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Symmetry
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Symmetry/Asymmetry in Fuzzy Control
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Symmetry/Asymmetry in Fuzzy Control

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 1959

Special Issue Editors

Dr. José R. García-Martínez

E-Mail Website
Guest Editor
Faculty of Electronics and Communications Engineering, Universidad Veracruzana, Poza Rica 93390, Mexico
Interests: fuzzy logic; motion control; fuzzy control; microcontrollers; IOT
Dr. Edson Eduardo Cruz-Miguel

E-Mail Website
Guest Editor
Faculty of Electronics and Communications Engineering, Universidad Veracruzana, Poza Rica 93390, Mexico
Interests: position controller; artificial intelligence; intelligent control; fuzzy controller; genetic algorithm; optimized controller
Prof. Dr. Juvenal Rodriguez-Resendiz

E-Mail Website
Guest Editor
Facultad de Ingeniería, Universidad Autónoma de Querétaro, Santiago de Querétaro 76010, Mexico
Interests: robotics; biomedical applications; instrumentation and measurement; signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issue “Symmetry/Asymmetry in Fuzzy Control” aims to analyze the transformative impact of fuzzy logic on the evolution of control methodologies applied to complex and uncertain systems. This issue focuses on the integration in key areas such as dynamical systems, robotics, renewable energy, adaptive and autonomous systems, and motion control, highlighting how fuzzy control increases adaptability, stability, and accuracy in diverse applications. In particular, the concept of symmetry in fuzzy controllers is explored, examining how the symmetric structure can simplify the design and improve the performance of control systems. At the same time, asymmetry allows for addressing more specific and complex scenarios by tuning controller responses to dynamic and nonlinear conditions. This collection seeks to provide new perspectives to address control challenges in modern engineering by promoting interdisciplinary collaboration, combining theoretical advances with practical implementations. Through algorithm development, comparative analysis, and case studies based on real applications, this Special Issue aims to demonstrate the revolutionary potential of fuzzy control in the design and operation of intelligent systems adapted to a constantly changing world.

Dr. José R. García-Martínez
Dr. Edson Eduardo Cruz-Miguel
Prof. Dr. Juvenal Rodriguez-Resendiz
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • robotics
  • motion control
  • embedded systems
  • fuzzy control
  • fuzzy sets
  • fuzzy reasoning
  • real-time systems

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Published Papers (4 papers)

