A INTERPOLATION-BASED APPROACH TO MOTION

GENERATION FOR HUMANOID ROBOTS

Koshiro Noritake, Shohei Kato and Hidenori Itoh

Dept. of Intelligence and Computer Science

Nagoya Institute of Technology

Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan

Keywords:

Humanoid robot, motion generation, Tai Chi Chuan, balance checking.

Abstract:

This paper proposes a static posture based motion generation system for humanoid robots. The system gener-

ates a sequence of motion from given several postures, and the motion is smooth and stable in the balance. We

have produced all the motions of Tai Chi Chuan by the system. Motion generation for humanoids has been

studied mainly based on the dynamics. Dynamic based method has, however, some defects: e.g., numerous

parameters which can not be always prepared, expensive computational cost and no guarantee that the motions

are stable in balance. We have, thus, studied less dependent-on-dynamics approach. A motion is described as

a sequence of postures. Our system ﬁgure out if we need extra postures to insert for stability. This method

enables humanoid robot, HOAP-1 to do Tai Chi Chuan.

1 INTRODUCTION

In recent years, robotics has greatly developed, es-

pecially, research for humanoid robots has attracted

much attention (e.g,(Nishiwaki et al., 2002), (Sug-

ihara et al., 2002), (Huang et al., 2001), (Yam-

aguchi et al., 1993), (Li et al., 1993), (Kagami et al.,

2001), (Kuffner et al., 2001), (Kuffner et al., 2002),

(Kuwayama et al., 2003)). Existing methods of mo-

tion generation for humanoid robots are mostly based

on the dynamic control theory and the optimization

technique. These methods are often specialized in

some particular motions, such as walk and standing,

which are simple, symmetric or cyclic. This presents

an obstacle to general-purpose. These methods may

require the mastery of dynamic for use. The method-

ologies based on the dynamics often require highly

expensive computational cost, and the motion control

for unconstraint motions is still hard problem. Me-

chanical characteristic of humanoid robot is an in-

crease in DOFs. There is, however, few studies for

motion control such that the DOFs are fully utilized.

In this research, we, thus, take an intelligent soft-

ware approach to motion control with useful interface

and application for various motions. In this paper,

we propose a motion generation system for humanoid

robots. Our system generates a sequence of motion

from given several postures, and the motion is smooth

and stable in the balance.

We have produced all the motions of Tai Chi Chuan

by the system. All motions have been performed by a

humanoid robot.

2 HUMANOID ROBOT AND THE

TARGET MOTIONS

2.1 Humanoid Robot

In this paper, we consider the motion control of a hu-

manoid robot, HOAP-1 (Humanoid for Open Archi-

tecture Platform) produced by Fujitsu(Murase et al.,

2001), shown in Figure 1. The total weight is 6 (kg)

and the height is 48 (cm). HOAP-1 has 20 DOFs

in total, 6 in each leg and 4 in each arm. The link

structure is shown in Figure 2. The sensor architec-

ture of HOAP-1 is consisted of 4 pressure sensors on

each sole and angular rate and acceleration sensors

mounted in breast. HOAP-1 is controlled with RT-

Linux OS on itself or computer connected with USB.

2.2 Tai Chi Chuan

We consider Tai Chi Chuan as the target motion for

humanoid robots. Tai chi has several styles. In this

paper, we adopted Tai Chi 48. Tai Chi motions have

various movement of entire body. Tai Chi motions are

Noritake K., Kato S. and Itoh H. (2004).

A INTERPOLATION-BASED APPROACH TO MOTION GENERATION FOR HUMANOID ROBOTS.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 41-47

DOI: 10.5220/0001143100410047

 SciTePress

Output: Sequence of Motions

Balance-Checker

Motion-Generator

Input: Postures

smooth interpolation

Figure 3: Data ﬂow in our motion generation system.

Figure 1: HOAP-1.

