{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T13:23:14Z","timestamp":1769088194435,"version":"3.49.0"},"reference-count":32,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Neurorobot."],"abstract":"<jats:p>Prosthetic knee joints are essential assistive technologies designed to replicate natural gait and improve mobility for individuals with lower-limb loss. This study presents a comprehensive nonlinear dynamic model of a two-degree-of-freedom prosthetic knee joint and introduces three robust nonlinear control strategies: Integral Sliding Mode Control, Conditional Super-Twisting Sliding Mode Control, and Conditional Adaptive Positive Semidefinite Barrier Function-based Sliding Mode Control. These controllers are designed to address the challenges associated with nonlinear joint dynamics, external disturbances, and modeling uncertainties during locomotion. To optimize control performance, the gain parameters of each controller were fine-tuned using Red Fox Optimization, a metaheuristic algorithm inspired by the intelligent hunting behavior of red foxes. Stability analysis is conducted using Lyapunov theory, and control effectiveness is evaluated through simulations in MATLAB\/Simulink and validated via hardware-in-the-loop testing using a C2000 Delfino F28379D microcontroller. Among the three controllers, the CoBA-based approach demonstrated the highest tracking accuracy, fastest convergence, and smoothest torque profile. The close agreement between simulation and experimental results confirms the practical applicability of the proposed control framework, offering a promising solution for intelligent and adaptive prosthetic knee systems.<\/jats:p>","DOI":"10.3389\/fnbot.2025.1681298","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T06:44:13Z","timestamp":1768977853000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Innovative approach of nonlinear controllers design for prosthetic knee performance"],"prefix":"10.3389","volume":"19","author":[{"given":"Atif","family":"Rehman","sequence":"first","affiliation":[{"name":"School of Interdisciplinary Engineering and Sciences, National University of Sciences and Technology","place":["Islamabad, Pakistan"]}]},{"given":"Rimsha","family":"Ghias","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Computer Science, National University of Sciences and Technology","place":["Islamabad, Pakistan"]}]},{"given":"Hammad Iqbal","family":"Sherazi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Qassim University","place":["Buraydah, Saudi Arabia"]}]},{"given":"Nadia","family":"Sultan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Center of Excellence in AI, Bahria School of Engineering & Applied Sciences","place":["Islamabad, Pakistan"]}]}],"member":"1965","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"108051","DOI":"10.1016\/j.est.2023.108051","article-title":"Barrier function based adaptive sliding mode controller for the hybrid energy storage system of plugin hybrid electric vehicles","volume":"72","author":"Ahmed","year":"2023","journal-title":"J. Energy Storage"},{"key":"B2","doi-asserted-by":"publisher","first-page":"103201","DOI":"10.1016\/j.est.2021.103201","article-title":"Conditioned-based robust nonlinear control of plug-in hybrid electric vehicle with saturated control actions","volume":"43","author":"Ahmed","year":"2021","journal-title":"J. Energy Storage"},{"key":"B3","doi-asserted-by":"publisher","first-page":"140270","DOI":"10.1109\/ACCESS.2025.3595958","article-title":"A gradient-based optimization algorithm for optimal control problems with general conformable fractional derivatives","volume":"13","author":"Alaia","year":"2025","journal-title":"IEEE Access"},{"key":"B4","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/B978-0-323-03735-8.50032-7","article-title":"\u201cAmputations,\u201d","volume-title":"Core Knowledge in Orthopaedics: Foot and Ankle","author":"Assal","year":"2007"},{"key":"B5","unstructured":"Assal\n              M.\n            \n            \n              Gordon\n              E.\n            \n          \n          Amputations\n          \n          2023"},{"key":"B6","doi-asserted-by":"crossref","first-page":"517","DOI":"10.23919\/ACC.2017.7963005","article-title":"\u201cRobust control of a powered transfemoral prosthesis device with experimental verification,\u201d","volume-title":"2017 American Control Conference (ACC)","author":"Azimi","year":"2017"},{"key":"B7","doi-asserted-by":"publisher","first-page":"89","DOI":"10.3390\/prosthesis7040089","article-title":"Comparing microprocessor-controlled and non-microprocessor-controlled prosthetic knees across all classified domains of the icf model: A pragmatic clinical trial","volume":"7","author":"Bosman","year":"2025","journal-title":"Prosthesis"},{"key":"B8","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.trc.2002.10.002","article-title":"Hardware-in-the-loop simulation","volume":"12","author":"Bullock","year":"2004","journal-title":"Transport. Res. Part C: Emerg. Technol"},{"key":"B9","volume-title":"Phantom Limb: Amputation, Embodiment, and Prosthetic Technology, volume 16","author":"Crawford","year":"2014"},{"key":"B10","doi-asserted-by":"publisher","first-page":"1894","DOI":"10.3390\/sym15101894","article-title":"Robust fault estimation and tolerant control for uncertain takagi\u2014sugeno fuzzy systems","volume":"15","author":"Dhahri","year":"2023","journal-title":"Symmetry"},{"key":"B11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/ETECTE63967.2024.10823894","article-title":"\u201cOptimized nonlinear control strategies for hybrid electric vehicles integrating photoelectrochemical and photovoltaic cells with fuel cells, batteries, and supercapacitors,\u201d","volume-title":"2024 3rd International Conference on Emerging Trends in Electrical, Control, and Telecommunication Engineering (ETECTE)","author":"Ghias","year":"2024"},{"key":"B12","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.mpsur.2018.12.008","article-title":"Amputation