2005 IEEE/RSJ International Conference on Intelligent Robots and Systems

Straight Leg ged Walking of a Biped Robot
Ryo Kurazume, Shuntaro Tanaka, Masahiro Yamashita
Tsutomu Hasegawa

Kyushu University
6-10-1, Hakozaki, Higashi-ku, Fukuoka, Japan
Email: kurazume @is.kyushu-u.ac.jp
Abstractm This paper presents a new methodology for generating a straight legged walking pattern for a biped robot utilizing
up-and-down motion of an upper body. Firstly, we define two
new indexes, the Knee Stretch Index (KSI) and the Knee TorqueIndex (KTI), which indicate how efficiently the knee joints
are utilized. Next, up-and-down motion of the upper bodyis automatically planned so that these indexes are optimized
and straight legged walking is realized. The basic idea of the
proposed method is, i) when a large number of DOFs of motion
are required for controlling the ZMP, a robot makes its bodyheight lower, ii) when there is a extra number of DOFs of motion,
the body is lifted and the knee joint is stretched. By stretching
the knee joints, human-like natural walking motion is obtained.
Moreover, energy efficiency is improved since required torqueand energy consumption to support the body weight become
small at knee joints. The effectiveness of the proposed method
is demonstrated by computer simulation and experiments using
a humanoid robot, HOAP-1.
Index TermsmBiped robot, Knee joint, Energy efficiency,
Knee Stretch Index, Knee Torque Index
I. INTRODUCTION

For a humanoid robot which will coexist in human environment such as welfare robots or entertainment robots, it
is important to perform human-like motion to avoid making
uncomfortable feeling for users. However, conventional motion of a humanoid robot is generally unnatural [1]-[9]. For
example, if we compare walking patterns of a human being
and a biped robot, we will find the following differences: A
human being utilizes up-and-down motion of an upper bodyor roll motion using a waist joint, knee joints, and ankle joints
simultaneously. Instead, a conventional biped robot seems towalk very carefully by lowering its waist position and bending
knee joints.
The main reasons for this unnatural motion of a humanoid
robot are as follows;
1) Mechanical factorsa) Different configuration of DOFs
freedoms)b) Limited range of joint motion(Degree-of-2) Control factorsa) Uniformity of motionb) Constraints related to control algorithms, for instance, singularity avoidanceThis paper mainly discusses the control algorithm of a bipedrobot for generating natural walking pattern.
In general, most biped robots developed so far walk stably
by bending their knee joints (Fig.2(a)). This is due to the fact

0-7803-8912-3/05/$20.00 ©2005 IEEE.

3095

Kan Yoneda

Tokyo Institute of Technology
2-12-1, Ookayama, Meguro-ku, Tokyo, Japan
Email: yoneda @robotics.mes.titech.ac.jp

that controlling the Zero Moment Point (ZMP) becomes quitedifficult when the knee joint is stretched and the some DOFs
of motion are degenerated. On the other hand, human utilizes
rotation of the waist joint and up-and-down motion of theupper body to secure the enough DOFs for stable walking.
Fig.1 shows an example of a human walking pattern measured
by motion capture system.
Waist

