{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T14:47:40Z","timestamp":1778510860529,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T00:00:00Z","timestamp":1705017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Rehabilitation robotics has seen growing popularity in recent years due to its immense potential for improving the lives of people with disabilities. However, the complex, uncertain dynamics of these systems present significant control challenges, requiring advanced techniques. This paper introduces a novel adaptive control framework integrating modified function approximation (MFAT) and double-integral non-singular terminal sliding mode control (DINTSMC). The goal is to achieve precise tracking performance, high robustness, a fast response, a finite convergence time, reduced chattering, and effective handling of unknown system dynamics. A key feature is the incorporation of a higher-order sliding mode observer, eliminating the need for velocity feedback. This provides a new solution for overcoming the inherent variations and uncertainties in robot manipulators, enabling improved accuracy within fixed convergence times. The efficacy of the proposed approach was validated through simulations and experiments on an exoskeleton robot. The results successfully demonstrated the controller\u2019s effectiveness. Stability analysis using Lyapunov theory proved the closed-loop system\u2019s uniform ultimate boundedness. This contribution is expected to enable enhanced control for rehabilitation robots and improved patient outcomes.<\/jats:p>","DOI":"10.3390\/s24020489","type":"journal-article","created":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T11:43:53Z","timestamp":1705059833000},"page":"489","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Adaptive-Robust Controller for Smart Exoskeleton Robot"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4486-0710","authenticated-orcid":false,"given":"Brahim","family":"Brahmi","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, College Ahuntsic, Montreal, QC H2M 1Y8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hicham","family":"Dahani","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, College Ahuntsic, Montreal, QC H2M 1Y8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Soraya","family":"Bououden","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Ferhat Abas Setif 1 University, Setif 19137, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6289-3049","authenticated-orcid":false,"given":"Raouf","family":"Fareh","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6370-8757","authenticated-orcid":false,"given":"Mohamed","family":"Rahman","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fareh, R., Elsabe, A., Baziyad, M., Kawser, T., Brahmi, B., and Rahman, M.H. (2023). Will Your Next Therapist Be a Robot?\u2014A Review of the Advancements in Robotic Upper Extremity Rehabilitation. Sensors, 23.","DOI":"10.3390\/s23115054"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1080\/10749357.2021.1943797","article-title":"A scoping review of design requirements for a home-based upper limb rehabilitation robot for stroke","volume":"29","author":"Li","year":"2022","journal-title":"Top. Stroke Rehabil."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1080\/17434440.2022.2096438","article-title":"Rehabilitation robotics after stroke: A bibliometric literature review","volume":"19","author":"Zuccon","year":"2022","journal-title":"Expert Rev. Med. Devices"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e12077","DOI":"10.1049\/csy2.12077","article-title":"Impedance learning adaptive super-twisting control of a robotic exoskeleton for physical human-robot interaction","volume":"5","author":"Brahmi","year":"2023","journal-title":"IET Cyber-Syst. Robot."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4343","DOI":"10.1007\/s11071-022-08042-w","article-title":"Predictive-adaptive sliding mode control method for reluctance actuator maglev system","volume":"111","author":"Xu","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3679","DOI":"10.1109\/TFUZZ.2023.3267549","article-title":"Improved Nonlinear Extended Observer Based Adaptive Fuzzy Output Feedback Control for a Class of Uncertain Nonlinear Systems with Unknown Input Hysteresis","volume":"31","author":"Nie","year":"2023","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.isatra.2023.05.010","article-title":"Iterative neural network adaptive robust control of a maglev planar motor with uncertainty compensation ability","volume":"140","author":"Xu","year":"2023","journal-title":"ISA Trans."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6139","DOI":"10.1109\/LRA.2022.3164448","article-title":"Adaptive sliding mode disturbance observer based robust control for robot manipulators towards assembly assistance","volume":"7","author":"Xi","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.isatra.2021.10.002","article-title":"Desired compensation adaptive robust repetitive control of a multi-DoFs industrial robot","volume":"128","author":"Hu","year":"2022","journal-title":"ISA Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3263","DOI":"10.1109\/TCYB.2022.3168030","article-title":"Adaptive sliding-mode disturbance observer-based finite-time control for unmanned aerial manipulator with prescribed performance","volume":"53","author":"Chen","year":"2022","journal-title":"IEEE Trans. Cybern."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.isatra.2021.12.044","article-title":"A new adaptive sliding mode controller based on the RBF neural network for an electro-hydraulic servo system","volume":"129","author":"Feng","year":"2022","journal-title":"ISA Trans."