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Utilization of Human-Like Pelvic Rotation for Running Robot

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The spring loaded inverted pendulum is used to model human running. It is based on a characteristic feature of human running, in which the linear-spring-like motion of the standing leg is produced by the joint stiffness of the knee and ankle. Although this model is widely used in robotics, it does not include human-like pelvic motion. In this study, we show that the pelvis actually contributes to the increase in jumping force and absorption of landing impact. On the basis of this finding, we propose a new model, spring loaded inverted pendulum with pelvis, to improve running in humanoid robots. The model is composed of a body mass, a pelvis, and leg springs, and, it can control its springs while running by use of pelvic movement in the frontal plane. To achieve running motions, we developed a running control system that includes a pelvic oscillation controller to attain control over jumping power and a landing placement controller to adjust the running speed. We also developed a new running robot by using the SLIP2 model and performed hopping and running experiments to evaluate the model. The developed robot could accomplish hopping motions only by pelvic movement. The results also established that the difference between the pelvic rotational phase and the oscillation phase of the vertical mass displacement affects the jumping force. In addition, the robot demonstrated the ability to run with a foot placement controller depending on the reference running speed.
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ORIGINAL RESEARCH
published: 08 July 2015
doi: 10.3389/frobt.2015.00017
Edited by:
Giuseppe Carbone,
University of Cassino and
South Latium, Italy
Reviewed by:
Ye Zhao,
The University of Texas at Austin, USA
Fernando Gomez-Bravo,
Huelva University, Spain
Mingfeng Wang,
University of Cassino and
South Latium, Italy
*Correspondence:
Takuya Otani,
Graduate School of Advanced
Science and Engineering, Waseda
University, #41-304, 17 Kikui-cho,
Shinjuku-ku, Tokyo 162-0044, Japan
t-otani@takanishi.mech.
waseda.ac.jp
Specialty section:
This article was submitted to
Humanoid Robotics, a section of the
journal Frontiers in Robotics and AI
Received: 21 April 2015
Accepted: 18 June 2015
Published: 08 July 2015
Citation:
Otani T, Hashimoto K, Yahara M,
Miyamae S, Isomichi T, Hanawa S,
Sakaguchi M, Kawakami Y, Lim H-o
and Takanishi A (2015) Utilization of
human-like pelvic rotation for
running robot.
Front. Robot. AI 2:17.
doi: 10.3389/frobt.2015.00017
Utilization of human-like pelvic
rotation for running robot
Takuya Otani
1,2
*
, Kenji Hashimoto
3,4
, Masaaki Yahara
5
, Shunsuke Miyamae
5
,
Takaya Isomichi
5
, Shintaro Hanawa
6
, Masanori Sakaguchi
6,7
, Yasuo Kawakami
6
,
Hun-ok Lim
4,8
and Atsuo Takanishi
4,9
1
Graduate School of Advanced Science and Engineering, Waseda University, Tokyo, Japan,
2
Japan Society for the Promotion
of Science, Tokyo, Japan,
3
Waseda Institute for Advanced Study, Tokyo, Japan,
4
Humanoid Robotics Institute (HRI), Waseda
University, Tokyo, Japan,
5
Graduate School of Creative Science and Engineering, Waseda University, Tokyo, Japan,
6
Faculty
of Sport Sciences, Waseda University, Tokyo, Japan,
7
Faculty of Kinesiology, University of Calgary, Calgary, AB, Canada,
8
Faculty of Engineering, Kanagawa University, Yokohama, Japan,
9
Department of Modern Mechanical Engineering, Waseda
University, Tokyo, Japan
The spring loaded inverted pendulum is used to model human running. It is based on
a characteristic feature of human running, in which the linear-spring-like motion of the
standing leg is produced by the joint stiffness of the knee and ankle. Although this model
is widely used in robotics, it does not include human-like pelvic motion. In this study, we
show that the pelvis actually contributes to the increase in jumping force and absorption
of landing impact. On the basis of this finding, we propose a new model, spring loaded
inverted pendulum with pelvis, to improve running in humanoid robots. The model is
composed of a body mass, a pelvis, and leg springs, and, it can control its springs while
running by use of pelvic movement in the frontal plane. To achieve running motions, we
developed a running control system that includes a pelvic oscillation controller to attain
control over jumping power and a landing placement controller to adjust the running
speed. We also developed a new running robot by using the SLIP
2
model and performed
hopping and running experiments to evaluate the model. The developed robot could
accomplish hopping motions only by pelvic movement. The results also established that
the difference between the pelvic rotational phase and the oscillation phase of the vertical
mass displacement affects the jumping force. In addition, the robot demonstrated the
ability to run with a foot placement controller depending on the reference running speed.
