# Paraconsistent Annotated Evidential Logic Eτ Applied to Autonomous Robots in Logistic Center

Flávio Amadeu Bernardini, Marcia Silva, Jair Minoro Abe, Luiz Lima

► To cite this version:

Flávio Amadeu Bernardini, Marcia Silva, Jair Minoro Abe, Luiz Lima. Paraconsistent Annotated Evidential Logic Eτ Applied to Autonomous Robots in Logistic Center. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2021, Nantes, France. pp.533-540, 10.1007/978-3-030-85906-0_58. hal-04022136

HAL Id: hal-04022136

https://inria.hal.science/hal-04022136

Submitted on 9 Mar 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
# Paraconsistent Annotated Evidential Logic $\mathcal{E}\tau$ Applied to Autonomous Robots in Logistic Center

Flávio Amadeu Bernardini¹[0000-0002-6292-0617], Marcia Terra da Silva¹[0000-0002-5314-4978], Jair Minoro Abe¹[0000-0003-2088-9065], Luiz Antonio de Lima¹[0000-0003-4228-2387]

¹Graduate Program in Production Engineering

Paulista University Rua Dr. Bacelar 1212 CEP 04026-002 – São Paulo – SP – BRAZIL

flavioambernar@gmail.com, marcia.terra@uol.com.br, jairabe@uol.com.br, luiz@wcisp.com.br

**Abstract.** Due to the momentum of Industry 4.0 in various product and service sectors, academic and business investments in the development of new technologies in the logistics sector also stand out. Based on these trends, bibliographical research was carried out of articles dedicated to robotics with application in the logistics sector. Based on the bibliographic survey results, this work proposes a prototype of an autonomous terrestrial mobile robot that must go through corridors in specific layouts in logistics centres focusing on the aid of control tasks and management information for decision making. The main contribution is testing a para-analyzer algorithm based on non-classical logic such as Paraconsistent Annotated Logic $\mathcal{E}\tau$, as the decision-making tool to avoid obstacles.

**Keywords:** Autonomous Technology, Non-Classic Logic, Paraconsistent Logic.

## 1 Introduction

The "Digital Transformation" driven by Industry 4.0 is about to change countless companies and organizational models profoundly. This also applies in the manufacturing sector, where many companies will face various challenges from different perspectives, which four key components will govern: CPS (Cyber-Physical Systems), IoT (Internet of Things), Internet of Services, Intelligent Factory [1].

For all this, an increasing number of companies seek to automate their production lines, streamline processes, improve the transportation of inputs in the productive sector, streamline all logistics processes, and reduce costs.

AGV (Automatically Guided Vehicles) is an excellent example used in large logistics centres, implemented by already well-established technologies. In research carried out in this work, it was found that several lines of research seek to enable the implementation of these technologies both in the logistics sector and in the manufacturing sector.

Because of this scenario, the authors [2] conducted bibliographic research on multi-robot localization in a highly symmetrical environment. A team of robots, adequately coordinated, can perform complex tasks such as surveillance, monitoring, mapping, etc. The correct and reliable location concerning a known map is essential in these tasks
and represents one of the most significant mobile robotics challenges. They have done
several studies on emerging technologies for the location and displacement of multi
robots and propose a solution free of external locators such as GPS, as they highlight
the possibility of interrupting this communication indoors. For the multi-robot locomo-
tion solution, the authors propose to perform small asymmetric markings in an environ-
ment of symmetrical corridors, such as in a logistics centre. These markings are the
references used by an algorithm based on Cartesian information about the site. They
used the Pioneer P3DX differential robot prototype equipped with ultrasonic sensors to
avoid obstacles.

Regarding navigation techniques, the authors [3] used a differential robot prototype equipped with three front ultrasonic sensors and, through an algorithm based on Fuzzy logic, controls displacement and avoids collision with obstacles. According to the authors, the robot's direction is controlled by the rotation of the front wheels, and the rear freewheel serves only as support. The front wheels are also equipped with sensors whose information is transformed into the robot's angular and linear speed, which are necessary for positioning in a Cartesian system.

