SUGISAKAMASANORI

Journal of Advances in Artificial Life Robotics
Vol. 3(4); March (2023), pp. 185–192
ON LINE ISSN 2435-8061; ISSN-L 2435-8061
https://alife-robotics.org/jallr.html

Research Article

A Nonlinear Oscillator Coupling Model to Provide the Hough
Transform Function Without the Discrete Voting Procedure
Amarbold Purev, Hiroaki Wagatsuma

Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu, Kitakyushu 808-0196, Japan

ARTICLE I N FO
Article History
Received 25 November 2022
Accepted 26 April 2023
Keywords
Hough transform
Line detection
Nonlinear dynamics
Coupled nonlinear oscillators
Kuramoto model

ABSTRACTThe most common algorithm for detecting straight lines in a digital image is the Hough Transform
method. The method involves two consecutive steps: transforming the image edge location onto
parameter space and voting procedure to acquire line characteristics. The former deals incontinuous space, and the latter counts votes in a discrete matrix, making the algorithm sensitive
to noise. We transformed each image pixel location to the parameter space as a Hough line andgenerated a nonlinear oscillator to attract them into the intersection with other lines. This concept
could contribute to a line detection problem in image processing using a consistent mathematicaldescription.

© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

nonlinear dynamics could solve the original HT’s
drawbacks.
This paper focused on the mathematical solution for
detecting straight lines, which can be obtained from
nonlinearoscillator
dynamics
thatproduces
synchronization phenomena in a limit cycle and the
projection space of HT. Moving points can automaticallyconcentrate on finding the intersection points of lines in
the projection space. Therefore, there is no need for the
voting process. Section 2 described the projection
method from the Cartesian coordinate system to theparameter space and its algorithm for computer
simulations. A typical nonlinear oscillator dynamic toreplace the voting process was described in Section 3. In
Section 4, we newly formulated the proposed system asa noise-resistant line detection method, followed bycomputer simulation results in Section 5 and a conclusion
in Section 6.

1. Introduction
Detecting lines in the image is crucial in computer
vision [1], [2], [3] since it lays the foundation for object
detection [4]. A common way to solve the problem is theHough Transform (HT), mathematically sounds for
detecting a unique focal point by projecting several line
elements to the parameter space. HT projects the image
data points from continuous spaces such as Cartesian topolar coordinate systems, while it requires the focal pointsearch in discrete grids by voting. This voting processprovides a trade-off problem, affecting the noise removal
depending on the resolution. It needs higher resolution
grids to achieve higher precision which needs morecomputational time. To overcome this limitation, we
proposed a mathematical model based on the continuous
space dynamics instead of the voting process. It is known
as nonlinear dynamics having attractor dynamics. Basedon ordinary differential equations, these dynamics can be
simulated in a computer using numerical integration
methods, such as the Euler and Runge-Kutta methods. A
new method of combining the dual space projection instandard HT and a synchronization of self-organizing
points to represent a single straight line based on the

2. Traditional Hough Transform Method
A technique for detecting shapes in an image using
image analysis is the Hough Transform (HT) [5]. Paul
Hough introduced this method in 1962, which has been
applied in various fields [6], [7], [8]. HT converts theCorresponding author’s E-mail: purev.amarbold118@mail.kyutech.jp, waga@brain.kyutech.ac.jp

185location of image points from Cartesian coordinates to amore concise representation in parameter space [9].
𝜌𝜌 = 𝑥𝑥 cos(𝜃𝜃) + 𝑦𝑦 sin (𝜃𝜃)

specialized hardware [16], and the use of artificial
intelligence [17], this problem still remains unsolved.
By using an accumulation array in the system, HT
cannot avoid difficulties, such as the array’s size
determination to adjust for precise detection. The method
becomes inaccurate if the grid size of the array is toolarge to discriminate the true spot, and the computationaltime becomes costly if the grid size is too small in an
unnecessary manner. Furthermore, HT only detects linesthat have infinite lengths. This is because HT uses its
parameters to represent lines that do not contain
information about the line length. Therefore, the HTcannot detect lines that have finite lengths.

