Journal of Robotics, Networking and Artificial Life
Vol. 6(2); September (2019), pp. 79–83
DOI: https://doi.org/10.2991/jrnal.k.190828.001; ISSN 2405-9021; eISSN 2352-6386
https://www.atlantis-press.com/journals/jrnal

Research Article

Suppression of Roll Oscillation in Turning of Quadruped
Robot by Asymmetric Amplification of Central Pattern
Generator Output Waveform
Makoto Kitani1, Ryo Asami1, Noritaka Sato1,*, Yoshifumi Morita1, Tomofumi Fujiwara2,
Takahiro Endo2, Fumitoshi Matsuno2
Morita and Sato Laboratory, Electrical and Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan
Matsuno Laboratory, Kyoto University, Kyoto daigaku-Katsura, Nishikyo-ku, Kyoto 615-8530 Japan

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2

ARTICLE INFO
Article History
Received 03 November 2018
Accepted 20 November 2018
Keywords
CPG
quadruped robot
suppression of roll oscillation

ABSTRACT
Quadruped robots experience excessive vibrations in the roll direction when turning by controlling their hip yaw joint. In thecase of image-based teleoperation of the robot, the operator cannot aware the situation of the robot, due to excessive vibrationsof the viewpoint of the image from the camera mounted on the robot. Especially, it is known that vibration in the roll direction
is most likely to cause motion sickness. To overcome this problem, we proposed the asymmetric amplification of the output
waveforms of central pattern generators. We implemented the proposed method on a robot in a dynamic simulator and verified
the effectiveness of the proposed method, during the turning operation. As a result, we confirmed that the proposal method can
suppress 43.7% vibration of the robot body in the roll direction and 7.4% vibration in the pitch direction compared with theconventional method.
© 2019 The Authors. Published by Atlantis Press SARL.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
Legged robots can move on various terrain because they have legs
and utilize their several degrees of freedom. They are controlled
by planning their motion based on a strict model of a robot andan environment. However, planning their motion based on a strictmodel for various environments is quite complex, and inefficient tomove various terrains at high speed.
To overcome this problem, Central Pattern Generators (CPGs) can beused. The mechanism of the CPG is related to rhythmical movements
such as walking and swimming [1,2]. The CPG, an animal motion
generation method, enables the motion of legged robots on various
terrain using only one algorithm because of a pull-in phenomenon.
Because of the above advantages, CPGs have been used in robots inseveral studies. Kimura et al. implemented the CPG on a real robot.
The robot “Patrush” can walk [3] and “Tekken4” can turn [4] onrough terrain. The turning motion is realized by controlling the
hip yaw joint. However, the vibrations of the robot body are large
because falling phenomenon in the roll direction occurred.
In the case of teleoperation of a legged robot, an operator controls
a robot while watching the images from a camera mounted on the
robot. Therefore, the image vibration should be small for the operator to understand the surroundings of the robot. In the experimentconducted by Kimura et al. [4], the robot experiences vibration in
Corresponding author. Email: sato.noritaka@nitech.ac.jp*

the roll direction. Figure 1a shows the graph of the posture of themain body (the roll and pitch direction) when turning on a flatground [4]. According to the body roll angle (thick black line) in
the graph, the robot vibrates, and it is finally overturned.
In the method proposed by Kimura et al., the camera image will
vibrate so that teleoperation will be difficult. According to the study
conducted by Tsubaki et al. [5], if the frequency of the image vibration is the same, a larger amplitude makes the operator uncomfortable. Therefore, in teleoperation, the image vibration should besmall. Figure 2b illustrates a graph showing the relation between
the subjective evaluation and the rotation angle for motion sickness[6]. Vibration in the roll direction is most likely to cause motion
sickness at any speed of rotation.
The vibration of the robot body causes discomfort to the operator.
There are many researches of robots installed CPG [7–9] without
considering suppression of roll direction vibration. On the other
hand, we found a research about suppression of quadruped robot
body vibration [10]. However, the research did not consider ofvibration during turning. Therefore, the purpose of this study is tosuppress roll vibration in a legged robot during turning. To suppressroll vibration, we proposed a turning method using the asymmetric
Adapted from “Realization of dynamic turning motion on irregular terrain of aquadruped robot “TEKKEN4” with neural oscillators” by Fukuoka and Kimura [4],Copyright 2006 by The Japan Society of Mechanical Engineers. This image is remade forthis paper.
b
Adapted from “Visually induced motion sickness” by Ujike [6], Copyright 2007 by The
Institute of Image Information and Television Engineers.
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state factor, t and t ′ are the time constants of ui and vi, respectively,
and wij is the connection factor that determines the influence of theother neurons. A pair of CPGs was mounted on each joint, and four
equations were formed corresponding to each leg. This method isbased on the biped walking program [11] of the CPG where theconnection factor is defined as follows:
w1 - Between the extensor and flexor of the same joint.

