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� ���������� � 18 � 2008
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kawazoe�sit.ac.jp
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686289:%;<�%&1�,.&�2%("1�*&�/$"�='(/>'-./"1�?*&/>*;�*+�@$A('#%;�2*1A� � � �
Yoshihiko KAWAZOE
Department of Human-Robotics, Faculty of Engineering, Saitama Institute of Technology
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In the previous paper, we realized the simple self-sustained humanlike robust walking & running NANBA
of humanoid biped robot GENBE based on distributed control of physical body in a martial art utilizing instability without ZMP (Zero Moment Point) control, which uses only small active power with simple chaotic limit cycle, further developing into autonomous walking, running, instantaneous turn and the simple autonomous shock avoidance during falling down and instantaneous rising up. Instability makes the natural movement. This paper made clear experimentally by using high-speed video camera the mechanism of robustness of humanoid biped robot GENBE who walks and runs everywhere even on the ice and snow.
Key Words: Robotics, Humanoid Biped Robot, Robustness, NANBA Walk and NANBA Run, Limit Cycle.
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(e) (f) (g) (h) � � � � � � (i) � � � Fig.1 Robustness of humanoid biped robot GENBE who walks and runs everywhere.�
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- 31 -
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Fig.2 Biped walking robot GENBE-No.2 with 6 freedom legs
(a) State 1�
(b) State 2
Fig.3 Fundamental States of NANBA Walking of GENBE- No.2 with 6 freedom legs
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Fig.4 Forward speed vs pitch speed of biped robot GENBE No.2 with legs of 6 joints.�
� FFiigg..55 HHumanoid biped robot GENBE No.4.with legs of 10joints.
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- 32 -
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� � � � � � � � � � � (a)� � � � � � � � � � � � � � � � � � � (b) � � � � � � � � � � � � � � � � � �� State 1
� � � � � � � � � �� (a)� � � � � � � � � � � � � � � � � (b) � � � � � � � � � � � � � � � � � � � State 2
� � � � � � � � � � � Fig.6 States of NANBA Walk and Run of biped robot GENBE No.4-2007.
� � �
� � (a) (b) � � (a) (b) � � (a) (b)� � � � � (a) (b) � � � State1 � � � State2 � � � � � State3 � � � State4 � Fig.7 Four States of NANBA Walk and Run of biped robot GENBE No.4-2007.
� � 0.00 s 0.33 s 0.67 s 1.00 s� � 1.33 s 1.67 s � � � 2.00 s 2.33 s � 2.67 s � � � 3.00 s � State 2� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 3
3.33 s 3.67 s� � � � 4.00 s 4.33 s 4.67 s 5.00 s� � � � 5.33 s 5.67 s � � � 6.00 s 6.33 s
Fig.8 State transition from State 2 (Statically stable) to State 3 (Statically unstable), falling down to the ground.
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- 33 -
(1) t = 0.000 s (3) t = 0.133 s (5) t = 0.266 s (7) t = 0.399 s (9) t = 0.532 s� � (11) t = 0.666 s
� � � � � � � � Fig.9 NANBA walking & running of YYoosshhiinnoorrii�� KKOOHHNNOO
�� � � t=0.00s t=0.06s � � t=0.12s � t=0.18s � t=0.24s � � t=0.30s� � � � � � � � t=0.36s � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State1� � � � � � � � � � � � � � � � � � � Nearly State2
t=0.42s � t=0.48s � t=0.54s � t=0.60s � � t=0.66s � � � � � � � � t=0.72s � t=0.78s � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State3� � � � � � � � � � � � � � � � � � Nearly State4 � � � �� (a) Operating Time ( Speed) :10, Forward speed:13.5cm/s, 2.43 steps/s
t=0.00 s t=0.04 s t=0.08 s � t=0.12 s t=0.16 s t=0.20 s � � t=0.24 s t=0.28 s � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 1
t=0.32 s t=0.36 s � t=0.40 s t=0.44 s� � � t=0.48 s t=0.52 s � � t=0.56 s� � � � t=0.62 s Nearly State 2� � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 3� � � � � � � � � � � Nearly State4 � (b ) Operating Time ( Speed) :7, Forward speed: 20.2cm/s, 3.52 steps/s
� � 0.00s 0.02 s 0.04 s 0.06 s 0.08 s 0.10 s 0.12 s 0.14 s 0.16 s � � � � � � � Nearly State4� � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State1� � � � � � Nearly State2
0.18 s 0.20 s 0.22 s 0.24 s 0.26 s 0.28 s 0.30 s 0.32 s 0.34 s � Nearly State3� � � � � � Nearly State4 � � � � (c ) Operating Time (Speed) : 3&4, Forward speed: 36.5 cm/s, 6.58 steps/s.� Fig.10 NANBA Walk and Run of biped robot GENBE No.4-2007. NANBA Run takes only 0.3 seconds for 2 steps. A%¯% } 1, } 2��_�J,°±�²@³°±�´J5�¥�ê� }9�J�*(
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_ 0 deg Þ 90 deg Þ 0 deg +ßI��8£_d�$�,g 13�ç¦�XCYSZ¶µ�9N&�´Âï[V�(g 145d�14 Operating Time Setting 0.178 s (Speed-7)_ 90 degrees ��×Kö÷9¢�µ�¹V���,�g 155d�14 Operating Time Setting 0.096 s (Speed-3)_ 90 degrees ����àáâã_�'�¾_ 250fps,0.02 s È�Û!�(g 165�ä��_�J,g 16(a)5,¢�µ�¹�1X'K
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� � � � � � � � � � (c) � � Fig.11 Servo-motor: KRS-788HV
Fig.12 Example of high speed camera measurement, Operating Time setting: 0.096 s (Speed-3), Angle Setting: 90 degrees, Measured actual max. angle: 26 degrees.