(1)

The location of points in the 𝑋𝑋𝑋𝑋 plane is transformed
into parameter space by Eq. (1). As a result, each point in
the 𝑋𝑋𝑋𝑋 plane becomes a sine curve. The length from theorigin 𝜌𝜌 and the angle 𝜃𝜃, a line perpendicular to the line
passing through edge points, are obtained by theintersection of these sine curves. Figure 1 showed thistransformation.
HT method provides an accumulation array of zero
values with 𝑅𝑅 × 𝑇𝑇 size to detect the intersection of edge
points in Figure 1(b). 𝑅𝑅 is the number of rows for the 𝜌𝜌value, and 𝑇𝑇 is the number of columns for the 𝜃𝜃 value.
The 𝜌𝜌 value for every point is computed for every 𝜃𝜃value, and the nearest 𝜌𝜌 value in the accumulation arrayis increase by 1. This procedure is known as the voting
procedure of HT. After going through all columns of theaccumulation array, the cell with the maximum points
describes the features of the perpendicular line. Thistransformation makes it possible to simplify the shapedetection problem to a peak detection problem inparameter space.

3. Coupled Nonlinear Oscillator Dynamics
3.1. Synchronization of Kuramoto Model
The Kuramoto model (KM) is a mathematical model
investigating oscillator synchronization [18]. It isfrequently used in areas such as physics [19], [20].
biology [21], and chemistry and has been utilized invarious contexts, such as neurophysiology [22], [23],distributed power generation [24], [25], and securecommunication [26], [27]. In this paper, we suggest using
modified model of KM to cluster edges in images basedon their collinearity.
The following equation describes the standard model ofthe KM
𝐾𝐾

𝜑𝜑̇ 𝑖𝑖 = ω𝑖𝑖 + ∑𝑁𝑁
𝑗𝑗=1 sin�𝜃𝜃𝑗𝑗 − 𝜃𝜃𝑖𝑖 �.
𝑁𝑁(2)

Eq. (2) represents a group of 𝑁𝑁 oscillators with a limit
cycle. These oscillators have natural frequencies 𝜔𝜔𝑖𝑖 andphases 𝜃𝜃 . The coupling constant 𝐾𝐾 , and the coupling
between oscillators is determined by the sine of thedifference in their phases. The phases change over time
according to first-order dynamics.
The KM is not commonly used in image processing
because oscillators are dynamic while image edges are
static. However, in [28], researchers applied it to segment
color images. Using a coupled network, they provided
three oscillating curves for the red, green, and blue pixel
values of color images. This produced a superposition ofoscillation for the image pixels.
It suggests that the KM’s attractor dynamics of coupled
nonlinear oscillators changes edge coordinates fromdiscrete to continuous space. This function will enable
the clusterization of edges in parameter space with theKM, removing the necessity for an accumulation array inthe standard HT method.

Fig. 1 Hough transformation. a) Points (𝒙𝒙𝟏𝟏 , 𝒚𝒚𝟏𝟏 ) and(𝒙𝒙𝟐𝟐 , 𝒚𝒚𝟐𝟐 ), a line with length 𝝆𝝆∗ and angle 𝜽𝜽∗ that isperpendicular to them in image space. b) Points
transformed into sine curves in parameter space.
The HT method has the key benefit of being simple,
enabling parallel information processing. This makes themethod resistant to noise and capable of detecting
partially hidden or distorted shapes. In addition, themethod could be set up to detect a fixed number of shapes
in an image.
However, the HT method’s simplicity becomes adrawback when detecting shapes other than straight lines.
The amount of computations grows as the number ofparameters required to define the shape grows [10], [11].
For instance, detecting a circle in an image would need athree-dimensional accumulation array for the circle’s
center (𝑥𝑥, 𝑦𝑦) and its radius 𝑟𝑟. With respect to efforts ofresearchers to enhance the HT method’s efficiency
through software optimization [12], [13], [14], [15].
186Definition 1. Let {𝝋𝝋𝒊𝒊 (𝒕𝒕)}𝟐𝟐𝒊𝒊=𝟏𝟏 be solution of oursystem. The oscillators converge to phasesynchronization if
lim �𝜑𝜑𝑖𝑖 (𝑡𝑡) − 𝜑𝜑𝑗𝑗 (𝑡𝑡)� = 0, for 𝑖𝑖 ≠ 𝑗𝑗.