Fig. 1. Up-downmotion of waist position while walking
This paper presents a new methodology for generating astraight legged walking pattern for a biped robot utilizing upand-down motion of an upper body (Fig.2(b)). Firstly, we
propose two new indexes, the Knee Stretch Index (KSI) andthe Knee Torque Index (KTI) for evaluating the efficiencyof the use of the knee joints quantitatively, The Knee Stretch
Index (KSI) is defined as the length between the line connecting the center of gravity (COG) and the ZMP, and the knee
rotation axis. The Knee Torque Index (KTI) is also definedas the length between the ZMP on a knee plane and the knee
rotation axis.
Next, the sway compensation trajectory [10] is modified sothat up-and-down motion is automatically planned to optimize
these indexes and straight legged walking is realized. The
basic idea of the proposed method is as follows: i) when anumber of DOFs of motion are required for precious controlof the ZMP, a robot makes his body height lower to secure
the enough DOFs, ii) when there is a extra number of DOFs
of motion, the body is lifted and the knee joint is stretchedin the same way as a walking pattern of human.
A few studies on straight legged walking have been reported so far. Recently, the Robo GARAGE, which is aventure company in Japan, announced a new humanoidtype robot named CHROINO [ll]!-~This robot is able towalk stably with stretching knee joints by devising joint
configuration.
The research group at Waseda University in Japan reported
straight legged walking of a biped robot using their humanoidtype robot named WABIAN-2 [12], [13]. They adopted different algorithms for the calculation of inverse kinematics insupporting and recovering phases. The singularity is avoided
by utilizing the roll motion of the waist joint.
Our method realizes the straight legged walking by controlling the height of the COG trajectory according to the stateof the ZMP controller. The singularity is avoided by bending
the knee joints when the ZMP has to be controlled precisely.
On the other hand, the knee joints are stretched if the desired
ZMP is almost attained and there is no need to control the
ZMP position so precisely.

(a) Conventional walking patternFig. 2.

(b) Proposed walking pattern

Height control during walking

There are several advantages for the straight legged andwaist-lifted walking. Some of them are as follows;
1) Human-like natural walking motion is obtained
2) Energy efficiency is improved since required torque andenergy consumption to support the body weight become
small at knee joints.

y.

c(~ + c~ ~ + .~t~ + .~t + .g-

Eqs.(4) and (5) consists of a particular solution and a generalsolution of equations, xg - A:~ = 0 and yg - A~)~ = 0. By
substituting these equations into Eq.(3), we obtain~o~O(~+ sin O(a~2AaV.2 + a~t + aV.2t'2)

~

}+~

.

j

COGtraj.

t~

/+~

~

(6)

.'PP

'PP

•

/~

-0.05

tr
"-,Right
''-z2
foot
aj.

-°~-0~

0

0'~

i/

i/

~

~

0',

o'3

i

o'4

05

X[m]
Fig. 3. An example of ZMP and COG trajectories projected on the groundfor straight path

In the following discussion, we assume the weight of legs
and arms are smaller than the body weight. In this case, thesystem can be regarded as a single mass model placed on(xg,yg,zg)
Assuming a floor is flat and the height of the point mass zg
is constant, the ZMP on the floor (x~mp, y~mp, 0) is obtained
as follows:)(i)where, A - ~ . Next, the diagonal line connecting the centerof the soles of support feet is defined as
sin0=d(2)Then, in order to keep the ZMP on this line, the COG has tosatisfy the following equation.
cos O(x. - A~'g) + sin O(y. - Ay'g) = d

B. Convergent calculation considering multiple mass model
The trajectories obtained as Eqs.(4) and (5) are based on theassumption of a simple single mass model. Therefore, more
precise trajectories and joint commands should be determinedbased on a multiple mass model for stable walk. To obtain
the precious ZMP trajectory based on the multiple massmodel, we proposed the method which utilizes convergencecalculation for rectifying the COG trajectory according to thecurrent ZMP errors.
Firstly, the ZMP X ~ p = ( x ~ p , y ~ p , 0) for a multiple
mass model is obtained from the following equations.
x~.w

-

E ~

(7)

(3)

Here, we assume that the robot moves along x axis and theposition of the body is expressed as~ 7 ~ + a ~ t 2 + a l tx+ ad-l /l /l /l''A. Definition of the sway compensation trajectoryxg-C~e~+C~e

2A..~ + .;t + ..~t 2)

f/Left foot~ROBOTS

t

-

qP

0.05

In this section, the sway compensation trajectory for bipedrobots is introduced [10]. The ZMP and the COG trajectories
are obtained by explicit functions of a sway width, a walking
speed, acceleration and lines connecting the center of the solesof support feet.

