yoneda @ roboics.mes.iech.ac.jp Absracm This paper presens a new mehodology for generaing a sraigh legged walking paern for a biped robo uilizing up-and-down moion of an upper body. Firsly, we define wo new indexes, he Knee Srech Index (KSI) and he Knee Torque Index (KTI), which indicae how efficienly he knee joins are uilized. Nex, up-and-down moion of he upper body is auomaically planned so ha hese indexes are opimized and sraigh legged walking is realized. The basic idea of he proposed mehod is, i) when a large number of DOFs of moion are required for conrolling he ZMP, a robo makes is body heigh lower, ii) when here is a exra number of DOFs of moion, he body is lifed and he knee join is sreched. By sreching he knee joins, human-like naural walking moion is obained. Moreover, energy efficiency is improved since required orque and energy consumpion o suppor he body weigh become small a knee joins. The effeciveness of he proposed mehod is demonsraed by compuer simulaion and experimens using a humanoid robo, HOAP-1. Index TermsmBiped robo, Knee join, Energy efficiency, Knee Srech Index, Knee Torque Index I. INTRODUCTION For a humanoid robo which will coexis in human environmen such as welfare robos or enerainmen robos, i is imporan o perform human-like moion o avoid making uncomforable feeling for users. However, convenional moion of a humanoid robo is generally unnaural [1]-[9]. For example, if we compare walking paerns of a human being and a biped robo, we will find he following differences: A human being uilizes up-and-down moion of an upper body or roll moion using a wais join, knee joins, and ankle joins simulaneously. Insead, a convenional biped robo seems o walk very carefully by lowering is wais posiion and bending knee joins. The main reasons for his unnaural moion of a humanoid robo are as follows; 1) Mechanical facors a) Differen configuraion of DOFs (Degree-offreedoms) b) Limied range of join moion 2) Conrol facors a) Uniformiy of moion b) Consrains relaed o conrol algorihms, for insance, singulariy avoidance This paper mainly discusses he conrol algorihm of a biped robo for generaing naural walking paern. In general, mos biped robos developed so far walk sably by bending heir knee joins (Fig.2(a)). This is due o he fac ha conrolling he Zero Momen Poin (ZMP) becomes quie difficul when he knee join is sreched and he some DOFs of moion are degeneraed. On he oher hand, human uilizes roaion of he wais join and up-and-down moion of he upper body o secure he enough DOFs for sable walking. Fig.1 shows an example of a human walking paern measured by moion capure sysem. Wais Fig. 1. Up-down moion of wais posiion while walking This paper presens a new mehodology for generaing a sraigh legged walking paern for a biped robo uilizing upand-down moion of an upper body (Fig.2(b)). Firsly, we propose wo new indexes, he Knee Srech Index (KSI) and he Knee Torque Index (KTI) for evaluaing he efficiency of he use of he knee joins quaniaively, The Knee Srech Index (KSI) is defined as he lengh beween he line connecing he cener of graviy (COG) and he ZMP, and he knee roaion axis. The Knee Torque Index (KTI) is also defined as he lengh beween he ZMP on a knee plane and he knee roaion axis. Nex, he sway compensaion rajecory [10] is modified so ha up-and-down moion is auomaically planned o opimize hese indexes and sraigh legged walking is realized. The basic idea of he proposed mehod is as follows: i) when a number of DOFs of moion are required for precious conrol of he ZMP, a robo makes his body heigh lower o secure he enough DOFs, ii) when here is a exra number of DOFs of moion, he body is lifed and he knee join is sreched in he same way as a walking paern of human. A few sudies on sraigh legged walking have been repored so far. Recenly, he Robo GARAGE, which is a venure company in Japan, announced a new humanoidype robo named CHROINO [ll]!