Fig.13 High speed camera measurement and analysis of dynamic characteristics of a servo-motor: Example of Setting Operation Time 0.096 s (Speed-3) of servo-motor for running between 0 and 90 degrees .
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- 35 -
t=0.00s t=0.02s t=0.04s t=0.06s t=0.08s
t=0.10s t=0.12s t=0.14s t=0.16s t=0.178s
t=0.18s t=0.20s t=0.22s t=0.24s t=0.26s
t=0.28s t=0.30s t=0.32 s t=0.34s t=0.36s
t=0.38s t=0.40s
Fig.14 Example of high speed camera measurement of dynamic characteristics of a servo-motor, Operating Time setting: 0.178 s (Speed-7), Angle Setting: 90 degrees, Measured actual max. angle: 61 degrees.
� (0) t=0.00s (1) t=0.02s (2) t=0.04s (3) t=0.06s� (4) t=0.08s (5) t=0.10s
(6) t=0.12s (7) t=0.14s� (8) t=0.16s (9) t=0.18s (10)t=0.20s (11) t=0.22s Fig.15 Example of high speed camera measurement of dynamic characteristics of a servo-motor, Operating Time setting: 0.096 s (Speed-3), Angle Setting: 90 degrees, Measured actual max. angle: 26 degrees.
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� (10) t=0.20 s (12) t=0.24 s (14) t=0.28 s� � (16) t=0.32 s (18) t=0.36 s (20) t=0.40 s (22) t=0.44 s (24) t=0.48 s � Nearly State 1� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 2
(26) t=0.52 s (28) t=0.56 s (30) t=0.60 s (32) t=0.64 s (34) t=0.68 s� � (36) t=0.72 s (38) t=0.76 s � � (40) t=0.80 s � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 3� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State4
(42) t=0.84 s (44) t=0.88 s� � (46) t=0.92 s (48) t=0.96 s� � (50) t=1.00 s (52) t=1.04 s (54) t=1.08 s � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 1 � Fig.17 Moves of legs in the air for NANBA walk of GENBE No.4-2007 with Operating Time ( Speed) : 10 ( 2 steps).
(9) t=0.18 s (11) t=0.22 s (13) t=0.26 s� (15) t=0.30 s (17) t=0.34 s (19) t=0.38 s� (21) t=0.42 s (23) t=0.46 sNearly State 1 � � � � � � � � � � � Nearly State 2� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly
(25) t=0.50 s (27) t=0.54 s (29) t=0.58 s (31) t=0.62 s (33) t=0.66 s � (35) t=0.70 s (37) t=0.74 s� (39) t=0.78 sState 3� � � � � � � � � � � � � Nearly State 4� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 1 Fig.18 Moves of legs in the air for NANBA walk of GENBE No.4-2007 with Operating Time ( Speed) : 7� (2 steps).
� t=0.00s t=0.02s t=0.04s t=0.06 s � t=0.08s t=0.10s� � � � t=0.12s t=0.14s � t=0.16s � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Nearly State 1� � � � � � � � � � Nearly State 2
� t=0.18s t=0.20s t=0.22s� � � � t=0.24s � t=0.26s t=0.28s t=0.30s t=0.32s t=0.34s � Nearly State 3� � � � � � � � � � Nearly State4 Fig.19 Moves of legs in the air for NANBA walk of GENBE No.4-2007 with Operating Time ( Speed) : 3&4 ( 2 steps).
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- 38 -
� � (a) Nearly State 1 ( t=0.28 s) (b) Nearly State 2 ( t=0.44 s )� � (c) Nearly State 3 ( t=0.68 s ) (d ) Nearly State 4 ( t=0.84 s )
Fig.20 Actual biped robot movement based on transions from STATE to STATE in program with Operating Time ( Speed) : 10 (250 fps).
� � � (a) Nearly State 1 (t=0.20s) (b) Nearly State 2 (t=0.30s)� (c) Nearly State 3 (t=0.48s) (d ) Nearly State 4 (t=0.66s)
Fig.21 Actual biped robot movement based on transions from STATE to STATE in program with Operating Time ( Speed) : 7 (250 fps).
(a) Nearly State 1 ( t=0.12 s) (b) Nearly State 2 ( t=0.16 s )� � (c) Nearly State 3 ( t=0.24 s ) (d ) Nearly State 4 ( t=0.28 s )
Fig.22 Actual biped robot movement based on transions from STATE to STATE in program with Operating Time ( Speed): 3- 4 (250 fps).
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Fig.26 Measurement of Forward Leaning Angle vs. Operating Time Setting of Servo-motors.�
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(0) 0 mm (1) 115 mm (2) 110 mm� (3) 79 mm � � � � (a) Operating Time setting (Speed) 10
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� � � � � � � Fig.30 Example of measured Strides vs. Operating Time Setting. y. �� æ � p@�,ª4¨¬/²U����¨,²U³
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