Team Desciption paper:
BabyTigers - R 2024
Yuka Komori, Shohei Yasuda, Kosuke Nakajima, Ryota Tanabe, and Wataru
Uemura[0000−0001−6012−0029]
Ryukoku University, 1-5, Seta Ohe, Otsu City, Shiga, Japan
robocup@vega.elec.ryukoku.ac.jp, wataru@rins.ryukoku.ac.jp
https://vega.elec.ryukoku.ac.jp/trac/wiki/BabyTigers-R

Abstract. This paper presents Baby-Tigers-R[1], a team comprising
members from Electronics, information and communication engineeringcourse, Faculty of advanced science and technology at Ryukoku University.
Within our laboratory, we are actively engaged in research concerning
autonomous mobile robots and visible light communication. The collaboration of autonomous mobile robots holds significant importance,
particularly in the evolving landscape of factory production, transitioning from low-mix mass production to high-mix low-volume production.
Our research focuses on exploring criteria for computer selection in autonomous mobile robots, pathfinding algorithms, and marker recognition
techniques.
Keywords: Logistics League, RoboCup, BabyTigers - R, robotino, autonomous mobile robot.

1Introcution

This paper introduces Baby-Tigers-R, which is a team consisted of members
belonging to Electronics, Information and communication engineering course,
Faculty of advanced science and technology, Ryukoku University. In our laboratory, we are conducting research related to autonomous mobile robots and visible
light communication. Autonomous mobile robots that work together with otherrobots are considered important. In addition, the mode of production in factories
is changing from low-mix mass production to high-mix low-volume production.
Our research aims to explore various aspects of this evolving field, including pathfinding algorithms, and marker recognition techniques. In Section 2, weinvestigate the repulsion and attraction phenomena in addressing the stopping
problem within the framework of potential fields methods[2]. Furthermore, Section 3 presents a proposal and evaluation concerning the optimal shape of reading cells, taking into account the directional blurring of AR markers[3] during
movement. Finally, we summarize our findings and conclusions in the subsequent
Section 4 of this paper.

2Team Description Paper: BabyTigers - R2

Deadlock Problem by the Relationship between
Repulsion and Attraction in Potential Field

2.1

Introduction

In recent years, autonomous mobile robots have emerged as a promising solution
to address labor shortages across various industries, leading to a surge in research
activities in this field. This research spans a wide array of areas, including sensor
technology, image processing, and path planning.
Path selection, in particular, has garnered significant attention within autonomous mobile robot research. Path selection involves determining the mostsuitable path for an autonomous robot to navigate to its destination. One commonly utilized method for path selection is the potential field method.
In the potential field method, an attractive force function is defined at thedestination, while a repulsive force function is defined at obstacles. The combined force of these functions determines the gradient vector, which guides therobot’s movement. Specifically, the gradient vector of the repulsive function directs the robot away from obstacles, while the gradient vector of the attractivefunction guides it towards the destination. However, if the gradient vector consistently points towards a particular point, the robot may become trapped atthat location.
Moreover, in this method, obstacles are treated as point sources of repulsion,
with the repulsive force uniformly spreading from the center coordinates of theobstacle. Similarly, the attractive force spreads uniformly from the destination
coordinates.
This paper explores the concept of ”anchorage ease” by examining the interplay between repulsion and attraction forces while considering the shape ofobstacles. By analyzing this relationship, the paper aims to enhance understanding of how obstacle shapes influence path planning and navigation strategies forautonomous mobile robots.
2.2

about effect by repulsion and attraction

Let the coordinates of the robot be (xr , yr ), the coordinates of the i-th obstacle be (xoi , yoi ), and the coordinates of the target position be (xg , yg ). Let kr
and kg represent the coefficients of repulsion and attraction, respectively. These
coefficients are adjustable parameters. The expression for the potential function
Fri for repulsion force is given by the equation: 1.
Fri = pkr
(xoi − xr )2 + (yoi − yr )2(1)The expression for the potential function Fg of the attractive force is given byEquation 2.
kg(2)
Fg = − p2xg − xr ) + (yg − yr )2

Team Desciption paper: BabyTigers - R 2024

3The expression for the function F representing the combined repulsive and attractive forces is given by Equation 3, where n is the number of obstacles.
nX
F =(Fr i ) + Fg

(3)