t-

From Eq.(6) and the boundary condition, all the parameterssuch as a~ are determined [10]. The trajectory expressed by
Eqs.(4) and (5) is named "the sway compensation trajectory".
Fig.3 shows an example of the ZMP and the COG trajectories in case that the robot walks 10 steps with the velocity
O.lm/s along the x axis from the initial position (0, 0).
It should be pointed out that obtained trajectories canbe easily modified and utilized if the moving direction is
gradually changed. This is because continuous ZMP and
COG trajectories are obtained by applying simple coordinatetransformation to original trajectories according to the moving
direction.

II. T H E S W A Y C O M P E N S A T I O N T R A J E C T O R Y F O R B I P E D

x cos0+y

(5)

ox

(4)

3096

Y~-w

N
~i=1

(~: + g)
7/~i

r ew,
f the
Here, we define the planned ZMP trajectory as X~.
refined COG trajectory to realize the planned ZMP trajectoryX f f ef I alnd the current COG trajectory as Xg. Then, current
status can be expressed as

as

X~,

- Xg - A Jig(9)

On the other hand, the goal status is shown as
X ~f c f v - Xgf c f - A J ~ ~f(10)

Thus, by subtracting above equations, we obtain
x~.~p - x~.~p - x ~ ~s - x g

A ( 2 ~ ~s

2g)

(11)

or,
e~p

(12)

= eg - A~g

where, ezmp -- X z ref
m p -Xzmp,
and eg - X ~ ~f - X g
By resampling this equation with sampling interval At, thefollowing equation is obtained.
tezra pt _ A~tgeg
t+s _ 2 e t +--%t _ A %-t-s(/xt)2 %(13)

are calculated from the current COG trajectory X2.
Note that the tip trajectories of hands and legs are
determined beforehand, and there is no change before
and after the convergent calculation.
3) The actual ZMP trajectory based on the multiple massmodel X~mp is calculated using Eqs.(7) and (8) and thejoint trajectories ~n.
4) The error between the ideal and the actual ZMP trajectories e~mp - X ~refp - X ~ p is obtained. This error
is discretized and the error at each time step e~pt is
calculated.
5) The rectification of COG trajectory e gt that minimizes
Eq.(15) is calculated using the convergence calculation
for all discretized error (The first loop) ! -~6) The refined COG trajectory X ~ +s - X ~ ef is obtainedusing Eq.(16).
7) The calculation is terminated if the sum of the rectification of COG trajectory e gt is small enough.
8) Go to Stop (2) (The second loop)
III. KNEE STRETCH INDEX AND KNEE TORQUE INDEX

Therefore, the rectified value of the COG trajectory e gt thatt p is obtained as the following
reduces the ZMP e r r o r ezra
equation.
t

eg

__

A
t+l + %t - 1 )e t~ p + gxTg(%
1+ 2 A(zXt)2(14)

However, several experiments showed that the refined COG
trajectory tends to be oscillational at discontinuous point of
the ZMP velocity, if the rectified value obtained from above
equation is added directly to the original COG trajectory.
Therefore, we choose the rectified value of the COG trajectory egt so that the following equation with the smoothness
constraint is minimized.
tA(et+s +

t-s)

e~v + ~%)'2+min(etg 1+ 2 A(zxt)2
t+s +
t+s
t-s +
t-s
t
eg
Xg
+ eg
Xg )2

The sway compensation trajectory is derived for a robot
which can change the COG position at will. Thus, the knee
joint has to be bent sufficiently to ensure enough DOFs of
motion. However, by stretching the knee joints and keeping
waist position high, several advantages can be considered as
mentioned above. Especially, if the torque produced at theknee joint is reduced, it is quite useful in practical design
since a small and light weight actuator.
However, no index has been proposed so far for indicating
how much the knee joints utilized efficiently. For evaluating
the efficiency of the use of the knee joints quantitatively, we
propose two new indexes, the Knee Stretch Index (KSI) andthe Knee Torque Index (KTI) in this section. Both indexes
indicate the required torque at the knee joints to support the
body weight with a simple calculation. Thus, it is possible toevaluate the efficiency of walking patterns using these indexes
without a precise calculation of joint torque.