Keywords: humanoid, human motion analysis, running, pelvis, joint elasticity
Introduction
To realize human motions, researchers performed motion capture experiments or simulations. In
motion capture experiments, researchers collect and analyze data, and on the basis of the results,
verify or refute their hypothesis to clarify the mechanisms of human motion. However, for ethical
reasons, motions that pose a risk of injury for human subjects cannot be tested, despite the possibility
of improving those motions by coordinated training (World Medical Association, 1964). Some inves-
tigators have used simulations to evaluate their models or hypotheses of human motion. However,
simulations have problems such as long processing time or model error (Rose and Gamble, 2005).
To resolve these problems, we have sought to conduct research on human motion and sport science
by using a biped humanoid robot that can mimic human motions. When such a humanoid robot
realizes human-like motion or uses an instrument as does a human, its human-like motions can
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 171
Otani et al. Utilization of human-like pelvic rotation
be compared with those that do not mimic human motions. By
using the humanoid robot, we can measure various data as joints
angle, angular velocity, torque, robots attitude, and so on. For
example, the risk of injury can be evaluated according to the
joints torque. This comparison should be useful for verifying the
characteristics of human motions and testing instruments, which
in turn should improve the performance characteristics of both
humans and robots.
We previously developed a biped humanoid robot named
WABIAN-2R to mimic human motions and their underlying
mechanisms (Ogura et al., 2006). WABIAN-2R, which is equipped
with a 2-degree-of-freedom (DOF: roll, yaw) pelvis, shows a
human-like gait with a stretched knee (Hashimoto et al., 2013,
2014). However, this robot is limited to walking. In human run-
ning, the joints of the standing leg require about 1000 W (Dalleau
et al., 1998), which is much higher than the power of the actuator
in WABIAN-2R.
In previous studies, running has been realized in a number
of robots. Raibert et al. developed running robots with a linear
spring leg (Raibert, 1986). Hyon et al. developed a biologically
inspired biped robot based on a model of a dog’s leg (Hyon et al.,
2003). These robots are not human-like. However, a few recent
studies have shown that biped humanoid robots can run. For
example, ASIMO can run at a speed of 2.5 m/s (Honda Motor
Company Ltd.; Takenaka et al., 2011). Furthermore, Toyotas
biped humanoid robot can also run, using a zero moment point
(ZMP)-based running control system (Tajima et al., 2009). The
athlete robot developed by Niiyama et al. has a human-like
musculoskeletal system built to achieve dynamic motions such as
running (Niiyama et al., 2012). The biped robot MABEL, which
has leg elasticity that originates from a leaf spring, can run the
fastest among all presently available biped robots, attaining a
speed of 3 m/s with axial constraints on the Y-axis (Grizzle et al.,
2009). However, none of these robots mimic human running
characteristics.
A number of important characteristics of human running
have been identified by researchers in the field of biomechanics
and sports science, including head stabilization (Pozzo et al.,
1990), moment compensation using the upper body and arms
(Collins et al., 2009), and leg stiffness (Gunther and Blickhan,
2002). However, a potentially important but as yet unreported
characteristic is that a humans pelvic movement in the frontal
plane increases takeoff forces and absorbs landing impacts. In this
paper, we provide evidence for this characteristic by an analysis of
human motion. We then propose a running model that combines
the traditional spring loaded inverted pendulum (SLIP) model
(Chapman and Caldwell, 1983; Blickhan, 1989; McMahon and
Cheng, 1990) and a pelvis. The proposed model, called spring
loaded inverted pendulum with pelvis (SLIP
2
), is composed of a
body mass, a pelvis, and leg springs. We then describe a running
control system composed of a pelvic oscillation controller
to attain control over jumping power, and a foot placement
controller to adjust the running speed, and a running robot that
uses the SLIP
2
model, with which we successfully conducted a
hopping and running experiment.