-~this robo is able o walk sably wih sreching knee joins by devising join configuraion. The research group a Waseda Universiy in Japan repored sraigh legged walking of a biped robo using heir humanoidype robo named WABIAN-2 [12], [13]. They adoped differen algorihms for he calculaion of inverse kinemaics in

c(~ 2AaV.2 2A..~ d supporing and recovering phases. The singulariy is avoided by uilizing he roll moion of he wais join. Our mehod realizes he sraigh legged walking by conrolling he heigh of he COG rajecory according o he sae of he ZMP conroller. The singulariy is avoided by bending he knee joins when he ZMP has o be conrolled precisely. On he oher hand, he knee joins are sreched if he desired ZMP is almos aained and here is no need o conrol he ZMP posiion so precisely. (a) Convenional walking paern Fig. 2. (b) Proposed walking paern Heigh conrol during walking There are several advanages for he sraigh legged and wais-lifed walking. Some of hem are as follows; 1) Human-like naural walking moion is obained 2) Energy efficiency is improved since required orque and energy consumpion o suppor he body weigh become small a knee joins. II. THE SWAY COMPENSATION TRAJECTORY FOR BIPED ROBOTS In his secion, he sway compensaion rajecory for biped robos is inroduced [10]. The ZMP and he COG rajecories are obained by explici funcions of a sway widh, a walking speed, acceleraion and lines connecing he cener of he soles of suppor fee. A. Definiion of he sway compensaion rajecory In he following discussion, we assume he weigh of legs and arms are smaller han he body weigh. In his case, he sysem can be regarded as a single mass model placed on (xg,yg,zg) Assuming a floor is fla and he heigh of he poin mass zg is consan, he ZMP on he floor (x~mp, y~mp, 0) is obained as follows: ) (i) where, A - ~. Nex, he diagonal line connecing he cener of he soles of suppor fee is defined as x cos0+y sin0=d (2) Then, in order o keep he ZMP on his line, he COG has o saisfy he following equaion. cos O(x. - A~'g) + sin O(y. - Ay'g) = d (3) Here, we assume ha he robo moves along x axis and he posiion of he body is expressed as x g-c~e~+c~e ~7~+a~ 2+al+a x o x (4) y. - + c~ ~ +.~~ +.~ +.g (5) Eqs.(4) and (5) consiss of a paricular soluion and a general soluion of equaions, xg - A:~ = 0 and yg - A~)~ = 0. By subsiuing hese equaions ino Eq.(3), we obain ~o~o(~ - + sin O(a~ - +.; +..~ 2) + a~ + av.2 '2) - (6) From Eq.(6) and he boundary condiion, all he parameers such as a~ are deermined [10]. The rajecory expressed by Eqs.(4) and (5) is named "he sway compensaion rajecory". Fig.3 shows an example of he ZMP and he COG rajecories in case ha he robo walks 10 seps wih he velociy O.lm/s along he x axis from he iniial posiion (0, 0). I should be poined ou ha obained rajecories can be easily modified and uilized if he moving direcion is gradually changed. This is because coninuous ZMP and COG rajecories are obained by applying simple coordinae ransformaion o original rajecories according o he moving direcion. f/lef foo j COG raj. qp ~ ~.'PP 'PP 0.05 ~ }+~ ~ /+~ /~. l /l /l /l '' i/ i/ i "-, ''-z2 Righ foo -0.05 r ~ ~ aj. - ~-0~ 0 0'~ 0', o'3 o'4 05 X[m] Fig. 3. An example of ZMP and COG rajecories projeced on he ground for sraigh pah B. Convergen calculaion considering muliple mass model The rajecories obained as Eqs.