(15)
A. K n e e Stretch Index

Consequently, the refined COG trajectory that realizes theplanned ZMP trajectory is obtained as the sum of the current
COG trajectory Xg and the rectified value e tg.
X ; ef t-- X g + egt

At first, we define the Knee Stretch Index (KSI). The KSI
reflects the knee torque to support the body weight under theassumption of the single mass model.

(16)

In practice, considering the resampling error and non linearity
of Eqs.(9) and (10), the above calculation should be repeateduntil egt becomes sufficiently small value.
In summary, the proposed method which consists of twoconvergent calculation loops is described as follows;
1) The ideal ZMP trajectory X~mp
~ f is designed from
Eqs.(1), (4), and (5). Then the COG trajectory Xg0 thatrealizes the ideal ZMP trajectory is obtained approximately using a single mass model.
2) The trajectory of the reference position (ex. the waist
position) and the joint trajectories of arms and legs (I)n

3097

COG

D1

~COG

.....,>~ :: i!

Knee stretch index = L1 +L------~

L2
Rotationaxis j @ ~ D 1
L~

D1
",,@

........... hmdex=

D1

~ZMP
F i g . 4.

ZMP

Definition of Knee Stretch Index

Fig.4 illustrates the definition of the Knee Stretch Index. If
we assume that all the mass of the robot body is concentrated
at the COG and the moment around the COG is negligible, thereactive force from the ground is exerted at the ZMP on thesole along the direction from the ZMP to the COG. Therefore,
the torque to support the body weight at the knee joint is
proportional to the distance from this line to the rotation axisof the knee joint. For example, in the case that the rotation
axis of the knee joint is on the line between the COG and
the ZMP, all the body weight is supported mechanically andthere is no need to produce the torque at the knee joint.
From the above consideration, the Knee Stretch Index(KSI) is defined as a ratio of the minimum length D1 between
the line connecting the COG and the ZMP, and the leg length
L, that is,
D1
Knee Stretch Index =(17)large number of DOFs of motion are required for precious
control of the ZMR a robot makes its body height lower tosecure the enough DOFs, ii) when there is a extra number of
DOFs of motion, the body is lifted so that the index proposedin the previous section is minimized and the knee joint isstretched, we modify the steps 4 of the procedure of the sway
compensation trajectory as follows:4) The error between the ideal and the actual ZMP traref
jectories ezrnp -- Xzrnp- Xzrnp is obtained. This error
is discretized and the error at each time step ezrnpt is
calculated. In addition, when the knee joint angle is not
180 degrees (bending), the waist position is modified as
egt __+ egt + APmin. Here, APmin is derived as follows:i) the COG position is moved slightly to new positions
on a small circle around the current COG position in
x-z plane (Fig.6), ii) the KSI (or the KTI) is calculated
at each position and the position where the index isminimized is selected as A P ~ i ~ .
Contrary to this, when the knee joint angle is already180 degrees and the ZMP error is larger than thet
pre-defined constant value a s ezrnp) eth, the waist
position is lowered as e~t --+ e~t - A H . Actually, we
use the smoothness constraint for e~t in the same way
as Eq.(15).