The remainder of the paper is organized as follows. In
Section “Introduction, we analyze human pelvic movement
and describe the running control method, which includes
control of pelvic movement and foot placement. In Section
“Materials and Methods, we describe the design of the running
robot used in this study. In Section “Results, we present and
discuss experimental results. Finally, in Section “Conclusions and
Future Work, we present the conclusions and future work.
Materials and Methods
Pelvic Movement Analysis
To identify characteristics of human running motion that could
be useful for designing a robot, we conducted a series of motion
capture experiments with human subjects. A motion capture
system with eight infrared cameras (Motion Analysis Corp.,
Santa Rosa, CA, USA) was used to determine three-dimensional
marker positions at 240 Hz. The spherical retro-reflective markers
were attached on the skin of the pelvis, thigh, shank, and rearfoot.
Ground reaction forces were simultaneously collected at 2400 Hz
using a force plate (Bertec Corp., Columbus, OH, USA) for
the identification of the stance phase. We asked seven subjects
(gender: male, height: 1724 ± 36 mm, weight: 64 ± 6 kg) to
perform regular running motion at 3.5 m/s and collected five
sets of data for each subject. None of the participants had any
muscular, neurological, or joint disorders that could affect their
performance. The study was approved by the Office of Research
Ethics at Waseda University and written informed consent was
obtained from all participants. These subjects were given several
practice trials to ensure that they could land with a natural
running style on the force plate. When the running speed was
within 5% of the target speed and the subject could land on the
force plate, data collection began.
-10
-8
-6
-4
-2
0
2
4
6
8
0 20 40 60 80 100
Pelvic rotaon deg
Running cycle %
Stance
Swing
HS
TO
HS
Y
Z
X
θ
pelvis
θ
pelvis
SL
FIGURE 1 | Human pelvic rotation in the frontal plane during running.
To compare the time course changes in joint angles between trials and
among subjects, the time-series data were time normalized to 101 data
points, with each time interval representing 1% of the stance phase (mean,
solid blue line; SD, solid gray line). First, at heel strike, the angle of the pelvis is
0.7°. Then, the pelvis rotates up to 3.0° until landing of the sole.
Subsequently, the pelvis rotates in the opposite direction up to 5.3° until
takeoff using the toe. After takeoff, the pelvis rotates to the initial angle for
landing with the other leg. HS, heel strike; SL, sole landing; TO, toe off.
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 172
Otani et al. Utilization of human-like pelvic rotation
Figure 1 shows the pelvic movement in the frontal plane during
running. The pelvis levels off at an angle of 0°. The measurements
show that the angle of the pelvis is 0.7° at heel strike, at which point
the idling leg is lowered. The pelvis then rotates up to 3.0° until
landing of the sole. Subsequently, the pelvis rotates in the opposite
direction up to 5.3° until takeoff using the toe. After takeoff, the
pelvis rotates to the initial angle for landing with the other leg, i.e.,
it rotates to lower the idling leg and then rotates in the opposite
direction to raise it.
The pelvic movement during the stance phase resembles a
sine wave. Usually, the vertical movement of the center of mass
during human running is modeled as a SLIP. We calculated the
characteristic oscillation period of the vertical movement of the
center of mass from data on the ground reaction force and vertical
movement of the center of mass, as well as that of the pelvic
movement, by measuring the period of peak-to-peak movement.
The characteristic oscillation period of the vertical movement of
the center of mass was 0.29 ± 0.03 s, and that of the pelvic move-
ment was 0.30 ± 0.03 s. Given the similarity of these values, pelvic
movement will affect movement of the center of mass effectively.
This result suggests that the pelvic movement in the frontal plane,
which acts as sine wave, increases the takeoff force and absorbs
the landing impact. The pelvic movement at landing absorbs
the landing impact, and the subsequent movement increases the
takeoff force.
SLIP
2
Model
In previous studies, human running was modeled by a SLIP
(McMahon and Cheng, 1990), whereas human walking was mod-
eled by an inverted pendulum (Kajita and Espiau, 2008). The
SLIP model is composed of a body mass and a spring leg and
is based on the linear relationship between the ground reaction
force and the vertical displacement of the body during running
(Chapman and Caldwell, 1983; Blickhan, 1989; McMahon and
Cheng, 1990). Moreover, the knee and ankle joints of the standing
leg act like torsion springs that give rise to leg stiffness (Gunther
and Blickhan, 2002), which along with joint stiffness vary with
the running speed (Farley and González, 1996). In this model,
movement in the flight phase is modeled as a parabolic motion
of a mass point. With this model, which describes human running
in a simple and straightforward way, the motion of the human leg
in the stance phase of running stores energy and releases it like a
spring. However, the SLIP model differs from the actual human
body because it does not take the pelvis into account.