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1109\/TCST.2017.2739107","article-title":"Adaptive\u2013robust control of Euler\u2013Lagrange systems with linearly parametrizable uncertainty bound","volume":"26","author":"Roy","year":"2017","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Roy, S., Roy, S.B., and Kar, I.N. (2018, January 9\u201311). A new design methodology of adaptive sliding mode control for a class of nonlinear systems with state dependent uncertainty bound. Proceedings of the 2018 15th International Workshop on Variable Structure Systems (VSS), Graz, Austria.","DOI":"10.1109\/VSS.2018.8460363"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1109\/TMECH.2019.2930711","article-title":"Overcoming the underestimation and overestimation problems in adaptive sliding mode control","volume":"24","author":"Roy","year":"2019","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/TNNLS.2018.2828813","article-title":"Design and adaptive control for an upper limb robotic exoskeleton in presence of input saturation","volume":"30","author":"He","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Al-Shuka, H.F., and Song, R. (2018, January 25\u201327). Hybrid regressor and approximation-based adaptive control of robotic manipulators with contact-free motion. Proceedings of the 2018 2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Xi\u2019an, China.","DOI":"10.1109\/IMCEC.2018.8469628"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.robot.2019.02.017","article-title":"Compliant adaptive control of human upper-limb exoskeleton robot with unknown dynamics based on a Modified Function Approximation Technique (MFAT)","volume":"117","author":"Brahmi","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1017\/S0263574705002031","article-title":"A FAT-based adaptive controller for robot manipulators without regressor matrix: Theory and experiments","volume":"24","author":"Huang","year":"2006","journal-title":"Robotica"},{"key":"ref_19","unstructured":"Chien, M.C., and Huang, A.C. (2006, January 14\u201316). Regressor-free adaptive impedance control of flexible-joint robots using FAT. Proceedings of the 2006 American Control Conference, Minneapolis, MN, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1080\/02533839.2007.9671312","article-title":"Adaptive control of electrically-driven robot without computation of regressor matrix","volume":"30","author":"Chien","year":"2007","journal-title":"J. Chin. Inst. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Huang, A.C., and Chien, M.C. (2010). Adaptive Control of Robot Manipulators: A Unified Regressor-Free Approach, World Scientific.","DOI":"10.1142\/9789814307420"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1017\/S0263574704000190","article-title":"Adaptive impedance control of robot manipulators based on function approximation technique","volume":"22","author":"Chien","year":"2004","journal-title":"Robotica"},{"key":"ref_23","first-page":"447","article-title":"Skill learning approach based on impedance control for spine surgical training simulators with haptic playback","volume":"237","author":"Brahmi","year":"2023","journal-title":"Proc. Inst. Mech. Eng. Part J. Syst. Control. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1016\/j.matcom.2021.07.016","article-title":"Impedance learning control for physical human-robot cooperative interaction","volume":"190","author":"Brahmi","year":"2021","journal-title":"Math. Comput. Simul."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.isatra.2022.08.006","article-title":"Barrier function-based adaptive nonsingular terminal sliding mode control technique for a class of disturbed nonlinear systems","volume":"134","author":"Mobayen","year":"2023","journal-title":"ISA Trans."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"108268","DOI":"10.1016\/j.asoc.2021.108268","article-title":"Fast terminal sliding mode control design for position control of induction motors using adaptive quantum neural networks","volume":"115","author":"Zirkohi","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3696","DOI":"10.1109\/TIA.2022.3162571","article-title":"High-order fast nonsingular terminal sliding mode control of permanent magnet linear motor based on double disturbance observer","volume":"58","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"105260","DOI":"10.1016\/j.conengprac.2022.105260","article-title":"Hybrid extended state observer-based integral sliding mode control of the propulsion for a hydraulic roofbolter","volume":"126","author":"Zhang","year":"2022","journal-title":"Control Eng. Pract."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Biswas, D.K., Debbarma, S., and Singh, P.P. (2023, January 15\u201317). Decentralized PID-Based Sliding Mode Load Frequency Control Scheme in Power Systems. Proceedings of the 2023 5th International Conference on Energy, Power and Environment: Towards Flexible Green Energy Technologies (ICEPE), Shillong, India.","DOI":"10.1109\/ICEPE57949.2023.10201634"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"105064","DOI":"10.1016\/j.conengprac.2022.105064","article-title":"Extreme-learning-machine-based robust integral terminal sliding mode control of bicycle robot","volume":"121","author":"Chen","year":"2022","journal-title":"Control Eng. Pract."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1080\/0020717031000099029","article-title":"Higher-order sliding modes, differentiation and output-feedback control","volume":"76","author":"Levant","year":"2003","journal-title":"Int. J. Control"},{"key":"ref_32","unstructured":"Craig, J.J. (2005). Introduction to Robotics: Mechanics and Control, Pearson\/Prentice Hall Upper Saddle River."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1016\/j.automatica.2005.07.001","article-title":"Continuous finite-time control for robotic manipulators with terminal sliding mode","volume":"41","author":"Yu","year":"2005","journal-title":"Automatica"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1002\/rnc.1624","article-title":"Attitude stabilization of rigid spacecraft with finite-time convergence","volume":"21","author":"Zhu","year":"2011","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Li, Z., Yang, C., and Fan, L. (2012). Advanced Control of Wheeled Inverted Pendulum Systems, Springer Science & Business Media.","DOI":"10.1007\/978-1-4471-2963-9"},{"key":"ref_36","unstructured":"Slotine, J.J.E., and Li, W. (1991). Applied Nonlinear Control, Prentice Hall."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.jmaa.2018.06.061","article-title":"On Young\u2019s inequality","volume":"469","author":"Alzer","year":"2019","journal-title":"J. Math. Anal. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2935","DOI":"10.1007\/s12555-017-0578-0","article-title":"Bio-inspired Decentralized Architecture for Walking of a 5-link Biped Robot with Compliant Knee Joints","volume":"16","author":"Yazdani","year":"2018","journal-title":"Int. J. Control. Autom. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1109\/TMECH.2021.3076956","article-title":"Flatness Based Control of a Novel Smart Exoskeleton Robot","volume":"27","author":"Brahmi","year":"2021","journal-title":"IEEE\/ASME Trans. Mechatron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/2\/489\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:45:50Z","timestamp":1760103950000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/2\/489"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,12]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["s24020489"],"URL":"https:\/\/doi.org\/10.3390\/s24020489","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,12]]}}}