A Robust Fuzzy Fractional Order PID Design Based On Multi-Objective Optimization For Rehabilitation Device Control

Intissar Zaway, Rim Jallouli-Khlif, Boutheina Maalej, Nabil Derbel

Abstract


In this context, Fuzzy Fractional Order Proportional Integral Derivative (FOPID-FLC) controllers are emerged as efficient approaches due to their flexibility and ability to handle nonlinearities and uncertainties. This paper proposes the use of a FOPID-FLC controller for a two-degree-of-freedom (2-DOF) lower limb exoskeleton. Our proposal is based on an enhanced control approach that combines fuzzy logic advantages and fractional calculus benefits. Contrary to popular existing methods, that use the FLC to tune the FOPID  parameters, the FLC in this work is used to generate the system torque depending on patient morphology. Indeed, our fundamental contribution is to design and implement an enhanced FOPID-FLC that achieves an adequate optimal control based on system rules composed of optimal torques and input data. The fractional calculus is approximated using successive first order filters. Next, a multi-objective optimization is established for the tuning of each FOPID parameters. Finally, the FLC is used to adjust the torque depending on the kid's age. The effectiveness of the proposed controller in various scenarios is validated based on numerical simulations. Extensive analyses prove that the FOPID-FLC outperforms the FOPID with a 90\% of improvement in terms of error performance indices and 20\% of improvement for the control action. Moreover, the controller exhibits improved robustness against uncertainties and disturbances encountered in rehabilitation environments.

Keywords


Rehabilitation robot- Fractional order PID controller- Fuzzy logic controller- Optimization- Genetic algorithm- Robustness

Full Text:

PDF

References


R. Pham, B. W. Mol, J. Gecz, A. H. MacLennan, S. C. MacLennan, M. A. Corbett, C.L. van Eyk, D. L. Webber, L. J. Palmer, and J. G. Berry, “Definition and diagnosis of cerebral palsy in genetic studies: a systematic review”. Developmental Medicine & Child Neurology, vol. 62, no. 9, pp. 1024-1030, 2020.

M. Sadowska, B. Sarecka-Hujar, and I. Kopyta, “Cerebral palsy: current opinions on definition, epidemiology, risk factors, classification and treatment options,” Neuropsychiatric disease and treatment, pp. 1505-1518, 2020.

D. R. Patel, M. Neelakantan, K. Pandher, and J. Merrick, “Cerebral palsy in children: a clinical overview,” Translational pediatrics, vol. 9, no. 1, p. S125, 2020.

A. Chauhan, M. Singh, N. Jaiswal, A. Agarwal, J. K. Sahu, and M. Singh, “Prevalence of cerebral palsy in Indian children: a systematic review and meta-analysis,” The Indian Journal of Pediatrics, vol. 86, pp. 1124-1130, 2019.

S. J. Hollung, I. J. Bakken, T. Vik, S. Lydersen, R. Wiik, K. M. Aaberg, and G. L. Andersen, “Comorbidities in cerebral palsy: a patient registry study,” Developmental Medicine & Child Neurology, vol. 62, no. 1, pp. 97-103, 2020.

K. Vitrikas, H. Dalton, and D. Breish, “Cerebral palsy: an overview,” American family physician, vol. 101, no. 4, pp. 213-220, 2020.

P. Illavarason, J. Arokia Renjit, P. Mohan Kumar, “Medical diagnosis of cerebral palsy rehabilitation using eye images in machine learning techniques,” Journal of medical systems, vol. 43, no. 8, p. 278, 2019.

D. R. Patel, M. Neelakantan, K. Pandher, and J. Merrick, “Cerebral palsy in children: a clinical overview,” Translational pediatrics, vol. 9, no. 1, p. S125, 2020.

M. A. Furtado, K. M. Ayupe, I. S. Christovao, R. R. Sousa Junior, P. Rosenbaum, A. C. Camargos, and H. R. Leite, “Physical therapy in children with cerebral palsy in Brazil: a scoping review,” Developmental Medicine & Child Neurology, vol. 64, no. 5, pp. 550-560, 2022.

B. E. Gibson, G. Teachman, V. Wright, D. Fehlings, N. L. Young, and P. McKeever, “Children’s and parents’ beliefs regarding the value of walking: rehabilitation implications for children with cerebral palsy,” Child: care, health and development, vol. 38, no. 1, pp. 61-69, 2012.