w2 - Between the right and left of the same extensor and flexor.
w3 - Between the knee and hip joints of the extensor.
w4 - Between the knee and hip joints of the flexor.
w5 - Others.
Figure 1 | Tekken body angle in turning on flat land [4a].

Figure 3 shows the proposed CPG configuration. We generated awaveform for walking by multiplying the different amplification
gain by the output value of the CPGs of each joint. The walking
waveform is given by Equation (4).
q joint = K joint ( y E - y F ) (4)		  qjoint is the target angle of the joint, Kjoint is the amplification gain at
the joint, yE and yF are the CPG output values of the extensor andflexor, respectively.

2.2. Robot for Experiment
A robot, which is used in the experiment, is shown in Figure 4.
We developed the robot using an open-source dynamic simulator,
named “Gazebo”. The CPG parameters are listed in Table 1.

Figure 2 | Subjective evaluation value of motion sickness with respect tospeed of rotation when rotation relative to yaw, pitch, and roll axis is given
in video [6b].

amplification of the CPG output waveform. In this study, we verified the effectiveness of the proposed method comparing with theprevious method [4], that uses the yaw hip joint for turning, by
carrying out an experiment using a dynamic simulator.

2. WALKING ON FLAT GROUND USING CPG
2.1. Nonlinear First-order Simultaneous
Differential Equations Constituting CPG

Figure 3 | Proposed CPG configuration.

The basic formula of the CPG is a nonlinear first-order simultaneous differential equation shown in Equations (1)–(3) [3].
nt u i = −ui − b vi + ∑wij y j + u0 + Feed i (1)
	    
j =1

	   t ′vi = −vi + yi (2)y = max(0, ui )	    i(3)ui, vi, and yi are the value, fatigue state, and output of the i-th
neuron, respectively, u0 is the steady input that generates oscillation, Feedi is the feedback such as the joint angle, b is the fatigue

Figure 4 | A robot in simulator.

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Table 1 | CPG parameters•• Proposed method:

Parameter

Value

Parameter

Value

u0
b
t
t′

3.0
2.5
0.10
0.080

w1
w2
w3
w4
w5

−2.0
−1.0
−0.50
−0.30
0

Table 2 | Amplification factor
Joint name
Hip
Knee

Gain (straight)

Gain (turning)

Right

Left

Right

Left

2.2
0.8

2.2
0.8

4.2
1.8

1.2
0.8

3. TURNING MOVEMENT
3.1. Turning Method with Yaw Joint(Conventional Method)
In the conventional method, the degree of freedom in the yaw direction is added to the hip joint. The turning radius can be changed by
the angle of the yaw axis of the leg. However, in this method, the left
front leg protrudes outside the robot. This increases the moment
around the falling axis. We assumed that large vibrations would
occur because of the increase in the moment.

The amplification factor of the joint angle - The “gain (turning)”column of Table 2.
Stationary input - 3.0.

4.2. Results and Discussion
Figures 5 and 6 show the graph of the robot posture when turningin orbit shown as Figure 7. The peak-to-peak value of the roll angle
in the conventional method is −0.2 to 0.15 [rad] and that in the
proposed method is −0.1 to 0.1 [rad].
In this study, we compared the conventional and proposed methods. As shown in Figure 5, the vibration in the roll direction could
be suppressed. By comparing the maximum peak-to-peak valueof both methods, we observed that the proposed method is able
to suppress 43.7% vibration in the roll direction. Moreover, theproposed method suppressed 7.4% vibration in the pitch direction
compared with the conventional method. We consider that thereason is the suppression of vibration around the falling axis.
Moreover, motion sickness can be reduced because the vibration in
the roll direction can be suppressed.