(4) and (5) are based on he assumpion of a simple single mass model. Therefore, more precise rajecories and join commands should be deermined based on a muliple mass model for sable walk. To obain he precious ZMP rajecory based on he muliple mass model, we proposed he mehod which uilizes convergence calculaion for recifying he COG rajecory according o he curren ZMP errors. Firsly, he ZMP X~p = (x~p,y~p, 0) for a muliple mass model is obained from he following equaions. E ~ x~.w - (7) Y~-w N (~: + g) ~i=1 7/~i ref Here, we define he planned ZMP rajecory as X~. w, he refined COG rajecory o realize he planned ZMP rajecory

- % as Xff ef I alnd he curren COG rajecory as Xg. Then, curren saus can be expressed as X~, - Xg - A Jig (9) On he oher hand, he goal saus is shown as fcf fcf - AJ~ ~f (10) X~ v - Xg Thus, by subracing above equaions, we obain or, x~.~p - x~.~p - x~ ~s - xg A(2~ ~s 2g) (11) e~p = eg - A~g (12) ref where, ezmp -- Xzm p -Xzmp, and eg - X~ ~f -Xg By resampling his equaion wih sampling inerval A, he following equaion is obained. ezra p -- _ A~g e g +s _ 2e + -s _ A % (/x)2 % (13) Therefore, he recified value of he COG rajecory e g ha reduces he ZMP error ezra p is obained as he following equaion. A +l +% -1 e~p + gxtg(% ) eg 1 + 2 A (14) (zx)2 However, several experimens showed ha he refined COG rajecory ends o be oscillaional a disconinuous poin of he ZMP velociy, if he recified value obained from above equaion is added direcly o he original COG rajecory. Therefore, we choose he recified value of he COG rajecory eg so ha he following equaion wih he smoohness consrain is minimized. A (e+s + -s) e~v + ~ % )'2+ min(eg - 1 + 2 A (zx)2 +s + +s -s + -s eg Xg + eg Xg )2 (15) Consequenly, he refined COG rajecory ha realizes he planned ZMP rajecory is obained as he sum of he curren COG rajecory Xg and he recified value e g. X; ef -- Xg + eg (16) In pracice, considering he resampling error and non lineariy of Eqs.(9) and (10), he above calculaion should be repeaed unil eg becomes sufficienly small value. In summary, he proposed mehod which consiss of wo convergen calculaion loops is described as follows; 1) The ideal ZMP rajecory X~mp ~f is designed from Eqs.(1), (4), and (5). Then he COG rajecory Xg 0 ha realizes he ideal ZMP rajecory is obained approximaely using a single mass model. 2) The rajecory of he reference posiion (ex. he wais posiion) and he join rajecories of arms and legs (I) n are calculaed from he curren COG rajecory X2. Noe ha he ip rajecories of hands and legs are deermined beforehand, and here is no change before and afer he convergen calculaion. 3) The acual ZMP rajecory based on he muliple mass model X~mp is calculaed using Eqs.(7) and (8) and he join rajecories ~n. 4) The error beween he ideal and he acual ZMP rajecories e~mp - X~p ref - X~p is obained. This error is discreized and he error a each ime sep e~p is calculaed. 5) The recificaion of COG rajecory e g ha minimizes Eq.(15) is calculaed using he convergence calculaion for all discreized error (The firs loop)! -~ 6) The refined COG rajecory X~ +s - X~ ef is obained using Eq.(16). 7) The calculaion is erminaed if he sum of he recificaion of COG rajecory e g is small enough. 