i=1

The gradient vector of the combined force, which represents the direction inwhich the robot is moving, is given by Equation 4.
∂F ∂F−∇F = −,(4)∂xr ∂yrTo enhance the ease of anchorage, we modify the repulsion and attraction forces
to align with the shape of the obstacle. Let (xei , yei ) denote the point where thestraight line intersects the obstacle when the coordinate points of the obstacle
and the robot are connected by a straight line.
The expression for the length di from the coordinate point of the obstacle isgiven by Equation 5.
q22
di = (xoi − xei ) + (yoi − yei )(5)We modify the conventional repulsion and attraction potential functions by multiplying them by di . This adjustment results in greater repulsion at greater distances from the center of the obstacle to the edge, with a corresponding increase
in attraction. Conversely, for portions of the obstacle where the distance fromthe center to the edge is small, both the repulsion and attraction forces arediminished accordingly.
gThe expression for the modified function of repulsion, denoted as Fci , isgiven by Equation 6.
q
22(xoi − xei ) + (yoi − oei )(6)
Fci = Fr × di = kr × q
22(xoi − xr ) + (yoi − yr )The expression for the modified function of attraction, denoted as FG , is givenby Equation 7.
q22(xoi − xei ) + (yoi − oei )(7)FG = Fg × di = −kg × q
22(xg − xr ) + (yg − yr )Fci varies with both the distance to the obstacle and the distance to the edgeof the obstacle, while FG varies with the distance from the coordinates of thetarget position to the robot’s coordinates.
The expression for Fp , the function representing the combined repulsive andattractive forces, is given by Equation 8.
!
nX
Fp =
Fci + FG(8)i=1

4Team Description Paper: BabyTigers - R

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Fig. 1. The experimental environment

2.3

Experiment

Numerical simulations are conducted to analyze the robot’s path using both theconventional potential field method and the modified potential field methods,
focusing on the ease of stopping.
The experimental setup involves a rectangular obstacle with dimensions x =1 meter and y = 3 meters located at coordinates (3.0, 4.0) within an areabounded by x = 6 meters and y = 8 meters, as depicted in Figure 1. The
origin is situated at the lower left corner.
In Case A of the experiment, we examine the differences between scenarios
where the robot comes to a stop and where it continues moving. The initial
position of the robot is set at (1.0, 2.0) with a destination of (4.0, 4.0). In Case
B, the initial position is (3.0, 1.0) with a destination of (3.0, 7.0) for the robot.
These experimental configurations aim to provide insights into the efficacy ofthe modified potential field methods in facilitating smoother and more efficient
stopping of the robot under various initial and destination conditions.
The paths for Case A and Case B are illustrated in Figure 2 and Figure
3, respectively. In both figures: The orange line represents the path generatedusing the conventional potential field method. The blue line represents the pathgenerated when both the repulsive and attractive forces are varied. The green
line represents the path generated when only the repulsive force is varied. The
red line represents the path generated when only the attractive force is varied.
These color-coded paths provide a visual comparison of the trajectories resulting
from different configurations of the potential field method.
In both Cases A and B, the robot failed to reach the target position andstopped when only the repulsive force was modified (green). In the experimentalresults, the system halted when only the repulsive force was adjusted. Figure
4 depicts the potential field for Case A with only the repulsive force modified.
Observing the potential field, we notice that the repulsion force spreads out in arectangular shape, while the attraction force spreads out in a circular manner.
This leads to a constricted potential field where the repulsion force dominates.
However, the potential field lacks a gradient vector that wraps around the obstacle, rendering it impossible for the robot to reach the target position. ThisTeam Desciption paper: BabyTigers - R 2024

Fig. 2. Path of the robot in case A

5Fig. 3. The Path of the robot in case B

Fig. 4. Potential field when only the repulsion is changed

indicates that if the repulsive and attractive forces are in close proximity or if
the repulsive force forms a regular circle, the potential field is less likely to beconstricted by the attractive force, reducing the likelihood of the robot coming
to a stop prematurely.

2.4

Conclusion

In this section, we have investigated the ease of stalls in potential field methods by varying the repulsive and attractive forces. In future research, we aim toexplore the relationship between repulsion and attraction forces in scenarios involving multiple obstacles. Additionally, we plan to develop an algorithm for thepotential field method that effectively prevents stalls from occurring. By further
investigating these aspects, we aim to enhance the robustness and efficiency ofpotential field-based navigation methods for autonomous mobile robots.

6Team Description Paper: BabyTigers - R

3Cell Shape Considerations Based on Robot Movement
Direction

3.1

Introduction

Autonomous mobile robots operate independently, requiring precise self-position
estimation to execute tasks accurately. ArUco markers are commonly employed
for indoor self-position estimation, including in the RoboCup Logistics League(RCLL), a competition focusing on warehouse and factory automation. In RCLL,ArUco markers identify Modular Production Systems (MPS) and facilitate selfposition estimation simultaneously.
However, capturing ArUco markers from a moving robot can lead to blurred
images, impeding marker recognition. To address this challenge, we propose arecognition method for ArUco markers that accounts for motion blur direction.
Motion blur noise typically appears horizontally in captured images frommoving robots. Therefore, when detecting ArUco markers, we selectively read
only the region with a short width of the cell, rather than the entire cell. Thisapproach reduces noise in the read cell, thereby enhancing the recognition rateof ArUco markers.
Experiments will be conducted at various robot speeds and distances fromthe markers to validate the effectiveness of the proposed method.
3.2

Recognition Method Considering Blurring

In essence, the moving robot exhibits forward/backward, horizontal, and rotational movements relative to the markers. As the robot moves back and forth,diagonal noise arises on captured markers, while horizontal noise occurs during horizontal movements or rotations. Additionally, vertical blurring can result
from the robot’s movement-induced vibration.
Considering that horizontal noise tends to be more pronounced than diagonal
and vertical noise, the shape of the cell during marker detection is altered froma square to a elongated rectangle, as depicted in Figure 5. This adjustment
effectively reduces the overall size of the cell, thereby accommodating the effectsof blurring.
Subsequently, during the marker identification step, the number of black andwhite pixels within the rectangle is tallied to determine the cell’s color.
3.3