On the basis of the human motion analysis presented in the
previous section, we propose a new model, SLIP
2
(Figure 2),
which is composed of an upper body, a pelvis, and spring legs.
During stance, human motion is modeled by SLIP
2
, whereas
during flight, it is modeled as a parabola. According to the SLIP
2
model, running is realized by two component processes: attaining
sufficient jumping power, and controlling the running speed. To
realize running, we implemented a pelvic oscillation controller
for attaining jumping power and a foot placement controller for
controlling the running speed.
Pelvic Oscillation Control
The pelvic oscillation control method is used for storing energy. In
this method, the pelvis is controlled by using the natural frequency
)(t
pelvis
k
)(tl
k
m
Z
Y
θ
)(tZ
m
)(tZ
f
)(tl
p
pw
l
s
l
FIGURE 2 | Spring-mass model with pelvis joint (SLIP
2
). The model is
composed of a body mass, a pelvis, and spring legs.
calculated from the mass weight and leg stiffness in the stance
phase, and controlled to move it to the landing joint angles of
pelvis in the flight phase, with the objective of attaining sufficient
jumping power. The hip roll axis is controlled to be aligned with
the pelvis roll axis. In the stance phase, the model, which has elastic
elements, can store and release the energy by resonance. The pelvic
movement is modeled as a linear displacement, and the equation
of motion in the vertical direction in the stance phase is given by:
m
¨
z
m
(t) + k(z
m
(t) l
s
l
p
(t) l
k
(0)) mg = 0
where m is the weight of the body mass; z
m
(t), the vertical dis-
placement of the mass; l
s
, the distance between the body mass and
the pelvis; l
p
(t), the vertical displacement of the pelvis caused by
its rotation; l
k
(t), the length of the leg spring; k, the leg stiffness;
g, the gravitational acceleration (= 9.8 m/s
2
); and t,the time of the
stance phase.
Based on the human motion analysis, the pelvic movement in
the stance phase is expressed as follows:
θ
pelvis
(t
stance
) = A sin(ωt
stance
+ φ)
where A is the pelvic rotation amplitude; ω, the natural frequency;
t
stance
, the time of the stance phase; and ϕ, the phase difference
between the mass vertical movement and the pelvic movement.
To use the resonance effectively, the phase difference between
the mass vertical movement and the pelvic movement in the stance
phase is important. To analyze the effect of the pelvic movement,
we calculated the mass vertical movement of the SLIP
2
model.
At first, the SLIP
2
model fell from the mass height; 0.9 m. After
landing, the SLIP
2
model moved its pelvis according to the above
equation.
We performed on the three conditions that: the pelvic rotation
amplitude was 0°, the phase difference was 0 rad or π rad for
verifying the influence of the phase difference. In this calculation,
we set the mass 55 kg, the leg stiffness 16 kN/m, and the pelvic
rotation amplitude or 5°. Figure 3 shows the mass height of
the body in this calculation. We plotted the results until the mass
height was at a peak after jumping. When the phase difference
was 0 rad, the mass height became higher than the fall height. On
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 173
Otani et al. Utilization of human-like pelvic rotation
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Mass height m
Time s
A=0
φ=π
φ=0
FIGURE 3 | Verification of the pelvic movement. We plotted the results
until the mass height was at a peak after jumping. When the phase difference
was 0 rad, the mass height became higher than the fall height. On the other
hand, when the phase difference was rad, the mass height after jumping
became lower than that on the condition that the pelvic rotation amplitude 0°.
the other hand, when the phase difference was π rad, the mass
height after jumping became lower than that on the condition
that the pelvic rotation amplitude 0°. Therefore, when the phase
of the mass movement and that of the pelvic movement are close,
the SLIP
2
can attain the high jumping power. When the phases
are not close, however, the SLIP
2
cannot jump because the pelvic
movement impedes the mass vertical movement. It indicates that
the pelvic movement influences on the mass vertical movement,
and the phase difference is important for the effectiveness of the
attaining jumping power using the pelvic movement.