H. A. Krebs and B. T. Volpe, Rehabilitation robotics., Handbook of clinical neurology, vol. 110, pp. 283-294, 2013.

V. Khoshdel and A. Akbarzadeh Tootoonchi, “Robust impedance control for rehabilitation robot,” Modares Mechanical Engineering, vol. 15, no. 8, pp. 429-437, 2015.

Y. Sun, Y. Tang, J. Zheng, D. Dong, X. Chen, and L. Bai, “From sensing to control of lower limb exoskeleton: A systematic review,” Annual Reviews in Control, 2022.

A. Te Velde, C. Morgan, I. Novak, E. Tantsis, and N. Badawi, “Early diagnosis and classification of cerebral palsy: an historical perspective and barriers to an early diagnosis,” Journal of Clinical Medicine, vol. 8, no. 10, p. 1599, 2019.

S. Bhardwaj, A. A. Khan, and M. Muzammil, “Lower limb rehabilitation robotics: The current understanding and technology,” Work, vol. 69, no. 3, pp. 775-793, 2021.

L. Zhang, J. Li, M. Dong, B. Fang, Y. Cui, S. Zuo, and K. Zhang, “Design and workspace analysis of a parallel ankle rehabilitation robot (PARR),” Journal of healthcare engineering, vol. 2019, 2019.

L. F. Aycardi, C. A. Cifuentes, M. Munera, C. Bayon, O. Ramirez, S. Lerma, A. Frizera, and E. Rocon, “Evaluation of biomechanical gait parameters of patients with Cerebral Palsy at three different levels of gait assistance using the CPWalker,” Journal of neuroengineering and rehabilitation, vol. 16, pp. 1-9, 2019.

N. Tejima, “Rehabilitation robotics: a review,” Advanced Robotics, vol. 14, no. 7, pp. 551-564, 2001.

H. M. Qassim and W. Z. Wan Hasan, “A review on upper limb rehabilitation robots,” Applied Sciences, vol. 10, no. 19, p. 6976, 2020.

I. Rojek, D. Mikołajewski, E. Dostatni, and J. Kopowski, “Specificity of 3D Printing and AI-Based Optimization of Medical Devices Using the Example of a Group of Exoskeletons,” Applied Sciences, vol. 13, no. 2, p. 1060, 2023.

T. Tsabedze, E. Hartman, and J. Zhang, “A compact, compliant, and biomimetic robotic assistive glove driven by twisted string actuators,” International Journal of Intelligent Robotics and Applications, vol. 5, pp. 381-394, 2021.

J. Allington, S. J. Spencer, J. Klein, M. Buell, D. J. Reinkensmeyer, and J. Bobrow, “Supinator extender (SUE): a pneumatically actuated robot for forearm/wrist rehabilitation after stroke,” 2011 annual international conference of the IEEE engineering in medicine and biology society, pp. 1579-1582, 2011.

M. Bernhardt, M. Frey, G. Colombo, and R. Riener, “Hybrid forceposition control yields cooperative behavior of the rehabilitation robot LOKOMAT,” 9th International Conference on Rehabilitation Robotics, pp. 536-539, 2005.

A. R. Alashram, G. Annino, and E. Padua, “Robot-assisted gait training in individuals with spinal cord injury: A systematic review for the clinical effectiveness of Lokomat,” Journal of Clinical Neuroscience, vol. 91, pp. 260-269, 2021.

L. Marchal-Crespo and R. Riener, “Technology of the Robotic Gait Orthosis Lokomat,” Neurorehabilitation Technology, pp. 665-681, Cham: Springer International Publishing, 2022.

B. C. Conner, N. M. Remec, and Z. F. Lerner, “Is robotic gait training effective for individuals with cerebral palsy?” A systematic review and meta-analysis of randomized controlled trials. Clinical Rehabilitation, vol. 36, no. 7, pp. 873-882, 2022.

R. Riener, M. Frey, M. Bernhardt, T. Nef, and G. Colombo, “Humancentered rehabilitation robotics,” 9th International Conference on Rehabilitation Robotics, pp. 319-322, 2005, June.

P. Chotikunnan and Y. Pititheeraphab, “Adaptive P Control and Adaptive Fuzzy Logic Controller with Expert System Implementation for Robotic Manipulator Application,” Journal of Robotics and Control (JRC), vol. 4, no. 2, pp. 217-226, 2023.