8) Go o Sop (2) (The second loop) III. KNEE STRETCH INDEX AND KNEE TORQUE INDEX The sway compensaion rajecory is derived for a robo which can change he COG posiion a will. Thus, he knee join has o be ben sufficienly o ensure enough DOFs of moion. However, by sreching he knee joins and keeping wais posiion high, several advanages can be considered as menioned above. Especially, if he orque produced a he knee join is reduced, i is quie useful in pracical design since a small and ligh weigh acuaor. However, no index has been proposed so far for indicaing how much he knee joins uilized efficienly. For evaluaing he efficiency of he use of he knee joins quaniaively, we propose wo new indexes, he Knee Srech Index (KSI) and he Knee Torque Index (KTI) in his secion. Boh indexes indicae he required orque a he knee joins o suppor he body weigh wih a simple calculaion. Thus, i is possible o evaluae he efficiency of walking paerns using hese indexes wihou a precise calculaion of join orque. A. Knee Srech Index A firs, we define he Knee Srech Index (KSI). The KSI reflecs he knee orque o suppor he body weigh under he assumpion of he single mass model. D1 ~COG.,>~ :: i! Knee srech index = L1 +L------~ L2 Roaion axis j@~d1 Fig. 4. L~ ",,@... hmdex = D1 ~ZMP Definiion of Knee Srech Index Fig.4 illusraes he definiion of he Knee Srech Index. If we assume ha all he mass of he robo body is concenraed a he COG and he momen around he COG is negligible, he D1 ZMP COG

reacive force from he ground is exered a he ZMP on he sole along he direcion from he ZMP o he COG. Therefore, he orque o suppor he body weigh a he knee join is proporional o he disance from his line o he roaion axis of he knee join. For example, in he case ha he roaion axis of he knee join is on he line beween he COG and he ZMP, all he body weigh is suppored mechanically and here is no need o produce he orque a he knee join. From he above consideraion, he Knee Srech Index (KSI) is defined as a raio of he minimum lengh D1 beween he line connecing he COG and he ZMP, and he leg lengh L, ha is, D1 Knee Srech Index = (17) L B. Knee Torque Index Nex, as a new index o evaluae he efficiency of he use of he knee joins more rigorously, we propose he Knee Torque Index (KTI). Imagine a plane which includes he represenaive poin on he roaion axis a he knee join and is parallel o ground. The represenaive poin can be a poin where, for example, he roaion axis inersecs wih he cener line of he leg. Then, he ZMP on his plane can be defined in he same manner as he convenional ZMP on he ground, and we call his ZMP he knee-plane ZMP (KZMP). Since no momen along roll and pich axes exiss a his KZMR if his KZMP is on he roaion axis of he knee axis, no orque is required a he knee join o suppor he body weigh. Therefore, we define he Knee Torque Index (KTI) as a raio of he lengh D2 beween he KZMP and knee roaion axis, and he leg lengh L such as D2 Knee Torque Index - (18) L Fig.5 indicaes he definiion of he Knee Torque Index (KTI). This KTI almos coincides wih he KSI if he roaion axis of he knee join is parallel o he ground and he momen around he COG is small. D2 Knee orque index - L1 +L2 Knee plane Roaion axis " ~ I ~ L ~ZMP Knee-plane ZMP Fig. 5. Definiion of Knee Torque Index IV. NEW STRAIGHT LEGGED WALKING PATTERN In his secion, we propose a new sraigh legged walking paern by conrolling he heigh of he COG rajecory according o he sae of he ZMP conroller. The sway compensaion rajecory described in secion 2 assumes he consan heigh of he wais posiion. In order o obain he adapive wais rajecory such as, i) when a large number of DOFs of moion are required for precious conrol of he ZMR a robo makes is body heigh lower o secure he enough DOFs, ii) when here is a exra number of DOFs of moion, he body is lifed so ha he index proposed in he previous secion is minimized and he knee join is sreched, we modify he seps 4 of he procedure of