To utilize the phase difference between the mass movement
and the pelvic movement effectively, the SLIP
2
model must land
with the defined joint angle of the pelvis and hip roll at landing.
When the joint angles at landing are different from the defined
angles, the phase of the mass movement in the vertical direction
while standing differs from that of the pelvic movement. The
defined angle can be calculated by the difference between the
phases to change the effectiveness of the pelvic movement for
attaining jumping power. To solve this problem, we estimated the
next landing time from the velocity of the mass in the vertical
direction on takeoff, and moved the pelvis to the angle θ
pelvis_ini
to
start pelvic oscillation from the same angle as in the previous run-
ning cycle. Because the movement of the mass traces a parabola in
the flight phase, the next landing time T
landing
is given by:
T
landing
=
2V
z
g
where V
z
is the velocity of the mass in the vertical direction at
takeoff.
The pelvic movement in the flight phase is expressed as follows:
θ
pelvis
(t
flight
)
=
{
θ
pelvis _ ini
θ
pelvis _ off
T
landing
t
flight
while reaching initial angle
θ
pelvis _ ini
after reaching
where θ
pelvis_ini
is the initial angle of the pelvis at landing; θ
pelvis_off
,
the angle of the pelvis at takeoff; and t
flight
, the time of the flight
phase.
Z
X
f
x
vT
f
x
acc
vx +
&
x
&
x
&
x
&
Acceleraon
Steady running
B
A
pitchhip _
θ
FIGURE 4 | Foot placement control. The position of the foot with respect
to the body when landing has a great influence on the running speed. In
steady running without changing the running speed, the SLIP model should
land its foot at the mid-point of the distance that the SLIP model moves while
standing (A). When the SLIP model accelerates, the SLIP model should land
in front of the mid-point for utilizing forward-fall rotation (B).
Foot Placement Control
We used a foot placement controller to control running speed in
the manner of Raibert (1986). This is achieved by moving the leg to
an appropriate position with respect to the body during the flight
phase in the SLIP model. The position of the foot with respect
to the body when landing has a great influence on the running
speed. In steady running without changing the running speed, the
SLIP model should land its foot at the mid-point of the distance
that the SLIP model moves while standing (Figure 4A). When the
SLIP model accelerates, the SLIP model should land in front of
the mid-point for utilizing forward-fall rotation (Figure 4B). In
simulated research, Wensing et al., extended this method for 3D
running (Wensing and Orin, 2013), and Zhao et al. used same con-
trol method for locomotion in rough terrains (Zhao and Sentis,
2012). As mentioned above, running can be modeled by a SLIP or
SLIP
2
. Some researchers developed the running control without
foot placement controller (Lee and Goswami, 2012). However, we
assume that the foot placement controller used for the SLIP model
embodies one of the key principles of human running. In fact,
humans change their foot position at the landing phase depending
on the running speed (Cavagna et al., 1988). To implement this
principle of human running, we used a foot placement controller.
The foot position is given by:
x
f
=
˙
xT
2
+ K(
˙
x
˙
x
ref
)
where x
f
is the foot placement; x, the body mass placement; T, the
stance time;
˙
x
ref
, the reference running speed, and K, the control
gain.
Finally, the robot determined the angle of its hip pitch joint for
landing according to the foot position and moved the hip pitch
joint by landing. The angle of the hip pitch joint for landing is
given by:
θ
hip _ pitch
= arcsin
(
x
f
l
leg
)
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Otani et al. Utilization of human-like pelvic rotation
Pelvis roll and
hip roll joint
Pelvis oscilla!on
control
Foot placement
control
Change
phase
hip_roll
rollpelvis
θ
θ
ω
θ
_
Phase
ref
x
&
Swing leg’s
hip pitch joint
pitchhip_
x
&
Yaw
Gyro sensor
Force sensor
F
phase
t
Guide roll
encoder
Z
V
s
z
Z
Y
X
Y
R
R
R
P
R
beam
L
landing
T
FIGURE 5 | Block diagram of running control. We implemented a pelvic oscillation controller for attaining jumping power and a foot placement controller for
controlling the running speed.
where l
leg
is the leg length. The control block diagram is shown in
Figure 5.