This article proposes applying the Paraconsistent Annotated Evidential Logic Eτ in a terrestrial mobile robot's navigation system in corridors of logistics centres and warehouses. This work's main objective is to develop a paraconsistent algorithm capable of avoiding obstacles and the possibility of integration with other navigation systems.

## 1.1 Paraconsistent Annotated Evidential Logic Eτ Applied in Robotics

The Paraconsistent Annotated Evidential Logic Eτ is a non-classical logics known as paraconsistent logics. Roughly, paraconsistent logic is a logic that serves as underlying logic for inconsistent but non-trivial theories. It has as atomic formulas propositions of the type *p*(*μ*, *λ*), where *p* is a proposition in a usual sense, and *μ*, *λ* ∈ [0, 1] (closed real unitary interval). The remaining formulas are obtained through Boolean combinations of connectives of the logic. Intuitively, *μ* indicates the degree of favourable evidence of *p*, and *λ* indicates the degree of unfavourable evidence of *p*. The reading of the *μ*, *λ*, depends on the most diverse applications considered and may change.

With these applications' effect, μ may be the degree of favourable belief, and λ may be the degree of belief contrary to proposition p. In some specific applications, μ may also indicate the probability expressed by p occurring and λ, the improbability expressed by p of occurring and other readings. An order relation is defined in [0, 1]²: (μ₁, λ₁) ≤ (μ₂, λ₂) ⇔ μ₁ ≤ μ₂ and λ₂ ≤ λ₁, forming a lattice, symbolized by τ, which is represented in Figure 1 [4].

Concerning the Paraconsistent Logic application, in 1999, the Emmy I autonomous mobile robot was built consisting of a mobile tower with a circular aluminium base of 30 cm diameter and 60 cm in height. The robot was designed on four overlapping electronic circuit boards separated by function in the control system to facilitate the visualization of each module's action in the robot's movement control [5]. The authors used two ultrasonic devices called Panasonic in front of the mobile robot to detect possible obstacles.
<figure><img src="image_3.png" /><figcaption>Fig. 1. The Lattice $\tau$ of decision-making</figcaption></figure>

Despite technical difficulties such as braking, lack of multi-speed and rotational tim-
ings between engines, they claim that the tests performed show that Paracontrol per-
formed well to solve problems related to robot navigation. The system demonstrated a
good ability to modify the robot's behaviour when unexpected changes occur in envi-
ronmental conditions.

In 2004 the Emmy II appeared with a significant reduction in the robot structure's height and with a diameter of 25 cm. Similarly, its predecessor also used two ultrasonic sensors to detect obstacles and programming based on the Annotated Paraconsistent Logic [6, 7]. According to the authors, the modifications made both in the structural parts and in the electronic circuit of the autonomous mobile robot allowed a significant improvement in the performance of the robot's movement. To show it, the robot was submitted to four performance tests in a square environment with a side of 3.3 m and with three internal obstacles. The authors recorded an average of 10 collisions per test and claimed that most were because of a deficiency of ultrasonic sensors, especially when obstacles are too close to the robot.

A more advanced version emerged in 2009 with the Emmy III prototype, whose
design was divided into three parts: mechanical subsystem, path planning and sensing.
The authors' main idea was to improve this version to expand the navigation capabilities
of the robot through a task with an origin and a destination to be fulfilled as a goal.

For this, they developed a computer system that receives information from sensors
distributed in the environment, maps the environment by coordinates, and transmits
commands to the robot's mechanical system during displacement. With the use of Par-
aconsistent Evidential Logic, the proposed sensing system aims to generate a degree
of favourable evidence in each environmental position. The degree of favourable evi-
dence is related to the sentence: "There is an obstacle in the position analyzed." Thus,
through the input information of the ultrasonic sensor, the distance between the sensor
and the obstacle, the angle between the horizontal axis of the environment and the di-
rection to the front of the sensor, the coordinate (X, Y) where the robot is about the
environment is determined. The authors performed three system performance tests and
presented Cartesian graphs with variations in the degree of favourable evidence, which
prove the correct functioning of the algorithm [8, 9].