he sway compensaion rajecory as follows: 4) The error beween he ideal and he acual ZMP raref jecories ezrnp -- Xzrnp - Xzrnp is obained. This error is discreized and he error a each ime sep ezrnp is calculaed. In addiion, when he knee join angle is no 180 degrees (bending), he wais posiion is modified as eg + eg + APmin. Here, APmin is derived as follows: i) he COG posiion is moved slighly o new posiions on a small circle around he curren COG posiion in x-z plane (Fig.6), ii) he KSI (or he KTI) is calculaed a each posiion and he posiion where he index is minimized is seleced as AP~i~. Conrary o his, when he knee join angle is already 180 degrees and he ZMP error is larger han he pre-defined consan value as ezrnp ) eh, he wais posiion is lowered as e~ --+ e~ - AH. Acually, we use he smoohness consrain for e~ in he same way as Eq.(15). inin(ez -- AH)2-~- ~z z --1 --1 e +l+x +l+e~ +X~ )2 (19) i; ~APmin... /////////////// /////////////// i i (a) COG is moved on a small (b) Recalculae KST or KTI and circle around curren COG. find he posiion where he index is minimized. Fig. 6. Calculaion of AP,~in As a consequence of he above procedure, he robo makes is wais posiion lower if he knee join is sreched and he some DOFs of moion are degeneraed even if he ZMP error is large. On he oher hand, he wais posiion is lifed and he KSI and/or he KTI are improved if he ZMP error is small and some DOFs of moion is redundan. Furhermore, he soluion of inverse kinemaics canno be obained when he knee join is compleely sreched in general. Thus, our mehod adops an approximaed soluion. Le's consider he case shown in Fig.7. Generally, he join angle of he knee join 04 is obained using he cosine formula as 04 -- 71- -- COS -1 L~ + L,~ - l 2 2L1L2 (20)

Where L~ and L2 are he lengh of he high and shank, and l is he lengh beween he ankle and he groin. However, he soluion of he Eq.(20) canno be obained if L~ + L2 < l. Therefore, we use he following soluion in his case as ~~ '~ i 'i ~ ~I~I~~ 04 -- { 71-- COS-171-L~-~-L~-lZ2L~Lz (oherwise)(l~ + L.2 _> l) (21) L 1 :i; ii: 04ii i~ L2- z :!4 Fig. 8. Convenional walking paern Fig. 7. Approximaed calculaion of Inverse Kinemaics A he singular poin where he knee join is sreched, huge angular velociy is produced in case ha he wais posiion is forced o be lowered. In our implemenaion, we defined he maximum and minimum values of he angular acceleraion a he knee join o avoid such case. By inroducing his procedure a he sep 2 in he above convergen calculaion, he join angle rajecory ha minimizes he ZMP error is obained under he consrain of he feasible angular velociy. V. EXPERIMENTS This secion inroduces some examples of he proposed sraigh legged walking paern hough compuer simulaions and walking experimens using he humanoid-ype biped robo named HOAP-1. A. Compuer simulaion Figs.8 and 9 show examples of he obained walking paerns using he mehod proposed in Secion III. Here, Fig.8 illusraes a convenional walking paern which keeps he low wais posiion and bends he knee joins. Fig.9 is an obained walking paern afer he convergen calculaion using he proposed mehod. In hese simulaions, he walking period is 4 [sec.] and he maximum angular acceleraion is se o 500[~.~d./~.~]. Fig.10 shows he change of he wais heigh before and afer he convergen calculaion. I is clear ha he periodical up-and-down moion of he wais posiion is obained gradually hrough he convergen calculaion. The join angle of he knee join is also shown in Fig.11. The lower figure of Fig.11 shows he join rajecory during one supporing phase. Afer convergen calculaion, he join angle of he knee join becomes abou 180 degrees wice in one,.waldl~ cycle. PigA2 sffov~s he ZMP rajecories before and afer convergen calculaion. From his, i is verified ha he ZMP error afer he convergen calculaion becomes smaller han iiiiiiiiii~ii~iiiiii~ii~i~i~i~i~iii~~ii~... ~ ~i~i~ii~iii~i~ii~iii~iiii~i~iiiiii~iiiiii~iii~i~i~ iii!!