Development of Running Robot with linear
spring leg
Next, we sought to develop a running robot that could successfully
execute running motion based on the SLIP
2
model. We deter-
mined the requirements for angular velocity and torque in the
hip roll joint on the basis of human running data acquired by
Ferber et al. (2003). We also fixed the requirements for the angular
velocity of the pelvis roll joint on the basis of human running data
acquired by Schache et al. (2002) and the requirements for the
hip pitch joint based on our human running data. To the best of
our knowledge, no work has previously been conducted on the
torque of the pelvis roll joint. We calculated these requirements
by substituting appropriate values in the equation of motion. The
requirements for the angular velocity and torque of the pelvis and
hip joints are summarized in Table 1.
We chose 150-W DC motors (Maxon Co., Ltd.), timing belts,
and harmonic drives to actuate the pelvis and hip joints (Figure 6).
The developed robot mimicked the humans parameters about the
mass of the whole body, the mass of the leg, the width between
the hip joints, the length of the leg, and the leg stiffness (Table 2).
These parameters are significant in the SLIP
2
model. To adjust the
mass, masses can be mounted on the upper part of the robot. We
selected a compression spring, shaft, set collar, and linear bush for
the leg spring. Owing to this mechanism, the compression spring
is not detached from its upper and lower parts when the spring is at
free length. In addition, the compression springs can be replaced
with others by adjusting the distance between the set collar and
the linear bush. We fixed the range of the spring’s stiffness from
16 to 40 kN/m on the basis of the previous study (Dalleau et al.,
1998). The developed robot is also equipped with an inertial
measurement unit (IMU) named Waseda bioinstrumentation-4
(WB-4) on the body for measuring its posture. WB-4 has a 3-axis
accelerometer sensor; 3-axis gyroscope; and 3-axis magnetometer
(Figure 7) (Lin et al., 2011). The developed robot with a pelvis is
shown in Figure 8.
TABLE 1 | Requirements.
Pelvis roll joint Hip roll joint Hip pitch joint
Max. velocity (rad/s) 2.3 1.2 2.9
Max. peak torque (Nm) 44 113 45
Pelvis
Hip
318
Z
Y
X
Hip pitch joint
Pelvis roll joint
DOF of the pelvis
Hip roll joint
CAD of the pelvis
A
B
FIGURE 6 | Developed pelvis. Length are in mm. The pelvis had five joints;
one pelvis roll joint, two hip pitch joints, two hip roll joints (A). We chose
150-W DC motors, timing belts, and harmonic drives to actuate the pelvis
and hip joints (B).
TABLE 2 | Configuration of the developed robot and human.
Robot Human
Mass of whole body
a
, m (kg) 55 64
Mass of leg 10 10
Pelvis width, l
pw
(m) 0.18 0.18
Leg length
b
, l
k
(t) (m) 0.7 0.7
Leg stiffness, k (kN/m) 16–40 16–40
Pelvic rotation amplitude, A (°) 5.0 5.3
a
Without additional mass for adjustment.
b
Leg spring is at free-length.
Results
Hopping Experiment
To evaluate the pelvic oscillation controller for attaining jump-
ing power, we performed a hopping experiment by using the
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 175
Otani et al. Utilization of human-like pelvic rotation
17mm
20mm
Magnet
-
ometer
Acceler
-
ometer
Y
X
Z
Gyroscope
FIGURE 7 | Inertial measurement unit (IMU) implemented on the robot
body
. The IMU is referred to as the WB-4 (Waseda bioinstrumentation-4)
sensor, which has a 3-axis accelerometer sensor, 3-axis gyroscope, and
3-axis magnetometer.
FIGURE 8 | Computer aided design of developed running robot. To
adjust the mass, weights can be mounted on the upper part of the robot. A
compression spring, shaft, set collar, and linear bush served as the spring of
the leg. Owing to this mechanism, the compression spring is not detached
from its upper and lower parts when the spring is at free length.
developed robot. In this experiment, the robot began the exper-
iment in the standing position and started to move its pelvis
according to the pelvic oscillation controller. The robot could
detect whether it stood on the ground by force sensors imple-
mented under the floor. On the basis of the ground reaction force
data, the robot oscillated its pelvis in the stance phase and moved
the pelvis to the landing angle by next landing in the flight phase.