𝑡𝑡→∞

(4)

Let us examine how our system behaves according to
Eq. (3) when applying different initial conditions.
Example 1. 𝜑𝜑1 (0), 𝜑𝜑2 (0) = 0

The solution to the equation is 𝜑𝜑1 (𝑡𝑡) = 0 and 𝜑𝜑2 (𝑡𝑡) =0. This means that there is phase synchronization.
𝜋𝜋Example 2. 𝜑𝜑1 (0) = 0, 𝜑𝜑2 (0) = , 𝐾𝐾 > 02𝜋𝜋𝜑𝜑2 (𝑡𝑡) = 𝐾𝐾 sin � − 0�2𝜋𝜋
= 𝐾𝐾 sin � �2= 𝐾𝐾

Fig. 2 Interaction between two nonlinear oscillators
𝝋𝝋𝟏𝟏 and 𝝋𝝋𝟐𝟐 . The initial positions are shown in a). The
behavior of the second oscillator is shown in b) when
𝑲𝑲 > 𝟎𝟎 and c) when 𝑲𝑲 < 𝟎𝟎. A black dot indicates astable point, and a white dot indicates an unstable
point.

(5)

Because 𝐾𝐾 > 0, 𝜑𝜑̇ 2 (𝑡𝑡) → 𝜋𝜋 and the second oscillator
converges to the anti-phase.
𝜋𝜋Example 3. 𝜑𝜑1 (0) = 0, 𝜑𝜑2 (0) = − , 𝐾𝐾 > 0
2

In order to analyze how the KM can detect lines inimages, we must first examine the behavior ofstraightforward systems. By understanding their
behavior, it leads a model to classify image edges basedon their collinearity accurately.

𝜋𝜋
− 0�
2
𝜋𝜋
= 𝐾𝐾 sin �− �
2
= −𝐾𝐾.

𝜑𝜑2 (𝑡𝑡) = 𝐾𝐾 sin �−

Because 𝜑𝜑̇ 2 (𝑡𝑡) < 0, 𝜑𝜑̇ 1 (𝑡𝑡) → −𝜋𝜋 the second oscillator
converges to the anti-phase as well.

3.2. Analysis of Stability for two Coupled
Nonlinear Oscillators
Let us assume that a system with two oscillators, 𝜑𝜑̇ 1 and𝜑𝜑̇ 2 , that behaves according to
𝜑𝜑̇ = 0
� 1
𝜑𝜑̇ 2 = 𝐾𝐾 sin(𝜑𝜑2 − 𝜑𝜑1 )(6)

Example 4. 𝜑𝜑1 (0) = 0, 𝜑𝜑2 (0) = 𝜋𝜋, 𝐾𝐾 > 0
𝜑𝜑2 (𝑡𝑡) = 𝐾𝐾 sin(𝜋𝜋 − 0)
= 𝐾𝐾 sin(𝜋𝜋)=0(3)The starting conditions are 𝜑𝜑𝑖𝑖 (0) = 𝜑𝜑𝑖𝑖0, where 𝜑𝜑 is thephase of the 𝑖𝑖th oscillator and 𝐾𝐾 is the coupling strength.
To simplify the analysis, it is assumed that 𝜑𝜑̇ 1 is always
equal to 0 and focused on the dynamics of the second(𝑛𝑛)oscillator. The initial values of 𝜑𝜑2 = [0, 𝜋𝜋/2, −𝜋𝜋/
2, 𝜋𝜋], 𝑛𝑛 = 1 … 4, as shown in Figure 2.
The description gives the definition of phasesynchronization as follows.

(7)

When the initial position of 𝜑𝜑2 (0) = 𝜋𝜋 and 𝜑𝜑2 (𝑡𝑡) = 0,
the second oscillator starts at the anti-phase stable pointof 𝜋𝜋 and does not move as 𝑡𝑡 → ∞.
Although both oscillators converge in Example 1, the 0point is unstable as shown in Examples 2, 3. 4. As a result,the system described by Eq. (3) converges to the antiphase. But, if the coupling strength is negative, the two
oscillators will converge after performing the same
calculations as in the previous examples.

187𝜌𝜌1 = 𝜌𝜌2
𝑥𝑥1 cos 𝜃𝜃 + 𝑦𝑦1 sin 𝜃𝜃 = 𝑥𝑥2 cos 𝜃𝜃 + 𝑦𝑦2 sin 𝜃𝜃(9)𝜃𝜃 = tan−1 (−(𝑥𝑥1 − 𝑥𝑥2 )/(𝑦𝑦1 − 𝑦𝑦2 ).