A. E. Hramov, V. A. Maksimenko, and A. N. Pisarchik, “Physical principles of brain–computer interfaces and their applications for rehabilitation, robotics and control of human brain states,” Physics Reports, vol. 918, pp. 1-133, 2021.

W. S. Harwin, T. Rahman, and R. A. Foulds, “A review of design issues in rehabilitation robotics with reference to North American research,” IEEE Transactions on Rehabilitation Engineering, vol. 3, no. 1, pp. 3-13, 1995.

X. Liang, H. Wang, and Y. Zhang, “Adaptive nonsingular terminal sliding mode control for rehabilitation robots,” Computers and Electrical Engineering, vol. 99, p. 107718, 2022.

B. Li, G. Li, Y. Sun, G. Jiang, J. Kong, and D. Jiang, “A review of rehabilitation robot,” 2017 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), pp. 907-911, 2017.

N. Robinson, R. Mane, T. Chouhan, and C. Guan, “Emerging trends in BCI-robotics for motor control and rehabilitation,” Current Opinion in Biomedical Engineering, vol. 20, p. 100354, 2021.

Q. Liu, J. Zuo, C. Zhu, and S. Q. Xie, “Design and control of soft rehabilitation robots actuated by pneumatic muscles: State of the art,” Future Generation Computer Systems, vol. 113, pp. 620-634, 2020.

H. M. Qassim and W. Z. Wan Hasan, “A review on upper limb rehabilitation robots,” Applied Sciences, vol. 10, no. 19, p. 6976, 2020.

Q. Ai, Z. Liu, W. Meng, Q. Liu, and S. Q. Xie, “Machine learning in robot assisted upper limb rehabilitation: A focused review,” IEEE Transactions on Cognitive and Developmental Systems, 2021.

D. Shi, W. Zhang, W. Zhang, L. Ju, and X. Ding, “Human-centred adaptive control of lower limb rehabilitation robot based on human–robot interaction dynamic model,” Mechanism and Machine Theory, vol. 162, p. 104340, 2021.

D. Shi, L. Wang, Y. Zhang, W. Zhang, H. Xiao, and X. Ding, “Review of human—robot coordination control for rehabilitation based on motor function evaluation,” Frontiers of Mechanical Engineering, vol. 17, no. 2, p. 28, 2022.

H. J. Asl, M. Yamashita, T. Narikiyo, and M. Kawanishi, “Field-based assist-as-needed control schemes for rehabilitation robots,” IEEE/ASME Transactions on Mechatronics, vol. 25, no. 4, pp. 2100-2111, 2020.

D. Shi, L. Wang, Y. Zhang, W. Zhang, H. Xiao, and X. Ding, “Review of human—robot coordination control for rehabilitation based on motor function evaluation,” Frontiers of Mechanical Engineering, vol. 17, no. 2, vol. 28, 2022.

H. M. Qassim and W. Z. Wan Hasan, “A review on upper limb rehabilitation robots,” Applied Sciences, vol. 10, no. 19, p. 6976, 2020.

F. Yakub, A. Z. M. Khudzari, and Y. Mori, “Recent trends for practical rehabilitation robotics, current challenges and the future,” International Journal of Rehabilitation Research, vol. 37, no. 1, pp. 9-21, 2014.

L. Liu, L. Zhang, G. Pan, and S. Zhang, “Robust yaw control of autonomous underwater vehicle based on fractional-order PID controller,” Ocean Engineering, vol. 257, p. 111493, 2022.

B. Hekimoglu, “Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm,” IEEE Access, vol. 7, pp. 38100-38114, 2019.

S. M. A. Altbawi, A. S. B. Mokhtar, T. A. Jumani, I. Khan, N. N. Hamadneh, and A. Khan, “Optimal design of Fractional order PID controller based Automatic voltage regulator system using gradient-based optimization algorithm,” Journal of King Saud University-Engineering Sciences, 2021.

A. A. Dastjerdi, B. M. Vinagre, Y. Chen, and S. H. HosseinNia, “Linear fractional order controllers; A survey in the frequency domain,” Annual Reviews in Control, vol. 47, pp. 51-70, 2019.