1.2 Project Proposal Structure and Prototype of the Mobile Robot

To develop the autonomous terrestrial robot project, a structure consisting of corridors was elaborated to simulate a production line's environment. Based on proportional relationships was defined width of 80 cm for corridors of the production line. Figure 2 shows the prototype of the robot in the simulation environment. The simulation of the robot navigation performance in this environment was significant for the tests foreseen in the project.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Terrestrial autonomous robot in a logistic centre</figcaption></figure>

The project proposal is to build a prototype of an autonomous terrestrial mobile robot that will go through corridors of production lines, which will perform monitoring, tracking, and transport of materials. Figure 3 shows the overall structure and all the electrical and electronic devices that were used. Two front ultrasonic sensors monitor the robot that sends signals to the microcontroller, warning of possible obstacles. The left and right side sensors inform the lateral distances so that the robot maintains a central position in the corridor during displacement.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Prototype of the terrestrial robot</figcaption></figure>
The Atmega 2560 microcontroller will be programmed in C language, with technology embedded in the concepts of the Paraconsistent Annotated Evidential Logic $E_τ$. After receiving the information from the sensors, the paraconsistent algorithm will assist in decision-making. This information will be transformed into electrical signals and sent to the control devices of the traction motors and the servo motor that will control the direction of the autonomous terrestrial mobile robot, thus avoiding collisions during displacement. A differential of this prototype will be installing an LCD for monitoring sensor readings and the angle of the steering control servo motor. During the mobile robot's trajectory, these variables will be observed to make the necessary adjustments in the programming of the paraconsistent algorithm. We opted for a Lithium battery to equip the prototype because it is very light and with considerable energy storage capacity.

## 2 Methodology

Initially, the concepts of Paraconsistent Annotated Evidential Logic $E_τ$, through a built-in paraconsistent algorithm, will play a fundamental role in decision-making assistance [10].

Then, based on the lattice properties represented in Figure 1 and on the proposition: "The front of the robot is free", Table 1 was elaborated. The distances measured by the left and right sensors were converted, respectively, by the $μ$ and $λ$, through a normalization calculation of these values.

<table><caption>Table 1. Paraconsistent algorithm values.</caption><thead><tr><th rowspan="2">Situation</th><th colspan="4">Front Sensors</th><th rowspan="2">Degree of uncertainty</th><th rowspan="2">Setpoint (°)</th></tr><tr><th>Left (cm)</th><th>μ</th><th>Right (cm)</th><th>λ</th></tr></thead><tbody><tr><td>1</td><td>20</td><td>0,1</td><td>200</td><td>0</td><td>-0,9</td><td>-85,23</td></tr><tr><td>2</td><td>40</td><td>0,2</td><td>180</td><td>0,1</td><td>-0,7</td><td>-66,29</td></tr><tr><td>3</td><td>60</td><td>0,3</td><td>160</td><td>0,2</td><td>-0,5</td><td>-47,35</td></tr><tr><td>4</td><td>80</td><td>0,4</td><td>140</td><td>0,3</td><td>-0,3</td><td>-28,41</td></tr><tr><td>5</td><td>100</td><td>0,5</td><td>120</td><td>0,4</td><td>-0,1</td><td>-9,47</td></tr><tr><td>6</td><td>120</td><td>0,6</td><td>100</td><td>0,5</td><td>0,1</td><td>9,47</td></tr><tr><td>7</td><td>140</td><td>0,7</td><td>80</td><td>0,6</td><td>0,3</td><td>28,41</td></tr><tr><td>8</td><td>160</td><td>0,8</td><td>60</td><td>0,7</td><td>0,5</td><td>47,35</td></tr><tr><td>9</td><td>180</td><td>0,9</td><td>40</td><td>0,8</td><td>0,7</td><td>66,29</td></tr><tr><td>10</td><td>200</td><td>1</td><td>20</td><td>0,9</td><td>0,9</td><td>85,23</td></tr></tbody></table>

Then, the degree of uncertainty was calculated through the concepts of Paraconsistent Logic and provided precise and decisive values to determine the servo motor's
correct position for each situation under the presence of obstacles. In the last column of Table 1, the setpoint values of the servo motor already calculated are observed.