When the starting phase of the first oscillator as 𝜑𝜑10 =tan−1 (−(𝑥𝑥1 − 𝑥𝑥2 )/(𝑦𝑦1 − 𝑦𝑦2 )), it goes where two Houghlines intersect and start the second oscillator at the fixed
point, where 𝜌𝜌2 = 0 . In Eq. (9) to get the 𝜃𝜃 =tan−1 (−𝑥𝑥2 /𝑦𝑦2 ) , 𝜑𝜑20 = tan−1 (−𝑥𝑥2 /𝑦𝑦2 ) , the couplingstrength 𝐾𝐾 is the highest 𝜌𝜌 value for each Hough line,
which is 𝐾𝐾𝑖𝑖 = 𝑥𝑥𝑖𝑖2 + 𝑦𝑦𝑖𝑖2 .
Nevertheless, it faces another problem to change thesign to refrain from the anti-phase synchronization
problem in Section 3.2.
Example 5 showed how to solve this problem.
Fig. 3 Example of pointsa) Image space. b) Hough space.

(1,1)

and

Example 5. Two points, 𝑝𝑝1 = (𝑥𝑥1 , 𝑦𝑦1 ) = (1,1) and 𝑝𝑝2 =(𝑥𝑥2 , 𝑦𝑦2 ) = (5,2) are given in the image space, as shownin Figure 3. For finding the initial values, two oscillatorsneed to converge with the same coupling as Eq. (9). 𝜑𝜑10 =tan−1 (−(𝑥𝑥1 − 𝑥𝑥2 )/(𝑦𝑦1 − 𝑦𝑦2 )) = 4.9574 rad, 𝜑𝜑20 =tan−1 (−𝑥𝑥2 /𝑦𝑦2 ) = 5.0929 rad, 𝐾𝐾2 = 𝑥𝑥22 + 𝑦𝑦22 = 29.

(5,2).

4. Coupled Nonlinear Oscillator-based Hough
Transform for Noise-Robust Line Detection

Figure 3 showed 𝜑𝜑𝑖𝑖0 has 2 solutions for each oscillator
in a 2𝜋𝜋 period. Therefore, our model needs to be able tochange the sign depending on where the initial phase of
the oscillator is. This provides a function to find the
direction of the oscillator by getting the slope of thesecond Hough line from the first derivative of 𝜌𝜌 function

4.1. Coupled Nonlinear Oscillator-based Hough
Transform with single attractor
The standard HT method is explained in Section 1.
Instead of the standard HT voting scheme, a model canbe considered by eliminating it with a nonlinear systemof equations as the proposed model. Each point in theimage space is considered as a separate nonlinear
oscillator and coupled together using the following
system of equations
𝜑𝜑̇ 1 = 0𝜌𝜌1 − 𝜌𝜌2
�𝜑𝜑̇ 2 =+ (𝜑𝜑1 − 𝜑𝜑2 )
𝐾𝐾 2

𝑑𝑑𝑑𝑑
= 𝑦𝑦 cos 𝜃𝜃 − 𝑥𝑥 cos 𝜃𝜃.
𝑑𝑑𝑑𝑑

(10)

Ultimately there can only be four distinct cases:
(i)
(ii)
(iii)
(iv)

(8)

The initial conditions 𝜑𝜑𝑖𝑖 (0) = 𝜑𝜑𝑖𝑖0, where 𝜑𝜑 is the phaseof the 𝑖𝑖th oscillator, 𝜌𝜌 is the amplitude of Hough line at
the 𝜑𝜑 phase and 𝐾𝐾 is the coupling strength based on the
maximum amplitude of the 𝜌𝜌 value.
For the sake of finding where both points meet in the
Hough space, the 𝜌𝜌 and 𝜃𝜃 values of each oscillator haveto take exact same values individually. According to Eq.
(3), it implies that 𝜑𝜑1 stops and then 𝜑𝜑2 moves towards
𝜑𝜑1 . Thus, the first oscillator will pull the second one toitself.
Consequently, choosing the initial phase of the first
oscillator at the intersection of Hough lines is essential
and can be calculated analytically