I. Ali, A. Rasheed, M. S. Anwar, M. Irfan, and Z. Hussain, “Fractional calculus approach for the phase dynamics of Josephson junction,” Chaos, Solitons and Fractals, vol. 143, p. 110572, 2021.

A. Ajoudani, A. M. Zanchettin, S. Ivaldi, A. Albu-Schaffer, K. Kosuge, and O. Khatib, “Progress and prospects of the human–robot collaboration,” Autonomous Robots, vol. 42, pp. 957-975, 2018.

H. Zeng, Y. Shen, X. Hu, A. Song, B. Xu, H. Li, Y. Wang, and P. Wen, “Semi-autonomous robotic arm reaching with hybrid gaze–brain machine interface,” Frontiers in neurorobotics, vol. 13, p. 111, 2020.

H. Wang and J. Lu “Research on fractional order fuzzy PID control of the pneumatic-hydraulic upper limb rehabilitation training system based on PSO,” International Journal of Control, Automation and Systems, vol. 20, no. 1, pp. 310-320, 2022.

B. Wang, T. Yu, T. Zhou, L. Wang, J. Li, and N. Xie, “Fractional order PIλ Dµ for tracking control of a novel rehabilitation robot based on IIMO-BP neural network algorithm,” Journal of Mechanics in Medicine and Biology, p. 2350010, 2022.

M. R. Islam, M. Rahmani, M. H. Rahman, “A novel exoskeleton with fractional sliding mode control for upper limb rehabilitation,” Robotica, vol. 38, no. 11, pp. 2099-2120, 2020.

M. Mariappan, M. R. Arshad, R. Akmeliawati, and C. S. Chong, Control Engineering in Robotics and Industrial Automation, Springer International Publishing, 2022.

G. Masengo, X. Zhang, R. Dong, A. B. Alhassan, K. Hamza, and E. Mudaheranwa, “Lower limb exoskeleton robot and its cooperative control: A review, trends, and challenges for future research,” Frontiers in Neurorobotics, vol. 16, 2023.

J. Yang, Z. Zhao, C. Du, W. Wang, Q. Peng, J. Qiu, and G. Wang, “The realization of robotic neurorehabilitation in clinical: use of computational intelligence and future prospects analysis,” Expert Review of Medical Devices, vol. 17, no. 12, pp. 1311-1322, 2020.

I. M. Batiha, J. Oudetallah, A. Ouannas, A. A. Al-Nana, and I. H. Jebril, “Tuning the fractional-order PID-controller for blood glucose level of diabetic patients,” Int. J. Advance Soft Compu. Appl, vol. 13, no. 2, pp. 1-10, 2021.

B. N. Kommula and V. R. Kota, “Design of MFA-PSO based fractional order PID controller for effective torque controlled BLDC motor,” Sustainable Energy Technologies and Assessments, vol. 49, p. 101644, 2022.

H. Peng, J. Zhou, and R. Song, “An Adaptive Fractional-order Admittance Model for a Lower Limb Rehabilitation Robot,” 2022 International Conference on Advanced Robotics and Mechatronics (ICARM), pp. 649-654, 2022.

I. Birs, C. Muresan, I. Nascu, and C. Ionescu, “A survey of recent advances in fractional order control for time delay systems,” IEEE Access, vol. 7, pp. 30951-30965, 2019.

R. Fareh, S. Khadraoui, M. Y. Abdallah, M. Baziyad, and M. Bettayeb, “Active disturbance rejection control for robotic systems: A review,” Mechatronics, vol. 80, p. 102671, 2021.

A. A. Moshaii, M. M. Moghaddam, and V. D. Niestanak, “Fuzzy sliding mode control of a wearable rehabilitation robot for wrist and finger,” Industrial Robot: the international journal of robotics research and application, vol. 46, no. 6, pp. 839-850, 2019.

N. El Ouanjli, S. Motahhir, A. Derouich, A. El Ghzizal, A. Chebabhi, and M. Taoussi, “Improved DTC strategy of doubly fed induction motor using fuzzy logic controller,” Energy Reports, vol. 5, pp. 271-279, 2019.

P. Chotikunnan, R. Chotikunnan, A. Nirapai, A. Wongkamhang, P. Imura, and M. Sangworasil, ”Optimizing Membership Function Tuning for Fuzzy Control of Robotic Manipulators Using PID-Driven Data Techniques,” Journal of Robotics and Control (JRC), vol. 4, no. 2, 2023.