The following is presenting a programming excerpt performed in C language, which was divided into three main blocks. Frontal paraconsistent logic, lateral paraconsistent logic, and servo motor control. In the first block, the variables perceived by the left and right frontal sensors (sr_lf and sr_rf) have already gone through the normalization process and follow the concepts of paraconsistent logic. These values were converted into the variables (mi1 and la1) respectively in μ₁ and λ₁, as described in the Lattice of Figure 1. Next, the degree of uncertainty of the frontal decision was calculated and stored in the variable (deg_unc1). In the second block, the same process is repeated for the values read by the left and right side sensors and converted to (mi2 and la2), respectively μ₂ and λ₂. Then, the degree of uncertainty of the lateral decision is stored in the variable (deg_unc2). The third block constantly receives the values of the degree of frontal and lateral uncertainty variables, so the microcontroller, through logical constraints, controls the variable (sv_setPt) of decision-making of the steering servo of the autonomous terrestrial robot.

```c
// frontal paraconsistent logic//
mi1 = (sr_lf/50); // conversion of left front sensor reading into mi1 variable
la1 = (1-(sr_rf*0.02)); // conversion of right front sensor reading into la1 variable
deg_unc1 = ((mi1+la1)-1); // calculation of the degree of uncertainty of the frontal sensors
//sv_setPt = 538.42*gra_unc+551.5; // determination of the servo motor set point
sv_setPt = 300*gra_unc1+511.5;
// lateral paraconsistent logic//
mi2 = (sr.ls/80); // conversion of left lateral side reading into mi2 variable
la2 = (1-(sr_rs*0.0125)); // conversion of right side sensor reading into la1 variable
deg_unc2 = ((mi2+la2)-1); // calculation of the degree of uncertainty of the lateral sensors
//sv_setPt = 538.42*gra_unc+551.5; // determination of the servo motor set point
sv_setPt = 200*gra_unc2+511.5;
// servo motor control//
valor = map(sv_setPt, 0, 1023, 0, 180); // servo motor control
servo.write (valor);
ang_sv = gra_inc1*95; // calculation of the angle of the servo motor
```

## 3 Experiments and Results

According to the project's initial proposal, the next step was to perform the physical tests and submit the terrestrial robot autonomous to move in a structured environment. This environment has an 80 cm wide corridor and 3 m long, which simulates a supposed production environment. Table 2 shows the tests were repeated ten times at each of the three standardized speeds to verify performance and possible collisions with obstacles or collisions with the side barriers.
<table><caption>**Table 2.** Robot performance tests.</caption><thead><tr><th colspan="3">Number of collisions X speed</th><th rowspan="2">Type of Obstacle</th></tr><tr><th>0.25m/s</th><th>0.5m/s</th><th>0.75m/s</th></tr></thead><tbody><tr><td>0</td><td>3</td><td>2</td><td>Left side boundary</td></tr><tr><td>0</td><td>1</td><td>3</td><td>Right side boundary</td></tr><tr><td>0</td><td>4</td><td>5</td><td>Rectangular obstacle object</td></tr></tbody></table>

The robot will be able to perform tasks such as providing components for these product lines. Figure 4 shows this test with an obstacle on the robot's right side, perceived by the right front sensor (Sensor $\lambda_1$).

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Robot navigation test in a structured environment</figcaption></figure>

At point A of the red line, there is a tendency to deviate to the left, and at point B, there is already a perception of the proximity to the left lateral limit by the left lateral sensor (Sensor $\mu_2$). At point C, the two lateral sensors (Sensor $\mu_2$ and $\lambda_2$) are responsible for maintaining the robot's rectilinear trajectory and maintaining the robot's displacement in the middle of the corridor. This test was also performed with an obstacle on the robot's left side, which similarly swerved to correct its trajectory.