𝜑𝜑10 > 𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) > 0
𝜑𝜑10 < 𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) < 0
𝜑𝜑10 > 𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) < 0
𝜑𝜑10 < 𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) > 0

By examining the options, four different groups were
defined into two categories, (i, ii) and (iii, iv), with theidentical effect. Then Eq. (8) changes into the following
system of equations𝜑𝜑̇ = 0⎧ 1 𝜌𝜌 − 𝜌𝜌
2⎪𝜑𝜑̇ = 1+ (𝜑𝜑1 − 𝜑𝜑2 ),2
𝐾𝐾 2⎨
𝜌𝜌2 − 𝜌𝜌1
⎪𝜑𝜑̇ 2 =+ (𝜑𝜑1 − 𝜑𝜑2 ),
⎩
𝐾𝐾 2

188

if A or B

if C or D(11)

where A = (𝜑𝜑10 > 𝜑𝜑20 , 𝜑𝜑2′ (𝜑𝜑20 ) < 0) , B = (𝜑𝜑10 <𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) > 0) , C = (𝜑𝜑10 > 𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) > 0) , D =(𝜑𝜑10 < 𝜑𝜑20 , 𝜌𝜌2′ (𝜑𝜑20 ) < 0).

4.2. Proposed Model for Pair-wise Coupling

then extracted two random points from the list, andsynchronized them until no points were left.
Then, for line points with noise, random noise points
were added to the lines in the previous experiment. This
experiment was conducted 20 times for each type of line,
a total of 80 experiments. Sample figures of each line
type are shown in Figure 5. Since pair-wise coupling
selects two random points out of all points, including line
and noise, all of the line points are not detected.
Additionally, a scenario with the distorted line in thepresence of noise was tested (Figure 4(f)). In this scenario
the proposed model struggles to distinguish between line
and noise points, because oscillators converge to theabsolute theoretical straight line. However, a distorted
line is theoretically not a single line but multiple lines. As
a result, the number of line points is significantly
decreased compared to the previous experiments, whichmakes it harder to detect line points.
Furthermore, a grid structure was tested to evaluate theproposed model’s ability to detect multiple lines, withand without noise. When no noise points are present in
the image, pair-wise coupling performs well. However,if the noise points disrupt the image, the model fails toprovide good results.
Lastly, the convergence rate based on points distance
was tested. In this experiment, 20 evenly distributed
points from 2 to 1000 were converged together and thenumber of iterations for convergence was registered.
Figure 6 shows the ratio between Euclidean distance andconvergence rate. The analysis shows the convergence
speed of oscillators based on their Euclidean distance =�(𝑥𝑥1 − 𝑥𝑥2 )2 + (𝑦𝑦1 − 𝑦𝑦2 )2 in image space with Δ𝑒𝑒 =10−6 precision. As shown in the graph, when the 𝐷𝐷 isclose to 0, it takes a significant number of iterations toconverge. However, the number of iterations quickly
drops to 100 when 𝐷𝐷 > 30 . A slight difference in 𝐷𝐷
means the difference 𝜌𝜌 is also insignificant, which affects
the oscillator’s speed to be slow.
Table 1 shows the average line detection rates (%) forline types in above described experiments. The pair-wise
coupling has high detection rates with high precisionthresholds.

The previous model in Eq. (11) has a significant
disadvantage in real-life scenarios. Because to analyze an
image in full, the algorithm has to run 𝑁𝑁 times for all theedge points, selecting a single edge point as an attractor
in each loop. Therefore, the pair-wise coupling is betterfrom an optimization standpoint, where two oscillators
attract each other at the same converging at theintersection of Hough line𝜌𝜌𝑗𝑗 − 𝜌𝜌𝑖𝑖
+ �𝜑𝜑𝑗𝑗 − 𝜑𝜑𝑖𝑖 �,𝐾𝐾𝑖𝑖
𝜑𝜑̇ 𝚤𝚤 = � 𝜌𝜌 − 𝜌𝜌𝑗𝑗𝑖𝑖
+ �𝜑𝜑𝑗𝑗 − 𝜑𝜑𝑖𝑖 �,−
𝐾𝐾𝑖𝑖

if A or B

otherwise(12)