and rehabilitation","volume":"37","author":"Guest","year":"2019","journal-title":"Surgery"},{"key":"B13","doi-asserted-by":"publisher","first-page":"102443","DOI":"10.1016\/j.mechatronics.2020.102443","article-title":"A survey on underactuated robotic systems: bio-inspiration, trajectory planning and control","volume":"72","author":"Liu","year":"2020","journal-title":"Mechatronics"},{"key":"B14","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1682\/JRRD.2008.09.0131","article-title":"Agonist-antagonist active knee prosthesis: a preliminary study in level-ground walking","volume":"46","author":"Martinez-Villalpando","year":"2009","journal-title":"J. Rehab. Res. Dev"},{"key":"B15","volume-title":"Biomechanical analysis of Total Knee Arthroplasty Performed on a 6 Degree of Freedom Joint Motion Simulator Linked to a Virtual Ligament Model in Mechanical and Kinematic Alignments","author":"McGale","year":"2020"},{"key":"B16","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1002\/asjc.1950","article-title":"A robust control scheme based on sliding mode observer to drive a knee-exoskeleton","volume":"21","author":"Mefoued","year":"2019","journal-title":"Asian J. Control"},{"key":"B17","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1002\/pmrj.13321","article-title":"The effects of microprocessor prosthetic knee use in early rehabilitation: a pilot randomized controlled trial","volume":"17","author":"Morgan","year":"2025","journal-title":"PM&R"},{"key":"B18","doi-asserted-by":"publisher","first-page":"108005","DOI":"10.1016\/j.neunet.2025.108005","article-title":"Tempered fractional gradient descent: Theory, algorithms, and robust learning applications","volume":"193","author":"Naifar","year":"2026","journal-title":"Neural Netw"},{"key":"B19","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.vlsi.2021.04.008","article-title":"Synchronization of mutual coupled fractional order one-sided lipschitz systems","volume":"80","author":"Naifar","year":"2021","journal-title":"Integration"},{"key":"B20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/ICEEST56292.2022.10077855","article-title":"\u201cIntegral sliding mode nonlinear controller design for prosthetic knee joint,\u201d","volume-title":"2022 International Conference on Electrical Engineering and Sustainable Technologies (ICEEST)","author":"Nazeer","year":"2022"},{"key":"B21","volume-title":"Development and Application of Semi-Active Prosthetic Foot-Ankle Systems","author":"Nichols","year":"2023"},{"key":"B22","author":"Noonan","year":"2010","journal-title":"Productivity Commission Submission Inquiry Into Disability Care"},{"key":"B23","doi-asserted-by":"publisher","first-page":"107485","DOI":"10.1016\/j.bspc.2024.107485","article-title":"Reinforcement learning based sliding mode control for optimal chemotherapy drug in cancerous tumor","volume":"103","author":"Rehman","year":"","journal-title":"Biomed. Signal Process. Control"},{"key":"B24","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s13534-024-00447-3","article-title":"Advanced optimized nonlinear control strategies for prosthetic knee joints","volume":"15","author":"Rehman","year":"","journal-title":"Biomed. Eng. Letters"},{"key":"B25","doi-asserted-by":"publisher","first-page":"106727","DOI":"10.1016\/j.bspc.2024.106727","article-title":"Enhancing antiviral therapies through nonlinear control of hepatitis c virus dynamics","volume":"97","author":"Rehman","year":"2024","journal-title":"Biomed. Signal Process. Control"},{"key":"B26","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1177\/0309364620969226","article-title":"Lower limb prosthetic interfaces: clinical and technological advancement and potential future direction","volume":"44","author":"Safari","year":"2020","journal-title":"Prosthet. Orthot. Int"},{"key":"B27","doi-asserted-by":"publisher","first-page":"49","DOI":"10.18280\/jesa.550105","article-title":"Optimal backstepping controller design for prosthetic knee joint","volume":"55","author":"Salman","year":"2022","journal-title":"Journal Europ\u00e9en des Syst\u00e8mes Automatis\u00e9s"},{"key":"B28","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/LARS.2008.12","article-title":"\u201cAdaptive knee joint control for an active amputee prosthesis,\u201d","volume-title":"2008 IEEE Latin American Robotic Symposium","author":"Scandaroli","year":"2008"},{"key":"B29","doi-asserted-by":"publisher","first-page":"eabo3996","DOI":"10.1126\/scirobotics.abo3996","article-title":"A lightweight robotic leg prosthesis replicating the biomechanics of the knee, ankle, and toe joint","volume":"7","author":"Tran","year":"2022","journal-title":"Sci. Robot"},{"key":"B30","volume-title":"Automatic Customization of Powered Knee Prostheses for Individual User Using Adaptive Dynamic Programming","author":"Wen","year":"2019"},{"key":"B31","first-page":"175","article-title":"Relationship between body image and psychological well-being in patients with morbid obesity","volume":"6","author":"Yazdani","year":"2018","journal-title":"Int. J. Commun. Based Nurs. Midwifery"},{"key":"B32","doi-asserted-by":"publisher","first-page":"2327","DOI":"10.3390\/app9112327","article-title":"Novel design and lateral stability tracking control of a four-wheeled rollator","volume":"9","author":"Zhang","year":"2019","journal-title":"Appl. Sci"}],"container-title":["Frontiers in Neurorobotics"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fnbot.2025.1681298\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T06:44:20Z","timestamp":1768977860000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fnbot.2025.1681298\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,21]]},"references-count":32,"alternative-id":["10.3389\/fnbot.2025.1681298"],"URL":"https:\/\/doi.org\/10.3389\/fnbot.2025.1681298","relation":{},"ISSN":["1662-5218"],"issn-type":[{"value":"1662-5218","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,21]]},"article-number":"1681298"}}