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Research

25 pages, 19451 KiB  
Article
Takagi–Sugeno–Kang Fuzzy Inference Tracking Controller for UAV Bicopter
by José R. Rivera-Ruiz, José R. García-Martínez, Trinidad Martínez-Sánchez, Edson E. Cruz-Miguel, Luis D. Ramírez-González, Omar A. Barra-Vázquez and Ákos Odry
Symmetry 2025, 17(5), 759; https://doi.org/10.3390/sym17050759 - 14 May 2025
Viewed by 236
Abstract
The UAV bicopter is a double-propeller system whose main objective is to stabilize a rod at a given angle by precisely controlling the rotation speed of each propeller. This mechanism generates asymmetric thrust forces that induce a torque on the bar, thus allowing [...] Read more.
The UAV bicopter is a double-propeller system whose main objective is to stabilize a rod at a given angle by precisely controlling the rotation speed of each propeller. This mechanism generates asymmetric thrust forces that induce a torque on the bar, thus allowing its pitch angle to be modified. Since its dynamics involve complex interactions between the thrust generated by the rotors, aerodynamic effects, and the pendulum behavior of the system, the bicopter is classified as a highly nonlinear system sensitive to external disturbances. To address this complexity, the implementation of a fuzzy Takagi–Sugeno–Kang (TSK) controller is proposed. This controller decomposes the nonlinear dynamics into multiple local linear models associated with a specific operating condition, such as different pitch angles and rotor speeds. The control strategy provides accurate trajectory tracking and effectively handles disturbances and varying conditions, making this approach a practical solution for both dynamic and uncertain environments. This strategy ensures precise trajectory tracking and demonstrates robust performance compared to other control methods, such as PID and LQR, which often struggle with disturbances and system nonlinearities. The TSK controller has proven its effectiveness in experimental trajectory tracking tests, achieving root mean square errors (RMSEs) of 0.2049, 0.3269, 0.3899, 0.3335, and 0.2494, which evaluate the average error in degrees of the system concerning the target position, for tracking trajectories of −10 to 10, −12 to 12, −15 to 15, −17 to 17, and −20 to 20 degrees, respectively. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)
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15 pages, 5325 KiB  
Article
Image-Tracking-Driven Symmetrical Steering Control with Long Short-Term Memory for Linear Charge-Coupled-Device-Based Two-Wheeled Self-Balancing Cart
by Yi-Jen Mon
Symmetry 2025, 17(5), 747; https://doi.org/10.3390/sym17050747 - 13 May 2025
Viewed by 136
Abstract
This paper presents a control framework for the image tracking of two-wheeled self-balancing carts, with the objective of achieving precise tracking control. Exploiting the remarkable memory capacity of the Long Short-Term Memory (LSTM) neural network for sequence signals, the framework conducts image memory [...] Read more.
This paper presents a control framework for the image tracking of two-wheeled self-balancing carts, with the objective of achieving precise tracking control. Exploiting the remarkable memory capacity of the Long Short-Term Memory (LSTM) neural network for sequence signals, the framework conducts image memory judgment and memorization, aiming to enhance control accuracy. After the training phase, comprehensive simulations and real-world experiments are carried out based on the established model to verify the effectiveness and practicality of the proposed control strategy. The system utilizes the TSL1401 linear array CCD lens to detect black tapes on the ground and identify and memorize surrounding images. Through the establishment of a continuous set of training sample points, the LSTM network is trained using Python and TensorFlow. This training process optimizes the network’s weights and generates weight files, which can be readily converted into machine code for physical implementation. Initially, the effectiveness of the control law is verified through simulating the symmetrical steering control of the two-wheeled cart. The simulation results demonstrate the validity of the proposed design method and its superior performance. Finally, a physical two-wheeled self-balancing cart is developed to further validate the feasibility of the framework. Experimental results confirm that this method is highly effective, demonstrating robust image tracking capabilities and optimal tracking performance. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)
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17 pages, 281 KiB  
Article
Fuzzy Double Yang Transform and Its Application to Fuzzy Parabolic Volterra Integro-Differential Equation
by Atanaska Georgieva, Slav I. Cholakov, Maria Vasileva and Yordanka Gudalova
Symmetry 2025, 17(4), 606; https://doi.org/10.3390/sym17040606 - 16 Apr 2025
Viewed by 190
Abstract
This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All [...] Read more.
This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All of the new results are applied to find an analytical solution to the fuzzy parabolic Volterra integro-differential equation (FPVIDE) with a suitably selected memory kernel. In addition, a numerical example is provided to illustrate how the proposed method might be helpful for solving FPVIDE utilizing symmetric triangular fuzzy numbers. Compared with other symmetric transforms, we conclude that our new approach is simpler and needs less calculations. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)
29 pages, 3567 KiB  
Article
Kinematic Fuzzy Logic-Based Controller for Trajectory Tracking of Wheeled Mobile Robots in Virtual Environments
by José G. Pérez-Juárez, José R. García-Martínez, Alejandro Medina Santiago, Edson E. Cruz-Miguel, Luis F. Olmedo-García, Omar A. Barra-Vázquez and Miguel A. Rojas-Hernández
Symmetry 2025, 17(2), 301; https://doi.org/10.3390/sym17020301 - 17 Feb 2025
Cited by 1 | Viewed by 788
Abstract
Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller [...] Read more.
Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller with a symmetric distribution of fuzzy numbers is proposed and designed for implementation in the kinematic model of a non-holonomic mobile robot. The symmetry in the distribution of triangular fuzzy numbers contributes to a balanced response to disturbances and minimizes systematic errors in direction estimation. Additionally, it improves the system’s adaptability to various reference paths, ensuring accurate tracking and optimized performance in robot navigation. Furthermore, this fuzzy logic-based controller emulates the behavior of a classic PID controller by offering a robust and flexible alternative to traditional methods. A virtual environment was also developed using the UNITY platform to evaluate the performance of the fuzzy controller. The results were evaluated by considering the average tracking error, maximum error, steady-state error, settling time, and total distance traveled, emphasizing the trajectory error. The circular trajectory showed high accuracy with an average error of 0.0089 m, while the cross trajectory presented 0.01814 m, reflecting slight deviations in the turns. The point-to-point trajectory registered a more significant error of 0.9531 m due to abrupt transitions, although with effective corrections in a steady state. The simulation results validate the robustness of the proposed fuzzy controller, providing quantitative insights into its precision and efficiency in a virtual environment, and demonstrating the effectiveness of the proposal. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)
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