## 4 Discussion

The authors [2] conducted studies on emerging technologies in robotic navigation and researched multi-robot use in structured and highly symmetrical environments, such as logistics centres and industrial production lines. The GPS robotic navigation technology researched by the authors showed some deficiencies in internal communication. In such cases of lack of communication, the navigation system with a paraconsistent algorithm could be used in conjunction with GPS and avoid collisions with obstacles. In other studies, the authors [3] and the authors [8] built prototypes of differential robots with a free rear wheel only as support. In these cases, the steering is determined by the difference in the rotation of the traction wheels. This type of prototype is very subject
to inaccuracies because of slippages. With the placement of the servomotor instead of
the freewheel, as in the case of this work, there is a better performance in the movement
of the robot's prototype due to the accuracy of the servomotor combined with the para-
consistent algorithm. The results obtained in the tests at a speed of 0.25 m/s without
collisions with obstacles or collisions with the lateral limits showed to be very promis-
ing.

**5 Conclusion**

This article began with the proposal to apply paraconsistent logic to control an autono-
mous terrestrial mobile robot. Historically, research has revealed numerous studies with
the application of the Paraconsistent Annotated Evidential Logic Eτ in the development
of robotic navigation systems. The paraconsistent algorithm developed in the C lan-
guage showed the possibility of integration with other robotic navigation systems to act
in symmetrical environments, such as logistics centres and industrial production lines.
Another observation of this work was using a servomotor for robot steering control to
improve the accuracy of movements. As future work, Paraconsistent Logic can be in-
tegrated with other navigation systems, such as odometric navigation. The algorithm
developed showed the possibility of implementing the prototype in logistic centres,
performing component transport and monitoring tasks.

Acknowledgements

"This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) -Finance Code 001"

References

1. Preindl, R., Nikolopoulos, K., Litsiou, K. Transformation strategies for the supply chain: the impact of industry 4.0 and digital transformation. In *Supply Chain Forum: An International Journal* (pp. 1-9). Taylor & Francis (2020)

2. Abrate, F., Bona, B., Indri, M., Rosa, S., Tibaldi, F. Multirobot localization in highly symmetrical environments. *Journal of Intelligent & Robotic Systems*, 71(3-4), 403-421 (2013)

3. Chen, Y. S., Juang, J. G. Intelligent obstacle avoidance control strategy for wheeled mobile robot. In *2009 ICCAS-SICE* (pp. 3199-3204). IEEE (2009)

4. Abe, J. M. Silva Filho, João Inácio da. Celestino, Uanderson. Araújo, Hélio Corrêa de. Lógica Paraconsistente Anotada Evidencial Eτ. Comunicar (2011)
5. Da Silva Filho, J. I., Abe, J. M., Torres, C. R., César, A. M., Mário, M. C., Santos, A. M., ... & Salles, D. M. Emmy: Robô móvel autônomo paraconsistente-protótipo 1. Coleção Documentos, Série Lógica e Teoria da Ciência, IEA-USP (1999)

6. Torres, C. R., Abe, J. M., Torres, G. L. Sistema inteligente paraconsistente para controle de robôs móveis autônomos. Portuguese, MSc Dissertation, Universidade Federal de Itajubá-UNIFEI, Itajubá (2004)

7. Abe, J. M., Nakamatsu, K., Akama, S., & Ahrary, A. (2018). Handling Paraconsistency and Paracompleteness in Robotics. In *2018 Innovations in Intelligent Systems and Applications (INISTA)* (pp. 1-7). IEEE.

8. Torres, C. R., Abe, J. M., Lambert-Torres, G., da Silva Filho, J. I., & Martins, H. G. Autonomous mobile robot emmy iii. In *New Advances in Intelligent Decision Technologies* (pp. 317-327). Springer, Berlin, Heidelber (2009)

9. Torres, C. R., Lambert-Torres, G., Abe, J. M., & da Silva Filho, J. I. (2011). The sensing system for the autonomous mobile robot Emmy III. In *2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)* (pp. 2928-2933). Ieee.

10. Abe, J. M., Akama, S., Nakamatsu, K. Introduction to annotated logics: foundations for paracomplete and paraconsistent reasoning (Vol. 88). Springer (2015)