N. C. Patel, B. K. Sahu, D. P. Bagarty, P. Das, and M. K. Debnath, “A novel application of ALO-based fractional order fuzzy PID controller for AGC of power system with diverse sources of generation,” The International Journal of Electrical Engineering and Education, vol. 58, no. 2, pp. 465-487, 2021.

Y. Bouteraa, I. B. Abdallah, A. ElMogy, A. Ibrahim, U. Tariq, and T. Ahmad, “A fuzzy logic architecture for rehabilitation robotic systems,” International Journal of Computers Communications and Control, vol. 15, no. 4, 2020.

A. K. Tanyildizi, O. Yakut, B. Tas¸ar, and A. B. Tatar, “Control of twindouble pendulum lower extremity exoskeleton system with fuzzy logic control method,” Neural Computing and Applications, vol. 33, pp. 8089-8103, 2021.

N. Aliman, R. Ramli, S. M. Haris, M. S. Amiri, and M. Van, “A robust adaptive-fuzzy-proportional-derivative controller for a rehabilitation lower limb exoskeleton,” Engineering Science and Technology, an International Journal, vol. 35, p. 101097, 2022.

R. Sharma, S. Bhasin, P. Gaur, and D. Joshi, “A switching-based collaborative fractional order fuzzy logic controllers for robotic manipulators,” Applied Mathematical Modelling, vol. 73, pp. 228-246, 2019.

H. Delavari and R. Jokar, “Intelligent fractional-order active faulttolerant sliding mode controller for a knee joint orthosis,” Journal of Intelligent & Robotic Systems, vol. 102, no. 2, p. 39, 2021.

R. Sharma, P. Gaur, S. Bhatt, and D. Joshi, “Optimal fuzzy logic-based control strategy for lower limb rehabilitation exoskeleton,” Applied Soft Computing, vol. 105, p. 107226, 2021.

N. Mirrashid, U. ˚ T. E. Alibeiki, and S. M. Rakhtala, “Development and control of an upper limb rehabilitation robot via ant colony optimizationPID and fuzzy-PID controllers,” International Journal of Engineering, vol. 35, no. 8, pp. 1488-1493, 2022.

M. Ghasemi, A. Foroutannia, and F. Nikdelfaz, “A PID controller for synchronization between master-slave neurons in fractional-order of neocortical network model,” Journal of Theoretical Biology, vol. 556, p. 111311, 2023.

N. Aliman, R. Ramli, S. M. Haris, M. S. Amiri, and M. Van, “A robust adaptive-fuzzy-proportional-derivative controller for a rehabilitation lower limb exoskeleton,” Engineering Science and Technology, an International Journal, vol. 35, p. 101097, 2022.

S. Q. Xie and P. K. Jamwal, “An iterative fuzzy controller for pneumatic muscle driven rehabilitation robot,” Expert Systems with Applications, vol. 38, no. 7, pp. 8128-8137, 2011.

J. Wu, P. D. Loprinzi, and Z. Ren, “The Rehabilitative effects of virtual reality games on balance performance among children with cerebral palsy: A meta-analysis of randomized controlled trials,” International journal of environmental research and public health, vol. 16, no. 21, p. 4161, 2019.

M. S. Ju, C. C. Lin, D. H. Lin, I. S. Hwang, and S. M. Chen, “A rehabilitation robot with force-position hybrid fuzzy controller: hybrid fuzzy control of rehabilitation robot,” IEEE transactions on neural systems and rehabilitation engineering, vol. 13, no. 3, pp. 349-358, 2005.

J. Yang, H. Su, Z. Li, D. Ao, and R. Song, “Adaptive control with a fuzzy tuner for cable-based rehabilitation robot,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 865-875, 2016.

A. Demofonti, G. Carpino, L. Zollo, and M. J. Johnson, “Affordable robotics for upper limb stroke rehabilitation in developing countries: a systematic review,” IEEE Transactions on Medical Robotics and Bionics, vol. 3, no. 1, pp. 11-20, 2021.

A. Chevalier, C. Francis, C. Copot, C. M. Ionescu, and R. De Keyser “Fractional-order PID design: Towards transition from state-of-art to state-of-use,” ISA transactions, vol. 84, pp. 178-186, 2019.