L

B. Knee Torque Index
Next, as a new index to evaluate the efficiency of the useof the knee joints more rigorously, we propose the Knee
Torque Index (KTI). Imagine a plane which includes therepresentative point on the rotation axis at the knee joint andis parallel to ground. The representative point can be a point
where, for example, the rotation axis intersects with the centerline of the leg. Then, the ZMP on this plane can be definedin the same manner as the conventional ZMP on the ground,
and we call this ZMP the knee-plane ZMP (KZMP). Since
no moment along roll and pitch axes exists at this KZMR
if this KZMP is on the rotation axis of the knee axis, notorque is required at the knee joint to support the body weight.
Therefore, we define the Knee Torque Index (KTI) as a ratioof the length D2 between the KZMP and knee rotation axis,
and the leg length L such as

K n e e Torque I n d e x -D2Linin(etz -- AH)2-~~z

e t + l + X t + l + e ~ t - - 1 + X ~ t - - 1 )2

i;

(18)

Fig.5 indicates the definition of the Knee Torque Index(KTI). This KTI almost coincides with the KSI if the rotation
axis of the knee joint is parallel to the ground and the moment
around the COG is small.

(19)~APmin.........
z/ / / / / / / / / / / / / /i////////////////(a) COG is moved on a small
circle around current COG.
D2
Knee torque index - L1 +L2
Knee-plane ZMPi(b) Recalculate KST or KTI andfind the position where the index
is minimized.

Fig. 6. Calculation of AP,~in

Knee plane
Rotation axis " ~ I ~ L~ZMP

Fig. 5. Definition of Knee Torque Index
IV. NEW STRAIGHT LEGGED WALKING PATTERN
In this section, we propose a new straight legged walking
pattern by controlling the height of the COG trajectory
according to the state of the ZMP controller.
The sway compensation trajectory described in section 2
assumes the constant height of the waist position. In orderto obtain the adaptive waist trajectory such as, i) when a3098

As a consequence of the above procedure, the robot makes
its waist position lower if the knee joint is stretched and thesome DOFs of motion are degenerated even if the ZMP error
is large. On the other hand, the waist position is lifted and the
KSI and/or the KTI are improved if the ZMP error is smalland some DOFs of motion is redundant.
Furthermore, the solution of inverse kinematics cannot
be obtained when the knee joint is completely stretched ingeneral. Thus, our method adopts an approximated solution.
Let's consider the case shown in Fig.7. Generally, the joint
angle of the knee joint 04 is obtained using the cosine formulaas04 - - 71- - - COS - 1

L~ + L,~ - l 2

2L1L2

(20)

Where L~ and L2 are the length of the thigh and shank,
and l is the length between the ankle and the groin. However,the solution of the Eq.(20) cannot be obtained if L~ + L2 < l.
Therefore, we use the following solution in this case as
04 -- { 71-- COS-171-L~-~-L~-lZ2L~Lz (otherwise)+(L~ L.2 _> l)~~'~i̧¸'i~~ I ~ I ~ ~(21)z
L 1 :i;ii:

04iii~::!4
L2Fig. 8. Conventional walking patternFig. 7. Approximated calculation of Inverse Kinematics
At the singular point where the knee joint is stretched, hugeangular velocity is produced in case that the waist position isforced to be lowered. In our implementation, we defined the
maximum and minimum values of the angular acceleration
at the knee joint to avoid such case. By introducing thisprocedure at the step 2 in the above convergent calculation,
the joint angle trajectory that minimizes the ZMP error is
obtained under the constraint of the feasible angular velocity.

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

V. EXPERIMENTS
This section introduces some examples of the proposed
straight legged walking pattern though computer simulations
and walking experiments using the humanoid-type bipedrobot named HOAP-1.