Figure 2: The link

structure of HOAP-1.

performed slowly, softly and with smooth and even

transitions between them. Tai Chi motions require

sophisticated balance control for robots. In addition

to stability or energy consumption, Tai Chi Chuan re-

quires concinnous forms. Unlike to walking, Tai Chi

motions should not be changed markedly in appear-

ance even for the stability.

3 MOTION GENERATION

SYSTEM

3.1 Interpolation-based Motion

Generation

The section describes a motion generation system

for humanoid robots. Figure 3 shows the out-

line of the system. Input to the system is a se-

quence of postures P = P

, P

, · · · , P

, (called

key-postures

). Each key-posture has characteristic

form of a motion to generate. In this system, we

suppose that each key-posture is statically stable in

balance. This supposition is supported by the key-

posture adjustment, such that the center of mass

(COM) of the upper body is positioned just above

the ankle of the supporting leg. Output from the

system is a motion sequence M = M

, M

, · · · ,

The basic function of motion generation is the

smooth interpolation between two postures, P

and

i+1

. The interpolated motions, needless to say,

should be stable in balance for humanoid robots.

Bal-

ance Checker

evaluates the distance between P

and

i+1

in balance space, and then, inserts a few inter-

mediate postures (corresponding to A

in Figure 3) if

the distance is over a threshold. It is, in general, dif-

ﬁcult to calculate the distance of postures in balance

space. We have, thus, made a rough approximation

described in the following section.

3.2 Classiﬁcation of the Postures in

Balance Space

Tai Chi Chuan, our target motion, has wide variation

in posture. Interpolation-based motion generation is,

however, vulnerable to wide or quick variation in pos-

tures. It is, thus, important to consider some relation

between two postures to be interpolated. The admissi-

bility of the interpolated motion may be estimated by

the relation. In this research, we consider the distance

in balance space as the admissibility.

To calculate the distance of postures in balance

space is hard problem. In this research, we give this

problem an audacious consideration that postures of

Tai Chi motion are classiﬁed into 13 groups (

posture

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5 6

Right Leg Standing

Both Leg Standing

Height of Tue

of Idling Leg

(1~4, 10~13)

High

Low

Height of COM

((5, 6, 9), 7, 8)

High

Low

Right Foot

Position of COM

(5, 6, 9)

Left Foot

Left Leg Standing

Figure 4: The directed graph of 13 posture classes.

class

, or simply

class

) and these groups are connected

by 26 arcs in the balance space. The balance space

is represented by a directed graph shown in Figure 4.

The classiﬁcation is based on the relative position of

COM and the relation of the supporting and idling

legs. Firstly, postures are classiﬁed into three classes:

both leg standing, right leg standing and left leg stand-

ing. Single leg standing is classiﬁed into four classes

according to the height of the idling leg in relation to

the supporting leg (see Figure 4):

• lower than the ankle (#4 and #10),

• higher or equal than the ankle and lower than the

knee (#3 and #11),

• higher or equal than the knee and lower than the hip

(#2 and #12),

• higher or equal than the hip (#1 and #13).

Both leg standing is classiﬁed into ﬁve classes accord-

ing to the position of the COM in relation to the COM

of the erect posture (see Figure 4):

• the vertical component is less than 80% (#8),

• the vertical component is more or equal than 80%

and less than 90% (#7),

• the vertical component is more or equal than 90%

and,

– the horizontal component leans to right more

than 20% (#5),

– the horizontal component leans to left more than

20% (#9),

– the horizontal component is within 20% from the

center of the both feet (#6).

The classiﬁcation enables our system to approxi-

mate the distance of two postures. Let a and b be

arbitrary postures to be interpolated, and let g

to g

be the classes which a and b belong to, respectively.

The distance between a and b is given by the distance

between g

and g

: the length of the path from g

. We, therefore, can estimate the admissibility of

the interpolated motion from a to b by the distance

between g

and g

The balance checker in our system utilizes the di-

rected graph in Figure 4 for the decision to insert an

intermediate posture or not. The directed graph give

a constraint for the stability in balance on the motion

generator. The constraint is that two postures to be in-

terpolated should belong to one class or adjoining two

classes. For example, interpolation from a posture in

class #6 to a posture in class #4 has the risk of tum-

ble. A posture in class #5 should be inserted between

them.