~i!iii~ i!i!ii!i iii iiii Fig. 9.... iii... i0ho0... Obained walking paern afer 100 ieraions he error wihou he convergen calculaion even if up-anddown moion of he wais posiion exiss and Eq.(1) is no saisfied. Fig.13 and Table I show he oal power consumpion and he energy consumpion in one walking cycle. The sum of he energy consumpion of all acuaors is l l.9[j] for he convenional walking paern (Fig.8) and 7.6 [J] for he proposed walking paern (Fig.9), respecively. Thus, i is clear ha he proposed sraigh legged walking is more effecive han he walking paern which bends he knee join in views of he energy consumpion. Finally, he proposed Knee Srech Index and he Knee TABLE I ENERGY CONSUMPTION IN ONE WALKING CYCLE Walking paern Convenional paern (Fig.7) Proposed paern (Fig.9) Energy consumpion 13.3 [J] 6.5 [J]

4,....< ~ Iniial offse(=0) -~ a= 0... Afer 50 ieraions O ~ / Aferl0ieraions,~,", ~/,i~;?~i~~~/, ~ -2... ~,,.. "..,~,.... /", / i/" i,--,, v ~',~ ' " V'" i "! '..-.'J ~ Fig. 10. 180-4 p ~Afer 100 ieraions 0 5 10 15 20 Yime[sec.] Heigh regulaion by convergen calculaion 16 ~!r\j iu, }"1 ' iqw!, i'l \'~.g! ~Proposed Paern) i I i 140! I i l i i (af... gen calculaion~ i i!...,! i " '~ i... < 1... ", I... '-...1 ::,2o i.,, i!i'.-"... ii!i'-.-"... i!i,,...,,,, i!!i!... i!i,... 80 0 5 i- 10 :(Co... 15 ional paern-)20 Fig. 11. Knee join angle Torque Index for he obained rajecories are shown in Figs.14 and 15!~ is clear ha boh he KSI and he KTI for he proposed sraigh legged walking paern becomes smaller han he ones for he convenional walking paern. This means ha he body weigh is suppored wih small join orque using he obained sraigh legged walking paern. Fig.16 shows he calculaed join orque a he knee join of he righ leg. The absolue value of he join orque becomes small as expeced from he KSI and he KTI if he proposed sraigh legged walking paern is used. From hese resuls, i is verified ha he efficiency of walking paerns can be evaluaed using hese indexes insead of calculaing precise join orque. / / ( Proposed paern ).-. (Convenional paern" 10 /{ } ii/~ ~i# /\ A A k ia ili IL I'.~ ilv,1 i/\,+4 I, "! [ i i/ ::iv,,,! Ii"4!/ if\j1 ~'"+.~,! =:l<,,-i i i;; :, ~ :, ',l '! ~ [ ',1 \ 4,! i i!~ i!~ i / ii i~ i ~ ii",,,ij'{/ j, J!'1i J,{/ j s"~ ~,,{, ii]/ j,{ ~!q{ i,{ E i < s~: i ii,~i #,',~s,,,,,,! 'I~:;,~ '/'"1 I~,~ [#' {A! >I~ i~ b!i ;,I I V~i ~q' ~,~ i,4' ',,!i! i/ i j,,i' ~., = g, ~ b.,.'~ L,,} ~,p {A ~,,$' L,,.'/ i~e' ::Y7 L,~, e 01 ' 0 D 10' 15 20 o3[ Fig. 13.,~0.2 ~ ~ \ Toal power consumpion (Convenional paern) L, i! i ~ Pr p sedpiiern )i "i 00 L! i: 00 5 ' 10 15 ~ '"~ 20 Fig. 14. B. Experimens using HOAP-1 Comparison of Knee Srech Index Walking experimens using he Humanoid-ype biped robo were carried ou. Fig.17 and 18 show he convenional and he proposed walking paerns of he HOAP-1. From hese experimens, i is verified ha he robo walks sably using he proposed sraigh legged walking paern even when he robo sreches he knee joins. VI. CONCLUSIONS This paper presens a new mehodology for generaing a sraigh legged walking paern for a biped robo uilizing upand-down moion of an upper body. The advanages of he sraigh legged and wais-lifed walking are as follows: 1) Human-like naural walking moion is obained 2) Required orque and energy consumpion o suppor he body weigh become small by sreching he knee joins 0.06 0.04 before convergen calculaion ---------- i..,... desired rajecory. 0.02 &0-0.02-0.04 afer convergen calculaion -0._0.106 0 0.1 0.2 0.3 0.4 0.5 x[m] - 0.2 0.1 00 5 10 15 Fig. 12. ZMP rajecory before and afer convergen calculaion Fig. 15. Comparison of Knee Torque Index