.......iiii....... .i0Ho0. . . . ..........
Fig. 9. Obtained walking pattern after 100 iterations

A. Computer simulation
Figs.8 and 9 show examples of the obtained walking
patterns using the method proposed in Section III. Here, Fig.8
illustrates a conventional walking pattern which keeps the low
waist position and bends the knee joints. Fig.9 is an obtained
walking pattern after the convergent calculation using the
proposed method. In these simulations, the walking period
is 4 [sec.] and the maximum angular acceleration is set to500[~.~d./~.~].
Fig.10 shows the change of the waist height before andafter the convergent calculation. It is clear that the periodical
up-and-down motion of the waist position is obtained gradually through the convergent calculation.
The joint angle of the knee joint is also shown in Fig.11.
The lower figure of Fig.11 shows the joint trajectory during
one supporting phase. After convergent calculation, the joint
angle of the knee joint becomes about 180 degrees twice in
one,.waltdl~ cycle.
PigA2 sffov~s the ZMP trajectories before and after convergent calculation. From this, it is verified that the ZMP
error after the convergent calculation becomes smaller than3099

the error without the convergent calculation even if up-anddown motion of the waist position exists and Eq.(1) is notsatisfied.
Fig.13 and Table I show the total power consumption
and the energy consumption in one walking cycle. The sumof the energy consumption of all actuators is l l.9[J] forthe conventional walking pattern (Fig.8) and 7.6 [J] for the
proposed walking pattern (Fig.9), respectively. Thus, it is clearthat the proposed straight legged walking is more effective
than the walking pattern which bends the knee joint in viewsof the energy consumption.
Finally, the proposed Knee Stretch Index and the Knee
TABLE IE N E R G Y C O N S U M P T I O N IN ONE WALKING CYCLE

Walking pattern
Conventional pattern (Fig.7)
Proposed pattern (Fig.9)

Energy consumption
13.3 [J]6.5 [J]

4
,....
.<
~ Initial offset(=0)-~ 0 ..............................................................................................................................................
a=After 50 iterationsO~/ Afterl0iterations,~ ,", ~ / , i ~ ; ? ~ i ~ ~ ~ /~, /",/-2 ....... ~ ,,.. "..,~,. . . .
t i/"i,--,,v ~',~ t' " t V'" i

-4 p
0

"t!

~After 100 iterations
10
15

5

10 /{
}
I,IL " !I'.~

4,
Ei

[#'
!ib
01

20

Yime[sec.]
Fig. 10.

.-.

0Height regulation by convergent calculation

o3[(Conventional pattern"ii/~ ~i#/\A
ilV,1 i/\,+4 ::iv,,, Ii"4!
!/,:,[ i~ i/:t

! i i!~,,ij'{/ j,tt'..-.'J ~( Proposedpattern )/<i ii,~i{A!

>I~t.,.'~
'

L,,}

! i/

i

J!'1i

s~:

j s"~

~,p,i'.gi i

V~i ~q'~,,$'

L,,.'/

~

L,

00

i

00
5

i- 10

~,~

t
::Y7

i~e'

10'

Time[sec.]

i,4' ',,
L,~,e

15

20

Total power consumption

~

\

!

i

5

:(Co . .15. . tional pattern-)20

Time[sec.]
Fig. 11.

, ~

i,{

i

(aft . . . . . . . . gent calculation~i i ! ......,! i " '~ i.................< 1............... ", I .... '-.....1::,2oi.,,i!i'.-"............
ii!i'-.-".............
ti!i,,...........,,,,,................
i!!i!........ it!i

80 0

ii",

I~,~

, }"1 ' iqw! , i'l \'~! ~Proposed Pattern) i I

i l

140 ! Iti~ i ~j,{~!q{,~ '/'"1

;,I I
=g

ili

iA

(Conventional pattern),~0.2

16°~ !r\J tiU

'I~:;

{A

~ .,

/

180

,,!

b!i

D

Fig. 13.

ii~,,t{, ii]/,~s ,,,,k~'"+.~,=:l<,,-ii;; t!
i'! ~ [',1 \',l!~ i /

J,{/

#,'t

i~

i j,

A

if\J1

Fig. 14.

~'Pr°p°sedpitiern )i10Time[sec.]