Experiment

We conducted experiments to test our proposed recognition method, which considers the direction of blurring in ArUco markers, in order to assess the impact
on the marker recognition rate.
As illustrated in Figure 6, the robot is maneuvered parallel to the marker,
maintaining distances of 2 meters and 3 meters when positioned directly in frontof the ArUco marker. The experiments were conducted at four different robot
speeds: 0.3 m/s, 0.4 m/s, 0.5 m/s, and 0.6 m/s. The length of one side of theTeam Desciption paper: BabyTigers - R 2024

7$U8FR PDUNHUP5RERWFig. 5. Cell for reading (blue box)
Fig. 6. An illustrated outline of experiment./012034/0567) 238/9./012034/0567) 238/9:;/</+297)238/9'!!"!#'!!"!#&%"!#&%"!#%!"!#%!"!#$%"!#$%"!#:;/</+297)238/9!"!#!"!#!"() *+!",) *+!"%) *+!"-) *+Fig. 7. Recognition ratio of conventional
and proposed methods at 2 meters.

!"() *+!",) *+!"%) *+!"-) *+Fig. 8. Recognition ratio of conventional
and proposed methods at 3 meters.

ArUco marker used is 13.5 cm. The shape of the cell to be read is adjusted to0.8 for the vertical ratio and 0.5 for the horizontal ratio, relative to the originalsquare shape.
The recognition rate is defined as the percentage of markers correctly identified from the captured images. The robot traveled three times in each direction(left and right), and the recognition rate was calculated based on a total of 6captures. To assess the effectiveness of our proposed method, we compared therecognition rates obtained when the cell shape was 1:1 and 0.8:0.5.
The mobile robot utilized in the experiments is a Festo Robotino 3. Thecamera used for image capture is a HD Pro Webcam C920 manufactured byLogitech.
As depicted in the graphs in Figure 7 and Figure 8, the recognition rate exhibited improvement across all speeds when utilizing our proposed method. For
the three scenarios where the recognition rate of the conventional method wasless than 10%, the proposed method led to an approximately tenfold improvement in the recognition rate. Moreover, the recognition rates for the remaining
data also demonstrated substantial enhancements. These findings suggest thatour proposed method has the potential to expedite the successful estimation ofself-location.

83.4

Team Description Paper: BabyTigers - RConclusion

In this section, we introduce a novel cell shape for self-position estimation using
ArUco markers during robot movement, considering the impact of noise inducedby vibration. Comparison experiments between the conventional method andour proposed method revealed that our approach effectively mitigates the effects
of motion blur and enhances the recognition rate of markers.
During the experiment, a consistent cell shape was utilized across all speeds.
However, given that the degree of blurring is likely to vary based on factors suchas the angle with the marker and the speed of the mobile robot, an area for
future exploration involves implementing automatic cell deformation based on
this information. This adaptive approach could further refine the accuracy androbustness of self-position estimation in dynamic environments.

4Conclusion

We have been exploring the integration of autonomous mobile robots into various settings, including manufacturing and medical facilities, amidst the transition from high-mix low-volume production to factory production. Our researchendeavors have encompassed investigating the selection criteria of computers forautonomous mobile robots and delving into pathfinding techniques.
Additionally, in our exploration of potential field methods, we have examinedthe ease of stopping by manipulating the repulsive and attractive forces. Notably,
we observed that changes in the repulsive force resulted in the robot coming toa halt. As a next step, we plan to explore the relationship between repulsive andattractive forces in scenarios involving multiple obstacles and develop algorithms
for potential field methods to prevent such unintended stops.
Moreover, we proposed a novel cell shape tailored to account for the effects ofvibration-induced noise when estimating self-position using ArUco markers during robot movement. Experimental comparisons between our proposed method
and conventional approaches revealed that our method effectively mitigated motion blur effects and improved marker recognition rates.
These collective research efforts signify our commitment to advancing the capabilities and reliability of autonomous mobile robots in real-world applications,with a focus on enhancing navigation, perception, and overall performance indynamic environments.

References
1. BabyTigers - R, https://friede.elec.ryukoku.ac.jp/trac/lab/wiki/BabyTigers-R
2. Jen-Hui Chuang, and Narendra Ahuja: ”An Analytically Tractable Potential Field
Model of Free Space and Its Application in Obstacle Avoidance”, IEEE TRANSACTIONS ON SYSTEMS,MAN,AND CYBERNETICS-PART B: CYBERNETICS,
Vol.28, No.5, pp.729–736, 1998.
3. S. Garrido-Jurado, R. Munoz-Salinas, F. J. Madrid-Cuevas, and M. J. MarinJimenez: ”Automatic generation and detection of highly reliable fiducial markers
under occlusion”, Pattern Recognition, 47(6),, pp.2280–2292, June 2014.