A INTERPOLATION-BASED APPROACH TO MOTION GENERATION FOR HUMANOID ROBOTS

6 9

9 6 7 6

6 5

6 6

(collision)

Figure 5: The snapshot of Tai Chi #7 motion by HOAP-1.

4 5 6 6

9 10 6

7 8

Figure 6: The snapshot of Tai Chi #17 motion by HOAP-1.

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2 3 4 5 6

9 10 6

11 12

Figure 7: The snapshot of Tai Chi #44 motion by HOAP-1.

4 EXPERIMENT

We have produced all the motions of Tai Chi Chuan

without tipping over. Firstly for data input to our

motion generation system, we have prepared key-

postures for 48 Tai Chi motions, from a tutorial book

(Defang, 1999). The system has, secondly, generated

the control sequences of servomotors for all the mo-

tions. In this particular examples, all motions are well

performed by HOAP-1. Table 1 and 2 show the listing

of Tai Chi motions and the numerical relation between

input and output postures by our system.

4.1 Performance Results

Figure 5, 6 and 7 show the snapshots of Tai Chi #07,

#17 and #44 motion by HOAP-1, respectively. Tai

Chi #7 composed of the basic walking motion, called

shang bu

. This is easy one in Tai Chi, however, it oc-

curs tipping over without our system. Tai Chi #17

composed of the motion keeping robot’s head low,

called

pu hu

. This motion HOAP is imbalance in

backward and forward movement. Tai Chi #44, which

contains high kick called

bai lian

, requires high skill

balance control of robot. This is one of the most difﬁ-

cult motions. HOAP-1 can support its weight with

one leg skillfully, although the imbalance becomes

very high. In these ﬁgures, the number in the lower

right of the each snapshot means the class which the

posture belongs to. The transition of classes satisﬁes

all constraints by the directed graph shown in Fig-

ure 4.

COM

z=0

LeftBottom(Pl,Wl)

RightBottom(Pr,Wr)

Figure 8: Components for balance quantiﬁcation.

4.2 Effectiveness of Balance Checker

To verify the effectiveness of our system, we have

evaluate the balancing performance for the motions.

In this paper, we suppose the quantity of balance as

follows. Let COM be the center of mass of whole

robot, let COM

be the vertical component of COM ,

and let COM

z=0

be the projection of COM on the

ﬂoor. Further, let P

and P

be the position of the

left and right sole, and let W

and W

be the weight

on the left and right sole, respectively (see Figure 8).

The balance is quantiﬁed as the following equation:

imbalance = |COM

z=0

− CW | · COM

, (1)

where

CW =

P r · W r + P l · W l

W r + W l

. (2)