The hip roll joints were controlled to move in the opposite direc-
tion of the pelvis to maintain the leg perpendicular to the ground
at all times. The hip pitch joint was controlled according to the
foot placement controller with a reference running speed of 0 m/s
to maintain vertical hopping. The robot motion was restricted
to the vertical and horizontal directions with a developed guide
(Figure 9), which had two passive joints, and was connected to
the body of the robot. Because this allowed the robot to go around
Z
Y
X
Y
R
R
R
P
R
FIGURE 9 | Degrees of freedom (DOF) of the developed running robot
with a 2-DOF running guide
. The robot motion was restricted to the vertical
and horizontal directions with the developed guide. It had two passive joints
and was connected to the robot’s body to allow the robot to go around the
guide.
1
1.05
1.1
1.15
0 1 2 3 4
Mass height m
Time s
0.5deg
2.0deg
5.0deg_without es!ma!on
5.0deg
FIGURE 10 | Body mass height during hopping experiments. When the
leg took off the ground, the mass height was 1.1 m. A mass height above
1.1 m indicates that the robot hopped. When the amplitude of the pelvic
oscillation was 0.5°, the robot could not hop. When the amplitude was more
than 2°, the robot successfully hopped after a few oscillations. In the
experiment without the landing time estimation, however, the robot could not
maintain its hopping. On the other hand, the robot continued to hop and the
mass height increased by using the landing time estimation.
the guide, we could calculate its running speed by the angular
velocity of the body in the yaw direction, ω
Yaw
, measured by a gyro
sensor implemented in the robots IMU. The running speed was
given by:
˙
x = L
beam
ω
Yaw
where L
beam
is the length of the beam connected to the robots body
and the pole of the guide. In this research, it was 1.5 m.
To measure the vertical displacement of the robot, a rotational
encoder was implemented on the roll joint of the guide. When
the leg spring is at free length, the body mass height is 1.1 m.
We calculated the vertical velocity of the body mass from its
displacement data in this experiment. The leg stiffness was based
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 176
Otani et al. Utilization of human-like pelvic rotation
FIGURE 11 | Running experiment. The robot began its pelvic oscillation at 0 s, and started to hop and run after a few oscillations at 1 s. Then, the robot
accelerated in forward direction by the foot placement control. In this experiment, the robot used only its pelvic motion for attaining jumping power.
on the human running data. And the phase difference was also
determined from the human running data;
3
8
π. For evaluating the
effect of the pelvic movement, we had this experiment under the
condition that the amplitude of the pelvic oscillation was 0.5°, 2°,
with the landing time estimation, and without the landing
time estimation.
Figure 10 shows the mass height of the body in the hopping
experiment. When the leg spring is at free length, the body mass
height is 1.1 m. A body mass height that exceeded 1.1 m indicated
that the robot hopped. When the amplitude of the pelvic oscilla-
tion was 0.5°, the robot could not hop. When the amplitude was
more than 2°, the robot successfully hopped after a few oscilla-
tions. From these results, the robot could hop higher according to
the amplitude of the pelvic oscillation. In the experiment with-
out the landing time estimation, however, the robot could not
maintain its hopping. After three hops, the mass height of the
body decreased. On the other hand, by using the landing time
estimation, the robot maintained its hopping and the mass height
increased.
This experimental result suggests that pelvic movement in
human running contributes to the increase in takeoff force. And
that the amplitude of the pelvic oscillation and the difference in the
pelvic rotational phase influence the effectiveness for the increase
in takeoff forces. Nevertheless, it is common to instruct superior
runners to emulate a running form in which the pelvis is station-
ary. This is because the pelvic movement in running can easily
hurt the pelvis (Schache et al., 2002). To use the pelvic movement
effectively and safely, it is assumed that runners should train their
muscles around the trunk and pelvis. As in this example, it is
possible that some motions posing a risk of injury improve human
physical performance; if so, using a humanoid robot would allow
us to verify the effects safely. It is also possible that humans use
resonance by not only the pelvis but also other parts of the body
(e.g., arms).
Running Experiment
We performed a running experiment by using the developed
robot to evaluate the pelvic oscillation and foot placement con-
trollers. The experimental conditions were identical to those for
the hopping experiment, except for the reference running speed of
0.1 m/s. The pelvic oscillation amplitude was 5.0°, and the control
gain of the foot placement control was 0.15.