3.2. Turning Method without Yaw Joint(Proposed Method)
To reduce the moment around the falling axis, we suggest a change
in the amplification factor of the CPG output between the left andright legs. The robot is able to turn when the amplification factor of
the joint angle on the outside of the turning circle is increased. The
turning radius can be changed by changing the amplification factor.
Table 2 lists the amplification factors at straight and turning, which
is used in the experiment.

Figure 5 | Robot body roll angle.

4. VERIFICATION EXPERIMENT
4.1. Verification Condition
To verify the proposed method, we used the Gazebo simulator as
described in Section 2. We made the robot, which can walk on a flatground using the simulator, installed two methods of turning, andevaluated their performances in the following sequence: adjusting
the steady input to have the same speed and turning radius, measuring the roll angle of the robot body when the robot walks on theturning trajectory, and comparing the data. The following conditions
were applied so that the robot can walk on the same turning radius.
•• Conventional method:
Rotation angle of front leg - 0.15 [rad].
Stationary input - 2.7.

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Figure 6 | Robot body pitch angle.

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REFERENCES

Figure 7 | Orbit of robot turning.

5. CONCLUSIONS AND FUTURE WORK
The purpose of this study is to suppress roll vibration in theturning motion of a legged robot. We suggest a turning methodthat changes the amplification factor of the joint angle between
the left and right legs to suppress the robot body vibration.
We verified the effectiveness of the proposed method using a
dynamic simulator compared with the conventional method.
As a result, we observed that the proposed method can suppress 43.7% vibration in the roll direction and 7.4% in the pitch
direction. The proposed method will reduce the motion sickness caused by the image vibration during teleoperation. In the
future, we will realize walking of legged robots on rough terrain
by installing CPG feedback.

CONFLICTS OF INTEREST
The authors declare they have no conflicts of interest.

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Authors Introduction
Mr. Makoto Kitani

Mr. Ryo Asami
He received Master of Engineering
degree from Nagoya Institute ofTechnology in 2019. His researchinterests include autonomous control
system, system integration and teleoperation system for legged rescue
robots.

He received Master of Engineering
degree from Nagoya Institute ofTechnology in 2018. His researchinterests include virtual reality,
system integration and teleoperation system for crawler-type rescue
robots.

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Dr. Noritaka SatoDr. Takahiro Endo

He received Doctor of Engineering
degree from The University ofElectro-Communications in 2009.
He was a Program-Specific AssistantProfessor of Kyoto University in
2009–2011, and is an AssistantProfessor of Nagoya Institute ofTechnology since 2011. His researchinterests include human robot interaction for rescue robots, rehabilitation-assist robots and industrial robots. He is a member of the IEEE, RSJ and SICE.

He received the PhD (Dr. Eng.)
degree from the Tokyo Instituteof Technology, Japan, in 2006.
Since April 2015, he has beenwith the Department of MechanicalEngi­
neering and Science, Kyoto
University, Kyoto, Japan, where heis currently an Associate Professor.
His research interests include haptic
interfaces, robotics, and the control
of infinite dimensional systems.

Prof. Yoshifumi Morita

Prof. Fumitoshi Matsuno
He is a Professor in the Department
of Electrical and MechanicalEngineering at Nagoya Institute ofTechnology. He received the PhD
degree from Nagoya Institute ofTechnology in 1998. His current
research interests are rehabilitation
support robot/device and robot
teaching.

Dr. Tomofumi Fujiwara
He received his B.S., M.S., and PhD
degrees in Engineering from Okayama
University, Japan, in 2010, 2012, and2016, respectively. From 2014 to 2015,
he was a guest researcher at Technical
University of Munich, Germany. From2016 to 2019, he worked as a ProgramSpecific Assistant Professor (ImPACT)
at Kyoto University, Japan. His researchinterests include rescue robots, interface systems for snake robots and legged robots, real-time 3D laser
scanners, and stereoscopic presentation of 3D point clouds. He is amember of the Robotics Society of Japan (RSJ).

He received the Dr. Eng. from Osaka
University in 1986. In 1986, hejoined the Department of Control
Engineering, Osaka University.
Since 2009, he has been a Professor
in the Department of MechanicalEngineering and Science, Kyoto
University. His current researchinterests lie in robotics, swarm intelligence, control of distributed parameter system and nonlinear system,
and rescue support system in disaster.
He is a Fellow member of the SICE, the JSME, the RSJ and amember of the IEEE among other organizations.