where 𝑖𝑖, 𝑗𝑗 – is the index of first and second oscillator inpair-wise coupling.
The only difference from Eq. (11) other than pair-wise
coupling, the initial phase of all oscillators 𝜑𝜑𝑖𝑖0 will be atthe 𝜃𝜃-axis in parameter space, which means𝑥𝑥𝑖𝑖 cos𝜑𝜑𝑖𝑖 + 𝑦𝑦𝑖𝑖 sin𝜑𝜑𝑖𝑖 = 0𝑥𝑥𝑖𝑖 cos𝜑𝜑𝑖𝑖 = −𝑦𝑦𝑖𝑖 sin𝜑𝜑𝑖𝑖
sin𝜑𝜑𝑖𝑖
𝑥𝑥𝑖𝑖= �− �
cos𝜑𝜑𝑖𝑖
𝑦𝑦𝑖𝑖
𝜑𝜑𝑖𝑖 = tan−1 �−

(13)
𝑥𝑥𝑖𝑖
�
𝑦𝑦𝑖𝑖

The above condition ensures that the oscillators will
have uniform behavior and derivative in Eq. (10) will
never have a 0 value at the start.
A detailed description of the coupled nonlinear
oscillator-based HT algorithm and the traditional HT
method is given in [29].
5. Results and Discussion
The following section shows the proposed algorithm’s
results for pair-wise coupling on various setups andevaluates the accuracy and error of detection.
5.1. Proposed Model for Pair-wise Coupling
The proposed model in Eq. (12) was tested extensively
in various situations. Figure 4 shows the experiment
setup: only line points (a-d), line points with noise (e),distorted line points with noise (f), grid structure (g), andvarying image size (h).
First, for only line points experiment, four experiments
were conducted for each type of line with only line points.
The number of line points 𝑁𝑁𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 100 , and the ofiterations up to 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 < 20000 was selected. The
proposed model initiated a list of all points in the image.,

6. Conclusion
Our mathematical formulation and computer
experiment clearly demonstrated the replacement of the
HT voting scheme by coupled nonlinear oscillator
dynamics. We analyzed single attractor model tounderstand oscillator behavior in simple cases and it was
successfully extended to the pair-wise model to improve
limitations on previous model. The model was
experimentally tested in different possible straight-line
189configurations. The pair-wise coupling method showshigh accuracy and precision.
By using coupled nonlinear oscillators, replacing theaccumulation array was achieved and the desired
precision can automatically be set in the proposed model.
In future work, performance improvement in real-time
applications will be developed based on the proposedmodel. applications will be developed based on the
proposed model.

Fig. 5 Single line points in a noisy environment with
their Hough space and detected line points using pairwise coupling. Blue dots in image space and blue lines
in hough space are line points, whereas gray dots andgray lines correspond to noise. Red dots in Hough
space are individual oscillators.
Table 1. Line point detection rate based on theset precision for pair-wise coupling ofoscillators.
Line Types

Fig. 4 Scope of the experiment on pair-wise coupling
model. a) – d) represents different types of straightlines with line points only. e) – f) represents straightline points in different scenarios. Blue points are thestraight line points, whereas black ones are noise
points.

Single Line

Precision (𝜀𝜀)Line and Noise
Distorted Line andNoise
Grid Line
Grid Line andNoise
Varying Image
Size

10−6

Line Ratio (%)
99.75

10−13

40.49

10−7

95.00

10−12
10−12
10−10

81.71
76.13
99.10

Acknowledgements
This work was supported in part by JSPS KAKENHI(16H01616, 17H06383), Project on Regional
Revitalization Through Advanced Robotics (Kyushu
Institute of Technology/Kitakyushu city, Japan) and the
190New Energy and Industrial Technology Development
Organization (NEDO).

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Authors Introduction
Mr. Amarbold Purev

He received his Master's degreefrom the School of MechanicalEngineering and Transportation,
Mongolian University of Science andTechnology, Mongolia in 2019. He iscurrently a Doctoral course student inKyushu Institute of Technology,
Japan.

Dr. Hiroaki Wagatsuma
He received his M.S., and Ph.D.
degrees
from
Tokyo
Denki
University, Japan, in 1997 and 2005,
respectively. In 2009, he joined
Kyushu Institute of Technology,
where he is currently Professor of the
Department of Human Intelligence
Systems. His research interests
include nonlinear dynamics androbotics. He is a member of IEEE.

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