Figure 9, 10 and 11 show the trajectories

imbalance of two Tai Chi by HOAP-1: our method

and without

Balance-Checker

for Tai Chi #7, #17 and

A INTERPOLATION-BASED APPROACH TO MOTION GENERATION FOR HUMANOID ROBOTS

Table 1: Key Postures of Tai Chi Generated by Our System

postures postures

# name after by

balance tutorial

checker book

(0) qi shi 4 4

1 bai he liang chi 5 4

2 zuo lou xi ao bu 4 4

3 zuo dan bian 20 10

4 zuo pi pa shi 4 3

5 lu ji shi 26 15

6 zuo ban lan chui 13 7

7 zuo peng lu ji an 19 11

8 xie shen kao 8 4

9 zhou di chui 11 7

10 dao juan gong 29 12

11 zhuan shen tui zhang 18 13

12 you pi pa shi 4 3

13 lou xi zai chui 9 6

14 bai she tu xin 9 6

15 pai jiao fu hu 31 18

16 zuo pie shen chui 11 5

17 chuan quan xia shi 9 4

18 du li cheng zhang 14 6

19 you dan bian 20 10

20 you yun shou 25 12

21 you zuo fen zong 13 7

22 gao tan ma 5 3

23 you deng jiao 10 6

24 shuang feng guan er 5 3

#44 motions, respectively. The result indicates that

our system can generate a stable Tai Chi motion for

HOAP-1, while the robot loses the balance without

our balance checker. In the ﬁgures, the numbers over

the graph correspond to the frame labeled the same

number in snapshots shown in Figure 5, 6 and 7. All

motions without balance check tipped over, and after

that, the imbalance is not accurate because sensors are

not calibrated.

5 CONCLUSION

In this paper, we proposed a motion generation sys-

tem for humanoid robot. The motion generated by our

system is smooth and stable in the balance. Humanoid

robot, HOAP-1 with our system has performed whole

48 Tai Chi motions in good balance. Our system per-

forms various and unrestricted motions for humanoid

robots without hard problem in dynamics. Our sys-

tem still has some constraints, that is, platform de-

pendent, interpolation interval, and at least one sole

on the ﬂoor.

Table 2: Key Postures of Tai Chi (continued)

postures postures

# name after by

balance tutorial

checker book

25 zuo deng jiao 8 4

26 yan shou liao quan 7 3

27 hai di zhen 6 3

28 shan tong bei 5 2

29 you zuo fen jiao 21 9

30 lou xi ao bu 15 7

31 shang bu qin da 10 4

32 ru feng shi bi 7 4

33 zuo yun shou 25 11

34 you pie hen chui 11 5

35 zuo you chuan suo 33 16

36 tui bu chuan zhang 5 2

37 xu bu ya zhang 6 2

38 du li tuo zhang 2 1

39 ma bu kao 9 3

40 zhuan shen da lu 9 5

41 liao zhang xia shi 11 7

42 shang bu qi xing 4 2

43 du li kua hu 7 4

44 zhuan shen bai lian 12 4

45 wan gong she hu 6 4

46 you ban lan chui 16 7

47 you peng lu ji an 19 11

48 shi zi shou 5 3

(49) shou shi 3 3

The future work will focus on three phases. Firstly,

we will deal with the automatic choreographing the

postures to insert. Secondly, we will dedicate to the

more generalized control of the motion generation.

Especially, it is important to let system free from in-

terpolating interval. Our system often makes motions

sprawly in time-axis. This is caused by our policy

that stability is more important than speed. There

are, however, scenes that speed is important, too. We

will respond to this tradeoff. Thirdly, we will dedi-

cate to some interpolation methods specialized to Tai

Chi Chuan. The value of the Tai Chi motion is not

only stability and speed, but also aesthetic sense and

smoothness of the motions. In this phase, we will

ﬁrstly focus on ﬁnding ordinality in the rhythm of Tai

Chi Chuan.

ACKNOWLEDGMENT

This work was supported in part by Artiﬁcial Intelli-

gence Research Promotion Foundation and Ministry

of Education, Science, Sports and Culture, Grant–in–

Aid for Scientiﬁc Research under grant #14780307.

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3000 6000 9000 12000 15000 18000 21000 24000 27000 30000

0.01

0.02

0.03

0.04

0.05

0.06

Tai Chi #7

Tai Chi #7 without balance check

time(ms)

imbalance(m^2)

original posture from the Tai Chi tutorial

intermediate posture by balance checker

Figure 9: The imbalance of Tai Chi #7.

0.01

0.02

0.03

0.04

0.05

0.06

3000 4500 6000 7500 9000 10500 12000 13500 15000 16500

Tai Chi #17

Tai Chi #17 without balance check

1 2 3

8 9

time(ms)

imbalance(m^2)

original posture from the Tai Chi tutorial

intermediate posture by balance checker

Figure 10: The imbalance of Tai Chi #17.

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A INTERPOLATION-BASED APPROACH TO MOTION GENERATION FOR HUMANOID ROBOTS