Figure 11 shows photographs of the experiment, and Figure 12
shows the running speed. We measured the running speed from
gyro sensor data during each flight phase because the foot place-
ment controller mainly affects the running speed during the flight
phase. The robot started its pelvic oscillation and started to hop
and run after a few oscillations. The robot succeeded in running
at approximately 0.1 m/s.
Although the developed robot has the potential to run at a speed
of up to roughly1 m/s, it cannot run as fast as a human. This is
because the robot used only its pelvis while standing and its hip
pitch joint during the flight phase. It did not kick the ground by
actively moving its hip joint. This movement and its stabilization
are required to run at a higher speed. In human running, the
trunk and arms are said to be used for stabilization (Collins
et al., 2009). Therefore, the upper body of the robot should be
developed to allow it to actively kick the ground with its hip joint.
As mentioned above, successful running has been demonstrated
in some humanoid robots. However, these robots use only the
hip joint, and not pelvic movement, for kicking. The results of
this study suggest that pelvic movement could be effective for
improving the running speed of these humanoid robots.
Conclusion and Future Work
Here, we described an analysis of human running motion focused
on pelvic movement in the frontal plane, and developed the
SLIP
2
model and a running control system. From the analysis,
we concluded that pelvic movement in the frontal plane, which
resembles a sine wave during the stance phase, can help to increase
takeoff forces and absorb landing impacts. We then newly devel-
oped the SLIP
2
model, composed of the SLIP model, as well as
a pelvis equipped with running control methods including pelvic
oscillation and foot placement controllers. To evaluate the SLIP
2
model and the running control methods, we executed hopping
and running experiments with the developed robot. The results
indicated that pelvic movement can help to increase the jumping
force and absorb the impact. The pelvic rotational phase difference
had an influence on the increase in takeoff forces.
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 177
Otani et al. Utilization of human-like pelvic rotation
-6
-4
-2
0
2
4
6
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 1 2 3 4
Pelvis angle deg
Running speed m/s
Time s
Speed reference 0.1m/s
Measured speed
Pelvis angle
FIGURE 12 | Running speed transition. The robot successfully ran according to the reference running speed of approximately 0.1 m/s.
These results suggest that the running robot can run at a higher
speed by using kicking and pelvic movement. Humans can run
stably at high speeds because the moment generated by the ground
reaction force and their leg movement are compensated for by the
use of their upper body and arms. In future studies, we intend to
combine the SLIP
2
model with an upper body to construct a new
full-body model that mimics this characteristic of human running.
Finally, we will develop a new stabilization control method that
uses the upper body and arms for high speed running by means
of kicking and pelvic movement.
Acknowledgments
This study was conducted with the support of the Research
Institute for Science and Engineering, Waseda University; Insti-
tute of Advanced Active Aging Research, Waseda University,
and as part of the humanoid project at the Humanoid Robotics
Institute, Waseda University. It was also supported in part by
the MEXT/JSPS KAKENHI Grant No. 25220005 and 25709019;
Mizuho Foundation for the Promotion of Sciences; SolidWorks
Japan K.K.; DYDEN Corporation and Cybernet Systems Co., Ltd.;
we thank all of them for the financial and technical support
provided.
Supplementary Material
The Supplementary Material for this article can be found online
at http://journal.frontiersin.org/article/10.3389/frobt.2015.00017
Video S1 | Running experiment. The robot began its pelvic oscillation at 0 s,
and started to hop and run after a few oscillations. Then, the robot accelerated in
forward direction by the foot placement control. In this experiment, the robot used
only its pelvic motion for attaining jumping power.
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Conflict of Interest Statement: The authors declare that the research was con-
ducted in the absence of any commercial or financial relationships that could be
construed as a potential conflict of interest.
Copyright © 2015 Otani, Hashimoto, Yahara, Miyamae, Isomichi, Hanawa, Sak-
aguchi, Kawakami, Lim and Takanishi. This is an open-access article distributed under
the terms of the Creative Commons Attribution License (CC BY). The use, distribution
or reproduction in other forums is permitted, provided the original author(s) or
licensor are credited and that the original publication in this journal is cited, in
accordance with accepted academic practice. No use, distribution or reproduction is
permitted which does not comply with these terms.
Frontiers in Robotics and AI | www.frontiersin.org July 2015 | Volume 2 | Article 179
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