3 /] /i (C... ~ional paern ~ / /y j, /, I!,/ ~ Pr;pos;d paern )i ii 0 5 10 15 20 Fig. 16. Torque a knee join of righ leg (absolue value) Fig. 18. Obained walking paern using he proposed mehod Fig. 17. li o Obained walking paern using a convenional walking paern Two new indexes which evaluae how efficienly he knee joins are uilized, ha is, he Knee Srech Index (KSI) and Knee Torque Index (KTI), are proposed. Boh indexes indicae he efficiency of he use of he knee joins quaniaively for he sraigh legged walking wih a simple calculaion. Upand-down moion of he upper body is auomaically planned so ha hese indexes are opimized and he sraigh legged walking is realized. Compuer simulaions and experimens are successfully carried ou using he humanoid-ype biped robo HOAP-1. ACKNOWLEDGMENT This research was parly suppored by he 21s Cenury COE Program "Reconsrucion of Social Infrasrucure Relaed o Informaion Science and Elecrical Engineering", and he Minisry of Public Managemen, Home Affairs, Poss and Telecommunicaions in Japan under Sraegic Informaion and Communicaions R&D Promoion Programme (SCOPE). [4] Q. Huang, S. Kajia, N. Koyachi, K. Kaneko, K. Yokoi, H. Arai, K. Komoriya, and K. Tanie, "A high sabiliy, smooh walking paern for a biped robos," in Proc. IEEE In. Conf. Roboics and Auomaion, 1999, pp. 65-71. [5] S. Kajia, O. Masumoo, and M. Saigo, "Real-ime 3d walking paern generaion for a biped robo wih elescopic legs," in Proc. IEEE In. Conf. Roboics and Auomaion, 2001, pp. 2299-2306. [6] S. Kajia, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi, and H. Hirukawa, "A realime paern generaor for biped walking," in Proc. of 2002 Inernaional Conference on Roboics and Auomaion, 2002, pp. 31-37. [7] K. Lofier, M. Gienger, and F. Pfeiffer, "Sensor and conrol design of a dynamically sable biped robo," in IEEE In. Conf. on Roboics and Auomaion, 2003, pp. 484-490. [8] S. Kajia, E Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, and H. Hirukawa, "Biped walking paern generaion by using preview conrol of zero-momen poin," in IEEE In. Conf. on Roboics and Auomaion, 2003, pp. 1620-1627. [9] S. Lohmeier, K. Lofier, M. Gienger, H. Ulbrich, and F. Pfeiffer, "Compuer sysem and conrol of biped "johnnie"," in IEEE In. Conf. on Roboics and Auomaion, 2004, pp. 4222-4227. [10] R. Kurazume, T. Hasegawa, and K. Yoneda, "The sway compensaion rajecory for a biped robo," in IEEE In. Conf. on Roboics and Auomaion, 2003, pp. 925-931. [11] R. GARAGE, CHROINO. hp://www.eone.ne.jp/ robogarage/english/frame.hml, 2004. [12] Y. Ogura, H. Akikawa, H. ok Lira, and A. Takanishi, "Realizaion of srech walking by biped robo (in japanese)," in Proc of Roboics Symposia, 2004, pp. 102-107. [13] --, "Developmen of a human-like walking robo having wo 7-dof legs and a 2-dof wais," in IEEE In. Conf. on Roboics and Auomaion, 2004, pp. 134-139. REFERENCES [1] A. Takanishi, M. Ishida, Y. Yamazaki, and I. Kao, "The realizaion of dynamic walking robo wl-10rd," in Proc. In. Conf. Advanced Roboics, 1985, pp. 459-466. [2] C. L. Shih, "Gai synhesis for a biped robo," Roboica, vol. 15, pp. 599-607, 1997. [3] --, "Ascending and descending sairs for a biped robo," IEEE Trans. Sysem, Man, and Cyberneics, vol. 29, no. 3, pp. -, 1999.