T. Aleksei, P. Eduard, and B. Juri, “A flexible MATLAB tool for optimal fractional-order PID controller design subject to specifications,” Proceedings of the 31st Chinese Control Conference, pp. 4698-4703, 2012.

O. Abu Arqub, “Numerical algorithm for the solutions of fractional order systems of Dirichlet function types with comparative analysis,” Fundamenta Informaticae, vol. 166, no. 2, pp. 111-137, 2019.

D. Xue, C. Zhao, and Y. Chen, “A modified approximation method of fractional order system,” 2006 international conference on mechatronics and automation, pp. 1043-1048, 2006.

F. Xie, Z. Yang, C. Yang, Y. Chen, B. Zhang, and D. Qiu, “Construction and Experimental Realization of the Fractional-order Transformer by Oustaloup Rational Approximation Method,” IEEE Transactions on Circuits and Systems II: Express Briefs, 2022.

A. T. Mohamed, M. F. Mahmoud, L. A. Said, and A. G. Radwan, “Design of FOPID controller for a DC motor using approximation techniques,” 2019 Novel Intelligent and Leading Emerging Sciences Conference, pp. 142-145, 2019, October.

K. Bingi, R. Ibrahim, M. N. Karsiti, S. M. Hassam, and V. R. Harindran, “Frequency response based curve fitting approximation of fractionalorder PID controllers,” International Journal of Applied Mathematics and Computer Science, vol. 29, no. 2, pp. 311-326, 2019.

S. Sharma and A. J. Obaid, “Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox,” Journal of Interdisciplinary Mathematics, vol. 23, no. 4, pp. 843-849, 2020.

A. Soukkou, M. C. Belhour, and S. Leulmi, “Review, design, optimization and stability analysis of fractional-order PID controller,” International Journal of Intelligent Systems and Applications, vol. 8, no. 7, p. 73, 2016.

Y. Chen, I. Petras, and D. Xue, “Fractional order control-a tutorial,” 2009 American control conference, pp. 1397-1411, 2009.

A. A. Jamil, W. F. Tu, S. W. Ali, Y. Terriche, and J. M. Guerrero, “Fractional-order PID controllers for temperature control: A review,” Energies, vol. 15, no. 10, p. 3800, 2022.

B. Maalej, R. J. Khlif, C. Mhiri, M. H. Elleuch, and N. Derbel, “L1 Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems,” Mathematical Problems in Engineering, vol. 2021, pp. 1-14, 2021.

S. N. Sivanandam, S. N. Deepa, S. N. Sivanandam, and S. N. Deepa, “Genetic algorithm optimization problems,” Introduction to genetic algorithms, pp. 165-209, 2008.

M. Z. Abd Elrehim, M. A. Eid, and M. G. Sayed, “Structural optimization of concrete arch bridges using Genetic Algorithms,” Ain Shams Engineering Journal, vol. 10, no. 3, pp. 507-516, 2019.

I. Zaway, R. Jallouli-Khlif, B. Maalej, H. Medhaffar, and N. Derbel, “Multi-objective Fractional Order PID Controller Optimization for Kid’s Rehabilitation Exoskeleton,” International Journal of Robotics and Control Systems, vol. 3, no. 1, pp. 32-49, 2023.

M. A. Faraj, B. Maalej, N. Derbel, and O. Naifar, “Adaptive FractionalOrder Super-Twisting Sliding Mode Controller for Lower Limb Rehabilitation Exoskeleton in Constraint Circumstances Based on the Grey Wolf Optimization Algorithm,” Mathematical Problems in Engineering, 2023.




DOI: https://doi.org/10.18196/jrc.v4i3.18411

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Intissar Zaway, Rim Jallouli-Khlif, Boutheina Boutheina Maalej Boutheina Maalej, Nabil Derbel

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 

Journal of Robotics and Control (JRC)

P-ISSN: 2715-5056 || E-ISSN: 2715-5072
Organized by Peneliti Teknologi Teknik Indonesia
Published by Universitas Muhammadiyah Yogyakarta in collaboration with Peneliti Teknologi Teknik Indonesia, Indonesia and the Department of Electrical Engineering
Website: http://journal.umy.ac.id/index.php/jrc
Email: jrcofumy@gmail.com

Kuliah Teknik Elektro Terbaik