15 ~

"i

L!i:
'"~

20

Comparison of Knee Stretch Index

Knee joint angle

B. Experiments using HOAP-1
Torque Index for the obtained trajectories are shown in
Figs.14 and 1 5 ! ~ t is clear that both the KSI and the KTI
for the proposed straight legged walking pattern becomes
smaller than the ones for the conventional walking pattern.
This means that the body weight is supported with small joint
torque using the obtained straight legged walking pattern.
Fig.16 shows the calculated joint torque at the knee joint of
the right leg. The absolute value of the joint torque becomes
small as expected from the KSI and the KTI if the proposed
straight legged walking pattern is used. From these results,
it is verified that the efficiency of walking patterns can beevaluated using these indexes instead of calculating precise
joint torque.

0.06
0.04

before convergent calculation ---------i..,...... desired trajectory

Walking experiments using the Humanoid-type biped robot
were carried out. Fig.17 and 18 show the conventional andthe proposed walking patterns of the HOAP-1. From theseexperiments, it is verified that the robot walks stably using
the proposed straight legged walking pattern even when the
robot stretches the knee joints.
VI. CONCLUSIONSThis paper presents a new methodology for generating astraight legged walking pattern for a biped robot utilizing upand-down motion of an upper body. The advantages of thestraight legged and waist-lifted walking are as follows:
1) Human-like natural walking motion is obtained
2) Required torque and energy consumption to support the
body weight become small by stretching the knee joints

.

0.02

- • 0.2

&0

-0.02

0.1

-0.04

after convergent calculation-0._0.106

0

0.1

0.2

0.3

0.4

0.5

00

Fig. 12.

5

10

15

Time[sec.]x[m]Z M P trajectory before and after convergent calculation

Fig. 15.

3100

Comparison of Knee Torque Index

3/]//iy (C. . . . . j,~ionalpattern/,~/I
0Fig. 16.

5!,/ ~ Pr;pos;d pattern )iii¢
10Time[sec.]

15

20

Torque at knee joint of right leg (absolute value)

Fig. 18.

litoFig. 17.

Obtained walking pattern using a conventional walking pattern

Two new indexes which evaluate how efficiently the knee
joints are utilized, that is, the Knee Stretch Index (KSI) andKnee Torque Index (KTI), are proposed. Both indexes indicate
the efficiency of the use of the knee joints quantitatively forthe straight legged walking with a simple calculation. Upand-down motion of the upper body is automatically planned
so that these indexes are optimized and the straight legged
walking is realized.
Computer simulations and experiments are successfully
carried out using the humanoid-type biped robot HOAP-1.
ACKNOWLEDGMENT

This research was partly supported by the 21st Century
COE Program "Reconstruction of Social Infrastructure Related to Information Science and Electrical Engineering", andthe Ministry of Public Management, Home Affairs, Posts andTelecommunications in Japan under Strategic Information andCommunications R&D Promotion Programme (SCOPE).
REFERENCES[1] A. Takanishi, M. Ishida, Y. Yamazaki, and I. Kato, "The realization of
dynamic walking robot wl-10rd," in Proc. Int. Conf. Advanced Robotics,
1985, pp. 459-466.
[2] C. L. Shih, "Gait synthesis for a biped robot," Robotica, vol. 15, pp.
599-607, 1997.
[3] - - , "Ascending and descending stairs for a biped robot," IEEE Trans.
System, Man, and Cybernetics, vol. 29, no. 3, pp. -, 1999.

3101

Obtained walking pattern using the proposed method[4] Q. Huang, S. Kajita, N. Koyachi, K. Kaneko, K. Yokoi, H. Arai,
K. Komoriya, and K. Tanie, "A high stability, smooth walking pattern
for a biped robots," in Proc. IEEE Int. Conf. Robotics and Automation,
1999, pp. 65-71.
[5] S. Kajita, O. Matsumoto, and M. Saigo, "Real-time 3d walking patterngeneration for a biped robot with telescopic legs," in Proc. IEEE Int.
Conf. Robotics and Automation, 2001, pp. 2299-2306.
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